# bibtab

bibtype: article
filename: fparith.bib
label: Agrawal:1983:ICA
author: D. P. Agrawal and T. R. N. Rao
title: Introduction: Computer Arithmetic
journal: j-IEEE-TRANS-COMPUT
volume: C-32
number: 4
pages: 329--330
month: apr
monthnumber: 4
year: 1983
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1983.1676232
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 10:01:08 MDT 2011
bibtimestamp: 2011.07.10 10:01:08 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676232
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: D. P. Agrawal and T. R. N. Rao
rawtitle: Introduction: Computer Arithmetic
entry:
@Article{Agrawal:1983:ICA,
  author =       "D. P. Agrawal and T. R. N. Rao",
  title =        "Introduction: Computer Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "4",
  pages =        "329--330",
  month =        apr,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676232",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:01:08 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676232",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Akamine:1983:SMQ
author: Masami Akamine and Tatsuo Higuchi
title: Synthesis of minimum quantization error digital filters using floating-point arithmetic
journal: j-ELECTRON-COMMUN-JPN
volume: 66
number: 10
pages: 29--38
year: 1983
CODEN: ECOJAL
ISSN: 0424-8368 OR 04248368
MRclass: 94A12
MRnumber: 85k:94010
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: Electronics and communications in Japan
acknowledgement: ack-nhfb
rawauthor: Masami Akamine and Tatsuo Higuchi
rawtitle: Synthesis of minimum quantization error digital filters using floating-point arithmetic
entry:
@Article{Akamine:1983:SMQ,
  author =       "Masami Akamine and Tatsuo Higuchi",
  title =        "Synthesis of minimum quantization error digital
                 filters using floating-point arithmetic",
  journal =      j-ELECTRON-COMMUN-JPN,
  volume =       "66",
  number =       "10",
  pages =        "29--38",
  year =         "1983",
  CODEN =        "ECOJAL",
  ISSN =         "0424-8368",
  MRclass =      "94A12",
  MRnumber =     "85k:94010",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics and communications in Japan",
}


bibtype: inproceedings
filename: fparith.bib
label: Annaratone:1983:MME
author: M. Annaratone and R. Stefanelli
title: A Multiplier with Multiple Error Correction Capability
crossref: IEEE:1983:PSC
pages: 44--51
year: 1983
bibdate: Tue Nov 13 15:58:57 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.13 15:58:57 ???
URL: http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Annaratone_Stefanelli.pdf
keywords: ARITH-6
acknowledgement: ack-nhfb
rawauthor: M. Annaratone and R. Stefanelli
rawtitle: A Multiplier with Multiple Error Correction Capability
abstract:
This paper presents a technique for increasing the reliability of arithmetic units. An error model is then presented: this model well represents the faulty behavior of many arithmetic units. The Residue Number System and its related properties are used in order to obtain a simple architecture (called Reliability Network, R-Net). The main characteristics of the presented technique are a significant reduction in the number of gates and a limited increase of global execution times. The extensive use of combinational logic makes it possible to implement the R-Net almost completely by means of Programmable Logic Arrays (PLA's). Finally, both the intrinsic regularity of the R-Net and its simple internal interconnection scheme make this approach suitable for a practical VLSI implementation.

rawabstract:
This paper presents a technique for increasing the reliability of arithmetic units. An error model is then presented: this model well represents the faulty behavior of many arithmetic units. The Residue Number System and its related properties are used in order to obtain a simple architecture (called Reliability Network, R-Net). The main characteristics of the presented technique are a significant reduction in the number of gates and a limited increase of global execution times. The extensive use of combinational logic makes it possible to implement the R-Net almost completely by means of Programmable Logic Arrays (PLA's). Finally, both the intrinsic regularity of the R-Net and its simple internal interconnection scheme make this approach suitable for a practical VLSI implementation.

entry:
@InProceedings{Annaratone:1983:MME,
  author =       "M. Annaratone and R. Stefanelli",
  title =        "A Multiplier with Multiple Error Correction
                 Capability",
  crossref =     "IEEE:1983:PSC",
  pages =        "44--51",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Annaratone_Stefanelli.pdf",
  abstract =     "This paper presents a technique for increasing the
                 reliability of arithmetic units. An error model is then
                 presented: this model well represents the faulty
                 behavior of many arithmetic units. The Residue Number
                 System and its related properties are used in order to
                 obtain a simple architecture (called Reliability
                 Network, R-Net). The main characteristics of the
                 presented technique are a significant reduction in the
                 number of gates and a limited increase of global
                 execution times. The extensive use of combinational
                 logic makes it possible to implement the R-Net almost
                 completely by means of Programmable Logic Arrays
                 (PLA's). Finally, both the intrinsic regularity of the
                 R-Net and its simple internal interconnection scheme
                 make this approach suitable for a practical VLSI
                 implementation.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6",
}


bibtype: article
filename: fparith.bib
label: Armer:1983:DCR
author: Paul Armer
title: 11. The Defense Calculator at the Rand Corporation
journal: j-ANN-HIST-COMPUT
volume: 5
number: 2
pages: 202--202
month: apr
monthnumber: 4
year: 1983
CODEN: AHCOE5
ISSN: 0164-1239 OR 01641239
ISSNL: 0164-1239 OR 01641239
bibdate: Fri Nov 1 15:29:20 MST 2002
bibtimestamp: 2002.11.01 15:29:20 MST
fjournal: Annals of the History of Computing
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650
rawauthor: Paul Armer
rawtitle: 11. The {Defense Calculator} at the {Rand Corporation}
URL:
http://dlib.computer.org/an/books/an1983/pdf/a2202a.pdf; http://www.computer.org/annals/an1983/a2202aabs.htm

entry:
@Article{Armer:1983:DCR,
  author =       "Paul Armer",
  title =        "11. The {Defense Calculator} at the {Rand
                 Corporation}",
  journal =      j-ANN-HIST-COMPUT,
  volume =       "5",
  number =       "2",
  pages =        "202--202",
  month =        apr # "\slash " # jun,
  year =         "1983",
  CODEN =        "AHCOE5",
  ISSN =         "0164-1239",
  ISSN-L =       "0164-1239",
  bibdate =      "Fri Nov 1 15:29:20 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://dlib.computer.org/an/books/an1983/pdf/a2202a.pdf;
                 http://www.computer.org/annals/an1983/a2202aabs.htm",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of the History of Computing",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650",
}


bibtype: article
filename: fparith.bib
label: Asai:1983:CPI
author: H. Asai
title: A Consideration of a Practical Implementation For a New Convergence Division
journal: j-INFO-PROC-LETT
volume: 17
number: 5
pages: 273--281
month: dec
monthnumber: 12
year: 1983
CODEN: IFPLAT
ISSN: 0020-0190 (print), 1872-6119 (electronic) OR 00200190 (print), 18726119 (electronic)
ISSNL: 0020-0190 OR 00200190
bibdate: Thu Sep 1 10:15:08 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:15:08 ???
fjournal: Information Processing Letters
acknowledgement: ack-nj
journalURL: http://www.sciencedirect.com/science/journal/00200190
rawauthor: H. Asai
rawtitle: A Consideration of a Practical Implementation For a New Convergence Division
entry:
@Article{Asai:1983:CPI,
  author =       "H. Asai",
  title =        "A Consideration of a Practical Implementation For a
                 New Convergence Division",
  journal =      j-INFO-PROC-LETT,
  volume =       "17",
  number =       "5",
  pages =        "273--281",
  month =        dec,
  year =         "1983",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  bibdate =      "Thu Sep 1 10:15:08 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
}


bibtype: article
filename: fparith.bib
label: Asai:1983:SOM
author: Hitohisa Asai and C. K. Cheng
title: Speeding Up an Overrelaxation Method of Division in Radix-$ 2^n $ Machine
journal: j-CACM
volume: 26
number: 3
pages: 216--220
year: 1983
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Mon Jan 22 06:22:06 MST 2001
bibtimestamp: 2001.01.22 06:22:06 MST
fjournal: Communications of the ACM
keywords: arithmetic
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Hitohisa Asai and C. K. Cheng
rawtitle: Speeding Up an Overrelaxation Method of Division in Radix-$ 2^n $ Machine
bibsource:
http://dblp.uni-trier.de/db/journals/cacm/cacm26.html#AsaiC83; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Asai:1983:SOM,
  author =       "Hitohisa Asai and C. K. Cheng",
  title =        "Speeding Up an Overrelaxation Method of Division in
                 Radix-$ 2^n $ Machine",
  journal =      j-CACM,
  volume =       "26",
  number =       "3",
  pages =        "216--220",
  year =         "1983",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 06:22:06 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm26.html#AsaiC83;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "arithmetic",
  oldlabel =     "AsaiC83",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/AsaiC83",
}


bibtype: mastersthesis
filename: fparith.bib
label: Aspinwall:1983:IIF
author: David Brian Masters Aspinwall
title: An implementation of the IEEE floating point standard on a VAX-11 / 780
type: Thesis (M.S.)
school: San Francisco State University
address: San Francisco, CA, USA
pages: ix + 138
year: 1983
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
acknowledgement: ack-nhfb
rawauthor: David Brian Masters Aspinwall
rawtitle: An implementation of the {IEEE} floating point standard on a {VAX-11\slash 780}
keywords:
Computer architecture.; Floating-point arithmetic.; Microprogramming.; VAX-11 (Computer) --- Programming.

entry:
@MastersThesis{Aspinwall:1983:IIF,
  author =       "David Brian Masters Aspinwall",
  title =        "An implementation of the {IEEE} floating point
                 standard on a {VAX-11\slash 780}",
  type =         "Thesis ({M.S.})",
  school =       "San Francisco State University",
  address =      "San Francisco, CA, USA",
  pages =        "ix + 138",
  year =         "1983",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer architecture.; Floating-point arithmetic.;
                 Microprogramming.; VAX-11 (Computer) --- Programming.",
}


bibtype: article
filename: fparith.bib
label: Aspinwall:1983:MVM
author: David B. Aspinwall and Yale N. Patt
title: Modifications to the VAX-11 / 780 microarchitecture to support IEEE floating point arithmetic
journal: j-SIGMICRO
volume: 14
number: 4
pages: 61--69
month: dec
monthnumber: 12
year: 1983
CODEN: SIGMDJ
DOI: https://doi.org/10.1145/1096419.1096429
ISSN: 0163-5751, 1050-916X OR 01635751, 1050916X
ISSNL: 0163-5751 OR 01635751
bibdate: Fri Apr 16 10:27:31 MDT 2021
bibtimestamp: 2021.04.16 10:27:31 MDT
URL: https://dl.acm.org/doi/10.1145/1096419.1096429
fjournal: ACM SIGMICRO Newsletter
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/sigmicro
rawauthor: David B. Aspinwall and Yale N. Patt
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/sigmicro.bib

abstract:
The VAX-11/780 was designed specifically to implement the VAX architecture. As such, it does not support the IEEE standard for floating point arithmetic. A project was undertaken to provide this support by modifying the 11/780 microarchitecture. Our objective was to produce a microengine that would efficiently execute a modified VAX instruction set, in particular, one that executes VAX floating point instructions consistent with the IEEE standard. We made minimal changes to the 11/780 hardware, relying primarily on changes to the microcode. This paper describes the work of this project.

rawabstract:
The VAX-11/780 was designed specifically to implement the VAX architecture. As such, it does not support the IEEE standard for floating point arithmetic. A project was undertaken to provide this support by modifying the 11/780 microarchitecture. Our objective was to produce a microengine that would efficiently execute a modified VAX instruction set, in particular, one that executes VAX floating point instructions consistent with the IEEE standard. We made minimal changes to the 11/780 hardware, relying primarily on changes to the microcode. This paper describes the work of this project.

rawtitle:
Modifications to the {VAX-11\slash 780} microarchitecture to support {IEEE} floating point arithmetic

entry:
@Article{Aspinwall:1983:MVM,
  author =       "David B. Aspinwall and Yale N. Patt",
  title =        "Modifications to the {VAX-11\slash 780}
                 microarchitecture to support {IEEE} floating point
                 arithmetic",
  journal =      j-SIGMICRO,
  volume =       "14",
  number =       "4",
  pages =        "61--69",
  month =        dec,
  year =         "1983",
  CODEN =        "SIGMDJ",
  DOI =          "https://doi.org/10.1145/1096419.1096429",
  ISSN =         "0163-5751, 1050-916X",
  ISSN-L =       "0163-5751",
  bibdate =      "Fri Apr 16 10:27:31 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigmicro.bib",
  URL =          "https://dl.acm.org/doi/10.1145/1096419.1096429",
  abstract =     "The VAX-11/780 was designed specifically to implement
                 the VAX architecture. As such, it does not support the
                 IEEE standard for floating point arithmetic. A project
                 was undertaken to provide this support by modifying the
                 11/780 microarchitecture. Our objective was to produce
                 a microengine that would efficiently execute a modified
                 VAX instruction set, in particular, one that executes
                 VAX floating point instructions consistent with the
                 IEEE standard. We made minimal changes to the 11/780
                 hardware, relying primarily on changes to the
                 microcode. This paper describes the work of this
                 project.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGMICRO Newsletter",
  journal-URL =  "https://dl.acm.org/loi/sigmicro",
}


bibtype: inproceedings
filename: fparith.bib
label: Avizienis:1983:AAE
author: Algirdas Avizienis and C. S. Raghavendra
title: Applications for Arithmetic Error Codes in Large, High-Performance Computers
crossref: IEEE:1983:PSC
pages: 169--173
year: 1983
bibdate: Tue Nov 13 15:58:57 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.13 15:58:57 ???
URL: http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Avizienis_Raghavendra.pdf
keywords: ARITH-6
acknowledgement: ack-nhfb
rawauthor: Algirdas Avizienis and C. S. Raghavendra
rawtitle: Applications for Arithmetic Error Codes in Large, High-Performance Computers
abstract:
Large, high-performance computers are too costly to allow full replication for fault detection and error correction in the communication and processing of numerical information. For this reason more cost-effective arithmetic error code applications offer an attractive alternative.par Part I of this paper presents a generalization of low-cost inverse residue codes into two-dimensional encodings. Error detecting and error correcting properties of two-dimensional inverse residue codes are discussed.par Part II discusses a multi-phase application of inverse residue codes in which the form of encoding is altered and additional time is allocated after faults occur. The goal is to defer repair and to continue operation at a slower speed until scheduled maintenance can take place.

rawabstract:
Large, high-performance computers are too costly to allow full replication for fault detection and error correction in the communication and processing of numerical information. For this reason more cost-effective arithmetic error code applications offer an attractive alternative.\par Part I of this paper presents a generalization of low-cost inverse residue codes into two-dimensional encodings. Error detecting and error correcting properties of two-dimensional inverse residue codes are discussed.\par Part II discusses a multi-phase application of inverse residue codes in which the form of encoding is altered and additional time is allocated after faults occur. The goal is to defer repair and to continue operation at a slower speed until scheduled maintenance can take place.

entry:
@InProceedings{Avizienis:1983:AAE,
  author =       "Algirdas Avizienis and C. S. Raghavendra",
  title =        "Applications for Arithmetic Error Codes in Large,
                 High-Performance Computers",
  crossref =     "IEEE:1983:PSC",
  pages =        "169--173",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Avizienis_Raghavendra.pdf",
  abstract =     "Large, high-performance computers are too costly to
                 allow full replication for fault detection and error
                 correction in the communication and processing of
                 numerical information. For this reason more
                 cost-effective arithmetic error code applications offer
                 an attractive alternative.\par

                 Part I of this paper presents a generalization of
                 low-cost inverse residue codes into two-dimensional
                 encodings. Error detecting and error correcting
                 properties of two-dimensional inverse residue codes are
                 discussed.\par

                 Part II discusses a multi-phase application of inverse
                 residue codes in which the form of encoding is altered
                 and additional time is allocated after faults occur.
                 The goal is to defer repair and to continue operation
                 at a slower speed until scheduled maintenance can take
                 place.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6",
}


bibtype: article
filename: fparith.bib
label: Bandeira:1983:TCA
author: N. Bandeira and K. Vaccaro and J. A. Howard
title: A Two's Complement Array Multiplier Using True Values of the Operands
journal: j-IEEE-TRANS-COMPUT
volume: C-32
number: 8
pages: 745--747
month: aug
monthnumber: 8
year: 1983
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1983.1676312
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 10:01:11 MDT 2011
bibtimestamp: 2011.07.10 10:01:11 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676312
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: N. Bandeira and K. Vaccaro and J. A. Howard
rawtitle: A Two's Complement Array Multiplier Using True Values of the Operands
entry:
@Article{Bandeira:1983:TCA,
  author =       "N. Bandeira and K. Vaccaro and J. A. Howard",
  title =        "A Two's Complement Array Multiplier Using True Values
                 of the Operands",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "8",
  pages =        "745--747",
  month =        aug,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676312",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:01:11 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676312",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Banerji:1983:RPF
author: D. K. Banerji and S. Kaushik
title: Representation and Processing of Fractions in a Residue System
crossref: IEEE:1983:PSC
pages: 29--36
year: 1983
bibdate: Tue Nov 13 15:58:57 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.13 15:58:57 ???
URL: http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Banerji_Kaushik.pdf
keywords: ARITH-6; residue number systems
acknowledgement: ack-nhfb
rawauthor: D. K. Banerji and S. Kaushik
rawtitle: Representation and Processing of Fractions in a Residue System
abstract:
This paper proposes a scheme for the representation and processing of fractions in a residue system. The scheme is based on a mixed radix representation of a fraction in a residue system. The algorithms for basic arithmetic operations of addition, subtraction, and multiplication involving fractions are developed and are shown to provide some improvement over an existing method. Application of these algorithms to division of two integers in the residue system has been shown.

rawabstract:
This paper proposes a scheme for the representation and processing of fractions in a residue system. The scheme is based on a mixed radix representation of a fraction in a residue system. The algorithms for basic arithmetic operations of addition, subtraction, and multiplication involving fractions are developed and are shown to provide some improvement over an existing method. Application of these algorithms to division of two integers in the residue system has been shown.

entry:
@InProceedings{Banerji:1983:RPF,
  author =       "D. K. Banerji and S. Kaushik",
  title =        "Representation and Processing of Fractions in a
                 Residue System",
  crossref =     "IEEE:1983:PSC",
  pages =        "29--36",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Banerji_Kaushik.pdf",
  abstract =     "This paper proposes a scheme for the representation
                 and processing of fractions in a residue system. The
                 scheme is based on a mixed radix representation of a
                 fraction in a residue system. The algorithms for basic
                 arithmetic operations of addition, subtraction, and
                 multiplication involving fractions are developed and
                 are shown to provide some improvement over an existing
                 method. Application of these algorithms to division of
                 two integers in the residue system has been shown.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6; residue number systems",
}


bibtype: article
filename: fparith.bib
label: Baxter:1983:CRS
author: I. Baxter
title: Code replication speeds multiplication
journal: j-EDN
volume: 28
number: 4
pages: 261--262
month: feb
monthnumber: 2
year: 1983
CODEN: EDNSBH
ISSN: 0012-7515, 0364-6637 OR 00127515, 03646637
bibdate: Thu Sep 1 10:15:08 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:15:08 ???
fjournal: EDN
acknowledgement: ack-nj
rawauthor: I. Baxter
rawtitle: Code replication speeds multiplication
entry:
@Article{Baxter:1983:CRS,
  author =       "I. Baxter",
  title =        "Code replication speeds multiplication",
  journal =      j-EDN,
  volume =       "28",
  number =       "4",
  pages =        "261--262",
  month =        feb,
  year =         "1983",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  bibdate =      "Thu Sep 1 10:15:08 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "EDN",
}


bibtype: inproceedings
filename: fparith.bib
label: Bayoumi:1983:MVI
author: M. A. Bayoumi and G. A. Jullien and W. C. Miller
title: Models for VLSI Implementation of Residue Number System Arithmetic Modules
crossref: IEEE:1983:PSC
pages: 174--183
year: 1983
bibdate: Tue Nov 13 15:58:57 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.13 15:58:57 ???
URL: http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Bayoumi_Jullien_Miller.pdf
keywords: ARITH-6; residue number systems
acknowledgement: ack-nhfb
rawauthor: M. A. Bayoumi and G. A. Jullien and W. C. Miller
rawtitle: Models for {VLSI} Implementation of Residue Number System Arithmetic Modules
abstract:
This paper discusses the implementation of RNS arithmetic modules using VLSI technology. The modules are based on the interconnection of readonly memory look-up tables. The paper first outlines a memory model for a single look-up table which allows the selection of the most efficient layout for memories which do not have power of $2$ dimensions. The paper then discusses various examples of interconnected memory modules with associated optimizing layout algorithms. Finally, an example is given of the application of one of the modules to a large prime modulus multiplier.

rawabstract:
This paper discusses the implementation of RNS arithmetic modules using VLSI technology. The modules are based on the interconnection of readonly memory look-up tables. The paper first outlines a memory model for a single look-up table which allows the selection of the most efficient layout for memories which do not have power of $2$ dimensions. The paper then discusses various examples of interconnected memory modules with associated optimizing layout algorithms. Finally, an example is given of the application of one of the modules to a large prime modulus multiplier.

entry:
@InProceedings{Bayoumi:1983:MVI,
  author =       "M. A. Bayoumi and G. A. Jullien and W. C. Miller",
  title =        "Models for {VLSI} Implementation of Residue Number
                 System Arithmetic Modules",
  crossref =     "IEEE:1983:PSC",
  pages =        "174--183",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Bayoumi_Jullien_Miller.pdf",
  abstract =     "This paper discusses the implementation of RNS
                 arithmetic modules using VLSI technology. The modules
                 are based on the interconnection of readonly memory
                 look-up tables. The paper first outlines a memory model
                 for a single look-up table which allows the selection
                 of the most efficient layout for memories which do not
                 have power of $2$ dimensions. The paper then discusses
                 various examples of interconnected memory modules with
                 associated optimizing layout algorithms. Finally, an
                 example is given of the application of one of the
                 modules to a large prime modulus multiplier.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6; residue number systems",
}


bibtype: inproceedings
filename: fparith.bib
label: Bhat:1983:HPF
author: J. Bhat
title: High Performance Floating Point Co-Processor for Protected Multi-User Systems
crossref: Mini-Micro:1983:MMN
pages: 7/2/1--5
year: 1983
bibdate: Wed Sep 7 22:31:27 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.07 22:31:27 ???
acknowledgement: ack-nj
rawauthor: J. Bhat
rawtitle: High Performance Floating Point Co-Processor for Protected Multi-User Systems
entry:
@InProceedings{Bhat:1983:HPF,
  author =       "J. Bhat",
  title =        "High Performance Floating Point Co-Processor for
                 Protected Multi-User Systems",
  crossref =     "Mini-Micro:1983:MMN",
  pages =        "7/2/1--5",
  year =         "1983",
  bibdate =      "Wed Sep 7 22:31:27 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: Blakley:1983:MAI
author: G. R. Blakley and I. Borosh
title: Modular arithmetic of iterated powers
journal: j-COMPUT-MATH-APPL
volume: 9
number: 4
pages: 567--581
year: 1983
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 18:51:24 MST 2017
bibtimestamp: 2017.03.01 18:51:24 MST
URL: http://www.sciencedirect.com/science/article/pii/0898122183901141
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221/
rawauthor: G. R. Blakley and I. Borosh
rawtitle: Modular arithmetic of iterated powers
bibsource:
https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Blakley:1983:MAI,
  author =       "G. R. Blakley and I. Borosh",
  title =        "Modular arithmetic of iterated powers",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "9",
  number =       "4",
  pages =        "567--581",
  month =        "????",
  year =         "1983",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 18:51:24 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122183901141",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221/",
}


bibtype: inproceedings
filename: fparith.bib
label: Boney:1983:FPPa
author: J. Boney and V. Shahan
title: Floating-point Power for the M68000 Family
crossref: Mini-Micro:1983:MMN
pages: 7/3/1--9
year: 1983
bibdate: Wed Sep 7 22:31:27 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.07 22:31:27 ???
acknowledgement: ack-nj
rawauthor: J. Boney and V. Shahan
rawtitle: Floating-point Power for the {M68000} Family
entry:
@InProceedings{Boney:1983:FPPa,
  author =       "J. Boney and V. Shahan",
  title =        "Floating-point Power for the {M68000} Family",
  crossref =     "Mini-Micro:1983:MMN",
  pages =        "7/3/1--9",
  year =         "1983",
  bibdate =      "Wed Sep 7 22:31:27 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: inproceedings
filename: fparith.bib
label: Boney:1983:FPPb
author: J. Boney and V. Shahan
title: Floating-point Power for the M68000 Family
crossref: Mini-Micro:1983:MMW
pages: 16/5/1--10
year: 1983
bibdate: Mon Sep 12 22:01:17 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.12 22:01:17 ???
acknowledgement: ack-nj
rawauthor: J. Boney and V. Shahan
rawtitle: Floating-point Power for the {M68000} Family
entry:
@InProceedings{Boney:1983:FPPb,
  author =       "J. Boney and V. Shahan",
  title =        "Floating-point Power for the {M68000} Family",
  crossref =     "Mini-Micro:1983:MMW",
  pages =        "16/5/1--10",
  year =         "1983",
  bibdate =      "Mon Sep 12 22:01:17 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: inproceedings
filename: fparith.bib
label: Brown:1983:NEA
author: W. S. Brown and C. S. Wetherell
title: A Numeric Error Algebra
crossref: IEEE:1983:PSC
pages: 86--93
year: 1983
bibdate: Tue Nov 13 15:58:57 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.13 15:58:57 ???
URL: http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Brown_Wetherell.pdf
keywords: ARITH-6
acknowledgement: ack-nhfb
rawauthor: W. S. Brown and C. S. Wetherell
rawtitle: A Numeric Error Algebra
abstract:
Wetherell recently described an algebra of error values that could be added to the ordinary arithmetic of a programming language. Along with ordinary arithmetic values, error values were included in the set of computational quantities. The error values could participate in all arithmetic operations and return meaningful results. Unfortunately, the definitions of the error values were not precise enough. Using Brown's model of computer arithmetic, we supply precise definitions for the error values, define the fundamental arithmetic operations on the new values, comment on their properties, and discuss briefly how they might be used and implemented. We also compare our model to the error handling features of the proposed IEEE floating point standard

rawabstract:
Wetherell recently described an algebra of error values that could be added to the ordinary arithmetic of a programming language. Along with ordinary arithmetic values, error values were included in the set of computational quantities. The error values could participate in all arithmetic operations and return meaningful results. Unfortunately, the definitions of the error values were not precise enough. Using Brown's model of computer arithmetic, we supply precise definitions for the error values, define the fundamental arithmetic operations on the new values, comment on their properties, and discuss briefly how they might be used and implemented. We also compare our model to the error handling features of the proposed IEEE floating point standard

entry:
@InProceedings{Brown:1983:NEA,
  author =       "W. S. Brown and C. S. Wetherell",
  title =        "A Numeric Error Algebra",
  crossref =     "IEEE:1983:PSC",
  pages =        "86--93",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Brown_Wetherell.pdf",
  abstract =     "Wetherell recently described an algebra of error
                 values that could be added to the ordinary arithmetic
                 of a programming language. Along with ordinary
                 arithmetic values, error values were included in the
                 set of computational quantities. The error values could
                 participate in all arithmetic operations and return
                 meaningful results. Unfortunately, the definitions of
                 the error values were not precise enough. Using Brown's
                 model of computer arithmetic, we supply precise
                 definitions for the error values, define the
                 fundamental arithmetic operations on the new values,
                 comment on their properties, and discuss briefly how
                 they might be used and implemented. We also compare our
                 model to the error handling features of the proposed
                 IEEE floating point standard",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6",
}


bibtype: article
filename: fparith.bib
label: Bushard:1983:MTS
author: L. B. Bushard
title: A Minimum Table Size Result for Higher Radix Nonrestoring Division
journal: j-IEEE-TRANS-COMPUT
volume: C-32
number: 6
pages: 521--526
month: jun
monthnumber: 6
year: 1983
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1983.1676273
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 10:01:09 MDT 2011
bibtimestamp: 2011.07.10 10:01:09 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676273
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: L. B. Bushard
rawtitle: A Minimum Table Size Result for Higher Radix Nonrestoring Division
entry:
@Article{Bushard:1983:MTS,
  author =       "L. B. Bushard",
  title =        "A Minimum Table Size Result for Higher Radix
                 Nonrestoring Division",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "6",
  pages =        "521--526",
  month =        jun,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676273",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:01:09 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676273",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Caraiscos:1983:REA
author: C. Caraiscos and Bede Liu
booktitle: IEEE International Conference on Acoustics, Speech, and Signal Processing: ICASSP '83
title: A round-off error analysis of the LMS adaptive algorithm
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 29--32
year: 1983
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: C. Caraiscos and Bede Liu
rawbooktitle: {IEEE} International Conference on Acoustics, Speech, and Signal Processing: {ICASSP '83}
rawtitle: A round-off error analysis of the {LMS} adaptive algorithm
entry:
@InProceedings{Caraiscos:1983:REA,
  author =       "C. Caraiscos and Bede Liu",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing: {ICASSP '83}",
  title =        "A round-off error analysis of the {LMS} adaptive
                 algorithm",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "29--32",
  year =         "1983",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:04 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "The steady state output error of the Least Mean Square
                 (LMS) Adaptive Algorithm due to the finite precision
                 arithmetic of a digital processor is analyzed. It is
                 found to consist of three terms: (1) the error due to
                 the input data quantization, (2) \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Chamrad:1983:FFP
author: V. Chamrad
title: A Fast Floating-Point Square-Rooting Routine for the 8080 / 8085 Microprocessors
journal: j-KYBERNETIKA
volume: 19
number: 4
pages: 335--344
year: 1983
CODEN: KYBNAI
ISSN: 0023-5954 OR 00235954
bibdate: Wed Sep 14 20:24:32 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.14 20:24:32 ???
fjournal: Kybernetika
acknowledgement: ack-nj
rawauthor: V. Chamrad
rawtitle: A Fast Floating-Point Square-Rooting Routine for the 8080\slash 8085 Microprocessors
entry:
@Article{Chamrad:1983:FFP,
  author =       "V. Chamrad",
  title =        "A Fast Floating-Point Square-Rooting Routine for the
                 8080\slash 8085 Microprocessors",
  journal =      j-KYBERNETIKA,
  volume =       "19",
  number =       "4",
  pages =        "335--344",
  month =        "????",
  year =         "1983",
  CODEN =        "KYBNAI",
  ISSN =         "0023-5954",
  bibdate =      "Wed Sep 14 20:24:32 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Kybernetika",
}


bibtype: article
filename: fparith.bib
label: Chan:1983:ACS
author: Tony F. Chan and Gene H. Golub and Randall J. LeVeque
title: Algorithms for computing the sample variance: Analysis and recommendations
journal: j-AMER-STAT
volume: 37
number: 3
pages: 242--247
month: aug
monthnumber: 8
year: 1983
CODEN: ASTAAJ
DOI: https://doi.org/10.2307/2683386
ISSN: 0003-1305 (print), 1537-2731 (electronic) OR 00031305 (print), 15372731 (electronic)
ISSNL: 0003-1305 OR 00031305
MRclass: 62-04
MRnumber: 84k:62003
bibdate: Mon May 5 09:19:29 MDT 1997
bibtimestamp: 1997.05.05 09:19:29 MDT
URL: http://www.jstor.org/stable/2683386
fjournal: The American Statistician
acknowledgement: ack-nhfb
authordates: Gene Howard Golub (February 29, 1932--November 16, 2007)
journalURL: http://www.tandfonline.com/loi/utas20
rawauthor: Tony F. Chan and Gene H. Golub and Randall J. LeVeque
rawtitle: Algorithms for computing the sample variance: Analysis and recommendations
bibsource:
Distributed/QLD.bib; Distributed/QLD/1983.bib; ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Chan:1983:ACS,
  author =       "Tony F. Chan and Gene H. Golub and Randall J.
                 LeVeque",
  title =        "Algorithms for computing the sample variance: Analysis
                 and recommendations",
  journal =      j-AMER-STAT,
  volume =       "37",
  number =       "3",
  pages =        "242--247",
  month =        aug,
  year =         "1983",
  CODEN =        "ASTAAJ",
  DOI =          "https://doi.org/10.2307/2683386",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  MRclass =      "62-04",
  MRnumber =     "84k:62003",
  bibdate =      "Mon May 5 09:19:29 MDT 1997",
  bibsource =    "Distributed/QLD.bib; Distributed/QLD/1983.bib;
                 ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.jstor.org/stable/2683386",
  acknowledgement = ack-nhfb,
  author-dates = "Gene Howard Golub (February 29, 1932--November 16,
                 2007)",
  country =      "USA",
  date =         "13/05/93",
  descriptors =  "Simulation; statistics; numeric calculation",
  enum =         "7109",
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
  location =     "SEL: Wi",
  references =   "0",
  revision =     "16/01/94",
}


bibtype: article
filename: fparith.bib
label: Chang:1983:HSN
author: Tung-Liang Chang and P. Fisher
title: High-speed normalization and rounding circuits for pipelined floating-point processors
journal: j-IEEE-TRANS-ACOUST-SPEECH
volume: 31
number: 6
pages: 1403--1408
month: dec
monthnumber: 12
year: 1983
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
fjournal: IEEE Transactions on Acoustics, Speech, and Signal Processing
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29
rawauthor: Tung-Liang Chang and P. Fisher
rawtitle: High-speed normalization and rounding circuits for pipelined floating-point processors
entry:
@Article{Chang:1983:HSN,
  author =       "Tung-Liang Chang and P. Fisher",
  title =        "High-speed normalization and rounding circuits for
                 pipelined floating-point processors",
  journal =      j-IEEE-TRANS-ACOUST-SPEECH,
  volume =       "31",
  number =       "6",
  pages =        "1403--1408",
  month =        dec,
  year =         "1983",
  CODEN =        "IETABA",
  ISSN =         "0096-3518",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Acoustics, Speech, and Signal
                 Processing",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
  summary =      "A fast leading/trailing-zero detection circuit
                 (LZDC/TZDC) is described, and then applied to the
                 design of a pipelined floating-point (FLP) processor.
                 This circuit has a total delay of 5{\Delta} and a
                 hardware complexity of(m + 1)(3 log_{2}(p) + 4
                 \ldots{}).",
}


bibtype: article
filename: fparith.bib
label: Chow:1983:PDA
author: P. Chow and Z. Vranesic and Jui Lin Yen
title: A Pipelined Distributed Arithmetic PFFT Processor
journal: j-IEEE-TRANS-COMPUT
volume: C-32
number: 12
pages: 1128--1136
month: dec
monthnumber: 12
year: 1983
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1983.1676173
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 10:01:13 MDT 2011
bibtimestamp: 2011.07.10 10:01:13 MDT
note: See correction cite Anonymous:1984:CPD.
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676173
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: P. Chow and Z. Vranesic and Jui Lin Yen
rawnote: See correction \cite{Anonymous:1984:CPD}.
rawtitle: A Pipelined Distributed Arithmetic {PFFT} Processor
entry:
@Article{Chow:1983:PDA,
  author =       "P. Chow and Z. Vranesic and Jui Lin Yen",
  title =        "A Pipelined Distributed Arithmetic {PFFT} Processor",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "12",
  pages =        "1128--1136",
  month =        dec,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676173",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:01:13 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  note =         "See correction \cite{Anonymous:1984:CPD}.",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676173",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Ciminiera:1983:FIM
author: L. Ciminiera and A. Serra
title: Fast Iterative Multiplying Array
crossref: IEEE:1983:PSC
pages: 60--66
year: 1983
bibdate: Tue Nov 13 15:58:57 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.13 15:58:57 ???
URL: http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Ciminiera_Serra.pdf
keywords: ARITH-6
acknowledgement: ack-nhfb
rawauthor: L. Ciminiera and A. Serra
rawtitle: Fast Iterative Multiplying Array
abstract:
A high speed multiplying array is presented. It is based on a new cell, which is able to generate and add a rectangular block of elementary products. A careful design of the cell allows us to obtain a small delay for the signals which should be propagated through the whole array. This feature leads to a remarkable improvement in the array speed.

rawabstract:
A high speed multiplying array is presented. It is based on a new cell, which is able to generate and add a rectangular block of elementary products. A careful design of the cell allows us to obtain a small delay for the signals which should be propagated through the whole array. This feature leads to a remarkable improvement in the array speed.

