# bibtab

bibtype: article
filename: fparith.bib
label: 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
monthnumber: 9
year: 1985
CODEN: ACMSCU
DOI: https://doi.org/10.1145/214408.214414
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Fri Aug 26 23:38:15 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.08.26 23:38:15 ???
note: See also cite Stewart:1986:CNC.
URL: http://www.acm.org/pubs/citations/journals/toms/1985-11-3/p238-stewart/
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms; complex arithmetic; computer arithmetic; na
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: G. W. Stewart
rawnote: See also \cite{Stewart:1986:CNC}.
rawtitle: A Note on Complex Division
abstract:
An algorithm for computing the quotient of two complex numbers is modified to make it more robust in the presence of underflows.

subject:
bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Reliability and robustness.

rawabstract:
An algorithm for computing the quotient of two complex numbers is modified to make it more robust in the presence of underflows.

entry:
@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.",
}


bibtype: article
filename: fparith.bib
label: 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) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
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
bibtimestamp: 1997.05.26 11:49:34 MDT
fjournal: Numerische Mathematik
acknowledgement: ack-nhfb
corpsource: Fachbereich Math., Johann Wolfgang Goethe-University, Frankfurt, West Germany
journalURL: http://link.springer.com/journal/211
treatment: T Theoretical or Mathematical
rawauthor: Friedrich Stummel
rawtitle: Forward error analysis of {Gaussian} elimination. {I}. Error and residual estimates
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

entry:
@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",
}


bibtype: inproceedings
filename: fparith.bib
label: 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
bibtimestamp: 2007.11.16 08:47:34 ???
URL: http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Swartzlander_Eldon.pdf
keywords: ARITH-7
acknowledgement: ack-nhfb
rawauthor: Earl {Swartzlander, Jr.} and John Eldon
rawtitle: Arithmetic for High Speed {FFT} Implementation
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.

rawabstract:
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.

entry:
@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",
}


bibtype: manual
filename: fparith.bib
label: Symbolics:1985:RGS
title: Reference Guide to Symbolics-Lisp
organization: Symbolics, Inc.
address: Cambridge, MA, USA
pages: 223--230
month: mar
monthnumber: 3
year: 1985
bibdate: Wed Jan 29 17:06:41 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.01.29 17:06:41 ???
remark: From cite Steele:2004:RHP: ``The number of digits printed is the `correct' numberldots ''
acknowledgement: ack-nhfb
rawtitle: Reference Guide to {Symbolics-Lisp}
entry:
@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{}''",
}


bibtype: article
filename: fparith.bib
label: 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) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Mon Sep 16 16:29:25 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.09.16 16:29:25 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: N. Takagi and H. Yasuura and S. Yajima
rawtitle: High-speed {VLSI} multiplication algorithm with a redundant binary addition tree
entry:
@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",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 10
year: 1985
CODEN: IJSCBC
ISSN: 0018-9200 (print), 1558-173X (electronic) OR 00189200 (print), 1558173X (electronic)
ISSNL: 0018-9200 OR 00189200
bibdate: Sat Jul 16 08:40:53 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:53 MDT
fjournal: IEEE Journal of Solid-State Circuits
acknowledgement: ack-nhfb
rawauthor: K. Takeda and F. Ishino and Y. Ito and T. Nakashima
rawtitle: A single-chip 80-bit floating point processor
entry:
@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{}",
}


bibtype: inproceedings
filename: fparith.bib
label: 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
bibtimestamp: 2007.11.16 08:47:34 ???
URL: http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Taniguchi.pdf
keywords: ARITH-7
acknowledgement: ack-nhfb
rawauthor: Kenji Taniguchi
rawtitle: Three Dimensional {IC}'s and Application to High Speed Image Processor
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.

rawabstract:
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.

entry:
@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",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 1
year: 1985
CODEN: ICSYBT
ISSN: 0098-4094 (print), 1558-1276 (electronic) OR 00984094 (print), 15581276 (electronic)
ISSNL: 0098-4094 OR 00984094
bibdate: Sat Jul 16 08:40:53 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:53 MDT
fjournal: IEEE Transactions on Circuits and Systems
acknowledgement: ack-nhfb
rawauthor: F. Taylor
rawtitle: A hybrid floating-point logarithmic number system processor
entry:
@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}",
}


bibtype: inproceedings
filename: fparith.bib
label: 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
bibtimestamp: 2007.11.16 08:47:34 ???
URL: http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Taylor1.pdf
keywords: ARITH-7
acknowledgement: ack-nhfb
rawauthor: Fred J. Taylor
rawtitle: A More Efficient Residue Arithmetic Implementation of the {FFT}
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.

rawabstract:
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.

entry:
@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",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 6
year: 1985
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1985.5009414
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 08:32:52 MDT 2011
bibtimestamp: 2011.07.10 08:32:52 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009414
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: F. J. Taylor and G. Papadourakis and A. Skavantzos and A. Stouraitis
rawtitle: A Radix-$4$ {FFT} Using Complex {RNS} Arithmetic
entry:
@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",
}


bibtype: inproceedings
filename: fparith.bib
label: Taylor:1985:RSD
author: George S. Taylor
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
bibtimestamp: 1998.04.02 08:38:35 ???
URL: http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Taylor.pdf
keywords: ARITH-7
acknowledgement: ack-sfo
rawauthor: 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

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 $, orpar (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.

rawabstract:
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.

rawtitle:
Radix 16 {SRT} dividers with overlapped quotient selection stages: a 225 Nanosecond Double Precision Divider for the {S-1 Mark IIB}

entry:
@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",
}


bibtype: mastersthesis
filename: fparith.bib
label: 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
bibtimestamp: 1996.02.24 15:01:45 MST
acknowledgement: ack-nhfb
rawauthor: Kurt Alan Tesnow
rawtitle: Implementation of the digital simulation of a synchronous machine using a floating-point processor
entry:
@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,
}


bibtype: book
filename: fparith.bib
label: Thies:1985:NPE
author: Klaus-Dieter Thies
publisher: pub-TEWI
address: pub-TEWI:adr
pages: 355
year: 1985
ISBN: 3-921803-53-5 OR 3921803535
ISBN13: 978-3-921803-53-0 OR 9783921803530
bibdate: Sat Nov 09 10:08:28 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.11.09 10:08:28 ???
acknowledgement: ack-nj
rawauthor: Klaus-Dieter Thies
title:
Die 8087 / 80287 numerischen Prozessor Erweiterungen fur 8086 / 80286 Systeme toenglish The 8087 / 80287 Numeric Processor Extension for 8086 / 80286 Systems endtoenglish 

rawtitle:
{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

entry:
@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,
}


bibtype: article
filename: fparith.bib
label: 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) OR 03736385 (print), 18832172 (electronic)
ISSNL: 0373-6385 OR 03736385
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
bibtimestamp: 1995.12.08 08:24:13 ???
acknowledgement: ack-nhfb
reviewer: Aurel Galantai
rawauthor: Kumiko Tsuji
rawtitle: Round-off errors in floating-point additions
fjournal:
Memoirs of the Faculty of Science, Kyushu Imperial University. Series A, Mathematics = Kyushu Teikoku Daigaku Rigakubu kiyo

entry:
@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",
}


bibtype: inproceedings
filename: fparith.bib
label: 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
bibtimestamp: 2002.11.09 08:26:18 MST
acknowledgement: ack-nhfb
rawauthor: J. W. von Gudenberg
rawtitle: Floating-point computation in {PASCAL-SC} with verified results
subject:
G. Mathematics of Computing; G.4 MATHEMATICAL SOFTWARE; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS

entry:
@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",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 7
year: 1985
CODEN: ICSYBT
ISSN: 0098-4094 (print), 1558-1276 (electronic) OR 00984094 (print), 15581276 (electronic)
ISSNL: 0098-4094 OR 00984094
bibdate: Sat Jul 16 08:40:53 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:53 MDT
fjournal: IEEE Transactions on Circuits and Systems
acknowledgement: ack-nhfb
rawauthor: D. Williamson and S. Sridharan and P. McCrea
rawtitle: A new approach for block floating-point arithmetic in recursive filters
entry:
@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{}",
}


bibtype: inproceedings
filename: fparith.bib
label: 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
bibtimestamp: 2007.11.16 08:47:34 ???
URL: http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Yun_Zhang.pdf
keywords: ARITH-7
acknowledgement: ack-nhfb
rawauthor: David Y. Y. Yun and Chang N. Zhang
rawtitle: Binary Paradigm and Systolic Array Implementation for Residue Arithmetic
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.

rawabstract:
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.

entry:
@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",
}


bibtype: inproceedings
filename: fparith.bib
label: 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
bibtimestamp: 2007.11.14 18:06:21 ???
URL: http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Zaccone_Barlow.pdf
keywords: ARITH-7
acknowledgement: ack-nhfb
rawauthor: Richar J. Zaccone and Jesse L. Barlow
rawtitle: Improved Normalization Results for Digit On-Line Arithmetic
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.

rawabstract:
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.

entry:
@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",
}


bibtype: inproceedings
filename: fparith.bib
label: Zadrozny:1985:AFP
author: Wlodzimierz Zadrozny
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
bibtimestamp: 2007.11.16 08:47:34 ???
URL: http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Zadrozny.pdf
keywords: ARITH-7
acknowledgement: ack-nhfb
rawauthor: W{\l}odzimierz Zadro{\'z}ny
rawtitle: Axiomatizations of Floating Point Arithmetics
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.

rawabstract:
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.

entry:
@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",
}


bibtype: article
filename: fparith.bib
label: Zorpette:1985:BBN
author: Glenn Zorpette
journal: j-IEEE-SPECTRUM
volume: 22
number: 9
pages: 65--71
month: sep
monthnumber: 9
year: 1985
CODEN: IEESAM
DOI: https://doi.org/10.1109/MSPEC.1985.6370815
ISSN: 0018-9235 (print), 1939-9340 (electronic) OR 00189235 (print), 19399340 (electronic)
ISSNL: 0018-9235 OR 00189235
bibdate: Mon Jan 20 06:41:24 2020
bibtimestamp: 2020.01.20 06:41:24 ???
fjournal: IEEE Spectrum
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6
rawauthor: 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

bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeespectrum1980.bib

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

rawtitle:
The beauty of 32 bits: This near-optimum bit width has unprecedented potential for the well-informed designer of microprocessor-based systems

entry:
@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",
}


bibtype: techreport
filename: fparith.bib
label: 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
bibtimestamp: 1996.02.24 15:01:45 MST
remark: Sponsored by DARPA. Monitored by Naval Electronic Systems Command.
acknowledgement: ack-nhfb
rawauthor: Glenn D. Adams
rawtitle: Functional specification and simulation of a floating point co-processor for {SPUR} [1]
keywords:
Computer architecture.; Floating-point arithmetic.; Integrated circuits --- Design and construction.

entry:
@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.",
}


bibtype: mastersthesis
filename: fparith.bib
label: 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
bibtimestamp: 1996.02.24 15:01:45 MST
acknowledgement: ack-nhfb
rawauthor: Glenn D. Adams
rawtitle:
Functional specification and simulation of a floating point co-processor for {SPUR}: research project

entry:
@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,
}


bibtype: article
filename: fparith.bib
label: Agarwal:1986:NSV
title: New Scalar and Vector Elementary Functions for the IBM System / 370
journal: j-IBM-JRD
volume: 30
number: 2
pages: 126--144
month: mar
monthnumber: 3
year: 1986
CODEN: IBMJAE
DOI: https://doi.org/10.1147/rd.302.0126
ISSN: 0018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)
ISSNL: 0018-8646 OR 00188646
MRclass: 76W05
MRnumber: 840 341
bibdate: Sat Jan 11 17:44:01 MST 1997
bibtimestamp: 1997.01.11 17:44:01 MST
note: See clarification cite Agarwal:1987:CNS.
fjournal: IBM Journal of Research and Development
acknowledgement: ack-nhfb
ajournal: IBM J. Res. Develop.
classcodes: C6140D (High level languages); C7310 (Mathematics computing)
corpsource: IBM Res. Div., Yorktown Heights, NY, USA
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520
journalabr: IBM J Res Dev
treatment: N New Development; P Practical
rawnote: See clarification \cite{Agarwal:1987:CNS}.
rawtitle: New Scalar and Vector Elementary Functions for the {IBM System\slash 370}
author:
Ramesh C. Agarwal and James W. Cooley and Fred G. Gustavson and James B. Shearer and Gordon Slishman and Bryant Tuckerman

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

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 / 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.

