# bibtab

bibtype: inproceedings
filename: fparith.bib
label: Kerkhoff:1982:LDM
author: H. G. Kerkhoff and H. A. J. Robroek
editor: IEEE
booktitle: Proceedings of the 12th International Symposium on Multiple-Valued Logic, May 1982
title: The Logic Design of Multiple-valued Logic Functions Using CCD's
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 35--44
year: 1982
bibdate: Sat Aug 22 09:16:45 2009
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2009.08.22 09:16:45 ???
acknowledgement: ack-nhfb
rawauthor: H. G. Kerkhoff and H. A. J. Robroek
rawbooktitle: Proceedings of the 12th International Symposium on Multiple-Valued Logic, May 1982
raweditor: {IEEE}
rawtitle: The Logic Design of Multiple-valued Logic Functions Using {CCD}'s
entry:
@InProceedings{Kerkhoff:1982:LDM,
  author =       "H. G. Kerkhoff and H. A. J. Robroek",
  editor =       "{IEEE}",
  booktitle =    "Proceedings of the 12th International Symposium on
                 Multiple-Valued Logic, May 1982",
  title =        "The Logic Design of Multiple-valued Logic Functions
                 Using {CCD}'s",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "35--44",
  year =         "1982",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Aug 22 09:16:45 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Korn:1982:EDF
author: G. A. Korn
journal: j-SIMULATION
volume: 38
number: 5
pages: 151--159
month: may
monthnumber: 5
year: 1982
CODEN: SIMUA2
ISSN: 0037-5497 (print), 1741-3133 (electronic) OR 00375497 (print), 17413133 (electronic)
ISSNL: 0037-5497 OR 00375497
bibdate: Sat Nov 9 08:26:18 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.11.09 08:26:18 MST
fjournal: Simulation
acknowledgement: ack-nhfb
journalURL: http://sim.sagepub.com/content/by/year
rawauthor: G. A. Korn
title:
EARLY DESIRE: a floating-point equation language simulation system for minicomputers and microcomputers

subject:
I. Computing Methodologies; I.6 SIMULATION AND MODELING; G. Mathematics of Computing; G.m MISCELLANEOUS; D. Software; D.4 OPERATING SYSTEMS

rawtitle:
{EARLY DESIRE}: a floating-point equation language simulation system for minicomputers and microcomputers

entry:
@Article{Korn:1982:EDF,
  author =       "G. A. Korn",
  title =        "{EARLY DESIRE}: a floating-point equation language
                 simulation system for minicomputers and
                 microcomputers",
  journal =      j-SIMULATION,
  volume =       "38",
  number =       "5",
  pages =        "151--159",
  month =        may,
  year =         "1982",
  CODEN =        "SIMUA2",
  ISSN =         "0037-5497 (print), 1741-3133 (electronic)",
  ISSN-L =       "0037-5497",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  catcode =      "I.6; G; D.4.7",
  CRclass =      "I.6.2 Simulation Languages; D.4.7 Organization and
                 Design; D.4.7 Interactive systems",
  descriptor =   "Computing Methodologies, SIMULATION AND MODELING,
                 Simulation Languages; Mathematics of Computing,
                 MISCELLANEOUS; Software, OPERATING SYSTEMS,
                 Organization and Design, Interactive systems",
  fjournal =     "Simulation",
  genterm =      "DESIGN; LANGUAGES",
  guideno =      "08785",
  journal-URL =  "http://sim.sagepub.com/content/by/year",
  subject =      "I. Computing Methodologies; I.6 SIMULATION AND
                 MODELING; G. Mathematics of Computing; G.m
                 MISCELLANEOUS; D. Software; D.4 OPERATING SYSTEMS",
}


bibtype: article
filename: fparith.bib
label: Leuprecht:1982:PAR
author: H. Leuprecht and W. Oberaigner
title: Parallel Algorithms for the Rounding-Exact Summation of Floating-Point Numbers
journal: j-COMPUTING
volume: 28
number: 2
pages: 89--104
year: 1982
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
MRclass: 68A05 (65G05)
MRnumber: 83c:68009
bibdate: Fri Dec 08 11:53:42 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 11:53:42 ???
fjournal: Computing: Archiv fur informatik und numerik
keywords: accurate floating-point summation
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/607
rawauthor: H. Leuprecht and W. Oberaigner
rawtitle: Parallel Algorithms for the Rounding-Exact Summation of Floating-Point Numbers
entry:
@Article{Leuprecht:1982:PAR,
  author =       "H. Leuprecht and W. Oberaigner",
  title =        "Parallel Algorithms for the Rounding-Exact Summation
                 of Floating-Point Numbers",
  journal =      j-COMPUTING,
  volume =       "28",
  number =       "2",
  pages =        "89--104",
  month =        "????",
  year =         "1982",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "68A05 (65G05)",
  MRnumber =     "83c:68009",
  bibdate =      "Fri Dec 08 11:53:42 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
  keywords =     "accurate floating-point summation",
}


bibtype: article
filename: fparith.bib
label: McCormick:1982:EFM
author: S. F. McCormick and G. D. Taylor and D. V. Pryor
title: Evaluation of Functions on Microcomputers: $ ln (x) $
journal: j-COMPUT-MATH-APPL
volume: 8
number: 5
pages: 389--392
year: 1982
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Thu Sep 15 18:41:01 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.15 18:41:01 ???
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nj
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: S. F. McCormick and G. D. Taylor and D. V. Pryor
rawtitle: Evaluation of Functions on Microcomputers: $ \ln (x) $
entry:
@Article{McCormick:1982:EFM,
  author =       "S. F. McCormick and G. D. Taylor and D. V. Pryor",
  title =        "Evaluation of Functions on Microcomputers: $ \ln (x)
                 $",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "8",
  number =       "5",
  pages =        "389--392",
  year =         "1982",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Thu Sep 15 18:41:01 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  xxmonth =      "(none)",
}


bibtype: article
filename: fparith.bib
label: McPherson:1982:LSG
author: John C. McPherson and Frank E. Hamilton and Robert R. Seeber, Jr.
title: A Large-Scale, general-Purpose Electronic Digital calculator: The SSEC
journal: j-ANN-HIST-COMPUT
volume: 4
number: 4
pages: 313--326
month: oct
monthnumber: 10
year: 1982
CODEN: AHCOE5
ISSN: 0164-1239 OR 01641239
ISSNL: 0164-1239 OR 01641239
bibdate: Fri Nov 1 15:29:19 MST 2002
bibtimestamp: 2002.11.01 15:29:19 MST
fjournal: Annals of the History of Computing
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650
rawauthor: John C. McPherson and Frank E. Hamilton and Robert R. {Seeber, Jr.}
rawtitle: A Large-Scale, general-Purpose Electronic Digital calculator: The {SSEC}
URL:
http://dlib.computer.org/an/books/an1982/pdf/a4313.pdf; http://www.computer.org/annals/an1982/a4313abs.htm

entry:
@Article{McPherson:1982:LSG,
  author =       "John C. McPherson and Frank E. Hamilton and Robert R.
                 {Seeber, Jr.}",
  title =        "A Large-Scale, general-Purpose Electronic Digital
                 calculator: The {SSEC}",
  journal =      j-ANN-HIST-COMPUT,
  volume =       "4",
  number =       "4",
  pages =        "313--326",
  month =        oct # "\slash " # dec,
  year =         "1982",
  CODEN =        "AHCOE5",
  ISSN =         "0164-1239",
  ISSN-L =       "0164-1239",
  bibdate =      "Fri Nov 1 15:29:19 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://dlib.computer.org/an/books/an1982/pdf/a4313.pdf;
                 http://www.computer.org/annals/an1982/a4313abs.htm",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of the History of Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650",
}


bibtype: article
filename: fparith.bib
label: Monroe:1982:FFP
author: Alfred J. Monroe
title: Forth Floating Point Package
journal: j-DDJ
volume: 7
number: 9
pages: 16--??
month: sep
monthnumber: 9
year: 1982
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: Alfred J. Monroe
rawtitle: {Forth} Floating Point Package
entry:
@Article{Monroe:1982:FFP,
  author =       "Alfred J. Monroe",
  title =        "{Forth} Floating Point Package",
  journal =      j-DDJ,
  volume =       "7",
  number =       "9",
  pages =        "16--??",
  month =        sep,
  year =         "1982",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Mon Sep 2 09:09:39 MDT 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}


