# bibtab

bibtype: article
filename: fparith.bib
label: Wu:1995:SRM
author: Youfeng Wu
title: Strength Reduction of Multiplications by Integer Constants
journal: j-SIGPLAN
volume: 30
number: 2
pages: 42--48
month: feb
monthnumber: 2
year: 1995
CODEN: SINODQ
ISSN: 0362-1340 (print), 1523-2867 (print), 1558-1160 OR 03621340 (print), 15232867 (print), 15581160
ISSNL: 0362-1340 OR 03621340
bibdate: Sun Dec 14 09:17:00 MST 2003
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.12.14 09:17:00 MST
fjournal: ACM SIGPLAN Notices
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J706
rawauthor: Youfeng Wu
rawtitle: Strength Reduction of Multiplications by Integer Constants
entry:
@Article{Wu:1995:SRM,
  author =       "Youfeng Wu",
  title =        "Strength Reduction of Multiplications by Integer
                 Constants",
  journal =      j-SIGPLAN,
  volume =       "30",
  number =       "2",
  pages =        "42--48",
  month =        feb,
  year =         "1995",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sun Dec 14 09:17:00 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
}


bibtype: article
filename: fparith.bib
label: Ypma:1995:HDN
author: Tjalling J. Ypma
title: Historical Development of the Newton--Raphson Method
journal: j-SIAM-REVIEW
volume: 37
number: 4
pages: 531--551
month: dec
monthnumber: 12
year: 1995
CODEN: SIREAD
DOI: https://doi.org/10.1137/1037125
ISSN: 0036-1445 (print), 1095-7200 (electronic) OR 00361445 (print), 10957200 (electronic)
ISSNL: 0036-1445 OR 00361445
MRclass: 01A05 (65-03)
MRnumber: 97b:01003
MRreviewer: M. Z. Nashed
bibdate: Sat Mar 29 09:55:35 MDT 2014
bibtimestamp: 2014.03.29 09:55:35 MDT
URL: http://epubs.siam.org/23425.htm; http://link.aip.org/link/?SIR/37/531/1
fjournal: SIAM Review
acknowledgement: ack-nhfb
affiliation: Western Washington Univ
affiliationaddress: Bellingham, WA, USA
journalURL: http://epubs.siam.org/sirev
journalabr: SIAM Rev
onlinedate: December 1995
rawauthor: Tjalling J. Ypma
rawtitle: Historical Development of the {Newton--Raphson} Method
bibsource:
Compendex database; http://epubs.siam.org/toc/siread/37/4; http://www.siam.org/journals/sirev/sirev374.htm; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib

abstract:
This expository paper traces the development of the Newton--Raphson method for solving nonlinear algebraic equations through the extant notes, letters, and publications of Isaac Newton, Joseph Raphson, and Thomas Simpson. It is shown how Newton's formulation differed from the iterative process of Raphson, and that Simpson was the first to give a general formulation, in terms of fluxional calculus, applicable to nonpolynomial equations. Simpson's extension of the method to systems of equations is exhibited.

keywords:
Algebra; Algorithms; Approximation theory; Differentiation (calculus); Finite difference method; Fluxional calculus; Isaac Newton; Iterative methods; Joseph Raphson; Linearization; Newton--Raphson method; Nonlinear algebraic equations; Nonlinear equations; Nonpolynomial equation; Polynomials; Secant method; Thomas Simpson

rawabstract:
This expository paper traces the development of the Newton--Raphson method for solving nonlinear algebraic equations through the extant notes, letters, and publications of Isaac Newton, Joseph Raphson, and Thomas Simpson. It is shown how Newton's formulation differed from the iterative process of Raphson, and that Simpson was the first to give a general formulation, in terms of fluxional calculus, applicable to nonpolynomial equations. Simpson's extension of the method to systems of equations is exhibited.

entry:
@Article{Ypma:1995:HDN,
  author =       "Tjalling J. Ypma",
  title =        "Historical Development of the {Newton--Raphson}
                 Method",
  journal =      j-SIAM-REVIEW,
  volume =       "37",
  number =       "4",
  pages =        "531--551",
  month =        dec,
  year =         "1995",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1037125",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  MRclass =      "01A05 (65-03)",
  MRnumber =     "97b:01003",
  MRreviewer =   "M. Z. Nashed",
  bibdate =      "Sat Mar 29 09:55:35 MDT 2014",
  bibsource =    "Compendex database;
                 http://epubs.siam.org/toc/siread/37/4;
                 http://www.siam.org/journals/sirev/sirev374.htm;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  URL =          "http://epubs.siam.org/23425.htm;
                 http://link.aip.org/link/?SIR/37/531/1",
  abstract =     "This expository paper traces the development of the
                 Newton--Raphson method for solving nonlinear algebraic
                 equations through the extant notes, letters, and
                 publications of Isaac Newton, Joseph Raphson, and
                 Thomas Simpson. It is shown how Newton's formulation
                 differed from the iterative process of Raphson, and
                 that Simpson was the first to give a general
                 formulation, in terms of fluxional calculus, applicable
                 to nonpolynomial equations. Simpson's extension of the
                 method to systems of equations is exhibited.",
  acknowledgement = ack-nhfb,
  affiliation =  "Western Washington Univ",
  affiliationaddress = "Bellingham, WA, USA",
  classification = "921.1; 921.2; 921.6",
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  journalabr =   "SIAM Rev",
  keywords =     "Algebra; Algorithms; Approximation theory;
                 Differentiation (calculus); Finite difference method;
                 Fluxional calculus; Isaac Newton; Iterative methods;
                 Joseph Raphson; Linearization; Newton--Raphson method;
                 Nonlinear algebraic equations; Nonlinear equations;
                 Nonpolynomial equation; Polynomials; Secant method;
                 Thomas Simpson",
  onlinedate =   "December 1995",
}


bibtype: inproceedings
filename: fparith.bib
label: Yu:1995:MRF
author: Robert K. Yu and Gregory B. Zyner
title: 167 MHz Radix-$4$ Floating Point Multiplier
crossref: Knowles:1995:PSC
pages: 149--154
year: 1995
bibdate: Mon May 20 06:05:24 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:05:24 MDT
URL: http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Yu.pdf
keywords: ARITH-12; UltraSPARC
acknowledgement: ack-nhfb
rawauthor: Robert K. Yu and Gregory B. Zyner
rawtitle: {167 MHz} Radix-$4$ Floating Point Multiplier
entry:
@InProceedings{Yu:1995:MRF,
  author =       "Robert K. Yu and Gregory B. Zyner",
  title =        "{167 MHz} Radix-$4$ Floating Point Multiplier",
  crossref =     "Knowles:1995:PSC",
  pages =        "149--154",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Yu.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12; UltraSPARC",
}


bibtype: article
filename: fparith.bib
label: Zaytoun:1995:SFR
author: M. M. Zaytoun and T. J. Owens
title: State feedback robust to rounding errors
journal: j-ELECT-LETTERS
volume: 31
number: 13
pages: 1108--1109
day: 22
month: jun
monthnumber: 6
year: 1995
CODEN: ELLEAK
ISSN: 0013-5194 (print), 1350-911X (electronic) OR 00135194 (print), 1350911X (electronic)
ISSNL: 0013-5194 OR 00135194
bibdate: Sat Jul 16 11:25:03 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:03 MDT
fjournal: Electronics Letters
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220
rawauthor: M. M. Zaytoun and T. J. Owens
rawtitle: State feedback robust to rounding errors
entry:
@Article{Zaytoun:1995:SFR,
  author =       "M. M. Zaytoun and T. J. Owens",
  title =        "State feedback robust to rounding errors",
  journal =      j-ELECT-LETTERS,
  volume =       "31",
  number =       "13",
  pages =        "1108--1109",
  day =          "22",
  month =        jun,
  year =         "1995",
  CODEN =        "ELLEAK",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Sat Jul 16 11:25:03 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  summary =      "An algorithm for delivering a state feedback
                 controller that assigns desired distinct closed-loop
                 eigenvalues to the closed-loop system and is robust to
                 rounding errors in the elements of the controller is
                 \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Zhou:1995:HSD
author: Feng Zhou and Peter Kornerup
title: High Speed DCT / IDCT Using a Pipelined CORDIC Algorithm
crossref: Knowles:1995:PSC
pages: 180--187
year: 1995
bibdate: Mon May 20 06:05:24 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:05:24 MDT
URL: http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Feng.pdf
keywords: ARITH-12
acknowledgement: ack-nhfb
rawauthor: Feng Zhou and Peter Kornerup
rawtitle: High Speed {DCT}\slash {IDCT} Using a Pipelined {CORDIC} Algorithm
entry:
@InProceedings{Zhou:1995:HSD,
  author =       "Feng Zhou and Peter Kornerup",
  title =        "High Speed {DCT}\slash {IDCT} Using a Pipelined
                 {CORDIC} Algorithm",
  crossref =     "Knowles:1995:PSC",
  pages =        "180--187",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Feng.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
}


bibtype: inproceedings
filename: fparith.bib
label: Ahrendt:1996:FHC
author: Timm Ahrendt
title: Fast High-Precision Computations of Complex Square Roots
crossref: LakshmanYN:1996:IPI
pages: 142--149
year: 1996
bibdate: Thu Mar 12 08:43:16 MST 1998
bibsource: http://www.acm.org/pubs/toc/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.03.12 08:43:16 MST
URL: http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p142-ahrendt/
keywords: algebraic computation; algorithms; ISSAC; measurement; SIGNUM; SIGSAM; symbolic computation
acknowledgement: ack-nhfb
rawauthor: Timm Ahrendt
rawtitle: Fast High-Precision Computations of Complex Square Roots
subject:
bf I.1.2 Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. bf G.1.0 Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. bf F.1.1 Theory of Computation, COMPUTATION BY ABSTRACT DEVICES, Models of Computation, Bounded-action devices. bf G.1.5 Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Iterative methods. bf G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS, Approximation.

entry:
@InProceedings{Ahrendt:1996:FHC,
  author =       "Timm Ahrendt",
  title =        "Fast High-Precision Computations of Complex Square
                 Roots",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "142--149",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p142-ahrendt/",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; algorithms; ISSAC; measurement;
                 SIGNUM; SIGSAM; symbolic computation",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf G.1.0} Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf
                 F.1.1} Theory of Computation, COMPUTATION BY ABSTRACT
                 DEVICES, Models of Computation, Bounded-action devices.
                 {\bf G.1.5} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Roots of Nonlinear Equations, Iterative
                 methods. {\bf G.1.2} Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation.",
  xxtitle =      "Fast high-precision computation of complex square
                 roots",
}


bibtype: techreport
filename: fparith.bib
label: Al-Twaijry:1996:OPR
author: H. Al-Twaijry and M. J. Flynn
title: Optimum placement and routing of multiplier partial product trees
type: Technical report
number: CSL-TR-96-706
institution: Computer Systems Laboratory, Stanford University
address: Stanford, CA, USA
pages: 142--149
month: sep
monthnumber: 9
year: 1996
bibdate: Mon Dec 24 10:13:01 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.12.24 10:13:01 ???
acknowledgement: ack-nhfb
rawauthor: H. Al-Twaijry and M. J. Flynn
rawtitle: Optimum placement and routing of multiplier partial product trees
entry:
@TechReport{Al-Twaijry:1996:OPR,
  author =       "H. Al-Twaijry and M. J. Flynn",
  title =        "Optimum placement and routing of multiplier partial
                 product trees",
  type =         "Technical report",
  number =       "CSL-TR-96-706",
  institution =  "Computer Systems Laboratory, Stanford University",
  address =      "Stanford, CA, USA",
  month =        sep,
  year =         "1996",
  bibdate =      "Mon Dec 24 10:13:01 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Alefeld:1996:EII
author: G. E. Alefeld and F. A. Potra and W. Voelker
title: Effective Improvements of the Internal-Newton-Method
crossref: Alefeld:1996:SCV
pages: 133--139
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: G. E. Alefeld and F. A. Potra and W. Voelker
rawtitle: Effective Improvements of the Internal-{Newton}-Method
entry:
@InProceedings{Alefeld:1996:EII,
  author =       "G. E. Alefeld and F. A. Potra and W. Voelker",
  title =        "Effective Improvements of the
                 Internal-{Newton}-Method",
  crossref =     "Alefeld:1996:SCV",
  pages =        "133--139",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Andraos:1996:FPU
author: S. Andraos
booktitle: IEEE 39th Midwest symposium on Circuits and Systems, 1996
title: Fixed point unsigned fractional representation in residue number system
volume: 1
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 555--558
year: 1996
DOI: https://doi.org/10.1109/MWSCAS.1996.594239
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: S. Andraos
rawbooktitle: {IEEE 39th} Midwest symposium on Circuits and Systems, 1996
rawtitle: Fixed point unsigned fractional representation in residue number system
entry:
@InProceedings{Andraos:1996:FPU,
  author =       "S. Andraos",
  booktitle =    "{IEEE 39th} Midwest symposium on Circuits and Systems,
                 1996",
  title =        "Fixed point unsigned fractional representation in
                 residue number system",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "555--558",
  year =         "1996",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/MWSCAS.1996.594239",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Representing fractions is one of the fundamental
                 problems in the Residue Number System (RNS) which is
                 considered an integer number system with no fractional
                 representation. This is one of its main drawbacks and
                 one of the main obstacles in its \ldots{}",
}


bibtype: mastersthesis
filename: fparith.bib
label: Angarai:1996:NRS
author: Vijayanand Jaganaathan Angarai
title: Number representation schemes for energy efficient computer arithmetic
type: Thesis (M.S.)
school: University of Texas at Dallas
address: Dallas, TX, USA
pages: ix + 57
year: 1996
bibdate: Mon Mar 05 14:32:21 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.03.05 14:32:21 ???
acknowledgement: ack-nhfb
rawauthor: Vijayanand Jaganaathan Angarai
rawtitle: Number representation schemes for energy efficient computer arithmetic
entry:
@MastersThesis{Angarai:1996:NRS,
  author =       "Vijayanand Jaganaathan Angarai",
  title =        "Number representation schemes for energy efficient
                 computer arithmetic",
  type =         "Thesis ({M.S.})",
  school =       "University of Texas at Dallas",
  address =      "Dallas, TX, USA",
  pages =        "ix + 57",
  year =         "1996",
  bibdate =      "Mon Mar 05 14:32:21 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: incollection
filename: fparith.bib
label: Anonymous:1996:DC
author: Anonymous
editor: Barry Cipra and Paul Zorn
booktitle: What's Happening in the Mathematical Sciences
title: Divide and Conquer
volume: 3
publisher: pub-AMS
address: pub-AMS:adr
pages: 39--47
year: 1996
ISBN: 0-8218-0355-7 (paperback) OR 0821803557 (paperback)
ISBN13: 978-0-8218-0355-4 (paperback) OR 9780821803554 (paperback)
LCCN: QA3 .C57 1996
bibdate: Thu Dec 08 16:31:52 2016
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2016.12.08 16:31:52 ???
URL: http://www.ams.org/samplings/math-history/divide.pdf
keywords: Pentium divide flaw
acknowledgement: ack-nhfb
bookpages: vi + 111
rawauthor: Anonymous
rawbooktitle: What's Happening in the Mathematical Sciences
raweditor: Barry Cipra and Paul Zorn
rawtitle: Divide and Conquer
entry:
@InCollection{Anonymous:1996:DC,
  author =       "Anonymous",
  editor =       "Barry Cipra and Paul Zorn",
  booktitle =    "What's Happening in the Mathematical Sciences",
  title =        "Divide and Conquer",
  volume =       "3",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  bookpages =    "vi + 111",
  pages =        "39--47",
  year =         "1996",
  ISBN =         "0-8218-0355-7 (paperback)",
  ISBN-13 =      "978-0-8218-0355-4 (paperback)",
  LCCN =         "QA3 .C57 1996",
  bibdate =      "Thu Dec 08 16:31:52 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.ams.org/samplings/math-history/divide.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "Pentium divide flaw",
}


bibtype: article
filename: fparith.bib
label: Anonymous:1996:FPF
author: Anonymous
title: Floating Point --- Finding Electronic / Mechanical Parts
journal: j-COMPUT-AIDED-ENG
volume: 15
number: 1
pages: 76--??
year: 1996
CODEN: CCAEDJ
ISSN: 0733-3536 (print), 2162-1365 (electronic) OR 07333536 (print), 21621365 (electronic)
ISSNL: 0733-3536 OR 07333536
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
fjournal: Computer-aided engineering: CAE
acknowledgement: ack-nhfb
rawauthor: Anonymous
rawtitle: Floating Point --- Finding Electronic\slash Mechanical Parts
entry:
@Article{Anonymous:1996:FPF,
  author =       "Anonymous",
  title =        "Floating Point --- Finding Electronic\slash Mechanical
                 Parts",
  journal =      j-COMPUT-AIDED-ENG,
  volume =       "15",
  number =       "1",
  pages =        "76--??",
  year =         "1996",
  CODEN =        "CCAEDJ",
  ISSN =         "0733-3536 (print), 2162-1365 (electronic)",
  ISSN-L =       "0733-3536",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer-aided engineering: CAE",
}


bibtype: article
filename: fparith.bib
label: Anonymous:1996:IBT
author: Anonymous
title: Inquiry Board Traces Ariane 5 Failure to Overflow Error
journal: j-SIAM-NEWS
volume: 29
number: 8
pages: 1, 12, 13
month: oct
monthnumber: 10
year: 1996
ISSN: 0036-1437 OR 00361437
ISSNL: 0036-1437 OR 00361437
bibdate: Sat Apr 28 18:48:53 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.04.28 18:48:53 ???
URL: http://www.siam.org/siamnews/general/ariane.htm
fjournal: SIAM News
acknowledgement: ack-nhfb
journalURL: https://sinews.siam.org/
rawauthor: Anonymous
rawtitle: Inquiry Board Traces {Ariane 5} Failure to Overflow Error
entry:
@Article{Anonymous:1996:IBT,
  author =       "Anonymous",
  title =        "Inquiry Board Traces {Ariane 5} Failure to Overflow
                 Error",
  journal =      j-SIAM-NEWS,
  volume =       "29",
  number =       "8",
  pages =        "1, 12, 13",
  month =        oct,
  year =         "1996",
  ISSN =         "0036-1437",
  ISSN-L =       "0036-1437",
  bibdate =      "Sat Apr 28 18:48:53 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.siam.org/siamnews/general/ariane.htm",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM News",
  journal-URL =  "https://sinews.siam.org/",
}


bibtype: book
filename: fparith.bib
label: Anonymous:1996:SROa
author: Anonymous
title: The Square Root of 3 to one million digits
volume: 628
publisher: pub-PROJECT-GUTENBERG
address: pub-PROJECT-GUTENBERG:adr
pages: 1, 12, 13
year: 1996
bibdate: Sun Jan 24 10:00:27 MST 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1999.01.24 10:00:27 MST
series: ser-PROJECT-GUTENBERG
URL: ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext96/3sqrt10.zip
subject: Mathematical constants.
acknowledgement: ack-nhfb
rawauthor: Anonymous
rawtitle: The Square Root of 3 to one million digits
entry:
@Book{Anonymous:1996:SROa,
  author =       "Anonymous",
  title =        "The Square Root of 3 to one million digits",
  volume =       "628",
  publisher =    pub-PROJECT-GUTENBERG,
  address =      pub-PROJECT-GUTENBERG:adr,
  year =         "1996",
  bibdate =      "Sun Jan 24 10:00:27 MST 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       ser-PROJECT-GUTENBERG,
  URL =          "ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext96/3sqrt10.zip",
  acknowledgement = ack-nhfb # " and " # ack-st,
  subject =      "Mathematical constants.",
}


bibtype: book
filename: fparith.bib
label: Anonymous:1996:SROb
author: Anonymous
title: The Square Root of 5 to one million digits
volume: 629
publisher: pub-PROJECT-GUTENBERG
address: pub-PROJECT-GUTENBERG:adr
pages: 1, 12, 13
year: 1996
bibdate: Sun Jan 24 10:00:27 MST 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1999.01.24 10:00:27 MST
series: ser-PROJECT-GUTENBERG
URL: ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext96/5sqrt10.zip
subject: Mathematical constants.
acknowledgement: ack-nhfb
rawauthor: Anonymous
rawtitle: The Square Root of 5 to one million digits
entry:
@Book{Anonymous:1996:SROb,
  author =       "Anonymous",
  title =        "The Square Root of 5 to one million digits",
  volume =       "629",
  publisher =    pub-PROJECT-GUTENBERG,
  address =      pub-PROJECT-GUTENBERG:adr,
  year =         "1996",
  bibdate =      "Sun Jan 24 10:00:27 MST 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       ser-PROJECT-GUTENBERG,
  URL =          "ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext96/5sqrt10.zip",
  acknowledgement = ack-nhfb # " and " # ack-st,
  subject =      "Mathematical constants.",
}