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

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

rawabstract:
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.

rawauthor:
Ramesh C. Agarwal and James W. Cooley and Fred G. Gustavson and James B. Shearer and Gordon Slishman and Bryant Tuckerman

entry:
@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",
}


bibtype: book
filename: fparith.bib
label: 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 OR 0201177412
ISBN13: 978-0-201-17741-1 OR 9780201177411
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
bibtimestamp: 2007.11.29 23:38:40 MST
note: See also cite Apple:1988:ANM,Apple:1994:IMP.
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
acknowledgement: ack-nhfb
rawauthor: {Apple Computer, Inc.} and Don Reed
rawnote: See also \cite{Apple:1988:ANM,Apple:1994:IMP}.
rawtitle: {Apple} Numerics Manual
entry:
@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",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 12
year: 1986
CODEN: ICSYBT
ISSN: 0098-4094 (print), 1558-1276 (electronic) OR 00984094 (print), 15581276 (electronic)
ISSNL: 0098-4094 OR 00984094
bibdate: Sat Jul 16 08:40:53 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:53 MDT
fjournal: IEEE Transactions on Circuits and Systems
acknowledgement: ack-nhfb
rawauthor: S. Ardalan
rawtitle: Floating-point error analysis of recursive least-squares and least-mean-squares adaptive filters
entry:
@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{}",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 9
year: 1986
CODEN: IVJODL
DOI: https://doi.org/10.1016/0167-9260(86)90004-0
ISSN: 0167-9260 (print), 1872-7522 (electronic) OR 01679260 (print), 18727522 (electronic)
ISSNL: 0167-9260 OR 01679260
bibdate: Thu Nov 18 09:57:37 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.11.18 09:57:37 ???
fjournal: Integration, the VLSI journal
keywords: area-time complexity; lower bounds; RNS; VLSI
acknowledgement: ack-nhfb
rawauthor: Magdy A. Bayoumi
rawtitle: Lower bounds for {VLSI} implementation of residue number system architectures
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.

rawabstract:
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.

entry:
@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",
}


bibtype: inproceedings
filename: fparith.bib
label: 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
bibtimestamp: 1994.09.14 19:13:54 ???
acknowledgement: ack-nj
rawauthor: B. Beims
rawtitle: The Floating-Point Performance Standard Gets Even Faster!
entry:
@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,
}


bibtype: inproceedings
filename: fparith.bib
label: 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
bibtimestamp: 1994.09.12 08:32:02 ???
acknowledgement: ack-nj
rawauthor: P. A. Berger
rawtitle: The {National NS32381} Floating Point Slave Processor
entry:
@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,
}


bibtype: article
filename: fparith.bib
label: Bernstein:1986:MIC
author: Robert L. Bernstein
title: Multiplication by Integer Constants
journal: j-SPE
volume: 16
number: 7
pages: 641--652
month: jul
monthnumber: 7
year: 1986
CODEN: SPEXBL
DOI: https://doi.org/10.1002/spe.4380160704
ISSN: 0038-0644 (print), 1097-024X (electronic) OR 00380644 (print), 1097024X (electronic)
ISSNL: 0038-0644 OR 00380644
bibdate: Sat May 31 13:36:16 MDT 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.05.31 13:36:16 MDT
fjournal: Software---Practice and Experience
acknowledgement: ack-nhfb
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X
rawauthor: Robert L. Bernstein
rawtitle: Multiplication by Integer Constants
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.

rawabstract:
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.

entry:
@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",
}


bibtype: article
filename: fparith.bib
label: Campbell:1986:NSR
author: R. A. Campbell
title: NS32000 Square Roots
journal: j-DDJ
volume: 11
number: 3
pages: 122--123, 106
month: mar
monthnumber: 3
year: 1986
CODEN: DDJOEB
ISSN: 1044-789X OR 1044789X
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
bibtimestamp: 1995.12.08 13:05:56 ???
fjournal: Dr. Dobb's Journal of Software Tools
acknowledgement: ack-nj
rawauthor: R. A. Campbell
rawtitle: {NS32000} Square Roots
entry:
@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",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 12
year: 1986
CODEN: DDJOEB
ISSN: 1044-789X OR 1044789X
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
bibtimestamp: 1994.09.01 10:15:57 ???
fjournal: Dr. Dobb's Journal of Software Tools
acknowledgement: ack-nj
rawauthor: R. A. Campbell
rawtitle: In Search of a Sine
entry:
@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",
}


bibtype: mastersthesis
filename: fparith.bib
label: 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
bibtimestamp: 1996.02.24 15:01:45 MST
note: Karl E. Stoffers, Chairperson.
keywords: Bit slice microprocessors.
acknowledgement: ack-nhfb
rawauthor: Hai Cao
rawnote: Karl E. Stoffers, Chairperson.
rawtitle: A bit-slice floating point processor
entry:
@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.",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 8
year: 1986
CODEN: DDJOEB
ISSN: 1044-789X OR 1044789X
bibdate: Thu Sep 08 07:59:25 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.08 07:59:25 ???
fjournal: Dr. Dobb's Journal of Software Tools
acknowledgement: ack-nj
rawauthor: J. Cathey
rawtitle: Letter to the editor [Integer Square Root]
entry:
@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",
}


bibtype: inproceedings
filename: fparith.bib
label: 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
bibtimestamp: 1994.09.07 22:31:45 ???
acknowledgement: ack-nj
rawauthor: K. Chadha
rawtitle: {Intel} 80387: high performance, single chip numerics coprocessor for the 80386
entry:
@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,
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 8
year: 1986
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1986.1676829
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 9 14:09:51 MDT 2011
bibtimestamp: 2011.07.09 14:09:51 MDT
fjournal: IEEE Transactions on Computers
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: N. B. Chakraborti and J. S. Soundararajan and A. L. N. Reddy
rawtitle: An Implementation of Mixed-Radix Conversion for Residue Number Applications
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

entry:
@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{}",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 1
year: 1986
CODEN: ICSYBT
ISSN: 0098-4094 (print), 1558-1276 (electronic) OR 00984094 (print), 15581276 (electronic)
ISSNL: 0098-4094 OR 00984094
bibdate: Sat Jul 16 11:25:06 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:06 MDT
fjournal: IEEE Transactions on Circuits and Systems
acknowledgement: ack-nhfb
rawauthor: N. Chowdary and W. Steenaart
rawtitle: Accumulation of product roundoff errors in modified {FFT}'s
entry:
@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{}",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 9
year: 1986
CODEN: CMAPDK
DOI: https://doi.org/10.1016/0898-1221(86)90233-6
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
MRclass: 33A70 (39B10 65G05)
MRnumber: MR0871348 (88a:33027)
bibdate: Fri Jul 09 06:27:26 2004
bibtimestamp: 2004.07.09 06:27:26 ???
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: C. W. Clenshaw and Daniel W. Lozier and F. W. J. Olver and P. R. Turner
rawtitle: Generalized Exponential and Logarithmic Functions
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.

rawabstract:
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.

entry:
@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",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 12
year: 1986
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01935054
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
MRclass: 65D20
MRnumber: 87k:65019
MRreviewer: Luciano Biasini
bibdate: Wed Jan 4 18:52:19 MST 2006
bibtimestamp: 2006.01.04 18:52:19 MST
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=26&issue=4&spage=475
fjournal: BIT (Nordisk tidskrift for informationsbehandling)
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: C. W. Clenshaw and F. W. J. Olver
rawtitle: Unrestricted algorithms for reciprocals and square roots
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

entry:
@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??",
}


bibtype: phdthesis
filename: fparith.bib
label: 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
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Binary system (Mathematics)
acknowledgement: ack-nhfb
rawauthor: Jerome Toby Coonen
rawtitle: Contributions to a proposed standard for binary floating-point arithmetic
entry:
@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)",
}


bibtype: mastersthesis
filename: fparith.bib
label: 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
bibtimestamp: 1996.02.24 15:01:45 MST
acknowledgement: ack-nhfb
rawauthor: Deborah Susan Crowell
rawtitle: Error-free computation using multiple-modulus residue arithmetic
keywords:
Algorithms.; Approximation theory --- Data processing.; Floating-point arithmetic.; Modular arithmetic.

entry:
@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.",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 5
year: 1986
CODEN: IEMIDZ
DOI: https://doi.org/10.1109/MM.1986.304680
ISSN: 0272-1732 (print), 1937-4143 (electronic) OR 02721732 (print), 19374143 (electronic)
ISSNL: 0272-1732 OR 02721732
bibdate: Thu Sep 08 00:48:52 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.08 00:48:52 ???
fjournal: IEEE Micro
acknowledgement: ack-nj
journalURL: http://www.computer.org/csdl/mags/mi/index.html
rawauthor: T. W. Curtis and P. Allison
rawtitle: A {CORDIC} Processor for Laser Trimming
entry:
@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",
}


bibtype: inproceedings
filename: fparith.bib
label: 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
bibtimestamp: 1994.09.07 22:31:45 ???
acknowledgement: ack-nj
rawauthor: B. Desrosiers and J.-L. Peter and C. Sitbon
rawtitle: Custom Floating Point Chip Designed with a Cohesive Structured Method
entry:
@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,
}


bibtype: inproceedings
filename: fparith.bib
label: 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
bibtimestamp: 1994.09.01 11:58:18 ???
acknowledgement: ack-nj
rawauthor: J. Du Croz
rawtitle: {FPV} -- a Floating-Point Validation Package
entry:
@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,
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 3
year: 1986
CODEN: AHESAN
DOI: https://doi.org/10.1007/BF00357439
ISSN: 0003-9519 (print), 1432-0657 (electronic) OR 00039519 (print), 14320657 (electronic)
ISSNL: 0003-9519 OR 00039519
MRclass: 01A05 (11-03 11A63)
MRnumber: 863340 (87m:01003)
MRreviewer: Donald Cook
bibdate: Fri Feb 4 21:50:24 MST 2011
bibtimestamp: 2011.02.04 21:50:24 MST
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0003-9519&volume=36&issue=1&spage=21
fjournal: Archive for History of Exact Sciences
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/407
rawauthor: Jacques Dutka
rawtitle: On square roots and their representations
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

entry:
@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",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 9
year: 1986
CODEN: MEGBBQ
ISSN: 0379-5527 OR 03795527
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
bibtimestamp: 1994.09.01 10:15:06 ???
fjournal: Mechanical Engineering Bulletin
acknowledgement: ack-nj
rawauthor: U. Dutta and D. Bhattacharya and A. D. Sarma
rawtitle: Implementation of Multibyte Floating Point Arithmetic in 8-bit Microprocessor
entry:
@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",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 4
year: 1986
CODEN: IJNADH
ISSN: 0272-4979 (print), 1464-3642 (electronic) OR 02724979 (print), 14643642 (electronic)
ISSNL: 0272-4979 OR 02724979
MRclass: 65G05
MRnumber: 89h:65065
bibdate: Sat Dec 23 14:52:49 2000
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2000.12.23 14:52:49 ???
fjournal: IMA Journal of Numerical Analysis
keywords: Benford's Law; Law of Anomalous Numbers; logarithmic distribution; overflow; underflow; Zipf's Law
acknowledgement: ack-nhfb
journalURL: http://imajna.oxfordjournals.org/content/by/year
rawauthor: Alan Feldstein and Peter Turner
rawtitle: Overflow, underflow, and severe loss of significance in floating-point addition and subtraction
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.

rawabstract:
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.