entry:
@InProceedings{Ciminiera:1983:FIM,
  author =       "L. Ciminiera and A. Serra",
  title =        "Fast Iterative Multiplying Array",
  crossref =     "IEEE:1983:PSC",
  pages =        "60--66",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Ciminiera_Serra.pdf",
  abstract =     "A high speed multiplying array is presented. It is
                 based on a new cell, which is able to generate and add
                 a rectangular block of elementary products. A careful
                 design of the cell allows us to obtain a small delay
                 for the signals which should be propagated through the
                 whole array. This feature leads to a remarkable
                 improvement in the array speed.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6",
}


bibtype: article
filename: fparith.bib
label: Cloutier:1983:PAR
author: Mark J. Cloutier and Matthew J. Friedman
title: Precision Averaging for Real-Time Analysis
journal: j-CACM
volume: 26
number: 7
pages: 525--529
year: 1983
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Mon Jan 22 06:31:47 MST 2001
bibtimestamp: 2001.01.22 06:31:47 MST
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Mark J. Cloutier and Matthew J. Friedman
rawtitle: Precision Averaging for Real-Time Analysis
bibsource:
http://dblp.uni-trier.de/db/journals/cacm/cacm26.html#CloutierF83; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Cloutier:1983:PAR,
  author =       "Mark J. Cloutier and Matthew J. Friedman",
  title =        "Precision Averaging for Real-Time Analysis",
  journal =      j-CACM,
  volume =       "26",
  number =       "7",
  pages =        "525--529",
  year =         "1983",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 06:31:47 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm26.html#CloutierF83;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  oldlabel =     "CloutierF83",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/CloutierF83",
}


bibtype: inproceedings
filename: fparith.bib
label: Cody:1983:GPI
author: W. J. Cody
title: A generalization of the proposed IEEE standard for floating-point arithmetic
crossref: Gentle:1983:CSS
pages: 133--139
year: 1983
bibdate: Thu Nov 17 10:41:05 1994
bibtimestamp: 1994.11.17 10:41:05 ???
note: Republication of cite Cody:1982:GPI.
keywords: standardization
acknowledgement: ack-nhfb
rawauthor: W. J. Cody
rawnote: Republication of \cite{Cody:1982:GPI}.
rawtitle: A generalization of the proposed {IEEE} standard for floating-point arithmetic
subject:
G.1.0 Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic K.7 Computing Milieux, THE COMPUTING PROFESSION, Miscellaneous K.1 Computing Milieux, THE COMPUTER INDUSTRY, Standards

entry:
@InProceedings{Cody:1983:GPI,
  author =       "W. J. Cody",
  title =        "A generalization of the proposed {IEEE} standard for
                 floating-point arithmetic",
  crossref =     "Gentle:1983:CSS",
  pages =        "133--139",
  year =         "1983",
  bibdate =      "Thu Nov 17 10:41:05 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Republication of \cite{Cody:1982:GPI}.",
  acknowledgement = ack-nhfb,
  keywords =     "standardization",
  subject =      "G.1.0 Mathematics of Computing, NUMERICAL ANALYSIS,
                 General, Computer arithmetic \\ K.7 Computing Milieux,
                 THE COMPUTING PROFESSION, Miscellaneous \\ K.1
                 Computing Milieux, THE COMPUTER INDUSTRY, Standards",
}


bibtype: article
filename: fparith.bib
label: Cohen:1983:CCP
author: Marty S. Cohen and T. E. Hull and V. Carl Hamacher
title: CADAC: a Controlled-Precision Decimal Arithmetic Unit
journal: j-IEEE-TRANS-COMPUT
volume: C-32
number: 4
pages: 370--377
month: apr
monthnumber: 4
year: 1983
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1983.1676238
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 10:01:08 MDT 2011
bibtimestamp: 2011.07.10 10:01:08 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676238
fjournal: IEEE Transactions on Computers
keywords: decimal floating-point arithmetic
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Marty S. Cohen and T. E. Hull and V. Carl Hamacher
rawtitle: {CADAC}: a Controlled-Precision Decimal Arithmetic Unit
abstract:
This paper describes the design of an arithmetic unit called CADAC (clean arithmetic with decimal base and controlled precision). Programming language specifications for carrying out `ideal' floating-point arithmetic are described first. These specifications include detailed requirements for dynamic precision control and exception handling, along with both complex and interval arithmetic at the level of a programming language such as Fortran or PL/I.par CADAC is an arithmetic unit which performs the four floating-point operations add / subtract / multiply / divide on decimal numbers in such a way as to support all the language requirements efficiently. A three-level pipeline is used to overlap two-digit-at-a-time serial processing of the partial products / remainders. Although the logic design is relatively complex, the performance is efficient, and the advantages gained by implementing programmer-controlled precision directly in the hardware are significant.

remark:
From MFC: Normalized decimal floating-point. Need for variable precision (intermediate > final, increasing precision, etc.). Base representation is BCD (2-32 digits). Hardware prototype built

rawabstract:
This paper describes the design of an arithmetic unit called CADAC (clean arithmetic with decimal base and controlled precision). Programming language specifications for carrying out `ideal' floating-point arithmetic are described first. These specifications include detailed requirements for dynamic precision control and exception handling, along with both complex and interval arithmetic at the level of a programming language such as Fortran or PL/I.\par CADAC is an arithmetic unit which performs the four floating-point operations add\slash subtract\slash multiply\slash divide on decimal numbers in such a way as to support all the language requirements efficiently. A three-level pipeline is used to overlap two-digit-at-a-time serial processing of the partial products\slash remainders. Although the logic design is relatively complex, the performance is efficient, and the advantages gained by implementing programmer-controlled precision directly in the hardware are significant.

entry:
@Article{Cohen:1983:CCP,
  author =       "Marty S. Cohen and T. E. Hull and V. Carl Hamacher",
  title =        "{CADAC}: a Controlled-Precision Decimal Arithmetic
                 Unit",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "4",
  pages =        "370--377",
  month =        apr,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676238",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:01:08 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676238",
  abstract =     "This paper describes the design of an arithmetic unit
                 called CADAC (clean arithmetic with decimal base and
                 controlled precision). Programming language
                 specifications for carrying out `ideal' floating-point
                 arithmetic are described first. These specifications
                 include detailed requirements for dynamic precision
                 control and exception handling, along with both complex
                 and interval arithmetic at the level of a programming
                 language such as Fortran or PL/I.\par

                 CADAC is an arithmetic unit which performs the four
                 floating-point operations add\slash subtract\slash
                 multiply\slash divide on decimal numbers in such a way
                 as to support all the language requirements
                 efficiently. A three-level pipeline is used to overlap
                 two-digit-at-a-time serial processing of the partial
                 products\slash remainders. Although the logic design is
                 relatively complex, the performance is efficient, and
                 the advantages gained by implementing
                 programmer-controlled precision directly in the
                 hardware are significant.",
  acknowledgement = ack-nhfb # "\slash " # ack-jr,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "decimal floating-point arithmetic",
  remark =       "From MFC: Normalized decimal floating-point. Need for
                 variable precision (intermediate > final, increasing
                 precision, etc.). Base representation is BCD (2-32
                 digits). Hardware prototype built",
}


bibtype: article
filename: fparith.bib
label: Collis:1983:MSZ
author: B. Collis
title: Macros speed 8080, Z80 multiplication
journal: j-EDN
volume: 28
number: 24
pages: 225
month: nov
monthnumber: 11
year: 1983
CODEN: EDNSBH
ISSN: 0012-7515, 0364-6637 OR 00127515, 03646637
bibdate: Thu Sep 1 10:15:08 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:15:08 ???
fjournal: EDN
acknowledgement: ack-nj
rawauthor: B. Collis
rawtitle: Macros speed 8080, {Z80} multiplication
entry:
@Article{Collis:1983:MSZ,
  author =       "B. Collis",
  title =        "Macros speed 8080, {Z80} multiplication",
  journal =      j-EDN,
  volume =       "28",
  number =       "24",
  pages =        "225",
  month =        nov,
  year =         "1983",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  bibdate =      "Thu Sep 1 10:15:08 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "EDN",
}


bibtype: article
filename: fparith.bib
label: Corbett:1983:EAF
author: Robert Paul Corbett
title: Enhanced arithmetic for Fortran
journal: j-SIGNUM
volume: 18
number: 1
pages: 24--28
month: jan
monthnumber: 1
year: 1983
CODEN: SNEWD6
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Tue Apr 12 07:50:11 MDT 2005
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.04.12 07:50:11 MDT
fjournal: ACM SIGNUM Newsletter
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/signum
rawauthor: Robert Paul Corbett
rawtitle: Enhanced arithmetic for {Fortran}
entry:
@Article{Corbett:1983:EAF,
  author =       "Robert Paul Corbett",
  title =        "Enhanced arithmetic for {Fortran}",
  journal =      j-SIGNUM,
  volume =       "18",
  number =       "1",
  pages =        "24--28",
  month =        jan,
  year =         "1983",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:11 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
}


bibtype: article
filename: fparith.bib
label: Coupe:1983:SPZ
author: B. Coupe
title: Superefficient programs for 8080 and Z80 multiply
journal: j-ELECTRONICS
volume: 56
number: 6
pages: 142--143
month: mar
monthnumber: 3
year: 1983
ISSN: 0883-4989 OR 08834989
bibdate: Thu Sep 1 10:15:08 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:15:08 ???
fjournal: Electronics
acknowledgement: ack-nj
journalURL: https://www.mdpi.com/journal/electronics
rawauthor: B. Coupe
rawtitle: Superefficient programs for 8080 and {Z80} multiply
entry:
@Article{Coupe:1983:SPZ,
  author =       "B. Coupe",
  title =        "Superefficient programs for 8080 and {Z80} multiply",
  journal =      j-ELECTRONICS,
  volume =       "56",
  number =       "6",
  pages =        "142--143",
  month =        mar,
  year =         "1983",
  ISSN =         "0883-4989",
  bibdate =      "Thu Sep 1 10:15:08 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Electronics",
  journal-URL =  "https://www.mdpi.com/journal/electronics",
}


bibtype: inproceedings
filename: fparith.bib
label: Dadda:1983:SSF
author: Luigi Dadda
title: Some Schemes for Fast Serial Input Multipliers
crossref: IEEE:1983:PSC
pages: 52--59
year: 1983
bibdate: Tue Nov 13 15:58:57 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.13 15:58:57 ???
URL: http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Dadda.pdf
keywords: ARITH-6
acknowledgement: ack-nhfb
authordates: 29 April 1923--26 October 2012
rawauthor: Luigi Dadda
rawtitle: Some Schemes for Fast Serial Input Multipliers
abstract:
The design of fast multipliers for binary numbers represented in serial form is considered according to a general scheme composed by an array generator and a summator. The bits of the product are generated with the least delay with respect to the operators bits. The array generator computes the elements of the multiplier array. The summator computes the sum of the array elements in order to generate the product bits. The array elements can be generated according to two different general schemes: the first computes all the new array elements at each step (arranged on a diagonal and on a row of the multiplier array), the second computes the multiplier array elements column by column. Several schemes of array generators are given and compared, and for each of them a suitable summator using parallel counters is illustrated.

rawabstract:
The design of fast multipliers for binary numbers represented in serial form is considered according to a general scheme composed by an array generator and a summator. The bits of the product are generated with the least delay with respect to the operators bits. The array generator computes the elements of the multiplier array. The summator computes the sum of the array elements in order to generate the product bits. The array elements can be generated according to two different general schemes: the first computes all the new array elements at each step (arranged on a diagonal and on a row of the multiplier array), the second computes the multiplier array elements column by column. Several schemes of array generators are given and compared, and for each of them a suitable summator using parallel counters is illustrated.

entry:
@InProceedings{Dadda:1983:SSF,
  author =       "Luigi Dadda",
  title =        "Some Schemes for Fast Serial Input Multipliers",
  crossref =     "IEEE:1983:PSC",
  pages =        "52--59",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Dadda.pdf",
  abstract =     "The design of fast multipliers for binary numbers
                 represented in serial form is considered according to a
                 general scheme composed by an array generator and a
                 summator. The bits of the product are generated with
                 the least delay with respect to the operators bits. The
                 array generator computes the elements of the multiplier
                 array. The summator computes the sum of the array
                 elements in order to generate the product bits. The
                 array elements can be generated according to two
                 different general schemes: the first computes all the
                 new array elements at each step (arranged on a diagonal
                 and on a row of the multiplier array), the second
                 computes the multiplier array elements column by
                 column. Several schemes of array generators are given
                 and compared, and for each of them a suitable summator
                 using parallel counters is illustrated.",
  acknowledgement = ack-nhfb,
  author-dates = "29 April 1923--26 October 2012",
  keywords =     "ARITH-6",
}


bibtype: inproceedings
filename: fparith.bib
label: Dao:1983:QCA
author: T. T. Dao
editor: IEEE
booktitle: Proceedings of the 13th International Symposium on Multiple-valued Logic, May 1983
title: A Quaternary Cellular Array Complex Number Multiplier
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 255--262
year: 1983
bibdate: Sat Aug 22 09:15:45 2009
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2009.08.22 09:15:45 ???
acknowledgement: ack-nhfb
rawauthor: T. T. Dao
rawbooktitle: Proceedings of the 13th International Symposium on Multiple-valued Logic, May 1983
raweditor: {IEEE}
rawtitle: A Quaternary Cellular Array Complex Number Multiplier
entry:
@InProceedings{Dao:1983:QCA,
  author =       "T. T. Dao",
  editor =       "{IEEE}",
  booktitle =    "Proceedings of the 13th International Symposium on
                 Multiple-valued Logic, May 1983",
  title =        "A Quaternary Cellular Array Complex Number
                 Multiplier",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "255--262",
  year =         "1983",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Aug 22 09:15:45 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Davis:1983:HSD
author: George R. Davis and Thomas M. King
title: A High-Speed Digital Divider
journal: j-IEEE-TRANS-INSTRUM-MEAS
volume: IM-32
number: 2
pages: 309--312
month: jun
monthnumber: 6
year: 1983
CODEN: IEIMAO
DOI: https://doi.org/10.1109/TIM.1983.4315069
ISSN: 0018-9456 (print), 1557-9662 (electronic) OR 00189456 (print), 15579662 (electronic)
ISSNL: 0018-9456 OR 00189456
bibdate: Tue Jan 08 22:43:51 2008
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2008.01.08 22:43:51 ???
fjournal: IEEE Transactions on Instrument & Measurement
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=19
rawauthor: George R. Davis and Thomas M. King
rawtitle: A High-Speed Digital Divider
abstract:
This paper describes an efficient method for generating the quotient of two binary numbers at speeds comparable to existing multiplier chips. A digital divider is designed using the BEST LINE segmentation approximation. The reciprocal curve is subdivided into small sections, and a least squares straight line approximation is used to recreate each section. An analysis is presented to determine the segmentation granularity and the binary word length of constants needed to closely approximate the curve. A compromise design based on statistical performance as well as the complexity of the hardware requirements are evaluated.

rawabstract:
This paper describes an efficient method for generating the quotient of two binary numbers at speeds comparable to existing multiplier chips. A digital divider is designed using the BEST LINE segmentation approximation. The reciprocal curve is subdivided into small sections, and a least squares straight line approximation is used to recreate each section. An analysis is presented to determine the segmentation granularity and the binary word length of constants needed to closely approximate the curve. A compromise design based on statistical performance as well as the complexity of the hardware requirements are evaluated.

entry:
@Article{Davis:1983:HSD,
  author =       "George R. Davis and Thomas M. King",
  title =        "A High-Speed Digital Divider",
  journal =      j-IEEE-TRANS-INSTRUM-MEAS,
  volume =       "IM-32",
  number =       "2",
  pages =        "309--312",
  month =        jun,
  year =         "1983",
  CODEN =        "IEIMAO",
  DOI =          "https://doi.org/10.1109/TIM.1983.4315069",
  ISSN =         "0018-9456 (print), 1557-9662 (electronic)",
  ISSN-L =       "0018-9456",
  bibdate =      "Tue Jan 08 22:43:51 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper describes an efficient method for
                 generating the quotient of two binary numbers at speeds
                 comparable to existing multiplier chips. A digital
                 divider is designed using the BEST LINE segmentation
                 approximation. The reciprocal curve is subdivided into
                 small sections, and a least squares straight line
                 approximation is used to recreate each section. An
                 analysis is presented to determine the segmentation
                 granularity and the binary word length of constants
                 needed to closely approximate the curve. A compromise
                 design based on statistical performance as well as the
                 complexity of the hardware requirements are
                 evaluated.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Instrument \& Measurement",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=19",
}


bibtype: article
filename: fparith.bib
label: Demsky:1983:MMC
author: J. Demsky and M. Schlesinger and R. D. Kent
title: Micro/mini computer program for calculating the square root of rationals at arbitrary precision
journal: j-COMP-PHYS-COMM
volume: 29
number: 3
pages: 237--244
month: may
monthnumber: 5
year: 1983
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(83)90004-8
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Mon Feb 13 10:28:04 MST 2012
bibtimestamp: 2012.02.13 10:28:04 MST
URL: http://www.sciencedirect.com/science/article/pii/0010465583900048
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: J. Demsky and M. Schlesinger and R. D. Kent
rawtitle: Micro/mini computer program for calculating the square root of rationals at arbitrary precision
bibsource:
https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Demsky:1983:MMC,
  author =       "J. Demsky and M. Schlesinger and R. D. Kent",
  title =        "Micro/mini computer program for calculating the square
                 root of rationals at arbitrary precision",
  journal =      j-COMP-PHYS-COMM,
  volume =       "29",
  number =       "3",
  pages =        "237--244",
  month =        may,
  year =         "1983",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(83)90004-8",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 10:28:04 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465583900048",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: article
filename: fparith.bib
label: Dietrich:1983:VQF
author: D. Dietrich
journal: j-ELEKTRONIKER
volume: 8
pages: EL-1--EL-6
year: 1983
CODEN: ELKRBL
ISSN: 0531-9218 OR 05319218
bibdate: Fri Dec 08 13:05:49 1995
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 13:05:49 ???
fjournal: Elektroniker (Switzerland)
acknowledgement: ack-nj
rawauthor: D. Dietrich
title:
Verfahren zur Losung von Quadratwurzeln fur Mikrorechnerprozeduren toenglish Methods for the Solution of Square Roots for Microprocessor Subroutines endtoenglish 

rawtitle:
{Verfahren zur L{\"o}sung von Quadratwurzeln f{\"u}r Mikrorechnerprozeduren} \toenglish {Methods for the Solution of Square Roots for Microprocessor Subroutines} \endtoenglish

entry:
@Article{Dietrich:1983:VQF,
  author =       "D. Dietrich",
  title =        "{Verfahren zur L{\"o}sung von Quadratwurzeln f{\"u}r
                 Mikrorechnerprozeduren} \toenglish {Methods for the
                 Solution of Square Roots for Microprocessor
                 Subroutines} \endtoenglish",
  journal =      j-ELEKTRONIKER,
  volume =       "8",
  pages =        "EL-1--EL-6",
  year =         "1983",
  CODEN =        "ELKRBL",
  ISSN =         "0531-9218",
  bibdate =      "Fri Dec 08 13:05:49 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Elektroniker (Switzerland)",
}


bibtype: inproceedings
filename: fparith.bib
label: Donthi:1983:BSM
author: Ravindra V. Donthi and Mohammed Saleem and Harpreet Singh
title: On Bit Sequential Multipliers
crossref: IEEE:1983:PSC
pages: 104--108
year: 1983
bibdate: Tue Nov 13 15:58:57 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.13 15:58:57 ???
URL: http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Donthi_Saleem_Singh.pdf
keywords: ARITH-6
acknowledgement: ack-nhfb
rawauthor: Ravindra V. Donthi and Mohammed Saleem and Harpreet Singh
rawtitle: On Bit Sequential Multipliers
abstract:
Recently bit sequential multiplier algorithms have been found more useful in the area of interconnection of multiple processors within a VLSI structure [1], [2]. The object of the present paper is to suggest modified bit sequential algorithms to achieve more speed and to attain its conformity with other algorithms such as division, square-rooting, etc. with a view to utilize them in future arithmetic arrays. In the present paper the following has been taken up: (a) Bit sequential multiplier using carry look-ahead technique, (b) Bit sequential multiplier using most significant bit first,and (c) Negabinary bit sequential multiplier.

rawabstract:
Recently bit sequential multiplier algorithms have been found more useful in the area of interconnection of multiple processors within a VLSI structure [1], [2]. The object of the present paper is to suggest modified bit sequential algorithms to achieve more speed and to attain its conformity with other algorithms such as division, square-rooting, etc. with a view to utilize them in future arithmetic arrays. In the present paper the following has been taken up: (a) Bit sequential multiplier using carry look-ahead technique, (b) Bit sequential multiplier using most significant bit first,and (c) Negabinary bit sequential multiplier.

entry:
@InProceedings{Donthi:1983:BSM,
  author =       "Ravindra V. Donthi and Mohammed Saleem and Harpreet
                 Singh",
  title =        "On Bit Sequential Multipliers",
  crossref =     "IEEE:1983:PSC",
  pages =        "104--108",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Donthi_Saleem_Singh.pdf",
  abstract =     "Recently bit sequential multiplier algorithms have
                 been found more useful in the area of interconnection
                 of multiple processors within a VLSI structure [1],
                 [2]. The object of the present paper is to suggest
                 modified bit sequential algorithms to achieve more
                 speed and to attain its conformity with other
                 algorithms such as division, square-rooting, etc. with
                 a view to utilize them in future arithmetic arrays. In
                 the present paper the following has been taken up: (a)
                 Bit sequential multiplier using carry look-ahead
                 technique, (b) Bit sequential multiplier using most
                 significant bit first,and (c) Negabinary bit sequential
                 multiplier.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6",
}


bibtype: article
filename: fparith.bib
label: Dubrulle:1983:CNM
author: Augustin A. Dubrulle
title: Class of Numerical Methods for the Computation of Pythagorean Sums
journal: j-IBM-JRD
volume: 27
number: 6
pages: 582--589
month: nov
monthnumber: 11
year: 1983
CODEN: IBMJAE
ISSN: 0018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)
ISSNL: 0018-8646 OR 00188646
bibdate: Tue Mar 25 14:26:59 MST 1997
bibsource: Compendex database; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.03.25 14:26:59 MST
note: See cite Moler:1983:RSR and generalization cite Jamieson:1989:SNR.
fjournal: IBM Journal of Research and Development
acknowledgement: ack-nhfb
classcodes: C4190 (Other numerical methods); C5230 (Digital arithmetic methods)
corpsource: IBM Sci. Centre, Palo Alto, CA, USA
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520
journalabr: IBM J Res Dev
treatment: T Theoretical or Mathematical
rawauthor: Augustin A. Dubrulle
rawnote: See \cite{Moler:1983:RSR} and generalization \cite{Jamieson:1989:SNR}.
rawtitle: Class of Numerical Methods for the Computation of {Pythagorean} Sums
abstract:
Moler and Morrison have described an iterative algorithm for the computation of the Pythagorean sum (a**2 plus b**2)** one-half of two real numbers a and b. This algorithm is immune to unwarranted floating-point overflows, has a cubic rate of convergence, and is easily transportable. This paper, which shows that the algorithm is essentially Halley's method applied to the computation of square roots, provides a generalization to any order of convergence. Formulas of orders 2 through 9 are illustrated with numerical examples. The generalization keeps the number of floating-point divisions constant and should be particularly useful for computation in high-precision floating-point arithmetic.

keywords:
computer programming; digital arithmetic; floating-point divisions; Halley's method; high-precision floating-point arithmetic; iterative algorithm; iterative methods; mathematical techniques --- Numerical Methods; Pythagorean sums; rate of convergence; square roots

rawabstract:
Moler and Morrison have described an iterative algorithm for the computation of the Pythagorean sum (a**2 plus b**2)** one-half of two real numbers a and b. This algorithm is immune to unwarranted floating-point overflows, has a cubic rate of convergence, and is easily transportable. This paper, which shows that the algorithm is essentially Halley's method applied to the computation of square roots, provides a generalization to any order of convergence. Formulas of orders 2 through 9 are illustrated with numerical examples. The generalization keeps the number of floating-point divisions constant and should be particularly useful for computation in high-precision floating-point arithmetic.

entry:
@Article{Dubrulle:1983:CNM,
  author =       "Augustin A. Dubrulle",
  title =        "Class of Numerical Methods for the Computation of
                 {Pythagorean} Sums",
  journal =      j-IBM-JRD,
  volume =       "27",
  number =       "6",
  pages =        "582--589",
  month =        nov,
  year =         "1983",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Tue Mar 25 14:26:59 MST 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Moler:1983:RSR} and generalization
                 \cite{Jamieson:1989:SNR}.",
  abstract =     "Moler and Morrison have described an iterative
                 algorithm for the computation of the Pythagorean sum
                 (a**2 plus b**2)** one-half of two real numbers a and
                 b. This algorithm is immune to unwarranted
                 floating-point overflows, has a cubic rate of
                 convergence, and is easily transportable. This paper,
                 which shows that the algorithm is essentially Halley's
                 method applied to the computation of square roots,
                 provides a generalization to any order of convergence.
                 Formulas of orders 2 through 9 are illustrated with
                 numerical examples. The generalization keeps the number
                 of floating-point divisions constant and should be
                 particularly useful for computation in high-precision
                 floating-point arithmetic.",
  acknowledgement = ack-nhfb,
  classcodes =   "C4190 (Other numerical methods); C5230 (Digital
                 arithmetic methods)",
  classification = "723; 921",
  corpsource =   "IBM Sci. Centre, Palo Alto, CA, USA",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  journalabr =   "IBM J Res Dev",
  keywords =     "computer programming; digital arithmetic;
                 floating-point divisions; Halley's method;
                 high-precision floating-point arithmetic; iterative
                 algorithm; iterative methods; mathematical techniques
                 --- Numerical Methods; Pythagorean sums; rate of
                 convergence; square roots",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: fparith.bib
label: Dyer:1983:ZRP
author: D. C. Dyer
title: Z80 routine performs 16-bit multiply
journal: j-EDN
volume: 28
number: 5
pages: 144
month: mar
monthnumber: 3
year: 1983
CODEN: EDNSBH
ISSN: 0012-7515, 0364-6637 OR 00127515, 03646637
bibdate: Thu Sep 1 10:15:08 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:15:08 ???
fjournal: EDN
acknowledgement: ack-nj
rawauthor: D. C. Dyer
rawtitle: {Z80} routine performs 16-bit multiply
entry:
@Article{Dyer:1983:ZRP,
  author =       "D. C. Dyer",
  title =        "{Z80} routine performs 16-bit multiply",
  journal =      j-EDN,
  volume =       "28",
  number =       "5",
  pages =        "144",
  month =        mar,
  year =         "1983",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  bibdate =      "Thu Sep 1 10:15:08 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "EDN",
}


bibtype: inproceedings
filename: fparith.bib
label: Ercegovac:1983:HRD
author: Milos D. Ercegovac
title: A Higher-Radix Division with Simple Selection of Quotient Digits
crossref: IEEE:1983:PSC
pages: 94--98
month: jun
monthnumber: 6
year: 1983
bibdate: Tue Nov 13 15:58:57 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.13 15:58:57 ???
URL: http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Ercegovac.pdf
keywords: ARITH-6; division
acknowledgement: ack-nhfb
rawauthor: Milo{\v{s}} D. Ercegovac
rawtitle: A Higher-Radix Division with Simple Selection of Quotient Digits
abstract:
A higher-radix division algorithm with simple selection of quotient digits is described. The proposed scheme is a combination of the multiplicative normalization used in the continued-product algorithms and the recursive division algorithm. The scheme consists of two parts: in the first part, the divisor and the dividend are transformed into the range which allows the quotient digits to be selected by rounding partial remainders to the most significant radix-$r$ digit in the second part. Since the selection requires only the most significant part of the partial remainder, limited carry-propagation adders can be used to form the partial remainders. The divisor and dividend transformations are performed in three steps using multipliers of the form $ 1 + s_k r^-k $ as in the continued product algorithm. The higher radix of the form $ r = 2^k, k = 2, 4, 8, ldots $ can be used to reduce the number of steps while retaining the simple quotient selection rules.

rawabstract:
A higher-radix division algorithm with simple selection of quotient digits is described. The proposed scheme is a combination of the multiplicative normalization used in the continued-product algorithms and the recursive division algorithm. The scheme consists of two parts: in the first part, the divisor and the dividend are transformed into the range which allows the quotient digits to be selected by rounding partial remainders to the most significant radix-$r$ digit in the second part. Since the selection requires only the most significant part of the partial remainder, limited carry-propagation adders can be used to form the partial remainders. The divisor and dividend transformations are performed in three steps using multipliers of the form $ 1 + s_k r^{-k} $ as in the continued product algorithm. The higher radix of the form $ r = 2^k, k = 2, 4, 8, \ldots {} $ can be used to reduce the number of steps while retaining the simple quotient selection rules.

entry:
@InProceedings{Ercegovac:1983:HRD,
  author =       "Milo{\v{s}} D. Ercegovac",
  title =        "A Higher-Radix Division with Simple Selection of
                 Quotient Digits",
  crossref =     "IEEE:1983:PSC",
  pages =        "94--98",
  month =        jun,
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Ercegovac.pdf",
  abstract =     "A higher-radix division algorithm with simple
                 selection of quotient digits is described. The proposed
                 scheme is a combination of the multiplicative
                 normalization used in the continued-product algorithms
                 and the recursive division algorithm. The scheme
                 consists of two parts: in the first part, the divisor
                 and the dividend are transformed into the range which
                 allows the quotient digits to be selected by rounding
                 partial remainders to the most significant radix-$r$
                 digit in the second part. Since the selection requires
                 only the most significant part of the partial
                 remainder, limited carry-propagation adders can be used
                 to form the partial remainders. The divisor and
                 dividend transformations are performed in three steps
                 using multipliers of the form $ 1 + s_k r^{-k} $ as in
                 the continued product algorithm. The higher radix of
                 the form $ r = 2^k, k = 2, 4, 8, \ldots {} $ can be
                 used to reduce the number of steps while retaining the
                 simple quotient selection rules.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6; division",
}


bibtype: inproceedings
filename: fparith.bib
label: Ferguson:1983:DTE
author: Joel Ferguson and John Paul Shen
title: The Design of Two Easily-Testable VLSI Array Multipliers
crossref: IEEE:1983:PSC
pages: 2--9
year: 1983
bibdate: Tue Nov 13 15:58:57 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.13 15:58:57 ???
URL: http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Ferguson_Shen.pdf
keywords: ARITH-6
acknowledgement: ack-nhfb
rawauthor: Joel Ferguson and John Paul Shen
rawtitle: The Design of Two Easily-Testable {VLSI} Array Multipliers
abstract:
Array multipliers are well-suited for VLSI implementation because of the regularity in their iterative structure. However, most VLSI circuits are very difficult to test. This paper shows that, with appropriate cell design, array multipliers can be designed to be very easily-testable. An array multiplier is called C-testable if all its adder cells can be exhaustively tested while requiring only a constant number of test patterns. The testability of two well-known array multiplier structures are [sic] studied. The conventional design of the carry-save array multiplier is shown to be not C-testable. However, a modified design, using a modified adder cell, is generated and shown to be C-testable and requires only 16 test patterns. Similar results are obtained for the Baugh--Wooley two's complement array multiplier. A modified design of the Baugh--Wooley array multiplier is shown to be C-testable and requires 55 test patterns. The implementation of a practical C-testable $ 16 times 16 $ array multiplier is also presented.

rawabstract:
Array multipliers are well-suited for VLSI implementation because of the regularity in their iterative structure. However, most VLSI circuits are very difficult to test. This paper shows that, with appropriate cell design, array multipliers can be designed to be very easily-testable. An array multiplier is called C-testable if all its adder cells can be exhaustively tested while requiring only a constant number of test patterns. The testability of two well-known array multiplier structures are [sic] studied. The conventional design of the carry-save array multiplier is shown to be not C-testable. However, a modified design, using a modified adder cell, is generated and shown to be C-testable and requires only 16 test patterns. Similar results are obtained for the Baugh--Wooley two's complement array multiplier. A modified design of the Baugh--Wooley array multiplier is shown to be C-testable and requires 55 test patterns. The implementation of a practical C-testable $ 16 \times 16 $ array multiplier is also presented.

entry:
@InProceedings{Ferguson:1983:DTE,
  author =       "Joel Ferguson and John Paul Shen",
  title =        "The Design of Two Easily-Testable {VLSI} Array
                 Multipliers",
  crossref =     "IEEE:1983:PSC",
  pages =        "2--9",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Ferguson_Shen.pdf",
  abstract =     "Array multipliers are well-suited for VLSI
                 implementation because of the regularity in their
                 iterative structure. However, most VLSI circuits are
                 very difficult to test. This paper shows that, with
                 appropriate cell design, array multipliers can be
                 designed to be very easily-testable. An array
                 multiplier is called C-testable if all its adder cells
                 can be exhaustively tested while requiring only a
                 constant number of test patterns. The testability of
                 two well-known array multiplier structures are [sic]
                 studied. The conventional design of the carry-save
                 array multiplier is shown to be not C-testable.
                 However, a modified design, using a modified adder
                 cell, is generated and shown to be C-testable and
                 requires only 16 test patterns. Similar results are
                 obtained for the Baugh--Wooley two's complement array
                 multiplier. A modified design of the Baugh--Wooley
                 array multiplier is shown to be C-testable and requires
                 55 test patterns. The implementation of a practical
                 C-testable $ 16 \times 16 $ array multiplier is also
                 presented.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6",
}


bibtype: inproceedings
filename: fparith.bib
label: Fraenkel:1983:SN
author: A. S. Fraenkel
title: Systems of Numeration
crossref: IEEE:1983:PSC
pages: 37--42
year: 1983
bibdate: Tue Nov 13 15:58:57 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.13 15:58:57 ???
URL: http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Fraenkel.pdf
keywords: ARITH-6; number systems
acknowledgement: ack-nhfb
rawauthor: A. S. Fraenkel
rawtitle: Systems of Numeration
abstract:
A numeration system is a set of integers (basis elements) such that every integer can be represented uniquely over the set using integer digits of bounded size. Such systems are scattered in many fields in mathematics and computer science. Many of the known ones and new ones are unified and derived from a basic result on recursively defined basis elements. Applications are indicated.

rawabstract:
A numeration system is a set of integers (basis elements) such that every integer can be represented uniquely over the set using integer digits of bounded size. Such systems are scattered in many fields in mathematics and computer science. Many of the known ones and new ones are unified and derived from a basic result on recursively defined basis elements. Applications are indicated.

entry:
@InProceedings{Fraenkel:1983:SN,
  author =       "A. S. Fraenkel",
  title =        "Systems of Numeration",
  crossref =     "IEEE:1983:PSC",
  pages =        "37--42",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Fraenkel.pdf",
  abstract =     "A numeration system is a set of integers (basis
                 elements) such that every integer can be represented
                 uniquely over the set using integer digits of bounded
                 size. Such systems are scattered in many fields in
                 mathematics and computer science. Many of the known
                 ones and new ones are unified and derived from a basic
                 result on recursively defined basis elements.
                 Applications are indicated.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6; number systems",
}


bibtype: article
filename: fparith.bib
label: Gaitanis:1983:NPC
author: N. Gaitanis and C. Halatsis
title: Near-Perfect Codes for Binary-Coded Radix-$r$ Arithmetic Units
journal: j-IEEE-TRANS-COMPUT
volume: C-32
number: 5
pages: 494--497
month: may
monthnumber: 5
year: 1983
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1983.1676261
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 10:01:09 MDT 2011
bibtimestamp: 2011.07.10 10:01:09 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676261
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: N. Gaitanis and C. Halatsis
rawtitle: Near-Perfect Codes for Binary-Coded Radix-$r$ Arithmetic Units
entry:
@Article{Gaitanis:1983:NPC,
  author =       "N. Gaitanis and C. Halatsis",
  title =        "Near-Perfect Codes for Binary-Coded Radix-$r$
                 Arithmetic Units",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "5",
  pages =        "494--497",
  month =        may,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676261",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:01:09 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676261",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Galand:1983:FD
author: C. Galand
title: Fast Division
journal: j-IBM-TDB
volume: 26
number: 3B
pages: 1537--1539
month: aug
monthnumber: 8
year: 1983
CODEN: IBMTAA
ISSN: 0018-8689 OR 00188689
bibdate: Thu Sep 1 10:15:08 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:15:08 ???
fjournal: IBM Technical Disclosure Bulletin
acknowledgement: ack-nj
rawauthor: C. Galand
rawtitle: Fast Division
entry:
@Article{Galand:1983:FD,
  author =       "C. Galand",
  title =        "Fast Division",
  journal =      j-IBM-TDB,
  volume =       "26",
  number =       "3B",
  pages =        "1537--1539",
  month =        aug,
  year =         "1983",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Thu Sep 1 10:15:08 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IBM Technical Disclosure Bulletin",
}


bibtype: article
filename: fparith.bib
label: Gavrielov:1983:CSF
author: M. Gavrielov and A. Kaminker and Y.-T. Sidi
title: Coprocessors Speed Floating Point Calculations
journal: j-COMP-DESIGN
volume: 22
number: 11
pages: 197--204
month: oct
monthnumber: 10
year: 1983
CODEN: CMPDAM
ISSN: 0010-4566 OR 00104566
bibdate: Sun Sep 11 11:55:54 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.11 11:55:54 ???
fjournal: Computer Design
acknowledgement: ack-nj
rawauthor: M. Gavrielov and A. Kaminker and Y.-T. Sidi
rawtitle: Coprocessors Speed Floating Point Calculations
entry:
@Article{Gavrielov:1983:CSF,
  author =       "M. Gavrielov and A. Kaminker and Y.-T. Sidi",
  title =        "Coprocessors Speed Floating Point Calculations",
  journal =      j-COMP-DESIGN,
  volume =       "22",
  number =       "11",
  pages =        "197--204",
  month =        oct,
  year =         "1983",
  CODEN =        "CMPDAM",
  ISSN =         "0010-4566",
  bibdate =      "Sun Sep 11 11:55:54 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Computer Design",
}


bibtype: article
filename: fparith.bib
label: Gnanasekaran:1983:BSI
author: R. Gnanasekaran
title: On a Bit-Serial Input and Bit-Serial Output Multiplier
journal: j-IEEE-TRANS-COMPUT
volume: C-32
number: 9
pages: 878--880
month: sep
monthnumber: 9
year: 1983
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1983.1676341
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 10:01:12 MDT 2011
bibtimestamp: 2011.07.10 10:01:12 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676341
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: R. Gnanasekaran
rawtitle: On a Bit-Serial Input and Bit-Serial Output Multiplier
entry:
@Article{Gnanasekaran:1983:BSI,
  author =       "R. Gnanasekaran",
  title =        "On a Bit-Serial Input and Bit-Serial Output
                 Multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "9",
  pages =        "878--880",
  month =        sep,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676341",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:01:12 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676341",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Gosling:1983:STF
author: J. B. Gosling
title: Some Tricks of the (Floating-Point) Trade
crossref: IEEE:1983:PSC
pages: 218--220
year: 1983
bibdate: Tue Nov 13 15:58:57 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.13 15:58:57 ???
URL: http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Gosling.pdf
keywords: ARITH-6
acknowledgement: ack-nhfb
rawauthor: J. B. Gosling
rawtitle: Some Tricks of the (Floating-Point) Trade
abstract:
In designing a floating-point arithmetic unit there are a number of places where the characteristics of the operations and the operands permit simplifications in the logical design. These have not been well documented, with the result that each new generation of designers has made the same mistakes as their predecessors. This paper describes some of these simplifications as they affect the mantissa section of a floating-point addition and subtraction unit. The areas covered include normalisation and rounding.