bibtype: book
filename: fparith.bib
label: Anonymous:1996:SROc
author: Anonymous
title: The Square Root of 6 to one million digits
volume: 630
publisher: pub-PROJECT-GUTENBERG
address: pub-PROJECT-GUTENBERG:adr
pages: 1, 12, 13
year: 1996
bibdate: Sun Jan 24 10:00:27 MST 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1999.01.24 10:00:27 MST
series: ser-PROJECT-GUTENBERG
URL: ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext96/6sqrt10.zip
subject: Mathematical constants.
acknowledgement: ack-nhfb
rawauthor: Anonymous
rawtitle: The Square Root of 6 to one million digits
entry:
@Book{Anonymous:1996:SROc,
  author =       "Anonymous",
  title =        "The Square Root of 6 to one million digits",
  volume =       "630",
  publisher =    pub-PROJECT-GUTENBERG,
  address =      pub-PROJECT-GUTENBERG:adr,
  year =         "1996",
  bibdate =      "Sun Jan 24 10:00:27 MST 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       ser-PROJECT-GUTENBERG,
  URL =          "ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext96/6sqrt10.zip",
  acknowledgement = ack-nhfb # " and " # ack-st,
  subject =      "Mathematical constants.",
}


bibtype: book
filename: fparith.bib
label: Anonymous:1996:SROd
author: Anonymous
title: The Square Root of 7 to one million digits
volume: 631
publisher: pub-PROJECT-GUTENBERG
address: pub-PROJECT-GUTENBERG:adr
pages: 1, 12, 13
year: 1996
bibdate: Sun Jan 24 10:00:27 MST 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1999.01.24 10:00:27 MST
series: ser-PROJECT-GUTENBERG
URL: ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext96/7sqrt10.zip
subject: Mathematical constants.
acknowledgement: ack-nhfb
rawauthor: Anonymous
rawtitle: The Square Root of 7 to one million digits
entry:
@Book{Anonymous:1996:SROd,
  author =       "Anonymous",
  title =        "The Square Root of 7 to one million digits",
  volume =       "631",
  publisher =    pub-PROJECT-GUTENBERG,
  address =      pub-PROJECT-GUTENBERG:adr,
  year =         "1996",
  bibdate =      "Sun Jan 24 10:00:27 MST 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       ser-PROJECT-GUTENBERG,
  URL =          "ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext96/7sqrt10.zip",
  acknowledgement = ack-nhfb # " and " # ack-st,
  subject =      "Mathematical constants.",
}


bibtype: book
filename: fparith.bib
label: Anonymous:1996:SROe
author: Anonymous
title: The Square Root of 8 to one million digits
volume: 632
publisher: pub-PROJECT-GUTENBERG
address: pub-PROJECT-GUTENBERG:adr
pages: 1, 12, 13
year: 1996
bibdate: Sun Jan 24 10:00:27 MST 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1999.01.24 10:00:27 MST
series: ser-PROJECT-GUTENBERG
URL: ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext96/8sqrt10.zip
subject: Mathematical constants.
acknowledgement: ack-nhfb
rawauthor: Anonymous
rawtitle: The Square Root of 8 to one million digits
entry:
@Book{Anonymous:1996:SROe,
  author =       "Anonymous",
  title =        "The Square Root of 8 to one million digits",
  volume =       "632",
  publisher =    pub-PROJECT-GUTENBERG,
  address =      pub-PROJECT-GUTENBERG:adr,
  year =         "1996",
  bibdate =      "Sun Jan 24 10:00:27 MST 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       ser-PROJECT-GUTENBERG,
  URL =          "ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext96/8sqrt10.zip",
  acknowledgement = ack-nhfb # " and " # ack-st,
  subject =      "Mathematical constants.",
}


bibtype: book
filename: fparith.bib
label: Anonymous:1996:SROf
author: Anonymous
title: The Square Root of 10 to one million digits
volume: 635
publisher: pub-PROJECT-GUTENBERG
address: pub-PROJECT-GUTENBERG:adr
pages: 1, 12, 13
year: 1996
bibdate: Sun Jan 24 10:00:27 MST 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1999.01.24 10:00:27 MST
series: ser-PROJECT-GUTENBERG
URL: ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext96/10srt10.zip
subject: Mathematical constants.
acknowledgement: ack-nhfb
rawauthor: Anonymous
rawtitle: The Square Root of 10 to one million digits
entry:
@Book{Anonymous:1996:SROf,
  author =       "Anonymous",
  title =        "The Square Root of 10 to one million digits",
  volume =       "635",
  publisher =    pub-PROJECT-GUTENBERG,
  address =      pub-PROJECT-GUTENBERG:adr,
  year =         "1996",
  bibdate =      "Sun Jan 24 10:00:27 MST 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       ser-PROJECT-GUTENBERG,
  URL =          "ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext96/10srt10.zip",
  acknowledgement = ack-nhfb # " and " # ack-st,
  subject =      "Mathematical constants.",
}


bibtype: inproceedings
filename: fparith.bib
label: Anuta:1996:BLA
author: M. A. Anuta and Daniel W. Lozier and N. Schabanel and P. R. Turner
title: Basic Linear Algebra Operations in SLI Arithmetic
crossref: Bouge:1996:EPP
pages: 193--202
year: 1996
DOI: https://doi.org/10.1007/BFb0024702
bibdate: Fri Jul 09 07:17:24 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.07.09 07:17:24 ???
acknowledgement: ack-nhfb
rawauthor: M. A. Anuta and Daniel W. Lozier and N. Schabanel and P. R. Turner
rawtitle: Basic Linear Algebra Operations in {SLI} Arithmetic
URL:
http://math.nist.gov/acmd/Staff/DLozier/publications/nistir5811.ps.Z; https://www.nist.gov/publications/basic-linear-algebra-operations-sli-arithmetic

entry:
@InProceedings{Anuta:1996:BLA,
  author =       "M. A. Anuta and Daniel W. Lozier and N. Schabanel and
                 P. R. Turner",
  title =        "Basic Linear Algebra Operations in {SLI} Arithmetic",
  crossref =     "Bouge:1996:EPP",
  pages =        "193--202",
  year =         "1996",
  DOI =          "https://doi.org/10.1007/BFb0024702",
  bibdate =      "Fri Jul 09 07:17:24 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://math.nist.gov/acmd/Staff/DLozier/publications/nistir5811.ps.Z;
                 https://www.nist.gov/publications/basic-linear-algebra-operations-sli-arithmetic",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Anuta:1996:MMC
author: M. A. Anuta and Daniel W. Lozier and P. R. Turner
title: The MasPar MP-1 as a Computer Arithmetic Laboratory
journal: j-J-RES-NATL-BUR-STAND
volume: 101
number: 2
pages: 165--174
month: mar
monthnumber: 3
year: 1996
CODEN: JRNBAG
DOI: https://doi.org/10.6028/jres.101.018
ISSN: 0091-0635 (print), 2376-5305 (electronic) OR 00910635 (print), 23765305 (electronic)
ISSNL: 0091-0635 OR 00910635
bibdate: Fri Jul 09 07:18:42 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.07.09 07:18:42 ???
URL: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4907584/
acknowledgement: ack-nhfb
journalURL: https://www.nist.gov/nist-research-library/journal-research-nist/past-papers
rawauthor: M. A. Anuta and Daniel W. Lozier and P. R. Turner
rawtitle: The {MasPar MP-1} as a Computer Arithmetic Laboratory
abstract:
This paper is a blueprint for the use of a massively parallel SIMD computer architecture for the simulation of various forms of computer arithmetic. The particular system used is a DEC/MasPar MP-1 with 4096 processors in a square array. This architecture has many advantages for such simulations due largely to the simplicity of the individual processors. Arithmetic operations can be spread across the processor array to simulate a hardware chip. Alternatively they may be performed on individual processors to allow simulation of a massively parallel implementation of the arithmetic. Compromises between these extremes permit speed-area tradeoffs to be examined. The paper includes a description of the architecture and its features. It then summarizes some of the arithmetic systems which have been, or are to be, implemented. The implementation of the level-index and symmetric level-index, LI and SLI, systems is described in some detail. An extensive bibliography is included.

keywords:
computer arithmetic, fixed-point and floating-point arithmetic, logarithmic and level-index arithmetic, residue number system arithmetic, serial and parallel simulation of computer arithmetic

rawabstract:
This paper is a blueprint for the use of a massively parallel SIMD computer architecture for the simulation of various forms of computer arithmetic. The particular system used is a DEC/MasPar MP-1 with 4096 processors in a square array. This architecture has many advantages for such simulations due largely to the simplicity of the individual processors. Arithmetic operations can be spread across the processor array to simulate a hardware chip. Alternatively they may be performed on individual processors to allow simulation of a massively parallel implementation of the arithmetic. Compromises between these extremes permit speed-area tradeoffs to be examined. The paper includes a description of the architecture and its features. It then summarizes some of the arithmetic systems which have been, or are to be, implemented. The implementation of the level-index and symmetric level-index, LI and SLI, systems is described in some detail. An extensive bibliography is included.

entry:
@Article{Anuta:1996:MMC,
  author =       "M. A. Anuta and Daniel W. Lozier and P. R. Turner",
  title =        "The {MasPar MP-1} as a Computer Arithmetic
                 Laboratory",
  journal =      j-J-RES-NATL-BUR-STAND,
  volume =       "101",
  number =       "2",
  pages =        "165--174",
  month =        mar # "\slash " # apr,
  year =         "1996",
  CODEN =        "JRNBAG",
  DOI =          "https://doi.org/10.6028/jres.101.018",
  ISSN =         "0091-0635 (print), 2376-5305 (electronic)",
  ISSN-L =       "0091-0635",
  bibdate =      "Fri Jul 09 07:18:42 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4907584/",
  abstract =     "This paper is a blueprint for the use of a massively
                 parallel SIMD computer architecture for the simulation
                 of various forms of computer arithmetic. The particular
                 system used is a DEC/MasPar MP-1 with 4096 processors
                 in a square array. This architecture has many
                 advantages for such simulations due largely to the
                 simplicity of the individual processors. Arithmetic
                 operations can be spread across the processor array to
                 simulate a hardware chip. Alternatively they may be
                 performed on individual processors to allow simulation
                 of a massively parallel implementation of the
                 arithmetic. Compromises between these extremes permit
                 speed-area tradeoffs to be examined. The paper includes
                 a description of the architecture and its features. It
                 then summarizes some of the arithmetic systems which
                 have been, or are to be, implemented. The
                 implementation of the level-index and symmetric
                 level-index, LI and SLI, systems is described in some
                 detail. An extensive bibliography is included.",
  acknowledgement = ack-nhfb,
  journal-URL =  "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
  keywords =     "computer arithmetic, fixed-point and floating-point
                 arithmetic, logarithmic and level-index arithmetic,
                 residue number system arithmetic, serial and parallel
                 simulation of computer arithmetic",
}


bibtype: article
filename: fparith.bib
label: Arioli:1996:REA
author: M. Arioli and C. Fassino
title: Roundoff error analysis of algorithms based on Krylov subspace methods
journal: j-BIT-NUM-MATH
volume: 36
number: 2
pages: 189--205
month: jun
monthnumber: 6
year: 1996
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01731978
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
MRclass: 65F10 (15A23 65G05)
MRnumber: 98e:65018
MRreviewer: Jean-Marie Chesneaux
bibdate: Wed Jan 4 18:52:24 MST 2006
bibtimestamp: 2006.01.04 18:52:24 MST
keywords: floating-point arithmetic; rounding errors
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: M. Arioli and C. Fassino
rawtitle: Roundoff error analysis of algorithms based on {Krylov} subspace methods
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=36&issue=2; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://www.mai.liu.se/BIT/contents/bit36.html; http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=36&issue=2&spage=189

entry:
@Article{Arioli:1996:REA,
  author =       "M. Arioli and C. Fassino",
  title =        "Roundoff error analysis of algorithms based on
                 {Krylov} subspace methods",
  journal =      j-BIT-NUM-MATH,
  volume =       "36",
  number =       "2",
  pages =        "189--205",
  month =        jun,
  year =         "1996",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01731978",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65F10 (15A23 65G05)",
  MRnumber =     "98e:65018",
  MRreviewer =   "Jean-Marie Chesneaux",
  bibdate =      "Wed Jan 4 18:52:24 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=36&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.mai.liu.se/BIT/contents/bit36.html;
                 http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=36&issue=2&spage=189",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "floating-point arithmetic; rounding errors",
}


bibtype: inproceedings
filename: fparith.bib
label: Bajard:1996:NED
author: J.-C. Bajard and L.-S. Didier and Jean-Michel Muller
title: A new Euclidean division algorithm for residue number systems
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 45--54
year: 1996
DOI: https://doi.org/10.1109/ASAP.1996.542800
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: J.-C. Bajard and L.-S. Didier and Jean-Michel Muller
rawtitle: A new {Euclidean} division algorithm for residue number systems
booktitle:
Proceedings of International Conference on Application Specific Systems, Architectures and Processors, 1996. ASAP 96

rawbooktitle:
Proceedings of International Conference on Application Specific Systems, Architectures and Processors, 1996. {ASAP 96}

entry:
@InProceedings{Bajard:1996:NED,
  author =       "J.-C. Bajard and L.-S. Didier and Jean-Michel Muller",
  booktitle =    "Proceedings of International Conference on Application
                 Specific Systems, Architectures and Processors, 1996.
                 {ASAP 96}",
  title =        "A new {Euclidean} division algorithm for residue
                 number systems",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "45--54",
  year =         "1996",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ASAP.1996.542800",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "We propose in this paper a new algorithm and
                 architecture for performing divisions in residue number
                 systems. Our algorithm is suitable for residue number
                 systems with large moduli, with the aim of manipulating
                 very large integers on a parallel \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Barber:1996:QAC
author: C. Bradford Barber and David P. Dobkin and Hannu Huhdanpaa
title: The Quickhull Algorithm for Convex Hulls
journal: j-TOMS
volume: 22
number: 4
pages: 469--483
month: dec
monthnumber: 12
year: 1996
CODEN: ACMSCU
DOI: https://doi.org/10.1145/235815.235821
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Thu Nov 8 14:50:36 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.08 14:50:36 ???
URL: http://www.acm.org/pubs/citations/journals/toms/1996-22-4/p469-barber/
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms, reliability
acknowledgement: ack-rfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: C. Bradford Barber and David P. Dobkin and Hannu Huhdanpaa
rawtitle: The {Quickhull Algorithm} for Convex Hulls
abstract:
The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the two-dimensional Quickhull Algorithm with the general-dimensional Beneath-Beyond Algorithm. It is similar to the randomized, incremental algorithms for convex hull and Delaunay triangulation. We provide empirical evidence that the algorithm runs faster when the input contains nonextreme points and that it uses less memory. Computational geometry algorithms have traditionally assumed that input sets are well behaved. When an algorithm is implemented with floating-point arithmetic, this assumption can lead to serious errors. We briefly describe a solution to this problem when computing the convex hull in two, three, or four dimensions. The output is a set of ``thick'' facets that contain all possible exact convex hulls of the input. A variation is effective in five or more dimensions.

subject:
bf I.3.5: Computing Methodologies, COMPUTER GRAPHICS, Computational Geometry and Object Modeling, Geometric algorithms, languages and systems.

rawabstract:
The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the two-dimensional Quickhull Algorithm with the general-dimensional Beneath-Beyond Algorithm. It is similar to the randomized, incremental algorithms for convex hull and Delaunay triangulation. We provide empirical evidence that the algorithm runs faster when the input contains nonextreme points and that it uses less memory. Computational geometry algorithms have traditionally assumed that input sets are well behaved. When an algorithm is implemented with floating-point arithmetic, this assumption can lead to serious errors. We briefly describe a solution to this problem when computing the convex hull in two, three, or four dimensions. The output is a set of ``thick'' facets that contain all possible exact convex hulls of the input. A variation is effective in five or more dimensions.

entry:
@Article{Barber:1996:QAC,
  author =       "C. Bradford Barber and David P. Dobkin and Hannu
                 Huhdanpaa",
  title =        "The {Quickhull Algorithm} for Convex Hulls",
  journal =      j-TOMS,
  volume =       "22",
  number =       "4",
  pages =        "469--483",
  month =        dec,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/235815.235821",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Nov 8 14:50:36 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1996-22-4/p469-barber/",
  abstract =     "The convex hull of a set of points is the smallest
                 convex set that contains the points. This article
                 presents a practical convex hull algorithm that
                 combines the two-dimensional Quickhull Algorithm with
                 the general-dimensional Beneath-Beyond Algorithm. It is
                 similar to the randomized, incremental algorithms for
                 convex hull and Delaunay triangulation. We provide
                 empirical evidence that the algorithm runs faster when
                 the input contains nonextreme points and that it uses
                 less memory. Computational geometry algorithms have
                 traditionally assumed that input sets are well behaved.
                 When an algorithm is implemented with floating-point
                 arithmetic, this assumption can lead to serious errors.
                 We briefly describe a solution to this problem when
                 computing the convex hull in two, three, or four
                 dimensions. The output is a set of ``thick'' facets
                 that contain all possible exact convex hulls of the
                 input. A variation is effective in five or more
                 dimensions.",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms, reliability",
  subject =      "{\bf I.3.5}: Computing Methodologies, COMPUTER
                 GRAPHICS, Computational Geometry and Object Modeling,
                 Geometric algorithms, languages and systems.",
}


bibtype: inproceedings
filename: fparith.bib
label: Berlejung:1996:PSM
author: H. M. E. Berlejung
title: Processing Software Metrics in an Integrated Development Environment for Pascal-XSC
crossref: Alefeld:1996:SCV
pages: 79--83
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: H. M. E. Berlejung
rawtitle: Processing Software Metrics in an Integrated Development Environment for {Pascal-XSC}
entry:
@InProceedings{Berlejung:1996:PSM,
  author =       "H. M. E. Berlejung",
  title =        "Processing Software Metrics in an Integrated
                 Development Environment for {Pascal-XSC}",
  crossref =     "Alefeld:1996:SCV",
  pages =        "79--83",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Berner:1996:PMV
author: S. Berner
title: A Parallel Method for Verified Global Optimization
crossref: Alefeld:1996:SCV
pages: 200--206
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: S. Berner
rawtitle: A Parallel Method for Verified Global Optimization
entry:
@InProceedings{Berner:1996:PMV,
  author =       "S. Berner",
  title =        "A Parallel Method for Verified Global Optimization",
  crossref =     "Alefeld:1996:SCV",
  pages =        "200--206",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Blum:1996:RPD
author: Manuel Blum and H. Wasserman
title: Reflections on the Pentium Division Bug
journal: j-IEEE-TRANS-COMPUT
volume: 45
number: 4
pages: 385--393
month: apr
monthnumber: 4
year: 1996
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.494097
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 19:47:10 MDT 2011
bibtimestamp: 2011.07.06 19:47:10 MDT
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Manuel Blum and H. Wasserman
rawtitle: Reflections on the {Pentium} Division Bug
URL:
http://http.cs.berkeley.edu/~blum/pentium.ps; http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=494097

abstract:
We review the field of em result-checking and suggest that it be extended to a methodology for enforcing hardware / software reliability. We thereby formulate a vision for ``self-monitoring'' hardware / software whose reliability is augmented through embedded suites of run-time correctness checkers. In particular, we suggest that embedded checkers and correctors may be employed to safeguard against arithmetic errors such as that which has bedeviled the Intel Pentium Microprocessor. We specify checkers and correctors suitable for monitoring the multiplication and division functionalities of an arbitrary arithmetic processor and seamlessly correcting erroneous output which may occur for any reason during the lifetime of the chip.

keywords:
Built-in testing; concurrent error detection; fault tolerance; Pentium; reliability; result-checking; verification

rawabstract:
We review the field of {\em result-checking\/} and suggest that it be extended to a methodology for enforcing hardware\slash software reliability. We thereby formulate a vision for ``self-monitoring'' hardware\slash software whose reliability is augmented through embedded suites of run-time correctness checkers. In particular, we suggest that embedded checkers and correctors may be employed to safeguard against arithmetic errors such as that which has bedeviled the Intel Pentium Microprocessor. We specify checkers and correctors suitable for monitoring the multiplication and division functionalities of an arbitrary arithmetic processor and seamlessly correcting erroneous output which may occur for any reason during the lifetime of the chip.