bibtype: article
filename: fparith.bib
label: Oklobdzija:1982:LSR
author: V. G. Oklobdzija and M. D. Ercegovac
title: An On-Line Square Root Algorithm
journal: j-IEEE-TRANS-COMPUT
volume: C-31
number: 1
pages: 70--75
month: jan
monthnumber: 1
year: 1982
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1982.1675887
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 10:33:09 MDT 2011
bibtimestamp: 2011.07.10 10:33:09 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675887
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: V. G. Oklobdzija and M. D. Ercegovac
rawtitle: An On-Line Square Root Algorithm
entry:
@Article{Oklobdzija:1982:LSR,
  author =       "V. G. Oklobdzija and M. D. Ercegovac",
  title =        "An On-Line Square Root Algorithm",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-31",
  number =       "1",
  pages =        "70--75",
  month =        jan,
  year =         "1982",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1982.1675887",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:33:09 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675887",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: misc
filename: fparith.bib
label: Palmer:1982:NDP
author: John Palmer and Bruce Ravenel and Rafi Nave
title: Numeric Data Processor
pages: 22
day: 6
month: jul
monthnumber: 7
year: 1982
bibdate: Sat Aug 23 06:33:14 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2025.08.23 06:33:14 ???
note: Filed 13 February, 1980. This general patent covers the breadth of 8087 features.
URL: https://ieeemilestones.ethw.org/w/images/6/6c/Patent_8087_coprocessor.pdf
acknowledgement: ack-nhfb
howpublished: US Patent 4,338,675.
rawauthor: John Palmer and Bruce Ravenel and Rafi Nave
rawnote: Filed 13 February, 1980. This general patent covers the breadth of 8087 features.
rawtitle: Numeric Data Processor
abstract:
A floating point, integrated, arithmetic circuit is organized around a file format having a floating point numeric domain exceeding that of any single or double precision floating point numbers, long or short integer words or BCD data upon which it must operate. As a result the circuit has a greater reliability, range and precision than ever previously achieved without entailing additional circuit complexity. Reliability is further enhanced by a systematic three bit rounding field, and by including means for detecting every error or exception condition with an optional expected response provided thereto by hardware. As a result of such organization, an unexpected increase of capacity is achieved wherein transcendental functions can be computed totally in hardware, and whereby mixed mode arithmetic can be implemented without difficulty. The numeric processor also includes a programmable shifter capable of arbitrary numbers of bit and byte shifts in a single clock cycle, as well as an arithmetic unit capable of implementing multiplication, division, modulo reduction and square roots directly in hardware.

entry:
@Misc{Palmer:1982:NDP,
  author =       "John Palmer and Bruce Ravenel and Rafi Nave",
  title =        "Numeric Data Processor",
  howpublished = "US Patent 4,338,675.",
  pages =        "22",
  day =          "6",
  month =        jul,
  year =         "1982",
  bibdate =      "Sat Aug 23 06:33:14 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Filed 13 February, 1980. This general patent covers
                 the breadth of 8087 features.",
  URL =          "https://ieeemilestones.ethw.org/w/images/6/6c/Patent_8087_coprocessor.pdf",
  abstract =     "A floating point, integrated, arithmetic circuit is
                 organized around a file format having a floating point
                 numeric domain exceeding that of any single or double
                 precision floating point numbers, long or short integer
                 words or BCD data upon which it must operate. As a
                 result the circuit has a greater reliability, range and
                 precision than ever previously achieved without
                 entailing additional circuit complexity. Reliability is
                 further enhanced by a systematic three bit rounding
                 field, and by including means for detecting every error
                 or exception condition with an optional expected
                 response provided thereto by hardware. As a result of
                 such organization, an unexpected increase of capacity
                 is achieved wherein transcendental functions can be
                 computed totally in hardware, and whereby mixed mode
                 arithmetic can be implemented without difficulty. The
                 numeric processor also includes a programmable shifter
                 capable of arbitrary numbers of bit and byte shifts in
                 a single clock cycle, as well as an arithmetic unit
                 capable of implementing multiplication, division,
                 modulo reduction and square roots directly in
                 hardware.",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Palmer:1982:VRN
author: J. F. Palmer
title: VLSI and the Revolution in Numeric Computation
crossref: Ruschitzka:1982:IWC
pages: 339--341
year: 1982
bibdate: Wed Sep 7 22:31:27 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.07 22:31:27 ???
acknowledgement: ack-nj
rawauthor: J. F. Palmer
rawtitle: {VLSI} and the Revolution in Numeric Computation
entry:
@InProceedings{Palmer:1982:VRN,
  author =       "J. F. Palmer",
  title =        "{VLSI} and the Revolution in Numeric Computation",
  crossref =     "Ruschitzka:1982:IWC",
  pages =        "339--341",
  year =         "1982",
  bibdate =      "Wed Sep 7 22:31:27 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: incollection
filename: fparith.bib
label: Phillips:1982:BC
author: E. William Phillips
title: Binary Calculation
crossref: Randell:1982:ODC
pages: 303--314
year: 1982
bibdate: Wed Oct 13 09:51:37 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.13 09:51:37 ???
acknowledgement: ack-nhfb
rawauthor: E. William Phillips
rawtitle: Binary Calculation
remark:
The 1936 epigraph credited to this author in cite [Chapter 7]Coonen:1984:CPS says: ``The ultimate aim is to persuade all of the civilized world to abandon the decimal numeration and to use octonal in its place; to discontinue counting in tens and to count in eights instead. However, it seems unlikely that the whole civilized world will be persuaded to complete this change during the next twelve months, having previously declined similar invitations.''

entry:
@InCollection{Phillips:1982:BC,
  author =       "E. William Phillips",
  title =        "Binary Calculation",
  crossref =     "Randell:1982:ODC",
  pages =        "303--314",
  year =         "1982",
  bibdate =      "Wed Oct 13 09:51:37 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "The 1936 epigraph credited to this author in
                 \cite[Chapter 7]{Coonen:1984:CPS} says: ``The ultimate
                 aim is to persuade all of the civilized world to
                 abandon the decimal numeration and to use octonal in
                 its place; to discontinue counting in tens and to count
                 in eights instead. However, it seems unlikely that the
                 whole civilized world will be persuaded to complete
                 this change during the next twelve months, having
                 previously declined similar invitations.''",
}


bibtype: inproceedings
filename: fparith.bib
label: Rall:1982:ACA
author: L. B. Rall
editor: Anonymous
booktitle: Proceedings of the 1982 Army Numerical Analysis and Computers Conference
title: Accurate computer arithmetic for scientific computation
volume: 82--83
publisher: US Army Research Office
address: Research Triangle Park, NC, USA
pages: 343--356
month: aug
monthnumber: 8
year: 1982
bibdate: Wed Oct 13 21:52:01 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.13 21:52:01 ???
note: Two volumes.
URL: http://books.google.com/books?id=pFb-QQAACAAJ
remark: The theme of the 1982 Conference was Grid Techniques for Partial Differential Equations.
acknowledgement: ack-nhfb
bookpages: xiv + 606
rawauthor: L. B. Rall
rawbooktitle: {Proceedings of the 1982 Army Numerical Analysis and Computers Conference}
raweditor: Anonymous
rawnote: Two volumes.
rawtitle: Accurate computer arithmetic for scientific computation
abstract:
The operations of accurate arithmetic can be implemented easily on a microcomputer or a computer with microprogrammable arithmetic operations. In addition, for accurate final results, a compiler is necessary which will select the appropriate operations. A language of this type (PASCAL-SC) was developed. Along with accurate real arithmetic, this compiler provides accurate complex arithmetic, real and complex interval arithmetic, and vector and matrix arithmetic over these data types. Some features of PASCAL-SC related to scientific and engineering computation are described. In most cases, the operations of accurate arithmetic are performed at the same speed as ordinary (uncontrolled) floating-point arithmetic.

keywords:
analysis (mathematics); arithmetic; computation; microcomputers; microprogramming; Pascal (programming language)

subject:
Numerical analysis; Computer programs; Congresses; Numerical Mathematics. Computer Hardware. Computers. Partial differential equations. Symposia. Numerical analysis. Grids. Computations. Methodology. Mathematical programming. Finite difference theory. Finite element analysis. Boundaries. Hydrodynamics. Gas dynamics. Interior ballistics. Autofrettage. Land mines. Blast loads. Conduction(heat transfer) Magnet coils. Water waves. Currents

rawabstract:
The operations of accurate arithmetic can be implemented easily on a microcomputer or a computer with microprogrammable arithmetic operations. In addition, for accurate final results, a compiler is necessary which will select the appropriate operations. A language of this type (PASCAL-SC) was developed. Along with accurate real arithmetic, this compiler provides accurate complex arithmetic, real and complex interval arithmetic, and vector and matrix arithmetic over these data types. Some features of PASCAL-SC related to scientific and engineering computation are described. In most cases, the operations of accurate arithmetic are performed at the same speed as ordinary (uncontrolled) floating-point arithmetic.