entry:
@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",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 8
year: 1986
CODEN: CMPDAM
ISSN: 0010-4566 OR 00104566
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
bibtimestamp: 2002.11.09 08:26:18 MST
fjournal: Computer Design
subject: B. Hardware; B.7 INTEGRATED CIRCUITS
acknowledgement: ack-nhfb
rawauthor: F. Ferro
rawtitle: {DSP} tackles floating-point arithmetic
entry:
@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",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 3
year: 1986
CODEN: IEMIDZ
DOI: https://doi.org/10.1109/MM.1986.304737
ISSN: 0272-1732 (print), 1937-4143 (electronic) OR 02721732 (print), 19374143 (electronic)
ISSNL: 0272-1732 OR 02721732
bibdate: Thu Dec 14 06:08:58 MST 2000
bibtimestamp: 2000.12.14 06:08:58 MST
fjournal: IEEE Micro
acknowledgement: ack-nj
affiliationaddress: Digital Equipment Corp, Hudson, MA, USA
corpsource: Digital Equipment Corp., Hudson, MA, USA
journalURL: http://www.computer.org/csdl/mags/mi/index.html
treatment: P Practical; R Product Review
rawauthor: Moshe Gavrielov and Lev Epstein
rawtitle: The {NS32081} Floating-Point Unit --- Architecture and Implementation
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)

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

classcodes:
B1265F (Microprocessors and microcomputers); B2570F (Other MOS integrated circuits); C5130 (Microprocessor chips); C5220 (Computer architecture); C5230 (Digital arithmetic methods)

entry:
@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",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 4
year: 1986
CODEN: EDNSBH
ISSN: 0012-7515, 0364-6637 OR 00127515, 03646637
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
bibtimestamp: 1994.09.01 10:15:42 ???
fjournal: EDN
acknowledgement: ack-nj
rawauthor: R. D. Grappel
rawtitle: Square-root algorithm is fast and simple
entry:
@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",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 9
year: 1986
CODEN: JPDCER
ISSN: 0743-7315 (print), 1096-0848 (electronic) OR 07437315 (print), 10960848 (electronic)
ISSNL: 0743-7315 OR 07437315
bibdate: Sat Apr 12 19:06:31 MDT 1997
bibsource: Compendex database; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.04.12 19:06:31 MDT
fjournal: Journal of Parallel and Distributed Computing
acknowledgement: ack-nhfb
affiliationaddress: Floating Point Systems Inc, Beaverton, OR, USA
corpsource: Floating Point Syst. Inc., Beaverton, OR, USA
journalURL: http://www.sciencedirect.com/science/journal/07437315
journalabr: J Parallel Distrib Comput
treatment: P Practical
rawauthor: John L. Gustafson and Stuart Hawkinson and Ken Scott
rawtitle: The architecture of a homogeneous vector supercomputer
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

entry:
@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",
}


bibtype: book
filename: fparith.bib
label: 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) OR 0486652416 (paperback)
ISBN13: 978-0-486-65241-2 (paperback) OR 9780486652412 (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
bibtimestamp: 2010.08.20 09:12:08 MDT
URL: http://www.loc.gov/catdir/description/dover032/86016226.html
remark: Reprint of cite Hamming:1973:NMS.
subject: numerical analysis; data processing
acknowledgement: ack-nhfb
rawauthor: R. W. (Richard Wesley) Hamming
rawtitle: Numerical methods for scientists and engineers
entry:
@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",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 8
year: 1986
CODEN: IETABA
ISSN: 0096-3518 OR 00963518
bibdate: Sat Jul 16 08:40:53 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:53 MDT
note: See cite Heath:1979:RDF.
fjournal: IEEE Transactions on Acoustics, Speech, and Signal Processing
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29
rawauthor: J. Heath
rawnote: See \cite{Heath:1979:RDF}.
rawtitle: A note on {``Realization of digital filters using input-scaled floating-point arithmetic''}
entry:
@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{}",
}


bibtype: article
filename: fparith.bib
label: Henning:1986:KBD
author: D. Henning
journal: Radio Fernsehen Elektronik
volume: 35
number: 11
pages: 731--733
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
bibtimestamp: 1994.09.16 16:30:41 ???
keywords: decimal floating-point arithmetic
acknowledgement: ack-nj
rawauthor: D. Henning
title:
Konvertierung binarer in dezimale Gleitkommazahlen fur mess technische Anwendungen toenglish Conversion of Binary [Numbers] to Decimal Floating-Point Numbers for Measurement Applications endtoenglish 

rawtitle:
{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

entry:
@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",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 7
year: 1986
CODEN: SNEWD6
DOI: https://doi.org/10.1145/1057958.1057960
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Thu Aug 07 18:41:01 2008
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2008.08.07 18:41:01 ???
fjournal: ACM SIGNUM Newsletter
keywords: decimal arithmetic
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/signum
rawauthor: T. F. Higginbotham
rawtitle: Another factor of $ (10^{31} - 1) / 9 $
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.

remark:
Maple 8 reports in 2 sec on a 1400 MHz Itanium IA-64: ifactor((10^31 - 1)/9) = (57336415063790604359) (6943319) (2791).

rawabstract:
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.

entry:
@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).",
}


bibtype: article
filename: fparith.bib
label: Hill:1986:DDS
title: Design decisions in SPUR
journal: j-COMPUTER
volume: 19
number: 11
pages: 8--22
month: nov
monthnumber: 11
year: 1986
CODEN: CPTRB4
ISSN: 0018-9162 (print), 1558-0814 (electronic) OR 00189162 (print), 15580814 (electronic)
ISSNL: 0018-9162 OR 00189162
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
bibtimestamp: 2002.11.09 08:26:18 MST
fjournal: Computer
acknowledgement: ack-nhfb
affiliation: University of California, Berkeley
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2
key: C.0.B RISC
reviewer: P. C. Patton
rawtitle: Design decisions in {SPUR}
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

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

rawauthor:
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

entry:
@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",
}


bibtype: article
filename: fparith.bib
label: Hongyuan:1986:CSL
author: Wang Hongyuan and S. C. Lee
title: Comments on ``Sign / Logarithm Arithmetic for FFT Implementation''
journal: j-IEEE-TRANS-COMPUT
volume: C-35
number: 5
pages: 482--484
month: may
monthnumber: 5
year: 1986
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1986.1676792
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 9 14:09:48 MDT 2011
bibtimestamp: 2011.07.09 14:09:48 MDT
note: See cite Swartzlander:1983:SLA.
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676792
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Wang Hongyuan and S. C. Lee
rawnote: See \cite{Swartzlander:1983:SLA}.
rawtitle: Comments on {``Sign\slash Logarithm Arithmetic for FFT Implementation''}
entry:
@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",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 6
year: 1986
CODEN: ACMSCU
DOI: https://doi.org/10.1145/6497.6498
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
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
bibtimestamp: 1994.09.04 21:17:51 ???
URL: http://www.acm.org/pubs/citations/journals/toms/1986-12-2/p79-hull/
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms; decimal floating-point arithmetic; theory; verification
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: T. E. Hull and A. Abrham
rawtitle: Variable Precision Exponential Function
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.

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.

rawabstract:
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.

entry:
@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.",
}


bibtype: techreport
filename: fparith.bib
label: 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
pages: 79--91
year: 1986
bibdate: Thu Jan 21 17:27:09 2016
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2016.01.21 17:27:09 ???
TOC: 1. General Information Manual 2. Program Description and User's Guide 3. Reference Summary
acknowledgement: ack-nhfb
rawauthor: {IBM Corporation}
rawtitle: {IBM High-Accuracy Arithmetic Subroutine Library (ACRITH)}
rawTOC: 1. General Information Manual \\ 2. Program Description and User's Guide \\ 3. Reference Summary
entry:
@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",
}


bibtype: book
filename: fparith.bib
label: IBM:1986:IRP
author: IBM
title: IBM RT Personal Computer Technology, publication SA23-1057
publisher: pub-IBM
address: pub-IBM:adr
pages: 79--91
year: 1986
bibdate: Sat Oct 28 08:16:44 2000
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2000.10.28 08:16:44 ???
acknowledgement: ack-nhfb
rawauthor: {IBM}
rawtitle: {IBM RT} Personal Computer Technology, publication {SA23-1057}
entry:
@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,
}


bibtype: inproceedings
filename: fparith.bib
label: 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
bibdate: Sat Jul 16 11:25:04 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:04 MDT
acknowledgement: ack-nhfb
rawauthor: Y. Iiguni and H. Sakai and H. Tokumaru
rawbooktitle: {IEEE} International Conference on Acoustics, Speech, and Signal Processing: {ICASSP '86}
rawtitle: Rounding error analysis of the triangular lattice and escalator algorithms
entry:
@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{}",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 3
year: 1986
CODEN: ACMSCU
DOI: https://doi.org/10.1145/5960.5962
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
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
bibtimestamp: 1994.08.13 17:26:53 MDT
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms; floating-point testing
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Paul Jansen and Peter Weidner
rawtitle: High-Accuracy Arithmetic Software --- Some Tests of the {ACRITH} Problem-Solving Routines
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.

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.

rawabstract:
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.

entry:
@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.",
}


bibtype: inproceedings
filename: fparith.bib
label: Johnson:1986:TRH
author: T. Johnson and G. Clark
crossref: IEEE:1986:III
volume: 11
pages: 2623--2626
month: apr
monthnumber: 4
year: 1986
CODEN: ITCOB4
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: T. Johnson and G. Clark
title:
Techniques for realization of high-speed recursive digital filters using residue number system arithmetic

rawtitle:
Techniques for realization of high-speed recursive digital filters using residue number system arithmetic

entry:
@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.",
}


bibtype: inproceedings
filename: fparith.bib
label: 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
bibdate: Sat Jul 16 11:25:04 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:04 MDT
acknowledgement: ack-nhfb
rawauthor: P. Kabal and B. Sayar
rawbooktitle: {IEEE} International Conference on Acoustics, Speech, and Signal Processing: {ICASSP '86}
rawtitle: Performance of fixed-point {FFT}'s: Rounding and scaling considerations
entry:
@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{}",
}


bibtype: techreport
filename: fparith.bib
label: 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
monthnumber: 9
year: 1986
bibdate: Sun Dec 18 15:33:08 GMT 1994
bibtimestamp: 1994.12.18 15:33:08 GMT
acknowledgement: ack-nhfb
rawauthor: W. Kahan
rawtitle: Rational Arithmetic in Floating-Point
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

entry:
@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,
}


bibtype: techreport
filename: fparith.bib
label: 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
bibtimestamp: 1996.02.24 15:01:45 MST
acknowledgement: ack-nhfb
rawauthor: Daniel E. Kreithen
rawtitle: Floating point calculation speeds for the image processing workstation
entry:
@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,
}


bibtype: inproceedings
filename: fparith.bib
label: 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
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: R. Krishnan and G. Jullien and W. Miller
rawbooktitle: {IEEE} International Conference on Acoustics, Speech, and Signal Processing, {ICASSP '86}
rawtitle: Computation of complex number theoretic transforms using quadratic residue number systems
entry:
@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{}",
}


bibtype: article
filename: fparith.bib
label: Krishnan:1986:CDS
author: R. Krishnan and G. Jullien and W. Miller
title: Complex digital signal processing using quadratic residue number systems
volume: 34
number: 1
pages: 166--177
month: feb
monthnumber: 2
year: 1986
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
URL: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=26196
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: R. Krishnan and G. Jullien and W. Miller
rawtitle: 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

entry:
@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{}",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 8
year: 1986
CODEN: ICSYBT
DOI: https://doi.org/10.1049/el:19850252
ISSN: 0098-4094 (print), 1558-1276 (electronic) OR 00984094 (print), 15581276 (electronic)
ISSNL: 0098-4094 OR 00984094
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
URL: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23583
fjournal: IEEE Transactions on Circuits and Systems
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: R. Krishnan and G. Jullien and W. Miller
rawtitle: Implementation of complex number theoretic transforms using quadratic residue number systems
entry:
@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{}",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 3
year: 1986
CODEN: ICSYBT
DOI: https://doi.org/10.1049/el:19850252
ISSN: 0098-4094 (print), 1558-1276 (electronic) OR 00984094 (print), 15581276 (electronic)
ISSNL: 0098-4094 OR 00984094
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
URL: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23578
fjournal: IEEE Transactions on Circuits and Systems
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: R. Krishnan and G. Jullien and W. Miller
rawtitle: The modified quadratic residue number system ({MQRNS}) for complex high-speed signal processing
entry:
@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{}",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 3
year: 1986
CODEN: SIREAD
DOI: https://doi.org/10.1137/1028001
ISSN: 0036-1445 (print), 1095-7200 (electronic) OR 00361445 (print), 10957200 (electronic)
ISSNL: 0036-1445 OR 00361445
MRclass: 65G10 (68M15)
MRnumber: 87e:65030
MRreviewer: G. Blanch
bibdate: Sat Mar 29 09:54:03 MDT 2014
bibtimestamp: 2014.03.29 09:54:03 MDT
fjournal: SIAM Review
acknowledgement: ack-nhfb
affiliationaddress: Univ of California, Computer Science Dep, Santa Barbara, CA, USA
journalURL: http://epubs.siam.org/sirev
journalabr: SIAM Rev
onlinedate: March 1986
rawauthor: Ulrich W. Kulisch and Willard L. Miranker
rawtitle: The Arithmetic of the Digital Computer: a New Approach
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.