entry:
@Article{Blum:1996:RPD,
  author =       "Manuel Blum and H. Wasserman",
  title =        "Reflections on the {Pentium} Division Bug",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "45",
  number =       "4",
  pages =        "385--393",
  month =        apr,
  year =         "1996",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.494097",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 19:47:10 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://http.cs.berkeley.edu/~blum/pentium.ps;
                 http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=494097",
  abstract =     "We review the field of {\em result-checking\/} and
                 suggest that it be extended to a methodology for
                 enforcing hardware\slash software reliability. We
                 thereby formulate a vision for ``self-monitoring''
                 hardware\slash software whose reliability is augmented
                 through embedded suites of run-time correctness
                 checkers. In particular, we suggest that embedded
                 checkers and correctors may be employed to safeguard
                 against arithmetic errors such as that which has
                 bedeviled the Intel Pentium Microprocessor. We specify
                 checkers and correctors suitable for monitoring the
                 multiplication and division functionalities of an
                 arbitrary arithmetic processor and seamlessly
                 correcting erroneous output which may occur for any
                 reason during the lifetime of the chip.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Built-in testing; concurrent error detection; fault
                 tolerance; Pentium; reliability; result-checking;
                 verification",
}


bibtype: article
filename: fparith.bib
label: Bockenfeld:1996:TNT
author: Don Bockenfeld
title: TSQRT: a New Trick for an Old Dog
journal: j-CCCUJ
volume: 14
number: 3
pages: 39--41
month: mar
monthnumber: 3
year: 1996
CODEN: CCUJEX
ISSN: 1075-2838 OR 10752838
bibdate: Sat Feb 10 08:57:37 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.10 08:57:37 ???
note: Implements a small table-driven square root function in C, using exclusively integer operations.
fjournal: C/C++ Users Journal
acknowledgement: ack-nhfb
rawauthor: Don Bockenfeld
rawnote: Implements a small table-driven square root function in C, using exclusively integer operations.
rawtitle: {TSQRT}: a New Trick for an Old Dog
entry:
@Article{Bockenfeld:1996:TNT,
  author =       "Don Bockenfeld",
  title =        "{TSQRT}: a New Trick for an Old Dog",
  journal =      j-CCCUJ,
  volume =       "14",
  number =       "3",
  pages =        "39--41",
  month =        mar,
  year =         "1996",
  CODEN =        "CCUJEX",
  ISSN =         "1075-2838",
  bibdate =      "Sat Feb 10 08:57:37 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Implements a small table-driven square root function
                 in C, using exclusively integer operations.",
  acknowledgement = ack-nhfb,
  fjournal =     "C/C++ Users Journal",
}


bibtype: article
filename: fparith.bib
label: Burger:1996:PFP
author: Robert G. Burger and R. Kent Dybvig
title: Printing Floating-Point Numbers Quickly and Accurately
journal: j-SIGPLAN
volume: 31
number: 5
pages: 108--116
month: may
monthnumber: 5
year: 1996
CODEN: SINODQ
DOI: https://doi.org/10.1145/231379.231397
ISSN: 0362-1340 (print), 1523-2867 (print), 1558-1160 OR 03621340 (print), 15232867 (print), 15581160
ISSNL: 0362-1340 OR 03621340
bibdate: Mon Feb 03 07:07:43 2003
bibtimestamp: 2003.02.03 07:07:43 ???
URL: http://www.acm.org:80/pubs/citations/proceedings/pldi/231379/p108-burger/
fjournal: ACM SIGPLAN Notices
keywords: algorithms; design; theory
acknowledgement: ack-nhfb
affiliation: Department of Computer Science, Indiana University, Bloomington, IN, USA
annote: Published as part of the Proceedings of PLDI'96.
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J706
rawauthor: Robert G. Burger and R. Kent Dybvig
rawtitle: Printing Floating-Point Numbers Quickly and Accurately
bibsource:
http://portal.acm.org/; http://www.acm.org/pubs/contents/proceedings/pldi/231379/index.html; https://www.math.utah.edu/pub/tex/bib/fparith.bib

note:
This paper offers a significantly faster algorithm than that of cite Steele:1990:HPF, together with a correctness proof and an implementation in Scheme. See also cite Clinger:1990:HRF,Abbott:1999:ASS,Steele:2004:RHP,Clinger:2004:RHR.

subject:
bf I.3.3 Computing Methodologies, COMPUTER GRAPHICS, Picture/Image Generation, Display algorithms. bf F.2.1 Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems. bf I.1.2 Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms.

rawnote:
This paper offers a significantly faster algorithm than that of \cite{Steele:1990:HPF}, together with a correctness proof and an implementation in Scheme. See also \cite{Clinger:1990:HRF,Abbott:1999:ASS,Steele:2004:RHP,Clinger:2004:RHR}.

entry:
@Article{Burger:1996:PFP,
  author =       "Robert G. Burger and R. Kent Dybvig",
  title =        "Printing Floating-Point Numbers Quickly and
                 Accurately",
  journal =      j-SIGPLAN,
  volume =       "31",
  number =       "5",
  pages =        "108--116",
  month =        may,
  year =         "1996",
  CODEN =        "SINODQ",
  DOI =          "https://doi.org/10.1145/231379.231397",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Mon Feb 03 07:07:43 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.acm.org/pubs/contents/proceedings/pldi/231379/index.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "This paper offers a significantly faster algorithm
                 than that of \cite{Steele:1990:HPF}, together with a
                 correctness proof and an implementation in Scheme. See
                 also
                 \cite{Clinger:1990:HRF,Abbott:1999:ASS,Steele:2004:RHP,Clinger:2004:RHR}.",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/pldi/231379/p108-burger/",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Computer Science, Indiana University,
                 Bloomington, IN, USA",
  annote =       "Published as part of the Proceedings of PLDI'96.",
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "algorithms; design; theory",
  subject =      "{\bf I.3.3} Computing Methodologies, COMPUTER
                 GRAPHICS, Picture/Image Generation, Display algorithms.
                 {\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems. {\bf I.1.2} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms.",
}


bibtype: techreport
filename: fparith.bib
label: Burnikel:1996:HPF
author: Christoph Burnikel and Jochen Konemann
title: High precision floating point numbers in LEDA
type: Report
number: MPI I 96 1 002
institution: Max-Planck-Institut fur Informatik
address: Saarbrucken, Germany
pages: 7
year: 1996
bibdate: Thu May 09 09:03:32 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.09 09:03:32 ???
acknowledgement: ack-nhfb
rawauthor: Christoph Burnikel and Jochen K{\"o}nemann
rawtitle: High precision floating point numbers in {LEDA}
entry:
@TechReport{Burnikel:1996:HPF,
  author =       "Christoph Burnikel and Jochen K{\"o}nemann",
  title =        "High precision floating point numbers in {LEDA}",
  type =         "Report",
  number =       "MPI I 96 1 002",
  institution =  "Max-Planck-Institut f{\"u}r Informatik",
  address =      "Saarbr{\"u}cken, Germany",
  pages =        "7",
  year =         "1996",
  bibdate =      "Thu May 09 09:03:32 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Candev:1996:AIA
author: M. Candev
title: On the Application of an Interval Algorithm for Set Inversion
crossref: Alefeld:1996:SCV
pages: 140--146
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: M. Candev
rawtitle: On the Application of an Interval Algorithm for Set Inversion
entry:
@InProceedings{Candev:1996:AIA,
  author =       "M. Candev",
  title =        "On the Application of an Interval Algorithm for Set
                 Inversion",
  crossref =     "Alefeld:1996:SCV",
  pages =        "140--146",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Cappuccino:1996:DDH
author: G. Cappuccino and P. Corsonello and G. Cocorullo
title: Design and demonstration of high throughput square rooting circuit
journal: j-ELECT-LETTERS
volume: 32
number: 5
pages: 434
year: 1996
CODEN: ELLEAK
ISSN: 0013-5194 (print), 1350-911X (electronic) OR 00135194 (print), 1350911X (electronic)
ISSNL: 0013-5194 OR 00135194
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
fjournal: Electronics Letters
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220
rawauthor: G. Cappuccino and P. Corsonello and G. Cocorullo
rawtitle: Design and demonstration of high throughput square rooting circuit
entry:
@Article{Cappuccino:1996:DDH,
  author =       "G. Cappuccino and P. Corsonello and G. Cocorullo",
  title =        "Design and demonstration of high throughput square
                 rooting circuit",
  journal =      j-ELECT-LETTERS,
  volume =       "32",
  number =       "5",
  pages =        "434",
  month =        "????",
  year =         "1996",
  CODEN =        "ELLEAK",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  summary =      "Not \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Chaitin-Chatelin:1996:FPA
author: F. Chaitin-Chatelin
title: Is Finite Precision Arithmetic Useful For Physics?
journal: j-J-UCS
volume: 2
number: 5
pages: 380--??
day: 28
month: may
monthnumber: 5
year: 1996
ISSN: 0948-6968 OR 09486968
ISSNL: 0948-6968 OR 09486968
bibdate: Wed May 28 19:32:35 MDT 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.05.28 19:32:35 MDT
URL: http://www.jucs.org/is_finite_precision_arithmetic_useful_for_physics
fjournal: J.UCS: Journal of Universal Computer Science
acknowledgement: ack-nhfb
journalURL: http://www.jucs.org/jucs
rawauthor: F. Chaitin-Chatelin
rawtitle: Is Finite Precision Arithmetic Useful For Physics?
entry:
@Article{Chaitin-Chatelin:1996:FPA,
  author =       "F. Chaitin-Chatelin",
  title =        "Is Finite Precision Arithmetic Useful For Physics?",
  journal =      j-J-UCS,
  volume =       "2",
  number =       "5",
  pages =        "380--??",
  day =          "28",
  month =        may,
  year =         "1996",
  CODEN =        "????",
  ISSN =         "0948-6968",
  ISSN-L =       "0948-6968",
  bibdate =      "Wed May 28 19:32:35 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.jucs.org/is_finite_precision_arithmetic_useful_for_physics",
  acknowledgement = ack-nhfb,
  fjournal =     "J.UCS: Journal of Universal Computer Science",
  journal-URL =  "http://www.jucs.org/jucs",
}


bibtype: book
filename: fparith.bib
label: Chaitin-Chatelin:1996:LFP
author: Francoise Chaitin-Chatelin and Valerie Fraysse
title: Lectures on Finite Precision Computations
publisher: pub-SIAM
address: pub-SIAM:adr
pages: xv + 235
year: 1996
ISBN: 0-89871-358-7 OR 0898713587
ISBN13: 978-0-89871-358-9 OR 9780898713589
LCCN: QA297 .C417 1996
bibdate: Wed Nov 16 14:38:30 MST 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2005.11.16 14:38:30 MST
series: Software, environments, tools
keywords: Matlab
subject: numerical calculations; data processing; error analysis (mathematics); toolbox PRECISE
acknowledgement: ack-nhfb
rawauthor: Fran{\c{c}}oise Chaitin-Chatelin and Val{\'e}rie Frayss{\'e}
rawtitle: Lectures on Finite Precision Computations
TOC:
1. General Presentation 2. Computability in Finite Precision 3. Measures of Stability for Regular Problems 4. Computation in the Neighbourhood of a Singularity 5. Arithmetic Quality of Reliable Algorithms 6. Numerical Stability in Finite Precision 7. Software Tools for Round-Off Error Analysis in Algorithms 8. The Toolbox PRECISE for Computer Experimentation 9. Experiments with PRECISE 10. Robustness to Nonnormality 11. Qualitative Computing 12. More Numerical Illustrations with PRECISE Annex: The Toolbox PRECISE for MATLAB.

rawTOC:
1. General Presentation \\ 2. Computability in Finite Precision \\ 3. Measures of Stability for Regular Problems \\ 4. Computation in the Neighbourhood of a Singularity \\ 5. Arithmetic Quality of Reliable Algorithms \\ 6. Numerical Stability in Finite Precision \\ 7. Software Tools for Round-Off Error Analysis in Algorithms \\ 8. The Toolbox PRECISE for Computer Experimentation \\ 9. Experiments with PRECISE \\ 10. Robustness to Nonnormality \\ 11. Qualitative Computing \\ 12. More Numerical Illustrations with PRECISE \\ Annex: The Toolbox PRECISE for MATLAB.

entry:
@Book{Chaitin-Chatelin:1996:LFP,
  author =       "Fran{\c{c}}oise Chaitin-Chatelin and Val{\'e}rie
                 Frayss{\'e}",
  title =        "Lectures on Finite Precision Computations",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xv + 235",
  year =         "1996",
  ISBN =         "0-89871-358-7",
  ISBN-13 =      "978-0-89871-358-9",
  LCCN =         "QA297 .C417 1996",
  bibdate =      "Wed Nov 16 14:38:30 MST 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Software, environments, tools",
  acknowledgement = ack-nhfb,
  keywords =     "Matlab",
  subject =      "numerical calculations; data processing; error
                 analysis (mathematics); toolbox PRECISE",
  tableofcontents = "1. General Presentation \\
                 2. Computability in Finite Precision \\
                 3. Measures of Stability for Regular Problems \\
                 4. Computation in the Neighbourhood of a Singularity
                 \\
                 5. Arithmetic Quality of Reliable Algorithms \\
                 6. Numerical Stability in Finite Precision \\
                 7. Software Tools for Round-Off Error Analysis in
                 Algorithms \\
                 8. The Toolbox PRECISE for Computer Experimentation \\
                 9. Experiments with PRECISE \\
                 10. Robustness to Nonnormality \\
                 11. Qualitative Computing \\
                 12. More Numerical Illustrations with PRECISE \\
                 Annex: The Toolbox PRECISE for MATLAB.",
}


bibtype: article
filename: fparith.bib
label: Chen:1996:VAC
title: Verification of All Circuits in a Floating-Point Unit Using Word-Level Model Checking
journal: j-LECT-NOTES-COMP-SCI
volume: 1166
pages: 19--33
year: 1996
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Jun 02 07:43:02 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.06.02 07:43:02 ???
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawtitle: Verification of All Circuits in a Floating-Point Unit Using Word-Level Model Checking
author:
Y.-A. Chen and E. Clarke and P.-H. Ho and Y. Hoskote and T. Kam and M. Khaira and J. O. Leary and X. Zhao

rawauthor:
Y.-A. Chen and E. Clarke and P.-H. Ho and Y. Hoskote and T. Kam and M. Khaira and J. O. Leary and X. Zhao

entry:
@Article{Chen:1996:VAC,
  author =       "Y.-A. Chen and E. Clarke and P.-H. Ho and Y. Hoskote
                 and T. Kam and M. Khaira and J. O. Leary and X. Zhao",
  title =        "Verification of All Circuits in a Floating-Point Unit
                 Using Word-Level Model Checking",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1166",
  pages =        "19--33",
  year =         "1996",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Jun 02 07:43:02 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: inproceedings
filename: fparith.bib
label: Chesneaux:1996:CSS
author: J.-M. Chesneaux and B. Troff
title: Computational Stability Study Using the CADNA Software Applied to the Navier--Stokes Solver PEGASE
crossref: Alefeld:1996:SCV
pages: 84--90
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: J.-M. Chesneaux and B. Troff
rawtitle:
Computational Stability Study Using the {CADNA} Software Applied to the {Navier--Stokes} Solver {PEGASE}

entry:
@InProceedings{Chesneaux:1996:CSS,
  author =       "J.-M. Chesneaux and B. Troff",
  title =        "Computational Stability Study Using the {CADNA}
                 Software Applied to the {Navier--Stokes} Solver
                 {PEGASE}",
  crossref =     "Alefeld:1996:SCV",
  pages =        "84--90",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Chren:1996:DPP
author: W. A. Chren, Jr. and C. H. Brogdon and D. Andrevska
booktitle: IEEE 39th Midwest symposium on Circuits and Systems, 1996
title: Delay-power product simulation results for one-hot residue number system arithmetic circuits
volume: 1
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 544--547
year: 1996
DOI: https://doi.org/10.1109/MWSCAS.1996.594237
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: W. A. {Chren, Jr.} and C. H. Brogdon and D. Andrevska
rawbooktitle: {IEEE 39th} Midwest symposium on Circuits and Systems, 1996
rawtitle: Delay-power product simulation results for one-hot residue number system arithmetic circuits
entry:
@InProceedings{Chren:1996:DPP,
  author =       "W. A. {Chren, Jr.} and C. H. Brogdon and D.
                 Andrevska",
  booktitle =    "{IEEE 39th} Midwest symposium on Circuits and Systems,
                 1996",
  title =        "Delay-power product simulation results for one-hot
                 residue number system arithmetic circuits",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "544--547",
  year =         "1996",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/MWSCAS.1996.594237",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "We present Spice simulations which verify previous
                 analytical estimates of the delay-power product of
                 One-Hot Residue adders and multipliers. These
                 simulations show greater than a 50\% reduction in the
                 product below binary adders and an order of \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Chren:1996:DSD
author: W. A. Chren, Jr.
title: Delta-sigma demodulator with large oversampling ratio using the one-hot residue number system
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 473--476
year: 1996
DOI: https://doi.org/10.1109/ISCAS.1996.541749
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: W. A. {Chren, Jr.}
rawtitle: Delta-sigma demodulator with large oversampling ratio using the one-hot residue number system
booktitle:
IEEE International Symposium on Circuits and Systems. ISCAS '96, Connecting the World, 12--15 May 1996

rawbooktitle:
{IEEE} International Symposium on Circuits and Systems. {ISCAS '96}, Connecting the World, 12--15 May 1996

entry:
@InProceedings{Chren:1996:DSD,
  author =       "W. A. {Chren, Jr.}",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems. {ISCAS '96}, Connecting the World, 12--15 May
                 1996",
  title =        "Delta-sigma demodulator with large oversampling ratio
                 using the one-hot residue number system",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "473--476",
  year =         "1996",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.1996.541749",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A residue number system-based delta-sigma demodulator
                 is presented which demonstrates a significant
                 improvement in oversampling ratio in comparison with
                 equivalent binary designs. The second order design
                 employs a two-stage cascade architecture with
                 \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Chren:1996:RDU
author: W. A. Chren, Jr. and C. H. Brogdon
booktitle: IEEE 39th Midwest symposium on Circuits and Systems, 1996
title: RSA decryption using the one-hot residue number system
volume: 1
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 551--554
year: 1996
DOI: https://doi.org/10.1109/MWSCAS.1996.594238
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: W. A. {Chren, Jr.} and C. H. Brogdon
rawbooktitle: {IEEE 39th} Midwest symposium on Circuits and Systems, 1996
rawtitle: {RSA} decryption using the one-hot residue number system
entry:
@InProceedings{Chren:1996:RDU,
  author =       "W. A. {Chren, Jr.} and C. H. Brogdon",
  booktitle =    "{IEEE 39th} Midwest symposium on Circuits and Systems,
                 1996",
  title =        "{RSA} decryption using the one-hot residue number
                 system",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "551--554",
  year =         "1996",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/MWSCAS.1996.594238",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "The design of an RSA decryption circuit which uses the
                 One-Hot Residue Number System is presented. Large
                 modulus adders and multipliers are described which
                 reduce the area of previous (barrel shifter-based)
                 designs while preserving their low power \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Ciminiera:1996:CSM
author: L. Ciminiera and P. Montuschi
title: Carry-save multiplication schemes without final addition
journal: j-IEEE-TRANS-COMPUT
volume: 45
number: 9
pages: 1050--1055
month: sep
monthnumber: 9
year: 1996
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.537128
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 19:47:13 MDT 2011
bibtimestamp: 2011.07.06 19:47:13 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=537128
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: L. Ciminiera and P. Montuschi
rawtitle: Carry-save multiplication schemes without final addition
entry:
@Article{Ciminiera:1996:CSM,
  author =       "L. Ciminiera and P. Montuschi",
  title =        "Carry-save multiplication schemes without final
                 addition",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "45",
  number =       "9",
  pages =        "1050--1055",
  month =        sep,
  year =         "1996",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.537128",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 19:47:13 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=537128",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Clarke:1996:VSD
author: E. M. Clarke and S. M. German and X. Zhao
title: Verifying the SRT division algorithm using theorem proving techniques
journal: j-LECT-NOTES-COMP-SCI
volume: 1102
pages: 111--??
year: 1996
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Fri Sep 6 19:46:15 MDT 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.09.06 19:46:15 MDT
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: E. M. Clarke and S. M. German and X. Zhao
rawtitle: Verifying the {SRT} division algorithm using theorem proving techniques
entry:
@Article{Clarke:1996:VSD,
  author =       "E. M. Clarke and S. M. German and X. Zhao",
  title =        "Verifying the {SRT} division algorithm using theorem
                 proving techniques",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1102",
  pages =        "111--??",
  year =         "1996",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Fri Sep 6 19:46:15 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: inproceedings
filename: fparith.bib
label: Clarke:1996:WLS
author: E. M. Clarke and M. Khaira and X. Zhao
title: Word-level symbolic model checking: avoiding the Pentium FDIV error
crossref: IEEE:1996:DAC
pages: 645--648
year: 1996
bibdate: Sat Jun 02 07:44:08 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.06.02 07:44:08 ???
acknowledgement: ack-nhfb
rawauthor: E. M. Clarke and M. Khaira and X. Zhao
rawtitle: Word-level symbolic model checking: avoiding the {Pentium FDIV} error
URL:
http://www.acm.org/pubs/articles/proceedings/dac/240518/p645-clarke/p645-clarke.pdf; http://www.acm.org/pubs/citations/proceedings/dac/240518/p645-clarke/; http://www.acm.org/pubs/contents/proceedings/dac/240518/

entry:
@InProceedings{Clarke:1996:WLS,
  author =       "E. M. Clarke and M. Khaira and X. Zhao",
  title =        "Word-level symbolic model checking: avoiding the
                 {Pentium FDIV} error",
  crossref =     "IEEE:1996:DAC",
  pages =        "645--648",
  year =         "1996",
  bibdate =      "Sat Jun 02 07:44:08 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/articles/proceedings/dac/240518/p645-clarke/p645-clarke.pdf;
                 http://www.acm.org/pubs/citations/proceedings/dac/240518/p645-clarke/;
                 http://www.acm.org/pubs/contents/proceedings/dac/240518/",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Corliss:1996:VPE
author: G. F. Corliss and R. Rihm
title: Validating an A Priori Enclosure Using High-Order Taylor Series
crossref: Alefeld:1996:SCV
pages: 228--238
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: G. F. Corliss and R. Rihm
rawtitle: Validating an {A} Priori Enclosure Using High-Order {Taylor} Series
entry:
@InProceedings{Corliss:1996:VPE,
  author =       "G. F. Corliss and R. Rihm",
  title =        "Validating an {A} Priori Enclosure Using High-Order
                 {Taylor} Series",
  crossref =     "Alefeld:1996:SCV",
  pages =        "228--238",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Crenshaw:1996:PTF
author: Jack W. Crenshaw
title: Programmer's Toolbox: Floating-Point Math, Part 3
journal: j-EMBED-SYS-PROG
volume: 9
number: 1
pages: 19--??
year: 1996
CODEN: EYPRE4
ISSN: 1040-3272 OR 10403272
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
fjournal: Embedded Systems Programming
acknowledgement: ack-nhfb
rawauthor: Jack W. Crenshaw
rawtitle: Programmer's Toolbox: Floating-Point Math, Part 3
entry:
@Article{Crenshaw:1996:PTF,
  author =       "Jack W. Crenshaw",
  title =        "Programmer's Toolbox: Floating-Point Math, Part 3",
  journal =      j-EMBED-SYS-PROG,
  volume =       "9",
  number =       "1",
  pages =        "19--??",
  year =         "1996",
  CODEN =        "EYPRE4",
  ISSN =         "1040-3272",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Embedded Systems Programming",
}


bibtype: techreport
filename: fparith.bib
label: Darcy:1996:FMF
author: Joseph D. Darcy and David Gay
title: FLECKmarks: Measuring Floating Point Performance using a FulL IEEE Compliant Arithmetic BenchmarK
type: Technical report
institution: Department of Computer Science, University of California, Berkeley
address: Berkeley, CA, USA
pages: 19--??
month: dec
monthnumber: 12
year: 1996
bibdate: Mon Feb 18 12:25:24 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.02.18 12:25:24 ???
URL: http://www.cs.berkeley.edu/~darcy/Research/fleckmrk.pdf
acknowledgement: ack-nhfb
rawauthor: Joseph D. Darcy and David Gay
remark:
From the first author's home Web page: ``Errata: The `subnormal' timings for x86 processors are incorrect; they do not perform operations on subnormals at full speed. However, what values are subnormals on the x86 are different than on other processors due to that architecture's unusual floating-point register design. On the x86, when a 64-bit double value is loaded into a register, it has the 15 bit exponent of the 80-bit double extended format instead of the 11 bit exponent of the double format. Confusingly, this occurs even if the processor's precision control is set to round to double precision. The test programs in this project used computations that would be subnormal in a pure double format, not in double with extended exponent range (non-zero subnormals in double with extended exponent range would round to zero in pure double). Operations on subnormals in double precision with extended exponent range should take about 100 cycles on the Pentium Pro and subsequent Intel x86 chips.par Thanks to David Scott of Intel for pointing out this error.