entry:
@InProceedings{Rall:1982:ACA,
  author =       "L. B. Rall",
  editor =       "Anonymous",
  booktitle =    "{Proceedings of the 1982 Army Numerical Analysis and
                 Computers Conference}",
  title =        "Accurate computer arithmetic for scientific
                 computation",
  volume =       "82--83",
  publisher =    "US Army Research Office",
  address =      "Research Triangle Park, NC, USA",
  bookpages =    "xiv + 606",
  pages =        "343--356",
  month =        aug,
  year =         "1982",
  bibdate =      "Wed Oct 13 21:52:01 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Two volumes.",
  URL =          "http://books.google.com/books?id=pFb-QQAACAAJ",
  abstract =     "The operations of accurate arithmetic can be
                 implemented easily on a microcomputer or a computer
                 with microprogrammable arithmetic operations. In
                 addition, for accurate final results, a compiler is
                 necessary which will select the appropriate operations.
                 A language of this type (PASCAL-SC) was developed.
                 Along with accurate real arithmetic, this compiler
                 provides accurate complex arithmetic, real and complex
                 interval arithmetic, and vector and matrix arithmetic
                 over these data types. Some features of PASCAL-SC
                 related to scientific and engineering computation are
                 described. In most cases, the operations of accurate
                 arithmetic are performed at the same speed as ordinary
                 (uncontrolled) floating-point arithmetic.",
  acknowledgement = ack-nhfb,
  keywords =     "analysis (mathematics); arithmetic; computation;
                 microcomputers; microprogramming; Pascal (programming
                 language)",
  meetingname =  "Army Numerical Analysis and Computers Conference (1982
                 : Vicksburg, Miss.)",
  remark =       "The theme of the 1982 Conference was Grid Techniques
                 for Partial Differential Equations.",
  subject =      "Numerical analysis; Computer programs; Congresses;
                 Numerical Mathematics. Computer Hardware. Computers.
                 Partial differential equations. Symposia. Numerical
                 analysis. Grids. Computations. Methodology.
                 Mathematical programming. Finite difference theory.
                 Finite element analysis. Boundaries. Hydrodynamics. Gas
                 dynamics. Interior ballistics. Autofrettage. Land
                 mines. Blast loads. Conduction(heat transfer) Magnet
                 coils. Water waves. Currents",
  xxtitle =      "Accurate arithmetic for scientific computation",
  xxvolume =     "82-3",
}


bibtype: inproceedings
filename: fparith.bib
label: Ramnarayan:1982:AER
author: R. Ramnarayan and F. Taylor
booktitle: IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP '82
title: Analysis of errors in residue number system (RNS) based IIR digital filters
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 56--59
year: 1982
DOI: https://doi.org/10.1049/el:19820632
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
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: R. Ramnarayan and F. Taylor
rawbooktitle: {IEEE} International Conference on Acoustics, Speech, and Signal Processing, {ICASSP '82}
rawtitle: Analysis of errors in residue number system ({RNS}) based {IIR} digital filters
entry:
@InProceedings{Ramnarayan:1982:AER,
  author =       "R. Ramnarayan and F. Taylor",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing, {ICASSP '82}",
  title =        "Analysis of errors in residue number system ({RNS})
                 based {IIR} digital filters",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "56--59",
  year =         "1982",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1049/el:19820632",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "The problem of analyzing errors in Residue Number
                 System (RNS) based IIR Digital filters is considered in
                 this paper. There are basically three types of errors
                 in RNS based digital filters, They are coefficient
                 quantization errors(1), scaling errors \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Rix:1982:UQA
author: P. Rix
title: Universeller Quadratwurzel-Algorithmus toenglish Universal Square Root Algorithms endtoenglish
journal: j-ELECTRONIK
volume: 23
pages: 81--82
year: 1982
CODEN: EKRKAR
ISSN: 0013-5658 OR 00135658
bibdate: Fri Sep 16 16:30:41 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.16 16:30:41 ???
fjournal: Elektronik
acknowledgement: ack-nj
rawauthor: P. Rix
rawtitle:
{Universeller Quad\-rat\-wurz\-el-Al\-go\-rith\-mus} \toenglish {Universal Square Root Algorithms} \endtoenglish

entry:
@Article{Rix:1982:UQA,
  author =       "P. Rix",
  title =        "{Universeller Quad\-rat\-wurz\-el-Al\-go\-rith\-mus}
                 \toenglish {Universal Square Root Algorithms}
                 \endtoenglish",
  journal =      j-ELECTRONIK,
  volume =       "23",
  pages =        "81--82",
  year =         "1982",
  CODEN =        "EKRKAR",
  ISSN =         "0013-5658",
  bibdate =      "Fri Sep 16 16:30:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Elektronik",
}


bibtype: article
filename: fparith.bib
label: Rump:1982:CR
author: Siegfried M. Rump
title: Computer und Rechengenauigkeit toenglish Computer and Computational Precision endtoenglish
journal: j-ELEK-RECHENANLAGEN
volume: 24
number: 6
pages: 268--277
month: dec
monthnumber: 12
year: 1982
CODEN: ELRAA4
ISSN: 0013-5720 OR 00135720
bibdate: Sat Feb 10 12:41:06 1996
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.10 12:41:06 ???
fjournal: Elektronische Rechenanlagen
acknowledgement: ack-nj
rawauthor: Siegfried M. Rump
rawtitle: {Computer und Rechengenauigkeit} \toenglish {Computer and Computational Precision} \endtoenglish
entry:
@Article{Rump:1982:CR,
  author =       "Siegfried M. Rump",
  title =        "{Computer und Rechengenauigkeit} \toenglish {Computer
                 and Computational Precision} \endtoenglish",
  journal =      j-ELEK-RECHENANLAGEN,
  volume =       "24",
  number =       "6",
  pages =        "268--277",
  month =        dec,
  year =         "1982",
  CODEN =        "ELRAA4",
  ISSN =         "0013-5720",
  bibdate =      "Sat Feb 10 12:41:06 1996",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Elektronische Rechenanlagen",
}


bibtype: article
filename: fparith.bib
label: Sacks-Davis:1982:ARN
author: R. Sacks-Davis
title: Applications of Redundant Number Representations to Decimal Arithmetic
journal: j-COMP-J
volume: 25
number: 4
pages: 471--477
month: nov
monthnumber: 11
year: 1982
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: C5260 (Digital signal processing)
corpsource: Department of Computer Sci., Monash University, Clayton, Vic., Australia
journalURL: http://comjnl.oxfordjournals.org/
treatment: T Theoretical or Mathematical
rawauthor: R. Sacks-Davis
rawtitle: Applications of Redundant Number Representations to Decimal Arithmetic
bibsource:
Compendex database; http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/471.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/472.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/473.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/474.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/475.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/476.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/477.tif

abstract:
A decimal arithmetic unit is proposed for both integer and floating-point computations. To achieve comparable speed to a binary arithmetic unit, the decimal unit is based on a redundant number representation. With this representation no loss of compactness is made relative to binary coded decimal (BCD) form. In this paper the hardware required for the implementation of the basic operations of addition, subtraction, multiplication and division are described and the properties of floating-point arithmetic based on a redundant number representation are investigated.

keywords:
addition; binary; binary arithmetic unit; coded decimal; computers, digital; decimal floating-point arithmetic; digital arithmetic; division; floating point arithmetic; floating-point; integer; multiplication; redundant number representations; subtraction

remark:
The redundant number representation postpones the need to carry during add, subtract, multiply, and divide, delaying it until the final rounding step in a store instruction. See cite Fahmy:2003:CRF,Fahmy:2003:RDF.

rawabstract:
A decimal arithmetic unit is proposed for both integer and floating-point computations. To achieve comparable speed to a binary arithmetic unit, the decimal unit is based on a redundant number representation. With this representation no loss of compactness is made relative to binary coded decimal (BCD) form. In this paper the hardware required for the implementation of the basic operations of addition, subtraction, multiplication and division are described and the properties of floating-point arithmetic based on a redundant number representation are investigated.

entry:
@Article{Sacks-Davis:1982:ARN,
  author =       "R. Sacks-Davis",
  title =        "Applications of Redundant Number Representations to
                 Decimal Arithmetic",
  journal =      j-COMP-J,
  volume =       "25",
  number =       "4",
  pages =        "471--477",
  month =        nov,
  year =         "1982",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Mar 25 13:51:56 MST 1997",
  bibsource =    "Compendex database;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/471.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/472.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/473.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/474.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/475.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/476.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/477.tif",
  abstract =     "A decimal arithmetic unit is proposed for both integer
                 and floating-point computations. To achieve comparable
                 speed to a binary arithmetic unit, the decimal unit is
                 based on a redundant number representation. With this
                 representation no loss of compactness is made relative
                 to binary coded decimal (BCD) form. In this paper the
                 hardware required for the implementation of the basic
                 operations of addition, subtraction, multiplication and
                 division are described and the properties of
                 floating-point arithmetic based on a redundant number
                 representation are investigated.",
  acknowledgement = ack-nhfb,
  classcodes =   "C5260 (Digital signal processing)",
  classification = "721; 723",
  corpsource =   "Department of Computer Sci., Monash University,
                 Clayton, Vic., Australia",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "addition; binary; binary arithmetic unit; coded
                 decimal; computers, digital; decimal floating-point
                 arithmetic; digital arithmetic; division; floating
                 point arithmetic; floating-point; integer;
                 multiplication; redundant number representations;
                 subtraction",
  remark =       "The redundant number representation postpones the need
                 to carry during add, subtract, multiply, and divide,
                 delaying it until the final rounding step in a store
                 instruction. See
                 \cite{Fahmy:2003:CRF,Fahmy:2003:RDF}.",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: inproceedings
filename: fparith.bib
label: Samsen:1982:AFP
author: G. R. Samsen
title: An Advanced Floating Point Processor to Enhance Speed of Mathematical Processing
crossref: Southcon:1982:SCR
pages: 16/1/1--3
year: 1982
bibdate: Wed Sep 7 22:31:27 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.07 22:31:27 ???
acknowledgement: ack-nj
rawauthor: G. R. Samsen
rawtitle: An Advanced Floating Point Processor to Enhance Speed of Mathematical Processing
entry:
@InProceedings{Samsen:1982:AFP,
  author =       "G. R. Samsen",
  title =        "An Advanced Floating Point Processor to Enhance Speed
                 of Mathematical Processing",
  crossref =     "Southcon:1982:SCR",
  pages =        "16/1/1--3",
  year =         "1982",
  bibdate =      "Wed Sep 7 22:31:27 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: Sasaki:1982:EGE
author: T. Sasaki and H. Murao
title: Efficient Gaussian elimination method for symbolic determinants and linear systems
journal: j-TOMS
volume: 8
number: 3
pages: 277--289
month: sep
monthnumber: 9
year: 1982
CODEN: ACMSCU
DOI: https://doi.org/10.1145/356004.356007
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sat Nov 9 08:26:18 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.11.09 08:26:18 MST
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
key: Symbolic_determinant; Symbolic_linear_systems; Gaussian_elimination
reviewer: R. J. Fateman; Fateman, R. J
rawauthor: T. Sasaki and H. Murao
rawtitle: Efficient {Gaussian} elimination method for symbolic determinants and linear systems
subject:
F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; I. Computing Methodologies; I.1 ALGEBRAIC MANIPULATION