keywords:
accurate floating-point summation; computer arithmetic; computer metatheory; computer programming languages; computers, digital; floating-point arithmetic

rawabstract:
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.

entry:
@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].",
}


bibtype: misc
filename: fparith.bib
label: Kulisch:1986:CGS
author: Ulrich Kulisch
title: Circuitry for generating scalar products and sums of floating point numbers with maximum accuracy
pages: 1--40
day: 11
month: nov
monthnumber: 11
year: 1986
bibdate: Mon Dec 29 16:20:01 2008
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2008.12.29 16:20:01 ???
URL: http://www.patentstorm.us/patents/4622650/fulltext.html
acknowledgement: ack-nhfb
howpublished: US Patent 4622650
rawauthor: Ulrich Kulisch
rawtitle: Circuitry for generating scalar products and sums of floating point numbers with maximum accuracy
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.

rawabstract:
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.

entry:
@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,
}


bibtype: article
filename: fparith.bib
label: 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 OR 00135658
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
bibtimestamp: 1994.09.16 16:30:40 ???
fjournal: Elektronik
acknowledgement: ack-nj
rawauthor: O. Lorang
rawtitle: {Schnelle Division} \toenglish {Fast Division} \endtoenglish
entry:
@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",
}


bibtype: article
filename: fparith.bib
label: 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 OR 07382022
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
bibtimestamp: 2002.11.09 08:26:18 MST
fjournal: Journal of FORTH Application and Research
acknowledgement: ack-nhfb
rawauthor: Ferren MacIntyre and Thomas Dowling
rawtitle: User-oriented suggestions for floating-point and complex-arithmetic {Forth} standard extensions
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

entry:
@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",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 5
year: 1986
CODEN: CMPDAM
ISSN: 0010-4566 OR 00104566
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
bibtimestamp: 2002.11.09 08:26:18 MST
fjournal: Computer Design
subject: B. Hardware; B.7 INTEGRATED CIRCUITS
acknowledgement: ack-nhfb
rawauthor: K. Marrin
rawtitle: Microprocessor brings floating-point capability to 32-bit market
entry:
@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",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 2
year: 1986
CODEN: CMPDAM
ISSN: 0010-4566 OR 00104566
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
bibtimestamp: 2002.11.09 08:26:18 MST
fjournal: Computer Design
acknowledgement: ack-nhfb
rawauthor: K. Marrin
rawtitle: Plug-in boards transform {PCs} into floating-point workstations
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

entry:
@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",
}


bibtype: inproceedings
filename: fparith.bib
label: 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
bibtimestamp: 1994.09.07 22:31:45 ???
acknowledgement: ack-nj
rawauthor: C. Melear and D. Tietjen
rawtitle: High Speed Math Using a Floating Point Coprocessor
entry:
@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,
}


bibtype: mastersthesis
filename: fparith.bib
label: 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
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Computer architecture.; Computer arithmetic and logic units.; Computers, Pipeline.
acknowledgement: ack-nhfb
rawauthor: Brian A. Moore
rawtitle: A pipelined floating-point systolic array arithmetic processor
entry:
@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.",
}


bibtype: article
filename: fparith.bib
label: Moshier:1986:CA
author: S. L. Moshier
title: Computer Approximations
journal: j-BYTE
volume: 11
number: 4
pages: 161--178
month: apr
monthnumber: 4
year: 1986
CODEN: BYTEDJ
ISSN: 0360-5280 (print), 1082-7838 (electronic) OR 03605280 (print), 10827838 (electronic)
ISSNL: 0360-5280 OR 03605280
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
bibtimestamp: 1994.09.01 10:15:40 ???
fjournal: BYTE Magazine
acknowledgement: ack-nj
rawauthor: S. L. Moshier
rawtitle: Computer Approximations
entry:
@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",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 3
year: 1986
CODEN: JPDCER
ISSN: 0743-7315 (print), 1096-0848 (electronic) OR 07437315 (print), 10960848 (electronic)
ISSNL: 0743-7315 OR 07437315
bibdate: Mon Apr 14 07:47:57 1997
bibsource: Compendex database; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.04.14 07:47:57 ???
fjournal: Journal of Parallel and Distributed Computing
acknowledgement: ack-nhfb
affiliationaddress: Stanford Univ, Stanford, CA, USA
corpsource: Department of Electr. Eng., Stanford University, CA, USA
journalURL: http://www.sciencedirect.com/science/journal/07437315
journalabr: J Parallel Distrib Comput
treatment: P Practical
rawauthor: Tin-Fook Ngai and Mary Jane Irwin and Shishpal Rawat
rawtitle: Regular, Area-Time Efficient Carry-Lookahead Adders
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

entry:
@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",
}


bibtype: article
filename: fparith.bib
label: Nowak:1986:HBU
author: M. Nowak
title: Hex-BCD-Umwandlung toenglish Hexadecimal-BCD Conversion endtoenglish
journal: j-MC
volume: 10
pages: 68
year: 1986
ISSN: 0720-4442, 0941-777x , 0943-5409 OR 07204442, 0941777x , 09435409
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
bibtimestamp: 1994.09.16 16:30:41 ???
fjournal: MC: Die Mikrocomputer-Zeitschrift
acknowledgement: ack-nj
rawauthor: M. Nowak
rawtitle: {Hex-BCD-Um\-wand\-lung} \toenglish {Hexadecimal-BCD Conversion} \endtoenglish
entry:
@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",
}


bibtype: phdthesis
filename: fparith.bib
label: Paez-Monzon:1986:ERC
author: Gerard Paez-Monzon
type: Doctorat d'Etat
school: Sciences Appliquees, Universite 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
bibtimestamp: 2002.05.09 09:55:31 ???
note: Sous la direction de Gerard Noguez.
language: French
acknowledgement: ack-nhfb
rawauthor: Gerard Paez-Monzon
rawnote: Sous la direction de Gerard Noguez.
title:
Etude et Realisation d'un Co-processeur Arithmetique en Virgule Flottante. (French) [Study and Implementation of a Floating-Point Coprocessor]

abstract:
Le premier chapitre d'introduction decrit l'etat de l'art dans le domaine des algorithmes-cables elementaires utilises dans l'arithmetique flottante. Nous y presentons une classification architecturale des coprocesseurs arithmetiques en virgule flottante. A partir d'une comparaison de trois standards de virgule flottante orientes vers les systemes bases sur microprocesseurs: IEEE-P754, VAX-DEC, et Hewlett--Packard, le deuxieme chapitre explique le choix de l'architecture externe de coprocesseur. Le troisieme chapitre presente l'architecture interne microprogrammee et l'organisation du coprocesseur developpe dans l'etude, nommee FPU-IP6. Dans le quatrieme chapitre, nous proposons une nouvelle methode pour le developpement des microprogrammes. La cle de la methode est la visualisation de la separation des phases de planification et d'implantation. Le cinquieme chapitre presente les microprogrammes developpes pour notre coprocesseur. Nous analysons les differents micro-algorithmes selon le type d'instruction (E/S, arith, etc) et la precision (simple, double). L'organisation de l'espace de la micromemoire est presentee. Le sixieme chapitre decrit l'etude realisee pour l'integration du coprocesseur dans le compilateur C et le systeme UNIX de la machine SM90.

rawabstract:
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.

rawtitle:
{{\'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]

entry:
@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",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 7
year: 1986
CODEN: SNEWD6
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Mon Apr 25 11:24:15 MDT 2005
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.04.25 11:24:15 MDT
fjournal: ACM SIGNUM Newsletter
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/signum
rawauthor: Mary H. Payne
rawtitle: Proposal for the transfer of floating point data
entry:
@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",
}


bibtype: article
filename: fparith.bib
label: Petkovic:1986:SIS
author: M. S. Petkovic and L. V. Stefanovic
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
monthnumber: 5
year: 1986
CODEN: JCAMDI
DOI: https://doi.org/10.1016/0377-0427(86)90235-9
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 11:59:55 MST 2017
bibtimestamp: 2017.02.25 11:59:55 MST
URL: http://www.sciencedirect.com/science/article/pii/0377042786902359
fjournal: Journal of Computational and Applied Mathematics
keywords: polynomial root finding
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: M. S. Petkovi{\'c} and L. V. Stefanovi{\'c}
rawtitle: On some improvements of square root iteration for polynomial complex zeros
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

entry:
@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",
}


bibtype: article
filename: fparith.bib
label: 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 OR 00135658
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
bibtimestamp: 1994.09.16 16:30:41 ???
fjournal: Elektronik
acknowledgement: ack-nj
rawauthor: E. Pfenninger
rawtitle: {Schneller Quadratwurzel-Algorithmus} \toenglish {Fast Square-Root Algorithms} \endtoenglish
entry:
@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",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 2
year: 1986
CODEN: CMPDAM
ISSN: 0010-4566 OR 00104566
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
bibtimestamp: 2002.11.09 08:26:18 MST
fjournal: Computer Design
acknowledgement: ack-nhfb
rawauthor: K. Porter and J. Kath
rawtitle: Floating-point methods combine to boost performance
subject:
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; K. Computing Milieux; K.1 THE COMPUTER INDUSTRY

entry:
@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",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 2
year: 1986
CODEN: EDNSBH
ISSN: 0012-7515, 0364-6637 OR 00127515, 03646637
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
bibtimestamp: 1994.09.07 22:31:45 ???
fjournal: EDN
acknowledgement: ack-nj
rawauthor: D. Quong
rawtitle: Floating-point $ \mu {P} $ implements high-speed math functions
entry:
@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",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 9
year: 1986
CODEN: ICSYBT
DOI: https://doi.org/10.1049/el:19850252
ISSN: 0098-4094 (print), 1558-1276 (electronic) OR 00984094 (print), 15581276 (electronic)
ISSNL: 0098-4094 OR 00984094
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
URL: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23584
fjournal: IEEE Transactions on Circuits and Systems
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: R. Ramnarayan and F. Taylor
rawtitle: Limit cycles in large moduli residue number system digital filters
entry:
@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",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 10
year: 1986
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1986.1676680
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 9 14:09:51 MDT 2011
bibtimestamp: 2011.07.09 14:09:51 MDT
note: See comments cite Smith:1989:CSB.
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676680
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: T. Rhyne and N. R. {Strader II}
rawnote: See comments \cite{Smith:1989:CSB}.
rawtitle: A Signed Bit-Sequential Multiplier
entry:
@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",
}


bibtype: techreport
filename: fparith.bib
label: 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
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Floating-point arithmetic.
remark: ``April 1986.''--Cover. ``UILU-ENG-86-1723.''--Cover. Bibliography: p. 13.
acknowledgement: ack-nhfb
rawauthor: James Evans Robertson
rawtitle: Normalization and quotient digit selection for a variable precision arithmetic unit
entry:
@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.",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 6
year: 1986
CODEN: INSKDW
ISSN: 0170-6012 (print), 1432-122X (electronic) OR 01706012 (print), 1432122X (electronic)
ISSNL: 0170-6012 OR 01706012
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
bibtimestamp: 1994.09.16 16:30:39 ???
fjournal: Informatik Spektrum
acknowledgement: ack-nj
journalURL: http://link.springer.com/journal/287
rawauthor: Siegfried M. Rump
rawtitle: {Sichere Ergebnisse auf Rechenanlagen} \toenglish {Safe Results from Computers} \endtoenglish
entry:
@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",
}


bibtype: article
filename: fparith.bib
label: 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 OR 0025584X
MRclass: 60F05
MRnumber: 87m:60059
bibdate: Fri Dec 8 08:24:13 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 08:24:13 ???
fjournal: Mathematische Nachrichten
acknowledgement: ack-nhfb
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616
reviewer: A. Fuchs
rawauthor: Peter Schatte
rawtitle: On the asymptotic logarithmic distribution of the floating-point mantissas of sums
entry:
@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",
}


bibtype: techreport
filename: fparith.bib
label: 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
address: Moffett Field, CA, USA
year: 1986
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
acknowledgement: ack-nhfb
rawauthor: Ronald D. Schmickley and David H. Bailey
rawtitle: A comparison of the {Cray-2} performance before and after the installation of memory psudo-banking
institution:
National Aeronautics and Space Administration, Ames Research Center; National Technical Information Service, distributor