rawtitle:
{FLECKmarks}: Measuring Floating Point Performance using a {FulL IEEE Compliant Arithmetic BenchmarK}

entry:
@TechReport{Darcy:1996:FMF,
  author =       "Joseph D. Darcy and David Gay",
  title =        "{FLECKmarks}: Measuring Floating Point Performance
                 using a {FulL IEEE Compliant Arithmetic BenchmarK}",
  type =         "Technical report",
  institution =  "Department of Computer Science, University of
                 California, Berkeley",
  address =      "Berkeley, CA, USA",
  month =        dec,
  year =         "1996",
  bibdate =      "Mon Feb 18 12:25:24 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~darcy/Research/fleckmrk.pdf",
  acknowledgement = ack-nhfb,
  remark =       "From the first author's home Web page: ``Errata: The
                 `subnormal' timings for x86 processors are incorrect;
                 they do not perform operations on subnormals at full
                 speed. However, what values are subnormals on the x86
                 are different than on other processors due to that
                 architecture's unusual floating-point register design.
                 On the x86, when a 64-bit double value is loaded into a
                 register, it has the 15 bit exponent of the 80-bit
                 double extended format instead of the 11 bit exponent
                 of the double format. Confusingly, this occurs even if
                 the processor's precision control is set to round to
                 double precision. The test programs in this project
                 used computations that would be subnormal in a pure
                 double format, not in double with extended exponent
                 range (non-zero subnormals in double with extended
                 exponent range would round to zero in pure double).
                 Operations on subnormals in double precision with
                 extended exponent range should take about 100 cycles on
                 the Pentium Pro and subsequent Intel x86
                 chips.\par

                 Thanks to David Scott of Intel for pointing out this
                 error.",
}


bibtype: inproceedings
filename: fparith.bib
label: Dimitrov:1996:NCD
author: V. Dimitrov and Saeid Sadeghi-Emamchaie and G. A. Jullien and W. C. Miller
title: Near Canonic Double-Based Number System (DBNS) with Applications in Digital Signal Processing
crossref: Luk:1996:PSC
pages: 14--25
year: 1996
DOI: https://doi.org/10.1117/12.255433
bibdate: Sat May 14 17:15:05 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2011.05.14 17:15:05 ???
URL: http://spie.org/x648.html?product_id=235316; http://www.gbv.de/dms/bowker/toc/9780819422347
keywords: Double-Based Number System (DBNS)
acknowledgement: ack-nhfb
rawauthor: V. Dimitrov and Saeid Sadeghi-Emamchaie and G. A. Jullien and W. C. Miller
rawtitle: Near Canonic Double-Based Number System ({DBNS}) with Applications in Digital Signal Processing
entry:
@InProceedings{Dimitrov:1996:NCD,
  author =       "V. Dimitrov and Saeid Sadeghi-Emamchaie and G. A.
                 Jullien and W. C. Miller",
  title =        "Near Canonic Double-Based Number System ({DBNS}) with
                 Applications in Digital Signal Processing",
  crossref =     "Luk:1996:PSC",
  pages =        "14--25",
  year =         "1996",
  DOI =          "https://doi.org/10.1117/12.255433",
  bibdate =      "Sat May 14 17:15:05 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://spie.org/x648.html?product_id=235316;
                 http://www.gbv.de/dms/bowker/toc/9780819422347",
  acknowledgement = ack-nhfb,
  keywords =     "Double-Based Number System (DBNS)",
}


bibtype: inproceedings
filename: fparith.bib
label: Dimitrov:1996:RNS
author: V. S. Dimitrov and G. A. Jullien and W. C. Miller
booktitle: IEEE 39th Midwest symposium on Circuits and Systems, 1996
volume: 1
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 533--536
year: 1996
DOI: https://doi.org/10.1109/MWSCAS.1996.594227
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: V. S. Dimitrov and G. A. Jullien and W. C. Miller
rawbooktitle: {IEEE 39th} Midwest symposium on Circuits and Systems, 1996
title:
A residue number system implementation of real orthogonal transforms via approximation over a direct product of quadratic number rings

rawtitle:
A residue number system implementation of real orthogonal transforms via approximation over a direct product of quadratic number rings

entry:
@InProceedings{Dimitrov:1996:RNS,
  author =       "V. S. Dimitrov and G. A. Jullien and W. C. Miller",
  booktitle =    "{IEEE 39th} Midwest symposium on Circuits and Systems,
                 1996",
  title =        "A residue number system implementation of real
                 orthogonal transforms via approximation over a direct
                 product of quadratic number rings",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "533--536",
  year =         "1996",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/MWSCAS.1996.594227",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Recent work has focused on doing residue computations
                 that are quantization within a dense ring of integers
                 in the real domain. The aims of the paper are to
                 provide and efficient algorithm for approximation of
                 the real input signal with arbitrarily \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Dimitrova:1996:NAS
author: N. S. Dimitrova
title: On a Numerical Approach for Solving a Class of Nonlinear Systems
crossref: Alefeld:1996:SCV
pages: 147--153
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: N. S. Dimitrova
rawtitle: On a Numerical Approach for Solving a Class of Nonlinear Systems
entry:
@InProceedings{Dimitrova:1996:NAS,
  author =       "N. S. Dimitrova",
  title =        "On a Numerical Approach for Solving a Class of
                 Nonlinear Systems",
  crossref =     "Alefeld:1996:SCV",
  pages =        "147--153",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Djebbari:1996:GAS
author: A. Djebbari and S. A. Elahmar and M. F. Belbachir and J. M. Rouvaen
booktitle: 3rd International Conference on Signal Processing, 1996
volume: 1
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 154--157
year: 1996
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: A. Djebbari and S. A. Elahmar and M. F. Belbachir and J. M. Rouvaen
rawbooktitle: 3rd International Conference on Signal Processing, 1996
title:
Global asymptotic stability of normal digital filters with rounding and two's complement truncation quantization

rawtitle:
Global asymptotic stability of normal digital filters with rounding and two's complement truncation quantization

entry:
@InProceedings{Djebbari:1996:GAS,
  author =       "A. Djebbari and S. A. Elahmar and M. F. Belbachir and
                 J. M. Rouvaen",
  booktitle =    "3rd International Conference on Signal Processing,
                 1996",
  title =        "Global asymptotic stability of normal digital filters
                 with rounding and two's complement truncation
                 quantization",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "154--157",
  year =         "1996",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:04 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Normal form digital filters are investigated for limit
                 cycles due to both two's complement truncation and
                 rounding quantization. Conditions for existence are
                 derived. A method, based on an exhaustive search and
                 applicable to above types of \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Dobner:1996:AAD
author: H.-J. Dobner and W. Klein
title: Application of Automatic Differentiation Techniques to Circuit Simulation
crossref: Alefeld:1996:SCV
pages: 329--333
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: H.-J. Dobner and W. Klein
rawtitle: Application of Automatic Differentiation Techniques to Circuit Simulation
entry:
@InProceedings{Dobner:1996:AAD,
  author =       "H.-J. Dobner and W. Klein",
  title =        "Application of Automatic Differentiation Techniques to
                 Circuit Simulation",
  crossref =     "Alefeld:1996:SCV",
  pages =        "329--333",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Dobronets:1996:PEE
author: B. S. Dobronets
title: A Posteriori Error Estimation for Partial Differential Equations
crossref: Alefeld:1996:SCV
pages: 239--244
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: B. S. Dobronets
rawtitle: A Posteriori Error Estimation for Partial Differential Equations
entry:
@InProceedings{Dobronets:1996:PEE,
  author =       "B. S. Dobronets",
  title =        "A Posteriori Error Estimation for Partial Differential
                 Equations",
  crossref =     "Alefeld:1996:SCV",
  pages =        "239--244",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: El-Guibaly:1996:HSC
author: Fayez El-Guibaly and A. Sabaa
title: High-speed CORDIC algorithm
crossref: Luk:1996:PSC
pages: 512--512
year: 1996
DOI: https://doi.org/10.1117/12.255460
bibdate: Tue Jun 14 18:26:06 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2011.06.14 18:26:06 ???
acknowledgement: ack-nhfb
rawauthor: Fayez El-Guibaly and A. Sabaa
rawtitle: High-speed {CORDIC} algorithm
entry:
@InProceedings{El-Guibaly:1996:HSC,
  author =       "Fayez El-Guibaly and A. Sabaa",
  title =        "High-speed {CORDIC} algorithm",
  crossref =     "Luk:1996:PSC",
  pages =        "512--512",
  year =         "1996",
  DOI =          "https://doi.org/10.1117/12.255460",
  bibdate =      "Tue Jun 14 18:26:06 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Farag:1996:LPR
author: Emad N. Farag and M. Anwarul Hasan and Mohamed I. Elmasry
title: Low-power radix 2 division algorithm with minimum add / sub operations
crossref: Luk:1996:PSC
pages: 39--511
year: 1996
DOI: https://doi.org/10.1117/12.255450
bibdate: Tue Jun 14 18:26:06 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2011.06.14 18:26:06 ???
acknowledgement: ack-nhfb
rawauthor: Emad N. Farag and M. Anwarul Hasan and Mohamed I. Elmasry
rawtitle: Low-power radix 2 division algorithm with minimum add\slash sub operations
entry:
@InProceedings{Farag:1996:LPR,
  author =       "Emad N. Farag and M. Anwarul Hasan and Mohamed I.
                 Elmasry",
  title =        "Low-power radix 2 division algorithm with minimum
                 add\slash sub operations",
  crossref =     "Luk:1996:PSC",
  pages =        "39--511",
  year =         "1996",
  DOI =          "https://doi.org/10.1117/12.255450",
  bibdate =      "Tue Jun 14 18:26:06 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Feldstein:1996:OUM
author: Alan Feldstein and Peter R. Turner
title: Overflow and underflow in multiplication and division
journal: j-APPL-NUM-MATH
volume: 21
number: 3
pages: 221--239
day: 20
month: aug
monthnumber: 8
year: 1996
CODEN: ANMAEL
ISSN: 0168-9274 (print), 1873-5460 (electronic) OR 01689274 (print), 18735460 (electronic)
ISSNL: 0168-9274 OR 01689274
MRclass: 65Y99
MRnumber: 97f:65086; 1 416 857
bibdate: Wed Jul 28 14:36:31 MDT 1999
bibtimestamp: 1999.07.28 14:36:31 MDT
fjournal: Applied Numerical Mathematics: Transactions of IMACS
acknowledgement: ack-nhfb
affiliation: Arizona State Univ
affiliationaddress: AZ, USA
journalURL: http://www.sciencedirect.com/science/journal/01689274
journalabr: Appl Numer Math
rawauthor: Alan Feldstein and Peter R. Turner
rawtitle: Overflow and underflow in multiplication and division
bibsource:
Compendex database; http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_free/browse/browse.cgi?year=1996&volume=21&issue=3; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_sub/browse/browse.cgi?year=1996&volume=21&issue=3&aid=692

keywords:
Differential equations; Digital arithmetic; Division; Floating point exponents; Floating point fractions; Logarithmic distribution; Mathematical models; Multiplication; Natural sciences computing; Overflow; Underflow

entry:
@Article{Feldstein:1996:OUM,
  author =       "Alan Feldstein and Peter R. Turner",
  title =        "Overflow and underflow in multiplication and
                 division",
  journal =      j-APPL-NUM-MATH,
  volume =       "21",
  number =       "3",
  pages =        "221--239",
  day =          "20",
  month =        aug,
  year =         "1996",
  CODEN =        "ANMAEL",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  MRclass =      "65Y99",
  MRnumber =     "97f:65086; 1 416 857",
  bibdate =      "Wed Jul 28 14:36:31 MDT 1999",
  bibsource =    "Compendex database;
                 http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_free/browse/browse.cgi?year=1996&volume=21&issue=3;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_sub/browse/browse.cgi?year=1996&volume=21&issue=3&aid=692",
  acknowledgement = ack-nhfb,
  affiliation =  "Arizona State Univ",
  affiliationaddress = "AZ, USA",
  classification = "721.1; 723.2; 921; 921.2; 921.6",
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274",
  journalabr =   "Appl Numer Math",
  keywords =     "Differential equations; Digital arithmetic; Division;
                 Floating point exponents; Floating point fractions;
                 Logarithmic distribution; Mathematical models;
                 Multiplication; Natural sciences computing; Overflow;
                 Underflow",
}


bibtype: article
filename: fparith.bib
label: Fenn:1996:MDD
author: S. T. J. Fenn and M. Benaissa and D. Taylor
title: $ mathrm GF(2^m) $ multiplication and division over the dual basis
journal: j-IEEE-TRANS-COMPUT
volume: 45
number: 3
pages: 319--327
month: mar
monthnumber: 3
year: 1996
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.485570
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 19:47:09 MDT 2011
bibtimestamp: 2011.07.06 19:47:09 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=485570
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: S. T. J. Fenn and M. Benaissa and D. Taylor
rawtitle: {$ \mathrm {GF}(2^m) $} multiplication and division over the dual basis
entry:
@Article{Fenn:1996:MDD,
  author =       "S. T. J. Fenn and M. Benaissa and D. Taylor",
  title =        "{$ \mathrm {GF}(2^m) $} multiplication and division
                 over the dual basis",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "45",
  number =       "3",
  pages =        "319--327",
  month =        mar,
  year =         "1996",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.485570",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 19:47:09 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=485570",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Flynn:1996:SPT
booktitle: NSF / MIPS Conference on Experimental Research on Computer Systems, June 1996
title: The SNAP Project: Towards Sub-Nanosecond Arithmetic
pages: ??--??
year: 1996
bibdate: Mon Jul 18 17:18:49 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.18 17:18:49 ???
URL: ftp://arith.stanford.edu/tr/snap_nsf.ps.Z
acknowledgement: ack-nhfb
rawbooktitle: {NSF\slash MIPS} Conference on Experimental Research on Computer Systems, June 1996
rawtitle: The {SNAP} Project: Towards Sub-Nanosecond Arithmetic
author:
Michael J. Flynn and Stuart Oberman and Steve Fu and Hesham Al-Twaijry and Kevin Nowka and Gary Bewick and Eric Schwarz and Nhon Quach

rawauthor:
Michael J. Flynn and Stuart Oberman and Steve Fu and Hesham Al-Twaijry and Kevin Nowka and Gary Bewick and Eric Schwarz and Nhon Quach

entry:
@InProceedings{Flynn:1996:SPT,
  author =       "Michael J. Flynn and Stuart Oberman and Steve Fu and
                 Hesham Al-Twaijry and Kevin Nowka and Gary Bewick and
                 Eric Schwarz and Nhon Quach",
  booktitle =    "{NSF\slash MIPS} Conference on Experimental Research
                 on Computer Systems, June 1996",
  title =        "The {SNAP} Project: Towards Sub-Nanosecond
                 Arithmetic",
  publisher =    "????",
  address =      "????",
  pages =        "??--??",
  year =         "1996",
  bibdate =      "Mon Jul 18 17:18:49 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://arith.stanford.edu/tr/snap_nsf.ps.Z",
  acknowledgement = ack-nhfb,
  pagecount =    "12",
}


bibtype: article
filename: fparith.bib
label: Fortune:1996:SAY
author: Steven Fortune and Christopher J. Van Wyk
title: Static analysis yields efficient exact integer arithmetic for computational geometry
journal: j-TOG
volume: 15
number: 3
pages: 223--248
month: jul
monthnumber: 7
year: 1996
CODEN: ATGRDF
ISSN: 0730-0301 (print), 1557-7368 (electronic) OR 07300301 (print), 15577368 (electronic)
ISSNL: 0730-0301 OR 07300301
bibdate: Sat Aug 31 16:39:46 MDT 1996
bibsource: http://www.acm.org/pubs/toc/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.08.31 16:39:46 MDT
URL: http://www.acm.org/pubs/toc/Abstracts/0730-0301/230533.html
fjournal: ACM Transactions on Graphics
keywords: algorithms; experimentation
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J778
rawauthor: Steven Fortune and Christopher J. {Van Wyk}
rawtitle: Static analysis yields efficient exact integer arithmetic for computational geometry
abstract:
Geometric algorithms as usually described assuming that arithmetic operations are performed exactly on real numbers. A program implemented using a naive substitution of floating-point arithmetic for real arithmetic can fail, since geometric primitives depend upon sign-evaluation and may not be reliable if evaluated approximately. Geometric primitives are reliable if evaluated exactly with integer arithmetic, but this degrades performance since software extended-precision arithmetic is required.par We describe static-analysis techniques that reduce the performance cost of exact integer arithmetic used to implement geometric algorithms. We have used the techniques for a number of examples, including line-segment intersection in two dimensions, Delaunay triangulations, and a tree-dimensional boundary-based polyhedral modeler. In general, the techniques are appropriate for algorithms that use primitives of relatively low algebraic total degree, e.g., those involving flat objects (points, lines, planes) in two or three dimensions. The techniques have been package in a preprocessor for reasonably convenient use.

subject:
bf I.3.5: Computing Methodologies, COMPUTER GRAPHICS, Computational Geometry and Object Modeling, Geometric algorithms, languages, and systems. bf D.3.4: Software, PROGRAMMING LANGUAGES, Processors, Preprocessors. bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency. bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Reliability and robustness.

rawabstract:
Geometric algorithms as usually described assuming that arithmetic operations are performed exactly on real numbers. A program implemented using a naive substitution of floating-point arithmetic for real arithmetic can fail, since geometric primitives depend upon sign-evaluation and may not be reliable if evaluated approximately. Geometric primitives are reliable if evaluated exactly with integer arithmetic, but this degrades performance since software extended-precision arithmetic is required.\par We describe static-analysis techniques that reduce the performance cost of exact integer arithmetic used to implement geometric algorithms. We have used the techniques for a number of examples, including line-segment intersection in two dimensions, Delaunay triangulations, and a tree-dimensional boundary-based polyhedral modeler. In general, the techniques are appropriate for algorithms that use primitives of relatively low algebraic total degree, e.g., those involving flat objects (points, lines, planes) in two or three dimensions. The techniques have been package in a preprocessor for reasonably convenient use.