entry:
@Article{Sasaki:1982:EGE,
  author =       "T. Sasaki and H. Murao",
  key =          "Symbolic_determinant; Symbolic_linear_systems;
                 Gaussian_elimination",
  title =        "Efficient {Gaussian} elimination method for symbolic
                 determinants and linear systems",
  journal =      j-TOMS,
  volume =       "8",
  number =       "3",
  pages =        "277--289",
  month =        sep,
  year =         "1982",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356004.356007",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  catcode =      "F.2; G.1.3; I.1.2",
  content =      "The computation of the solution of a linear system
                 whose entries are indeterminates or polynomials is of
                 interest both for theoretic and practical reasons. The
                 similar problem of computing the determinant is
                 important because of the relationship of the
                 determinant and resultant to factorization, polynomial
                 greatest-common-divisor calculations, and computation
                 with algebraic functions. Engineering application areas
                 of this material include the analysis of electrical or
                 other networks.\par

                 These computation problems are quite distinct from
                 others which would appear to be superficially similar,
                 namely numerical linear algebra problems. The result of
                 computing a numerical determinant is a floating point
                 number with an associated error. The result of
                 computing an exact algebraic determinant is, typically,
                 a large expression whose terms may be rearranged into
                 various ``factored'' forms for savings in computation
                 time and space. This answer has no error
                 whatsoever.\par

                 Clever and efficient programs in each domain have been
                 shown to be disastrous in the other. Thus one of the
                 best algebraic techniques for determinant calculations
                 for ``sparse polynomial'' matrices is expansion by
                 minors [1]; whereas Gaussian elimination is far
                 superior \ldots{}",
  CRclass =      "F.2.1 Numerical Algorithms and Problems; G.1.3
                 Numerical Linear Algebra; G.1.3 Linear systems (direct
                 and iterative methods); I.1.2 Algorithms; I.1.2
                 Algebraic algorithms",
  CRnumber =     "40106",
  descriptor =   "Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems;
                 Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
                 Linear Algebra, Linear systems (direct and iterative
                 methods); Computing Methodologies, ALGEBRAIC
                 MANIPULATION, Algorithms, Algebraic algorithms",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  genterm =      "ALGORITHMS; PERFORMANCE",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "R. J. Fateman; Fateman, R. J",
  subject =      "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
                 G.1 NUMERICAL ANALYSIS; I. Computing Methodologies; I.1
                 ALGEBRAIC MANIPULATION",
}


bibtype: article
filename: fparith.bib
label: Sasaki:1982:PFM
author: T. Sasaki and Y. Kanada
title: Practically Fast Multiple Precision Evaluation of LOG ($ X $)
journal: j-INFO-PROC
volume: 5
number: 4
pages: 247--250
year: 1982
bibdate: Thu Sep 8 08:20:54 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.08 08:20:54 ???
acknowledgement: ack-nj
rawauthor: T. Sasaki and Y. Kanada
rawtitle: Practically Fast Multiple Precision Evaluation of {LOG} ($ {X} $)
entry:
@Article{Sasaki:1982:PFM,
  author =       "T. Sasaki and Y. Kanada",
  title =        "Practically Fast Multiple Precision Evaluation of
                 {LOG} ($ {X} $)",
  journal =      j-INFO-PROC,
  volume =       "5",
  number =       "4",
  pages =        "247--250",
  month =        "????",
  year =         "1982",
  bibdate =      "Thu Sep 8 08:20:54 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: Schatte:1982:FPF
author: P. Schatte
title: The Frequency of Postshifts in Floating-Point Multiplication
journal: Elektronische Informationsverarbeitung und Kybernetik
volume: 18
number: 9
pages: 523--526
year: 1982
bibdate: Thu Sep 1 10:15:07 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:15:07 ???
acknowledgement: ack-nj
rawauthor: P. Schatte
rawtitle: The Frequency of Postshifts in Floating-Point Multiplication
entry:
@Article{Schatte:1982:FPF,
  author =       "P. Schatte",
  title =        "The Frequency of Postshifts in Floating-Point
                 Multiplication",
  journal =      "Elektronische Informationsverarbeitung und
                 Kybernetik",
  volume =       "18",
  number =       "9",
  pages =        "523--526",
  month =        "????",
  year =         "1982",
  bibdate =      "Thu Sep 1 10:15:07 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: Sewell:1982:RLT
author: B. T. Sewell
title: A Rapid Lookup Table Method for Trigonometric Functions
journal: j-SPE
volume: 12
number: 10
pages: 885--887
month: oct
monthnumber: 10
year: 1982
CODEN: SPEXBL
ISSN: 0038-0644 (print), 1097-024X (electronic) OR 00380644 (print), 1097024X (electronic)
ISSNL: 0038-0644 OR 00380644
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: Software---Practice and Experience
keywords: algorithms
acknowledgement: ack-nj
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X
rawauthor: B. T. Sewell
rawtitle: A Rapid Lookup Table Method for Trigonometric Functions
subject:
G Mathematics of Computing, MISCELLANEOUS J.2 Computer Applications, PHYSICAL SCIENCES AND ENGINEERING, Chemistry

entry:
@Article{Sewell:1982:RLT,
  author =       "B. T. Sewell",
  title =        "A Rapid Lookup Table Method for Trigonometric
                 Functions",
  journal =      j-SPE,
  volume =       "12",
  number =       "10",
  pages =        "885--887",
  month =        oct,
  year =         "1982",
  CODEN =        "SPEXBL",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  bibdate =      "Thu Sep 1 10:15:56 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Software---Practice and Experience",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
  keywords =     "algorithms",
  subject =      "G Mathematics of Computing, MISCELLANEOUS \\ J.2
                 Computer Applications, PHYSICAL SCIENCES AND
                 ENGINEERING, Chemistry",
}