rawabstract:
In designing a floating-point arithmetic unit there are a number of places where the characteristics of the operations and the operands permit simplifications in the logical design. These have not been well documented, with the result that each new generation of designers has made the same mistakes as their predecessors. This paper describes some of these simplifications as they affect the mantissa section of a floating-point addition and subtraction unit. The areas covered include normalisation and rounding.

entry:
@InProceedings{Gosling:1983:STF,
  author =       "J. B. Gosling",
  title =        "Some Tricks of the (Floating-Point) Trade",
  crossref =     "IEEE:1983:PSC",
  pages =        "218--220",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Gosling.pdf",
  abstract =     "In designing a floating-point arithmetic unit there
                 are a number of places where the characteristics of the
                 operations and the operands permit simplifications in
                 the logical design. These have not been well
                 documented, with the result that each new generation of
                 designers has made the same mistakes as their
                 predecessors. This paper describes some of these
                 simplifications as they affect the mantissa section of
                 a floating-point addition and subtraction unit. The
                 areas covered include normalisation and rounding.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6",
}


bibtype: article
filename: fparith.bib
label: Grappel:1983:FPP
author: R. D. Grappel
title: Floating-point-processing unit improves 16-bit-$ mu P $ performance
journal: j-EDN
volume: 28
number: 19
pages: 181--188
month: sep
monthnumber: 9
year: 1983
CODEN: EDNSBH
ISSN: 0012-7515, 0364-6637 OR 00127515, 03646637
bibdate: Wed Sep 7 22:31:27 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.07 22:31:27 ???
fjournal: EDN
acknowledgement: ack-nj
rawauthor: R. D. Grappel
rawtitle: Floating-point-processing unit improves 16-bit-$ \mu {P} $ performance
entry:
@Article{Grappel:1983:FPP,
  author =       "R. D. Grappel",
  title =        "Floating-point-processing unit improves 16-bit-$ \mu
                 {P} $ performance",
  journal =      j-EDN,
  volume =       "28",
  number =       "19",
  pages =        "181--188",
  month =        sep,
  year =         "1983",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  bibdate =      "Wed Sep 7 22:31:27 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "EDN",
}


bibtype: inproceedings
filename: fparith.bib
label: Grnarov:1983:LMN
author: A. L. Grnarov and M. D. Ercegovac
title: On-line multiplicative normalization
crossref: IEEE:1983:PSC
pages: 151--155
year: 1983
bibdate: Tue Nov 13 15:44:54 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.13 15:44:54 ???
URL: http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Grnarov_Ercegovac.pdf
keywords: ARITH-6; elementary functions; on-line arithmetic
acknowledgement: ack-nhfb
rawauthor: A. L. Grnarov and M. D. Ercegovac
rawtitle: On-line multiplicative normalization
abstract:
In this article we describe a derivation and an algorithm for on-line multiplicative normalization of fractions. The algorithm is a variation of the continued product normalization algorithm and it is used for on-line evaluation of elementary functions.

rawabstract:
In this article we describe a derivation and an algorithm for on-line multiplicative normalization of fractions. The algorithm is a variation of the continued product normalization algorithm and it is used for on-line evaluation of elementary functions.

entry:
@InProceedings{Grnarov:1983:LMN,
  author =       "A. L. Grnarov and M. D. Ercegovac",
  title =        "On-line multiplicative normalization",
  crossref =     "IEEE:1983:PSC",
  pages =        "151--155",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:44:54 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Grnarov_Ercegovac.pdf",
  abstract =     "In this article we describe a derivation and an
                 algorithm for on-line multiplicative normalization of
                 fractions. The algorithm is a variation of the
                 continued product normalization algorithm and it is
                 used for on-line evaluation of elementary functions.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6; elementary functions; on-line arithmetic",
}


bibtype: inproceedings
filename: fparith.bib
label: Guibas:1983:FBA
author: L. Guibas and J. E. Vuillemin
title: On Fast Binary Addition in MOS Technologies
crossref: IEEE:1983:PSC
pages: 22--23
year: 1983
bibdate: Tue Nov 13 15:58:57 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.13 15:58:57 ???
URL: http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Guibas_Vuillemin.pdf
keywords: addition; ARITH-6
remark: Paper did not arrive in time for the proceedings.
acknowledgement: ack-nhfb
rawauthor: L. Guibas and J. E. Vuillemin
rawtitle: On Fast Binary Addition in {MOS} Technologies
entry:
@InProceedings{Guibas:1983:FBA,
  author =       "L. Guibas and J. E. Vuillemin",
  title =        "On Fast Binary Addition in {MOS} Technologies",
  crossref =     "IEEE:1983:PSC",
  pages =        "22--23",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Guibas_Vuillemin.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "addition; ARITH-6",
  remark =       "Paper did not arrive in time for the proceedings.",
}


bibtype: article
filename: fparith.bib
label: Halatsis:1983:ECC
author: C. Halatsis and N. Gaitanis and M. Sigala
title: Error-Correcting Codes in Binary-Coded Radix-$r$ Arithmetic
journal: j-IEEE-TRANS-COMPUT
volume: C-32
number: 3
pages: 326--328
month: mar
monthnumber: 3
year: 1983
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1983.1676227
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 10:01:08 MDT 2011
bibtimestamp: 2011.07.10 10:01:08 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676227
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: C. Halatsis and N. Gaitanis and M. Sigala
rawtitle: Error-Correcting Codes in Binary-Coded Radix-$r$ Arithmetic
entry:
@Article{Halatsis:1983:ECC,
  author =       "C. Halatsis and N. Gaitanis and M. Sigala",
  title =        "Error-Correcting Codes in Binary-Coded Radix-$r$
                 Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "3",
  pages =        "326--328",
  month =        mar,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676227",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:01:08 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676227",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Hamada:1983:UUR
author: H. Hamada
title: URR: Universal representation of real numbers
journal: j-NEW-GEN-COMP
volume: 1
number: 2
pages: 205--209
month: jun
monthnumber: 6
year: 1983
CODEN: NGCOE5
DOI: https://doi.org/10.1007/BF03037427
ISSN: 0288-3635 (print), 1882-7055 (electronic) OR 02883635 (print), 18827055 (electronic)
ISSNL: 0288-3635 OR 02883635
bibdate: Thu Dec 14 16:45:14 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.14 16:45:14 ???
fjournal: New Generation Computing
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/newg
rawauthor: H. Hamada
rawtitle: {URR}: Universal representation of real numbers
entry:
@Article{Hamada:1983:UUR,
  author =       "H. Hamada",
  title =        "{URR}: Universal representation of real numbers",
  journal =      j-NEW-GEN-COMP,
  volume =       "1",
  number =       "2",
  pages =        "205--209",
  month =        jun,
  year =         "1983",
  CODEN =        "NGCOE5",
  DOI =          "https://doi.org/10.1007/BF03037427",
  ISSN =         "0288-3635 (print), 1882-7055 (electronic)",
  ISSN-L =       "0288-3635",
  bibdate =      "Thu Dec 14 16:45:14 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "New Generation Computing",
  journal-URL =  "https://dl.acm.org/loi/newg",
}


bibtype: article
filename: fparith.bib
label: Heninger:1983:ZZF
author: A. Heninger
title: Zilog's Z8070 Floating Point Processor
crossref: Mini-Micro:1983:MMN
pages: 16/2/1--7
year: 1983
bibdate: Wed Sep 7 22:31:27 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.07 22:31:27 ???
acknowledgement: ack-nj
rawauthor: A. Heninger
rawtitle: {Zilog}'s {Z8070} Floating Point Processor
entry:
@Article{Heninger:1983:ZZF,
  author =       "A. Heninger",
  title =        "{Zilog}'s {Z8070} Floating Point Processor",
  crossref =     "Mini-Micro:1983:MMN",
  pages =        "16/2/1--7",
  year =         "1983",
  bibdate =      "Wed Sep 7 22:31:27 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: incollection
filename: fparith.bib
label: HP:1983:CDR
author: Hewlett Packard
booktitle: Software Internal Design Specification for the HP-71, Vol. 1
title: Chapter 13: Data Representations
publisher: Hewlett Packard Company
address: Palo Alto, CA, USA
pages: 13.1--13.17
month: dec
monthnumber: 12
year: 1983
bibdate: Fri Nov 28 17:17:29 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 17:17:29 ???
note: Part #00071-90068. Manual available from em The Museum of HP Calculators.
URL: http://www.hpmuseum.org/
acknowledgement: ack-mfc
rawauthor: {Hewlett Packard}
rawbooktitle: Software Internal Design Specification for the {HP-71}, Vol. 1
rawnote: Part \#00071-90068. Manual available from {\em The Museum of HP Calculators}.
rawtitle: Chapter 13: Data Representations
entry:
@InCollection{HP:1983:CDR,
  author =       "{Hewlett Packard}",
  booktitle =    "Software Internal Design Specification for the
                 {HP-71}, Vol. 1",
  title =        "Chapter 13: Data Representations",
  publisher =    "Hewlett Packard Company",
  address =      "Palo Alto, CA, USA",
  pages =        "13.1--13.17",
  month =        dec,
  year =         "1983",
  bibdate =      "Fri Nov 28 17:17:29 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Part \#00071-90068. Manual available from {\em The
                 Museum of HP Calculators}.",
  URL =          "http://www.hpmuseum.org/",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Huang:1983:FPM
author: C. H. Huang
title: A Fully Parallel Mixed-Radix Conversion Algorithm for Residue Number Applications
journal: j-IEEE-TRANS-COMPUT
volume: C-32
number: 4
pages: 398--402
month: apr
monthnumber: 4
year: 1983
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1983.1676242
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 10:01:08 MDT 2011
bibtimestamp: 2011.07.10 10:01:08 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: C. H. Huang
rawtitle: A Fully Parallel Mixed-Radix Conversion Algorithm for Residue Number Applications
URL:
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676242; http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12; http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35226

entry:
@Article{Huang:1983:FPM,
  author =       "C. H. Huang",
  title =        "A Fully Parallel Mixed-Radix Conversion Algorithm for
                 Residue Number Applications",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "4",
  pages =        "398--402",
  month =        apr,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676242",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:01:08 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676242;
                 http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35226",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A new, fully parallel mixed-radix conversion (MRC)
                 algorithm which utilizes the maximum parallelism that
                 exists in the residues (RNS) to mixed-radix (MR) digits
                 conversion to achieve high throughput rate and very
                 short conversion time is presented. \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Huntsman:1983:MFP
author: Clayton Huntsman and Duane Cawthron
title: The MC68881 Floating-Point Coprocessor
journal: j-IEEE-MICRO
volume: 3
number: 6
pages: 44--54
month: nov
monthnumber: 11
year: 1983
CODEN: IEMIDZ
DOI: https://doi.org/10.1109/MM.1983.291185
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
corpsource: Motorola Inc., Austin, TX, USA
journalURL: http://www.computer.org/csdl/mags/mi/index.html
treatment: P Practical; T Theoretical or Mathematical
rawauthor: Clayton Huntsman and Duane Cawthron
rawtitle: The {MC68881} Floating-Point Coprocessor
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:
arithmetic; computer architecture; computers; coprocessor; digital arithmetic; floating-point; floating-point arithmetic; IEEE arithmetic; IEEE standard; integrated circuits, VLSI --- Applications; M68000 family; M68000 microprocessor; MC68881 floating-point processor; microprocessor chips; real-number computations; satellite; standards

classcodes:
B1265F (Microprocessors and microcomputers); C5130 (Microprocessor chips); C5230 (Digital arithmetic methods)

entry:
@Article{Huntsman:1983:MFP,
  author =       "Clayton Huntsman and Duane Cawthron",
  title =        "The {MC68881} Floating-Point Coprocessor",
  journal =      j-IEEE-MICRO,
  volume =       "3",
  number =       "6",
  pages =        "44--54",
  month =        nov # "\slash " # dec,
  year =         "1983",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/MM.1983.291185",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Thu Dec 14 06:08:58 MST 2000",
  bibsource =    "Compendex database;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 Science Citation Index database (1980--2000)",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  classcodes =   "B1265F (Microprocessors and microcomputers); C5130
                 (Microprocessor chips); C5230 (Digital arithmetic
                 methods)",
  classification = "714; 723; 902",
  corpsource =   "Motorola Inc., Austin, TX, USA",
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
  keywords =     "arithmetic; computer architecture; computers;
                 coprocessor; digital arithmetic; floating-point;
                 floating-point arithmetic; IEEE arithmetic; IEEE
                 standard; integrated circuits, VLSI --- Applications;
                 M68000 family; M68000 microprocessor; MC68881
                 floating-point processor; microprocessor chips;
                 real-number computations; satellite; standards",
  treatment =    "P Practical; T Theoretical or Mathematical",
}


bibtype: article
filename: fparith.bib
label: Iffrig:1983:ULC
author: L. D. Iffrig
title: Use less code for fast 8080 multiply
journal: j-EDN
volume: 28
number: 13
pages: 293
month: jun
monthnumber: 6
year: 1983
CODEN: EDNSBH
ISSN: 0012-7515, 0364-6637 OR 00127515, 03646637
bibdate: Thu Sep 1 10:15:08 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:15:08 ???
fjournal: EDN
acknowledgement: ack-nj
rawauthor: L. D. Iffrig
rawtitle: Use less code for fast 8080 multiply
entry:
@Article{Iffrig:1983:ULC,
  author =       "L. D. Iffrig",
  title =        "Use less code for fast 8080 multiply",
  journal =      j-EDN,
  volume =       "28",
  number =       "13",
  pages =        "293",
  month =        jun,
  year =         "1983",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  bibdate =      "Thu Sep 1 10:15:08 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "EDN",
}


bibtype: techreport
filename: fparith.bib
label: Ingram:1983:ACW
author: Windell F. Ingram and Radhakrishnan, N. (Narayanswamy) and Deborah F. Dent
title: Accuracy considerations when using some minicomputers for scientific and engineering problems
address: Vicksburg, MS, USA
pages: 76 + 6 + 3
year: 1983
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Floating-point arithmetic.; Minicomputers.; Programming (Electronic computers).
acknowledgement: ack-nhfb
rawauthor: Windell F. Ingram and Radhakrishnan, N. (Narayanswamy) and Deborah F. Dent
rawtitle: Accuracy considerations when using some minicomputers for scientific and engineering problems
institution:
U.S. Army Engineer Waterways Experiment Station; available from National Technical Information Service

series:
Technical report; K-83-2 Technical report (U.S. Army Engineer Waterways Experiment Station); K-83-2.

remark:
Cover title. ``September 1983.'' ``Prepared for Office, Chief of Engineers, U.S. Army.'' Funded by Office, Chief of Engineers.

entry:
@TechReport{Ingram:1983:ACW,
  author =       "Windell F. Ingram and Radhakrishnan, N. (Narayanswamy)
                 and Deborah F. Dent",
  title =        "Accuracy considerations when using some minicomputers
                 for scientific and engineering problems",
  institution =  "U.S. Army Engineer Waterways Experiment Station;
                 available from National Technical Information Service",
  address =      "Vicksburg, MS, USA",
  pages =        "76 + 6 + 3",
  year =         "1983",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Technical report; K-83-2 Technical report (U.S. Army
                 Engineer Waterways Experiment Station); K-83-2.",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.; Minicomputers.;
                 Programming (Electronic computers).",
  remark =       "Cover title. ``September 1983.'' ``Prepared for
                 Office, Chief of Engineers, U.S. Army.'' Funded by
                 Office, Chief of Engineers.",
}


bibtype: book
filename: fparith.bib
label: Intel:1983:HRM
author: Intel
title: The iAPX 286 Hardware Reference Manual
publisher: pub-INTEL
address: pub-INTEL:adr
pages: 76 + 6 + 3
year: 1983
LCCN: QA76.8.I264 I14 1983
bibdate: Wed Feb 9 09:02:53 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.02.09 09:02:53 ???
acknowledgement: ack-nhfb
rawauthor: Intel
rawtitle: The {iAPX} 286 Hardware Reference Manual
note:
The definitive statement of the 80286 and 80287 hardware at a strongly technical level. Not an instruction set reference, but does contain instruction timing tables. See also cite Intel:1985:PRM.

rawnote:
The definitive statement of the 80286 and 80287 hardware at a strongly technical level. Not an instruction set reference, but does contain instruction timing tables. See also \cite{Intel:1985:PRM}.

entry:
@Book{Intel:1983:HRM,
  author =       "Intel",
  title =        "The {iAPX} 286 Hardware Reference Manual",
  publisher =    pub-INTEL,
  address =      pub-INTEL:adr,
  year =         "1983",
  LCCN =         "QA76.8.I264 I14 1983",
  bibdate =      "Wed Feb 9 09:02:53 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "The definitive statement of the 80286 and 80287
                 hardware at a strongly technical level. Not an
                 instruction set reference, but does contain instruction
                 timing tables. See also \cite{Intel:1985:PRM}.",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Irwin:1983:NLD
author: Mary Jane Irwin and Robert Michael Owens
title: Numerical Limitation on the Design of Digit On-Line Networks
crossref: IEEE:1983:PSC
pages: 156--161
year: 1983
bibdate: Tue Nov 13 15:50:08 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.13 15:50:08 ???
URL: http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Owens_Irwin.pdf
keywords: ARITH-6; on-line arithmetic
acknowledgement: ack-nhfb
rawauthor: Mary Jane Irwin and Robert Michael Owens
rawtitle: Numerical Limitation on the Design of Digit On-Line Networks
abstract:
A fully digit online arithmetic unit generates at least the $i$ most (least) significant digits of the result after having been supplied no more than the $ (i + k) $ most (least) significant digits of each operand, where $k$ is a small constant. This digit serial property can be used to reduce the aggregate fill and flush times of a chained array of digit online arithmetic units and to reduce their VLSI interconnection complexity. However, because of this digit serial property, unique and inherent limitations may have to be imposed on any arithmetic unit which performs digit online operations. For some calculations, these limitations may be so severe as to make digit online evaluation virtually impossible. We show several important signal processing problems where these limitations have either been avoided or their effect greatly reduced.

rawabstract:
A fully digit online arithmetic unit generates at least the $i$ most (least) significant digits of the result after having been supplied no more than the $ (i + k) $ most (least) significant digits of each operand, where $k$ is a small constant. This digit serial property can be used to reduce the aggregate fill and flush times of a chained array of digit online arithmetic units and to reduce their VLSI interconnection complexity. However, because of this digit serial property, unique and inherent limitations may have to be imposed on any arithmetic unit which performs digit online operations. For some calculations, these limitations may be so severe as to make digit online evaluation virtually impossible. We show several important signal processing problems where these limitations have either been avoided or their effect greatly reduced.

entry:
@InProceedings{Irwin:1983:NLD,
  author =       "Mary Jane Irwin and Robert Michael Owens",
  title =        "Numerical Limitation on the Design of Digit On-Line
                 Networks",
  crossref =     "IEEE:1983:PSC",
  pages =        "156--161",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:50:08 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Owens_Irwin.pdf",
  abstract =     "A fully digit online arithmetic unit generates at
                 least the $i$ most (least) significant digits of the
                 result after having been supplied no more than the $ (i
                 + k) $ most (least) significant digits of each operand,
                 where $k$ is a small constant. This digit serial
                 property can be used to reduce the aggregate fill and
                 flush times of a chained array of digit online
                 arithmetic units and to reduce their VLSI
                 interconnection complexity. However, because of this
                 digit serial property, unique and inherent limitations
                 may have to be imposed on any arithmetic unit which
                 performs digit online operations. For some
                 calculations, these limitations may be so severe as to
                 make digit online evaluation virtually impossible. We
                 show several important signal processing problems where
                 these limitations have either been avoided or their
                 effect greatly reduced.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6; on-line arithmetic",
}


bibtype: article
filename: fparith.bib
label: James:1983:RDB
author: F. V. James
title: An 8085 routine divides 32-bit unsigned numbers
journal: j-ELECTRONICS
volume: 56
number: 22
pages: 163--165
month: nov
monthnumber: 11
year: 1983
ISSN: 0883-4989 OR 08834989
bibdate: Thu Sep 1 10:15:08 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:15:08 ???
fjournal: Electronics
acknowledgement: ack-nj
journalURL: https://www.mdpi.com/journal/electronics
rawauthor: F. V. James
rawtitle: An 8085 routine divides 32-bit unsigned numbers
entry:
@Article{James:1983:RDB,
  author =       "F. V. James",
  title =        "An 8085 routine divides 32-bit unsigned numbers",
  journal =      j-ELECTRONICS,
  volume =       "56",
  number =       "22",
  pages =        "163--165",
  month =        nov,
  year =         "1983",
  ISSN =         "0883-4989",
  bibdate =      "Thu Sep 1 10:15:08 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Electronics",
  journal-URL =  "https://www.mdpi.com/journal/electronics",
}


bibtype: article
filename: fparith.bib
label: Jankowski:1983:NFS
author: M. Jankowski and A. Smoktunowicz and H. Wozniakowski
title: A note on floating-point summation of very many terms
journal: Elektron. Informationsverarb. Kybernet.
volume: 19
number: 9
pages: 435--440
year: 1983
MRclass: 65V05
MRnumber: 85c:65161
bibdate: Fri Dec 8 08:24:13 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 08:24:13 ???
keywords: accurate floating-point summation
acknowledgement: ack-nhfb
rawauthor: M. Jankowski and A. Smoktunowicz and H. Wo{\'z}niakowski
rawtitle: A note on floating-point summation of very many terms
entry:
@Article{Jankowski:1983:NFS,
  author =       "M. Jankowski and A. Smoktunowicz and H.
                 Wo{\'z}niakowski",
  title =        "A note on floating-point summation of very many
                 terms",
  journal =      "Elektron. Informationsverarb. Kybernet.",
  volume =       "19",
  number =       "9",
  pages =        "435--440",
  year =         "1983",
  MRclass =      "65V05",
  MRnumber =     "85c:65161",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  altjournal =   "Journal of Information Processing and Cybernetics ---
                 EIK",
  keywords =     "accurate floating-point summation",
}


bibtype: article
filename: fparith.bib
label: Jenkins:1983:DEC
author: W. K. Jenkins
title: The Design of Error Checkers for Self-Checking Residue Number Arithmetic
journal: j-IEEE-TRANS-COMPUT
volume: C-32
number: 4
pages: 388--396
month: apr
monthnumber: 4
year: 1983
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1983.1676240
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 10:01:08 MDT 2011
bibtimestamp: 2011.07.10 10:01:08 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: W. K. Jenkins
rawtitle: The Design of Error Checkers for Self-Checking Residue Number Arithmetic
URL:
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676240; http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12; http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35226

entry:
@Article{Jenkins:1983:DEC,
  author =       "W. K. Jenkins",
  title =        "The Design of Error Checkers for Self-Checking Residue
                 Number Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "4",
  pages =        "388--396",
  month =        apr,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676240",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:01:08 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676240;
                 http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35226",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "During the last few years residue number (RNS)
                 arithmetic has gained increasing importance for
                 providing high speed fault tolerant performance in
                 dedicated digital signal processors. One factor that
                 has limited the use of redundant RNS theory in
                 \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Johnsen:1983:IFP
author: K. Johnsen
title: An IEEE Floating Point Arithmetic Implementation
crossref: IEEE:1983:PSC
pages: 130--135
year: 1983
bibdate: Tue Nov 13 15:50:08 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.13 15:50:08 ???
URL: http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Johnsen.pdf
keywords: ARITH-6; correct rounding; floating-point arithmetic; IEEE 754
acknowledgement: ack-nhfb
rawauthor: K. Johnsen
rawtitle: An {IEEE} Floating Point Arithmetic Implementation
abstract:
This article describes some of the methods and algorithms used in an implementation of floating point arithmetic following (almost) the IEEE standard defined in (1). The description is more directly algorithm-oriented than the `Implementation Guide' for this standard (2), since the latter does not treat an actual implementation. The article consists of two parts. One concerns the problem of getting the preliminary result from each of the arithmetic operations, this result is the basis for a correct rounding. The other part treats the multiword arithmetic, i.e., the routines to perform an $ m times n $ bit operation, using the corresponding $n$ bit operation supplied by the hardware. Only multiplication and division are described, since the add / subtract routines are trivial. For division also a method for getting an $n$ bit inverse is included, since the hardware in the case had no division operation.

rawabstract:
This article describes some of the methods and algorithms used in an implementation of floating point arithmetic following (almost) the IEEE standard defined in (1). The description is more directly algorithm-oriented than the `Implementation Guide' for this standard (2), since the latter does not treat an actual implementation. The article consists of two parts. One concerns the problem of getting the preliminary result from each of the arithmetic operations, this result is the basis for a correct rounding. The other part treats the multiword arithmetic, i.e., the routines to perform an $ m \times n $ bit operation, using the corresponding $n$ bit operation supplied by the hardware. Only multiplication and division are described, since the add\slash subtract routines are trivial. For division also a method for getting an $n$ bit inverse is included, since the hardware in the case had no division operation.

entry:
@InProceedings{Johnsen:1983:IFP,
  author =       "K. Johnsen",
  title =        "An {IEEE} Floating Point Arithmetic Implementation",
  crossref =     "IEEE:1983:PSC",
  pages =        "130--135",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:50:08 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Johnsen.pdf",
  abstract =     "This article describes some of the methods and
                 algorithms used in an implementation of floating point
                 arithmetic following (almost) the IEEE standard defined
                 in (1). The description is more directly
                 algorithm-oriented than the `Implementation Guide' for
                 this standard (2), since the latter does not treat an
                 actual implementation. The article consists of two
                 parts. One concerns the problem of getting the
                 preliminary result from each of the arithmetic
                 operations, this result is the basis for a correct
                 rounding. The other part treats the multiword
                 arithmetic, i.e., the routines to perform an $ m \times
                 n $ bit operation, using the corresponding $n$ bit
                 operation supplied by the hardware. Only multiplication
                 and division are described, since the add\slash
                 subtract routines are trivial. For division also a
                 method for getting an $n$ bit inverse is included,
                 since the hardware in the case had no division
                 operation.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6; correct rounding; floating-point arithmetic;
                 IEEE 754",
}


bibtype: mastersthesis
filename: fparith.bib
label: Jung:1983:BRR
author: C. Jung
type: Diplomarbeit
school: Institut fur Angewandte Mathematik, Universitat Karlsruhe
address: Karlsruhe, Germany
month: sep
monthnumber: 9
year: 1983
bibdate: Fri Sep 16 16:30:40 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.16 16:30:40 ???
acknowledgement: ack-nj
rawauthor: C. Jung
title:
Berechnung der reellen und reellintervallwertigen Standard- funktionen mit maximaler Genauigkeit in einem hexadezimalen Gleitkommaformat toenglish Computation of the Real and Real Interval Valued Standard Functions with Maximal Accuracy in a Hexadecimal Floating-Point Format endtoenglish 

rawtitle:
{Berechnung der reellen und reellintervallwertigen Standard- funktionen mit maximaler Genauigkeit in einem hexadezimalen Gleitkommaformat} \toenglish {Computation of the Real and Real Interval Valued Standard Functions with Maximal Accuracy in a Hexadecimal Floating-Point Format} \endtoenglish

entry:
@MastersThesis{Jung:1983:BRR,
  author =       "C. Jung",
  title =        "{Berechnung der reellen und reellintervallwertigen
                 Standard- funktionen mit maximaler Genauigkeit in einem
                 hexadezimalen Gleitkommaformat} \toenglish {Computation
                 of the Real and Real Interval Valued Standard Functions
                 with Maximal Accuracy in a Hexadecimal Floating-Point
                 Format} \endtoenglish",
  type =         "{Diplomarbeit}",
  school =       "Institut f{\"u}r Angewandte Mathematik,
                 Universit{\"a}t Karlsruhe",
  address =      "Karlsruhe, Germany",
  pages =        "??",
  month =        sep,
  year =         "1983",
  bibdate =      "Fri Sep 16 16:30:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: techreport
filename: fparith.bib
label: Kahan:1983:M
author: W. Kahan
title: Minimizing $ q rm * m - n $
address: Berkeley, CA, USA
month: mar
monthnumber: 3
year: 1983
bibdate: Fri May 03 12:26:29 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.03 12:26:29 ???
URL: http://www.cs.berkeley.edu/~wkahan/testpi/nearpi.c
acknowledgement: ack-nhfb
rawauthor: W. Kahan
rawtitle: Minimizing $ q {\rm *} m - n $
institution:
Department of Mathematics and Department of Electrical Engineering and Computer Science, University of California, Berkeley

remark:
Nearpi, a C program to exhibit large floating-point numbers $ Z = m * 2^L $ very close to integer multiples of $ pi / 2 $.

entry:
@TechReport{Kahan:1983:M,
  author =       "W. Kahan",
  title =        "Minimizing $ q {\rm *} m - n $",
  institution =  "Department of Mathematics and Department of Electrical
                 Engineering and Computer Science, University of
                 California, Berkeley",
  address =      "Berkeley, CA, USA",
  month =        mar,
  year =         "1983",
  bibdate =      "Fri May 03 12:26:29 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/testpi/nearpi.c",
  acknowledgement = ack-nhfb,
  remark =       "Nearpi, a C program to exhibit large floating-point
                 numbers $ Z = m * 2^L $ very close to integer multiples
                 of $ \pi / 2 $.",
}


bibtype: inproceedings
filename: fparith.bib
label: Kahan:1983:MWS
author: W. Kahan
title: Mathematics Written in Sand --- The HP-15C, Intel 8087, etc.
crossref: Anonymous:1983:PSC
pages: 12--26
year: 1983
bibdate: Fri May 03 12:02:15 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.03 12:02:15 ???
URL: http://www.cs.berkeley.edu/~wkahan/MathSand.pdf
acknowledgement: ack-nhfb
bookpages: vi + 344
rawauthor: W. Kahan
rawtitle: Mathematics Written in Sand --- The {HP-15C}, {Intel 8087}, etc.
remark:
The original published version was a photoreduction of dot-matrix printer output; the URL points to a cleaner version.

entry:
@InProceedings{Kahan:1983:MWS,
  author =       "W. Kahan",
  title =        "Mathematics Written in Sand --- The {HP-15C}, {Intel
                 8087}, etc.",
  crossref =     "Anonymous:1983:PSC",
  bookpages =    "vi + 344",
  pages =        "12--26",
  year =         "1983",
  bibdate =      "Fri May 03 12:02:15 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MathSand.pdf",
  acknowledgement = ack-nhfb,
  remark =       "The original published version was a photoreduction of
                 dot-matrix printer output; the URL points to a cleaner
                 version.",
}


bibtype: techreport
filename: fparith.bib
label: Kanada:1983:CDP
author: Y. Kanada and Y. Tamura and S. Yoshino and Y. Ushiro
type: Technical report
number: CCUT-TR-84-01
institution: Computer Centre, University of Tokyo
address: Bunkyo-ky, Yayoi 2-11-16, Tokyo 113, Japan
pages: 12--26
month: dec
monthnumber: 12
year: 1983
bibdate: Mon Jul 18 17:50:42 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.18 17:50:42 ???
acknowledgement: ack-nhfb
rawauthor: Y. Kanada and Y. Tamura and S. Yoshino and Y. Ushiro
title:
Calculation of $ pi $ to 10,013,395 Decimal Places Based on the Gauss--Legendre Algorithm and Gauss Arctangent Relation

rawtitle:
Calculation of $ \pi $ to 10,013,395 Decimal Places Based on the {Gauss--Legendre} Algorithm and {Gauss} Arctangent Relation

entry:
@TechReport{Kanada:1983:CDP,
  author =       "Y. Kanada and Y. Tamura and S. Yoshino and Y. Ushiro",
  title =        "Calculation of $ \pi $ to 10,013,395 Decimal Places
                 Based on the {Gauss--Legendre} Algorithm and {Gauss}
                 Arctangent Relation",
  type =         "Technical report",
  number =       "CCUT-TR-84-01",
  institution =  "Computer Centre, University of Tokyo",
  address =      "Bunkyo-ky, Yayoi 2-11-16, Tokyo 113, Japan",
  month =        dec,
  year =         "1983",
  bibdate =      "Mon Jul 18 17:50:42 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Kaushik:1983:SDN
author: S. Kaushik
title: Sign Detection in Non-Redundant Residue Number System with Reduced Information
crossref: IEEE:1983:PSC
pages: 24--28
year: 1983
bibdate: Tue Nov 13 15:50:08 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.13 15:50:08 ???
URL: http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Kaushik.pdf
keywords: ARITH-6; residue number systems
acknowledgement: ack-nhfb
rawauthor: S. Kaushik
rawtitle: Sign Detection in Non-Redundant Residue Number System with Reduced Information
abstract:
A necessary and sufficient condition for sign detection in Non-Redundant Residue Number System by reducing the information of a residue digit has been obtained. The function to reduce the information of a residue digit $ x_p $ corresponding to a modulus $ m_p $ has been assumed to be periodic with the period length $ hat m_p $, where $ hat m_p = M / m_p $ and $ M = prod _i = 1^n m_i $. A sequential method for determining the sign of a number is shown to demonstrate the applicability of the results thus proved.

rawabstract:
A necessary and sufficient condition for sign detection in Non-Redundant Residue Number System by reducing the information of a residue digit has been obtained. The function to reduce the information of a residue digit $ x_p $ corresponding to a modulus $ m_p $ has been assumed to be periodic with the period length $ \hat {m}_p $, where $ \hat {m}_p = M / m_p $ and $ M = \prod_{i = 1}^n m_i $. A sequential method for determining the sign of a number is shown to demonstrate the applicability of the results thus proved.

entry:
@InProceedings{Kaushik:1983:SDN,
  author =       "S. Kaushik",
  title =        "Sign Detection in Non-Redundant Residue Number System
                 with Reduced Information",
  crossref =     "IEEE:1983:PSC",
  pages =        "24--28",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:50:08 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Kaushik.pdf",
  abstract =     "A necessary and sufficient condition for sign
                 detection in Non-Redundant Residue Number System by
                 reducing the information of a residue digit has been
                 obtained. The function to reduce the information of a
                 residue digit $ x_p $ corresponding to a modulus $ m_p
                 $ has been assumed to be periodic with the period
                 length $ \hat {m}_p $, where $ \hat {m}_p = M / m_p $
                 and $ M = \prod_{i = 1}^n m_i $. A sequential method
                 for determining the sign of a number is shown to
                 demonstrate the applicability of the results thus
                 proved.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6; residue number systems",
}


bibtype: mastersthesis
filename: fparith.bib
label: Kirk:1983:MFP
author: Patrick Donald Kirk
title: Microcomputer and floating point firmware design
type: Thesis (M.S.)
school: California State University, Long Beach
address: Long Beach, CA, USA
pages: 2 + xi + 237
year: 1983
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Floating-point arithmetic.; Microcomputers --- Programming.
acknowledgement: ack-nhfb
rawauthor: Patrick Donald Kirk
rawtitle: Microcomputer and floating point firmware design
entry:
@MastersThesis{Kirk:1983:MFP,
  author =       "Patrick Donald Kirk",
  title =        "Microcomputer and floating point firmware design",
  type =         "Thesis ({M.S.})",
  school =       "California State University, Long Beach",
  address =      "Long Beach, CA, USA",
  pages =        "2 + xi + 237",
  year =         "1983",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.; Microcomputers ---
                 Programming.",
}


bibtype: inproceedings
filename: fparith.bib
label: Kobayashi:1983:AHS
author: Hideaki Kobayashi and Ronald D. Bonnell
title: Arithmetic for a High-Speed Adaptive Learning Network Element
crossref: IEEE:1983:PSC
pages: 164--168
year: 1983
bibdate: Tue Nov 13 15:58:57 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.13 15:58:57 ???
URL: http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Kobayashi_Bonnel.pdf
keywords: ARITH-6
acknowledgement: ack-nhfb
rawauthor: Hideaki Kobayashi and Ronald D. Bonnell
rawtitle: Arithmetic for a High-Speed Adaptive Learning Network Element
abstract:
This paper presents a novel arithmetic scheme for a high-speed adaptive learning network (ALN) element. An ALN is a self-organizing scheme for implementing the Kolmogorov--Gabor (K-G) polynomial which maps an input vector $X$ into an output scalar $Y$. In the first layer of an ALN there are $ n(n - 1) / 2 $ elements. In the next layer the number of elements needed depends upon the number of outputs that are propagated from the first layer. In this paper only the design of a single element is considered. An array of memories (RAMs) and a parallel adder are used to perform multinomial arithmetic for the element. The memory array contains subfunction values which are calculated by an external host computer and downloaded to the memory array. All the memories operate on the input variables concurrently via a common address bus. The subfunction values from the memory array are then summed by a parallel adder to obtain the output of the element. complete ALN implemented with the proposed ALN elements has advantages in operation speed and less hardware.