entry:
@Article{Fortune:1996:SAY,
  author =       "Steven Fortune and Christopher J. {Van Wyk}",
  title =        "Static analysis yields efficient exact integer
                 arithmetic for computational geometry",
  journal =      j-TOG,
  volume =       "15",
  number =       "3",
  pages =        "223--248",
  month =        jul,
  year =         "1996",
  CODEN =        "ATGRDF",
  ISSN =         "0730-0301 (print), 1557-7368 (electronic)",
  ISSN-L =       "0730-0301",
  bibdate =      "Sat Aug 31 16:39:46 MDT 1996",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/toc/Abstracts/0730-0301/230533.html",
  abstract =     "Geometric algorithms as usually described assuming
                 that arithmetic operations are performed exactly on
                 real numbers. A program implemented using a naive
                 substitution of floating-point arithmetic for real
                 arithmetic can fail, since geometric primitives depend
                 upon sign-evaluation and may not be reliable if
                 evaluated approximately. Geometric primitives are
                 reliable if evaluated exactly with integer arithmetic,
                 but this degrades performance since software
                 extended-precision arithmetic is required.\par

                 We describe static-analysis techniques that reduce the
                 performance cost of exact integer arithmetic used to
                 implement geometric algorithms. We have used the
                 techniques for a number of examples, including
                 line-segment intersection in two dimensions, Delaunay
                 triangulations, and a tree-dimensional boundary-based
                 polyhedral modeler. In general, the techniques are
                 appropriate for algorithms that use primitives of
                 relatively low algebraic total degree, e.g., those
                 involving flat objects (points, lines, planes) in two
                 or three dimensions. The techniques have been package
                 in a preprocessor for reasonably convenient use.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Graphics",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J778",
  keywords =     "algorithms; experimentation",
  subject =      "{\bf I.3.5}: Computing Methodologies, COMPUTER
                 GRAPHICS, Computational Geometry and Object Modeling,
                 Geometric algorithms, languages, and systems. {\bf
                 D.3.4}: Software, PROGRAMMING LANGUAGES, Processors,
                 Preprocessors. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Efficiency. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Reliability and robustness.",
}


bibtype: article
filename: fparith.bib
label: Ganesan:1996:CSM
author: Ravikanth Ganesan and Kannan Govindarajan and Min-You Wu
title: Comparing SIMD and MIMD Programming Modes
journal: j-J-PAR-DIST-COMP
volume: 35
number: 1
pages: 91--96
day: 25
month: may
monthnumber: 5
year: 1996
CODEN: JPDCER
DOI: https://doi.org/10.1006/jpdc.1996.0071
ISSN: 0743-7315 (print), 1096-0848 (electronic) OR 07437315 (print), 10960848 (electronic)
ISSNL: 0743-7315 OR 07437315
bibdate: Thu Mar 9 09:19:00 MST 2000
bibtimestamp: 2000.03.09 09:19:00 MST
fjournal: Journal of Parallel and Distributed Computing
acknowledgement: ack-nhfb
corpsource: Department of Computer Science, State University of New York, Buffalo, NY, USA
journalURL: http://www.sciencedirect.com/science/journal/07437315
treatment: P Practical
rawauthor: Ravikanth Ganesan and Kannan Govindarajan and Min-You Wu
rawtitle: Comparing {SIMD} and {MIMD} Programming Modes
URL:
http://www.idealibrary.com/links/doi/10.1006/jpdc.1996.0071/production; http://www.idealibrary.com/links/doi/10.1006/jpdc.1996.0071/production/pdf

keywords:
application benchmarks; arithmetic operations; CM; CM-5; communication; Connection Machine; Fortran; message-passing Fortran; MIMD; parallel architectures; parallel programming; performance evaluation; programming modes; SIMD; software; synthetic benchmarks; time

entry:
@Article{Ganesan:1996:CSM,
  author =       "Ravikanth Ganesan and Kannan Govindarajan and Min-You
                 Wu",
  title =        "Comparing {SIMD} and {MIMD} Programming Modes",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "35",
  number =       "1",
  pages =        "91--96",
  day =          "25",
  month =        may,
  year =         "1996",
  CODEN =        "JPDCER",
  DOI =          "https://doi.org/10.1006/jpdc.1996.0071",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Thu Mar 9 09:19:00 MST 2000",
  bibsource =    "http://www.idealibrary.com/servlet/useragent?func=showAllIssues&curIssueID=jpdc;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.idealibrary.com/links/doi/10.1006/jpdc.1996.0071/production;
                 http://www.idealibrary.com/links/doi/10.1006/jpdc.1996.0071/production/pdf",
  acknowledgement = ack-nhfb,
  classification = "C5220P (Parallel architecture); C6110P (Parallel
                 programming)",
  corpsource =   "Department of Computer Science, State University of
                 New York, Buffalo, NY, USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  keywords =     "application benchmarks; arithmetic operations; CM;
                 CM-5; communication; Connection Machine; Fortran;
                 message-passing Fortran; MIMD; parallel architectures;
                 parallel programming; performance evaluation;
                 programming modes; SIMD; software; synthetic
                 benchmarks; time",
  treatment =    "P Practical",
}


bibtype: inproceedings
filename: fparith.bib
label: Garg:1996:FTP
author: H. K. Garg and F. V. C. Mendis
booktitle: Conference Record of the Thirtieth Asilomar Conference on Signals, Systems and Computers, 1996
title: On fault-tolerant polynomial residue number systems
volume: 1
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 206--209
year: 1996
DOI: https://doi.org/10.1109/ACSSC.1996.600858
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: H. K. Garg and F. V. C. Mendis
rawbooktitle: Conference Record of the Thirtieth Asilomar Conference on Signals, Systems and Computers, 1996
rawtitle: On fault-tolerant polynomial residue number systems
entry:
@InProceedings{Garg:1996:FTP,
  author =       "H. K. Garg and F. V. C. Mendis",
  booktitle =    "Conference Record of the Thirtieth Asilomar Conference
                 on Signals, Systems and Computers, 1996",
  title =        "On fault-tolerant polynomial residue number systems",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "206--209",
  year =         "1996",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ACSSC.1996.600858",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Fault-tolerant convolution techniques have been
                 described for polynomials defined over the fields of
                 complex and real numbers. Fault-tolerant convolution
                 schemes are derived for polynomials defined over finite
                 integer rings. A new algorithm for \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Gibb:1996:FFI
author: S. Gibb and P. J. W. Graumann and Laurence E. Turner
title: FIR filter implementation using bit-serial arithmetic and partial summation trees
crossref: Luk:1996:PSC
pages: 63--74
year: 1996
DOI: https://doi.org/10.1117/12.255462
bibdate: Tue Jun 14 18:26:06 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2011.06.14 18:26:06 ???
acknowledgement: ack-nhfb
rawauthor: S. Gibb and P. J. W. Graumann and Laurence E. Turner
rawtitle: {FIR} filter implementation using bit-serial arithmetic and partial summation trees
entry:
@InProceedings{Gibb:1996:FFI,
  author =       "S. Gibb and P. J. W. Graumann and Laurence E. Turner",
  title =        "{FIR} filter implementation using bit-serial
                 arithmetic and partial summation trees",
  crossref =     "Luk:1996:PSC",
  pages =        "63--74",
  year =         "1996",
  DOI =          "https://doi.org/10.1117/12.255462",
  bibdate =      "Tue Jun 14 18:26:06 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: incollection
filename: fparith.bib
label: Goldberg:1996:CA
author: David Goldberg
title: Computer Arithmetic
crossref: Hennessy:1996:CAQ
chapter: A
pages: A-1--A-77
year: 1996
bibdate: Mon May 20 10:05:22 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.20 10:05:22 ???
acknowledgement: ack-nhfb
rawauthor: David Goldberg
rawtitle: Computer Arithmetic
entry:
@InCollection{Goldberg:1996:CA,
  author =       "David Goldberg",
  title =        "Computer Arithmetic",
  crossref =     "Hennessy:1996:CAQ",
  chapter =      "A",
  pages =        "A-1--A-77",
  year =         "1996",
  bibdate =      "Mon May 20 10:05:22 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Goldstine:1996:ENI
author: H. H. Goldstine and A. Goldstine
title: The Electronic Numerical Integrator and Computer (ENIAC)
journal: j-IEEE-ANN-HIST-COMPUT
volume: 18
number: 1
pages: 10--16
month: Spring
year: 1996
CODEN: IAHCEX
DOI: https://doi.org/10.1109/85.476557
ISSN: 1058-6180 (print), 1934-1547 (electronic) OR 10586180 (print), 19341547 (electronic)
ISSNL: 1058-6180 OR 10586180
bibdate: Fri Nov 28 16:50:50 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 16:50:50 ???
note: Reprint of 1946 technical report and cite Goldstine:1946:ENI.
URL: http://ieeexplore.ieee.org/iel4/85/10202/00476557.pdf
fjournal: IEEE Annals of the History of Computing
keywords: decimal floating-point arithmetic
acknowledgement: ack-mfc
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=85
rawauthor: H. H. Goldstine and A. Goldstine
rawnote: Reprint of 1946 technical report and \cite{Goldstine:1946:ENI}.
rawtitle: The {Electronic Numerical Integrator and Computer} ({ENIAC})
abstract:
It is our purpose in the succeeding pages to give a brief description of the ENIAC and an indication of the kinds of problems for which it can be used. This general purpose electronic computing machine was recently made public by the Army Ordnance Department for which it was developed by the Moore School of Electrical Engineering. The machine was developed primarily for the purpose of calculating firing tables for the armed forces. Its design is, however, sufficiently general to permit the solution of a large class of numerical problems which could hardly be attempted by more conventional computing tools.par In order easily to obtain sufficient accuracy for scientific computations, the ENIAC was designed as a digital device. The equipment normally handles signed 10-digit numbers expressed in the decimal system. It is, however, so constructed that operations with as many as 20 digits are possible.par The machine is automatically sequenced in the sense that all instructions needed to carry out a computation are given to it before the computation commences. It will be seen below how these instructions are given to the machine.

rawabstract:
It is our purpose in the succeeding pages to give a brief description of the ENIAC and an indication of the kinds of problems for which it can be used. This general purpose electronic computing machine was recently made public by the Army Ordnance Department for which it was developed by the Moore School of Electrical Engineering. The machine was developed primarily for the purpose of calculating firing tables for the armed forces. Its design is, however, sufficiently general to permit the solution of a large class of numerical problems which could hardly be attempted by more conventional computing tools.\par In order easily to obtain sufficient accuracy for scientific computations, the ENIAC was designed as a digital device. The equipment normally handles signed 10-digit numbers expressed in the decimal system. It is, however, so constructed that operations with as many as 20 digits are possible.\par The machine is automatically sequenced in the sense that all instructions needed to carry out a computation are given to it before the computation commences. It will be seen below how these instructions are given to the machine.

entry:
@Article{Goldstine:1996:ENI,
  author =       "H. H. Goldstine and A. Goldstine",
  title =        "The {Electronic Numerical Integrator and Computer}
                 ({ENIAC})",
  journal =      j-IEEE-ANN-HIST-COMPUT,
  volume =       "18",
  number =       "1",
  pages =        "10--16",
  month =        "Spring",
  year =         "1996",
  CODEN =        "IAHCEX",
  DOI =          "https://doi.org/10.1109/85.476557",
  ISSN =         "1058-6180 (print), 1934-1547 (electronic)",
  ISSN-L =       "1058-6180",
  bibdate =      "Fri Nov 28 16:50:50 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprint of 1946 technical report and
                 \cite{Goldstine:1946:ENI}.",
  URL =          "http://ieeexplore.ieee.org/iel4/85/10202/00476557.pdf",
  abstract =     "It is our purpose in the succeeding pages to give a
                 brief description of the ENIAC and an indication of the
                 kinds of problems for which it can be used. This
                 general purpose electronic computing machine was
                 recently made public by the Army Ordnance Department
                 for which it was developed by the Moore School of
                 Electrical Engineering. The machine was developed
                 primarily for the purpose of calculating firing tables
                 for the armed forces. Its design is, however,
                 sufficiently general to permit the solution of a large
                 class of numerical problems which could hardly be
                 attempted by more conventional computing tools.\par

                 In order easily to obtain sufficient accuracy for
                 scientific computations, the ENIAC was designed as a
                 digital device. The equipment normally handles signed
                 10-digit numbers expressed in the decimal system. It
                 is, however, so constructed that operations with as
                 many as 20 digits are possible.\par

                 The machine is automatically sequenced in the sense
                 that all instructions needed to carry out a computation
                 are given to it before the computation commences. It
                 will be seen below how these instructions are given to
                 the machine.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  fjournal =     "IEEE Annals of the History of Computing",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=85",
  keywords =     "decimal floating-point arithmetic",
}


bibtype: inproceedings
filename: fparith.bib
label: Gudenberg:1996:HSI
author: J. W. Von Gudenberg
title: Hardware Support for Interval Arithmetic
crossref: Alefeld:1996:SCV
pages: 32--37
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: J. W. Von Gudenberg
rawtitle: Hardware Support for Interval Arithmetic
entry:
@InProceedings{Gudenberg:1996:HSI,
  author =       "J. W. Von Gudenberg",
  title =        "Hardware Support for Interval Arithmetic",
  crossref =     "Alefeld:1996:SCV",
  pages =        "32--37",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: fparith.bib
label: Guedj:1996:EN
author: Denis Guedj
title: L'empire des nombres
publisher: Gallimard
address: Paris, France
pages: 176
year: 1996
ISBN: 2-07-053373-5 OR 2070533735
ISBN13: 978-2-07-053373-2 OR 9782070533732
bibdate: Sat Nov 29 06:57:01 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.29 06:57:01 ???
acknowledgement: ack-nhfb
rawauthor: Denis Guedj
rawtitle: {L}'empire des nombres
entry:
@Book{Guedj:1996:EN,
  author =       "Denis Guedj",
  title =        "{L}'empire des nombres",
  publisher =    "Gallimard",
  address =      "Paris, France",
  pages =        "176",
  year =         "1996",
  ISBN =         "2-07-053373-5",
  ISBN-13 =      "978-2-07-053373-2",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 06:57:01 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Gupta:1996:AAG
author: S. Gupta and J. Rajski and J. Tyszer
title: Arithmetic additive generators of pseudo-exhaustive test patterns
journal: j-IEEE-TRANS-COMPUT
volume: 45
number: 8
pages: 939--949
month: aug
monthnumber: 8
year: 1996
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.536236
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 19:47:13 MDT 2011
bibtimestamp: 2011.07.06 19:47:13 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=536236
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: S. Gupta and J. Rajski and J. Tyszer
rawtitle: Arithmetic additive generators of pseudo-exhaustive test patterns
entry:
@Article{Gupta:1996:AAG,
  author =       "S. Gupta and J. Rajski and J. Tyszer",
  title =        "Arithmetic additive generators of pseudo-exhaustive
                 test patterns",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "45",
  number =       "8",
  pages =        "939--949",
  month =        aug,
  year =         "1996",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.536236",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 19:47:13 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=536236",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Guyot:1996:STD
author: A. Guyot and M. Renaudin and B. El Hassan and V. Levering
booktitle: Proceedings of the Ninth International Conference on VLSI Design, 1996
title: Self timed division and square-root extraction
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 376--381
year: 1996
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: A. Guyot and M. Renaudin and B. El Hassan and V. Levering
rawbooktitle: Proceedings of the Ninth International Conference on {VLSI} Design, 1996
rawtitle: Self timed division and square-root extraction
entry:
@InProceedings{Guyot:1996:STD,
  author =       "A. Guyot and M. Renaudin and B. El Hassan and V.
                 Levering",
  booktitle =    "Proceedings of the Ninth International Conference on
                 {VLSI} Design, 1996",
  title =        "Self timed division and square-root extraction",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "376--381",
  year =         "1996",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "This paper describes a self-timed integrated circuit
                 for division and square-root extraction. First it
                 concentrates on the development and the proof of a new
                 mathematical algorithm. Then the design methodology and
                 the architecture of a self-timed \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Haller:1996:AFP
author: G. M. Haller and D. R. Freytag
journal: j-IEEE-TRANS-NUCL-SCI
volume: 43
number: 3
pages: 1610--1614
month: jun
monthnumber: 6
year: 1996
CODEN: IRNSAM
ISSN: 0018-9499 (print), 1558-1578 (electronic) OR 00189499 (print), 15581578 (electronic)
ISSNL: 0018-9499 OR 00189499
bibdate: Sat Jul 16 08:40:52 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:52 MDT
fjournal: IEEE Transactions on Nuclear Science
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=23
rawauthor: G. M. Haller and D. R. Freytag
title:
Analog floating-point BiCMOS sampling chip and architecture of the BaBar CsI calorimeter front-end electronics system at the SLAC B-factory

rawtitle:
Analog floating-point {BiCMOS} sampling chip and architecture of the {BaBar CsI} calorimeter front-end electronics system at the {SLAC} {B}-factory

entry:
@Article{Haller:1996:AFP,
  author =       "G. M. Haller and D. R. Freytag",
  title =        "Analog floating-point {BiCMOS} sampling chip and
                 architecture of the {BaBar CsI} calorimeter front-end
                 electronics system at the {SLAC} {B}-factory",
  journal =      j-IEEE-TRANS-NUCL-SCI,
  volume =       "43",
  number =       "3",
  pages =        "1610--1614",
  month =        jun,
  year =         "1996",
  CODEN =        "IRNSAM",
  ISSN =         "0018-9499 (print), 1558-1578 (electronic)",
  ISSN-L =       "0018-9499",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Nuclear Science",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=23",
  summary =      "The design and implementation of an analog
                 floating-point sampling integrated circuit for the
                 BaBar detector at the SLAC B-Factory is described. The
                 CARE (Custom Auto-Range Encoding) circuit is part of an
                 18-bit dynamic range sampling system with a \ldots{}",
}


bibtype: book
filename: fparith.bib
label: Hamacher:1996:CO
author: V. Carl Hamacher and Zvonko G. Vranesic and Safwat G. Zaky
title: Computer organization
publisher: pub-MCGRAW-HILL
address: pub-MCGRAW-HILL:adr
edition: Fourth
pages: xix + 555
year: 1996
ISBN: 0-07-025883-X OR 007025883X
ISBN13: 978-0-07-025883-9 OR 9780070258839
LCCN: QA76.9.C643 H36 1996
bibdate: Sat May 18 14:24:11 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.18 14:24:11 ???
series: McGraw-Hill series in computer organization and architecture
acknowledgement: ack-nhfb
rawauthor: V. Carl Hamacher and Zvonko G. Vranesic and Safwat G. Zaky
rawtitle: Computer organization
entry:
@Book{Hamacher:1996:CO,
  author =       "V. Carl Hamacher and Zvonko G. Vranesic and Safwat G.
                 Zaky",
  title =        "Computer organization",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  edition =      "Fourth",
  pages =        "xix + 555",
  year =         "1996",
  ISBN =         "0-07-025883-X",
  ISBN-13 =      "978-0-07-025883-9",
  LCCN =         "QA76.9.C643 H36 1996",
  bibdate =      "Sat May 18 14:24:11 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "McGraw-Hill series in computer organization and
                 architecture",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Hartwig:1996:RNA
author: F. Hartwig and A. Lacroix
title: Roundoff noise analysis on the basis of an improved floating point error model
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 133--136
year: 1996
bibdate: Sat Jul 16 11:25:07 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:07 MDT
acknowledgement: ack-nhfb
rawauthor: F. Hartwig and A. Lacroix
rawtitle: Roundoff noise analysis on the basis of an improved floating point error model
booktitle:
IEEE International Symposium on Circuits and Systems: ISCAS '96, `Connecting the World', 12--15 May 1996

rawbooktitle:
{IEEE} International Symposium on Circuits and Systems: {ISCAS '96}, `Connecting the World', 12--15 May 1996

entry:
@InProceedings{Hartwig:1996:RNA,
  author =       "F. Hartwig and A. Lacroix",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems: {ISCAS '96}, `Connecting the World', 12--15
                 May 1996",
  title =        "Roundoff noise analysis on the basis of an improved
                 floating point error model",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "133--136",
  year =         "1996",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:07 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Until now floating point roundoff analysis utilized
                 the assumption of statistical decorrelation between
                 roundoff error and internal signals subject to a signal
                 flow graph. A quantization within a signal flow graph
                 has been treated like a single \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Hauser:1996:HFE
author: John R. Hauser
title: Handling floating-point exceptions in numeric programs
journal: j-TOPLAS
volume: 18
number: 2
pages: 139--174
month: mar
monthnumber: 3
year: 1996
CODEN: ATPSDT
DOI: https://doi.org/10.1145/227699.227701
ISSN: 0164-0925 (print), 1558-4593 (electronic) OR 01640925 (print), 15584593 (electronic)
ISSNL: 0164-0925 OR 01640925
bibdate: Tue Aug 13 11:46:35 MDT 1996
bibsource: http://www.acm.org/pubs/toc/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.08.13 11:46:35 MDT
URL: http://www.acm.org/pubs/toc/Abstracts/0164-0925/227701.html
fjournal: ACM Transactions on Programming Languages and Systems
keywords: accurate floating-point summation; algorithms; design; languages; performance; standardization
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J783
rawauthor: John R. Hauser
rawtitle: Handling floating-point exceptions in numeric programs
abstract:
There are a number of schemes for handling arithmetic exceptions that can be used to improve the speed (or alternatively the reliability) of numeric code. Overflow and underflow are the most troublesome exceptions, and depending on the context in which the exception can occur, they may be addressed either: (1) through a ``brute force'' reevaluation with extended range, (2) by reevaluating using a technique known as em scaling, (3) by substituting an infinity or zero, or (4) in the case of underflow, with gradual underflow. In the first two of these cases, the offending computation is simply reevaluated using a safer but slower method. The latter two cases are cheaper, more automated schemes that ideally are built in as options within the computer system. Other arithmetic exceptions can be handled with similar methods. These and some other techniques are examined with an eye toward determining the support programming languages and computer systems ought to provide for floating-point exception handling. It is argued that the cheapest short-term solution would be to give full support to most of the em required (as opposed to recommended) special features of the IEC/IEEE Standard for Binary Floating-Point Arithmetic. An essential part of this support would include standardized access from high-level languages to the exception flags defined by the standard. Some possibilities outside the IEEE Standard are also considered, and a few thought on possible better-structured support within programming languages are discussed.