bibtype: incollection
filename: fparith.bib
label: Sheldon:1982:ICP
author: John W. Sheldon and Liston Tatum
title: The IBM Card-Programmed Electronic Calculator (1951)
crossref: Randell:1982:ODC
pages: 233--239
year: 1982
bibdate: Sun Nov 03 08:36:11 2002
bibtimestamp: 2002.11.03 08:36:11 ???
acknowledgement: ack-nhfb
rawauthor: John W. Sheldon and Liston Tatum
rawtitle: The {IBM} Card-Programmed Electronic Calculator (1951)
entry:
@InCollection{Sheldon:1982:ICP,
  author =       "John W. Sheldon and Liston Tatum",
  title =        "The {IBM} Card-Programmed Electronic Calculator
                 (1951)",
  crossref =     "Randell:1982:ODC",
  pages =        "233--239",
  year =         "1982",
  bibdate =      "Sun Nov 03 08:36:11 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: mastersthesis
filename: fparith.bib
label: Sippel:1982:FRI
author: Timothy N. Sippel
title: Floating RISCS: implementation and analysis of floating point on RISC I
type: Electrical Engineering and Computer Sciences Master of Science Report
school: University of California, Department of Electrical Engineering and Computer Sciences
address: Berkeley, CA, USA
pages: various
year: 1982
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
acknowledgement: ack-nhfb
rawauthor: Timothy N. Sippel
rawtitle: Floating {RISCS}: implementation and analysis of floating point on {RISC} {I}
entry:
@MastersThesis{Sippel:1982:FRI,
  author =       "Timothy N. Sippel",
  title =        "Floating {RISCS}: implementation and analysis of
                 floating point on {RISC} {I}",
  type =         "Electrical Engineering and Computer Sciences Master of
                 Science Report",
  school =       "University of California, Department of Electrical
                 Engineering and Computer Sciences",
  address =      "Berkeley, CA, USA",
  pages =        "various",
  year =         "1982",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Sips:1982:CPM
author: H. J. Sips
title: Comments on ``An $ O(n) $ Parallel Multiplier with Bit-Sequential Input and Output''
journal: j-IEEE-TRANS-COMPUT
volume: C-31
number: 4
pages: 325--327
month: apr
monthnumber: 4
year: 1982
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1982.1676000
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 10:33:11 MDT 2011
bibtimestamp: 2011.07.10 10:33:11 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676000
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: H. J. Sips
rawtitle: Comments on {``An $ O(n) $ Parallel Multiplier with Bit-Sequential Input and Output''}
entry:
@Article{Sips:1982:CPM,
  author =       "H. J. Sips",
  title =        "Comments on {``An $ O(n) $ Parallel Multiplier with
                 Bit-Sequential Input and Output''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-31",
  number =       "4",
  pages =        "325--327",
  month =        apr,
  year =         "1982",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1982.1676000",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:33:11 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676000",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Strader:1982:CBS
author: N. R. Strader and V. T. Rhyne
title: A Canonical Bit-Sequential Multiplier
journal: j-IEEE-TRANS-COMPUT
volume: C-31
number: 8
pages: 791--795
month: aug
monthnumber: 8
year: 1982
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1982.1676085
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 10:33:14 MDT 2011
bibtimestamp: 2011.07.10 10:33:14 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676085
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: N. R. Strader and V. T. Rhyne
rawtitle: A Canonical Bit-Sequential Multiplier
entry:
@Article{Strader:1982:CBS,
  author =       "N. R. Strader and V. T. Rhyne",
  title =        "A Canonical Bit-Sequential Multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-31",
  number =       "8",
  pages =        "791--795",
  month =        aug,
  year =         "1982",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1982.1676085",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:33:14 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676085",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Tan:1982:ADC
author: Chung-I Tan and B. McInnis
title: Adaptive digital control implemented using residue number systems
journal: j-IEEE-TRANS-AUTOMAT-CONTR
volume: 27
number: 2
pages: 499--502
month: apr
monthnumber: 4
year: 1982
CODEN: IETAA9
DOI: https://doi.org/10.1109/CDC.1981.269326
ISSN: 0018-9286 (print), 1558-2523 (electronic) OR 00189286 (print), 15582523 (electronic)
ISSNL: 0018-9286 OR 00189286
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
note: See comments cite Pei:1984:CAD.
URL: https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=24189
fjournal: IEEE Transactions on Automatic Control
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9
rawauthor: Chung-I Tan and B. McInnis
rawnote: See comments \cite{Pei:1984:CAD}.
rawtitle: Adaptive digital control implemented using residue number systems
entry:
@Article{Tan:1982:ADC,
  author =       "Chung-I Tan and B. McInnis",
  title =        "Adaptive digital control implemented using residue
                 number systems",
  journal =      j-IEEE-TRANS-AUTOMAT-CONTR,
  volume =       "27",
  number =       "2",
  pages =        "499--502",
  month =        apr,
  year =         "1982",
  CODEN =        "IETAA9",
  DOI =          "https://doi.org/10.1109/CDC.1981.269326",
  ISSN =         "0018-9286 (print), 1558-2523 (electronic)",
  ISSN-L =       "0018-9286",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See comments \cite{Pei:1984:CAD}.",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=24189",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Automatic Control",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9",
  keywords =     "residue arithmetic; residue number system",
  summary =      "The application of residue number systems for the
                 implementation of adaptive digital controllers is
                 presented. Division operations are avoided through the
                 use of iteration to solve for the value of the control.
                 Decoding computations are simplified \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Taylor:1982:ARM
author: F. J. Taylor and C. H. Huang
title: An Autoscale Residue Multiplier
journal: j-IEEE-TRANS-COMPUT
volume: C-31
number: 4
pages: 321--325
month: apr
monthnumber: 4
year: 1982
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1982.1675999
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Fri Nov 09 19:30:01 2007
bibtimestamp: 2007.11.09 19:30:01 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: F. J. Taylor and C. H. Huang
rawtitle: An Autoscale Residue Multiplier
entry:
@Article{Taylor:1982:ARM,
  author =       "F. J. Taylor and C. H. Huang",
  title =        "An Autoscale Residue Multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-31",
  number =       "4",
  pages =        "321--325",
  month =        apr,
  year =         "1982",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1982.1675999",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 09 19:30:01 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Taylor:1982:VRA
author: F. J. Taylor
title: A VLSI Residue Arithmetic Multiplier
journal: j-IEEE-TRANS-COMPUT
volume: C-31
number: 6
pages: 540--546
month: jun
monthnumber: 6
year: 1982
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1982.1676036
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 10:33:12 MDT 2011
bibtimestamp: 2011.07.10 10:33:12 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676036
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: F. J. Taylor
rawtitle: A {VLSI} Residue Arithmetic Multiplier
entry:
@Article{Taylor:1982:VRA,
  author =       "F. J. Taylor",
  title =        "A {VLSI} Residue Arithmetic Multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-31",
  number =       "6",
  pages =        "540--546",
  month =        jun,
  year =         "1982",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1982.1676036",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:33:12 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676036",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Teachey:1982:SRX
author: R. D. Teachey
title: Square-Root-X Comparison --- New Results Discovered
journal: j-IEEE-MICRO
volume: 2
number: 4
pages: 5--5
month: oct
monthnumber: 10
year: 1982
CODEN: IEMIDZ
DOI: https://doi.org/10.1109/MM.1982.290929
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
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; Science Citation Index database (1980--2000)
bibtimestamp: 2000.12.14 06:08:58 MST
fjournal: IEEE Micro
acknowledgement: ack-nhfb
journalURL: http://www.computer.org/csdl/mags/mi/index.html
rawauthor: R. D. Teachey
rawtitle: Square-Root-{X} Comparison --- New Results Discovered
entry:
@Article{Teachey:1982:SRX,
  author =       "R. D. Teachey",
  title =        "Square-Root-{X} Comparison --- New Results
                 Discovered",
  journal =      j-IEEE-MICRO,
  volume =       "2",
  number =       "4",
  pages =        "5--5",
  month =        oct # "\slash " # dec,
  year =         "1982",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/MM.1982.290929",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Thu Dec 14 06:08:58 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 Science Citation Index database (1980--2000)",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
}


bibtype: incollection
filename: fparith.bib
label: TorresyQuevedo:1982:EAD
author: Leonardo Torres y Quevedo
title: Essays on Automatics --- Its Definitions --- Theoretical Extent of its Applications (1914)
crossref: Randell:1982:ODC
pages: 89--107
year: 1982
bibdate: Sun Nov 03 08:36:11 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.11.03 08:36:11 ???
acknowledgement: ack-nhfb
rawauthor: Leonardo {Torres y Quevedo}
rawtitle: Essays on Automatics --- Its Definitions --- Theoretical Extent of its Applications (1914)
remark:
This translation and reprint contains a description of what is believed to be the first design, albeit purely theoretical, and for an electromechanical device, of floating-point arithmetic. See, however, the independent work, and first practical implementation of floating-point arithmetic of Zuse cite Zuse:1982:MAE,Zuse:1982:OCD.

entry:
@InCollection{TorresyQuevedo:1982:EAD,
  author =       "Leonardo {Torres y Quevedo}",
  title =        "Essays on Automatics --- Its Definitions ---
                 Theoretical Extent of its Applications (1914)",
  crossref =     "Randell:1982:ODC",
  pages =        "89--107",
  year =         "1982",
  bibdate =      "Sun Nov 03 08:36:11 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "This translation and reprint contains a description of
                 what is believed to be the first design, albeit purely
                 theoretical, and for an electromechanical device, of
                 floating-point arithmetic. See, however, the
                 independent work, and first practical implementation of
                 floating-point arithmetic of Zuse
                 \cite{Zuse:1982:MAE,Zuse:1982:OCD}.",
}


bibtype: article
filename: fparith.bib
label: Turner:1982:DLS
author: Peter R. Turner
title: The distribution of leading significant digits
journal: j-IMA-J-NUMER-ANAL
volume: 2
number: 4
pages: 407--412
year: 1982
CODEN: IJNADH
ISSN: 0272-4979 (print), 1464-3642 (electronic) OR 02724979 (print), 14643642 (electronic)
ISSNL: 0272-4979 OR 02724979
MRclass: 65G99 (60E05)
MRnumber: 84f:65038
MRreviewer: Seppo Linnainmaa
bibdate: Sat Dec 23 17:06:35 MST 2000
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; MathSciNet database
bibtimestamp: 2000.12.23 17:06:35 MST
fjournal: IMA Journal of Numerical Analysis
keywords: Benford's Law; Law of Anomalous Numbers; Zipf's Law
acknowledgement: ack-nhfb
journalURL: http://imajna.oxfordjournals.org/content/by/year
rawauthor: Peter R. Turner
rawtitle: The distribution of leading significant digits
entry:
@Article{Turner:1982:DLS,
  author =       "Peter R. Turner",
  title =        "The distribution of leading significant digits",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "2",
  number =       "4",
  pages =        "407--412",
  year =         "1982",
  CODEN =        "IJNADH",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  MRclass =      "65G99 (60E05)",
  MRnumber =     "84f:65038",
  MRreviewer =   "Seppo Linnainmaa",
  bibdate =      "Sat Dec 23 17:06:35 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 MathSciNet database",
  acknowledgement = ack-nhfb,
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}