rawabstract:
This paper presents a novel arithmetic scheme for a high-speed adaptive learning network (ALN) element. An ALN is a self-organizing scheme for implementing the Kolmogorov--Gabor (K-G) polynomial which maps an input vector $X$ into an output scalar $Y$. In the first layer of an ALN there are $ n(n - 1) / 2 $ elements. In the next layer the number of elements needed depends upon the number of outputs that are propagated from the first layer. In this paper only the design of a single element is considered. An array of memories (RAMs) and a parallel adder are used to perform multinomial arithmetic for the element. The memory array contains subfunction values which are calculated by an external host computer and downloaded to the memory array. All the memories operate on the input variables concurrently via a common address bus. The subfunction values from the memory array are then summed by a parallel adder to obtain the output of the element. complete ALN implemented with the proposed ALN elements has advantages in operation speed and less hardware.

entry:
@InProceedings{Kobayashi:1983:AHS,
  author =       "Hideaki Kobayashi and Ronald D. Bonnell",
  title =        "Arithmetic for a High-Speed Adaptive Learning Network
                 Element",
  crossref =     "IEEE:1983:PSC",
  pages =        "164--168",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Kobayashi_Bonnel.pdf",
  abstract =     "This paper presents a novel arithmetic scheme for a
                 high-speed adaptive learning network (ALN) element. An
                 ALN is a self-organizing scheme for implementing the
                 Kolmogorov--Gabor (K-G) polynomial which maps an input
                 vector $X$ into an output scalar $Y$. In the first
                 layer of an ALN there are $ n(n - 1) / 2 $ elements. In
                 the next layer the number of elements needed depends
                 upon the number of outputs that are propagated from the
                 first layer. In this paper only the design of a single
                 element is considered. An array of memories (RAMs) and
                 a parallel adder are used to perform multinomial
                 arithmetic for the element. The memory array contains
                 subfunction values which are calculated by an external
                 host computer and downloaded to the memory array. All
                 the memories operate on the input variables
                 concurrently via a common address bus. The subfunction
                 values from the memory array are then summed by a
                 parallel adder to obtain the output of the element.
                 complete ALN implemented with the proposed ALN elements
                 has advantages in operation speed and less hardware.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6",
}


bibtype: article
filename: fparith.bib
label: Kornerup:1983:FPR
author: Peter Kornerup and David W. Matula
title: Finite precision rational arithmetic: An arithmetic unit
journal: j-IEEE-TRANS-COMPUT
volume: C-32
number: 4
pages: 378--388
month: apr
monthnumber: 4
year: 1983
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1983.1676239
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 10:01:08 MDT 2011
bibtimestamp: 2011.07.10 10:01:08 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676239
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Peter Kornerup and David W. Matula
rawtitle: Finite precision rational arithmetic: An arithmetic unit
abstract:
The foundations of an arithmetic unit performing the add, subtract, multiply, and divide operations on rational operands are developed. The unit uses the classical Euclidean algorithm as one unified algorithm for all the arithmetic operations, including rounding. Binary implementations are discussed, based on techniques known from SRT division, and utilizing ripple-free borrow-save and carry-save addition. Average time behavior is investigated.

rawabstract:
The foundations of an arithmetic unit performing the add, subtract, multiply, and divide operations on rational operands are developed. The unit uses the classical Euclidean algorithm as one unified algorithm for all the arithmetic operations, including rounding. Binary implementations are discussed, based on techniques known from SRT division, and utilizing ripple-free borrow-save and carry-save addition. Average time behavior is investigated.

entry:
@Article{Kornerup:1983:FPR,
  author =       "Peter Kornerup and David W. Matula",
  title =        "Finite precision rational arithmetic: An arithmetic
                 unit",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "4",
  pages =        "378--388",
  month =        apr,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676239",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:01:08 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676239",
  abstract =     "The foundations of an arithmetic unit performing the
                 add, subtract, multiply, and divide operations on
                 rational operands are developed. The unit uses the
                 classical Euclidean algorithm as one unified algorithm
                 for all the arithmetic operations, including rounding.
                 Binary implementations are discussed, based on
                 techniques known from SRT division, and utilizing
                 ripple-free borrow-save and carry-save addition.
                 Average time behavior is investigated.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Krishnamurthy:1983:FID
author: E. V. Krishnamurthy and V. K. Murthy
title: Fast Iterative Division of $p$-adic Numbers
journal: j-IEEE-TRANS-COMPUT
volume: C-32
number: 4
pages: 396--398
month: apr
monthnumber: 4
year: 1983
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1983.1676241
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 10:01:08 MDT 2011
bibtimestamp: 2011.07.10 10:01:08 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676241
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: E. V. Krishnamurthy and V. K. Murthy
rawtitle: Fast Iterative Division of $p$-adic Numbers
entry:
@Article{Krishnamurthy:1983:FID,
  author =       "E. V. Krishnamurthy and V. K. Murthy",
  title =        "Fast Iterative Division of $p$-adic Numbers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "4",
  pages =        "396--398",
  month =        apr,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676241",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:01:08 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676241",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Lastman:1983:DFP
author: G. J. Lastman
title: Determination of Floating Point Characteristics for a Personal Computer
crossref: IEEE:1983:IEE
pages: 424--427
year: 1983
bibdate: Thu Sep 01 12:11:33 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 12:11:33 ???
acknowledgement: ack-nj
rawauthor: G. J. Lastman
rawtitle: Determination of Floating Point Characteristics for a Personal Computer
entry:
@InProceedings{Lastman:1983:DFP,
  author =       "G. J. Lastman",
  title =        "Determination of Floating Point Characteristics for a
                 Personal Computer",
  crossref =     "IEEE:1983:IEE",
  pages =        "424--427",
  year =         "1983",
  bibdate =      "Thu Sep 01 12:11:33 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: Linnainmaa:1983:ELE
author: Seppo Linnainmaa
journal: j-BIT
volume: 23
number: 3
pages: 346--359
month: sep
monthnumber: 9
year: 1983
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01934463
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
MRclass: 65G05 (65J05)
MRnumber: 85e:65020
bibdate: Wed Jan 4 18:52:18 MST 2006
bibtimestamp: 2006.01.04 18:52:18 MST
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=23&issue=3&spage=346
fjournal: BIT (Nordisk tidskrift for informationsbehandling)
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: Seppo Linnainmaa
title:
Error linearization as an effective tool for experimental analysis of the numerical stability of algorithms

bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=23&issue=3; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

rawtitle:
Error linearization as an effective tool for experimental analysis of the numerical stability of algorithms

entry:
@Article{Linnainmaa:1983:ELE,
  author =       "Seppo Linnainmaa",
  title =        "Error linearization as an effective tool for
                 experimental analysis of the numerical stability of
                 algorithms",
  journal =      j-BIT,
  volume =       "23",
  number =       "3",
  pages =        "346--359",
  month =        sep,
  year =         "1983",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01934463",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65G05 (65J05)",
  MRnumber =     "85e:65020",
  bibdate =      "Wed Jan 4 18:52:18 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=23&issue=3;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=23&issue=3&spage=346",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}


bibtype: article
filename: fparith.bib
label: Lozier:1983:UFP
author: Daniel W. Lozier
title: The use of floating-point and interval arithmetic in the computation of error bounds
journal: j-IEEE-TRANS-COMPUT
volume: C-32
number: 4
pages: 411--417
month: apr
monthnumber: 4
year: 1983
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1983.1676245
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
MRclass: 65G05
MRnumber: 85f:65042
bibdate: Sun Jul 10 10:01:08 MDT 2011
bibtimestamp: 2011.07.10 10:01:08 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676245
fjournal: IEEE Transactions on Computers
subject: G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
reviewer: N. N. Abdelmalek
rawauthor: Daniel W. Lozier
rawtitle: The use of floating-point and interval arithmetic in the computation of error bounds
bibsource:
ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib

abstract:
Three forms of interval floating-point arithmetic are defined in terms of absolute precision, relative precision, and combined absolute and relative precision. The absolute-precision form corresponds to the centered form of conventional rounded-interval arithmetic. The three forms are compared on the basis of the number of floating-point operations needed to generate error bounds for inner-product accumulation.

rawabstract:
Three forms of interval floating-point arithmetic are defined in terms of absolute precision, relative precision, and combined absolute and relative precision. The absolute-precision form corresponds to the centered form of conventional rounded-interval arithmetic. The three forms are compared on the basis of the number of floating-point operations needed to generate error bounds for inner-product accumulation.

entry:
@Article{Lozier:1983:UFP,
  author =       "Daniel W. Lozier",
  title =        "The use of floating-point and interval arithmetic in
                 the computation of error bounds",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "4",
  pages =        "411--417",
  month =        apr,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676245",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  MRclass =      "65G05",
  MRnumber =     "85f:65042",
  bibdate =      "Sun Jul 10 10:01:08 MDT 2011",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676245",
  abstract =     "Three forms of interval floating-point arithmetic are
                 defined in terms of absolute precision, relative
                 precision, and combined absolute and relative
                 precision. The absolute-precision form corresponds to
                 the centered form of conventional rounded-interval
                 arithmetic. The three forms are compared on the basis
                 of the number of floating-point operations needed to
                 generate error bounds for inner-product accumulation.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  catcode =      "G.1.0",
  CRclass =      "G.1.0 General; G.1.0 Error analysis",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Error analysis",
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  genterm =      "ALGORITHMS; PERFORMANCE",
  guideno =      "06575",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  reviewer =     "N. N. Abdelmalek",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}


bibtype: inproceedings
filename: fparith.bib
label: Majerski:1983:SRA
author: Stanislaw Majerski
title: Square-Root Algorithms for High-Speed Digital Circuits
crossref: IEEE:1983:PSC
pages: 99--102
year: 1983
bibdate: Tue Nov 13 15:58:57 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.13 15:58:57 ???
URL: http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Majerski.pdf
keywords: ARITH-6; square root
acknowledgement: ack-nhfb
rawauthor: Stanislaw Majerski
rawtitle: Square-Root Algorithms for High-Speed Digital Circuits
abstract:
Two binary algorithms for the square rooting of a sum of two numbers are presented. They are designed for high-speed digital circuits and are based on the classical nonrestoring method. The main difference lies in the replacement of subtractions and additions by the parallel reduction of three summands to two, their sum being unchanged to eliminate a carry propagation. The term ``parallel reduction'' is introduced here for the carry-save addition of three summands, positive and negative as well. The two result summands form a successive partial remainder. Their most significant three-bit groups are used to determine the ``digits'' $1$, $0$, $ + 1 $ of the square root in a redundant notation. These digits are transformed into the conventional-notation bits, which are used in the further steps of the square-rooting process

rawabstract:
Two binary algorithms for the square rooting of a sum of two numbers are presented. They are designed for high-speed digital circuits and are based on the classical nonrestoring method. The main difference lies in the replacement of subtractions and additions by the parallel reduction of three summands to two, their sum being unchanged to eliminate a carry propagation. The term ``parallel reduction'' is introduced here for the carry-save addition of three summands, positive and negative as well. The two result summands form a successive partial remainder. Their most significant three-bit groups are used to determine the ``digits'' $1$, $0$, $ + 1 $ of the square root in a redundant notation. These digits are transformed into the conventional-notation bits, which are used in the further steps of the square-rooting process

entry:
@InProceedings{Majerski:1983:SRA,
  author =       "Stanislaw Majerski",
  title =        "Square-Root Algorithms for High-Speed Digital
                 Circuits",
  crossref =     "IEEE:1983:PSC",
  pages =        "99--102",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Majerski.pdf",
  abstract =     "Two binary algorithms for the square rooting of a sum
                 of two numbers are presented. They are designed for
                 high-speed digital circuits and are based on the
                 classical nonrestoring method. The main difference lies
                 in the replacement of subtractions and additions by the
                 parallel reduction of three summands to two, their sum
                 being unchanged to eliminate a carry propagation. The
                 term ``parallel reduction'' is introduced here for the
                 carry-save addition of three summands, positive and
                 negative as well. The two result summands form a
                 successive partial remainder. Their most significant
                 three-bit groups are used to determine the ``digits''
                 $1$, $0$, $ + 1 $ of the square root in a redundant
                 notation. These digits are transformed into the
                 conventional-notation bits, which are used in the
                 further steps of the square-rooting process",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6; square root",
}


bibtype: article
filename: fparith.bib
label: Maric:1983:PBC
author: I. Maric and L. Cucancic
title: On the Possibilities of the BCD Code Application in the Floating-Point Arithmetic Algorithms
journal: j-INT-J-MINI-MICROCOMPUTERS
volume: 5
number: 2
pages: 19--22
year: 1983
CODEN: IJMMDE
ISSN: 0702-0481 OR 07020481
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: International Journal of Mini and Microcomputers
acknowledgement: ack-nj
rawauthor: I. Maric and L. Cucancic
rawtitle: On the Possibilities of the {BCD} Code Application in the Floating-Point Arithmetic Algorithms
entry:
@Article{Maric:1983:PBC,
  author =       "I. Maric and L. Cucancic",
  title =        "On the Possibilities of the {BCD} Code Application in
                 the Floating-Point Arithmetic Algorithms",
  journal =      j-INT-J-MINI-MICROCOMPUTERS,
  volume =       "5",
  number =       "2",
  pages =        "19--22",
  month =        "????",
  year =         "1983",
  CODEN =        "IJMMDE",
  ISSN =         "0702-0481",
  bibdate =      "Thu Sep 1 10:16:11 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "International Journal of Mini and Microcomputers",
}


bibtype: inproceedings
filename: fparith.bib
label: Markov:1983:NAF
author: Svetoslav Markov
title: On the Numerical Algorithms Formulated in Computer Arithmetic
crossref: IEEE:1983:PSC
pages: 82--85
year: 1983
bibdate: Tue Nov 13 15:58:57 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.13 15:58:57 ???
URL: http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Markov.pdf
keywords: ARITH-6
acknowledgement: ack-nhfb
rawauthor: Svetoslav Markov
rawtitle: On the Numerical Algorithms Formulated in Computer Arithmetic
abstract:
We discuss some mathematical tools and techniques supporting the construction of rigorous bounds producing, numerically convergent algorithms, which are formulated in terms of computer arithmetic operations. Two important computer-arithmetic effects are considered and their application as stopping criteria is illustrated.

rawabstract:
We discuss some mathematical tools and techniques supporting the construction of rigorous bounds producing, numerically convergent algorithms, which are formulated in terms of computer arithmetic operations. Two important computer-arithmetic effects are considered and their application as stopping criteria is illustrated.

entry:
@InProceedings{Markov:1983:NAF,
  author =       "Svetoslav Markov",
  title =        "On the Numerical Algorithms Formulated in Computer
                 Arithmetic",
  crossref =     "IEEE:1983:PSC",
  pages =        "82--85",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Markov.pdf",
  abstract =     "We discuss some mathematical tools and techniques
                 supporting the construction of rigorous bounds
                 producing, numerically convergent algorithms, which are
                 formulated in terms of computer arithmetic operations.
                 Two important computer-arithmetic effects are
                 considered and their application as stopping criteria
                 is illustrated.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6",
}


bibtype: inproceedings
filename: fparith.bib
label: Martin:1983:FPS
author: G. R. Martin
title: Floating Point Support for the NS16000 Family -- The NS16081
crossref: Mini-Micro:1983:MMW
pages: 16/3/1--3
year: 1983
bibdate: Wed Sep 07 22:33:22 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.07 22:33:22 ???
acknowledgement: ack-nj
rawauthor: G. R. Martin
rawtitle: Floating Point Support for the {NS16000} Family -- The {NS16081}
entry:
@InProceedings{Martin:1983:FPS,
  author =       "G. R. Martin",
  title =        "Floating Point Support for the {NS16000} Family -- The
                 {NS16081}",
  crossref =     "Mini-Micro:1983:MMW",
  pages =        "16/3/1--3",
  year =         "1983",
  bibdate =      "Wed Sep 07 22:33:22 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: inproceedings
filename: fparith.bib
label: Matula:1983:OPF
author: David W. Matula and Peter Kornerup
title: An Order Preserving Finite Binary Encoding of the Rationals
crossref: IEEE:1983:PSC
pages: 201--209
year: 1983
bibdate: Tue Nov 13 15:50:08 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.13 15:50:08 ???
URL: http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Matula_Kornerup.pdf
keywords: ARITH-6; lexicographic continued fraction (LCF); rational arithmetic
acknowledgement: ack-nhfb
rawauthor: David W. Matula and Peter Kornerup
rawtitle: An Order Preserving Finite Binary Encoding of the Rationals
abstract:
We describe a new binary encoding for numbers termed lexicographic continued fraction (LCF) representation that provides a one-to-one order preserving finite bit string representation for every rational. Conversion either way between binary integer numerator-denominator pair representation and LCF representation is shown feasible in time linear with bit string length, given registers of length sufficient to hold the numerator and denominator. LCF bit string length is about $ 2 max log _2 P, log _2 q $ for the irreducible fraction $ p / q $. Realization of arithmetic $ ( +, -, times , divide ) $ on LCF bit string encoded operands is shown feasible. Some relations between the theory of best rational approximation and the values represented by truncated LCF bit strings are noted to assess the feasibility of a finite precision arithmetic based on LCF representation.

rawabstract:
We describe a new binary encoding for numbers termed lexicographic continued fraction (LCF) representation that provides a one-to-one order preserving finite bit string representation for every rational. Conversion either way between binary integer numerator-denominator pair representation and LCF representation is shown feasible in time linear with bit string length, given registers of length sufficient to hold the numerator and denominator. LCF bit string length is about $ 2 \max \{ \log_2 P, \log_2 q \} $ for the irreducible fraction $ p / q $. Realization of arithmetic $ ( +, -, \times, \divide) $ on LCF bit string encoded operands is shown feasible. Some relations between the theory of best rational approximation and the values represented by truncated LCF bit strings are noted to assess the feasibility of a finite precision arithmetic based on LCF representation.

entry:
@InProceedings{Matula:1983:OPF,
  author =       "David W. Matula and Peter Kornerup",
  title =        "An Order Preserving Finite Binary Encoding of the
                 Rationals",
  crossref =     "IEEE:1983:PSC",
  pages =        "201--209",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:50:08 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Matula_Kornerup.pdf",
  abstract =     "We describe a new binary encoding for numbers termed
                 lexicographic continued fraction (LCF) representation
                 that provides a one-to-one order preserving finite bit
                 string representation for every rational. Conversion
                 either way between binary integer numerator-denominator
                 pair representation and LCF representation is shown
                 feasible in time linear with bit string length, given
                 registers of length sufficient to hold the numerator
                 and denominator. LCF bit string length is about $ 2
                 \max \{ \log_2 P, \log_2 q \} $ for the irreducible
                 fraction $ p / q $. Realization of arithmetic $ ( +, -,
                 \times, \divide) $ on LCF bit string encoded operands
                 is shown feasible. Some relations between the theory of
                 best rational approximation and the values represented
                 by truncated LCF bit strings are noted to assess the
                 feasibility of a finite precision arithmetic based on
                 LCF representation.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6; lexicographic continued fraction (LCF);
                 rational arithmetic",
}


bibtype: article
filename: fparith.bib
label: McCool:1983:NDC
author: Thomas E. McCool
title: 4. NSA's Defense Calculator, 1952--1953
journal: j-ANN-HIST-COMPUT
volume: 5
number: 2
pages: 186--187
month: apr
monthnumber: 4
year: 1983
CODEN: AHCOE5
ISSN: 0164-1239 OR 01641239
ISSNL: 0164-1239 OR 01641239
bibdate: Fri Nov 1 15:29:20 MST 2002
bibtimestamp: 2002.11.01 15:29:20 MST
fjournal: Annals of the History of Computing
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650
rawauthor: Thomas E. McCool
rawtitle: 4. {NSA}'s {Defense Calculator}, 1952--1953
URL:
http://dlib.computer.org/an/books/an1983/pdf/a2186.pdf; http://www.computer.org/annals/an1983/a2186abs.htm

entry:
@Article{McCool:1983:NDC,
  author =       "Thomas E. McCool",
  title =        "4. {NSA}'s {Defense Calculator}, 1952--1953",
  journal =      j-ANN-HIST-COMPUT,
  volume =       "5",
  number =       "2",
  pages =        "186--187",
  month =        apr # "\slash " # jun,
  year =         "1983",
  CODEN =        "AHCOE5",
  ISSN =         "0164-1239",
  ISSN-L =       "0164-1239",
  bibdate =      "Fri Nov 1 15:29:20 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://dlib.computer.org/an/books/an1983/pdf/a2186.pdf;
                 http://www.computer.org/annals/an1983/a2186abs.htm",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of the History of Computing",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650",
}


bibtype: article
filename: fparith.bib
label: McGuire:1983:PCB
author: D. W. McGuire
title: 8048 program computes 16-by-8-bit quotient
journal: j-ELECTRONICS
volume: 56
number: 10
pages: 152--153
month: may
monthnumber: 5
year: 1983
ISSN: 0883-4989 OR 08834989
bibdate: Thu Sep 1 10:15:08 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:15:08 ???
fjournal: Electronics
acknowledgement: ack-nj
journalURL: https://www.mdpi.com/journal/electronics
rawauthor: D. W. McGuire
rawtitle: 8048 program computes 16-by-8-bit quotient
entry:
@Article{McGuire:1983:PCB,
  author =       "D. W. McGuire",
  title =        "8048 program computes 16-by-8-bit quotient",
  journal =      j-ELECTRONICS,
  volume =       "56",
  number =       "10",
  pages =        "152--153",
  month =        may,
  year =         "1983",
  ISSN =         "0883-4989",
  bibdate =      "Thu Sep 1 10:15:08 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Electronics",
  journal-URL =  "https://www.mdpi.com/journal/electronics",
}


bibtype: techreport
filename: fparith.bib
label: Midttun:1983:FMP
author: G. Midttun
title: A fast micro-programmable floating point processor
type: Technical report
number: CERN DD 83-16
institution: CERT
address: Geneva, Switzerland
pages: 31
month: sep
monthnumber: 9
year: 1983
bibdate: Fri May 25 05:43:42 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.05.25 05:43:42 ???
URL: http://weblib.cern.ch/format/showfull?uid=1451323_18194&base=CERCER&sysnb=0058382
keywords: emulation; MICE; microcode; PDP11
acknowledgement: ack-nhfb
rawauthor: G. Midttun
rawtitle: A fast micro-programmable floating point processor
entry:
@TechReport{Midttun:1983:FMP,
  author =       "G. Midttun",
  title =        "A fast micro-programmable floating point processor",
  type =         "Technical report",
  number =       "CERN DD 83-16",
  institution =  "CERT",
  address =      "Geneva, Switzerland",
  pages =        "31",
  month =        sep,
  year =         "1983",
  bibdate =      "Fri May 25 05:43:42 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://weblib.cern.ch/format/showfull?uid=1451323_18194&base=CERCER&sysnb=0058382",
  acknowledgement = ack-nhfb,
  keywords =     "emulation; MICE; microcode; PDP11",
}


bibtype: article
filename: fparith.bib
label: Mikov:1983:PAFa
author: A. I. Mikov
title: Probabilistic analysis of floating-point addition (Russian)
journal: Kibernetika (Kiev)
volume: 3
pages: 87--93
year: 1983
MRclass: 60K99 (65G05)
MRnumber: 85h:60154
bibdate: Fri Dec 8 08:24:13 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 08:24:13 ???
note: English translation in cite Mikov:1983:PAFb.
language: Russian
acknowledgement: ack-nhfb
rawauthor: A. I. Mikov
rawnote: English translation in \cite{Mikov:1983:PAFb}.
rawtitle: Probabilistic analysis of floating-point addition ({Russian})
entry:
@Article{Mikov:1983:PAFa,
  author =       "A. I. Mikov",
  title =        "Probabilistic analysis of floating-point addition
                 ({Russian})",
  journal =      "Kibernetika (Kiev)",
  volume =       "3",
  pages =        "87--93",
  year =         "1983",
  MRclass =      "60K99 (65G05)",
  MRnumber =     "85h:60154",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "English translation in \cite{Mikov:1983:PAFb}.",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}


bibtype: article
filename: fparith.bib
label: Mikov:1983:PAFb
author: A. I. Mikov
title: Probabilistic analysis of floating-point addition
journal: j-CYBER
volume: 19
number: 3
pages: 401--410
month: may
monthnumber: 5
year: 1983
CODEN: CYBNAW
DOI: https://doi.org/10.1007/BF01072156
ISSN: 0011-4235 (print), 2375-0189 (electronic) OR 00114235 (print), 23750189 (electronic)
MRclass: 60K99 (65G05)
MRnumber: 85h:60154
bibdate: Fri Dec 8 08:24:13 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 08:24:13 ???
note: Translated from cite Mikov:1983:PAFa.
URL: http://link.springer.com/article/10.1007/BF01072156
fjournal: Cybernetics
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10559
rawauthor: A. I. Mikov
rawnote: Translated from \cite{Mikov:1983:PAFa}.
rawtitle: Probabilistic analysis of floating-point addition
entry:
@Article{Mikov:1983:PAFb,
  author =       "A. I. Mikov",
  title =        "Probabilistic analysis of floating-point addition",
  journal =      j-CYBER,
  volume =       "19",
  number =       "3",
  pages =        "401--410",
  month =        may,
  year =         "1983",
  CODEN =        "CYBNAW",
  DOI =          "https://doi.org/10.1007/BF01072156",
  ISSN =         "0011-4235 (print), 2375-0189 (electronic)",
  MRclass =      "60K99 (65G05)",
  MRnumber =     "85h:60154",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Translated from \cite{Mikov:1983:PAFa}.",
  URL =          "http://link.springer.com/article/10.1007/BF01072156",
  acknowledgement = ack-nhfb,
  fjournal =     "Cybernetics",
  journal-URL =  "http://link.springer.com/journal/10559",
}


bibtype: article
filename: fparith.bib
label: Miller:1983:RNS
author: D. D. Miller and J. N. Polky
title: A Residue Number System Implementation of the LMS Algorithm Using Optical Waveguide Circuits
journal: j-IEEE-TRANS-COMPUT
volume: C-32
number: 11
pages: 1013--1028
month: nov
monthnumber: 11
year: 1983
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1983.1676152
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 10:01:12 MDT 2011
bibtimestamp: 2011.07.10 10:01:12 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: D. D. Miller and J. N. Polky
rawtitle: A Residue Number System Implementation of the {LMS} Algorithm Using Optical Waveguide Circuits
URL:
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676152; http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12; http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35222

entry:
@Article{Miller:1983:RNS,
  author =       "D. D. Miller and J. N. Polky",
  title =        "A Residue Number System Implementation of the {LMS}
                 Algorithm Using Optical Waveguide Circuits",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "11",
  pages =        "1013--1028",
  month =        nov,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676152",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:01:12 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676152;
                 http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35222",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A detailed design of a real-time data processor based
                 on the residue number system is presented which uses
                 near-term optical waveguide devices and concepts. The
                 optical computational units consist of cascaded,
                 mask-programmable arrays of total \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Miola:1983:UVA
author: A. Miola
title: A Unified View of Approximate Rational Arithmetic and Rational Interpolation
crossref: IEEE:1983:PSC
pages: 210--215
year: 1983
bibdate: Tue Nov 13 15:58:57 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.13 15:58:57 ???
URL: http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Miola.pdf
keywords: ARITH-6; rational arithmetic; rational interpolation
acknowledgement: ack-nhfb
rawauthor: A. Miola
rawtitle: A Unified View of Approximate Rational Arithmetic and Rational Interpolation
abstract:
In this paper we cover the problem of approximation of numbers and of functions by presenting some well known results in a unified view that could help in better understanding the algebraic bases of the problem. In fact, the Extended Euclid's algorithm happens to be the unique and common tool solving the approximation problems both for numbers and for functions.

rawabstract:
In this paper we cover the problem of approximation of numbers and of functions by presenting some well known results in a unified view that could help in better understanding the algebraic bases of the problem. In fact, the Extended Euclid's algorithm happens to be the unique and common tool solving the approximation problems both for numbers and for functions.

entry:
@InProceedings{Miola:1983:UVA,
  author =       "A. Miola",
  title =        "A Unified View of Approximate Rational Arithmetic and
                 Rational Interpolation",
  crossref =     "IEEE:1983:PSC",
  pages =        "210--215",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Miola.pdf",
  abstract =     "In this paper we cover the problem of approximation of
                 numbers and of functions by presenting some well known
                 results in a unified view that could help in better
                 understanding the algebraic bases of the problem. In
                 fact, the Extended Euclid's algorithm happens to be the
                 unique and common tool solving the approximation
                 problems both for numbers and for functions.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6; rational arithmetic; rational interpolation",
}


bibtype: article
filename: fparith.bib
label: Moler:1983:RSR
author: Cleve B. Moler and Donald Morrison
title: Replacing Square Roots by Pythagorean Sums
journal: j-IBM-JRD
volume: 27
number: 6
pages: 577--581
month: nov
monthnumber: 11
year: 1983
CODEN: IBMJAE
ISSN: 0018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)
ISSNL: 0018-8646 OR 00188646
bibdate: Thu Sep 1 10:15:41 1994
bibtimestamp: 1994.09.01 10:15:41 ???
note: See cite Dubrulle:1983:CNM and generalization cite Jamieson:1989:SNR.
URL: http://www.research.ibm.com/journal/rd/276/ibmrd2706P.pdf
fjournal: IBM Journal of Research and Development
acknowledgement: ack-nj
classcodes: C4190 (Other numerical methods); C5230 (Digital arithmetic methods)
corpsource: Department of Computer Sci., University of New Mexico, Albuquerque, NM, USA
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520
treatment: T Theoretical or Mathematical
rawauthor: Cleve B. Moler and Donald Morrison
rawnote: See \cite{Dubrulle:1983:CNM} and generalization \cite{Jamieson:1989:SNR}.
rawtitle: Replacing Square Roots by {Pythagorean} Sums
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
An algorithm is presented for computing a 'Pythagorean sum' a(+)b= square root a/sup 2/+b/sup 2/ directly from a and b without computing their squares or taking a square root. No destructive floating point overflows or underflows are possible. The algorithm can be extended to compute the Euclidean norm of a vector. The resulting subroutine is short, portable, robust, and accurate, but not as efficient as some other possibilities. The algorithm is particularly attractive for computers where space and reliability are more important than speed

keywords:
algorithms; digital arithmetic; Euclidean norm; floating-point arithmetic; iterative methods; performance; Pythagorean sums; subroutine; vector

subject:
G.1 Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations F.2.1 Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials F.2.2 Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Geometrical problems and computations

rawabstract:
An algorithm is presented for computing a 'Pythagorean sum' a(+)b= square root a/sup 2/+b/sup 2/ directly from a and b without computing their squares or taking a square root. No destructive floating point overflows or underflows are possible. The algorithm can be extended to compute the Euclidean norm of a vector. The resulting subroutine is short, portable, robust, and accurate, but not as efficient as some other possibilities. The algorithm is particularly attractive for computers where space and reliability are more important than speed

entry:
@Article{Moler:1983:RSR,
  author =       "Cleve B. Moler and Donald Morrison",
  title =        "Replacing Square Roots by {Pythagorean} Sums",
  journal =      j-IBM-JRD,
  volume =       "27",
  number =       "6",
  pages =        "577--581",
  month =        nov,
  year =         "1983",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Thu Sep 1 10:15:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Dubrulle:1983:CNM} and generalization
                 \cite{Jamieson:1989:SNR}.",
  URL =          "http://www.research.ibm.com/journal/rd/276/ibmrd2706P.pdf",
  abstract =     "An algorithm is presented for computing a 'Pythagorean
                 sum' a(+)b= square root a/sup 2/+b/sup 2/ directly from
                 a and b without computing their squares or taking a
                 square root. No destructive floating point overflows or
                 underflows are possible. The algorithm can be extended
                 to compute the Euclidean norm of a vector. The
                 resulting subroutine is short, portable, robust, and
                 accurate, but not as efficient as some other
                 possibilities. The algorithm is particularly attractive
                 for computers where space and reliability are more
                 important than speed",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  classcodes =   "C4190 (Other numerical methods); C5230 (Digital
                 arithmetic methods)",
  corpsource =   "Department of Computer Sci., University of New Mexico,
                 Albuquerque, NM, USA",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  keywords =     "algorithms; digital arithmetic; Euclidean norm;
                 floating-point arithmetic; iterative methods;
                 performance; Pythagorean sums; subroutine; vector",
  review =       "ACM CR 8406-0463",
  subject =      "G.1 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Roots of Nonlinear Equations \\ F.2.1 Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials \\ F.2.2 Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Nonnumerical Algorithms and Problems,
                 Geometrical problems and computations",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: fparith.bib
label: Moran:1983:BRB
author: Bruce T. Moran
journal: j-ISIS
volume: 74
number: 3
pages: 448--449
month: sep
monthnumber: 9
year: 1983
CODEN: ISISA4
ISSN: 0021-1753 (print), 1545-6994 (electronic) OR 00211753 (print), 15456994 (electronic)
ISSNL: 0021-1753 OR 00211753
bibdate: Tue Jul 30 21:22:47 MDT 2013
bibtimestamp: 2013.07.30 21:22:47 MDT
URL: http://www.jstor.org/stable/232640
fjournal: Isis
acknowledgement: ack-nhfb
journalURL: http://www.jstor.org/journal/isis
rawauthor: Bruce T. Moran
title:
Book Review: booktitle Wissenschaftsgeschichte um Wilhelm Schickard: Vortrage bei dem Symposion der Universitat Tubingen im 500 Jahr ihres Bestehens am 24. und 25. Juni 1977 by Friedrich Seck

bibsource:
http://www.jstor.org/action/showPublication?journalCode=isis; http://www.jstor.org/stable/i211164; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/isis1980.bib

rawtitle:
Book Review: {{\booktitle{Wissenschaftsgeschichte um Wilhelm Schickard: Vortr{\"a}ge bei dem Symposion der Universitat T{\"u}bingen im 500 Jahr ihres Bestehens am 24. und 25. Juni 1977}} by Friedrich Seck}

entry:
@Article{Moran:1983:BRB,
  author =       "Bruce T. Moran",
  title =        "Book Review: {{\booktitle{Wissenschaftsgeschichte um
                 Wilhelm Schickard: Vortr{\"a}ge bei dem Symposion der
                 Universitat T{\"u}bingen im 500 Jahr ihres Bestehens am
                 24. und 25. Juni 1977}} by Friedrich Seck}",
  journal =      j-ISIS,
  volume =       "74",
  number =       "3",
  pages =        "448--449",
  month =        sep,
  year =         "1983",
  CODEN =        "ISISA4",
  ISSN =         "0021-1753 (print), 1545-6994 (electronic)",
  ISSN-L =       "0021-1753",
  bibdate =      "Tue Jul 30 21:22:47 MDT 2013",
  bibsource =    "http://www.jstor.org/action/showPublication?journalCode=isis;
                 http://www.jstor.org/stable/i211164;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/isis1980.bib",
  URL =          "http://www.jstor.org/stable/232640",
  acknowledgement = ack-nhfb,
  fjournal =     "Isis",
  journal-URL =  "http://www.jstor.org/journal/isis",
}


bibtype: inproceedings
filename: fparith.bib
label: Morrison:1983:EHL
author: R. Morrison and A. J. Cole and P. J. Bailey and M. A. Wolfe and M. Shearer
title: Experience with a High Level Language that Supports Interval Arithmetic
crossref: IEEE:1983:PSC
pages: 74--78
year: 1983
bibdate: Tue Nov 13 15:58:57 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.13 15:58:57 ???
URL: http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Morrison_Cole_Bailey_Wolfe_Shearer.pdf
keywords: Algol 60; ARITH-6; interval arithmetic; S-Algol; Triplex (Algol)
acknowledgement: ack-nhfb
rawauthor: R. Morrison and A. J. Cole and P. J. Bailey and M. A. Wolfe and M. Shearer
rawtitle: Experience with a High Level Language that Supports Interval Arithmetic
abstract:
An extension of the language S-algol called Triplex which facilitates the use of interval arithmetic and which is similar to triplex algol 60 is described. Experience in the use of Triplex is reported. In particular, a Triplex program corresponding to a triplex algol 60 program of Nickel is given, together with numerical results.

rawabstract:
An extension of the language S-algol called Triplex which facilitates the use of interval arithmetic and which is similar to triplex algol 60 is described. Experience in the use of Triplex is reported. In particular, a Triplex program corresponding to a triplex algol 60 program of Nickel is given, together with numerical results.