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.

entry:
@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.",
}


bibtype: article
filename: fparith.bib
label: 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
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
bibtimestamp: 1994.09.01 10:15:09 ???
acknowledgement: ack-nj
rawauthor: I. Semba
rawtitle: An Algorithm for Division of Large Integers
entry:
@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,
}


bibtype: mastersthesis
filename: fparith.bib
label: Shukla:1986:IMN
author: Pankaj N. Shukla
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
bibtimestamp: 1996.02.24 15:01:45 MST
acknowledgement: ack-nhfb
rawauthor: Pankaj N. Shukla
title:
An implementation on a MC68000 / NS32081 microcomputer of binary floating-point arithmetic based on the IEEE 754 standard

keywords:
Michigan Technological University. --- Theses (M.S.).; MTU Electrical Engineering. --- Thesis (M.S.).

rawtitle:
An implementation on a {MC68000\slash NS32081} microcomputer of binary floating-point arithmetic based on the {IEEE 754} standard

entry:
@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.}).",
}


bibtype: inproceedings
filename: fparith.bib
label: 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
bibtimestamp: 1994.09.07 23:14:42 ???
acknowledgement: ack-nj
rawauthor: R. J. Simcoe and A. Fisher and B. M. Leary and W. R. Bidermann and W. R. Wheeler
rawtitle: The {MicroVAX} 78132 Floating Point Chip
entry:
@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,
}


bibtype: book
filename: fparith.bib
label: 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 OR 087942205X
ISBN13: 978-0-87942-205-9 OR 9780879422059
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
bibtimestamp: 2007.11.14 14:28:02 MST
series: IEEE Press selected reprint series
subject: modular arithmetic; signal processing; digital techniques; computer programming
acknowledgement: ack-nhfb
raweditor: Michael A. Soderstrand and W. K. Jenkins and G. A. Graham and F. J. Taylor
rawtitle: Residue number system arithmetic: modern applications in digital signal processing
entry:
@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",
}


bibtype: article
filename: fparith.bib
label: Soderstrand:1986:VIM
author: M. Soderstrand and R. Escott
journal: j-IEEE-TRANS-CIRCUITS-SYST
volume: 33
number: 1
pages: 5--25
month: jan
monthnumber: 1
year: 1986
CODEN: ICSYBT
DOI: https://doi.org/10.1049/el:19850252
ISSN: 0098-4094 (print), 1558-1276 (electronic) OR 00984094 (print), 15581276 (electronic)
ISSNL: 0098-4094 OR 00984094
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
URL: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23573
fjournal: IEEE Transactions on Circuits and Systems
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: M. Soderstrand and R. Escott
title:
VLSI implementation in multiple-valued logic of an FIR digital filter using residue number system arithmetic

rawtitle:
{VLSI} implementation in multiple-valued logic of an {FIR} digital filter using residue number system arithmetic

entry:
@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{}",
}


bibtype: techreport
filename: fparith.bib
label: 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
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
bibtimestamp: 1994.09.12 23:54:04 ???
acknowledgement: ack-nj
rawauthor: E. H. Spafford and J. C. Flaspohler
rawtitle: A Report on the Accuracy of Some Floating-Point Math Functions on Selected Computers
entry:
@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,
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 3
year: 1986
CODEN: LOGNEM
ISSN: 1044-6397 (print), 2169-9364 (electronic) OR 10446397 (print), 21699364 (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
bibtimestamp: 1996.02.20 15:42:13 MST
fjournal: ;login: the USENIX Association newsletter
acknowledgement: ack-nhfb
affiliation: Georgia Institute of Technology
rawauthor: Eugene H. Spafford and John C. Flaspohler
rawtitle: A Report on the Accuracy of Some Floating Point Math Functions on Selected Computers
entry:
@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",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 9
year: 1986
CODEN: ACMSCU
DOI: https://doi.org/10.1145/7921.356182
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sun Sep 04 21:20:12 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.04 21:20:12 ???
note: See cite Stewart:1985:NCD.
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: G. W. Stewart
rawnote: See \cite{Stewart:1985:NCD}.
rawtitle: Corrigendum: ``{A} Note on Complex Division''
entry:
@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",
}


bibtype: inproceedings
filename: fparith.bib
label: Strobach:1986:NFL
author: P. Strobach
booktitle: IEEE International Conference on Acoustics, Speech, and Signal Processing: ICASSP '86
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 573--576
year: 1986
bibdate: Sat Jul 16 11:25:04 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:04 MDT
acknowledgement: ack-nhfb
rawauthor: P. Strobach
rawbooktitle: {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

rawtitle:
New forms of least squares lattice algorithms and a comparison of their round-off error characteristics

entry:
@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{}",
}


bibtype: article
filename: fparith.bib
label: Stummel:1986:SOP
author: F. Stummel
journal: j-COMPUTING
volume: 37
number: 2
pages: 103--124
year: 1986
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
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
bibtimestamp: 1995.12.08 08:24:13 ???
fjournal: Computing: Archiv fur informatik und numerik
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/607
reviewer: Alfonso Laratta
rawauthor: F. Stummel
title:
Strict optimal a posteriori error and residual bounds for Gaussian elimination in floating-point arithmetic

rawtitle:
Strict optimal a posteriori error and residual bounds for {Gaussian} elimination in floating-point arithmetic

entry:
@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",
}


bibtype: manual
filename: fparith.bib
label: 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
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Computer arithmetic and logic units.; Floating-point arithmetic.
remark: ``Part Number 800-1552-10.''
acknowledgement: ack-nhfb
rawtitle: Floating-point programmer's guide for the {Sun} workstation
entry:
@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.''",
}


bibtype: article
filename: fparith.bib
label: Thun:1986:RNS
author: R. Thun
title: On residue number system decoding
volume: 34
number: 5
pages: 1346--1347
month: oct
monthnumber: 10
year: 1986
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
URL: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=26200
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: R. Thun
rawtitle: On residue number system decoding
journal:
Acoustics, Speech, and Signal Processing [see also IEEE Transactions on Signal Processing], IEEE Transactions on

entry:
@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{}",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 6
year: 1986
CODEN: IJSCBC
ISSN: 0018-9200 (print), 1558-173X (electronic) OR 00189200 (print), 1558173X (electronic)
ISSNL: 0018-9200 OR 00189200
bibdate: Sat Jul 16 08:40:53 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:53 MDT
fjournal: IEEE Journal of Solid-State Circuits
acknowledgement: ack-nhfb
rawauthor: W. W. Troutman and P. W. Diodato and A. K. Goksel and Mean-Sea Tsay and R. H. Krambeck
rawtitle: Design of a Standard Floating-Point Chip
entry:
@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{}",
}


bibtype: article
filename: fparith.bib
label: Truong:1986:TCD
author: T. K. Truong and J. J. Chang and I. S. Hsu and D. Y. Pei and I. S. Reed
journal: j-IEEE-TRANS-COMPUT
volume: C-35
number: 11
pages: 1008--1012
month: nov
monthnumber: 11
year: 1986
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1986.1676704
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 9 14:09:53 MDT 2011
bibtimestamp: 2011.07.09 14:09:53 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676704
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: 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

rawtitle:
Techniques for Computing the Discrete {Fourier} Transform Using the Quadratic Residue {Fermat} Number Systems

entry:
@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",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 4
year: 1986
CODEN: CMPDAM
ISSN: 0010-4566 OR 00104566
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
bibtimestamp: 2002.11.09 08:26:18 MST
fjournal: Computer Design
subject: B. Hardware; B.7 INTEGRATED CIRCUITS; C. Computer Systems Organization; C.4 PERFORMANCE OF SYSTEMS
acknowledgement: ack-nhfb
rawauthor: W. Twaddell
rawtitle: Higher performance marks floating-point chips
entry:
@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",
}


bibtype: inproceedings
filename: fparith.bib
label: Vaccaro:1986:SDF
author: J. Vaccaro and B. Johnson and C. Nowacki
booktitle: IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP '86
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1157--1160
month: aug
monthnumber: 8
year: 1986
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: J. Vaccaro and B. Johnson and C. Nowacki
rawbooktitle: {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

rawtitle:
A systolic discrete {Fourier} transform using residue number systems over the ring of {Gaussian} integers

entry:
@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.",
}


bibtype: mastersthesis
filename: fparith.bib
label: 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
bibtimestamp: 1996.02.24 15:01:45 MST
acknowledgement: ack-nhfb
rawauthor: Deepak Verma
rawtitle: Design of an efficient floating point vector coprocessor of an advanced microcomputer system
entry:
@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,
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 3
year: 1986
CODEN: AMMYAE
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
bibdate: Mon Jun 28 12:38:15 MDT 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database
bibtimestamp: 1999.06.28 12:38:15 MDT
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
journalURL: https://www.jstor.org/journals/00029890.htm
rawauthor: William C. Waterhouse
rawtitle: The Teaching of Mathematics: Why Square Roots are Irrational
entry:
@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",
}


bibtype: techreport
filename: fparith.bib
label: Weitek:1986:WSW
author: Weitek Corporation
title: WTL 1164 / WTL 1165 64-bit IEEE Floating-Point Multiplier / Divider and ALU
institution: pub-WEITEK
address: pub-WEITEK:adr
pages: 213--214
month: jul
monthnumber: 7
year: 1986
bibdate: Thu Nov 8 14:50:32 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.08 14:50:32 ???
acknowledgement: ack-nj
rawauthor: {Weitek Corporation}
rawtitle: {WTL} 1164\slash {WTL} 1165 64-bit {IEEE} Float\-ing-Point Multiplier\slash Divider and {ALU}
entry:
@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,
}


bibtype: techreport
filename: fparith.bib
label: 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
bibtimestamp: 1996.02.24 15:01:45 MST
series: NPL report; DITC 76/86
keywords: Algorithms.; Floating-point arithmetic.
acknowledgement: ack-nhfb
rawauthor: Brian A. Wichmann
rawtitle: Floating point interval arithmetic for validation
entry:
@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.",
}


bibtype: article
filename: fparith.bib
label: Wollenberg:1986:SRD
author: R. Wollenberg and R. Milnikel
journal: j-ELECTRONIK
volume: 6
pages: 79--82
year: 1986
CODEN: EKRKAR
ISSN: 0013-5658 OR 00135658
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
bibtimestamp: 1994.09.16 16:30:41 ???
fjournal: Elektronik
acknowledgement: ack-nj
rawauthor: R. Wollenberg and R. Milnikel
title:
Schnelles Radizierverfahren durch Tabellenzugriff toenglish Fast Square-rooting Method by Means of Table Lookup endtoenglish 

rawtitle:
{Schnelles Radizierverfahren durch Tabellenzugriff} \toenglish {Fast Square-rooting Method by Means of Table Lookup} \endtoenglish

entry:
@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",
}


bibtype: inproceedings
filename: fparith.bib
label: Agrawal:1987:CEF
author: J. C. Agrawal and P. S. Sehdev
title: Comparison and Evaluation of Floating Point Representations in IBM / 370 and VAX-11 / 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
bibtimestamp: 1994.09.14 20:23:44 ???
acknowledgement: ack-nj
rawauthor: J. C. Agrawal and P. S. Sehdev
rawtitle:
Comparison and Evaluation of Floating Point Representations in {IBM\slash 370} and {VAX-11\slash 780}

entry:
@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,
}


bibtype: article
filename: fparith.bib
label: Agarwal:1987:CNS
journal: j-IBM-JRD
volume: 31
number: 2
pages: 274--274
month: mar
monthnumber: 3
year: 1987
CODEN: IBMJAE
DOI: https://doi.org/10.1147/rd.312.0274
ISSN: 0018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)
ISSNL: 0018-8646 OR 00188646
MRclass: 76W05
MRnumber: MR894626
bibdate: Mon Feb 12 08:07:08 2001
bibtimestamp: 2001.02.12 08:07:08 ???
note: See cite Agarwal:1986:NSV.
fjournal: IBM Journal of Research and Development
acknowledgement: ack-nhfb
ajournal: IBM J. Res. Develop.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520
rawnote: See \cite{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:
Clarification: ``New scalar and vector elementary functions for the IBM System/370'' [IBM J. Res. Develop. bf 30 (1986), no. 2, 126--144]