bibtype: article
filename: fparith.bib
label: Velasevic:1982:RLC
author: Dusan M. Velasevic
title: Right-to-Left Code Generation for Arithmetic Expressions
journal: j-COMP-J
volume: 25
number: 3
pages: 316--326
month: aug
monthnumber: 8
year: 1982
CODEN: CMPJA6
DOI: https://doi.org/10.1093/comjnl/25.3.316
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
bibdate: Tue Dec 4 14:48:13 MST 2012
bibtimestamp: 2012.12.04 14:48:13 MST
fjournal: The Computer Journal
acknowledgement: ack-nhfb
classcodes: C6110 (Systems analysis and programming); C6120 (File organisation)
corpsource: Faculty of Electrical Engng., University of Belgrade, Belgrade, Yugoslavia
journalURL: http://comjnl.oxfordjournals.org/
treatment: P Practical
rawauthor: Dusan M. Velasevi{\'c}
rawtitle: Right-to-Left Code Generation for Arithmetic Expressions
bibsource:
Compendex database; http://comjnl.oxfordjournals.org/content/25/3.toc; http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/; https://www.math.utah.edu/pub/tex/bib/compj1980.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://comjnl.oxfordjournals.org/content/25/3/316.full.pdf+html; http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/316.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/317.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/318.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/319.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/320.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/321.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/322.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/323.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/324.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/325.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/326.tif

keywords:
arithmetic; automatic programming; binary tree structure; code generator; codes, symbolic; data structures; expressions; FORTRAN; notation; postfix; right-to-left code generation; translation grammar; vector-generatrice

entry:
@Article{Velasevic:1982:RLC,
  author =       "Dusan M. Velasevi{\'c}",
  title =        "Right-to-Left Code Generation for Arithmetic
                 Expressions",
  journal =      j-COMP-J,
  volume =       "25",
  number =       "3",
  pages =        "316--326",
  month =        aug,
  year =         "1982",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/25.3.316",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Dec 4 14:48:13 MST 2012",
  bibsource =    "Compendex database;
                 http://comjnl.oxfordjournals.org/content/25/3.toc;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/;
                 https://www.math.utah.edu/pub/tex/bib/compj1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://comjnl.oxfordjournals.org/content/25/3/316.full.pdf+html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/316.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/317.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/318.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/319.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/320.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/321.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/322.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/323.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/324.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/325.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/326.tif",
  acknowledgement = ack-nhfb,
  classcodes =   "C6110 (Systems analysis and programming); C6120 (File
                 organisation)",
  classification = "723",
  corpsource =   "Faculty of Electrical Engng., University of Belgrade,
                 Belgrade, Yugoslavia",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "arithmetic; automatic programming; binary tree
                 structure; code generator; codes, symbolic; data
                 structures; expressions; FORTRAN; notation; postfix;
                 right-to-left code generation; translation grammar;
                 vector-generatrice",
  treatment =    "P Practical",
}


bibtype: article
filename: fparith.bib
label: Ware:1982:BMF
author: F. A. Ware and W. H. McAllister and J. R. Carlson and D. K. Sun and R. J. Vlach
title: 64 Bit Monolithic Floating Point Processors
journal: j-IEEE-J-SOLID-STATE-CIRCUITS
volume: SC-17
number: 5
pages: 898--907
month: oct
monthnumber: 10
year: 1982
CODEN: IJSCBC
ISSN: 0018-9200 (print), 1558-173X (electronic) OR 00189200 (print), 1558173X (electronic)
ISSNL: 0018-9200 OR 00189200
bibdate: Sat Jul 16 08:40:53 MDT 2005
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:53 MDT
fjournal: IEEE Journal of Solid-State Circuits
acknowledgement: ack-nj
rawauthor: F. A. Ware and W. H. McAllister and J. R. Carlson and D. K. Sun and R. J. Vlach
rawtitle: 64 Bit Monolithic Floating Point Processors
entry:
@Article{Ware:1982:BMF,
  author =       "F. A. Ware and W. H. McAllister and J. R. Carlson and
                 D. K. Sun and R. J. Vlach",
  title =        "64 Bit Monolithic Floating Point Processors",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "SC-17",
  number =       "5",
  pages =        "898--907",
  month =        oct,
  year =         "1982",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  summary =      "Describes a set of three processor chips capable of
                 performing 32 and 64 bit floating point add/subtract,
                 multiply, and divide operations. The chips can perform
                 over one million scalar floating point operations per
                 second, and over four million vector \ldots{}",
}


bibtype: book
filename: fparith.bib
label: Waser:1982:IAD
author: Shlomo Waser and Michael J. Flynn
title: Introduction to Arithmetic for Digital Systems Designers
publisher: pub-HRW
address: pub-HRW:adr
pages: xvii + 308
year: 1982
ISBN: 0-03-060571-7 OR 0030605717
ISBN13: 978-0-03-060571-0 OR 9780030605710
LCCN: TK7895 A65 W37 1982
bibdate: Sat Sep 03 09:25:17 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.03 09:25:17 ???
acknowledgement: ack-nj
rawauthor: Shlomo Waser and Michael J. Flynn
rawtitle: Introduction to Arithmetic for Digital Systems Designers
note:
Master copy output on Alphatype CRS high-resolution phototypesetter. This book went to press while the IEEE 754 Floating-Point Standard was still in development; consequently, some of the material on that system was invalidated by the final Standard (1985) cite IEEE:1985:AIS.

TOC:
Preface Acknowledgments Abbreviations and Symbols 1. Numeric Data Representation 2. Residue Numbers and the Limits of Fast Arithmetic 3. Addition and Subtraction 4. Multiplication 5. Division 6. Pipelining of Arithmetic Operations Appendix. References. Index.

rawnote:
Master copy output on Alphatype CRS high-resolution phototypesetter. This book went to press while the IEEE 754 Floating-Point Standard was still in development; consequently, some of the material on that system was invalidated by the final Standard (1985) \cite{IEEE:1985:AIS}.

rawTOC:
Preface\\ Acknowledgments\\ Abbreviations and Symbols\\ 1. Numeric Data Representation\\ 2. Residue Numbers and the Limits of Fast Arithmetic\\ 3. Addition and Subtraction\\ 4. Multiplication\\ 5. Division\\ 6. Pipelining of Arithmetic Operations\\ Appendix.\\ References.\\ Index.

entry:
@Book{Waser:1982:IAD,
  author =       "Shlomo Waser and Michael J. Flynn",
  title =        "Introduction to Arithmetic for Digital Systems
                 Designers",
  publisher =    pub-HRW,
  address =      pub-HRW:adr,
  pages =        "xvii + 308",
  year =         "1982",
  ISBN =         "0-03-060571-7",
  ISBN-13 =      "978-0-03-060571-0",
  LCCN =         "TK7895 A65 W37 1982",
  bibdate =      "Sat Sep 03 09:25:17 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Master copy output on Alphatype CRS high-resolution
                 phototypesetter. This book went to press while the IEEE
                 754 Floating-Point Standard was still in development;
                 consequently, some of the material on that system was
                 invalidated by the final Standard (1985)
                 \cite{IEEE:1985:AIS}.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  tableofcontents = "Preface\\
                 Acknowledgments\\
                 Abbreviations and Symbols\\
                 1. Numeric Data Representation\\
                 2. Residue Numbers and the Limits of Fast Arithmetic\\
                 3. Addition and Subtraction\\
                 4. Multiplication\\
                 5. Division\\
                 6. Pipelining of Arithmetic Operations\\
                 Appendix.\\
                 References.\\
                 Index.",
}


bibtype: book
filename: fparith.bib
label: Wilkes:1982:PPE
author: M. V. (Maurice Vincent) Wilkes and David J. Wheeler and Stanley Gill
volume: 1
publisher: pub-TOMASH
address: pub-TOMASH:adr
pages: xxxi + 167
year: 1982
ISBN: 0-262-23118-2 (MIT Press 1984), 0-938228-03-X OR 0262231182 (MIT Press 1984), 093822803X
LCCN: QA76.6 .W545 1982
bibdate: Mon Feb 10 11:33:59 MST 2020
bibtimestamp: 2020.02.10 11:33:59 MST
note: With a new introduction by Martin Campbell-Kelly.
series: Charles Babbage Institute reprint series for the history of computing
acknowledgement: ack-nhfb
rawauthor: M. V. (Maurice Vincent) Wilkes and David J. Wheeler and Stanley Gill
rawnote: With a new introduction by Martin Campbell-Kelly.
title:
The Preparation of Programs for an Electronic Digital Computer: with Special Reference to the EDSAC and the Use of a Library of Subroutines