entry:
@InProceedings{Morrison:1983:EHL,
  author =       "R. Morrison and A. J. Cole and P. J. Bailey and M. A.
                 Wolfe and M. Shearer",
  title =        "Experience with a High Level Language that Supports
                 Interval Arithmetic",
  crossref =     "IEEE:1983:PSC",
  pages =        "74--78",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Morrison_Cole_Bailey_Wolfe_Shearer.pdf",
  abstract =     "An extension of the language S-algol called Triplex
                 which facilitates the use of interval arithmetic and
                 which is similar to triplex algol 60 is described.
                 Experience in the use of Triplex is reported. In
                 particular, a Triplex program corresponding to a
                 triplex algol 60 program of Nickel is given, together
                 with numerical results.",
  acknowledgement = ack-nhfb,
  keywords =     "Algol 60; ARITH-6; interval arithmetic; S-Algol;
                 Triplex (Algol)",
}


bibtype: article
filename: fparith.bib
label: Murugesan:1983:ACF
author: S. Murugesan and V. K. Agrawal
title: Algorithm converts fractions to BCD
journal: j-EDN
volume: 28
number: 19
pages: 245--246
month: sep
monthnumber: 9
year: 1983
CODEN: EDNSBH
ISSN: 0012-7515, 0364-6637 OR 00127515, 03646637
bibdate: Thu Sep 1 10:16:10 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:16:10 ???
fjournal: EDN
acknowledgement: ack-nj
rawauthor: S. Murugesan and V. K. Agrawal
rawtitle: Algorithm converts fractions to {BCD}
entry:
@Article{Murugesan:1983:ACF,
  author =       "S. Murugesan and V. K. Agrawal",
  title =        "Algorithm converts fractions to {BCD}",
  journal =      j-EDN,
  volume =       "28",
  number =       "19",
  pages =        "245--246",
  month =        sep,
  year =         "1983",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  bibdate =      "Thu Sep 1 10:16:10 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "EDN",
}


bibtype: article
filename: fparith.bib
label: Nagpal:1983:PAT
author: H. K. Nagpal and G. A. Jullien and W. C. Miller
journal: j-IEEE-TRANS-COMPUT
volume: C-32
number: 11
pages: 989--1001
month: nov
monthnumber: 11
year: 1983
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1983.1676150
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 10:01:12 MDT 2011
bibtimestamp: 2011.07.10 10:01:12 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676150
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: H. K. Nagpal and G. A. Jullien and W. C. Miller
title:
Processor Architectures for Two-Dimensional Convolvers Using a Single Multiplexed Computational Element with Finite Field Arithmetic

rawtitle:
Processor Architectures for Two-Dimensional Convolvers Using a Single Multiplexed Computational Element with Finite Field Arithmetic

entry:
@Article{Nagpal:1983:PAT,
  author =       "H. K. Nagpal and G. A. Jullien and W. C. Miller",
  title =        "Processor Architectures for Two-Dimensional Convolvers
                 Using a Single Multiplexed Computational Element with
                 Finite Field Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "11",
  pages =        "989--1001",
  month =        nov,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676150",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:01:12 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676150",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Nave:1983:ITF
author: R. Nave
title: Implementation of Transcendental Functions on a Numerics Processor
journal: j-MICROPROC-MICROPROG
volume: 11
number: 3--4
pages: 221--225
month: mar
monthnumber: 3
year: 1983
CODEN: MMICDT
ISSN: 0165-6074 (print), 1878-7061 (electronic) OR 01656074 (print), 18787061 (electronic)
ISSNL: 0165-6074 OR 01656074
bibdate: Fri Dec 08 13:05:28 1995
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 13:05:28 ???
fjournal: Microprocessing and Microprogramming
acknowledgement: ack-nj
rawauthor: R. Nave
rawtitle: Implementation of Transcendental Functions on a Numerics Processor
entry:
@Article{Nave:1983:ITF,
  author =       "R. Nave",
  title =        "Implementation of Transcendental Functions on a
                 Numerics Processor",
  journal =      j-MICROPROC-MICROPROG,
  volume =       "11",
  number =       "3--4",
  pages =        "221--225",
  month =        mar # "--" # apr,
  year =         "1983",
  CODEN =        "MMICDT",
  ISSN =         "0165-6074 (print), 1878-7061 (electronic)",
  ISSN-L =       "0165-6074",
  bibdate =      "Fri Dec 08 13:05:28 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Microprocessing and Microprogramming",
}


bibtype: inproceedings
filename: fparith.bib
label: Ni:1983:VRM
author: Lionel M. Ni and Kai Hwang
title: Vector Reduction Methods for Arithmetic Pipelines
crossref: IEEE:1983:PSC
pages: 144--150
year: 1983
bibdate: Tue Nov 13 15:58:57 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.13 15:58:57 ???
URL: http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Ni_Hwang.pdf
keywords: ARITH-6
acknowledgement: ack-nhfb
rawauthor: Lionel M. Ni and Kai Hwang
rawtitle: Vector Reduction Methods for Arithmetic Pipelines
abstract:
Vector reduction arithmetic accepts a vector as input and produces a scalar output. This class of vector operations forms the basis of many scientific computations. In a pipelined processor, a feedback loop is required to reduce vectors. Since the output of the pipeline depends on previous outputs, improper control of the feedback loop will destroy the benefit from pipelining. A generalized computing model is proposed to schedule the activities in a vector reduction pipeline. Two new vector reduction methods, symmetric and asymmetric, are proposed and analyzed for pipelined processing. These two methods compare favorably with the known recursive reduction method in achieving higher pipeline utilization and in eliminating large memory for intermediate results. An interleaving method is proposed to reduce multiple vectors to multiple scalars in a single arithmetic pipeline. The pipeline can be fully utilized by interleaved multiple vector processing.

rawabstract:
Vector reduction arithmetic accepts a vector as input and produces a scalar output. This class of vector operations forms the basis of many scientific computations. In a pipelined processor, a feedback loop is required to reduce vectors. Since the output of the pipeline depends on previous outputs, improper control of the feedback loop will destroy the benefit from pipelining. A generalized computing model is proposed to schedule the activities in a vector reduction pipeline. Two new vector reduction methods, symmetric and asymmetric, are proposed and analyzed for pipelined processing. These two methods compare favorably with the known recursive reduction method in achieving higher pipeline utilization and in eliminating large memory for intermediate results. An interleaving method is proposed to reduce multiple vectors to multiple scalars in a single arithmetic pipeline. The pipeline can be fully utilized by interleaved multiple vector processing.

entry:
@InProceedings{Ni:1983:VRM,
  author =       "Lionel M. Ni and Kai Hwang",
  title =        "Vector Reduction Methods for Arithmetic Pipelines",
  crossref =     "IEEE:1983:PSC",
  pages =        "144--150",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Ni_Hwang.pdf",
  abstract =     "Vector reduction arithmetic accepts a vector as input
                 and produces a scalar output. This class of vector
                 operations forms the basis of many scientific
                 computations. In a pipelined processor, a feedback loop
                 is required to reduce vectors. Since the output of the
                 pipeline depends on previous outputs, improper control
                 of the feedback loop will destroy the benefit from
                 pipelining. A generalized computing model is proposed
                 to schedule the activities in a vector reduction
                 pipeline. Two new vector reduction methods, symmetric
                 and asymmetric, are proposed and analyzed for pipelined
                 processing. These two methods compare favorably with
                 the known recursive reduction method in achieving
                 higher pipeline utilization and in eliminating large
                 memory for intermediate results. An interleaving method
                 is proposed to reduce multiple vectors to multiple
                 scalars in a single arithmetic pipeline. The pipeline
                 can be fully utilized by interleaved multiple vector
                 processing.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6",
}


bibtype: inproceedings
filename: fparith.bib
label: Ohlsson:1983:MML
author: Lennart Ohlsson and Bertil Svensson
title: Matrix Multiplication on LUCAS
crossref: IEEE:1983:PSC
pages: 116--122
year: 1983
bibdate: Tue Nov 13 15:58:57 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.13 15:58:57 ???
URL: http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Ohlsson_Svensson.pdf
keywords: ARITH-6; LUCAS (Lund University Content Addressable System)
acknowledgement: ack-nhfb
rawauthor: Lennart Ohlsson and Bertil Svensson
rawtitle: Matrix Multiplication on {LUCAS}
abstract:
Multiplication of two $N$ by $N$ matrices involves $ N^3 $ multiplications of elements. The task allows a large amount of parallelism to be utilized, indicating that it can be efficiently executed on a parallel computer. This paper describes how matrix multiplication is performed on LUCAS, an SIMD type parallel processor with bit-serial processing elements. The interconnection network is of Perfect Shuffle / Exchange type. The case of study is when the number of processing elements is between $ N^2 $ and $ N^3 $. The algorithm presented can be applied to any computer with the same interconnection structure. Formulas showing how the execution time depends on data length and matrix size are presented together with measured values from execution on LUCAS.

rawabstract:
Multiplication of two $N$ by $N$ matrices involves $ N^3 $ multiplications of elements. The task allows a large amount of parallelism to be utilized, indicating that it can be efficiently executed on a parallel computer. This paper describes how matrix multiplication is performed on LUCAS, an SIMD type parallel processor with bit-serial processing elements. The interconnection network is of Perfect Shuffle\slash Exchange type. The case of study is when the number of processing elements is between $ N^2 $ and $ N^3 $. The algorithm presented can be applied to any computer with the same interconnection structure. Formulas showing how the execution time depends on data length and matrix size are presented together with measured values from execution on LUCAS.

entry:
@InProceedings{Ohlsson:1983:MML,
  author =       "Lennart Ohlsson and Bertil Svensson",
  title =        "Matrix Multiplication on {LUCAS}",
  crossref =     "IEEE:1983:PSC",
  pages =        "116--122",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Ohlsson_Svensson.pdf",
  abstract =     "Multiplication of two $N$ by $N$ matrices involves $
                 N^3 $ multiplications of elements. The task allows a
                 large amount of parallelism to be utilized, indicating
                 that it can be efficiently executed on a parallel
                 computer. This paper describes how matrix
                 multiplication is performed on LUCAS, an SIMD type
                 parallel processor with bit-serial processing elements.
                 The interconnection network is of Perfect Shuffle\slash
                 Exchange type. The case of study is when the number of
                 processing elements is between $ N^2 $ and $ N^3 $. The
                 algorithm presented can be applied to any computer with
                 the same interconnection structure. Formulas showing
                 how the execution time depends on data length and
                 matrix size are presented together with measured values
                 from execution on LUCAS.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6; LUCAS (Lund University Content Addressable
                 System)",
}


bibtype: inproceedings
filename: fparith.bib
label: Ong:1983:CAS
author: Shauchi Ong and D. E. Atkins
title: A Comparison of ALU Structures for VLSI Technology
crossref: IEEE:1983:PSC
pages: 10--16
year: 1983
bibdate: Tue Nov 13 15:58:57 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.13 15:58:57 ???
URL: http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Ong_Atkins.pdf
keywords: ARITH-6
acknowledgement: ack-nhfb
rawauthor: Shauchi Ong and D. E. Atkins
rawtitle: A Comparison of {ALU} Structures for {VLSI} Technology
abstract:
Although many of the basic techniques of computer arithmetic have been known since the earliest days of electronic computing, there is a continuing need to re-evaluate them in the context of developments in VLSI circuit technology. Furthermore, recent work in complexity of algorithms, particularly the solution of recurrence relations, suggests new candidate structures for generating the carry vector and raises the questions as to their practicality in modern logic design practice.

rawabstract:
Although many of the basic techniques of computer arithmetic have been known since the earliest days of electronic computing, there is a continuing need to re-evaluate them in the context of developments in VLSI circuit technology. Furthermore, recent work in complexity of algorithms, particularly the solution of recurrence relations, suggests new candidate structures for generating the carry vector and raises the questions as to their practicality in modern logic design practice.

entry:
@InProceedings{Ong:1983:CAS,
  author =       "Shauchi Ong and D. E. Atkins",
  title =        "A Comparison of {ALU} Structures for {VLSI}
                 Technology",
  crossref =     "IEEE:1983:PSC",
  pages =        "10--16",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Ong_Atkins.pdf",
  abstract =     "Although many of the basic techniques of computer
                 arithmetic have been known since the earliest days of
                 electronic computing, there is a continuing need to
                 re-evaluate them in the context of developments in VLSI
                 circuit technology. Furthermore, recent work in
                 complexity of algorithms, particularly the solution of
                 recurrence relations, suggests new candidate structures
                 for generating the carry vector and raises the
                 questions as to their practicality in modern logic
                 design practice.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6",
}


bibtype: article
filename: fparith.bib
label: Owens:1983:TRI
author: R. M. Owens
title: Techniques to Reduce the Inherent Limitations of Fully Digit On-Line Arithmetic
journal: j-IEEE-TRANS-COMPUT
volume: C-32
number: 4
pages: 406--411
month: apr
monthnumber: 4
year: 1983
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1983.1676244
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 10:01:08 MDT 2011
bibtimestamp: 2011.07.10 10:01:08 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676244
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: R. M. Owens
rawtitle: Techniques to Reduce the Inherent Limitations of Fully Digit On-Line Arithmetic
entry:
@Article{Owens:1983:TRI,
  author =       "R. M. Owens",
  title =        "Techniques to Reduce the Inherent Limitations of Fully
                 Digit On-Line Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "4",
  pages =        "406--411",
  month =        apr,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676244",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:01:08 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676244",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Ozawa:1983:AIK
author: K. Ozawa
title: Analysis and Improvement of Kahan's Summation Algorithm
journal: j-INFO-PROC
volume: 6
number: 4
pages: 226--230
year: 1983
bibdate: Mon Sep 12 08:06:17 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.12 08:06:17 ???
keywords: accurate floating-point summation
acknowledgement: ack-nj
rawauthor: K. Ozawa
rawtitle: Analysis and Improvement of {Kahan}'s Summation Algorithm
entry:
@Article{Ozawa:1983:AIK,
  author =       "K. Ozawa",
  title =        "Analysis and Improvement of {Kahan}'s Summation
                 Algorithm",
  journal =      j-INFO-PROC,
  volume =       "6",
  number =       "4",
  pages =        "226--230",
  year =         "1983",
  bibdate =      "Mon Sep 12 08:06:17 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  keywords =     "accurate floating-point summation",
}


bibtype: inproceedings
filename: fparith.bib
label: Palmer:1983:VSN
author: J. F. Palmer
title: VLSI starts a numeric revolution
crossref: IEEE:1983:PII
pages: 186--189
year: 1983
bibdate: Wed Sep 7 22:31:27 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.07 22:31:27 ???
acknowledgement: ack-nj
rawauthor: J. F. Palmer
rawtitle: {VLSI} starts a numeric revolution
entry:
@InProceedings{Palmer:1983:VSN,
  author =       "J. F. Palmer",
  title =        "{VLSI} starts a numeric revolution",
  crossref =     "IEEE:1983:PII",
  pages =        "186--189",
  year =         "1983",
  bibdate =      "Wed Sep 7 22:31:27 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: Pan:1983:ALC
author: V. Ya Pan
title: The additive and logical complexities of linear and bilinear arithmetic algorithms
journal: j-J-ALG
volume: 4
number: 1
pages: 1--34
month: mar
monthnumber: 3
year: 1983
CODEN: JOALDV
DOI: https://doi.org/10.1016/0196-6774(83)90031-7
ISSN: 0196-6774 (print), 1090-2678 (electronic) OR 01966774 (print), 10902678 (electronic)
ISSNL: 0196-6774 OR 01966774
bibdate: Tue Dec 11 09:14:02 MST 2012
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/jalg.bib
bibtimestamp: 2012.12.11 09:14:02 MST
URL: http://www.sciencedirect.com/science/article/pii/0196677483900317
fjournal: Journal of Algorithms
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01966774
rawauthor: V. Ya Pan
rawtitle: The additive and logical complexities of linear and bilinear arithmetic algorithms
entry:
@Article{Pan:1983:ALC,
  author =       "V. Ya Pan",
  title =        "The additive and logical complexities of linear and
                 bilinear arithmetic algorithms",
  journal =      j-J-ALG,
  volume =       "4",
  number =       "1",
  pages =        "1--34",
  month =        mar,
  year =         "1983",
  CODEN =        "JOALDV",
  DOI =          "https://doi.org/10.1016/0196-6774(83)90031-7",
  ISSN =         "0196-6774 (print), 1090-2678 (electronic)",
  ISSN-L =       "0196-6774",
  bibdate =      "Tue Dec 11 09:14:02 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jalg.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0196677483900317",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Algorithms",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01966774",
}


bibtype: article
filename: fparith.bib
label: Patel:1983:CED
author: J. H. Patel and L. Y. Fung
title: Concurrent Error Detection in Multiply and Divide Arrays
journal: j-IEEE-TRANS-COMPUT
volume: C-32
number: 4
pages: 417--422
month: apr
monthnumber: 4
year: 1983
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1983.1676246
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 10:01:08 MDT 2011
bibtimestamp: 2011.07.10 10:01:08 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676246
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: J. H. Patel and L. Y. Fung
rawtitle: Concurrent Error Detection in Multiply and Divide Arrays
entry:
@Article{Patel:1983:CED,
  author =       "J. H. Patel and L. Y. Fung",
  title =        "Concurrent Error Detection in Multiply and Divide
                 Arrays",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "4",
  pages =        "417--422",
  month =        apr,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676246",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:01:08 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676246",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Payne:1983:DRT
author: M. H. Payne and R. N. Hanek
title: Degree Reduction for Trigonometric Functions
journal: j-SIGNUM
volume: 18
number: 2
pages: 18--19
month: apr
monthnumber: 4
year: 1983
CODEN: SNEWD6
DOI: https://doi.org/10.1145/1057605.1057606
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Thu Sep 1 10:15:56 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:15:56 ???
fjournal: ACM SIGNUM Newsletter
keywords: range reduction
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/signum
rawauthor: M. H. Payne and R. N. Hanek
rawtitle: Degree Reduction for Trigonometric Functions
abstract:
This report is a companion to Reference 1 on radian reduction. As in Reference 1 cite Payne:1983:RRT, the motivation arises from a desire to eliminate messages like ``argument too large'' in trigonometric function routines. The presence of very large arguments in the VAX H format, on the Cray 1, and on an IEEE machine with extended registers, make this a real problem. As for the radian reduction algorithm, the degree algorithm will reduce any argument, however large, so long as it is representable; its speed is nearly independent of the size of the argument to be reduced; and full accuracy is maintained in the neighborhoods of the zeros of the desired function. We believe that the approach is new and represents a significant improvement over procedures currently in use. A variant of the procedure is used in Version 3 of the VAX Math Library.

rawabstract:
This report is a companion to Reference 1 on radian reduction. As in Reference 1 \cite{Payne:1983:RRT}, the motivation arises from a desire to eliminate messages like ``argument too large'' in trigonometric function routines. The presence of very large arguments in the VAX H format, on the Cray 1, and on an IEEE machine with extended registers, make this a real problem. As for the radian reduction algorithm, the degree algorithm will reduce any argument, however large, so long as it is representable; its speed is nearly independent of the size of the argument to be reduced; and full accuracy is maintained in the neighborhoods of the zeros of the desired function. We believe that the approach is new and represents a significant improvement over procedures currently in use. A variant of the procedure is used in Version 3 of the VAX Math Library.

entry:
@Article{Payne:1983:DRT,
  author =       "M. H. Payne and R. N. Hanek",
  title =        "Degree Reduction for Trigonometric Functions",
  journal =      j-SIGNUM,
  volume =       "18",
  number =       "2",
  pages =        "18--19",
  month =        apr,
  year =         "1983",
  CODEN =        "SNEWD6",
  DOI =          "https://doi.org/10.1145/1057605.1057606",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Thu Sep 1 10:15:56 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This report is a companion to Reference 1 on radian
                 reduction. As in Reference 1 \cite{Payne:1983:RRT}, the
                 motivation arises from a desire to eliminate messages
                 like ``argument too large'' in trigonometric function
                 routines. The presence of very large arguments in the
                 VAX H format, on the Cray 1, and on an IEEE machine
                 with extended registers, make this a real problem. As
                 for the radian reduction algorithm, the degree
                 algorithm will reduce any argument, however large, so
                 long as it is representable; its speed is nearly
                 independent of the size of the argument to be reduced;
                 and full accuracy is maintained in the neighborhoods of
                 the zeros of the desired function. We believe that the
                 approach is new and represents a significant
                 improvement over procedures currently in use. A variant
                 of the procedure is used in Version 3 of the VAX Math
                 Library.",
  acknowledgement = ack-nj,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "range reduction",
}


bibtype: article
filename: fparith.bib
label: Payne:1983:RRT
author: M. H. Payne and R. N. Hanek
title: Radian Reduction for Trigonometric Functions
journal: j-SIGNUM
volume: 18
number: 1
pages: 19--24
month: jan
monthnumber: 1
year: 1983
CODEN: SNEWD6
DOI: https://doi.org/10.1145/1057600.1057602
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Thu Sep 1 10:15:56 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:15:56 ???
fjournal: ACM SIGNUM Newsletter
keywords: correct rounding; floating-point arithmetic; range reduction
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/signum
rawauthor: M. H. Payne and R. N. Hanek
rawtitle: Radian Reduction for Trigonometric Functions
abstract:
An accurate reduction poses little difficulty for arguments of a few radians. However for, say, a CRAY 1, H format on the VAX, or double extended in the proposed IEEE standard, the maximum argument which might be presented for reduction is of the order of $ 2^16000 $ radians. Accurate reduction of such an argument would require storage of $ pi $ (or its reciprocal) to over 16,000 bits. Direct reduction by division (or multiplication) then requires generation of a somewhat larger number of bits in the result in order to guarantee the accuracy of the reduction. Of these bits only the low few bits of the integer part of the quotient (product) and enough bits to correctly round the remainder are relevant; the rest will be discarded.

rawabstract:
An accurate reduction poses little difficulty for arguments of a few radians. However for, say, a CRAY 1, H format on the VAX, or double extended in the proposed IEEE standard, the maximum argument which might be presented for reduction is of the order of $ 2^{16000} $ radians. Accurate reduction of such an argument would require storage of $ \pi $ (or its reciprocal) to over 16,000 bits. Direct reduction by division (or multiplication) then requires generation of a somewhat larger number of bits in the result in order to guarantee the accuracy of the reduction. Of these bits only the low few bits of the integer part of the quotient (product) and enough bits to correctly round the remainder are relevant; the rest will be discarded.

entry:
@Article{Payne:1983:RRT,
  author =       "M. H. Payne and R. N. Hanek",
  title =        "Radian Reduction for Trigonometric Functions",
  journal =      j-SIGNUM,
  volume =       "18",
  number =       "1",
  pages =        "19--24",
  month =        jan,
  year =         "1983",
  CODEN =        "SNEWD6",
  DOI =          "https://doi.org/10.1145/1057600.1057602",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Thu Sep 1 10:15:56 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "An accurate reduction poses little difficulty for
                 arguments of a few radians. However for, say, a CRAY 1,
                 H format on the VAX, or double extended in the proposed
                 IEEE standard, the maximum argument which might be
                 presented for reduction is of the order of $ 2^{16000}
                 $ radians. Accurate reduction of such an argument would
                 require storage of $ \pi $ (or its reciprocal) to over
                 16,000 bits. Direct reduction by division (or
                 multiplication) then requires generation of a somewhat
                 larger number of bits in the result in order to
                 guarantee the accuracy of the reduction. Of these bits
                 only the low few bits of the integer part of the
                 quotient (product) and enough bits to correctly round
                 the remainder are relevant; the rest will be
                 discarded.",
  acknowledgement = ack-nj,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "correct rounding; floating-point arithmetic; range
                 reduction",
}


bibtype: article
filename: fparith.bib
label: Preparata:1983:MCA
author: F. P. Preparata
title: A Mesh-Connected Area-Time Optimal VLSI Multiplier of Large Integers
journal: j-IEEE-TRANS-COMPUT
volume: C-32
number: 2
pages: 194--198
month: feb
monthnumber: 2
year: 1983
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1983.1676203
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 10:01:07 MDT 2011
bibtimestamp: 2011.07.10 10:01:07 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676203
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: F. P. Preparata
rawtitle: A Mesh-Connected Area-Time Optimal {VLSI} Multiplier of Large Integers
entry:
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  author =       "F. P. Preparata",
  title =        "A Mesh-Connected Area-Time Optimal {VLSI} Multiplier
                 of Large Integers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "2",
  pages =        "194--198",
  month =        feb,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676203",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:01:07 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676203",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Prosser:1983:NCS
author: C. J. Prosser
title: A note on computing the square root of an integer
journal: j-COMP-J
volume: 26
number: 2
pages: 187--188
month: may
monthnumber: 5
year: 1983
CODEN: CMPJA6
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
bibdate: Tue Mar 25 13:51:56 MST 1997
bibtimestamp: 1997.03.25 13:51:56 MST
fjournal: The Computer Journal
acknowledgement: ack-nhfb
classcodes: C4190 (Other numerical methods); C7310 (Mathematics computing)
corpsource: Rutherford and Appleton Lab., Chilton, Didcot, UK
journalURL: http://comjnl.oxfordjournals.org/
treatment: P Practical
rawauthor: C. J. Prosser
rawtitle: A note on computing the square root of an integer
bibsource:
http://www3.oup.co.uk/computer_journal/hdb/Volume_26/Issue_02/; https://www.math.utah.edu/pub/tex/bib/compj1980.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://www3.oup.co.uk/computer_journal/hdb/Volume_26/Issue_02/tiff/187.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_26/Issue_02/tiff/188.tif

keywords:
binary; computer; fixed-point number; integer; interactive methods; iterative methods; PASCAL; Pascal implementation; square root; subroutines; successive subtraction

entry:
@Article{Prosser:1983:NCS,
  author =       "C. J. Prosser",
  title =        "A note on computing the square root of an integer",
  journal =      j-COMP-J,
  volume =       "26",
  number =       "2",
  pages =        "187--188",
  month =        may,
  year =         "1983",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Mar 25 13:51:56 MST 1997",
  bibsource =    "http://www3.oup.co.uk/computer_journal/hdb/Volume_26/Issue_02/;
                 https://www.math.utah.edu/pub/tex/bib/compj1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_26/Issue_02/tiff/187.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_26/Issue_02/tiff/188.tif",
  acknowledgement = ack-nhfb,
  classcodes =   "C4190 (Other numerical methods); C7310 (Mathematics
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  corpsource =   "Rutherford and Appleton Lab., Chilton, Didcot, UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "binary; computer; fixed-point number; integer;
                 interactive methods; iterative methods; PASCAL; Pascal
                 implementation; square root; subroutines; successive
                 subtraction",
  treatment =    "P Practical",
}


bibtype: article
filename: fparith.bib
label: Prosser:1983:SNN
author: C. J. Prosser
title: Short Notes: a Note on Computing the Square Root of an Integer
journal: j-COMP-J
volume: 26
number: 2
pages: 187--188
month: may
monthnumber: 5
year: 1983
CODEN: CMPJA6
DOI: https://doi.org/10.1093/comjnl/26.2.187
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
bibdate: Tue Dec 4 14:48:14 MST 2012
bibtimestamp: 2012.12.04 14:48:14 MST
fjournal: The Computer Journal
acknowledgement: ack-nhfb
classcodes: C4190 (Other numerical methods); C7310 (Mathematics computing)
corpsource: Rutherford and Appleton Lab., Chilton, Didcot, UK
journalURL: http://comjnl.oxfordjournals.org/
treatment: P Practical
rawauthor: C. J. Prosser
rawtitle: Short Notes: a Note on Computing the Square Root of an Integer
bibsource:
http://comjnl.oxfordjournals.org/content/26/2.toc; http://www3.oup.co.uk/computer_journal/hdb/Volume_26/Issue_02/; https://www.math.utah.edu/pub/tex/bib/compj1980.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://comjnl.oxfordjournals.org/content/26/2/187.full.pdf+html; http://www3.oup.co.uk/computer_journal/hdb/Volume_26/Issue_02/tiff/187.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_26/Issue_02/tiff/188.tif

keywords:
binary; computer; fixed-point number; integer; iterative methods; PASCAL; Pascal implementation; square root; subroutines; successive subtraction

entry:
@Article{Prosser:1983:SNN,
  author =       "C. J. Prosser",
  title =        "Short Notes: a Note on Computing the Square Root of an
                 Integer",
  journal =      j-COMP-J,
  volume =       "26",
  number =       "2",
  pages =        "187--188",
  month =        may,
  year =         "1983",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/26.2.187",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Dec 4 14:48:14 MST 2012",
  bibsource =    "http://comjnl.oxfordjournals.org/content/26/2.toc;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_26/Issue_02/;
                 https://www.math.utah.edu/pub/tex/bib/compj1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://comjnl.oxfordjournals.org/content/26/2/187.full.pdf+html;
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                 http://www3.oup.co.uk/computer_journal/hdb/Volume_26/Issue_02/tiff/188.tif",
  acknowledgement = ack-nhfb,
  classcodes =   "C4190 (Other numerical methods); C7310 (Mathematics
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  corpsource =   "Rutherford and Appleton Lab., Chilton, Didcot, UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "binary; computer; fixed-point number; integer;
                 iterative methods; PASCAL; Pascal implementation;
                 square root; subroutines; successive subtraction",
  treatment =    "P Practical",
}


bibtype: article
filename: fparith.bib
label: Quinn:1983:EPR
author: Kevin Quinn
title: Ever Had Problems Rounding Off Figures? This Stock Exchange Has
journal: j-WALL-ST-J
pages: 37--37
day: 8
month: nov
monthnumber: 11
year: 1983
CODEN: WSJOAF
ISSN: 0099-9660 OR 00999660
bibdate: Thu Oct 17 06:28:35 2019
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2019.10.17 06:28:35 ???
fjournal: Wall Street Journal
acknowledgement: ack-nhfb
rawauthor: Kevin Quinn
rawtitle: Ever Had Problems Rounding Off Figures? {This} Stock Exchange Has
entry:
@Article{Quinn:1983:EPR,
  author =       "Kevin Quinn",
  title =        "Ever Had Problems Rounding Off Figures? {This} Stock
                 Exchange Has",
  journal =      j-WALL-ST-J,
  volume =       "??",
  number =       "??",
  pages =        "37--37",
  day =          "8",
  month =        nov,
  year =         "1983",
  CODEN =        "WSJOAF",
  ISSN =         "0099-9660",
  bibdate =      "Thu Oct 17 06:28:35 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Wall Street Journal",
}


bibtype: article
filename: fparith.bib
label: Rall:1983:BRB
author: L. B. Rall
journal: j-SIAM-REVIEW
volume: 25
number: 4
pages: 585--588
year: 1983
CODEN: SIREAD
DOI: https://doi.org/10.1137/1025138
ISSN: 0036-1445 (print), 1095-7200 (electronic) OR 00361445 (print), 10957200 (electronic)
ISSNL: 0036-1445 OR 00361445
bibdate: Sat Mar 29 09:53:41 MDT 2014
bibtimestamp: 2014.03.29 09:53:41 MDT
fjournal: SIAM Review
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sirev
onlinedate: October 1983
rawauthor: L. B. Rall
title:
Book Review: booktitle Computer Arithmetic in Theory and Practice (Ulrich W. Kulisch and Willard L. Miranker)

bibsource:
http://epubs.siam.org/toc/siread/25/4; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib

rawtitle:
Book Review: {{\booktitle{Computer Arithmetic in Theory and Practice}} (Ulrich W. Kulisch and Willard L. Miranker)}

entry:
@Article{Rall:1983:BRB,
  author =       "L. B. Rall",
  title =        "Book Review: {{\booktitle{Computer Arithmetic in
                 Theory and Practice}} (Ulrich W. Kulisch and Willard L.
                 Miranker)}",
  journal =      j-SIAM-REVIEW,
  volume =       "25",
  number =       "4",
  pages =        "585--588",
  month =        "????",
  year =         "1983",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1025138",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Sat Mar 29 09:53:41 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/25/4;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "October 1983",
}


bibtype: article
filename: fparith.bib
label: Rall:1983:CAT
author: L. B. Rall
title: Computer Arithmetic in Theory and Practice --- Kulisch, U. W., Miranker, W. L.
journal: j-SIAM-REVIEW
volume: 25
number: 4
pages: 585--588
year: 1983
CODEN: SIREAD
DOI: https://doi.org/10.1137/1025138
ISSN: 0036-1445 (print), 1095-7200 (electronic) OR 00361445 (print), 10957200 (electronic)
ISSNL: 0036-1445 OR 00361445
bibdate: Fri Jun 21 11:25:02 MDT 2013
bibtimestamp: 2013.06.21 11:25:02 MDT
fjournal: SIAM Review
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sirev
rawauthor: L. B. Rall
rawtitle: Computer Arithmetic in Theory and Practice --- {Kulisch, U. W., Miranker, W. L.}
entry:
@Article{Rall:1983:CAT,
  author =       "L. B. Rall",
  title =        "Computer Arithmetic in Theory and Practice ---
                 {Kulisch, U. W., Miranker, W. L.}",
  journal =      j-SIAM-REVIEW,
  volume =       "25",
  number =       "4",
  pages =        "585--588",
  month =        "????",
  year =         "1983",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1025138",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Fri Jun 21 11:25:02 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
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  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
}


bibtype: article
filename: fparith.bib
label: Ramachandran:1983:SRE
author: V. Ramachandran
title: Single Residue Error Correction in Residue Number Systems
journal: j-IEEE-TRANS-COMPUT
volume: C-32
number: 5
pages: 504--507
month: may
monthnumber: 5
year: 1983
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1983.1676264
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 10:01:09 MDT 2011
bibtimestamp: 2011.07.10 10:01:09 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: V. Ramachandran
rawtitle: Single Residue Error Correction in Residue Number Systems
URL:
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676264; http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12; http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35227

entry:
@Article{Ramachandran:1983:SRE,
  author =       "V. Ramachandran",
  title =        "Single Residue Error Correction in Residue Number
                 Systems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "5",
  pages =        "504--507",
  month =        may,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676264",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:01:09 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676264;
                 http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35227",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "We present a new method to correct single errors in an
                 n-residue number system through the use of r redundant
                 moduli. The method requires {\lceil}2n/r{\rceil} + 2
                 recombinations of n residues in the worst case. This is
                 of lower complexity than any \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Rao:1983:ICS
author: T. R. N. Rao and P. Kornerup
title: IEEE Computer Society Sixth Symposium on Computer Arithmetic
crossref: IEEE:1983:PSC
pages: 1--1
year: 1983
bibdate: Tue Nov 13 15:58:57 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.13 15:58:57 ???
URL: http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Rao_Kornerup.pdf
keywords: ARITH-6
acknowledgement: ack-nhfb
rawauthor: T. R. N. Rao and P. Kornerup
rawtitle: {IEEE Computer Society Sixth Symposium on Computer Arithmetic}
entry:
@InProceedings{Rao:1983:ICS,
  author =       "T. R. N. Rao and P. Kornerup",
  title =        "{IEEE Computer Society Sixth Symposium on Computer
                 Arithmetic}",
  crossref =     "IEEE:1983:PSC",
  pages =        "1--1",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Rao_Kornerup.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6",
}


bibtype: inproceedings
filename: fparith.bib
label: Robertson:1983:CDM
author: James E. Robertson
crossref: IEEE:1983:PSC
pages: 67--71
year: 1983
bibdate: Tue Nov 13 15:58:57 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.13 15:58:57 ???
URL: http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Robertson.pdf
keywords: ARITH-6
acknowledgement: ack-nhfb
rawauthor: James E. Robertson
title:
Conditions for the Distributivity of Multiplication with Respect to Set Addition and Their Effect on the Design of Array Multipliers

abstract:
Some conditions for distributivity of multiplication with respect to set addition are determined. In particular, distributivity holds if positive numbers are used, but does not hold for negative numbers in radix complement form. Use of simple recoding methods to achieve distributivity is not helpful, since costs of elementary multipliers and summing networks are increased. Distributivity does hold for the digit sets used for signed-digit arithmetic, and the requirement for distributivity provides guidance for the design of elementary multipliers.

rawabstract:
Some conditions for distributivity of multiplication with respect to set addition are determined. In particular, distributivity holds if positive numbers are used, but does not hold for negative numbers in radix complement form. Use of simple recoding methods to achieve distributivity is not helpful, since costs of elementary multipliers and summing networks are increased. Distributivity does hold for the digit sets used for signed-digit arithmetic, and the requirement for distributivity provides guidance for the design of elementary multipliers.