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/

rawtitle:
Clarification: {``New scalar and vector elementary functions for the IBM System/370''} [{IBM J. Res. Develop. {\bf 30} (1986), no. 2, 126--144}]

entry:
@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",
}


bibtype: article
filename: fparith.bib
label: Ahmad:1987:IDA
author: M. Ahmad
title: Implementable Decimal Arithmetic Algorithms for Micro / Minicomputers
journal: j-MICROPROC-MICROPROG
volume: 19
number: 2
pages: 119--128
month: feb
monthnumber: 2
year: 1987
CODEN: MMICDT
ISSN: 0165-6074 (print), 1878-7061 (electronic) OR 01656074 (print), 18787061 (electronic)
ISSNL: 0165-6074 OR 01656074
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
bibtimestamp: 1994.09.01 10:16:11 ???
fjournal: Microprocessing and Microprogramming
keywords: decimal floating-point arithmetic
acknowledgement: ack-nj
rawauthor: M. Ahmad
rawtitle: Implementable Decimal Arithmetic Algorithms for Micro\slash Minicomputers
entry:
@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",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 8
year: 1987
CODEN: IBMTAA
ISSN: 0018-8689 OR 00188689
bibdate: Thu Oct 17 12:06:22 2019
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2019.10.17 12:06:22 ???
fjournal: IBM Technical Disclosure Bulletin
keywords: FMA; fused multiply-add
acknowledgement: ack-nhfb
rawauthor: Anonymous
rawtitle: Multiply-Addition --- An Ultra High Performance Dataflow
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.

entry:
@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.",
}


bibtype: book
filename: fparith.bib
label: ANSI:1987:AIS
author: ANSI / IEEE
publisher: pub-IEEE-STD
address: pub-IEEE-STD:adr
pages: v + 14
day: 5
month: oct
monthnumber: 10
year: 1987
ISBN: 0-7381-1167-8 OR 0738111678
ISBN13: 978-0-7381-1167-4 OR 9780738111674
bibdate: Thu Mar 02 09:40:18 2006
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2006.03.02 09:40:18 ???
note: Revised 1994. INSPEC Accession Number: 3095617.
acknowledgement: ack-nhfb
rawauthor: {ANSI\slash IEEE}
rawnote: Revised 1994. INSPEC Accession Number: 3095617.
title:
ANSI / IEEE Std 854-1987: An American National Standard: IEEE Standard for Radix-Independent Floating-Point Arithmetic

URL:
http://ieeexplore.ieee.org/iel1/2502/1121/00027840.pdf; http://ieeexplore.ieee.org/xpl/standardstoc.jsp?isnumber=1121&isYear=1987

rawtitle:
{ANSI\slash IEEE Std 854-1987: An American National Standard: IEEE Standard for Radix-Independent Floating-Point Arithmetic}

entry:
@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,
}


bibtype: article
filename: fparith.bib
label: Ardalan:1987:FPR
author: S. Ardalan and S. Alexander
journal: j-IEEE-TRANS-ACOUST-SPEECH
volume: 35
number: 6
pages: 770--783
month: jun
monthnumber: 6
year: 1987
CODEN: IETABA
ISSN: 0096-3518 OR 00963518
bibdate: Sat Jul 16 11:25:06 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:06 MDT
fjournal: IEEE Transactions on Acoustics, Speech, and Signal Processing
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29
rawauthor: S. Ardalan and S. Alexander
title:
Fixed-point roundoff error analysis of the exponentially windowed RLS algorithm for time-varying systems

rawtitle:
Fixed-point roundoff error analysis of the exponentially windowed {RLS} algorithm for time-varying systems

entry:
@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{}",
}


bibtype: mastersthesis
filename: fparith.bib
label: 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
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Computer arithmetic.; Floating-point arithmetic.
acknowledgement: ack-nhfb
rawauthor: Aqil M. Azmi
rawtitle: A floating point system with variable-length exponent
entry:
@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.",
}


bibtype: inproceedings
filename: fparith.bib
label: 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
bibtimestamp: 2007.11.14 18:22:26 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Balsara_Owens.pdf
keywords: ARITH-8
acknowledgement: ack-nhfb
rawauthor: Paras T. Balsara and Robert M. Owens
rawtitle: Systolic and Semi-Systolic Digit Serial Multipliers
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.

rawabstract:
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.

entry:
@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",
}


bibtype: mastersthesis
filename: fparith.bib
label: 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
bibtimestamp: 1996.02.24 15:01:45 MST
acknowledgement: ack-nhfb
rawauthor: Michael L. Baranyk
rawtitle: Extensions beyond the proposed {IEEE} standard number 754 for binary floating point arithmetic
keywords:
Binary system (Mathematics); Floating-point arithmetic.; Institute of Electrical and Electronics Engineers. --- IEEE; standard 754.

entry:
@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.",
}


bibtype: inproceedings
filename: fparith.bib
label: 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
bibtimestamp: 2004.11.24 12:49:55 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Barrett.pdf
keywords: ARITH-8
acknowledgement: ack-nhfb
rawauthor: Geoff Barrett
rawtitle: A formal approach to rounding
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.

rawabstract:
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.

entry:
@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",
}


bibtype: techreport
filename: fparith.bib
label: 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
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Binary system (Mathematics).; Floating-point arithmetic.; Formal languages.
acknowledgement: ack-nhfb
rawauthor: Geoff Barrett
rawtitle: Formal methods applied to a floating point number system
entry:
@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.",
}


bibtype: article
filename: fparith.bib
label: Boettner:1987:QA
author: H. Bottner
title: Quadratwurzel-Algorithmus toenglish Square-Root Algorithms endtoenglish
journal: j-MC
volume: 5
pages: 58
year: 1987
ISSN: 0720-4442, 0941-777x , 0943-5409 OR 07204442, 0941777x , 09435409
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
bibtimestamp: 1994.09.16 16:30:41 ???
fjournal: MC: Die Mikrocomputer-Zeitschrift
acknowledgement: ack-nj
rawauthor: H. B{\"o}ttner
rawtitle: {Quadratwurzel-Algorithmus} \toenglish {Square-Root Algorithms} \endtoenglish
entry:
@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",
}


bibtype: incollection
filename: fparith.bib
label: 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
bibtimestamp: 2003.11.28 11:46:56 ???
keywords: decimal floating-point arithmetic
acknowledgement: ack-nhfb
rawauthor: G. Bohlender and T. Teufel
rawtitle: A Decimal Floating-Point Processor for Optimal Arithmetic
entry:
@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",
}


bibtype: article
filename: fparith.bib
label: Boisvert:1987:AAH
author: Ronald F. Boisvert
title: Algorithm 651: Algorithm HFFT --- High-Order Fast-Direct Solution of the Helmholtz Equation
journal: j-TOMS
volume: 13
number: 3
pages: 235--249
month: sep
monthnumber: 9
year: 1987
CODEN: ACMSCU
DOI: https://doi.org/10.1145/29380.214342
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 65V05
MRnumber: 918 578
bibdate: Sun Sep 4 21:40:33 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.04 21:40:33 ???
note: See also cite Johnson:1987:CES.
URL: http://www.acm.org/pubs/citations/journals/toms/1987-13-3/p235-boisvert/
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms; theory; verification
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Ronald F. Boisvert
rawnote: See also \cite{Johnson:1987:CES}.
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.

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.

rawabstract:
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.

rawtitle:
{Algorithm 651}: Algorithm {HFFT}\emdash High-Order Fast-Direct Solution of the {Helmholtz} Equation

entry:
@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.",
}


bibtype: article
filename: fparith.bib
label: 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
year: 1987
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 19:01:00 MST 2017
bibtimestamp: 2017.03.01 19:01:00 MST
URL: http://www.sciencedirect.com/science/article/pii/0898122187900824
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: B. Bose
rawtitle: $2$-dimensional arithmetic residue check codes
entry:
@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",
}


bibtype: inproceedings
filename: fparith.bib
label: 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
bibtimestamp: 2007.11.14 18:22:26 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Bose_Pei_Taylor_Patterson.pdf
keywords: ARITH-8
acknowledgement: ack-nhfb
rawauthor: B. K. Bose and L. Pei and G. S. Taylor and D. A. Patterson
rawtitle: Fast Multiply and Divide for a {VLSI} Floating-Point Unit
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.

rawabstract:
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.

entry:
@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",
}


bibtype: phdthesis
filename: fparith.bib
label: Braune:1987:HSF
author: K. Braune
type: Dissertation
school: Universitat Karlsruhe
address: Karlsruhe, Germany
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
bibtimestamp: 1994.09.16 16:30:40 ???
acknowledgement: ack-nj
rawauthor: K. Braune
title:
Hochgenaue Standardfunktionen fur 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 

rawtitle:
{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

entry:
@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,
}


bibtype: incollection
filename: fparith.bib
label: 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
bibtimestamp: 1994.09.01 12:25:00 ???
acknowledgement: ack-nj
rawauthor: P. T. Breuer
rawtitle: A New Method for Real Rational Uniform Approximation
entry:
@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,
}


bibtype: inproceedings
filename: fparith.bib
label: 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
bibtimestamp: 2007.11.16 21:39:46 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Carter.pdf
keywords: ARITH-8
acknowledgement: ack-nhfb
rawauthor: Tony M. Carter
rawtitle: Structured Arithmetic Tiling of Integrated Circuits
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.

rawabstract:
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.

entry:
@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",
}


bibtype: inproceedings
filename: fparith.bib
label: 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
bibtimestamp: 2007.11.16 21:39:46 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Cavallaro_Luk.pdf
keywords: ARITH-8
acknowledgement: ack-nhfb
rawauthor: Joseph R. Cavallaro and Franklin T. Luk
rawtitle: {CORDIC} Arithmetic for an {SVD} Processor
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.

rawabstract:
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.

entry:
@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",
}


bibtype: article
filename: fparith.bib
label: Chandra:1987:ACR
author: D. V. Chandra
journal: j-IEEE-TRANS-ACOUST-SPEECH
volume: 35
number: 11
pages: 1633--1636
month: nov
monthnumber: 11
year: 1987
CODEN: IETABA
ISSN: 0096-3518 OR 00963518
bibdate: Sat Jul 16 11:25:06 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:06 MDT
fjournal: IEEE Transactions on Acoustics, Speech, and Signal Processing
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29
rawauthor: D. V. Chandra
title:
Accumulation of coefficient roundoff error in fast Fourier transforms implemented with logarithmic number system

rawtitle:
Accumulation of coefficient roundoff error in fast {Fourier} transforms implemented with logarithmic number system

entry:
@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{}",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 7
year: 1987
CODEN: CKCKDZ
ISSN: 0253-3839 OR 02533839
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
bibtimestamp: 2002.11.09 08:26:18 MST
fjournal: Journal of the Chinese Institute of Engineers = Chung-kuo kung ch'eng hsueh kan
acknowledgement: ack-nhfb
affiliation: Tatung Institute of Technology, Taipei, Taiwan
rawauthor: Chang-Fuu Chen
rawtitle: A modified floating-point code for voice coding and its applications
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

entry:
@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",
}


bibtype: inproceedings
filename: fparith.bib
label: Ciminiera:1987:PMB
author: Luigi Ciminiera
title: Parallel Multipliers Based on Horizontal Compressors
crossref: Irwin:1987:PSC
pages: 63--69
month: may
monthnumber: 5
year: 1987
bibdate: Wed Nov 14 18:22:26 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 18:22:26 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Ciminiera.pdf
keywords: ARITH-8
acknowledgement: ack-nhfb
rawauthor: Luigi Ciminiera
rawtitle: Parallel Multipliers Based on Horizontal Compressors
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.