ISBN13:
978-0-262-23118-3 (MIT Press 1984), 978-0-938228-03-5 OR 9780262231183 (MIT Press 1984), 9780938228035

bibsource:
fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

rawtitle:
The Preparation of Programs for an Electronic Digital Computer: with Special Reference to the {EDSAC} and the Use of a Library of Subroutines

entry:
@Book{Wilkes:1982:PPE,
  author =       "M. V. (Maurice Vincent) Wilkes and David J. Wheeler
                 and Stanley Gill",
  title =        "The Preparation of Programs for an Electronic Digital
                 Computer: with Special Reference to the {EDSAC} and the
                 Use of a Library of Subroutines",
  volume =       "1",
  publisher =    pub-TOMASH,
  address =      pub-TOMASH:adr,
  pages =        "xxxi + 167",
  year =         "1982",
  ISBN =         "0-262-23118-2 (MIT Press 1984), 0-938228-03-X",
  ISBN-13 =      "978-0-262-23118-3 (MIT Press 1984),
                 978-0-938228-03-5",
  LCCN =         "QA76.6 .W545 1982",
  bibdate =      "Mon Feb 10 11:33:59 MST 2020",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "With a new introduction by Martin Campbell-Kelly.",
  series =       "Charles Babbage Institute reprint series for the
                 history of computing",
  acknowledgement = ack-nhfb,
}


bibtype: incollection
filename: fparith.bib
label: Wilson:1982:PC
author: Kenneth G. Wilson
title: Experiences with a floating point systems array processor
crossref: Rodrigue:1982:AC
pages: 279--314
year: 1982
MRclass: 65W05
MRnumber: 759 559
bibdate: Fri Dec 8 08:24:14 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 08:24:14 ???
acknowledgement: ack-nhfb
rawauthor: Kenneth G. Wilson
rawtitle: Experiences with a floating point systems array processor
entry:
@InCollection{Wilson:1982:PC,
  author =       "Kenneth G. Wilson",
  title =        "Experiences with a floating point systems array
                 processor",
  crossref =     "Rodrigue:1982:AC",
  pages =        "279--314",
  year =         "1982",
  MRclass =      "65W05",
  MRnumber =     "759 559",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: mastersthesis
filename: fparith.bib
label: Wu:1982:DFA
author: Market Wen-Han Wu
title: Design of a fast addressable hardware floating-point arithmetic package for small computer
type: Thesis (M.S.)
school: Tufts University. Department of Engineering
address: Boston, MA, USA
pages: iii + 102
year: 1982
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Floating-point arithmetic.; Microcomputers --- Programming.
acknowledgement: ack-nhfb
rawauthor: Market Wen-Han Wu
rawtitle: Design of a fast addressable hardware floating-point arithmetic package for small computer
entry:
@MastersThesis{Wu:1982:DFA,
  author =       "Market Wen-Han Wu",
  title =        "Design of a fast addressable hardware floating-point
                 arithmetic package for small computer",
  type =         "Thesis ({M.S.})",
  school =       "Tufts University. Department of Engineering",
  address =      "Boston, MA, USA",
  pages =        "iii + 102",
  year =         "1982",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.; Microcomputers ---
                 Programming.",
}


bibtype: incollection
filename: fparith.bib
label: Zuse:1982:MAE
author: Konrad Zuse
title: Method for Automatic Execution of Calculations with the aid of Computers (1936)
crossref: Randell:1982:ODC
pages: 163--170
year: 1982
bibdate: Sun Nov 03 08:36:11 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.11.03 08:36:11 ???
acknowledgement: ack-nhfb
rawauthor: Konrad Zuse
rawtitle: Method for Automatic Execution of Calculations with the aid of Computers (1936)
remark:
This translation and reprint of a German patent application of 11 April 1936 briefly describes the floating-point system that was first successfully implemented in a digital computer, the Zuse Z3, in 1941.

entry:
@InCollection{Zuse:1982:MAE,
  author =       "Konrad Zuse",
  title =        "Method for Automatic Execution of Calculations with
                 the aid of Computers (1936)",
  crossref =     "Randell:1982:ODC",
  pages =        "163--170",
  year =         "1982",
  bibdate =      "Sun Nov 03 08:36:11 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "This translation and reprint of a German patent
                 application of 11 April 1936 briefly describes the
                 floating-point system that was first successfully
                 implemented in a digital computer, the Zuse Z3, in
                 1941.",
}


bibtype: inproceedings
filename: fparith.bib
label: Agrawal:1983:DPV
author: Dharma P. Agrawal and Girish C. Pathak and Nikunja K. Swain and Shuwan K. Agrawal
title: On Design and Performance of VLSI Based Parallel Multiplier
crossref: IEEE:1983:PSC
pages: 17--21
year: 1983
bibdate: Tue Nov 13 15:58:57 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.13 15:58:57 ???
URL: http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Agrawal_Pathak_Swain_Agrawal.pdf
keywords: ARITH-6
acknowledgement: ack-nhfb
rawauthor: Dharma P. Agrawal and Girish C. Pathak and Nikunja K. Swain and Shuwan K. Agrawal
rawtitle: On Design and Performance of {VLSI} Based Parallel Multiplier
abstract:
This paper introduces the VLSI design and layout of a $ (log ^2 n) $ time $n$-bit binary parallel multiplier for two unsigned operands. Proposed design consists of partitioning the multiplier and multiplicand bits into four groups of $ n / 4 $ bits each and then reducing the matrix of sixteen product terms using three to two parallel counters and Brent-Kung $ (log n) $ time parallel adder. Area-time performance of the present scheme has been compared with the existing schemes for parallel multipliers. Regular and recursive design of the multiplier is shown to be suitable for VLSI implementation and an improved table look up multiplier has been used to form the basis of the recursive design scheme.

rawabstract:
This paper introduces the VLSI design and layout of a $ (\log^2 n) $ time $n$-bit binary parallel multiplier for two unsigned operands. Proposed design consists of partitioning the multiplier and multiplicand bits into four groups of $ n / 4 $ bits each and then reducing the matrix of sixteen product terms using three to two parallel counters and Brent-Kung $ (\log n) $ time parallel adder. Area-time performance of the present scheme has been compared with the existing schemes for parallel multipliers. Regular and recursive design of the multiplier is shown to be suitable for VLSI implementation and an improved table look up multiplier has been used to form the basis of the recursive design scheme.

entry:
@InProceedings{Agrawal:1983:DPV,
  author =       "Dharma P. Agrawal and Girish C. Pathak and Nikunja K.
                 Swain and Shuwan K. Agrawal",
  title =        "On Design and Performance of {VLSI} Based Parallel
                 Multiplier",
  crossref =     "IEEE:1983:PSC",
  pages =        "17--21",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Agrawal_Pathak_Swain_Agrawal.pdf",
  abstract =     "This paper introduces the VLSI design and layout of a
                 $ (\log^2 n) $ time $n$-bit binary parallel multiplier
                 for two unsigned operands. Proposed design consists of
                 partitioning the multiplier and multiplicand bits into
                 four groups of $ n / 4 $ bits each and then reducing
                 the matrix of sixteen product terms using three to two
                 parallel counters and Brent-Kung $ (\log n) $ time
                 parallel adder. Area-time performance of the present
                 scheme has been compared with the existing schemes for
                 parallel multipliers. Regular and recursive design of
                 the multiplier is shown to be suitable for VLSI
                 implementation and an improved table look up multiplier
                 has been used to form the basis of the recursive design
                 scheme.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6",
}


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: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676232
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://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 =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676232",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://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: https://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 =  "https://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: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676312
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://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 =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676312",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://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: Boney:1983:FPPc
author: J. Boney and V. Shahan and P. Harvey
booktitle: Proceedings of Maecon, September 1983
title: Floating-point Power for the M68000 Family
pages: 1--9
year: 1983
bibdate: Thu Nov 13 10:21:25 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2025.11.13 10:21:25 ???
acknowledgement: ack-nhfb
rawauthor: J. Boney and V. Shahan and P. Harvey
rawbooktitle: Proceedings of {Maecon, September 1983}
rawtitle: Floating-point Power for the {M68000} Family
entry:
@InProceedings{Boney:1983:FPPc,
  author =       "J. Boney and V. Shahan and P. Harvey",
  editor =       "????",
  booktitle =    "Proceedings of {Maecon, September 1983}",
  title =        "Floating-point Power for the {M68000} Family",
  publisher =    "????",
  address =      "????",
  pages =        "1--9",
  year =         "1983",
  bibdate =      "Thu Nov 13 10:21:25 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


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: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676273
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://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 =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676273",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://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: https://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 =  "https://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: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676173
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://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 =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676173",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://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: https://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: https://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/ieeetranscomput1980.bib",
  URL =          "https://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 =  "https://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
bibsource:
https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

rawtitle:
Micro\slash mini computer program for calculating the square root of rationals at arbitrary precision

entry:
@Article{Demsky:1983:MMC,
  author =       "J. Demsky and M. Schlesinger and R. D. Kent",
  title =        "Micro\slash 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: https://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 =  "https://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: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676261
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://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 =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676261",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://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: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676341
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://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 =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676341",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://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: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676227
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://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 =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676227",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://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: https://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/xpl/RecentIssue.jsp?punumber=12; http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35226; https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676242

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/ieeetranscomput1980.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35226;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676242",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://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
ajournal: IEEE Micro
corpsource: Motorola Inc., Austin, TX, USA
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; https://www.math.utah.edu/pub/tex/bib/ieeemicro.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)

journalURL:
http://www.computer.org/csdl/mags/mi/index.html; https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=40