rawtitle:
Conditions for the Distributivity of Multiplication with Respect to Set Addition and Their Effect on the Design of Array Multipliers

entry:
@InProceedings{Robertson:1983:CDM,
  author =       "James E. Robertson",
  title =        "Conditions for the Distributivity of Multiplication
                 with Respect to Set Addition and Their Effect on the
                 Design of Array Multipliers",
  crossref =     "IEEE:1983:PSC",
  pages =        "67--71",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Robertson.pdf",
  abstract =     "Some conditions for distributivity of multiplication
                 with respect to set addition are determined. In
                 particular, distributivity holds if positive numbers
                 are used, but does not hold for negative numbers in
                 radix complement form. Use of simple recoding methods
                 to achieve distributivity is not helpful, since costs
                 of elementary multipliers and summing networks are
                 increased. Distributivity does hold for the digit sets
                 used for signed-digit arithmetic, and the requirement
                 for distributivity provides guidance for the design of
                 elementary multipliers.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6",
}


bibtype: article
filename: fparith.bib
label: Robison:1983:USF
author: A. D. Robison
title: Use Squares for Fast Multiplication
journal: j-EDN
volume: 28
number: 21
pages: 263, 267
month: oct
monthnumber: 10
year: 1983
CODEN: EDNSBH
ISSN: 0012-7515, 0364-6637 OR 00127515, 03646637
bibdate: Thu Sep 1 10:15:08 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:15:08 ???
fjournal: EDN
acknowledgement: ack-nj
rawauthor: A. D. Robison
rawtitle: Use Squares for Fast Multiplication
entry:
@Article{Robison:1983:USF,
  author =       "A. D. Robison",
  title =        "Use Squares for Fast Multiplication",
  journal =      j-EDN,
  volume =       "28",
  number =       "21",
  pages =        "263, 267",
  month =        oct,
  year =         "1983",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  bibdate =      "Thu Sep 1 10:15:08 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "EDN",
}


bibtype: mastersthesis
filename: fparith.bib
label: Rosenblum:1983:IIS
author: David Samuel Rosenblum
type: Thesis (M.S.)
school: North Texas State University
address: Denton, TX, USA
pages: vi + 83
month: aug
monthnumber: 8
year: 1983
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.; Microprocessors --- Programming.
acknowledgement: ack-nhfb
rawauthor: David Samuel Rosenblum
title:
An implementation of the IEEE standard for binary floating-point arithmetic for the Motorola 6809 microprocessor

rawtitle:
An implementation of the {IEEE} standard for binary floating-point arithmetic for the {Motorola} 6809 microprocessor

entry:
@MastersThesis{Rosenblum:1983:IIS,
  author =       "David Samuel Rosenblum",
  title =        "An implementation of the {IEEE} standard for binary
                 floating-point arithmetic for the {Motorola} 6809
                 microprocessor",
  type =         "Thesis ({M.S.})",
  school =       "North Texas State University",
  address =      "Denton, TX, USA",
  pages =        "vi + 83",
  month =        aug,
  year =         "1983",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer arithmetic.; Microprocessors ---
                 Programming.",
}


bibtype: inproceedings
filename: fparith.bib
label: Rump:1983:SAP
author: Siegfried M. Rump
title: Solving algebraic problems with high accuracy
crossref: Kulisch:1983:NAS
pages: 51--120
year: 1983
bibdate: Sat Nov 9 08:26:18 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.11.09 08:26:18 MST
acknowledgement: ack-nhfb
reviewer: Z. Zlatev; Zlatev, Z
rawauthor: Siegfried M. Rump
rawtitle: Solving algebraic problems with high accuracy
subject:
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS

entry:
@InProceedings{Rump:1983:SAP,
  author =       "Siegfried M. Rump",
  title =        "Solving algebraic problems with high accuracy",
  crossref =     "Kulisch:1983:NAS",
  pages =        "51--120",
  year =         "1983",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  catcode =      "G.1; G.1.3; G.1.0; G.1.0",
  content =      "Numerical methods for the following applications are
                 surveyed in this paper: solving systems of linear
                 algebraic equations; obtaining the inverse of a given
                 matrix; finding zeros of functions and polynomials;
                 computing eigenvalues and eigenvectors of a matrix;
                 treating linear, quadratic and convex programming
                 problems; and calculating the values of arithmetic
                 expressions. Both the case where the coefficient matrix
                 is square and the case where the coefficient matrix is
                 rectangular are handled in connection with the solution
                 of systems of linear algebraic equations. Moreover,
                 methods for the special, but important, cases where the
                 coefficient matrix of a system of linear algebraic
                 equations is band or sparse are given. (In the latter
                 case, it is assumed that the system is solved by
                 iterative processes.) The common feature of all these
                 methods is that by studying carefully the basic
                 properties of the computer arithmetic (sketched in the
                 beginning of the paper), one can avoid the round-off
                 errors and, thus, achieve a high degree of accuracy. If
                 the data are exactly representable on the computer
                 under consideration, \ldots{}",
  CRclass =      "G.1.3 Numerical Linear Algebra; G.1.3 Numerical Linear
                 Algebra; G.1.3 Sparse and very large systems; G.1.0
                 General; G.1.0 Computer arithmetic; G.1.0 General;
                 G.1.0 Error analysis",
  CRnumber =     "8503-0216",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Numerical Linear Algebra; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse
                 and very large systems; Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Computer arithmetic;
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Error analysis",
  genterm =      "ALGORITHMS; PERFORMANCE",
  reviewer =     "Z. Zlatev; Zlatev, Z",
  source =       "in A new approach to scientific computation. Proc. of
                 the symposium on a new approach to scientific
                 computation (Yorktown Heights, NY, August 3, 1982), U.
                 Kulisch and W. Miranker (Eds.), Academic Press, Inc.,
                 New York, NY, 1983",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}


bibtype: inproceedings
filename: fparith.bib
label: Sand:1983:DIP
author: J. R. Sand and J. O. Bumgarner
title: Dysan IEEE P-754 Binary Floating Point Architecture
crossref: Ranocchia:1983:RFA
pages: 185--194
year: 1983
bibdate: Sat Nov 12 21:59:00 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.11.12 21:59:00 ???
acknowledgement: ack-nj
rawauthor: J. R. Sand and J. O. Bumgarner
rawtitle: {Dysan IEEE P-754} Binary Floating Point Architecture
entry:
@InProceedings{Sand:1983:DIP,
  author =       "J. R. Sand and J. O. Bumgarner",
  title =        "{Dysan IEEE P-754} Binary Floating Point
                 Architecture",
  crossref =     "Ranocchia:1983:RFA",
  pages =        "185--194",
  year =         "1983",
  bibdate =      "Sat Nov 12 21:59:00 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: inproceedings
filename: fparith.bib
label: Sandesara:1983:ZZF
author: S. Sandesara
title: Zilog's Z8070 Floating-Point Processor
crossref: Mini-Micro:1983:MMN
pages: 7/4/1--3
year: 1983
bibdate: Mon Sep 12 08:05:44 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.12 08:05:44 ???
acknowledgement: ack-nj
rawauthor: S. Sandesara
rawtitle: {Zilog}'s {Z8070} Floating-Point Processor
entry:
@InProceedings{Sandesara:1983:ZZF,
  author =       "S. Sandesara",
  title =        "{Zilog}'s {Z8070} Floating-Point Processor",
  crossref =     "Mini-Micro:1983:MMN",
  pages =        "7/4/1--3",
  year =         "1983",
  bibdate =      "Mon Sep 12 08:05:44 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: Schelin:1983:CFA
author: Charles W. Schelin
title: Calculator function approximation
journal: j-AMER-MATH-MONTHLY
volume: 90
number: 5
pages: 317--325
month: may
monthnumber: 5
year: 1983
CODEN: AMMYAE
DOI: https://doi.org/10.2307/2975781
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
MRclass: 65D15 (65-03 65-04)
MRnumber: 84h:65021
MRreviewer: J. Albrycht
bibdate: Wed Dec 3 17:17:33 MST 1997
bibtimestamp: 1997.12.03 17:17:33 MST
URL: https://www.jstor.org/stable/2975781
fjournal: American Mathematical Monthly
keywords: Computer Function Evaluation; CORDIC Scheme; tabular function values
acknowledgement: ack-nhfb
journalURL: https://www.jstor.org/journals/00029890.htm
rawauthor: Charles W. Schelin
rawtitle: Calculator function approximation
bibsource:
http://www.jstor.org/journals/00029890.htm; https://www.math.utah.edu/pub/tex/bib/amermathmonthly1980.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Schelin:1983:CFA,
  author =       "Charles W. Schelin",
  title =        "Calculator function approximation",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "90",
  number =       "5",
  pages =        "317--325",
  month =        may,
  year =         "1983",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.2307/2975781",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "65D15 (65-03 65-04)",
  MRnumber =     "84h:65021",
  MRreviewer =   "J. Albrycht",
  bibdate =      "Wed Dec 3 17:17:33 MST 1997",
  bibsource =    "http://www.jstor.org/journals/00029890.htm;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.jstor.org/stable/2975781",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
  keywords =     "Computer Function Evaluation; CORDIC Scheme; tabular
                 function values",
}


bibtype: inproceedings
filename: fparith.bib
label: Scherson:1983:MOA
author: Isaac Scherson and Smil Ruhman
title: Multi-operand Associative Arithmetic
crossref: IEEE:1983:PSC
pages: 123--129
year: 1983
bibdate: Tue Nov 13 15:58:57 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.13 15:58:57 ???
URL: http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Scherson_Ruhman.pdf
acknowledgement: ack-nhfb
rawauthor: Isaac Scherson and Smil Ruhman
rawtitle: Multi-operand Associative Arithmetic
abstract:
Multi-operand associative techniques attain their full power in algorithms where the data may be recast into disjoint data sets, all acted upon concurrently, each by a different operand common to the set. But the multi-operand approach can also serve to enhance arithmetic operations significantly. The speed-up of associative multiplication by handling a number of multiplier bits at a time is described and analyzed, including an effective algorithm for a limited sum of products. The most complex process treated is convolution, which serves to illustrate the enhancement of an extended sum of products. Any number of vectors stored in memory can be convolved simultaneously by a common filter vector. Execution time is 45 milliseconds for 1024 element data and filter vectors, 2048 element results, and 16-bit precision.

rawabstract:
Multi-operand associative techniques attain their full power in algorithms where the data may be recast into disjoint data sets, all acted upon concurrently, each by a different operand common to the set. But the multi-operand approach can also serve to enhance arithmetic operations significantly. The speed-up of associative multiplication by handling a number of multiplier bits at a time is described and analyzed, including an effective algorithm for a limited sum of products. The most complex process treated is convolution, which serves to illustrate the enhancement of an extended sum of products. Any number of vectors stored in memory can be convolved simultaneously by a common filter vector. Execution time is 45 milliseconds for 1024 element data and filter vectors, 2048 element results, and 16-bit precision.

entry:
@InProceedings{Scherson:1983:MOA,
  author =       "Isaac Scherson and Smil Ruhman",
  title =        "Multi-operand Associative Arithmetic",
  crossref =     "IEEE:1983:PSC",
  pages =        "123--129",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Scherson_Ruhman.pdf",
  abstract =     "Multi-operand associative techniques attain their full
                 power in algorithms where the data may be recast into
                 disjoint data sets, all acted upon concurrently, each
                 by a different operand common to the set. But the
                 multi-operand approach can also serve to enhance
                 arithmetic operations significantly. The speed-up of
                 associative multiplication by handling a number of
                 multiplier bits at a time is described and analyzed,
                 including an effective algorithm for a limited sum of
                 products. The most complex process treated is
                 convolution, which serves to illustrate the enhancement
                 of an extended sum of products. Any number of vectors
                 stored in memory can be convolved simultaneously by a
                 common filter vector. Execution time is 45 milliseconds
                 for 1024 element data and filter vectors, 2048 element
                 results, and 16-bit precision.",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: fparith.bib
label: Schmid:1983:DC
author: Hermann Schmid
title: Decimal Computation
publisher: pub-R-E-KRIEGER
address: pub-R-E-KRIEGER:adr
pages: xi + 266
year: 1983
ISBN: 0-89874-318-4 OR 0898743184
ISBN13: 978-0-89874-318-0 OR 9780898743180
LCCN: QA75 .S34 1983
bibdate: Thu Sep 1 10:14:05 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:14:05 ???
note: Reprint of cite Schmid:1974:DC.
keywords: binary-coded decimal system; calculators--circuits; decimal floating-point arithmetic
acknowledgement: ack-nhfb
rawauthor: Hermann Schmid
rawnote: Reprint of \cite{Schmid:1974:DC}.
rawtitle: Decimal Computation
entry:
@Book{Schmid:1983:DC,
  author =       "Hermann Schmid",
  title =        "Decimal Computation",
  publisher =    pub-R-E-KRIEGER,
  address =      pub-R-E-KRIEGER:adr,
  pages =        "xi + 266",
  year =         "1983",
  ISBN =         "0-89874-318-4",
  ISBN-13 =      "978-0-89874-318-0",
  LCCN =         "QA75 .S34 1983",
  bibdate =      "Thu Sep 1 10:14:05 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprint of \cite{Schmid:1974:DC}.",
  acknowledgement = ack-nhfb,
  keywords =     "binary-coded decimal system; calculators--circuits;
                 decimal floating-point arithmetic",
}


bibtype: inproceedings
filename: fparith.bib
label: Seidensticker:1983:CFH
author: R. B. Seidensticker
title: Continued Fractions For High-Speed and High-Accuracy Computer Arithmetic
crossref: IEEE:1983:PSC
pages: 184--193
year: 1983
bibdate: Tue Nov 13 15:50:08 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.13 15:50:08 ???
URL: http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Seidensticker.pdf
keywords: ARITH-6; continued fractions
acknowledgement: ack-nhfb
rawauthor: R. B. Seidensticker
rawtitle: Continued Fractions For High-Speed and High-Accuracy Computer Arithmetic
abstract:
Continued fraction representation has many advantages for fast and high-accuracy computation when compared with positional notation. A continued fraction is a number of the formpar $$ p_1 + q_1 / (p_2 + q_2 / (p_3 + cdots )) $$,par noindent where $p$ and $q$ are integers. Some of the benefits of continued fraction representation for computer arithmetic are: faster multiply and divide than with positional notation, fast evaluation of trigonometric, logarithmic, and other unary functions, easy extension to infinite-precision arithmetic, infinite-precision representation of many transcendental numbers, no roundoff or truncation errors, and improved software transportability because accuracy is not hardware dependent. A unified system for continued fraction arithmetic is given along with an outline of a hardware architecture for evaluating these functions.

rawabstract:
Continued fraction representation has many advantages for fast and high-accuracy computation when compared with positional notation. A continued fraction is a number of the form\par $$ p_1 + q_1 / (p_2 + q_2 / (p_3 + \cdots {})) $$,\par \noindent where $p$ and $q$ are integers. Some of the benefits of continued fraction representation for computer arithmetic are: faster multiply and divide than with positional notation, fast evaluation of trigonometric, logarithmic, and other unary functions, easy extension to infinite-precision arithmetic, infinite-precision representation of many transcendental numbers, no roundoff or truncation errors, and improved software transportability because accuracy is not hardware dependent. A unified system for continued fraction arithmetic is given along with an outline of a hardware architecture for evaluating these functions.

entry:
@InProceedings{Seidensticker:1983:CFH,
  author =       "R. B. Seidensticker",
  title =        "Continued Fractions For High-Speed and High-Accuracy
                 Computer Arithmetic",
  crossref =     "IEEE:1983:PSC",
  pages =        "184--193",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:50:08 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Seidensticker.pdf",
  abstract =     "Continued fraction representation has many advantages
                 for fast and high-accuracy computation when compared
                 with positional notation. A continued fraction is a
                 number of the form\par

                  $$ p_1 + q_1 / (p_2 + q_2 / (p_3 + \cdots {}))
                 $$,\par

                 \noindent where $p$ and $q$ are integers. Some of the
                 benefits of continued fraction representation for
                 computer arithmetic are: faster multiply and divide
                 than with positional notation, fast evaluation of
                 trigonometric, logarithmic, and other unary functions,
                 easy extension to infinite-precision arithmetic,
                 infinite-precision representation of many
                 transcendental numbers, no roundoff or truncation
                 errors, and improved software transportability because
                 accuracy is not hardware dependent. A unified system
                 for continued fraction arithmetic is given along with
                 an outline of a hardware architecture for evaluating
                 these functions.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6; continued fractions",
}


bibtype: mastersthesis
filename: fparith.bib
label: Shah:1983:FPP
author: Kamalesh Ramanlal Shah
title: Floating point processor for STOIC instrumentation
type: Thesis (M.S. in Engineering)
school: University of Texas at Austin
address: Austin, TX, USA
pages: xi + 188
year: 1983
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
acknowledgement: ack-nhfb
rawauthor: Kamalesh Ramanlal Shah
rawtitle: Floating point processor for {STOIC} instrumentation
keywords:
Medical electronics.; Medical instruments and apparatus --- Design and construction.; Microprocessors.

entry:
@MastersThesis{Shah:1983:FPP,
  author =       "Kamalesh Ramanlal Shah",
  title =        "Floating point processor for {STOIC} instrumentation",
  type =         "Thesis ({M.S. in Engineering})",
  school =       "University of Texas at Austin",
  address =      "Austin, TX, USA",
  pages =        "xi + 188",
  year =         "1983",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Medical electronics.; Medical instruments and
                 apparatus --- Design and construction.;
                 Microprocessors.",
}


bibtype: article
filename: fparith.bib
label: Smith:1983:FPA
author: Burks Smith
title: Floating Point Arithmetic and Numeric Representation in Computers [letter] in DDC
journal: j-DDJ
volume: 8
number: 2
pages: 55--??
month: feb
monthnumber: 2
year: 1983
CODEN: DDJOEB
ISSN: 1044-789X OR 1044789X
bibdate: Mon Sep 2 09:09:39 MDT 1996
bibsource: http://www.ddj.com/index/author/index.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.09.02 09:09:39 MDT
fjournal: Dr. Dobb's Journal of Software Tools
acknowledgement: ack-nhfb
rawauthor: Burks Smith
rawtitle: Floating Point Arithmetic and Numeric Representation in Computers [letter] in {DDC}
entry:
@Article{Smith:1983:FPA,
  author =       "Burks Smith",
  title =        "Floating Point Arithmetic and Numeric Representation
                 in Computers [letter] in {DDC}",
  journal =      j-DDJ,
  volume =       "8",
  number =       "2",
  pages =        "55--??",
  month =        feb,
  year =         "1983",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Mon Sep 2 09:09:39 MDT 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}


bibtype: article
filename: fparith.bib
label: Soderstrand:1983:IRN
author: M. Soderstrand and C. Vernia and Jui-Hua Chang
title: An improved residue number system digital-to-analog converter
journal: j-IEEE-TRANS-CIRCUITS-SYST
volume: 30
number: 12
pages: 903--907
month: dec
monthnumber: 12
year: 1983
CODEN: ICSYBT
DOI: https://doi.org/10.1049/el:19820632
ISSN: 0098-4094 (print), 1558-1276 (electronic) OR 00984094 (print), 15581276 (electronic)
ISSNL: 0098-4094 OR 00984094
bibdate: Fri Nov 9 11:38:57 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:57 MST
URL: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23540
fjournal: IEEE Transactions on Circuits and Systems
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: M. Soderstrand and C. Vernia and Jui-Hua Chang
rawtitle: An improved residue number system digital-to-analog converter
entry:
@Article{Soderstrand:1983:IRN,
  author =       "M. Soderstrand and C. Vernia and Jui-Hua Chang",
  title =        "An improved residue number system digital-to-analog
                 converter",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "30",
  number =       "12",
  pages =        "903--907",
  month =        dec,
  year =         "1983",
  CODEN =        "ICSYBT",
  DOI =          "https://doi.org/10.1049/el:19820632",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23540",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A new technique for Residue Number System (RNS)
                 Digital-to-Binary or Digital-to-Analog conversion based
                 on the Chinese Remainder Theorem allows conversion with
                 only one level of ROM and one level of Adders. The
                 ROM's are small (e.g., 256 x 8) and \ldots{}",
}


bibtype: techreport
filename: fparith.bib
label: Spafford:1983:RAP
author: Eugene Howard Spafford
type: GIT-ICS
number: 83/09
institution: School of Information and Computer Science, Georgia Institute of Technology
address: Atlanta, GA, USA
pages: v + 57
year: 1983
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Computers.
acknowledgement: ack-nhfb
rawauthor: Eugene Howard Spafford
title:
A report on the accuracy of PRIME computers' floating point software and hardware and the SWT math library user's guide

rawtitle:
A report on the accuracy of {PRIME} computers' floating point software and hardware and the {SWT} math library user's guide

entry:
@TechReport{Spafford:1983:RAP,
  author =       "Eugene Howard Spafford",
  title =        "A report on the accuracy of {PRIME} computers'
                 floating point software and hardware and the {SWT} math
                 library user's guide",
  type =         "{GIT-ICS}",
  number =       "83/09",
  institution =  "School of Information and Computer Science, Georgia
                 Institute of Technology",
  address =      "Atlanta, GA, USA",
  pages =        "v + 57",
  year =         "1983",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computers.",
}


bibtype: article
filename: fparith.bib
label: Speiser:1983:SFP
author: Jeffrey Speiser
title: Savage Floating Point Benchmark in PASCAL in 16BST
journal: j-DDJ
volume: 8
number: 11
pages: 112--??
month: nov
monthnumber: 11
year: 1983
CODEN: DDJOEB
ISSN: 1044-789X OR 1044789X
bibdate: Mon Sep 2 09:09:39 MDT 1996
bibsource: http://www.ddj.com/index/author/index.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.09.02 09:09:39 MDT
fjournal: Dr. Dobb's Journal of Software Tools
acknowledgement: ack-nhfb
rawauthor: Jeffrey Speiser
rawtitle: {Savage} Floating Point Benchmark in {PASCAL} in {16BST}
entry:
@Article{Speiser:1983:SFP,
  author =       "Jeffrey Speiser",
  title =        "{Savage} Floating Point Benchmark in {PASCAL} in
                 {16BST}",
  journal =      j-DDJ,
  volume =       "8",
  number =       "11",
  pages =        "112--??",
  month =        nov,
  year =         "1983",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Mon Sep 2 09:09:39 MDT 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}


bibtype: techreport
filename: fparith.bib
label: Springer:1983:FP
author: Charles Towne Springer
title: Floating point
institution: Mountain View Pr.
address: Mountain View, CA, USA
pages: 22
year: 1983
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
series: MVP-FORTH series; v. 3
remark: Title on cover: FORTH floating point. ``Pre-publication.''
acknowledgement: ack-nhfb
rawauthor: Charles Towne Springer
rawtitle: Floating point
keywords:
Electronic digital computers --- Programming.; Floating-point arithmetic.; FORTH (Computer program language)

entry:
@TechReport{Springer:1983:FP,
  author =       "Charles Towne Springer",
  title =        "Floating point",
  institution =  "Mountain View Pr.",
  address =      "Mountain View, CA, USA",
  pages =        "22",
  year =         "1983",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "MVP-FORTH series; v. 3",
  acknowledgement = ack-nhfb,
  keywords =     "Electronic digital computers --- Programming.;
                 Floating-point arithmetic.; FORTH (Computer program
                 language)",
  remark =       "Title on cover: FORTH floating point.
                 ``Pre-publication.''",
}


bibtype: article
filename: fparith.bib
label: Swartzlander:1983:SLA
author: E. E. Swartzlander, Jr. and D. V. Satish Chandra and H. T. Nagle, Jr. and S. A. Starks
title: Sign / Logarithm Arithmetic for FFT Implementation
journal: j-IEEE-TRANS-COMPUT
volume: C-32
number: 6
pages: 526--534
month: jun
monthnumber: 6
year: 1983
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1983.1676274
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 10:01:09 MDT 2011
bibtimestamp: 2011.07.10 10:01:09 MDT
note: See comments cite Hongyuan:1986:CSL.
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676274
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: E. E. {Swartzlander, Jr.} and D. V. Satish Chandra and H. T. {Nagle, Jr.} and S. A. Starks
rawnote: See comments \cite{Hongyuan:1986:CSL}.
rawtitle: Sign\slash Logarithm Arithmetic for {FFT} Implementation
entry:
@Article{Swartzlander:1983:SLA,
  author =       "E. E. {Swartzlander, Jr.} and D. V. Satish Chandra and
                 H. T. {Nagle, Jr.} and S. A. Starks",
  title =        "Sign\slash Logarithm Arithmetic for {FFT}
                 Implementation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "6",
  pages =        "526--534",
  month =        jun,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676274",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:01:09 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  note =         "See comments \cite{Hongyuan:1986:CSL}.",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676274",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Takefuji:1983:FMS
author: Yoshiyasu Takefuji and Takakazu Kurokawa and Hideo Aiso
title: Fast Matrix Solver in $ mathrm GF(2) $
crossref: IEEE:1983:PSC
pages: 138--143
year: 1983
bibdate: Tue Nov 13 15:58:57 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.13 15:58:57 ???
URL: http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Takefuji_Kurokawa_Aiso.pdf
keywords: ARITH-6
acknowledgement: ack-nhfb
rawauthor: Yoshiyasu Takefuji and Takakazu Kurokawa and Hideo Aiso
rawtitle: Fast Matrix Solver in {$ \mathrm {GF}(2) $}
abstract:
In this paper a parallel and pipelined fast matrix equation solver in $ mathrm GF(2) $ is proposed where the elements are 0s or 1s. The solver employing the iterative logic circuits which are suitable for VLSI implementation can be realized by the conventional Gauss--Jordan Elimination Method. $ O(n) $ gate stages in the pipeline and $ O(n^2) $ total gates are required for solving $ A X = b $ where $A$ is a matrix of $ n times n $, $X$ and $b$ are vectors respectively. The organization of the solver is discussed in this paper.

rawabstract:
In this paper a parallel and pipelined fast matrix equation solver in $ \mathrm {GF}(2) $ is proposed where the elements are 0s or 1s. The solver employing the iterative logic circuits which are suitable for VLSI implementation can be realized by the conventional Gauss--Jordan Elimination Method. $ O(n) $ gate stages in the pipeline and $ O(n^2) $ total gates are required for solving $ A X = b $ where $A$ is a matrix of $ n \times n $, $X$ and $b$ are vectors respectively. The organization of the solver is discussed in this paper.

entry:
@InProceedings{Takefuji:1983:FMS,
  author =       "Yoshiyasu Takefuji and Takakazu Kurokawa and Hideo
                 Aiso",
  title =        "Fast Matrix Solver in {$ \mathrm {GF}(2) $}",
  crossref =     "IEEE:1983:PSC",
  pages =        "138--143",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Takefuji_Kurokawa_Aiso.pdf",
  abstract =     "In this paper a parallel and pipelined fast matrix
                 equation solver in $ \mathrm {GF}(2) $ is proposed
                 where the elements are 0s or 1s. The solver employing
                 the iterative logic circuits which are suitable for
                 VLSI implementation can be realized by the conventional
                 Gauss--Jordan Elimination Method. $ O(n) $ gate stages
                 in the pipeline and $ O(n^2) $ total gates are required
                 for solving $ A X = b $ where $A$ is a matrix of $ n
                 \times n $, $X$ and $b$ are vectors respectively. The
                 organization of the solver is discussed in this
                 paper.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6",
}


bibtype: techreport
filename: fparith.bib
label: Tamura:1983:CDB
author: Y. Tamura and Y. Kanada
title: Calculation of $ pi $ to 4,194,293 Decimals Based on the Gauss--Legendre Algorithm
type: Technical report
number: CCUT-TR-83-01
institution: Computer Centre, University of Tokyo
address: Tokyo, Japan
pages: 138--143
month: may
monthnumber: 5
year: 1983
bibdate: Mon Jul 18 17:46:12 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.18 17:46:12 ???
acknowledgement: ack-nhfb
rawauthor: Y. Tamura and Y. Kanada
rawtitle: Calculation of $ \pi $ to 4,194,293 Decimals Based on the {Gauss--Legendre} Algorithm
entry:
@TechReport{Tamura:1983:CDB,
  author =       "Y. Tamura and Y. Kanada",
  title =        "Calculation of $ \pi $ to 4,194,293 Decimals Based on
                 the {Gauss--Legendre} Algorithm",
  type =         "Technical report",
  number =       "CCUT-TR-83-01",
  institution =  "Computer Centre, University of Tokyo",
  address =      "Tokyo, Japan",
  month =        may,
  year =         "1983",
  bibdate =      "Mon Jul 18 17:46:12 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Taylor:1983:AE
author: George S. Taylor
title: Arithmetic on the ELXSI 6400
crossref: IEEE:1983:PSC
pages: 110--115
year: 1983
bibdate: Tue Nov 13 15:50:05 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.13 15:50:05 ???
URL: http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Taylor.pdf
keywords: ARITH-6; ELXSI 6400
acknowledgement: ack-nhfb
rawauthor: George S. Taylor
rawtitle: Arithmetic on the {ELXSI 6400}
abstract:
The ELXSI System 6400 is a new 64-bit general-purpose mainframe computer [1]. This paper describes its arithmetic instruction set architecture and the organization of the arithmetic processor. The ELXSI instruction set supports a complete implementation of the proposed IEEE floating point standard [2], plus integer and decimal arithmetic. The System 6400 arithmetic processor uses ECL gate arrays to execute these instructions at high speed using a single board of hardware.

rawabstract:
The ELXSI System 6400 is a new 64-bit general-purpose mainframe computer [1]. This paper describes its arithmetic instruction set architecture and the organization of the arithmetic processor. The ELXSI instruction set supports a complete implementation of the proposed IEEE floating point standard [2], plus integer and decimal arithmetic. The System 6400 arithmetic processor uses ECL gate arrays to execute these instructions at high speed using a single board of hardware.

entry:
@InProceedings{Taylor:1983:AE,
  author =       "George S. Taylor",
  title =        "Arithmetic on the {ELXSI 6400}",
  crossref =     "IEEE:1983:PSC",
  pages =        "110--115",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:50:05 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Taylor.pdf",
  abstract =     "The ELXSI System 6400 is a new 64-bit general-purpose
                 mainframe computer [1]. This paper describes its
                 arithmetic instruction set architecture and the
                 organization of the arithmetic processor. The ELXSI
                 instruction set supports a complete implementation of
                 the proposed IEEE floating point standard [2], plus
                 integer and decimal arithmetic. The System 6400
                 arithmetic processor uses ECL gate arrays to execute
                 these instructions at high speed using a single board
                 of hardware.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6; ELXSI 6400",
}


bibtype: article
filename: fparith.bib
label: Taylor:1983:OFR
author: F. J. Taylor
title: An Overflow-Free Residue Multiplier
journal: j-IEEE-TRANS-COMPUT
volume: C-32
number: 5
pages: 501--504
month: may
monthnumber: 5
year: 1983
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1983.1676263
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 10:01:09 MDT 2011
bibtimestamp: 2011.07.10 10:01:09 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676263
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
rawtitle: An Overflow-Free Residue Multiplier
entry:
@Article{Taylor:1983:OFR,
  author =       "F. J. Taylor",
  title =        "An Overflow-Free Residue Multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "5",
  pages =        "501--504",
  month =        may,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676263",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:01:09 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676263",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: mastersthesis
filename: fparith.bib
label: Thomas:1983:HLM
author: James W. Thomas
title: High-level language management of the IEEE floating-point environment: research project
type: Thesis (M.S. in Electrical Engineering)
school: University of California, Berkeley. Dept. of Electrical Engineering and Computer Sciences
address: Berkeley, CA, USA
pages: 27
year: 1983
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
acknowledgement: ack-nhfb
rawauthor: James W. Thomas
rawtitle: High-level language management of the {IEEE} floating-point environment: research project
entry:
@MastersThesis{Thomas:1983:HLM,
  author =       "James W. Thomas",
  title =        "High-level language management of the {IEEE}
                 floating-point environment: research project",
  type =         "Thesis ({M.S. in Electrical Engineering})",
  school =       "University of California, Berkeley. Dept. of
                 Electrical Engineering and Computer Sciences",
  address =      "Berkeley, CA, USA",
  pages =        "27",
  year =         "1983",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: mastersthesis
filename: fparith.bib
label: Tseng:1983:FIP
author: Yeong-Jeng Tseng
title: A floating-point inner product step processor for use in a VLSI Systolic array
type: Thesis (M.S.)
school: Michigan State University
address: East Lansing, MI 48824, USA
pages: ix + 63
year: 1983
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
acknowledgement: ack-nhfb
rawauthor: Yeong-Jeng Tseng
rawtitle: A floating-point inner product step processor for use in a {VLSI} Systolic array
keywords:
Computer arithmetic and logic units; Electronic digital computers --- Circuits; Floating-point arithmetic; Integrated circuits --- Very large scale integration.

entry:
@MastersThesis{Tseng:1983:FIP,
  author =       "Yeong-Jeng Tseng",
  title =        "A floating-point inner product step processor for use
                 in a {VLSI} Systolic array",
  type =         "Thesis ({M.S.})",
  school =       "Michigan State University",
  address =      "East Lansing, MI 48824, USA",
  pages =        "ix + 63",
  year =         "1983",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer arithmetic and logic units; Electronic
                 digital computers --- Circuits; Floating-point
                 arithmetic; Integrated circuits --- Very large scale
                 integration.",
}


bibtype: article
filename: fparith.bib
label: Ulman:1983:SDI
author: Z. D. Ulman
title: Sign Detection and Implicit-Explicit Conversion of Numbers in Residue Arithmetic
journal: j-IEEE-TRANS-COMPUT
volume: C-32
number: 6
pages: 590--594
month: jun
monthnumber: 6
year: 1983
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1983.1676282
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 10:01:10 MDT 2011
bibtimestamp: 2011.07.10 10:01:10 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676282
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Z. D. Ulman
rawtitle: Sign Detection and Implicit-Explicit Conversion of Numbers in Residue Arithmetic
entry:
@Article{Ulman:1983:SDI,
  author =       "Z. D. Ulman",
  title =        "Sign Detection and Implicit-Explicit Conversion of
                 Numbers in Residue Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "6",
  pages =        "590--594",
  month =        jun,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676282",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:01:10 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676282",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Voelz:1983:CAE
author: H. Volz
journal: j-NACH-ELEK
volume: 33
number: 12
pages: 506--510
year: 1983
CODEN: NTELAP
ISSN: 0323-4657 OR 03234657
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: Nachrichtentechnik Elektronik
acknowledgement: ack-nj
rawauthor: H. V{\"o}lz
title:
CORDIC und ahnliche Algorithmen der elementaren Funktionen mit besonderer Eignung fur Mikrorechner toenglish CORDIC and Similar Algorithms for Elementary Functions with Particular Aptitude for Microcomputers endtoenglish 

rawtitle:
{CORDIC und {\"a}hnliche Algorithmen der elementaren Funktionen mit besonderer Eignung f{\"u}r Mikrorechner} \toenglish {CORDIC and Similar Algorithms for Elementary Functions with Particular Aptitude for Microcomputers} \endtoenglish

entry:
@Article{Voelz:1983:CAE,
  author =       "H. V{\"o}lz",
  title =        "{CORDIC und {\"a}hnliche Algorithmen der elementaren
                 Funktionen mit besonderer Eignung f{\"u}r Mikrorechner}
                 \toenglish {CORDIC and Similar Algorithms for
                 Elementary Functions with Particular Aptitude for
                 Microcomputers} \endtoenglish",
  journal =      j-NACH-ELEK,
  volume =       "33",
  number =       "12",
  pages =        "506--510",
  month =        "????",
  year =         "1983",
  CODEN =        "NTELAP",
  ISSN =         "0323-4657",
  bibdate =      "Fri Sep 16 16:30:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Nachrichtentechnik Elektronik",
}


bibtype: article
filename: fparith.bib
label: Vogt:1983:AFM
author: R. Vogt and R. Waser
journal: j-ELECTRONIK
volume: 20
pages: 85--92
year: 1983
CODEN: EKRKAR
ISSN: 0013-5658 OR 00135658
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: Elektronik
acknowledgement: ack-nj
rawauthor: R. Vogt and R. Waser
title:
Arithmetikroutinen fur die Mess datenverarbeitung toenglish Arithmetic Routines for Measurement Applications endtoenglish 

rawtitle:
{Arithmetikroutinen f{\"u}r die Me{\ss}\-dat\-en\-ver\-ar\-beit\-ung} \toenglish {Arithmetic Routines for Measurement Applications} \endtoenglish

entry:
@Article{Vogt:1983:AFM,
  author =       "R. Vogt and R. Waser",
  title =        "{Arithmetikroutinen f{\"u}r die
                 Me{\ss}\-dat\-en\-ver\-ar\-beit\-ung} \toenglish
                 {Arithmetic Routines for Measurement Applications}
                 \endtoenglish",
  journal =      j-ELECTRONIK,
  volume =       "20",
  pages =        "85--92",
  year =         "1983",
  CODEN =        "EKRKAR",
  ISSN =         "0013-5658",
  bibdate =      "Fri Sep 16 16:30:39 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Elektronik",
}


bibtype: inproceedings
filename: fparith.bib
label: Wallis:1983:AFP
author: Peter J. L. Wallis
title: Ada Floating-Point Arithmetic as a Basis for Portable Numerical Software
crossref: IEEE:1983:PSC
pages: 79--81
year: 1983
bibdate: Tue Nov 13 15:58:57 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.13 15:58:57 ???
URL: http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Wallis.pdf
keywords: Ada; ARITH-6
acknowledgement: ack-nhfb
rawauthor: Peter J. L. Wallis
rawtitle: {Ada} Floating-Point Arithmetic as a Basis for Portable Numerical Software
abstract:
Ada supports two different schemes for floating-point arithmetic portability -- one based on the use of the underlying machine arithmetic and the other based on the `model arithmetic' that the underlying machine supports, Features of both schemes are explained in the context of their suitability as bases for the production of portable numerical software.

rawabstract:
Ada supports two different schemes for floating-point arithmetic portability -- one based on the use of the underlying machine arithmetic and the other based on the `model arithmetic' that the underlying machine supports, Features of both schemes are explained in the context of their suitability as bases for the production of portable numerical software.