subject:
bf D.3.3: Software, PROGRAMMING LANGUAGES, Language Constructs and Features, Control structures. bf D.3.0: Software, PROGRAMMING LANGUAGES, General, Standards. bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic. bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms.

rawabstract:
There are a number of schemes for handling arithmetic exceptions that can be used to improve the speed (or alternatively the reliability) of numeric code. Overflow and underflow are the most troublesome exceptions, and depending on the context in which the exception can occur, they may be addressed either: (1) through a ``brute force'' reevaluation with extended range, (2) by reevaluating using a technique known as {\em scaling}, (3) by substituting an infinity or zero, or (4) in the case of underflow, with gradual underflow. In the first two of these cases, the offending computation is simply reevaluated using a safer but slower method. The latter two cases are cheaper, more automated schemes that ideally are built in as options within the computer system. Other arithmetic exceptions can be handled with similar methods. These and some other techniques are examined with an eye toward determining the support programming languages and computer systems ought to provide for floating-point exception handling. It is argued that the cheapest short-term solution would be to give full support to most of the {\em required\/} (as opposed to recommended) special features of the IEC/IEEE Standard for Binary Floating-Point Arithmetic. An essential part of this support would include standardized access from high-level languages to the exception flags defined by the standard. Some possibilities outside the IEEE Standard are also considered, and a few thought on possible better-structured support within programming languages are discussed.

entry:
@Article{Hauser:1996:HFE,
  author =       "John R. Hauser",
  title =        "Handling floating-point exceptions in numeric
                 programs",
  journal =      j-TOPLAS,
  volume =       "18",
  number =       "2",
  pages =        "139--174",
  month =        mar,
  year =         "1996",
  CODEN =        "ATPSDT",
  DOI =          "https://doi.org/10.1145/227699.227701",
  ISSN =         "0164-0925 (print), 1558-4593 (electronic)",
  ISSN-L =       "0164-0925",
  bibdate =      "Tue Aug 13 11:46:35 MDT 1996",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/toc/Abstracts/0164-0925/227701.html",
  abstract =     "There are a number of schemes for handling arithmetic
                 exceptions that can be used to improve the speed (or
                 alternatively the reliability) of numeric code.
                 Overflow and underflow are the most troublesome
                 exceptions, and depending on the context in which the
                 exception can occur, they may be addressed either: (1)
                 through a ``brute force'' reevaluation with extended
                 range, (2) by reevaluating using a technique known as
                 {\em scaling}, (3) by substituting an infinity or zero,
                 or (4) in the case of underflow, with gradual
                 underflow. In the first two of these cases, the
                 offending computation is simply reevaluated using a
                 safer but slower method. The latter two cases are
                 cheaper, more automated schemes that ideally are built
                 in as options within the computer system. Other
                 arithmetic exceptions can be handled with similar
                 methods. These and some other techniques are examined
                 with an eye toward determining the support programming
                 languages and computer systems ought to provide for
                 floating-point exception handling. It is argued that
                 the cheapest short-term solution would be to give full
                 support to most of the {\em required\/} (as opposed to
                 recommended) special features of the IEC/IEEE Standard
                 for Binary Floating-Point Arithmetic. An essential part
                 of this support would include standardized access from
                 high-level languages to the exception flags defined by
                 the standard. Some possibilities outside the IEEE
                 Standard are also considered, and a few thought on
                 possible better-structured support within programming
                 languages are discussed.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Programming Languages and
                 Systems",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J783",
  keywords =     "accurate floating-point summation; algorithms; design;
                 languages; performance; standardization",
  subject =      "{\bf D.3.3}: Software, PROGRAMMING LANGUAGES, Language
                 Constructs and Features, Control structures. {\bf
                 D.3.0}: Software, PROGRAMMING LANGUAGES, General,
                 Standards. {\bf G.1.0}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Computer arithmetic. {\bf
                 G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS,
                 General, Numerical algorithms.",
}


bibtype: book
filename: fparith.bib
label: Heck:1996:IM
author: Andre Heck
title: Introduction to Maple
publisher: pub-SV
address: pub-SV:adr
edition: Second
pages: xx + 699
year: 1996
DOI: https://doi.org/10.1007/978-1-4684-0484-5
LCCN: QA155.7.E4H43 1993
MRclass: 65-01, 65B10, 65D18, 65Dxx, 65Fxx, 65Lxx, 68-01, 68N15, 68W30, 68NXX
MRnumber: MR1405611 (97c:68076)
bibdate: Tue Jun 06 17:57:02 1995
bibtimestamp: 1995.06.06 17:57:02 ???
acknowledgement: ack-nhfb
rawauthor: Andr{\'e} Heck
rawtitle: Introduction to {Maple}
ISBN:
0-387-94535-0 (hardcover), 1-4684-0484-9, 1-4684-0486-5 OR 0387945350 (hardcover), 1468404849, 1468404865

ISBN13:
978-0-387-94535-4 (hardcover), 978-1-4684-0484-5, 978-1-4684-0486-9 OR 9780387945354 (hardcover), 9781468404845, 9781468404869

bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/maple-extract.bib; https://www.math.utah.edu/pub/tex/bib/master.bib

abstract:
The first edition of this book has been very well received by the community. The new version 4 of Maple V contains so many new mathematical features and improvements in the user interface that Waterloo Maple Inc. markets it as ``the Power Edition.'' These two facts have made it necessary to write a second edition within a short period of the first. I corrected typographical errors, rephrased text, updated and improved many examples, and added much new material. Hardly any chapter has been left untouched. Substantially changed or added sections and chapters address the assume facility, I/O, approximation theory, integration, composite data types, simplification, graphics, differential equations, and matrix algebra. Tables summarize features, command options, etc., and constitute a quick reference. The enlarged index of the book has been carefully compiled to make locating search items quick and easy. Many new examples have been included showing how to use Maple as a problem solver, how to assist the system during computations, and how to extend its built-in facilities. About the Maple Version Used: The second edition of this book is fully revised and updated to Maple V Release 4. More precisely, the second edition of this book was produced with Maple V Release 4, beta 3 on a SUN SPARCstation 20, Model 71. There should be hardly any difference between this beta version and the final release; only minor differences in the user interface are not excluded.

TOC:
Preface to the Second Edition / v Preface to the First Edition / ix List of Tables / xix 1 Introduction to Computer Algebra / 1 1.1 What is Computer Algebra? / 1 1.2 Computer Algebra Systems / 2 1.3 Some Properties of Computer Algebra Systems / 5 1.4 Advantages of Computer Algebra / 11 1.5 Limitations of Computer Algebra / 24 1.6 Design of Maple / 30 2 The First Steps: Calculus on Numbers / 35 2.1 Getting Started / 35 2.2 Getting Help / 38 2.3 Integers and Rational Numbers / 44 2.4 Irrational Numbers and Floating-Point Numbers / 48 2.5 Algebraic Numbers / 54 2.6 Complex Numbers / 59 2.7 Exercises / 63 3 Variables and Names / 65 3.1 Assignment and Unassignment / 65 3.2 Evaluation / 73 3.3 Names of Variables / 77 3.4 Basic Data Types / 82 3.5 Attributes / 86 3.6 Properties / 87 3.7 Exercises / 92 4 Getting Around with Maple / 95 4.1 Maple Input and Output / 95 4.2 The Maple Library / 101 4.3 Reading and Writing Files / 105 4.4 Importing and Exporting Numerical Data / 110 4.5 Low-Level I/O / 113 4.6 Code Generation / 123 4.7 Changing Maple to Your Own Taste / 129 4.8 Exercises / 133 5 Polynomials and Rational Functions / 135 5.1 Univariate Polynomials / 135 5.2 Multivariate Polynomials / 140 5.3 Rational Functions / 142 5.4 Conversions / 144 5.5 Exercises / 147 6 Internal Data Representation and Substitution / 149 6.1 Internal Representation of Polynomials / 149 6.2 Generalized Rational Expressions / 155 6.3 Substitution / 158 6.4 Exercises / 170 7 Manipulation of Polynomials and Rational Expressions / 173 7.1 Expansion / 173 7.2 Factorization / 176 7.3 Canonical Form and Normal Form / 179 7.4 Normalization / 181 7.5 Collection / 183 7.6 Sorting / 186 7.7 Exercises / 186 8 Functions / 189 8.1 Mathematical Functions / 189 8.2 Arrow Operators / 193 8.3 Piecewise Defined Functions / 195 8.4 Maple Procedures / 202 8.5 Recursive Procedure Definitions / 204 8.6 unapply / 209 8.7 Operations on Functions / 210 8.8 Anonymous Functions / 211 8.9 Exercises / 212 9 Differentiation / 213 9.1 Symbolic Differentiation / 213 9.2 Automatic Differentiation / 221 9.3 Exercises / 224 10 Integration and Summation / 227 10.1 Indefinite Integration / 227 10.2 Definite Integration / 236 10.3 Numerical Integration / 241 10.4 Integral Transforms / 242 10.5 Assisting Maple's Integrator / 252 10.6 Summation / 256 10.7 Exercises / 261 11 Series, Approximation, and Limits / 267 11.1 Truncated Series / 267 11.2 Approximation of Functions / 278 11.3 Power Series / 285 11.4 Limits / 288 11.5 Exercises / 291 12 Composite Data Types / 293 12.1 Sequence / 293 12.2 Set / 296 12.3 List / 298 12.4 Array / 304 12.5 Table / 310 12.6 Last Name Evaluation / 314 12.7 Function Call / 317 12.8 Conversion Between Composite Data Types / 319 12.9 Exercises / 322 13 The Assume Facility / 325 13.1 The Need for an Assume Facility / 325 13.2 Basics of assume / 329 13.3 An Algebra of Properties / 332 13.4 Implementation of assume / 335 13.5 Exercises / 340 13.6 Hierarchy of Properties / 340 14 Simplification / 343 14.1 Automatic Simplification / 344 14.2 expand / 346 14.3 combine / 353 14.4 simplify / 358 14.5 convert / 364 14.6 Trigonometrie Simplification / 367 14.7 Simplification w.r.t. Side Relations / 370 14.8 Control Over Simplification / 374 14.9 Defining Your Own Simplification Routines / 378 14.10 Exercises / 383 14.11 Simplification Chart / 385 15 Graphics / 387 15.1 Some Basic Two-Dimensional Plots / 389 15.2 Options of plot / 393 15.3 The Structure of Two-Dimensional Graphics / 406 15.4 The plottools Package / 412 15.5 Special Two-Dimensional Plots / 416 15.6 Two-Dimensional Geometry / 429 15.7 Plot Aliasing / 432 15.8 A Common Mistake / 433 15.9 Some Basic Three-Dimensional Plots / 434 15.10 Options of plot3d / 436 15.11 The Structure of Three-Dimensional Graphics / 444 15.12 Special Three-Dimensional Plots / 449 15.13 Data Plotting / 457 15.14 Animation / 467 15.15 List of Plot Options / 469 15.16 Exercises / 475 16 Solving Equations / 479 16.1 Equations in One Unknown / 479 16.2 Abbreviations in solve / 480 16.3 Some Difficulties / 481 16.4 Systems of Equations / 488 16.5 The Grobner Basis Method / 499 16.6 Inequalities / 505 16.7 Numerical Solvers / 507 16.8 Other Solvers in Maple / 509 16.9 Exercises / 515 17 Differential Equations / 519 17.1 First Glance at ODEs / 519 17.2 Analytic Solutions / 520 17.3 Taylor Series Method / 532 17.4 Power Series Method / 534 17.5 Numerical Solutions / 536 17.6 DEtools / 548 17.7 Perturbation Methods / 555 17.8 Partial Differential Equations / 567 17.9 Lie Point Symmetries of PDEs / 569 17.10 Exercises / 572 18 Linear Algebra: The linaig Package / 575 18.1 Loading the linaig Package / 575 18.2 Creating New Vectors and Matrices / 576 18.3 Vector and Matrix Arithmetic / 580 18.4 Basic Matrix Functions / 584 18.5 Structural Operations / 589 18.6 Vector Operations / 592 18.7 Standard Forms of Matrices / 592 18.8 Exercises / 597 19 Linear Algebra: Applications / 601 19.1 Kinematics of the Stanford Manipulator / 601 19.2 A Three-Compartment Model of Cadmium Transfer / 606 19.3 Molecular-Orbital Huckel Theory / 618 19.4 Vector Analysis / 623 19.5 Moore--Penrose Inverse / 631 19.6 Exercises / 633 References / 635 Index / 651

rawabstract:
The first edition of this book has been very well received by the community. The new version 4 of Maple V contains so many new mathematical features and improvements in the user interface that Waterloo Maple Inc. markets it as ``the Power Edition.'' These two facts have made it necessary to write a second edition within a short period of the first. I corrected typographical errors, rephrased text, updated and improved many examples, and added much new material. Hardly any chapter has been left untouched. Substantially changed or added sections and chapters address the assume facility, I/O, approximation theory, integration, composite data types, simplification, graphics, differential equations, and matrix algebra. Tables summarize features, command options, etc., and constitute a quick reference. The enlarged index of the book has been carefully compiled to make locating search items quick and easy. Many new examples have been included showing how to use Maple as a problem solver, how to assist the system during computations, and how to extend its built-in facilities. About the Maple Version Used: The second edition of this book is fully revised and updated to Maple V Release 4. More precisely, the second edition of this book was produced with Maple V Release 4, beta 3 on a SUN SPARCstation 20, Model 71. There should be hardly any difference between this beta version and the final release; only minor differences in the user interface are not excluded.

rawTOC:
Preface to the Second Edition / v \\ Preface to the First Edition / ix \\ List of Tables / xix \\ 1 Introduction to Computer Algebra / 1 \\ 1.1 What is Computer Algebra? / 1 \\ 1.2 Computer Algebra Systems / 2 \\ 1.3 Some Properties of Computer Algebra Systems / 5 \\ 1.4 Advantages of Computer Algebra / 11 \\ 1.5 Limitations of Computer Algebra / 24 \\ 1.6 Design of Maple / 30 \\ 2 The First Steps: Calculus on Numbers / 35 \\ 2.1 Getting Started / 35 \\ 2.2 Getting Help / 38 \\ 2.3 Integers and Rational Numbers / 44 \\ 2.4 Irrational Numbers and Floating-Point Numbers / 48 \\ 2.5 Algebraic Numbers / 54 \\ 2.6 Complex Numbers / 59 \\ 2.7 Exercises / 63 \\ 3 Variables and Names / 65 \\ 3.1 Assignment and Unassignment / 65 \\ 3.2 Evaluation / 73 \\ 3.3 Names of Variables / 77 \\ 3.4 Basic Data Types / 82 \\ 3.5 Attributes / 86 \\ 3.6 Properties / 87 \\ 3.7 Exercises / 92 \\ 4 Getting Around with Maple / 95 \\ 4.1 Maple Input and Output / 95 \\ 4.2 The Maple Library / 101 \\ 4.3 Reading and Writing Files / 105 \\ 4.4 Importing and Exporting Numerical Data / 110 \\ 4.5 Low-Level I/O / 113 \\ 4.6 Code Generation / 123 \\ 4.7 Changing Maple to Your Own Taste / 129 \\ 4.8 Exercises / 133 \\ 5 Polynomials and Rational Functions / 135 \\ 5.1 Univariate Polynomials / 135 \\ 5.2 Multivariate Polynomials / 140 \\ 5.3 Rational Functions / 142 \\ 5.4 Conversions / 144 \\ 5.5 Exercises / 147 \\ 6 Internal Data Representation and Substitution / 149 \\ 6.1 Internal Representation of Polynomials / 149 \\ 6.2 Generalized Rational Expressions / 155 \\ 6.3 Substitution / 158 \\ 6.4 Exercises / 170 \\ 7 Manipulation of Polynomials and Rational Expressions / 173 \\ 7.1 Expansion / 173 \\ 7.2 Factorization / 176 \\ 7.3 Canonical Form and Normal Form / 179 \\ 7.4 Normalization / 181 \\ 7.5 Collection / 183 \\ 7.6 Sorting / 186 \\ 7.7 Exercises / 186 \\ 8 Functions / 189 \\ 8.1 Mathematical Functions / 189 \\ 8.2 Arrow Operators / 193 \\ 8.3 Piecewise Defined Functions / 195 \\ 8.4 Maple Procedures / 202 \\ 8.5 Recursive Procedure Definitions / 204 \\ 8.6 unapply / 209 \\ 8.7 Operations on Functions / 210 \\ 8.8 Anonymous Functions / 211 \\ 8.9 Exercises / 212 \\ 9 Differentiation / 213 \\ 9.1 Symbolic Differentiation / 213 \\ 9.2 Automatic Differentiation / 221 \\ 9.3 Exercises / 224 \\ 10 Integration and Summation / 227 \\ 10.1 Indefinite Integration / 227 \\ 10.2 Definite Integration / 236 \\ 10.3 Numerical Integration / 241 \\ 10.4 Integral Transforms / 242 \\ 10.5 Assisting Maple's Integrator / 252 \\ 10.6 Summation / 256 \\ 10.7 Exercises / 261 \\ 11 Series, Approximation, and Limits / 267 \\ 11.1 Truncated Series / 267 \\ 11.2 Approximation of Functions / 278 \\ 11.3 Power Series / 285 \\ 11.4 Limits / 288 \\ 11.5 Exercises / 291 \\ 12 Composite Data Types / 293 \\ 12.1 Sequence / 293 \\ 12.2 Set / 296 \\ 12.3 List / 298 \\ 12.4 Array / 304 \\ 12.5 Table / 310 \\ 12.6 Last Name Evaluation / 314 \\ 12.7 Function Call / 317 \\ 12.8 Conversion Between Composite Data Types / 319 \\ 12.9 Exercises / 322 \\ 13 The Assume Facility / 325 \\ 13.1 The Need for an Assume Facility / 325 \\ 13.2 Basics of assume / 329 \\ 13.3 An Algebra of Properties / 332 \\ 13.4 Implementation of assume / 335 \\ 13.5 Exercises / 340 \\ 13.6 Hierarchy of Properties / 340 \\ 14 Simplification / 343 \\ 14.1 Automatic Simplification / 344 \\ 14.2 expand / 346 \\ 14.3 combine / 353 \\ 14.4 simplify / 358 \\ 14.5 convert / 364 \\ 14.6 Trigonometrie Simplification / 367 \\ 14.7 Simplification w.r.t. Side Relations / 370 \\ 14.8 Control Over Simplification / 374 \\ 14.9 Defining Your Own Simplification Routines / 378 \\ 14.10 Exercises / 383 \\ 14.11 Simplification Chart / 385 \\ 15 Graphics / 387 \\ 15.1 Some Basic Two-Dimensional Plots / 389 \\ 15.2 Options of plot / 393 \\ 15.3 The Structure of Two-Dimensional Graphics / 406 \\ 15.4 The plottools Package / 412 \\ 15.5 Special Two-Dimensional Plots / 416 \\ 15.6 Two-Dimensional Geometry / 429 \\ 15.7 Plot Aliasing / 432 \\ 15.8 A Common Mistake / 433 \\ 15.9 Some Basic Three-Dimensional Plots / 434 \\ 15.10 Options of plot3d / 436 \\ 15.11 The Structure of Three-Dimensional Graphics / 444 \\ 15.12 Special Three-Dimensional Plots / 449 \\ 15.13 Data Plotting / 457 \\ 15.14 Animation / 467 \\ 15.15 List of Plot Options / 469 \\ 15.16 Exercises / 475 \\ 16 Solving Equations / 479 \\ 16.1 Equations in One Unknown / 479 \\ 16.2 Abbreviations in solve / 480 \\ 16.3 Some Difficulties / 481 \\ 16.4 Systems of Equations / 488 \\ 16.5 The Gr{\"o}bner Basis Method / 499 \\ 16.6 Inequalities / 505 \\ 16.7 Numerical Solvers / 507 \\ 16.8 Other Solvers in Maple / 509 \\ 16.9 Exercises / 515 \\ 17 Differential Equations / 519 \\ 17.1 First Glance at ODEs / 519 \\ 17.2 Analytic Solutions / 520 \\ 17.3 Taylor Series Method / 532 \\ 17.4 Power Series Method / 534 \\ 17.5 Numerical Solutions / 536 \\ 17.6 DEtools / 548 \\ 17.7 Perturbation Methods / 555 \\ 17.8 Partial Differential Equations / 567 \\ 17.9 Lie Point Symmetries of PDEs / 569 \\ 17.10 Exercises / 572 \\ 18 Linear Algebra: The linaig Package / 575 \\ 18.1 Loading the linaig Package / 575 \\ 18.2 Creating New Vectors and Matrices / 576 \\ 18.3 Vector and Matrix Arithmetic / 580 \\ 18.4 Basic Matrix Functions / 584 \\ 18.5 Structural Operations / 589 \\ 18.6 Vector Operations / 592 \\ 18.7 Standard Forms of Matrices / 592 \\ 18.8 Exercises / 597 \\ 19 Linear Algebra: Applications / 601 \\ 19.1 Kinematics of the Stanford Manipulator / 601 \\ 19.2 A Three-Compartment Model of Cadmium Transfer / 606 \\ 19.3 Molecular-Orbital H{\"u}ckel Theory / 618 \\ 19.4 Vector Analysis / 623 \\ 19.5 Moore--Penrose Inverse / 631 \\ 19.6 Exercises / 633 \\ References / 635 \\ Index / 651