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;
                 https://www.math.utah.edu/pub/tex/bib/ieeemicro.bib;
                 Science Citation Index database (1980--2000)",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  ajournal =     "IEEE Micro",
  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;
                 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=40",
  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: https://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/xpl/RecentIssue.jsp?punumber=12; http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35226; https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676240

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/ieeetranscomput1980.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35226;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676240",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://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: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676239
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://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/ieeetranscomput1980.bib",
  URL =          "https://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 =  "https://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: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676241
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://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 =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676241",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://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: https://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: https://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/ieeetranscomput1980.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/ieeetranscomput1980.bib",
  URL =          "https://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",
  fjournal =     "IEEE Transactions on Computers",
  genterm =      "ALGORITHMS; PERFORMANCE",
  guideno =      "06575",
  journal-URL =  "https://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: https://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 =  "https://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: https://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/xpl/RecentIssue.jsp?punumber=12; http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35222; https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676152

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/ieeetranscomput1980.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35222;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676152",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://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: https://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 =  "https://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: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676150
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://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 =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676150",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://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
DOI: https://doi.org/10.1016/0165-6074(83)90151-5
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
bibtimestamp: 1995.12.08 13:05:28 ???
fjournal: Microprocessing and Microprogramming
acknowledgement: ack-nj
journalURL: https://www.sciencedirect.com/journal/microprocessing-and-microprogramming/issues
rawauthor: R. Nave
rawtitle: Implementation of Transcendental Functions on a Numerics Processor
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
https://ieeemilestones.ethw.org/w/images/8/8b/Nave_implenent_transcendental_algos_1983.pdf; https://www.sciencedirect.com/science/article/pii/0165607483901515

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",
  DOI =          "https://doi.org/10.1016/0165-6074(83)90151-5",
  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/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeemilestones.ethw.org/w/images/8/8b/Nave_implenent_transcendental_algos_1983.pdf;
                 https://www.sciencedirect.com/science/article/pii/0165607483901515",
  acknowledgement = ack-nj,
  fjournal =     "Microprocessing and Microprogramming",
  journal-URL =  "https://www.sciencedirect.com/journal/microprocessing-and-microprogramming/issues",
}


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: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676244
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://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 =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676244",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://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: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676246
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://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 =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676246",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://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: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676203
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://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:
@Article{Preparata:1983:MCA,
  author =       "F. P. Preparata",
  title =        "A Mesh-Connected Area-Time Optimal {VLSI} Multiplier
                 of Large Integers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "2",
  pages =        "194--198",
  month =        feb,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676203",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:01:07 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676203",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://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
                 computing)",
  corpsource =   "Rutherford and Appleton Lab., Chilton, Didcot, UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "binary; computer; fixed-point number; integer;
                 interactive methods; iterative methods; PASCAL; Pascal
                 implementation; square root; subroutines; successive
                 subtraction",
  treatment =    "P Practical",
}


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;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_26/Issue_02/tiff/187.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_26/Issue_02/tiff/188.tif",
  acknowledgement = ack-nhfb,
  classcodes =   "C4190 (Other numerical methods); C7310 (Mathematics
                 computing)",
  corpsource =   "Rutherford and Appleton Lab., Chilton, Didcot, UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "binary; computer; fixed-point number; integer;
                 iterative methods; PASCAL; Pascal implementation;
                 square root; subroutines; successive subtraction",
  treatment =    "P Practical",
}


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;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  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: https://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/xpl/RecentIssue.jsp?punumber=12; http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35227; https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676264

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/ieeetranscomput1980.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35227;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676264",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://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/cordic.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/cordic.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: Simington:1983:INP
author: R. B. Simington
journal: j-BYTE
volume: 8
number: 4
pages: 154--175
month: apr
monthnumber: 4
year: 1983
CODEN: BYTEDJ
ISSN: 0360-5280 (print), 1082-7838 (electronic) OR 03605280 (print), 10827838 (electronic)
ISSNL: 0360-5280 OR 03605280
bibdate: Sat Aug 23 06:48:26 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2025.08.23 06:48:26 ???
note: Overview of the 8087 and its close ties to the host 8086 or 8088 CPU.
fjournal: BYTE Magazine
acknowledgement: ack-nhfb
rawauthor: R. B. Simington
rawnote: Overview of the 8087 and its close ties to the host 8086 or 8088 CPU.
title:
The Intel 8087 Numerics Processor Extension: this chip lets you perform mathematical operations with 18-decimal digits of accuracy.

URL:
https://ieeemilestones.ethw.org/w/images/8/85/Simington_The_Intel_8087_Numerics_Processor_Extension.pdf

rawtitle:
The {Intel 8087} Numerics Processor Extension: this chip lets you perform mathematical operations with 18-decimal digits of accuracy.

entry:
@Article{Simington:1983:INP,
  author =       "R. B. Simington",
  title =        "The {Intel 8087} Numerics Processor Extension: this
                 chip lets you perform mathematical operations with
                 18-decimal digits of accuracy.",
  journal =      j-BYTE,
  volume =       "8",
  number =       "4",
  pages =        "154--175",
  month =        apr,
  year =         "1983",
  CODEN =        "BYTEDJ",
  ISSN =         "0360-5280 (print), 1082-7838 (electronic)",
  ISSN-L =       "0360-5280",
  bibdate =      "Sat Aug 23 06:48:26 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Overview of the 8087 and its close ties to the host
                 8086 or 8088 CPU.",
  URL =          "https://ieeemilestones.ethw.org/w/images/8/85/Simington_The_Intel_8087_Numerics_Processor_Extension.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "BYTE Magazine",
}


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: https://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 =          "https://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: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676274
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://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 =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676274",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://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: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676263
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://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/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676263",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://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: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676282
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://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 =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676282",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


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: article
filename: fparith.bib
label: Volz:1983:CAA
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
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. (German) [CORDIC and Similar Algorithms for Elementary Functions with Particular Aptitude for Microcomputers]

bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

rawtitle:
{CORDIC und {\"a}hnliche Algorithmen der elementaren Funktionen mit besonderer Eignung f{\"u}r Mikrorechner}. ({German}) [{CORDIC} and Similar Algorithms for Elementary Functions with Particular Aptitude for Microcomputers]

entry:
@Article{Volz:1983:CAA,
  author =       "H. V{\"o}lz",
  title =        "{CORDIC und {\"a}hnliche Algorithmen der elementaren
                 Funktionen mit besonderer Eignung f{\"u}r
                 Mikrorechner}. ({German}) [{CORDIC} and Similar
                 Algorithms for Elementary Functions with Particular
                 Aptitude for Microcomputers]",
  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/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Nachrichtentechnik Elektronik",
  itle =         "{CORDIC und {\"a}hnliche Algorithmen der elementaren
                 Funktionen mit besonderer Eignung f{\"u}r
                 Mikrorechner}. ({German}) [{CORDIC} and Similar
                 Algorithms for Elementary Functions with Particular
                 Aptitude for Microcomputers]",
}


bibtype: article
filename: fparith.bib
label: Vuillemin:1983:VFM
author: Jean E. Vuillemin
title: A very fast multiplication algorithm VLSI implementation
journal: j-INTEGRATION-VLSI-J
volume: 1
number: 1
pages: 30--52
month: apr
monthnumber: 4
year: 1983
CODEN: IVJODL
DOI: https://doi.org/10.1016/0167-9260(83)90005-6
ISSN: 0167-9260 (print), 1872-7522 (electronic) OR 01679260 (print), 18727522 (electronic)
ISSNL: 0167-9260 OR 01679260
bibdate: Thu Nov 13 08:11:40 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2025.11.13 08:11:40 ???
URL: https://www.sciencedirect.com/science/article/pii/0167926083900056
fjournal: Integration, the VLSI Journal
acknowledgement: ack-nhfb
journalURL: https://www.sciencedirect.com/journal/integration/issues
rawauthor: Jean E. Vuillemin
rawtitle: A very fast multiplication algorithm {VLSI} implementation
entry:
@Article{Vuillemin:1983:VFM,
  author =       "Jean E. Vuillemin",
  title =        "A very fast multiplication algorithm {VLSI}
                 implementation",
  journal =      j-INTEGRATION-VLSI-J,
  volume =       "1",
  number =       "1",
  pages =        "30--52",
  month =        apr,
  year =         "1983",
  CODEN =        "IVJODL",
  DOI =          "https://doi.org/10.1016/0167-9260(83)90005-6",
  ISSN =         "0167-9260 (print), 1872-7522 (electronic)",
  ISSN-L =       "0167-9260",
  bibdate =      "Thu Nov 13 08:11:40 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.sciencedirect.com/science/article/pii/0167926083900056",
  acknowledgement = ack-nhfb,
  fjournal =     "Integration, the VLSI Journal",
  journal-URL =  "https://www.sciencedirect.com/journal/integration/issues",
}


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: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676236
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://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/ieeetranscomput1980.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/ieeetranscomput1980.bib",
  URL =          "https://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",
  fjournal =     "IEEE Transactions on Computers",
  guideno =      "06565",
  journal-URL =  "https://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",
}