entry:
@InProceedings{Wallis:1983:AFP,
  author =       "Peter J. L. Wallis",
  title =        "{Ada} Floating-Point Arithmetic as a Basis for
                 Portable Numerical Software",
  crossref =     "IEEE:1983:PSC",
  pages =        "79--81",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Wallis.pdf",
  abstract =     "Ada supports two different schemes for floating-point
                 arithmetic portability -- one based on the use of the
                 underlying machine arithmetic and the other based on
                 the `model arithmetic' that the underlying machine
                 supports, Features of both schemes are explained in the
                 context of their suitability as bases for the
                 production of portable numerical software.",
  acknowledgement = ack-nhfb,
  keywords =     "Ada; ARITH-6",
}


bibtype: mastersthesis
filename: fparith.bib
label: Walsh:1983:FGE
author: Edmund John Walsh
type: Thesis (M.S.)
school: Boston University
address: Boston, MA, USA
pages: v + 121
year: 1983
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Boston University. --- College of Engineering --- Theses.
acknowledgement: ack-nhfb
rawauthor: Edmund John Walsh
title:
Floating gatefield effect transistor operating point changes: causes, characterization, and effect on electric field measurement by the device

rawtitle:
Floating gatefield effect transistor operating point changes: causes, characterization, and effect on electric field measurement by the device

entry:
@MastersThesis{Walsh:1983:FGE,
  author =       "Edmund John Walsh",
  title =        "Floating gatefield effect transistor operating point
                 changes: causes, characterization, and effect on
                 electric field measurement by the device",
  type =         "Thesis ({M.S.})",
  school =       "Boston University",
  address =      "Boston, MA, USA",
  pages =        "v + 121",
  year =         "1983",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Boston University. --- College of Engineering ---
                 Theses.",
}


bibtype: article
filename: fparith.bib
label: Watanuki:1983:EAC
author: Osaaki Watanuki and Milos D. Ercegovac
title: Error analysis of certain floating-point on-line algorithms
journal: j-IEEE-TRANS-COMPUT
volume: C-32
number: 4
pages: 352--358
month: apr
monthnumber: 4
year: 1983
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1983.1676236
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
MRclass: 65G05
MRnumber: 85h:65099
bibdate: Sun Jul 10 10:01:08 MDT 2011
bibtimestamp: 2011.07.10 10:01:08 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676236
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
reviewer: Oliver, J
rawauthor: Osaaki Watanuki and Milo{\v{s}} D. Ercegovac
rawtitle: Error analysis of certain floating-point on-line algorithms
bibsource:
ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib

abstract:
he properties of redundant number system in significand (mantissa) representation are studied and the range of redundant significand is derived. From the range of the redundant significand and the absolute error of on-line operations, the MRRE (maximum relative representation error) is defined and analyzed for floating-point on-line addition and multiplication.

subject:
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS

rawabstract:
he properties of redundant number system in significand (mantissa) representation are studied and the range of redundant significand is derived. From the range of the redundant significand and the absolute error of on-line operations, the MRRE (maximum relative representation error) is defined and analyzed for floating-point on-line addition and multiplication.

entry:
@Article{Watanuki:1983:EAC,
  author =       "Osaaki Watanuki and Milo{\v{s}} D. Ercegovac",
  title =        "Error analysis of certain floating-point on-line
                 algorithms",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "4",
  pages =        "352--358",
  month =        apr,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676236",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  MRclass =      "65G05",
  MRnumber =     "85h:65099",
  bibdate =      "Sun Jul 10 10:01:08 MDT 2011",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676236",
  abstract =     "he properties of redundant number system in
                 significand (mantissa) representation are studied and
                 the range of redundant significand is derived. From the
                 range of the redundant significand and the absolute
                 error of on-line operations, the MRRE (maximum relative
                 representation error) is defined and analyzed for
                 floating-point on-line addition and multiplication.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  catcode =      "G.1.0; G.1.0",
  CRclass =      "G.1.0 General; G.1.0 Error analysis; G.1.0 General;
                 G.1.0 Parallel algorithms",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Error analysis; Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Parallel algorithms",
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  guideno =      "06565",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  reviewer =     "Oliver, J",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}


bibtype: mastersthesis
filename: fparith.bib
label: Williams:1983:BFP
author: Bertrand Jeffery Williams
title: A bit-serial floating point multiply / add architecture for signal processing applications
type: Electrical Engineering Thesis (M.S.)
school: Texas A&M University
address: College Station, TX, USA
pages: x + 97
year: 1983
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Computer architecture.; Floating-point arithmetic.; Signal processing.
acknowledgement: ack-nhfb
rawauthor: Bertrand Jeffery Williams
rawtitle: A bit-serial floating point multiply\slash add architecture for signal processing applications
entry:
@MastersThesis{Williams:1983:BFP,
  author =       "Bertrand Jeffery Williams",
  title =        "A bit-serial floating point multiply\slash add
                 architecture for signal processing applications",
  type =         "Electrical Engineering Thesis ({M.S.})",
  school =       "Texas A\&M University",
  address =      "College Station, TX, USA",
  pages =        "x + 97",
  year =         "1983",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer architecture.; Floating-point arithmetic.;
                 Signal processing.",
}


bibtype: article
filename: fparith.bib
label: Wingert:1983:ITA
author: J. A. Wingert
title: Improved Table-assisted Addition and Multiplication Methods
journal: j-IBM-TDB
volume: 25
number: 9
pages: 4742--4743
month: feb
monthnumber: 2
year: 1983
CODEN: IBMTAA
ISSN: 0018-8689 OR 00188689
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: IBM Technical Disclosure Bulletin
acknowledgement: ack-nj
rawauthor: J. A. Wingert
rawtitle: Improved Table-assisted Addition and Multiplication Methods
entry:
@Article{Wingert:1983:ITA,
  author =       "J. A. Wingert",
  title =        "Improved Table-assisted Addition and Multiplication
                 Methods",
  journal =      j-IBM-TDB,
  volume =       "25",
  number =       "9",
  pages =        "4742--4743",
  month =        feb,
  year =         "1983",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Thu Sep 1 10:16:11 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IBM Technical Disclosure Bulletin",
}


bibtype: inproceedings
filename: fparith.bib
label: Yoshida:1983:FPR
author: Kaoru Yoshida
title: Floating-Point Recurring Rational Arithmetic System
crossref: IEEE:1983:PSC
pages: 194--200
year: 1983
bibdate: Tue Nov 13 15:58:57 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.13 15:58:57 ???
URL: http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Yoshida.pdf
keywords: ARITH-6; rational arithmetic
acknowledgement: ack-nhfb
rawauthor: Kaoru Yoshida
rawtitle: Floating-Point Recurring Rational Arithmetic System
abstract:
Major computer arithmetic systems are based on the concept of realizing only terminate rationals in positional notation. This paper proposes a new arithmetic scheme of indicating periodicity in the radix representation of a mantissa to realize recurring rationals as well as terminate rationals. A new arithmetic system adopting the scheme, called the ``FLP/R* arithmetic system'', is proposed. Properties of the FLP/R* numbers and the procedure of the FLP/R* arithmetic are described.

rawabstract:
Major computer arithmetic systems are based on the concept of realizing only terminate rationals in positional notation. This paper proposes a new arithmetic scheme of indicating periodicity in the radix representation of a mantissa to realize recurring rationals as well as terminate rationals. A new arithmetic system adopting the scheme, called the ``FLP/R* arithmetic system'', is proposed. Properties of the FLP/R* numbers and the procedure of the FLP/R* arithmetic are described.

entry:
@InProceedings{Yoshida:1983:FPR,
  author =       "Kaoru Yoshida",
  title =        "Floating-Point Recurring Rational Arithmetic System",
  crossref =     "IEEE:1983:PSC",
  pages =        "194--200",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Yoshida.pdf",
  abstract =     "Major computer arithmetic systems are based on the
                 concept of realizing only terminate rationals in
                 positional notation. This paper proposes a new
                 arithmetic scheme of indicating periodicity in the
                 radix representation of a mantissa to realize recurring
                 rationals as well as terminate rationals. A new
                 arithmetic system adopting the scheme, called the
                 ``FLP/R* arithmetic system'', is proposed. Properties
                 of the FLP/R* numbers and the procedure of the FLP/R*
                 arithmetic are described.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6; rational arithmetic",
}


bibtype: article
filename: fparith.bib
label: Ypma:1983:ERE
author: T. J. Ypma
title: The effect of rounding errors on Newtonlike methods
journal: j-IMA-J-NUMER-ANAL
volume: 3
number: 1
pages: 109--118
year: 1983
CODEN: IJNADH
ISSN: 0272-4979 (print), 1464-3642 (electronic) OR 02724979 (print), 14643642 (electronic)
ISSNL: 0272-4979 OR 02724979
MRclass: 65G05 (65H05)
MRnumber: 84h:65047
MRreviewer: Ren{\'e} Alt
bibdate: Sat Dec 23 17:06:35 MST 2000
bibtimestamp: 2000.12.23 17:06:35 MST
fjournal: IMA Journal of Numerical Analysis
acknowledgement: ack-nhfb
journalURL: http://imajna.oxfordjournals.org/content/by/year
rawauthor: T. J. Ypma
rawtitle: The effect of rounding errors on {Newtonlike} methods
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib; MathSciNet database

entry:
@Article{Ypma:1983:ERE,
  author =       "T. J. Ypma",
  title =        "The effect of rounding errors on {Newtonlike}
                 methods",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "3",
  number =       "1",
  pages =        "109--118",
  year =         "1983",
  CODEN =        "IJNADH",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  MRclass =      "65G05 (65H05)",
  MRnumber =     "84h:65047",
  MRreviewer =   "Ren{\'e} Alt",
  bibdate =      "Sat Dec 23 17:06:35 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib;
                 MathSciNet database",
  acknowledgement = ack-nhfb,
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
}


bibtype: inproceedings
filename: fparith.bib
label: Abruzzo:1984:ACA
author: J. Abruzzo
title: Applicability of CORDIC Algorithm to Arithmetic Processing
crossref: Kirk:1984:CRE
pages: 79--86
year: 1984
bibdate: Thu Sep 01 11:21:05 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 11:21:05 ???
acknowledgement: ack-nj
rawauthor: J. Abruzzo
rawtitle: Applicability of {CORDIC} Algorithm to Arithmetic Processing
entry:
@InProceedings{Abruzzo:1984:ACA,
  author =       "J. Abruzzo",
  title =        "Applicability of {CORDIC} Algorithm to Arithmetic
                 Processing",
  crossref =     "Kirk:1984:CRE",
  pages =        "79--86",
  year =         "1984",
  bibdate =      "Thu Sep 01 11:21:05 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: Agrawal:1984:ACB
author: V. K. Agrawal and S. Murugesan
title: Algorithm converts BCD fractions to binary
journal: j-EDN
volume: 29
number: 13
pages: 278--280
month: jun
monthnumber: 6
year: 1984
CODEN: EDNSBH
ISSN: 0012-7515, 0364-6637 OR 00127515, 03646637
bibdate: Thu Sep 1 10:16:10 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:16:10 ???
fjournal: EDN
acknowledgement: ack-nj
rawauthor: V. K. Agrawal and S. Murugesan
rawtitle: Algorithm converts {BCD} fractions to binary
entry:
@Article{Agrawal:1984:ACB,
  author =       "V. K. Agrawal and S. Murugesan",
  title =        "Algorithm converts {BCD} fractions to binary",
  journal =      j-EDN,
  volume =       "29",
  number =       "13",
  pages =        "278--280",
  month =        jun,
  year =         "1984",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  bibdate =      "Thu Sep 1 10:16:10 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "EDN",
}


bibtype: article
filename: fparith.bib
label: Alia:1984:VAD
author: G. Alia and E. Martinelli
journal: j-IEEE-TRANS-CIRCUITS-SYST
volume: 31
number: 12
pages: 1033--1039
month: dec
monthnumber: 12
year: 1984
CODEN: ICSYBT
DOI: https://doi.org/10.1109/TC.1984.1676355
ISSN: 0098-4094 (print), 1558-1276 (electronic) OR 00984094 (print), 15581276 (electronic)
ISSNL: 0098-4094 OR 00984094
bibdate: Fri Nov 9 11:38:57 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:57 MST
URL: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23552
fjournal: IEEE Transactions on Circuits and Systems
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: G. Alia and E. Martinelli
title:
A VLSI algorithm for direct and reverse conversion from weighted binary number system to residue number system

rawtitle:
A {VLSI} algorithm for direct and reverse conversion from weighted binary number system to residue number system

entry:
@Article{Alia:1984:VAD,
  author =       "G. Alia and E. Martinelli",
  title =        "A {VLSI} algorithm for direct and reverse conversion
                 from weighted binary number system to residue number
                 system",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "31",
  number =       "12",
  pages =        "1033--1039",
  month =        dec,
  year =         "1984",
  CODEN =        "ICSYBT",
  DOI =          "https://doi.org/10.1109/TC.1984.1676355",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23552",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  keywords =     "residue arithmetic; residue number system",
  summary =      "Residue Number Systems (RNS) are proved to be useful
                 in many applications, as for example in signal
                 processing. In this paper, a VLSI computing
                 architecture is proposed for converting an integer
                 number N from the weighted binary representation into
                 \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Ancona:1984:PET
author: M. Ancona and G. Dodero and F. Ricci
title: A portable environment for teaching mathematical software development
crossref: Ford:1984:TML
pages: 135--145
year: 1984
bibdate: Sat Nov 9 08:26:18 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.11.09 08:26:18 MST
note: See main entry CR, Rev. 8508--0689.
acknowledgement: ack-nhfb
rawauthor: M. Ancona and G. Dodero and F. Ricci
rawnote: See main entry CR, Rev. 8508--0689.
rawtitle: A portable environment for teaching mathematical software development
subject:
G. Mathematics of Computing; G.4 MATHEMATICAL SOFTWARE; K. Computing Milieux; K.6 MANAGEMENT OF COMPUTING AND INFORMATION SYSTEMS; D. Software; D.2 SOFTWARE ENGINEERING; K. Computing Milieux; K.3 COMPUTERS AND EDUCATION

entry:
@InProceedings{Ancona:1984:PET,
  author =       "M. Ancona and G. Dodero and F. Ricci",
  title =        "A portable environment for teaching mathematical
                 software development",
  crossref =     "Ford:1984:TML",
  pages =        "135--145",
  year =         "1984",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See main entry CR, Rev. 8508--0689.",
  acknowledgement = ack-nhfb,
  content =      "ALGORITHMS; DESIGN; LANGUAGES; STANDARDIZATION",
  procloc =      "Proceedings paper",
  subject =      "G. Mathematics of Computing; G.4 MATHEMATICAL
                 SOFTWARE; K. Computing Milieux; K.6 MANAGEMENT OF
                 COMPUTING AND INFORMATION SYSTEMS; D. Software; D.2
                 SOFTWARE ENGINEERING; K. Computing Milieux; K.3
                 COMPUTERS AND EDUCATION",
  subjects =     "mathematics of computing, mathematical software,
                 portability; computing milieux, management of computing
                 and information systems, software management, software
                 development; software, software engineering,
                 distribution and maintenance, portability; computing
                 milieux, computers and education, computer and
                 information science education, computer science
                 education",
  wsub =         "A. C. R. Newbery",
}


bibtype: article
filename: fparith.bib
label: Anonymous:1984:CPD
author: Anonymous
title: Correction to ``A Pipelined Distributed Arithmetic PFFT Processor''
journal: j-IEEE-TRANS-COMPUT
volume: C-33
number: 3
pages: 288--288
month: mar
monthnumber: 3
year: 1984
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1984.1676429
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 09:22:50 MDT 2011
bibtimestamp: 2011.07.10 09:22:50 MDT
note: See cite Chow:1983:PDA.
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676429
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Anonymous
rawnote: See \cite{Chow:1983:PDA}.
rawtitle: Correction to {``A Pipelined Distributed Arithmetic PFFT Processor''}
entry:
@Article{Anonymous:1984:CPD,
  author =       "Anonymous",
  title =        "Correction to {``A Pipelined Distributed Arithmetic
                 PFFT Processor''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-33",
  number =       "3",
  pages =        "288--288",
  month =        mar,
  year =         "1984",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1984.1676429",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 09:22:50 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  note =         "See \cite{Chow:1983:PDA}.",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676429",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Bell:1984:RMR
author: M. Bell, Jr. and W. Jenkins
booktitle: IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP '84
title: A residue to mixed radix converter and error checker for a five-moduli residue number system
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 242--245
year: 1984
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: M. {Bell, Jr.} and W. Jenkins
rawbooktitle: {IEEE} International Conference on Acoustics, Speech, and Signal Processing, {ICASSP '84}
rawtitle: A residue to mixed radix converter and error checker for a five-moduli residue number system
entry:
@InProceedings{Bell:1984:RMR,
  author =       "M. {Bell, Jr.} and W. Jenkins",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing, {ICASSP '84}",
  title =        "A residue to mixed radix converter and error checker
                 for a five-moduli residue number system",
  volume =       "??",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "242--245",
  year =         "1984",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A design is presented for an experimental device which
                 converts data from residue representation to mixed
                 radix representation while simultaneously checking for
                 single digit errors. The experimental system has a high
                 speed pipelined architecture and \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Black:1984:NIS
author: Cheryl M. Black and Robert P. Burton and Thomas M. Miller
title: The Need for an Industry Standard of Accuracy for Elementary-Function Programs
journal: j-TOMS
volume: 10
number: 4
pages: 361--366
month: dec
monthnumber: 12
year: 1984
CODEN: ACMSCU
DOI: https://doi.org/10.1145/2701.356101
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sun Sep 04 20:32:29 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.04 20:32:29 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Cheryl M. Black and Robert P. Burton and Thomas M. Miller
rawtitle: The Need for an Industry Standard of Accuracy for Elementary-Function Programs
entry:
@Article{Black:1984:NIS,
  author =       "Cheryl M. Black and Robert P. Burton and Thomas M.
                 Miller",
  title =        "The Need for an Industry Standard of Accuracy for
                 Elementary-Function Programs",
  journal =      j-TOMS,
  volume =       "10",
  number =       "4",
  pages =        "361--366",
  month =        dec,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2701.356101",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 20:32:29 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: fparith.bib
label: Bollen:1984:NSD
author: J. A. M. Bollen
title: Numerical Stability of Descent Methods for Solving Linear Equations
journal: j-NUM-MATH
volume: 43
number: 3
pages: 361--377
year: 1984
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
MRclass: 65G05 (65F10)
MRnumber: 85f:65041
bibdate: Mon May 26 11:49:34 MDT 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.05.26 11:49:34 MDT
fjournal: Numerische Mathematik
acknowledgement: ack-nhfb
corpsource: Department of Appl. Maths., Twente University of Technol., Enschede, Netherlands
journalURL: http://link.springer.com/journal/211
treatment: T Theoretical or Mathematical
rawauthor: J. A. M. Bollen
rawtitle: Numerical Stability of Descent Methods for Solving Linear Equations
keywords:
descent methods; digital arithmetic; error analysis; floating point arithmetic; Gauss-Southwell method; gradient method; linear differential equations; linear equations; linear systems; numerical stability; roundoff error analysis; stability

entry:
@Article{Bollen:1984:NSD,
  author =       "J. A. M. Bollen",
  title =        "Numerical Stability of Descent Methods for Solving
                 Linear Equations",
  journal =      j-NUM-MATH,
  volume =       "43",
  number =       "3",
  pages =        "361--377",
  year =         "1984",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65G05 (65F10)",
  MRnumber =     "85f:65041",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "B0290B (Error analysis in numerical methods); C4110
                 (Error analysis in numerical methods)",
  corpsource =   "Department of Appl. Maths., Twente University of
                 Technol., Enschede, Netherlands",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "descent methods; digital arithmetic; error analysis;
                 floating point arithmetic; Gauss-Southwell method;
                 gradient method; linear differential equations; linear
                 equations; linear systems; numerical stability;
                 roundoff error analysis; stability",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: inproceedings
filename: fparith.bib
label: Boney:1984:GTD
author: J. Boney
title: Goals and tradeoffs in the design of the MC68881 floating point coprocessor
crossref: NCC:1984:ACP
pages: 107--113
year: 1984
bibdate: Wed Sep 7 22:31:45 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.07 22:31:45 ???
acknowledgement: ack-nj
rawauthor: J. Boney
rawtitle: Goals and tradeoffs in the design of the {MC68881} floating point coprocessor
entry:
@InProceedings{Boney:1984:GTD,
  author =       "J. Boney",
  title =        "Goals and tradeoffs in the design of the {MC68881}
                 floating point coprocessor",
  crossref =     "NCC:1984:ACP",
  pages =        "107--113",
  year =         "1984",
  bibdate =      "Wed Sep 7 22:31:45 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: Borwein:1984:AGM
author: J. M. Borwein and P. B. Borwein
title: The Arithmetic-Geometric Mean and Fast Computation of Elementary Functions
journal: j-SIAM-REVIEW
volume: 26
number: 3
pages: 351--366
month: jul
monthnumber: 7
year: 1984
CODEN: SIREAD
DOI: https://doi.org/10.1137/1026073
ISSN: 0036-1445 (print), 1095-7200 (electronic) OR 00361445 (print), 10957200 (electronic)
ISSNL: 0036-1445 OR 00361445
MRclass: 65D20 (26A09)
MRnumber: 86d:65029
MRreviewer: S. Conde
bibdate: Sat Mar 29 09:53:48 MDT 2014
bibtimestamp: 2014.03.29 09:53:48 MDT
fjournal: SIAM Review
acknowledgement: ack-nhfb
affiliationaddress: Dalhousie Univ, Halifax, NS, Can
journalURL: http://epubs.siam.org/sirev
journalabr: SIAM Rev
onlinedate: July 1984
rawauthor: J. M. Borwein and P. B. Borwein
rawtitle: The Arithmetic-Geometric Mean and Fast Computation of Elementary Functions
bibsource:
Compendex database; ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; http://epubs.siam.org/toc/siread/26/3; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib

abstract:
We produce a self contained account of the relationship between the Gaussian arithmetic-geometric mean iteration and the fast computation of elementary functions. A particularly pleasant algorithm for pi is one of the by-products.

keywords:
AGM (Arithmetic-Geometric Mean); arithmetic-geometric mean; calculation of pi; computational methods; elliptic functions; Iterative Methods; mathematical techniques; numerical mathematics

rawabstract:
We produce a self contained account of the relationship between the Gaussian arithmetic-geometric mean iteration and the fast computation of elementary functions. A particularly pleasant algorithm for pi is one of the by-products.

entry:
@Article{Borwein:1984:AGM,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "The Arithmetic-Geometric Mean and Fast Computation of
                 Elementary Functions",
  journal =      j-SIAM-REVIEW,
  volume =       "26",
  number =       "3",
  pages =        "351--366",
  month =        jul,
  year =         "1984",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1026073",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  MRclass =      "65D20 (26A09)",
  MRnumber =     "86d:65029",
  MRreviewer =   "S. Conde",
  bibdate =      "Sat Mar 29 09:53:48 MDT 2014",
  bibsource =    "Compendex database;
                 ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 http://epubs.siam.org/toc/siread/26/3;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  abstract =     "We produce a self contained account of the
                 relationship between the Gaussian arithmetic-geometric
                 mean iteration and the fast computation of elementary
                 functions. A particularly pleasant algorithm for pi is
                 one of the by-products.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliationaddress = "Dalhousie Univ, Halifax, NS, Can",
  classification = "723; 921",
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  journalabr =   "SIAM Rev",
  keywords =     "AGM (Arithmetic-Geometric Mean); arithmetic-geometric
                 mean; calculation of pi; computational methods;
                 elliptic functions; Iterative Methods; mathematical
                 techniques; numerical mathematics",
  onlinedate =   "July 1984",
}


bibtype: inproceedings
filename: fparith.bib
label: Braddock:1984:ASP
author: M. Braddock and V. Shahan
title: Amplifying System Performance in Floating-point Intensive Applications with the MC68881
crossref: Mini-Micro:1984:MMS
pages: 6/2/1--7
year: 1984
bibdate: Wed Sep 7 22:31:45 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.07 22:31:45 ???
acknowledgement: ack-nj
rawauthor: M. Braddock and V. Shahan
rawtitle: Amplifying System Performance in Floating-point Intensive Applications with the {MC68881}
entry:
@InProceedings{Braddock:1984:ASP,
  author =       "M. Braddock and V. Shahan",
  title =        "Amplifying System Performance in Floating-point
                 Intensive Applications with the {MC68881}",
  crossref =     "Mini-Micro:1984:MMS",
  pages =        "6/2/1--7",
  year =         "1984",
  bibdate =      "Wed Sep 7 22:31:45 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: Butterfield:1984:MT
author: J. Butterfield
title: Math and Tables
journal: j-COMPUTE
volume: 6
number: 9
pages: 134--135
month: sep
monthnumber: 9
year: 1984
CODEN: COMPER
ISSN: 0194-357X OR 0194357X
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: Compute
acknowledgement: ack-nj
rawauthor: J. Butterfield
rawtitle: Math and Tables
entry:
@Article{Butterfield:1984:MT,
  author =       "J. Butterfield",
  title =        "Math and Tables",
  journal =      j-COMPUTE,
  volume =       "6",
  number =       "9",
  pages =        "134--135",
  month =        sep,
  year =         "1984",
  CODEN =        "COMPER",
  ISSN =         "0194-357X",
  bibdate =      "Thu Sep 1 10:15:30 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Compute",
}


bibtype: article
filename: fparith.bib
label: Caraiscos:1984:REA
author: C. Caraiscos and Bede Liu
title: A roundoff error analysis of the LMS adaptive algorithm
journal: j-IEEE-TRANS-ACOUST-SPEECH
volume: 32
number: 1
pages: 34--41
month: feb
monthnumber: 2
year: 1984
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: C. Caraiscos and Bede Liu
rawtitle: A roundoff error analysis of the {LMS} adaptive algorithm
entry:
@Article{Caraiscos:1984:REA,
  author =       "C. Caraiscos and Bede Liu",
  title =        "A roundoff error analysis of the {LMS} adaptive
                 algorithm",
  journal =      j-IEEE-TRANS-ACOUST-SPEECH,
  volume =       "32",
  number =       "1",
  pages =        "34--41",
  month =        feb,
  year =         "1984",
  CODEN =        "IETABA",
  ISSN =         "0096-3518",
  bibdate =      "Sat Jul 16 11:25:06 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Acoustics, Speech, and Signal
                 Processing",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
  summary =      "The steady state output error of the least mean square
                 (LMS) adaptive algorithm due to the finite precision
                 arithmetic of a digital processor is analyzed. It is
                 found to consist of three terms: (1) the error due to
                 the input data quantization, (2) the \ldots{}",
}


bibtype: book
filename: fparith.bib
label: Cavanagh:1984:DCA
author: Joseph J. F. Cavanagh
title: Digital Computer Arithmetic: Design and Implementation
publisher: pub-WILEY
address: pub-WILEY:adr
pages: xi + 468
year: 1984
ISBN: 0-07-010282-1 OR 0070102821
ISBN13: 978-0-07-010282-8 OR 9780070102828
LCCN: QA76.9.C62 C38 1984
bibdate: Sat May 18 14:16:35 2002
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.18 14:16:35 ???
acknowledgement: ack-nj
rawauthor: Joseph J. F. Cavanagh
rawtitle: Digital Computer Arithmetic: Design and Implementation
entry:
@Book{Cavanagh:1984:DCA,
  author =       "Joseph J. F. Cavanagh",
  title =        "Digital Computer Arithmetic: Design and
                 Implementation",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xi + 468",
  year =         "1984",
  ISBN =         "0-07-010282-1",
  ISBN-13 =      "978-0-07-010282-8",
  LCCN =         "QA76.9.C62 C38 1984",
  bibdate =      "Sat May 18 14:16:35 2002",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$21.95",
  acknowledgement = ack-nj,
}


bibtype: mastersthesis
filename: fparith.bib
label: Cheng:1984:FPC
author: Doreen Y. Cheng
title: A floating point coprocessor for the Butterfly multiprocessor system: research project
type: Thesis (M.S. in Electrical Engineering)
school: University of California, Berkeley. Dept. of Electrical Engineering and Computer Sciences
address: Berkeley, CA, USA
pages: 51 + 38
month: may
monthnumber: 5
year: 1984
bibdate: Wed Nov 25 08:35:11 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.11.25 08:35:11 ???
acknowledgement: ack-nhfb
rawauthor: Doreen Y. Cheng
rawtitle: A floating point coprocessor for the {Butterfly} multiprocessor system: research project
entry:
@MastersThesis{Cheng:1984:FPC,
  author =       "Doreen Y. Cheng",
  title =        "A floating point coprocessor for the {Butterfly}
                 multiprocessor system: research project",
  type =         "Thesis ({M.S. in Electrical Engineering})",
  school =       "University of California, Berkeley. Dept. of
                 Electrical Engineering and Computer Sciences",
  address =      "Berkeley, CA, USA",
  pages =        "51 + 38",
  month =        may,
  year =         "1984",
  bibdate =      "Wed Nov 25 08:35:11 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Clarke:1984:AAR
author: M. R. Clarke
title: An Analytical Approach to Rounding
journal: j-J-APPL-STAT
volume: 11
number: 1
pages: 12--20
year: 1984
DOI: https://doi.org/10.1080/02664768400000003
ISSN: 0266-4763 (print), 1360-0532 (electronic) OR 02664763 (print), 13600532 (electronic)
ISSNL: 0266-4763 OR 02664763
bibdate: Tue Sep 6 11:15:48 MDT 2011
bibtimestamp: 2011.09.06 11:15:48 MDT
fjournal: Journal of Applied Statistics
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/cjas20
onlinedate: 28 Jul 2006
rawauthor: M. R. Clarke
rawtitle: An Analytical Approach to Rounding
bibsource:
http://www.tandf.co.uk/journals/routledge/02664763.html; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Clarke:1984:AAR,
  author =       "M. R. Clarke",
  title =        "An Analytical Approach to Rounding",
  journal =      j-J-APPL-STAT,
  volume =       "11",
  number =       "1",
  pages =        "12--20",
  year =         "1984",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/02664768400000003",
  ISSN =         "0266-4763 (print), 1360-0532 (electronic)",
  ISSN-L =       "0266-4763",
  bibdate =      "Tue Sep 6 11:15:48 MDT 2011",
  bibsource =    "http://www.tandf.co.uk/journals/routledge/02664763.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Statistics",
  journal-URL =  "http://www.tandfonline.com/loi/cjas20",
  onlinedate =   "28 Jul 2006",
}


bibtype: article
filename: fparith.bib
label: Clenshaw:1984:BFP
author: C. W. Clenshaw and F. W. J. Olver
title: Beyond Floating Point
journal: j-J-ACM
volume: 31
number: 2
pages: 319--328
month: apr
monthnumber: 4
year: 1984
CODEN: JACOAH
DOI: https://doi.org/10.1145/62.322429
ISSN: 0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)
ISSNL: 0004-5411 OR 00045411
MRclass: 65G05
MRnumber: 819 141
bibdate: Wed Jan 15 18:12:53 MST 1997
bibtimestamp: 1997.01.15 18:12:53 MST
fjournal: Journal of the Association for Computing Machinery
acknowledgement: ack-nhfb
affiliationaddress: Univ of Lancaster, Dep of Mathematics, Lancaster, Engl
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J401
journalabr: J Assoc Comput Mach
rawauthor: C. W. Clenshaw and F. W. J. Olver
rawtitle: Beyond Floating Point
bibsource:
Compendex database; ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/jacm.bib

abstract:
A new number system is proposed for computer arithmetic based on iterated exponential functions. The main advantage is to eradicate overflow and underflow, but there are several other advantages and these are described and discussed.

keywords:
computer arithmetic; computer metatheory; error analysis; mathematical techniques --- Digital Arithmetic; overflow; rounding error; underflow

rawabstract:
A new number system is proposed for computer arithmetic based on iterated exponential functions. The main advantage is to eradicate overflow and underflow, but there are several other advantages and these are described and discussed.

entry:
@Article{Clenshaw:1984:BFP,
  author =       "C. W. Clenshaw and F. W. J. Olver",
  title =        "Beyond Floating Point",
  journal =      j-J-ACM,
  volume =       "31",
  number =       "2",
  pages =        "319--328",
  month =        apr,
  year =         "1984",
  CODEN =        "JACOAH",
  DOI =          "https://doi.org/10.1145/62.322429",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  MRclass =      "65G05",
  MRnumber =     "819 141",
  bibdate =      "Wed Jan 15 18:12:53 MST 1997",
  bibsource =    "Compendex database;
                 ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jacm.bib",
  abstract =     "A new number system is proposed for computer
                 arithmetic based on iterated exponential functions. The
                 main advantage is to eradicate overflow and underflow,
                 but there are several other advantages and these are
                 described and discussed.",
  acknowledgement = ack-nhfb,
  affiliationaddress = "Univ of Lancaster, Dep of Mathematics,
                 Lancaster, Engl",
  classification = "723",
  fjournal =     "Journal of the Association for Computing Machinery",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
  journalabr =   "J Assoc Comput Mach",
  keywords =     "computer arithmetic; computer metatheory; error
                 analysis; mathematical techniques --- Digital
                 Arithmetic; overflow; rounding error; underflow",
}


bibtype: article
filename: fparith.bib
label: Cody:1984:PRW
title: A Proposed Radix- and Word-length-independent Standard for Floating-Point Arithmetic
journal: j-IEEE-MICRO
volume: 4
number: 4
pages: 86--100
month: jul
monthnumber: 7
year: 1984
CODEN: IEMIDZ
DOI: https://doi.org/10.1109/MM.1984.291224
ISSN: 0272-1732 (print), 1937-4143 (electronic) OR 02721732 (print), 19374143 (electronic)
ISSNL: 0272-1732 OR 02721732
bibdate: Thu Nov 8 14:50:28 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.08 14:50:28 ???
fjournal: IEEE Micro
acknowledgement: ack-nj
journalURL: http://www.computer.org/csdl/mags/mi/index.html
rawtitle: A Proposed Radix- and Word-length-independent Standard for Floating-Point Arithmetic
author:
William J. Cody, Jr. and Jerome T. Coonen and David M. Gay and K. Hanson and David Hough and W. Kahan and R. Karpinski and John F. Palmer and F. N. Ris and D. Stevenson

rawauthor:
William J. {Cody, Jr.} and Jerome T. Coonen and David M. Gay and K. Hanson and David Hough and W. Kahan and R. Karpinski and John F. Palmer and F. N. Ris and D. Stevenson

entry:
@Article{Cody:1984:PRW,
  author =       "William J. {Cody, Jr.} and Jerome T. Coonen and David
                 M. Gay and K. Hanson and David Hough and W. Kahan and
                 R. Karpinski and John F. Palmer and F. N. Ris and D.
                 Stevenson",
  title =        "A Proposed Radix- and Word-length-independent Standard
                 for Floating-Point Arithmetic",
  journal =      j-IEEE-MICRO,
  volume =       "4",
  number =       "4",
  pages =        "86--100",
  month =        jul # "\slash " # aug,
  year =         "1984",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/MM.1984.291224",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Thu Nov 8 14:50:28 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
}


bibtype: phdthesis
filename: fparith.bib
label: Coonen:1984:CPS
author: Jerome Toby Coonen
title: Contributions to a Proposed Standard for Binary Floating-Point Arithmetic
type: Thesis (Ph.D. in Mathematics)
school: Department of Mathematics, University of California at Berkeley
address: Berkeley, CA, USA
pages: 320
day: 18
month: dec
monthnumber: 12
year: 1984
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
remark: Doctoral degree conferred December 18, 1984.
acknowledgement: ack-nj
advisor: William M. Kahan
rawauthor: Jerome Toby Coonen
rawtitle: Contributions to a Proposed Standard for Binary Floating-Point Arithmetic
abstract:
In the fall of 1977 the Institute of Electrical and Electronics Engineers commissioned working group 754 to draft a standard for binary floating-point arithmetic. It was intended to prevent the proliferation of disparate arithmetics in the new microprocessor industry. At that time there were so many different flavors of arithmetic available on mainframes and minicomputers that the cost of reconciling their differences in numerical software had become, and remains, staggering. Now, more than five years later, draft 10.0 of the proposed standard has been voted out of the working group for IEEE approval.par This thesis consists of a set of ``footnotes'' to the proposed standard. The first of them, an implementation guide published in January 1980, served as a working draft of the standard for over a year. The remaining chapters unfolded as the proposed standard did. They include an analysis of gradual underflow, the most controversial feature of the standard; an exhaustive discussion of radix conversion, which has been specified in the proposed standard only up to a worst-case error bound; and a revised version of the arithmetic test suite which has been available in machine-readable form from the working group.

rawabstract:
In the fall of 1977 the Institute of Electrical and Electronics Engineers commissioned working group 754 to draft a standard for binary floating-point arithmetic. It was intended to prevent the proliferation of disparate arithmetics in the new microprocessor industry. At that time there were so many different flavors of arithmetic available on mainframes and minicomputers that the cost of reconciling their differences in numerical software had become, and remains, staggering. Now, more than five years later, draft 10.0 of the proposed standard has been voted out of the working group for IEEE approval.\par This thesis consists of a set of ``footnotes'' to the proposed standard. The first of them, an implementation guide published in January 1980, served as a working draft of the standard for over a year. The remaining chapters unfolded as the proposed standard did. They include an analysis of gradual underflow, the most controversial feature of the standard; an exhaustive discussion of radix conversion, which has been specified in the proposed standard only up to a worst-case error bound; and a revised version of the arithmetic test suite which has been available in machine-readable form from the working group.

entry:
@PhdThesis{Coonen:1984:CPS,
  author =       "Jerome Toby Coonen",
  title =        "Contributions to a Proposed Standard for Binary
                 Floating-Point Arithmetic",
  type =         "Thesis ({Ph.D.} in Mathematics)",
  school =       "Department of Mathematics, University of California at
                 Berkeley",
  address =      "Berkeley, CA, USA",
  pages =        "320",
  day =          "18",
  month =        dec,
  year =         "1984",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In the fall of 1977 the Institute of Electrical and
                 Electronics Engineers commissioned working group 754 to
                 draft a standard for binary floating-point arithmetic.
                 It was intended to prevent the proliferation of
                 disparate arithmetics in the new microprocessor
                 industry. At that time there were so many different
                 flavors of arithmetic available on mainframes and
                 minicomputers that the cost of reconciling their
                 differences in numerical software had become, and
                 remains, staggering. Now, more than five years later,
                 draft 10.0 of the proposed standard has been voted out
                 of the working group for IEEE approval.\par