rawabstract:
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.

entry:
@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",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 4
year: 1987
CODEN: SJNAAM
DOI: https://doi.org/10.1137/0724034
ISSN: 0036-1429 (print), 1095-7170 (electronic) OR 00361429 (print), 10957170 (electronic)
ISSNL: 0036-1429 OR 00361429
MRclass: 65G05 (65G99)
MRnumber: 881377
MRreviewer: F. Szidarovszky
bibdate: Sun Nov 12 06:18:24 2023
bibtimestamp: 2023.11.12 06:18:24 ???
fjournal: SIAM Journal on Numerical Analysis
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sinum
rawauthor: C. W. Clenshaw and Frank W. J. Olver
rawtitle: Level-Index Arithmetic Operations
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.

authordates:
Charles William Clenshaw (15 March 1926--23 September 2004); Frank William John Olver (15 December 1924--23 April 2013)

rawabstract:
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.

entry:
@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",
}


bibtype: inproceedings
filename: fparith.bib
label: 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
bibtimestamp: 2007.11.16 21:39:46 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Colagrossi_Miola.pdf
keywords: ARITH-8
acknowledgement: ack-nhfb
rawauthor: A. Colagrossi and A. Miola
rawtitle: A Normalization Algorithm for Truncated $p$-{ADIC} Arithmetic
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.

rawabstract:
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.

entry:
@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",
}


bibtype: inproceedings
filename: fparith.bib
label: Cosnard:1987:FAC
title: The FELIN Arithmetic Coprocessor Chip
crossref: Irwin:1987:PSC
pages: 107--112
month: may
monthnumber: 5
year: 1987
bibdate: Wed Nov 14 18:22:26 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 18:22:26 ???
keywords: ARITH-8
acknowledgement: ack-nhfb
rawtitle: The {FELIN} Arithmetic Coprocessor Chip
author:
M. Cosnard and A. Guyot and B. Hochet and Jean-Michel Muller and H. Ouaouicha and P. Paul and E. Zysman

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 ELementaires INtegrees'' is the French for ``integrated elementary functions'').

rawabstract:
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'').

rawauthor:
M. Cosnard and A. Guyot and B. Hochet and Jean-Michel Muller and H. Ouaouicha and P. Paul and E. Zysman

entry:
@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",
}


bibtype: techreport
filename: fparith.bib
label: 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
year: 1987
bibdate: Wed Sep 14 20:24:43 1994
bibtimestamp: 1994.09.14 20:24:43 ???
series: NASA contractor report; 178364 ICASE interim report; 4 NASA contractor report; NASA CR-178364.
keywords: Computer networks; FORTRAN (Computer program language)
acknowledgement: ack-nj
rawauthor: Thomas W. Crockett
rawtitle: Performance of {Fortran} Floating-Point Operations on the {Flex/32} Multicomputer
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

remark:
Distributed to depository libraries in microfiche. Microfiche. [Washington, D.C.?: National Aeronautics and Space Administration], 1987. 1 microfiche.

entry:
@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.",
}


bibtype: incollection
filename: fparith.bib
label: 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
bibtimestamp: 2002.11.09 08:26:18 MST
acknowledgement: ack-nhfb
rawauthor: Charles Crowell
rawtitle: Floating-point arithmetic with the {TMS32020}
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

entry:
@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",
}


bibtype: inproceedings
filename: fparith.bib
label: 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
DOI: https://doi.org/10.1109/ARITH.1987.6158694
bibdate: Thu Aug 23 06:14:44 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.08.23 06:14:44 ???
URL: http://www.netlib.org/na-digest/91/v91n39
keywords: ARITH-8
acknowledgement: ack-nhfb
rawauthor: James W. Demmel
rawtitle: On error analysis in arithmetic with varying relative precision
abstract:
Recently Clenshaw / Olver and Iri / 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 / 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 / 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.

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.

rawabstract:
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.

entry:
@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.",
}


bibtype: techreport
filename: fparith.bib
label: 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
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Titan (Computer)
acknowledgement: ack-nhfb
rawauthor: Jeremy Dion and David Reeves Boggs and Norman P. Jouppi
rawtitle: {MultiTitan}: four architecture papers
series:
WRL research report. Digital Equipment Corporation. Western Research Laboratory; 87-8 Digital Equipment Corporation. Western Research Laboratory. WRL research report; 87/8.

entry:
@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)",
}


bibtype: inproceedings
filename: fparith.bib
label: 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
bibtimestamp: 2007.11.16 21:39:46 ???
keywords: ARITH-8
remark: Paper not received in time for publication.
acknowledgement: ack-nhfb
rawauthor: J. {Du Croz} and M. Pont
rawtitle: The Development of a Floating-Point Validation Package
entry:
@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.",
}


bibtype: article
filename: fparith.bib
label: Duff:1987:EAP
author: Iain S. Duff and Jacques Laminie and Alain Lichnewsky and Francois Thomasset
title: An experiment with arithmetic precision in linear algebra computations
journal: j-INT-J-NUM-METH-FLUIDS
volume: 7
pages: 1077--1092
year: 1987
bibdate: Mon Jan 02 17:53:34 2006
bibtimestamp: 2006.01.02 17:53:34 ???
acknowledgement: ack-nhfb
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0363
rawauthor: Iain S. Duff and Jacques Laminie and Alain Lichnewsky and Fran{\c{c}}ois Thomasset
rawtitle: An experiment with arithmetic precision in linear algebra computations
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@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",
}


bibtype: manual
filename: fparith.bib
label: Duhamel:1987:ASR
author: Bob Duhamel
title: Atari System Reference Manual
address: 6915 Casselberry Way, San Diego, CA 92119, USA
pages: 1077--1092
year: 1987
bibdate: Sat Mar 04 16:04:10 2006
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2006.03.04 16:04:10 ???
note: See Chapter 11: The Floating Point Arithmetic Package.
keywords: decimal floating-point arithmetic
acknowledgement: ack-nhfb
rawauthor: Bob Duhamel
rawnote: See Chapter 11: The Floating Point Arithmetic Package.
rawtitle: {Atari} System Reference Manual
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

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.

entry:
@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.",
}


bibtype: article
filename: fparith.bib
label: Dunham:1987:PMA
author: C. B. Dunham
title: Provably Monotone Approximations II
journal: j-SIGNUM
volume: 22
number: 3
pages: 30--31
month: jul
monthnumber: 7
year: 1987
CODEN: SNEWD6
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Tue Sep 13 09:01:31 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.13 09:01:31 ???
fjournal: ACM SIGNUM Newsletter
keywords: theory
subject: G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS, Approximation
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/signum
rawauthor: C. B. Dunham
rawtitle: Provably Monotone Approximations {II}
entry:
@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",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 7
year: 1987
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1987.1676986
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Apr 2 08:38:35 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.04.02 08:38:35 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-sfo
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: M. D. Ercegovac and T. Lang
rawtitle: On-the-fly conversion of redundant into conventional representations
entry:
@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",
}


bibtype: inproceedings
filename: fparith.bib
label: Ercegovac:1987:LSC
author: Milos 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
bibtimestamp: 2007.11.16 21:39:46 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Ercegovac_Lang.pdf
keywords: ARITH-8
acknowledgement: ack-nhfb
rawauthor: Milo{\v{s}} D. Ercegovac and Tomas Lang
rawtitle: On-Line Scheme for Computing Rotation Factors
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.

rawabstract:
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.

entry:
@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",
}


bibtype: inproceedings
filename: fparith.bib
label: 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
bibtimestamp: 2007.11.14 18:22:26 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Fandrianto.pdf
keywords: ARITH-8; correct rounding; floating-point arithmetic
acknowledgement: ack-nhfb
rawauthor: Jan Fandrianto
rawtitle: Algorithms for High Speed Shared Radix 4 Division and Radix 4 Square-Root
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 / root prediction PLA, a divisor / 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 / 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 / square-root will be discussed.

rawabstract:
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.

entry:
@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",
}


bibtype: periodical
filename: fparith.bib
label: FPS:1987:AR
author: Floating Point Systems, Inc.
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
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Computer industry --- United States --- Periodicals.; Floating Point Systems, Inc. --- Periodicals.
remark: Description based on: 1987.
acknowledgement: ack-nhfb
key: FPS
rawauthor: {Floating Point Systems, Inc.}
rawtitle: Annual report
entry:
@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.",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 1
year: 1987
CODEN: AALEE5
ISSN: 1094-3641 (print), 1557-9476 (electronic) OR 10943641 (print), 15579476 (electronic)
ISSNL: 1094-3641 OR 10943641
bibdate: Sat Aug 9 09:05:24 MDT 2003
bibtimestamp: 2003.08.09 09:05:24 MDT
fjournal: ACM SIGAda Ada Letters
keywords: languages; theory
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/citation.cfm?id=J32
rawauthor: Terry Froggatt
rawtitle: Fixed-point conversion, multiplication, and division in {Ada}
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

subject:
D.3.2 Software, PROGRAMMING LANGUAGES, Language Classifications, Ada G.1.0 Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic

entry:
@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",
}


bibtype: article
filename: fparith.bib
label: 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 OR 00361437
ISSNL: 0036-1437 OR 00361437
bibdate: Sat Feb 8 10:30:07 2020
bibtimestamp: 2020.02.08 10:30:07 ???
fjournal: SIAM News
acknowledgement: ack-nhfb
journalURL: https://sinews.siam.org/
rawauthor: Eric Grosse and Cleve Moler
rawtitle: Underflow can be Harmful
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/g/grosse-eric.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@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/",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 10
year: 1987
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1987.1676855
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 9 09:28:56 MDT 2011
bibtimestamp: 2011.07.09 09:28:56 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676855
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Alain Guyot and Bertrand Hochet and Jean-Michel Muller
rawtitle: A Way to Build Efficient Carry-Skip Adders
entry:
@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",
}


bibtype: inproceedings
filename: fparith.bib
label: Hamada:1987:NRN
author: Hozumi Hamada
title: A New Real Number Representation and Its Operation
crossref: Irwin:1987:PSC
pages: 153--157
month: may
monthnumber: 5
year: 1987
bibdate: Wed Nov 14 18:22:26 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 18:22:26 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Hamada.pdf
keywords: ARITH-8
acknowledgement: ack-nhfb
rawauthor: Hozumi Hamada
rawtitle: A New Real Number Representation and Its Operation
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 / 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.

rawabstract:
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.

entry:
@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",
}


bibtype: inproceedings
filename: fparith.bib
label: 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
bibtimestamp: 2007.11.14 18:22:26 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Han_Carlson.pdf
keywords: ARITH-8
acknowledgement: ack-nhfb
rawauthor: Tackdon Han and David A. Carlson
rawtitle: Fast Area-Efficient {VLSI} Adders
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.

rawabstract:
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.