entry:
@Book{Heck:1996:IM,
  author =       "Andr{\'e} Heck",
  title =        "Introduction to {Maple}",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Second",
  pages =        "xx + 699",
  year =         "1996",
  DOI =          "https://doi.org/10.1007/978-1-4684-0484-5",
  ISBN =         "0-387-94535-0 (hardcover), 1-4684-0484-9,
                 1-4684-0486-5",
  ISBN-13 =      "978-0-387-94535-4 (hardcover), 978-1-4684-0484-5,
                 978-1-4684-0486-9",
  LCCN =         "QA155.7.E4H43 1993",
  MRclass =      "65-01, 65B10, 65D18, 65Dxx, 65Fxx, 65Lxx, 68-01,
                 68N15, 68W30, 68NXX",
  MRnumber =     "MR1405611 (97c:68076)",
  bibdate =      "Tue Jun 06 17:57:02 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  price =        "US\$39.00",
  abstract =     "The first edition of this book has been very well
                 received by the community. The new version 4 of Maple V
                 contains so many new mathematical features and
                 improvements in the user interface that Waterloo Maple
                 Inc. markets it as ``the Power Edition.'' These two
                 facts have made it necessary to write a second edition
                 within a short period of the first. I corrected
                 typographical errors, rephrased text, updated and
                 improved many examples, and added much new material.
                 Hardly any chapter has been left untouched.
                 Substantially changed or added sections and chapters
                 address the assume facility, I/O, approximation theory,
                 integration, composite data types, simplification,
                 graphics, differential equations, and matrix algebra.
                 Tables summarize features, command options, etc., and
                 constitute a quick reference. The enlarged index of the
                 book has been carefully compiled to make locating
                 search items quick and easy. Many new examples have
                 been included showing how to use Maple as a problem
                 solver, how to assist the system during computations,
                 and how to extend its built-in facilities. About the
                 Maple Version Used: The second edition of this book is
                 fully revised and updated to Maple V Release 4. More
                 precisely, the second edition of this book was produced
                 with Maple V Release 4, beta 3 on a SUN SPARCstation
                 20, Model 71. There should be hardly any difference
                 between this beta version and the final release; only
                 minor differences in the user interface are not
                 excluded.",
  acknowledgement = ack-nhfb,
  tableofcontents = "Preface to the Second Edition / v \\
                 Preface to the First Edition / ix \\
                 List of Tables / xix \\
                 1 Introduction to Computer Algebra / 1 \\
                 1.1 What is Computer Algebra? / 1 \\
                 1.2 Computer Algebra Systems / 2 \\
                 1.3 Some Properties of Computer Algebra Systems / 5 \\
                 1.4 Advantages of Computer Algebra / 11 \\
                 1.5 Limitations of Computer Algebra / 24 \\
                 1.6 Design of Maple / 30 \\
                 2 The First Steps: Calculus on Numbers / 35 \\
                 2.1 Getting Started / 35 \\
                 2.2 Getting Help / 38 \\
                 2.3 Integers and Rational Numbers / 44 \\
                 2.4 Irrational Numbers and Floating-Point Numbers / 48
                 \\
                 2.5 Algebraic Numbers / 54 \\
                 2.6 Complex Numbers / 59 \\
                 2.7 Exercises / 63 \\
                 3 Variables and Names / 65 \\
                 3.1 Assignment and Unassignment / 65 \\
                 3.2 Evaluation / 73 \\
                 3.3 Names of Variables / 77 \\
                 3.4 Basic Data Types / 82 \\
                 3.5 Attributes / 86 \\
                 3.6 Properties / 87 \\
                 3.7 Exercises / 92 \\
                 4 Getting Around with Maple / 95 \\
                 4.1 Maple Input and Output / 95 \\
                 4.2 The Maple Library / 101 \\
                 4.3 Reading and Writing Files / 105 \\
                 4.4 Importing and Exporting Numerical Data / 110 \\
                 4.5 Low-Level I/O / 113 \\
                 4.6 Code Generation / 123 \\
                 4.7 Changing Maple to Your Own Taste / 129 \\
                 4.8 Exercises / 133 \\
                 5 Polynomials and Rational Functions / 135 \\
                 5.1 Univariate Polynomials / 135 \\
                 5.2 Multivariate Polynomials / 140 \\
                 5.3 Rational Functions / 142 \\
                 5.4 Conversions / 144 \\
                 5.5 Exercises / 147 \\
                 6 Internal Data Representation and Substitution / 149
                 \\
                 6.1 Internal Representation of Polynomials / 149 \\
                 6.2 Generalized Rational Expressions / 155 \\
                 6.3 Substitution / 158 \\
                 6.4 Exercises / 170 \\
                 7 Manipulation of Polynomials and Rational Expressions
                 / 173 \\
                 7.1 Expansion / 173 \\
                 7.2 Factorization / 176 \\
                 7.3 Canonical Form and Normal Form / 179 \\
                 7.4 Normalization / 181 \\
                 7.5 Collection / 183 \\
                 7.6 Sorting / 186 \\
                 7.7 Exercises / 186 \\
                 8 Functions / 189 \\
                 8.1 Mathematical Functions / 189 \\
                 8.2 Arrow Operators / 193 \\
                 8.3 Piecewise Defined Functions / 195 \\
                 8.4 Maple Procedures / 202 \\
                 8.5 Recursive Procedure Definitions / 204 \\
                 8.6 unapply / 209 \\
                 8.7 Operations on Functions / 210 \\
                 8.8 Anonymous Functions / 211 \\
                 8.9 Exercises / 212 \\
                 9 Differentiation / 213 \\
                 9.1 Symbolic Differentiation / 213 \\
                 9.2 Automatic Differentiation / 221 \\
                 9.3 Exercises / 224 \\
                 10 Integration and Summation / 227 \\
                 10.1 Indefinite Integration / 227 \\
                 10.2 Definite Integration / 236 \\
                 10.3 Numerical Integration / 241 \\
                 10.4 Integral Transforms / 242 \\
                 10.5 Assisting Maple's Integrator / 252 \\
                 10.6 Summation / 256 \\
                 10.7 Exercises / 261 \\
                 11 Series, Approximation, and Limits / 267 \\
                 11.1 Truncated Series / 267 \\
                 11.2 Approximation of Functions / 278 \\
                 11.3 Power Series / 285 \\
                 11.4 Limits / 288 \\
                 11.5 Exercises / 291 \\
                 12 Composite Data Types / 293 \\
                 12.1 Sequence / 293 \\
                 12.2 Set / 296 \\
                 12.3 List / 298 \\
                 12.4 Array / 304 \\
                 12.5 Table / 310 \\
                 12.6 Last Name Evaluation / 314 \\
                 12.7 Function Call / 317 \\
                 12.8 Conversion Between Composite Data Types / 319 \\
                 12.9 Exercises / 322 \\
                 13 The Assume Facility / 325 \\
                 13.1 The Need for an Assume Facility / 325 \\
                 13.2 Basics of assume / 329 \\
                 13.3 An Algebra of Properties / 332 \\
                 13.4 Implementation of assume / 335 \\
                 13.5 Exercises / 340 \\
                 13.6 Hierarchy of Properties / 340 \\
                 14 Simplification / 343 \\
                 14.1 Automatic Simplification / 344 \\
                 14.2 expand / 346 \\
                 14.3 combine / 353 \\
                 14.4 simplify / 358 \\
                 14.5 convert / 364 \\
                 14.6 Trigonometrie Simplification / 367 \\
                 14.7 Simplification w.r.t. Side Relations / 370 \\
                 14.8 Control Over Simplification / 374 \\
                 14.9 Defining Your Own Simplification Routines / 378
                 \\
                 14.10 Exercises / 383 \\
                 14.11 Simplification Chart / 385 \\
                 15 Graphics / 387 \\
                 15.1 Some Basic Two-Dimensional Plots / 389 \\
                 15.2 Options of plot / 393 \\
                 15.3 The Structure of Two-Dimensional Graphics / 406
                 \\
                 15.4 The plottools Package / 412 \\
                 15.5 Special Two-Dimensional Plots / 416 \\
                 15.6 Two-Dimensional Geometry / 429 \\
                 15.7 Plot Aliasing / 432 \\
                 15.8 A Common Mistake / 433 \\
                 15.9 Some Basic Three-Dimensional Plots / 434 \\
                 15.10 Options of plot3d / 436 \\
                 15.11 The Structure of Three-Dimensional Graphics / 444
                 \\
                 15.12 Special Three-Dimensional Plots / 449 \\
                 15.13 Data Plotting / 457 \\
                 15.14 Animation / 467 \\
                 15.15 List of Plot Options / 469 \\
                 15.16 Exercises / 475 \\
                 16 Solving Equations / 479 \\
                 16.1 Equations in One Unknown / 479 \\
                 16.2 Abbreviations in solve / 480 \\
                 16.3 Some Difficulties / 481 \\
                 16.4 Systems of Equations / 488 \\
                 16.5 The Gr{\"o}bner Basis Method / 499 \\
                 16.6 Inequalities / 505 \\
                 16.7 Numerical Solvers / 507 \\
                 16.8 Other Solvers in Maple / 509 \\
                 16.9 Exercises / 515 \\
                 17 Differential Equations / 519 \\
                 17.1 First Glance at ODEs / 519 \\
                 17.2 Analytic Solutions / 520 \\
                 17.3 Taylor Series Method / 532 \\
                 17.4 Power Series Method / 534 \\
                 17.5 Numerical Solutions / 536 \\
                 17.6 DEtools / 548 \\
                 17.7 Perturbation Methods / 555 \\
                 17.8 Partial Differential Equations / 567 \\
                 17.9 Lie Point Symmetries of PDEs / 569 \\
                 17.10 Exercises / 572 \\
                 18 Linear Algebra: The linaig Package / 575 \\
                 18.1 Loading the linaig Package / 575 \\
                 18.2 Creating New Vectors and Matrices / 576 \\
                 18.3 Vector and Matrix Arithmetic / 580 \\
                 18.4 Basic Matrix Functions / 584 \\
                 18.5 Structural Operations / 589 \\
                 18.6 Vector Operations / 592 \\
                 18.7 Standard Forms of Matrices / 592 \\
                 18.8 Exercises / 597 \\
                 19 Linear Algebra: Applications / 601 \\
                 19.1 Kinematics of the Stanford Manipulator / 601 \\
                 19.2 A Three-Compartment Model of Cadmium Transfer /
                 606 \\
                 19.3 Molecular-Orbital H{\"u}ckel Theory / 618 \\
                 19.4 Vector Analysis / 623 \\
                 19.5 Moore--Penrose Inverse / 631 \\
                 19.6 Exercises / 633 \\
                 References / 635 \\
                 Index / 651",
}


bibtype: article
filename: fparith.bib
label: Hecker:1996:LGF
author: Chris Hecker
title: Let's get to the (floating) point
journal: Game Developer
volume: 2
pages: 19--24
month: feb
monthnumber: 2
year: 1996
ISSN: 1073-922X OR 1073922X
bibdate: Fri Jan 06 07:46:23 2006
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2006.01.06 07:46:23 ???
note: accurate floating-point summation; splitting of floating-point numbers into high and low parts
acknowledgement: ack-nhfb
rawauthor: Chris Hecker
rawnote: accurate floating-point summation; splitting of floating-point numbers into high and low parts
rawtitle: Let's get to the (floating) point
URL:
http://chrishecker.com/images/f/fb/Gdmfp.pdf; https://www.gamasutra.com/php-bin/store.php?item_id=220&category=22&book=

entry:
@Article{Hecker:1996:LGF,
  author =       "Chris Hecker",
  title =        "Let's get to the (floating) point",
  journal =      "Game Developer",
  volume =       "2",
  number =       "??",
  pages =        "19--24",
  month =        feb # "\slash " # mar,
  year =         "1996",
  ISSN =         "1073-922X",
  bibdate =      "Fri Jan 06 07:46:23 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "accurate floating-point summation; splitting of
                 floating-point numbers into high and low parts",
  URL =          "http://chrishecker.com/images/f/fb/Gdmfp.pdf;
                 https://www.gamasutra.com/php-bin/store.php?item_id=220&category=22&book=",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Heikes:1996:DFP
author: Craig Heikes and Glenn Colon-Bonet
title: A Dual Floating Point Coprocessor with an FMAC Architecture
crossref: Wuorinen:1996:DTP
pages: 354--355
year: 1996
bibdate: Fri Jun 24 10:49:14 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.06.24 10:49:14 ???
acknowledgement: ack-nhfb
rawauthor: Craig Heikes and Glenn Colon-Bonet
rawtitle: A Dual Floating Point Coprocessor with an {FMAC} Architecture
entry:
@InProceedings{Heikes:1996:DFP,
  author =       "Craig Heikes and Glenn Colon-Bonet",
  title =        "A Dual Floating Point Coprocessor with an {FMAC}
                 Architecture",
  crossref =     "Wuorinen:1996:DTP",
  pages =        "354--355",
  year =         "1996",
  bibdate =      "Fri Jun 24 10:49:14 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Heindl:1996:MVC
author: G. Heindl
crossref: Alefeld:1996:SCV
pages: 207--213
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: G. Heindl
title:
A Method for Verified Computing of Inner and Outer Approximations of the Interval Hull of a Tolerance Polyhedron

rawtitle:
A Method for Verified Computing of Inner and Outer Approximations of the Interval Hull of a Tolerance Polyhedron

entry:
@InProceedings{Heindl:1996:MVC,
  author =       "G. Heindl",
  title =        "A Method for Verified Computing of Inner and Outer
                 Approximations of the Interval Hull of a Tolerance
                 Polyhedron",
  crossref =     "Alefeld:1996:SCV",
  pages =        "207--213",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Heinrich:1996:AAF
author: Peter Heinrich
title: Algorithm Alley: a Fast Integer Square Root
journal: j-DDJ
volume: 21
number: 4
pages: 113--114, 130
month: apr
monthnumber: 4
year: 1996
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: Peter Heinrich
rawtitle: Algorithm Alley: a Fast Integer Square Root
entry:
@Article{Heinrich:1996:AAF,
  author =       "Peter Heinrich",
  title =        "Algorithm Alley: a Fast Integer Square Root",
  journal =      j-DDJ,
  volume =       "21",
  number =       "4",
  pages =        "113--114, 130",
  month =        apr,
  year =         "1996",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Mon Sep 2 09:09:39 MDT 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}


bibtype: inproceedings
filename: fparith.bib
label: Herzberger:1996:OCC
author: J. Herzberger
crossref: Alefeld:1996:SCV
pages: 154--159
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: J. Herzberger
title:
On the $R$-Order of Convergence of a Class of Simultaneous Methods for the Inclusions of Polynomial Roots

rawtitle:
On the {$R$}-Order of Convergence of a Class of Simultaneous Methods for the Inclusions of Polynomial Roots

entry:
@InProceedings{Herzberger:1996:OCC,
  author =       "J. Herzberger",
  title =        "On the {$R$}-Order of Convergence of a Class of
                 Simultaneous Methods for the Inclusions of Polynomial
                 Roots",
  crossref =     "Alefeld:1996:SCV",
  pages =        "154--159",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: fparith.bib
label: Hickey:1996:FSP
author: Timothy J. Hickey and Qun Ju
title: Fast, Sound, and Precise Narrowing of the Exponential Function
type: Technical report
institution: Computer Science Department, Brandeis University
address: Waltham, MA, USA 02254
pages: 154--159
month: mar
monthnumber: 3
year: 1996
bibdate: Sat Nov 05 15:42:23 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.11.05 15:42:23 ???
URL: http://www.cs.brandeis.edu/~tim/Papers/eiianuia.ps.gz
acknowledgement: ack-nhfb
rawauthor: Timothy J. Hickey and Qun Ju
rawtitle: Fast, Sound, and Precise Narrowing of the Exponential Function
entry:
@TechReport{Hickey:1996:FSP,
  author =       "Timothy J. Hickey and Qun Ju",
  title =        "Fast, Sound, and Precise Narrowing of the Exponential
                 Function",
  type =         "Technical report",
  institution =  "Computer Science Department, Brandeis University",
  address =      "Waltham, MA, USA 02254",
  month =        mar,
  year =         "1996",
  bibdate =      "Sat Nov 05 15:42:23 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.brandeis.edu/~tim/Papers/eiianuia.ps.gz",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: fparith.bib
label: Higham:1996:ASN
author: Nicholas J. Higham
title: Accuracy and Stability of Numerical Algorithms
publisher: pub-SIAM
address: pub-SIAM:adr
pages: xxviii + 688
year: 1996
ISBN: 0-89871-355-2 (paperback) OR 0898713552 (paperback)
ISBN13: 978-0-89871-355-8 (paperback) OR 9780898713558 (paperback)
LCCN: QA297.H53 1996
MRclass: 65Fxx, 15-04, 65-02, 65G50
bibdate: Tue Jan 30 11:01:35 1996
bibtimestamp: 1996.01.30 11:01:35 ???
URL: http://www.ma.man.ac.uk/~higham/asna.html
remark: Typeset with LaTeX 2e.
acknowledgement: ack-njh
rawauthor: Nicholas J. Higham
rawtitle: Accuracy and Stability of Numerical Algorithms
bibsource:
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TOC:
Principles of Finite Precision Computation Relative Error and Significant Digits Sources of Errors Precision Versus Accuracy Backward and Forward Errors Conditioning Cancellation Solving a Quadratic Equation Computing the Sample Variance Solving Linear Equations Accumulation of Rounding Errors Instability Without Cancellation Increasing the Precision Cancellation of Rounding Errors Rounding Errors Can Be Beneficial Stability of an Algorithm Depends on the Problem Rounding Errors Are Not Random Designing Stable Algorithms Misconceptions Rounding Errors in Numerical Analysis Floating Point Arithmetic Floating Point Number System Model of Arithmetic IEEE Arithmetic Aberrant Arithmetics Exact Subtraction Fused Multiply-Add Operation Choice of Base and Distribution of Numbers Statistical Distribution of Rounding Errors Alternative Number Systems Elementary Functions Accuracy Tests Inner and Outer Products The Purpose of Rounding Error Analysis Running Error Analysis Notation for Error Analysis Matrix Multiplication Complex Arithmetic Miscellany Error Analysis Demystified Other Approaches Summation Summation Methods Error Analysis Compensated Summation Other Summation Methods Statistical Estimates of Accuracy Choice of Method Polynomials Horner's Method Evaluating Derivatives The Newton Form and Polynomial Interpolation Matrix Polynomials Norms Vector Norms

rawTOC:
Principles of Finite Precision Computation \\ Relative Error and Significant Digits \\ Sources of Errors \\ Precision Versus Accuracy \\ Backward and Forward Errors \\ Conditioning \\ Cancellation \\ Solving a Quadratic Equation \\ Computing the Sample Variance \\ Solving Linear Equations \\ Accumulation of Rounding Errors \\ Instability Without Cancellation \\ Increasing the Precision \\ Cancellation of Rounding Errors \\ Rounding Errors Can Be Beneficial \\ Stability of an Algorithm Depends on the Problem \\ Rounding Errors Are Not Random \\ Designing Stable Algorithms \\ Misconceptions \\ Rounding Errors in Numerical Analysis \\ Floating Point Arithmetic \\ Floating Point Number System \\ Model of Arithmetic \\ IEEE Arithmetic \\ Aberrant Arithmetics \\ Exact Subtraction \\ Fused Multiply-Add Operation \\ Choice of Base and Distribution of Numbers \\ Statistical Distribution of Rounding Errors \\ Alternative Number Systems \\ Elementary Functions \\ Accuracy Tests \\ Inner and Outer Products \\ The Purpose of Rounding Error Analysis \\ Running Error Analysis \\ Notation for Error Analysis \\ Matrix Multiplication \\ Complex Arithmetic \\ Miscellany \\ Error Analysis Demystified \\ Other Approaches \\ Summation \\ Summation Methods \\ Error Analysis \\ Compensated Summation \\ Other Summation Methods \\ Statistical Estimates of Accuracy \\ Choice of Method \\ Polynomials \\ Horner's Method \\ Evaluating Derivatives \\ The Newton Form and Polynomial Interpolation \\ Matrix Polynomials \\ Norms \\ Vector Norms