                 This thesis consists of a set of ``footnotes'' to the
                 proposed standard. The first of them, an implementation
                 guide published in January 1980, served as a working
                 draft of the standard for over a year. The remaining
                 chapters unfolded as the proposed standard did. They
                 include an analysis of gradual underflow, the most
                 controversial feature of the standard; an exhaustive
                 discussion of radix conversion, which has been
                 specified in the proposed standard only up to a
                 worst-case error bound; and a revised version of the
                 arithmetic test suite which has been available in
                 machine-readable form from the working group.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  advisor =      "William M. Kahan",
  remark =       "Doctoral degree conferred December 18, 1984.",
}


bibtype: incollection
filename: fparith.bib
label: Corliss:1984:AGT
author: George F. Corliss and Louis B. Rall
crossref: Anonymous:1984:TFA
pages: 177--209
year: 1984
bibdate: Fri Dec 8 13:09:09 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 13:09:09 ???
keywords: automatic differentiation; stability.; Taylor series
acknowledgement: ack-nj
rawauthor: George F. Corliss and Louis B. Rall
title:
Automatic generation of Taylor series in Pascal-SC: Basic operations and applications to differential equations

abstract:
Pascal-SC supports user-defined data types, user-defined operators, and accurate floating point and interval arithmetic for numerical computations. The authors implement data types TAYLOR and ITAYLOR (Interval Taylor) with operators $+$, $-$, $*$, $/$, $ ** $, and the functions SQR, SQRT, EXP, SIN, COS, ARCTAN, and LN. An initial value problem $ y' = y^2 $, $ y(0) = 1 $, is solved with TAYLOR and with ITAYLOR types to show that the series generation exhibits a mild instability which has no significant effect on the values of the solution computed by analytic continuation.

rawabstract:
Pascal-SC supports user-defined data types, user-defined operators, and accurate floating point and interval arithmetic for numerical computations. The authors implement data types TAYLOR and ITAYLOR (Interval Taylor) with operators $+$, $-$, $*$, $/$, $ ** $, and the functions SQR, SQRT, EXP, SIN, COS, ARCTAN, and LN. An initial value problem $ y' = y^2 $, $ y(0) = 1 $, is solved with TAYLOR and with ITAYLOR types to show that the series generation exhibits a mild instability which has no significant effect on the values of the solution computed by analytic continuation.

rawtitle:
Automatic generation of {Taylor} series in {Pascal-SC}: {Basic} operations and applications to differential equations

entry:
@InCollection{Corliss:1984:AGT,
  author =       "George F. Corliss and Louis B. Rall",
  title =        "Automatic generation of {Taylor} series in
                 {Pascal-SC}: {Basic} operations and applications to
                 differential equations",
  crossref =     "Anonymous:1984:TFA",
  pages =        "177--209",
  year =         "1984",
  bibdate =      "Fri Dec 8 13:09:09 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Pascal-SC supports user-defined data types,
                 user-defined operators, and accurate floating point and
                 interval arithmetic for numerical computations. The
                 authors implement data types TAYLOR and ITAYLOR
                 (Interval Taylor) with operators $+$, $-$, $*$, $/$, $
                 ** $, and the functions SQR, SQRT, EXP, SIN, COS,
                 ARCTAN, and LN. An initial value problem $ y' = y^2 $,
                 $ y(0) = 1 $, is solved with TAYLOR and with ITAYLOR
                 types to show that the series generation exhibits a
                 mild instability which has no significant effect on the
                 values of the solution computed by analytic
                 continuation.",
  acknowledgement = ack-nj,
  comment =      "Also appeared as {\sl MRC Technical Summary Report No.
                 2497}, Mathematics Research Center, University of
                 Wisconsin-Madison, 1983.",
  keywords =     "automatic differentiation; stability.; Taylor series",
}


bibtype: article
filename: fparith.bib
label: Cowlishaw:1984:DRL
author: M. F. Cowlishaw
title: The Design of the REXX Language
journal: j-IBM-SYS-J
volume: 23
number: 4
pages: 326--335
year: 1984
CODEN: IBMSA7
ISSN: 0018-8670 OR 00188670
bibdate: Wed Jan 08 16:35:07 1997
bibsource: Compendex database; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.01.08 16:35:07 ???
note: First published as IBM Hursley Technical Report TR12.223, October 1983.
fjournal: IBM Systems Journal
acknowledgement: ack-nhfb
affiliation: IBM UK Ltd, Scientific Cent, Winchester, Engl
affiliationaddress: IBM UK Ltd, Scientific Cent, Winchester, Engl
journalabr: IBM Syst J
rawauthor: M. F. Cowlishaw
rawnote: First published as IBM Hursley Technical Report TR12.223, October 1983.
rawtitle: The Design of the {REXX} Language
abstract:
One way of classifying computer languages is by two classes: languages needing skilled programmers, and personal languages used by an expanding population of general users. REstructured eXtended eXecutor (REXX) is a flexible personal language designed with particular attention to feedback from its users. It has proved to be effective and easy to use, yet it is sufficiently general and powerful to fulfill the needs of many demanding professional applications. REXX is system and hardware independent, so that it has been possible to integrate it experimentally into several operating systems. Here REXX is used for such purposes as command and macro programming, prototyping, education, and personal programming. This study introduces REXX and describes the basic design principles that were followed in developing it.

keywords:
command program interpreters; computer operating systems; computer programming languages; decimal floating-point arithmetic; language concepts; personal language; REXX language

remark:
REXX supports arbitrary precision arithmetic with up to $ 10^9 $ digits, and an exponent range of $ pm 10^9 $. This capability was added to REXX in 1981.

rawabstract:
One way of classifying computer languages is by two classes: languages needing skilled programmers, and personal languages used by an expanding population of general users. REstructured eXtended eXecutor (REXX) is a flexible personal language designed with particular attention to feedback from its users. It has proved to be effective and easy to use, yet it is sufficiently general and powerful to fulfill the needs of many demanding professional applications. REXX is system and hardware independent, so that it has been possible to integrate it experimentally into several operating systems. Here REXX is used for such purposes as command and macro programming, prototyping, education, and personal programming. This study introduces REXX and describes the basic design principles that were followed in developing it.

entry:
@Article{Cowlishaw:1984:DRL,
  author =       "M. F. Cowlishaw",
  title =        "The Design of the {REXX} Language",
  journal =      j-IBM-SYS-J,
  volume =       "23",
  number =       "4",
  pages =        "326--335",
  year =         "1984",
  CODEN =        "IBMSA7",
  ISSN =         "0018-8670",
  bibdate =      "Wed Jan 08 16:35:07 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "First published as IBM Hursley Technical Report
                 TR12.223, October 1983.",
  abstract =     "One way of classifying computer languages is by two
                 classes: languages needing skilled programmers, and
                 personal languages used by an expanding population of
                 general users. REstructured eXtended eXecutor (REXX) is
                 a flexible personal language designed with particular
                 attention to feedback from its users. It has proved to
                 be effective and easy to use, yet it is sufficiently
                 general and powerful to fulfill the needs of many
                 demanding professional applications. REXX is system and
                 hardware independent, so that it has been possible to
                 integrate it experimentally into several operating
                 systems. Here REXX is used for such purposes as command
                 and macro programming, prototyping, education, and
                 personal programming. This study introduces REXX and
                 describes the basic design principles that were
                 followed in developing it.",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM UK Ltd, Scientific Cent, Winchester, Engl",
  affiliationaddress = "IBM UK Ltd, Scientific Cent, Winchester, Engl",
  classification = "723",
  fjournal =     "IBM Systems Journal",
  journalabr =   "IBM Syst J",
  keywords =     "command program interpreters; computer operating
                 systems; computer programming languages; decimal
                 floating-point arithmetic; language concepts; personal
                 language; REXX language",
  remark =       "REXX supports arbitrary precision arithmetic with up
                 to $ 10^9 $ digits, and an exponent range of $ \pm 10^9
                 $. This capability was added to REXX in 1981.",
}


bibtype: article
filename: fparith.bib
label: Demmel:1984:URN
author: James Demmel
title: Underflow and the reliability of numerical software
journal: j-SIAM-J-SCI-STAT-COMP
volume: 5
number: 4
pages: 887--919
month: dec
monthnumber: 12
year: 1984
CODEN: SIJCD4
ISSN: 0196-5204 OR 01965204
MRclass: 65G05
MRnumber: 85m:65035
MRreviewer: G. Alefeld
bibdate: Tue Apr 29 19:18:28 MDT 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.04.29 19:18:28 MDT
fjournal: SIAM Journal on Scientific and Statistical Computing
acknowledgement: ack-nhfb
corpsource: Div. of Computer Science, California University, Berkeley, CA, USA
journalURL: http://epubs.siam.org/loi/sijcd4
treatment: T Theoretical or Mathematical
rawauthor: James Demmel
rawtitle: Underflow and the reliability of numerical software
keywords:
codes; digital arithmetic; eigenvalue calculation; Gaussian elimination; gradual underflow; numerical software; polynomial evaluation; reliability; roundoff; roundoff errors; store zero; uncertainty; underflow mechanisms

entry:
@Article{Demmel:1984:URN,
  author =       "James Demmel",
  title =        "Underflow and the reliability of numerical software",
  journal =      j-SIAM-J-SCI-STAT-COMP,
  volume =       "5",
  number =       "4",
  pages =        "887--919",
  month =        dec,
  year =         "1984",
  CODEN =        "SIJCD4",
  ISSN =         "0196-5204",
  MRclass =      "65G05",
  MRnumber =     "85m:65035",
  MRreviewer =   "G. Alefeld",
  bibdate =      "Tue Apr 29 19:18:28 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C5230 (Digital arithmetic methods)",
  corpsource =   "Div. of Computer Science, California University,
                 Berkeley, CA, USA",
  fjournal =     "SIAM Journal on Scientific and Statistical Computing",
  journal-URL =  "http://epubs.siam.org/loi/sijcd4",
  keywords =     "codes; digital arithmetic; eigenvalue calculation;
                 Gaussian elimination; gradual underflow; numerical
                 software; polynomial evaluation; reliability; roundoff;
                 roundoff errors; store zero; uncertainty; underflow
                 mechanisms",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: fparith.bib
label: Demsky:1984:MMC
author: J. Demsky and M. Schlesinger and R. D. Kent
title: Micro/mini computer program for calculating the square root of rationals at arbitrary precision
journal: j-COMP-PHYS-COMM
volume: 35
number: 1--3
pages: C-877
year: 1984
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/S0010-4655(84)82981-1
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Sat Feb 25 10:56:58 MST 2012
bibtimestamp: 2012.02.25 10:56:58 MST
URL: http://www.sciencedirect.com/science/article/pii/S0010465584829811
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: J. Demsky and M. Schlesinger and R. D. Kent
rawtitle: Micro/mini computer program for calculating the square root of rationals at arbitrary precision
bibsource:
https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Demsky:1984:MMC,
  author =       "J. Demsky and M. Schlesinger and R. D. Kent",
  title =        "Micro/mini computer program for calculating the square
                 root of rationals at arbitrary precision",
  journal =      j-COMP-PHYS-COMM,
  volume =       "35",
  number =       "1--3",
  pages =        "C-877",
  month =        "????",
  year =         "1984",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(84)82981-1",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Feb 25 10:56:58 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465584829811",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: article
filename: fparith.bib
label: Dietrich:1984:FPR
author: D. Dietrich and R. Fischer
journal: j-ELEKTRONIKER
volume: 8
pages: 49--54
year: 1984
CODEN: ELKRBL
ISSN: 0531-9218 OR 05319218
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: Elektroniker (Switzerland)
acknowledgement: ack-nj
rawauthor: D. Dietrich and R. Fischer
title:
Floating-Point-Routinen, entwickelt fur Mikrorechner toenglish Floating-point Routines Developed for Microcomputers endtoenglish 

rawtitle:
{Floating-Point-Routinen, entwickelt f{\"u}r Mikrorechner} \toenglish {Floating-point Routines Developed for Microcomputers} \endtoenglish

entry:
@Article{Dietrich:1984:FPR,
  author =       "D. Dietrich and R. Fischer",
  title =        "{Floating-Point-Routinen, entwickelt f{\"u}r
                 Mikrorechner} \toenglish {Floating-point Routines
                 Developed for Microcomputers} \endtoenglish",
  journal =      j-ELEKTRONIKER,
  volume =       "8",
  pages =        "49--54",
  year =         "1984",
  CODEN =        "ELKRBL",
  ISSN =         "0531-9218",
  bibdate =      "Fri Sep 16 16:30:39 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Elektroniker (Switzerland)",
}


bibtype: article
filename: fparith.bib
label: Duncan:1984:FSF
author: Ray Duncan and Martin Tracy
title: The FVG Standard Floating-Point Extension
journal: j-DDJ
volume: 9
number: 9
pages: 110--??
month: sep
monthnumber: 9
year: 1984
CODEN: DDJOEB
ISSN: 1044-789X OR 1044789X
bibdate: Mon Sep 2 09:09:39 MDT 1996
bibsource: http://www.ddj.com/index/author/index.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.09.02 09:09:39 MDT
fjournal: Dr. Dobb's Journal of Software Tools
acknowledgement: ack-nhfb
rawauthor: Ray Duncan and Martin Tracy
rawtitle: The {FVG} Standard Floating-Point Extension
entry:
@Article{Duncan:1984:FSF,
  author =       "Ray Duncan and Martin Tracy",
  title =        "The {FVG} Standard Floating-Point Extension",
  journal =      j-DDJ,
  volume =       "9",
  number =       "9",
  pages =        "110--??",
  month =        sep,
  year =         "1984",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Mon Sep 2 09:09:39 MDT 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
  xxnote =       "??Check author order??",
}


bibtype: article
filename: fparith.bib
label: Dunford:1984:SFPa
author: Christopher J. Dunford
title: Savage floating-point benchmark in 8088 / 8087 assembly language in 16BST
journal: j-DDJ
volume: 9
number: 7
pages: 116--??
month: jul
monthnumber: 7
year: 1984
CODEN: DDJOEB
ISSN: 1044-789X OR 1044789X
bibdate: Mon Sep 2 09:09:39 MDT 1996
bibsource: http://www.ddj.com/index/author/index.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.09.02 09:09:39 MDT
fjournal: Dr. Dobb's Journal of Software Tools
acknowledgement: ack-nhfb
rawauthor: Christopher J. Dunford
rawtitle: {Savage} floating-point benchmark in 8088\slash 8087 assembly language in {16BST}
entry:
@Article{Dunford:1984:SFPa,
  author =       "Christopher J. Dunford",
  title =        "{Savage} floating-point benchmark in 8088\slash 8087
                 assembly language in {16BST}",
  journal =      j-DDJ,
  volume =       "9",
  number =       "7",
  pages =        "116--??",
  month =        jul,
  year =         "1984",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Mon Sep 2 09:09:39 MDT 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}


bibtype: article
filename: fparith.bib
label: Dunford:1984:SFPb
author: Christopher J. Dunford
title: Savage floating-point benchmark in Modula-2 in 16BST
journal: j-DDJ
volume: 9
number: 8
pages: 106--??
month: aug
monthnumber: 8
year: 1984
CODEN: DDJOEB
ISSN: 1044-789X OR 1044789X
bibdate: Mon Sep 2 09:09:39 MDT 1996
bibsource: http://www.ddj.com/index/author/index.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.09.02 09:09:39 MDT
fjournal: Dr. Dobb's Journal of Software Tools
acknowledgement: ack-nhfb
rawauthor: Christopher J. Dunford
rawtitle: {Savage} floating-point benchmark in {Modula-2} in {16BST}
entry:
@Article{Dunford:1984:SFPb,
  author =       "Christopher J. Dunford",
  title =        "{Savage} floating-point benchmark in {Modula-2} in
                 {16BST}",
  journal =      j-DDJ,
  volume =       "9",
  number =       "8",
  pages =        "106--??",
  month =        aug,
  year =         "1984",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Mon Sep 2 09:09:39 MDT 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}


bibtype: article
filename: fparith.bib
label: Ercegovac:1984:LAO
author: Milos D. Ercegovac
title: On-line arithmetic: An overview
journal: j-SPIE
volume: 495
pages: 86--93
year: 1984
bibdate: Fri Nov 30 06:32:39 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.30 06:32:39 ???
note: Real Time Signal Processing VII.
acknowledgement: ack-nhfb
rawauthor: Milo{\v{s}} D. Ercegovac
rawnote: Real Time Signal Processing VII.
rawtitle: On-line arithmetic: An overview
entry:
@Article{Ercegovac:1984:LAO,
  author =       "Milo{\v{s}} D. Ercegovac",
  title =        "On-line arithmetic: An overview",
  journal =      j-SPIE,
  volume =       "495",
  pages =        "86--93",
  year =         "1984",
  bibdate =      "Fri Nov 30 06:32:39 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Real Time Signal Processing VII.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Ferguson:1984:SFP
author: Kenneth M. Ferguson
title: Savage floating-point benchmark deficiencies of in 16BST
journal: j-DDJ
volume: 9
number: 8
pages: 107--??
month: aug
monthnumber: 8
year: 1984
CODEN: DDJOEB
ISSN: 1044-789X OR 1044789X
bibdate: Mon Sep 2 09:09:39 MDT 1996
bibsource: http://www.ddj.com/index/author/index.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.09.02 09:09:39 MDT
fjournal: Dr. Dobb's Journal of Software Tools
acknowledgement: ack-nhfb
rawauthor: Kenneth M. Ferguson
rawtitle: {Savage} floating-point benchmark deficiencies of in {16BST}
entry:
@Article{Ferguson:1984:SFP,
  author =       "Kenneth M. Ferguson",
  title =        "{Savage} floating-point benchmark deficiencies of in
                 {16BST}",
  journal =      j-DDJ,
  volume =       "9",
  number =       "8",
  pages =        "107--??",
  month =        aug,
  year =         "1984",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Mon Sep 2 09:09:39 MDT 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}


bibtype: article
filename: fparith.bib
label: Fisher:1984:UAP
author: Gerry Fisher
title: Universal Arithmetic Packages
journal: j-SIGADA-LETTERS
volume: 3
number: 6
pages: 30--47
month: may
monthnumber: 5
year: 1984
CODEN: AALEE5
DOI: https://doi.org/10.1145/998388.998389
ISSN: 1094-3641 (print), 1557-9476 (electronic) OR 10943641 (print), 15579476 (electronic)
ISSNL: 1094-3641 OR 10943641
bibdate: Thu Sep 28 07:33:23 MDT 2000
bibtimestamp: 2000.09.28 07:33:23 MDT
note: See erratum cite Froggatt:2015:EAU.
fjournal: ACM SIGAda Ada Letters
keywords: universal integer, universal real, rational arithmetic
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/citation.cfm?id=J32
rawauthor: Gerry Fisher
rawnote: See erratum \cite{Froggatt:2015:EAU}.
rawtitle: Universal Arithmetic Packages
bibsource:
ftp://ftp.uu.net/library/bibliography; http://www.adahome.com/Resources/Bibliography/articles.ref; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/sigada.bib

entry:
@Article{Fisher:1984:UAP,
  author =       "Gerry Fisher",
  title =        "Universal Arithmetic Packages",
  journal =      j-SIGADA-LETTERS,
  volume =       "3",
  number =       "6",
  pages =        "30--47",
  month =        may # "\slash " # jun,
  year =         "1984",
  CODEN =        "AALEE5",
  DOI =          "https://doi.org/10.1145/998388.998389",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Thu Sep 28 07:33:23 MDT 2000",
  bibsource =    "ftp://ftp.uu.net/library/bibliography;
                 http://www.adahome.com/Resources/Bibliography/articles.ref;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigada.bib",
  note =         "See erratum \cite{Froggatt:2015:EAU}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "universal integer, universal real, rational
                 arithmetic",
}


bibtype: incollection
filename: fparith.bib
label: Gautschi:1984:QNC
author: Walter Gautschi
title: Questions of numerical condition related to polynomials
crossref: Golub:1984:SNA
volume: 24
pages: 140--177
year: 1984
MRclass: 65F35 (65H05)
MRnumber: 925213
bibdate: Fri Feb 9 15:28:14 2018
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2018.02.09 15:28:14 ???
acknowledgement: ack-nhfb
rawauthor: Walter Gautschi
rawtitle: Questions of numerical condition related to polynomials
entry:
@InCollection{Gautschi:1984:QNC,
  author =       "Walter Gautschi",
  title =        "Questions of numerical condition related to
                 polynomials",
  crossref =     "Golub:1984:SNA",
  volume =       "24",
  pages =        "140--177",
  year =         "1984",
  MRclass =      "65F35 (65H05)",
  MRnumber =     "925213",
  bibdate =      "Fri Feb 9 15:28:14 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: phdthesis
filename: fparith.bib
label: Gleditsch:1984:FTR
author: Torstein Gleditsch
type: Hovedoppgave i informatikk (cand.scient)
school: Universitetet i Oslo
address: Oslo, Norway
pages: 140--177
year: 1984
bibdate: Thu May 09 08:19:32 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.09 08:19:32 ???
language: Norwegian
acknowledgement: ack-nhfb
rawauthor: Torstein Gleditsch
title:
Forslag til rask prosessor for flerformat floating-point aritmetikk. (Norwegian) [Proposal for a fast processor for multiformat floating-point arithmetic]

rawtitle:
Forslag til rask prosessor for flerformat floating-point aritmetikk. ({Norwegian}) [{Proposal} for a fast processor for multiformat floating-point arithmetic]

entry:
@PhdThesis{Gleditsch:1984:FTR,
  author =       "Torstein Gleditsch",
  title =        "Forslag til rask prosessor for flerformat
                 floating-point aritmetikk. ({Norwegian}) [{Proposal}
                 for a fast processor for multiformat floating-point
                 arithmetic]",
  type =         "Hovedoppgave i informatikk (cand.scient)",
  school =       "Universitetet i Oslo",
  address =      "Oslo, Norway",
  year =         "1984",
  bibdate =      "Thu May 09 08:19:32 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  language =     "Norwegian",
}


bibtype: article
filename: fparith.bib
label: Goldberg:1984:LVS
author: Morton Goldberg
title: LISP Version of the Savage Floating Point Benchmark in 16BST
journal: j-DDJ
volume: 9
number: 6
pages: 82--??
month: jun
monthnumber: 6
year: 1984
CODEN: DDJOEB
ISSN: 1044-789X OR 1044789X
bibdate: Mon Sep 2 09:09:39 MDT 1996
bibsource: http://www.ddj.com/index/author/index.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.09.02 09:09:39 MDT
fjournal: Dr. Dobb's Journal of Software Tools
acknowledgement: ack-nhfb
rawauthor: Morton Goldberg
rawtitle: {LISP} Version of the {Savage} Floating Point Benchmark in {16BST}
entry:
@Article{Goldberg:1984:LVS,
  author =       "Morton Goldberg",
  title =        "{LISP} Version of the {Savage} Floating Point
                 Benchmark in {16BST}",
  journal =      j-DDJ,
  volume =       "9",
  number =       "6",
  pages =        "82--??",
  month =        jun,
  year =         "1984",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Mon Sep 2 09:09:39 MDT 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}


bibtype: book
filename: fparith.bib
label: Gregory:1984:MAE
author: Robert Todd Gregory and E. V. Krishnamurthy
title: Methods and Applications of Error-Free Computation
publisher: pub-SV
address: pub-SV:adr
pages: xii + 194
year: 1984
ISBN: 0-387-90967-2 OR 0387909672
ISBN13: 978-0-387-90967-7 OR 9780387909677
LCCN: QA297.5 .G735 1984
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
series: Texts and monographs in computer science
keywords: Approximation theory --- Data processing.; Floating-point arithmetic.
acknowledgement: ack-nhfb
rawauthor: Robert Todd Gregory and E. V. Krishnamurthy
rawtitle: Methods and Applications of Error-Free Computation
TOC:
Glossary of Notation / xi I: Residue or Modular Arithmetic / 1 1. Introduction / 1 2. Single-Modulus Residue Arithmetic / 3 3. Multiple-Modulus Residue Arithmetic / 11 4. Mapping Standard Residue Representations onto Integers / 17 5. Single-Modulus Residue Arithmetic with Rational Numbers / 23 6. The Forward Mapping and the Inverse Mapping / 31 7. Multiple-Modulus Residue Arithmetic with Rational Numbers / 49 II: Finite-Segment p-adic Arithmetic / 63 1. Introduction / 63 2. The Field of p-adic Numbers / 63 3. Arithmetic in QP / 73 4. A Finite-Segment p-adic Number System / 79 5. Arithmetic Operations on Hensel Codes / 90 6. Removing a Leading Zero from a Hensel Code / 99 7. Mapping a Hensel Code onto a Unique Order-N Farey Fraction / 100 III: Exact Computation of Generalized Inverses / 109 1. Introduction / 109 2. Properties of g-inverses / 110 3. Applications of g-inverses / 116 4. Exact Computation of A+ if A Is a Rational Matrix / 118 5. Failures of Residue Arithmetic and Precautionary Measures / 131 IV: Integer Solutions to Linear Equations / 134 1. Introduction / 134 2. Theoretical Background / 135 3. The Matrix Formulation of Chemical Equations / 138 4. Solving the Homogeneous System / 140 5. Solving a Non-Homogeneous System / 148 6. Solving Interval Linear Programming Problems / 150 7. The Solution of Systems of Mixed-Integer Linear Equations / 155 V: Iterative Matrix Inversion and the Iterative Solution of Linear Equations / 162 1. Introduction / 162 2. The Newton--Schultz Method for the Matrix Inverse / 163 3. Iterative Solution of a Linear System / 169 4. Iterative Computation of g-inverses / 174 VI: The Exact Computation of the Characteristic Polynomial of a Matrix / 180 1. Introduction / 180 2. The Algorithm Applied to Lower Hessenberg Matrices / 181 Bibliography / 186 Index / 191

shortTOC:
Glossary of Notation / xi I: Residue or Modular Arithmetic / 1 II: Finite-Segment p-adic Arithmetic / 63 III: Exact Computation of Generalized Inverses / 109 IV: Integer Solutions to Linear Equations / 134 V: Iterative Matrix Inversion and the Iterative Solution of Linear Equations / 162 VI: The Exact Computation of the Characteristic Bibliography / 186 Index / 191

rawshortTOC:
Glossary of Notation / xi \\ I: Residue or Modular Arithmetic / 1 \\ II: Finite-Segment p-adic Arithmetic / 63 \\ III: Exact Computation of Generalized Inverses / 109 IV: Integer Solutions to Linear Equations / 134 \\ V: Iterative Matrix Inversion and the Iterative Solution of Linear Equations / 162 \\ VI: The Exact Computation of the Characteristic Bibliography / 186 \\ Index / 191

rawTOC:
Glossary of Notation / xi \\ I: Residue or Modular Arithmetic / 1 \\ 1. Introduction / 1 \\ 2. Single-Modulus Residue Arithmetic / 3 \\ 3. Multiple-Modulus Residue Arithmetic / 11 \\ 4. Mapping Standard Residue Representations onto Integers / 17 \\ 5. Single-Modulus Residue Arithmetic with Rational Numbers / 23 \\ 6. The Forward Mapping and the Inverse Mapping / 31 \\ 7. Multiple-Modulus Residue Arithmetic with Rational Numbers / 49 \\ II: Finite-Segment p-adic Arithmetic / 63 \\ 1. Introduction / 63 \\ 2. The Field of p-adic Numbers / 63 \\ 3. Arithmetic in QP / 73 \\ 4. A Finite-Segment p-adic Number System / 79 \\ 5. Arithmetic Operations on Hensel Codes / 90 \\ 6. Removing a Leading Zero from a Hensel Code / 99 \\ 7. Mapping a Hensel Code onto a Unique Order-N Farey Fraction / 100 \\ III: Exact Computation of Generalized Inverses / 109 \\ 1. Introduction / 109 \\ 2. Properties of g-inverses / 110 \\ 3. Applications of g-inverses / 116 \\ 4. Exact Computation of A+ if A Is a Rational Matrix / 118 \\ 5. Failures of Residue Arithmetic and Precautionary Measures / 131 \\ IV: Integer Solutions to Linear Equations / 134 \\ 1. Introduction / 134 \\ 2. Theoretical Background / 135 \\ 3. The Matrix Formulation of Chemical Equations / 138 \\ 4. Solving the Homogeneous System / 140 \\ 5. Solving a Non-Homogeneous System / 148 \\ 6. Solving Interval Linear Programming Problems / 150 \\ 7. The Solution of Systems of Mixed-Integer Linear Equations / 155 \\ V: Iterative Matrix Inversion and the Iterative Solution of Linear Equations / 162 \\ 1. Introduction / 162 \\ 2. The Newton--Schultz Method for the Matrix Inverse / 163 \\ 3. Iterative Solution of a Linear System / 169 \\ 4. Iterative Computation of g-inverses / 174 \\ VI: The Exact Computation of the Characteristic Polynomial of a Matrix / 180 \\ 1. Introduction / 180 \\ 2. The Algorithm Applied to Lower Hessenberg Matrices / 181 \\ Bibliography / 186 \\ Index / 191

entry:
@Book{Gregory:1984:MAE,
  author =       "Robert Todd Gregory and E. V. Krishnamurthy",
  title =        "Methods and Applications of Error-Free Computation",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xii + 194",
  year =         "1984",
  ISBN =         "0-387-90967-2",
  ISBN-13 =      "978-0-387-90967-7",
  LCCN =         "QA297.5 .G735 1984",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Texts and monographs in computer science",
  acknowledgement = ack-nhfb,
  keywords =     "Approximation theory --- Data processing.;
                 Floating-point arithmetic.",
  shorttableofcontents = "Glossary of Notation / xi \\
                 I: Residue or Modular Arithmetic / 1 \\
                 II: Finite-Segment p-adic Arithmetic / 63 \\
                 III: Exact Computation of Generalized Inverses / 109
                 IV: Integer Solutions to Linear Equations / 134 \\
                 V: Iterative Matrix Inversion and the Iterative
                 Solution of Linear Equations / 162 \\
                 VI: The Exact Computation of the Characteristic
                 Bibliography / 186 \\
                 Index / 191",
  tableofcontents = "Glossary of Notation / xi \\
                 I: Residue or Modular Arithmetic / 1 \\
                 1. Introduction / 1 \\
                 2. Single-Modulus Residue Arithmetic / 3 \\
                 3. Multiple-Modulus Residue Arithmetic / 11 \\
                 4. Mapping Standard Residue Representations onto
                 Integers / 17 \\
                 5. Single-Modulus Residue Arithmetic with Rational
                 Numbers / 23 \\
                 6. The Forward Mapping and the Inverse Mapping / 31 \\
                 7. Multiple-Modulus Residue Arithmetic with Rational
                 Numbers / 49 \\
                 II: Finite-Segment p-adic Arithmetic / 63 \\
                 1. Introduction / 63 \\
                 2. The Field of p-adic Numbers / 63 \\
                 3. Arithmetic in QP / 73 \\
                 4. A Finite-Segment p-adic Number System / 79 \\
                 5. Arithmetic Operations on Hensel Codes / 90 \\
                 6. Removing a Leading Zero from a Hensel Code / 99 \\
                 7. Mapping a Hensel Code onto a Unique Order-N Farey
                 Fraction / 100 \\
                 III: Exact Computation of Generalized Inverses / 109
                 \\
                 1. Introduction / 109 \\
                 2. Properties of g-inverses / 110 \\
                 3. Applications of g-inverses / 116 \\
                 4. Exact Computation of A+ if A Is a Rational Matrix /
                 118 \\
                 5. Failures of Residue Arithmetic and Precautionary
                 Measures / 131 \\
                 IV: Integer Solutions to Linear Equations / 134 \\
                 1. Introduction / 134 \\
                 2. Theoretical Background / 135 \\
                 3. The Matrix Formulation of Chemical Equations / 138
                 \\
                 4. Solving the Homogeneous System / 140 \\
                 5. Solving a Non-Homogeneous System / 148 \\
                 6. Solving Interval Linear Programming Problems / 150
                 \\
                 7. The Solution of Systems of Mixed-Integer Linear
                 Equations / 155 \\
                 V: Iterative Matrix Inversion and the Iterative
                 Solution of Linear Equations / 162 \\
                 1. Introduction / 162 \\
                 2. The Newton--Schultz Method for the Matrix Inverse /
                 163 \\
                 3. Iterative Solution of a Linear System / 169 \\
                 4. Iterative Computation of g-inverses / 174 \\
                 VI: The Exact Computation of the Characteristic
                 Polynomial of a Matrix / 180 \\
                 1. Introduction / 180 \\
                 2. The Algorithm Applied to Lower Hessenberg Matrices /
                 181 \\
                 Bibliography / 186 \\
                 Index / 191",
}


bibtype: article
filename: fparith.bib
label: Guest:1984:RNS
author: C. C. Guest and M. M. Mirsalehi and T. K. Gaylord
title: Residue Number System Truth-Table Look-Up Processing --- Moduli Selection and Logical Minimization
journal: j-IEEE-TRANS-COMPUT
volume: C-33
number: 10
pages: 927--931
month: oct
monthnumber: 10
year: 1984
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1984.1676355
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 09:22:55 MDT 2011
bibtimestamp: 2011.07.10 09:22:55 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: C. C. Guest and M. M. Mirsalehi and T. K. Gaylord
rawtitle: Residue Number System Truth-Table Look-Up Processing --- Moduli Selection and Logical Minimization
URL:
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676355; http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12; http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35232

entry:
@Article{Guest:1984:RNS,
  author =       "C. C. Guest and M. M. Mirsalehi and T. K. Gaylord",
  title =        "Residue Number System Truth-Table Look-Up Processing
                 --- Moduli Selection and Logical Minimization",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-33",
  number =       "10",
  pages =        "927--931",
  month =        oct,
  year =         "1984",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1984.1676355",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 09:22:55 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676355;
                 http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35232",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "Truth table look-up processing using binary coded
                 residue numbers is investigated for full-precision
                 addition and multiplication for implementations using
                 either electronic or optical technologies. The
                 logically minimized numbers of input \ldots{}",
}


bibtype: book
filename: fparith.bib
label: Hamacher:1984:CO
author: V. Carl Hamacher and Zvonko G. Vranesic and Safwat G. Zaky
title: Computer organization
publisher: pub-MCGRAW-HILL
address: pub-MCGRAW-HILL:adr
edition: Second
pages: xvi + 590
year: 1984
ISBN: 0-07-025683-7 OR 0070256837
ISBN13: 978-0-07-025683-5 OR 9780070256835
LCCN: QA76.9.A73 H351 1984
bibdate: Sat Nov 9 08:26:18 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.11.09 08:26:18 MST
series: McGraw-Hill series in computer organization and architecture
subject: C. Computer Systems Organization; C.0 GENERAL; B. Hardware; B.0 GENERAL
acknowledgement: ack-nhfb
reviewer: A. Deb
rawauthor: V. Carl Hamacher and Zvonko G. Vranesic and Safwat G. Zaky
rawtitle: Computer organization
entry:
@Book{Hamacher:1984:CO,
  author =       "V. Carl Hamacher and Zvonko G. Vranesic and Safwat G.
                 Zaky",
  title =        "Computer organization",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  edition =      "Second",
  pages =        "xvi + 590",
  year =         "1984",
  ISBN =         "0-07-025683-7",
  ISBN-13 =      "978-0-07-025683-5",
  LCCN =         "QA76.9.A73 H351 1984",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$34.95",
  series =       "McGraw-Hill series in computer organization and
                 architecture",
  acknowledgement = ack-nhfb,
  catcode =      "C; B",
  content =      "The reviewer recommends this book to those who are
                 interested in learning the basics of computer
                 organization, particularly at the hardware and device
                 level. This book does not deal with the concepts
                 related to computer organization from an abstract,
                 mathematical level. It also does not attempt to
                 describe the computer organization using a high-level
                 language. Instead, the authors concentrate on
                 uniprocessing systems, with a large number of examples
                 drawn from VAX-11, IBM 370, and HP 3000. The book does
                 not cover multiprocessors.\par

                 The organization of the book is summarized here.
                 Chapter 1 introduces a number of terms. Chapters 2 and
                 3 concentrate in detail (a total of 101 pages) on the
                 addressing methods and instruction sets, with examples
                 taken primarily from the above mentioned machines.
                 Chapters 4 and 5 (a total of 50 pages) deal with the
                 control unit for the instruction fetch and execute,
                 with Chapter 5 being devoted to microprogrammed control
                 and bit slice designs. In Chapter 6 (a total of 64
                 pages) the authors cover Input/Output organization,
                 which includes a good deal about the
                 synchronous/asynchronous I/O operations, I/O
                 interfaces, etc. Chapter 7 presents the usual material
                 on the fixed- and floating-point arithmetic. \ldots{}",
  CRnumber =     "8509-0786",
  descriptor =   "Computer Systems Organization, GENERAL; Hardware,
                 GENERAL",
  genterm =      "DESIGN",
  reviewer =     "A. Deb",
  subject =      "C. Computer Systems Organization; C.0 GENERAL; B.
                 Hardware; B.0 GENERAL",
}