entry:
@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",
}


bibtype: book
filename: fparith.bib
label: 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 OR 0889201528
ISBN13: 978-0-88920-152-1 OR 9780889201521
LCCN: A481.H47 1987
bibdate: Thu Jul 10 08:02:28 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.07.10 08:02:28 ???
acknowledgement: ack-nhfb
rawauthor: Roger Herz-Fischler
rawtitle: A mathematical history of division in extreme and mean ratio
entry:
@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.",
}


bibtype: book
filename: fparith.bib
label: 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) OR 0486653633 (paperback)
ISBN13: 978-0-486-65363-1 (paperback) OR 9780486653631 (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
bibtimestamp: 2010.08.20 09:19:58 MDT
URL: http://www.loc.gov/catdir/description/dover032/87005370.html
remark: Unabridged, slightly corrected republication of cite Hildebrand:1974:INA.
subject: Numerical analysis
acknowledgement: ack-nhfb
rawauthor: Francis Begnaud Hildebrand
rawtitle: Introduction to numerical analysis
entry:
@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",
}


bibtype: article
filename: fparith.bib
label: Himmeroeder:1987:CKC
author: H.-J. Himmeroder and R. M. Toschke
journal: j-CT
volume: 1
pages: 152--158
year: 1987
ISSN: 0724-8679 OR 07248679
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
bibtimestamp: 1996.02.24 09:05:58 ???
fjournal: C T: Magazin fur Computer Technik (Hannover)
acknowledgement: ack-nj
rawauthor: 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 

rawtitle:
{c't-KAT-Ce. Ein 68000-Einplatinenrechner, Teil 3: REAL-Arithmetik} \toenglish {c't-KAT-Ce. A 68000 Single-Board Computer} \endtoenglish

entry:
@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)",
}


bibtype: inproceedings
filename: fparith.bib
label: 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
bibtimestamp: 2007.11.16 21:39:46 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Hochet_Quinton_Robert.pdf
keywords: ARITH-8
acknowledgement: ack-nhfb
rawauthor: Bertrand Hochet and Patrice Quinton and Yves Robert
rawtitle: Systolic Solution of Linear Systems over {$ \mathrm {GF}(p) $} with Partial Pivoting
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) $.

rawabstract:
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) $.

entry:
@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",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 9
year: 1987
CODEN: IEMIDZ
DOI: https://doi.org/10.1109/MM.1987.305012
ISSN: 0272-1732 (print), 1937-4143 (electronic) OR 02721732 (print), 19374143 (electronic)
ISSNL: 0272-1732 OR 02721732
bibdate: Thu Dec 14 06:08:58 MST 2000
bibtimestamp: 2000.12.14 06:08:58 MST
fjournal: IEEE Micro
acknowledgement: ack-nj
affiliationaddress: Inmos Ltd, Bristol, Engl
classcodes: B1265F (Microprocessors and microcomputers); C5130 (Microprocessor chips)
corpsource: Inmos Ltd., Bristol, UK
journalURL: http://www.computer.org/csdl/mags/mi/index.html
treatment: P Practical; R Product Review
rawauthor: Mark Homewood and David May and David Shepherd and Roger Shepherd
rawtitle: The {IMS T800} Transputer
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)

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

entry:
@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",
}


bibtype: incollection
filename: fparith.bib
label: 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
monthnumber: 10
year: 1987
bibdate: Fri Nov 28 17:12:16 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 17:12:16 ???
URL: http://www.hpmuseum.org/
acknowledgement: ack-mfc
rawauthor: {Hewlett Packard}
rawbooktitle: {HP-71} Reference Manual
rawtitle: The {IEEE} Proposal for Handling Math Exceptions
note:
Mfg. #0071-90110, Reorder #0071-90010. First edition October 1983. Manual available from em The Museum of HP Calculators.

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.

rawabstract:
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.

rawnote:
Mfg. \#0071-90110, Reorder \#0071-90010. First edition October 1983. Manual available from {\em The Museum of HP Calculators}.

entry:
@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,
}


bibtype: mastersthesis
filename: fparith.bib
label: 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
bibtimestamp: 1996.02.24 15:01:45 MST
acknowledgement: ack-nhfb
rawauthor: Timothy Hu
rawtitle: Circuit design techniques for a floating-point processor: research project
entry:
@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,
}


bibtype: inproceedings
filename: fparith.bib
label: 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
bibtimestamp: 2003.11.28 11:41:31 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Hull_Cohen.pdf
keywords: ARITH-8; decimal floating-point arithmetic
acknowledgement: ack-nhfb
rawauthor: T. E. Hull and M. S. Cohen
rawtitle: Toward an Ideal Computer Arithmetic
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.

rawabstract:
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.

entry:
@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",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 2
year: 1987
CODEN: SINODQ
DOI: https://doi.org/10.1109/IEEESTD.1985.82928
ISSN: 0362-1340 (print), 1523-2867 (print), 1558-1160 OR 03621340 (print), 15232867 (print), 15581160
ISSNL: 0362-1340 OR 03621340
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
bibtimestamp: 1994.09.09 12:55:55 ???
fjournal: ACM SIGPLAN Notices
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J706
rawauthor: {IEEE}
rawtitle: {IEEE} Standard for Binary Floating-Point Arithmetic
entry:
@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",
}


bibtype: book
filename: fparith.bib
label: 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 OR 155937859X
ISBN13: 978-1-55937-859-8 OR 9781559378598
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
bibtimestamp: 2000.04.24 07:02:34 ???
note: Revised 1994.
URL: http://standards.ieee.org/reading/ieee/std_public/description/busarch/854-1987_desc.html
keywords: floating point arithmetic; Floating-point arithmetic.; Standards
acknowledgement: ack-nj
raweditor: {IEEE}
rawnote: Revised 1994.
rawtitle: {854-1987 (R1994) IEEE Standard for Radix-Independent Floating-Point Arithmetic}
remark:
At head of title: An American National Standard. ``Approved March 12, 1987 IEEE Standards Board; Approved September 10, 1987 American National Standards Institute.''

entry:
@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.''",
}


bibtype: mastersthesis
filename: fparith.bib
label: 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
bibtimestamp: 1996.02.24 15:01:45 MST
acknowledgement: ack-nhfb
rawauthor: Debby Jensen
rawtitle: Control implementation for the {SPUR} floating point coprocessor: research project
entry:
@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,
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 6
year: 1987
CODEN: ACMSCU
DOI: https://doi.org/10.1145/328512.328520
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
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
bibtimestamp: 1994.09.01 10:15:42 ???
note: See also cite Johnson:1987:CES.
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/toms
rawauthor: Kenneth C. Johnson
rawnote: See also \cite{Johnson:1987:CES}.
rawtitle: {Algorithm 650}: Efficient Square Root Implementation on the 68000
entry:
@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",
}


bibtype: article
filename: fparith.bib
label: Johnson:1987:CES
author: Kenneth C. Johnson
journal: j-TOMS
volume: 13
number: 3
pages: 320--320
month: sep
monthnumber: 9
year: 1987
CODEN: ACMSCU
DOI: https://doi.org/10.1145/29380.356210
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
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
bibtimestamp: 2020.02.08 10:30:18 ???
note: See cite Johnson:1987:AES,Monahan:1987:AGC,Boisvert:1987:AAH.
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Kenneth C. Johnson
rawnote: See \cite{Johnson:1987:AES,Monahan:1987:AGC,Boisvert:1987:AAH}.
title:
Corrigendum: ``Algorithm 650: efficient square root implementation on the 68000'' [ACM Trans. Math. Software bf 13 (1987), no. 2, 138--151]

rawtitle:
Corrigendum: {``Algorithm 650: efficient square root implementation on the 68000'' [ACM Trans. Math. Software {\bf 13} (1987), no. 2, 138--151]}

entry:
@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",
}


bibtype: inproceedings
filename: fparith.bib
label: 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
bibtimestamp: 1997.01.11 17:44:01 MST
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
rawauthor: W. Kahan
rawtitle: Branch Cuts for Complex Elementary Functions or Much Ado About Nothing's Sign Bit
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

entry:
@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,
}


bibtype: unpublished
filename: fparith.bib
label: Kahan:1987:CWF
author: W. Kahan
title: Checking whether floating-point division is correctly rounded
pages: 165--211
year: 1987
bibdate: Mon Apr 25 05:40:03 2005
bibtimestamp: 2005.04.25 05:40:03 ???
note: Lecture notes.
keywords: correct rounding; floating-point arithmetic; rounding errors
acknowledgement: ack-nhfb
rawauthor: W. Kahan
rawnote: Lecture notes.
rawtitle: Checking whether floating-point division is correctly rounded
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@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",
}


bibtype: misc
filename: fparith.bib
label: Kahan:1987:DPI
author: W. Kahan
title: Doubled-precision IEEE Standard 754 floating-point arithmetic
pages: 165--211
month: feb
monthnumber: 2
year: 1987
bibdate: Thu May 09 07:25:40 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.09 07:25:40 ???
keywords: accurate floating-point summation
remark: Cited in cite Higham:1993:AFP.
acknowledgement: ack-nhfb
howpublished: Manuscript
rawauthor: W. Kahan
rawtitle: Doubled-precision {IEEE Standard 754} floating-point arithmetic
entry:
@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}.",
}


bibtype: techreport
filename: fparith.bib
label: Kahan:1987:HAE
author: W. Kahan
title: Handling Arithmetic Exceptions
type: Report
institution: inst-BERKELEY-MATH-EECS
address: inst-BERKELEY-MATH-EECS:adr
pages: 165--211
day: 14
month: may
monthnumber: 5
year: 1987
bibdate: Mon Aug 26 10:42:10 2024
bibtimestamp: 2024.08.26 10:42:10 ???
URL: http://www.arithmazium.org/classroom/lib//Kahan_Handling_Arithmetic_Exceptions.pdf
acknowledgement: ack-nhfb
rawauthor: W. Kahan
rawtitle: Handling Arithmetic Exceptions
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

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.

rawabstract:
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.

entry:
@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,
}


bibtype: book
filename: fparith.bib
label: Kane:1987:MRR
author: Gerry Kane
title: MIPS R2000 RISC Architecture
publisher: pub-PH
address: pub-PH:adr
pages: 165--211
year: 1987
ISBN: 0-13-584749-4 OR 0135847494
ISBN13: 978-0-13-584749-7 OR 9780135847497
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
bibtimestamp: 1993.12.15 17:51:38 ???
acknowledgement: ack-nhfb
rawauthor: Gerry Kane
rawtitle: {MIPS R2000 RISC} Architecture
entry:
@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,
}


bibtype: inproceedings
filename: fparith.bib
label: 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
bibtimestamp: 2007.11.16 21:39:46 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Kao_Taylor.pdf
keywords: ARITH-8
acknowledgement: ack-nhfb
rawauthor: Rom-Shen Kao and Fred J. Taylor
rawtitle: Implementation of the Single Modulus Complex {ALU}
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.

rawabstract:
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.

entry:
@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",
}


bibtype: inproceedings
filename: fparith.bib
label: 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
bibtimestamp: 2007.11.16 21:39:46 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Kirchner_Kulisch.pdf
keywords: ARITH-8
acknowledgement: ack-nhfb
rawauthor: R. Kirchner and U. Kulisch
rawtitle: Arithmetic for Vector Processors
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.

rawabstract:
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.

entry:
@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",
}


bibtype: article
filename: fparith.bib
label: Kirchner:1987:SVS
author: Reinhard Kirchner and Ulrich Kulisch
journal: Beitrage 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
bibtimestamp: 1995.12.08 12:20:44 ???
language: German
acknowledgement: ack-nhfb
rawauthor: 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]

rawtitle:
{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]

entry:
@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",
}


bibtype: article
filename: fparith.bib
label: Koopman:1987:TF
author: P. Koopman
title: Transcendental Functions
journal: j-FORTH-DIMENSIONS
volume: 9
number: 4
pages: 21--22
month: dec
monthnumber: 12
year: 1987
CODEN: FODMD5
ISSN: 0884-0822 OR 08840822
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
bibtimestamp: 1994.09.01 10:15:30 ???
fjournal: Forth Dimensions
acknowledgement: ack-nj
rawauthor: P. Koopman
rawtitle: Transcendental Functions
entry:
@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",
}


bibtype: inproceedings
filename: fparith.bib
label: 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
bibtimestamp: 2007.11.16 21:39:46 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Kornerup_Matula.pdf
keywords: ARITH-8
acknowledgement: ack-nhfb
rawauthor: Peter Kornerup and David W. Matula
rawtitle: A Bit-Serial Arithmetic Unit for Rational Arithmetic
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.

rawabstract:
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.

entry:
@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",
}