entry:
@Book{Higham:1996:ASN,
  author =       "Nicholas J. Higham",
  title =        "Accuracy and Stability of Numerical Algorithms",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xxviii + 688",
  year =         "1996",
  ISBN =         "0-89871-355-2 (paperback)",
  ISBN-13 =      "978-0-89871-355-8 (paperback)",
  LCCN =         "QA297.H53 1996",
  MRclass =      "65Fxx, 15-04, 65-02, 65G50",
  bibdate =      "Tue Jan 30 11:01:35 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/texbook2.bib",
  price =        "US\$39.00",
  URL =          "http://www.ma.man.ac.uk/~higham/asna.html",
  acknowledgement = ack-njh # " and " # ack-nhfb,
  remark =       "Typeset with \LaTeX2e.",
  tableofcontents = "Principles of Finite Precision Computation \\
                 Relative Error and Significant Digits \\
                 Sources of Errors \\
                 Precision Versus Accuracy \\
                 Backward and Forward Errors \\
                 Conditioning \\
                 Cancellation \\
                 Solving a Quadratic Equation \\
                 Computing the Sample Variance \\
                 Solving Linear Equations \\
                 Accumulation of Rounding Errors \\
                 Instability Without Cancellation \\
                 Increasing the Precision \\
                 Cancellation of Rounding Errors \\
                 Rounding Errors Can Be Beneficial \\
                 Stability of an Algorithm Depends on the Problem \\
                 Rounding Errors Are Not Random \\
                 Designing Stable Algorithms \\
                 Misconceptions \\
                 Rounding Errors in Numerical Analysis \\
                 Floating Point Arithmetic \\
                 Floating Point Number System \\
                 Model of Arithmetic \\
                 IEEE Arithmetic \\
                 Aberrant Arithmetics \\
                 Exact Subtraction \\
                 Fused Multiply-Add Operation \\
                 Choice of Base and Distribution of Numbers \\
                 Statistical Distribution of Rounding Errors \\
                 Alternative Number Systems \\
                 Elementary Functions \\
                 Accuracy Tests \\
                 Inner and Outer Products \\
                 The Purpose of Rounding Error Analysis \\
                 Running Error Analysis \\
                 Notation for Error Analysis \\
                 Matrix Multiplication \\
                 Complex Arithmetic \\
                 Miscellany \\
                 Error Analysis Demystified \\
                 Other Approaches \\
                 Summation \\
                 Summation Methods \\
                 Error Analysis \\
                 Compensated Summation \\
                 Other Summation Methods \\
                 Statistical Estimates of Accuracy \\
                 Choice of Method \\
                 Polynomials \\
                 Horner's Method \\
                 Evaluating Derivatives \\
                 The Newton Form and Polynomial Interpolation \\
                 Matrix Polynomials \\
                 Norms \\
                 Vector Norms",
}


bibtype: article
filename: fparith.bib
label: Hong:1996:NMM
author: Seong-Min Hong and Sang-Yeop Oh and Hyunsoo Yoon
title: New Modular Multiplication Algorithms for Fast Modular Exponentiation
journal: j-LECT-NOTES-COMP-SCI
volume: 1070
pages: 166--??
year: 1996
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Mon Feb 4 12:02:22 MST 2002
bibtimestamp: 2002.02.04 12:02:22 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Seong-Min Hong and Sang-Yeop Oh and Hyunsoo Yoon
rawtitle: New Modular Multiplication Algorithms for Fast Modular Exponentiation
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t1070.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/1070/10700166.htm; http://link.springer-ny.com/link/service/series/0558/papers/1070/10700166.pdf

entry:
@Article{Hong:1996:NMM,
  author =       "Seong-Min Hong and Sang-Yeop Oh and Hyunsoo Yoon",
  title =        "New Modular Multiplication Algorithms for Fast Modular
                 Exponentiation",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1070",
  pages =        "166--??",
  year =         "1996",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Mon Feb 4 12:02:22 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1070.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1070/10700166.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/1070/10700166.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: inproceedings
filename: fparith.bib
label: Hyvoenen:1996:SCE
author: E. Hyvoenen and S. De Pascale
title: Shared Computations for Efficient Interval Functions Evaluation
crossref: Alefeld:1996:SCV
pages: 38--44
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: E. Hyvoenen and S. De Pascale
rawtitle: Shared Computations for Efficient Interval Functions Evaluation
entry:
@InProceedings{Hyvoenen:1996:SCE,
  author =       "E. Hyvoenen and S. De Pascale",
  title =        "Shared Computations for Efficient Interval Functions
                 Evaluation",
  crossref =     "Alefeld:1996:SCV",
  pages =        "38--44",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Inacio:1996:DDF
author: Christopher Inacio and Denise Ombres
title: The DSP decision: fixed point or floating?
journal: j-IEEE-SPECTRUM
volume: 33
number: 9
pages: 72--74
month: sep
monthnumber: 9
year: 1996
CODEN: IEESAM
DOI: https://doi.org/10.1109/6.535397
ISSN: 0018-9235 (print), 1939-9340 (electronic) OR 00189235 (print), 19399340 (electronic)
ISSNL: 0018-9235 OR 00189235
bibdate: Thu Sep 01 16:15:25 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2011.09.01 16:15:25 ???
fjournal: IEEE Spectrum
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6
rawauthor: Christopher Inacio and Denise Ombres
rawtitle: The {DSP} decision: fixed point or floating?
entry:
@Article{Inacio:1996:DDF,
  author =       "Christopher Inacio and Denise Ombres",
  title =        "The {DSP} decision: fixed point or floating?",
  journal =      j-IEEE-SPECTRUM,
  volume =       "33",
  number =       "9",
  pages =        "72--74",
  month =        sep,
  year =         "1996",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/6.535397",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Thu Sep 01 16:15:25 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
}


bibtype: article
filename: fparith.bib
label: ISO:1996:TRF
author: ISO / IEC JTC1 / SC22 / WG5 --- N1231
title: Technical report for floating-point exception handling
journal: j-FORTRAN-FORUM
volume: 15
number: 3
pages: 1--28
month: dec
monthnumber: 12
year: 1996
ISSN: 1061-7264 (print), 1931-1311 (electronic) OR 10617264 (print), 19311311 (electronic)
ISSNL: 1061-7264 OR 10617264
bibdate: Wed Feb 6 18:50:06 MST 2002
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.02.06 18:50:06 MST
note: 7th October 1996.
fjournal: ACM Fortran Forum
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/toc.cfm?id=J286
issue: 47
rawauthor: {ISO\slash IEC JTC1\slash SC22\slash WG5 --- N1231}
rawnote: 7th October 1996.
rawtitle: Technical report for floating-point exception handling
entry:
@Article{ISO:1996:TRF,
  author =       "{ISO\slash IEC JTC1\slash SC22\slash WG5 --- N1231}",
  title =        "Technical report for floating-point exception
                 handling",
  journal =      j-FORTRAN-FORUM,
  volume =       "15",
  number =       "3",
  pages =        "1--28",
  month =        dec,
  year =         "1996",
  CODEN =        "????",
  ISSN =         "1061-7264 (print), 1931-1311 (electronic)",
  ISSN-L =       "1061-7264",
  bibdate =      "Wed Feb 6 18:50:06 MST 2002",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "7th October 1996.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Fortran Forum",
  issue =        "47",
  journal-URL =  "http://portal.acm.org/toc.cfm?id=J286",
}


bibtype: article
filename: fparith.bib
label: Ito:1996:SRI
author: Masayuki Ito and Naofumi Takagi and Shuzo Yajima
title: Square rooting by iterative multiply-additions
journal: j-INFO-PROC-LETT
volume: 60
number: 5
pages: 267--269
day: 8
month: dec
monthnumber: 12
year: 1996
CODEN: IFPLAT
ISSN: 0020-0190 (print), 1872-6119 (electronic) OR 00200190 (print), 18726119 (electronic)
ISSNL: 0020-0190 OR 00200190
MRclass: 68M07
MRnumber: 97i:68014
bibdate: Wed Nov 11 12:16:26 MST 1998
bibtimestamp: 1998.11.11 12:16:26 MST
fjournal: Information Processing Letters
acknowledgement: ack-nhfb
corpsource: Department of Inf. Sci., Kyoto University, Japan
journalURL: http://www.sciencedirect.com/science/journal/00200190
treatment: T Theoretical or Mathematical
rawauthor: Masayuki Ito and Naofumi Takagi and Shuzo Yajima
rawtitle: Square rooting by iterative multiply-additions
bibsource:
http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/; https://www.math.utah.edu/pub/tex/bib/fparith.bib

keywords:
computer arithmetic; convergence of numerical methods; digital arithmetic; iterative methods; iterative multiply-additions; linear converging ratio; multiplicative methods; Newton--Raphson method; read-only storage; ROM sizes; square root algorithm

entry:
@Article{Ito:1996:SRI,
  author =       "Masayuki Ito and Naofumi Takagi and Shuzo Yajima",
  title =        "Square rooting by iterative multiply-additions",
  journal =      j-INFO-PROC-LETT,
  volume =       "60",
  number =       "5",
  pages =        "267--269",
  day =          "8",
  month =        dec,
  year =         "1996",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  MRclass =      "68M07",
  MRnumber =     "97i:68014",
  bibdate =      "Wed Nov 11 12:16:26 MST 1998",
  bibsource =    "http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C4130 (Interpolation and function approximation);
                 C5230 (Digital arithmetic methods)",
  corpsource =   "Department of Inf. Sci., Kyoto University, Japan",
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
  keywords =     "computer arithmetic; convergence of numerical methods;
                 digital arithmetic; iterative methods; iterative
                 multiply-additions; linear converging ratio;
                 multiplicative methods; Newton--Raphson method;
                 read-only storage; ROM sizes; square root algorithm",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: fparith.bib
label: Jayasuriya:1996:MAU
author: Kumara Jayasuriya
title: Multiprecision arithmetic using fast Hartley transforms
journal: j-APPL-MATH-COMP
volume: 75
number: 2--3
pages: 239--251
day: 15
month: mar
monthnumber: 3
year: 1996
CODEN: AMHCBQ
DOI: https://doi.org/10.1016/0096-3003(96)90067-3
ISSN: 0096-3003 (print), 1873-5649 (electronic) OR 00963003 (print), 18735649 (electronic)
ISSNL: 0096-3003 OR 00963003
bibdate: Tue Nov 20 21:02:36 MST 2012
bibtimestamp: 2012.11.20 21:02:36 MST
URL: http://www.sciencedirect.com/science/article/pii/0096300396900673
fjournal: Applied Mathematics and Computation
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00963003/
rawauthor: Kumara Jayasuriya
rawtitle: Multiprecision arithmetic using fast {Hartley} transforms
bibsource:
https://www.math.utah.edu/pub/tex/bib/applmathcomput1995.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Jayasuriya:1996:MAU,
  author =       "Kumara Jayasuriya",
  title =        "Multiprecision arithmetic using fast {Hartley}
                 transforms",
  journal =      j-APPL-MATH-COMP,
  volume =       "75",
  number =       "2--3",
  pages =        "239--251",
  day =          "15",
  month =        mar,
  year =         "1996",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/0096-3003(96)90067-3",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Tue Nov 20 21:02:36 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput1995.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0096300396900673",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}


bibtype: article
filename: fparith.bib
label: Jessani:1996:FPU
author: R. M. Jessani and C. H. Olson
title: The floating point unit of the PowerPC 603e microprocessor
journal: j-IBM-JRD
volume: 40
number: 5
pages: 559--566
month: sep
monthnumber: 9
year: 1996
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: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.03.25 14:26:59 MST
URL: http://www.almaden.ibm.com/journal/rd40-5.html#four
fjournal: IBM Journal of Research and Development
acknowledgement: ack-nhfb
corpsource: Somerset Design Center, Motorola Inc., Austin, TX, USA
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520
treatment: A Application; P Practical
rawauthor: R. M. Jessani and C. H. Olson
rawtitle: The floating point unit of the {PowerPC 603e} microprocessor
abstract:
The IBM PowerPC 603e* floating-point unit (FPU) is an on-chip functional unit to support IEEE 754 standard single- and double-precision binary floating-point arithmetic operations. The design objectives are to be a low-cost, low-power, high-performance engine in a single-chip superscalar microprocessor. Using less than 15 mm$^2$ of the available silicon area on the chip (the size of the PowerPC 603e microprocessor is 98 mm$^2$) and operating at the peak clock frequency of 100 MHz, an average single-pumping multiply-add-fuse instruction has one-cycle throughput and four-cycle latency. An average double-pumping multiply-add-fuse instruction has two-cycle throughput and five-cycle latency. The estimated performance at 100 MHz is 105 against the SPECfp92** benchmark.

keywords:
add-fuse instruction; design objectives; digital arithmetic; double-pumping multiply-add-fuse; floating point unit; functional unit; IEEE 754 standard; instruction; microprocessor chips; on-chip; peak clock frequency; PowerPC 603e microprocessor; silicon area; single-pumping multiply-

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

rawabstract:
The IBM PowerPC 603e* floating-point unit (FPU) is an on-chip functional unit to support IEEE 754 standard single- and double-precision binary floating-point arithmetic operations. The design objectives are to be a low-cost, low-power, high-performance engine in a single-chip superscalar microprocessor. Using less than 15 mm$^2$ of the available silicon area on the chip (the size of the PowerPC 603e microprocessor is 98 mm$^2$) and operating at the peak clock frequency of 100 MHz, an average single-pumping multiply-add-fuse instruction has one-cycle throughput and four-cycle latency. An average double-pumping multiply-add-fuse instruction has two-cycle throughput and five-cycle latency. The estimated performance at 100 MHz is 105 against the SPECfp92** benchmark.

entry:
@Article{Jessani:1996:FPU,
  author =       "R. M. Jessani and C. H. Olson",
  title =        "The floating point unit of the {PowerPC 603e}
                 microprocessor",
  journal =      j-IBM-JRD,
  volume =       "40",
  number =       "5",
  pages =        "559--566",
  month =        sep,
  year =         "1996",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Tue Mar 25 14:26:59 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.almaden.ibm.com/journal/rd40-5.html#four",
  abstract =     "The IBM PowerPC 603e* floating-point unit (FPU) is an
                 on-chip functional unit to support IEEE 754 standard
                 single- and double-precision binary floating-point
                 arithmetic operations. The design objectives are to be
                 a low-cost, low-power, high-performance engine in a
                 single-chip superscalar microprocessor. Using less than
                 15 mm$^2$ of the available silicon area on the chip
                 (the size of the PowerPC 603e microprocessor is 98
                 mm$^2$) and operating at the peak clock frequency of
                 100 MHz, an average single-pumping multiply-add-fuse
                 instruction has one-cycle throughput and four-cycle
                 latency. An average double-pumping multiply-add-fuse
                 instruction has two-cycle throughput and five-cycle
                 latency. The estimated performance at 100 MHz is 105
                 against the SPECfp92** benchmark.",
  acknowledgement = ack-nhfb,
  classcodes =   "B1265F (Microprocessors and microcomputers); C5130
                 (Microprocessor chips); C5230 (Digital arithmetic
                 methods)",
  corpsource =   "Somerset Design Center, Motorola Inc., Austin, TX,
                 USA",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  keywords =     "add-fuse instruction; design objectives; digital
                 arithmetic; double-pumping multiply-add-fuse; floating
                 point unit; functional unit; IEEE 754 standard;
                 instruction; microprocessor chips; on-chip; peak clock
                 frequency; PowerPC 603e microprocessor; silicon area;
                 single-pumping multiply-",
  treatment =    "A Application; P Practical",
  xxlibnote =    "Issue missing from UofUtah Marriott Library",
}


bibtype: inproceedings
filename: fparith.bib
label: Jullien:1996:VDS
author: Graham A. Jullien
title: VLSI Digital Signal Processing: Some Arithmetic Issues
crossref: Luk:1996:PSC
pages: 1--13
year: 1996
DOI: https://doi.org/10.1117/12.255423
bibdate: Tue Jun 14 18:18:32 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2011.06.14 18:18:32 ???
URL: http://www.atips.ca/research/documents/ca/aa/1996_keynote.pdf
remark: Keynote address: VLSI Arithmetic and DSP Implementations.
acknowledgement: ack-nhfb
rawauthor: Graham A. Jullien
rawtitle: {VLSI} Digital Signal Processing: Some Arithmetic Issues
entry:
@InProceedings{Jullien:1996:VDS,
  author =       "Graham A. Jullien",
  title =        "{VLSI} Digital Signal Processing: Some Arithmetic
                 Issues",
  crossref =     "Luk:1996:PSC",
  pages =        "1--13",
  year =         "1996",
  DOI =          "https://doi.org/10.1117/12.255423",
  bibdate =      "Tue Jun 14 18:18:32 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.atips.ca/research/documents/ca/aa/1996_keynote.pdf",
  acknowledgement = ack-nhfb,
  remark =       "Keynote address: VLSI Arithmetic and DSP
                 Implementations.",
}


bibtype: misc
filename: fparith.bib
label: Kahan:1996:BEC
author: W. Kahan
title: The baleful effect of computer benchmarks upon applied mathematics, physics, and chemistry
pages: 1--13
year: 1996
bibdate: Sat Apr 28 18:52:17 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.04.28 18:52:17 ???
URL: http://www.cs.berkeley.edu/~wkahan/ieee754status/baleful.ps
acknowledgement: ack-nhfb
howpublished: World-Wide Web document.
rawauthor: W. Kahan
rawtitle: The baleful effect of computer benchmarks upon applied mathematics, physics, and chemistry
entry:
@Misc{Kahan:1996:BEC,
  author =       "W. Kahan",
  title =        "The baleful effect of computer benchmarks upon applied
                 mathematics, physics, and chemistry",
  howpublished = "World-Wide Web document.",
  year =         "1996",
  bibdate =      "Sat Apr 28 18:52:17 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/ieee754status/baleful.ps",
  acknowledgement = ack-nhfb,
}


bibtype: misc
filename: fparith.bib
label: Kahan:1996:LNS
author: W. Kahan
title: Lecture notes on the status of IEEE Standard 754 for binary floating-point arithmetic
pages: 1--13
year: 1996
bibdate: Sat Apr 28 18:52:17 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.04.28 18:52:17 ???
URL: http://www.cs.berkeley.edu/~wkahan/ieee754status/ieee754.ps
acknowledgement: ack-nhfb
howpublished: World-Wide Web document.
rawauthor: W. Kahan
rawtitle: Lecture notes on the status of {IEEE Standard 754} for binary floating-point arithmetic
entry:
@Misc{Kahan:1996:LNS,
  author =       "W. Kahan",
  title =        "Lecture notes on the status of {IEEE Standard 754} for
                 binary floating-point arithmetic",
  howpublished = "World-Wide Web document.",
  year =         "1996",
  bibdate =      "Sat Apr 28 18:52:17 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/ieee754status/ieee754.ps",
  acknowledgement = ack-nhfb,
}


bibtype: unpublished
filename: fparith.bib
label: Kahan:1996:WCY
author: W. Kahan
title: What can you learn about floating-point arithmetic in one hour?
institution: inst-BERKELEY-EECS
address: inst-BERKELEY-EECS:adr
pages: 23
year: 1996
bibdate: Mon Apr 25 17:58:22 2005
bibtimestamp: 2005.04.25 17:58:22 ???
URL: http://www.cs.berkeley.edu/~wkahan/ieee754status/cs267fp.ps
acknowledgement: ack-nhfb
key: Kah96a
rawauthor: W. Kahan
rawtitle: What can you learn about floating-point arithmetic in one hour?
note:
Postscript version accessible electronically at path =http://http.cs.berkeley.edu/~wkahan/ieee754status=.

rawnote:
Postscript version accessible electronically at \path=http://http.cs.berkeley.edu/~wkahan/ieee754status=.

entry:
@Unpublished{Kahan:1996:WCY,
  author =       "W. Kahan",
  key =          "Kah96a",
  title =        "What can you learn about floating-point arithmetic in
                 one hour?",
  institution =  inst-BERKELEY-EECS,
  address =      inst-BERKELEY-EECS:adr,
  pages =        "23",
  year =         "1996",
  bibdate =      "Mon Apr 25 17:58:22 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Postscript version accessible electronically at
                 \path=http://http.cs.berkeley.edu/~wkahan/ieee754status=.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/ieee754status/cs267fp.ps",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Kalantari:1996:HOI
author: B. Kalantari and I. Kalantari
title: High order iterative methods for approximating square roots
journal: j-BIT-NUM-MATH
volume: 36
number: 2
pages: 395--399
month: jun
monthnumber: 6
year: 1996
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01731991
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
MRclass: 65D15 (65H99)
MRnumber: 97k:65039
bibdate: Wed Jan 4 18:52:24 MST 2006
bibtimestamp: 2006.01.04 18:52:24 MST
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: B. Kalantari and I. Kalantari
rawtitle: High order iterative methods for approximating square roots
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=36&issue=2; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://www.mai.liu.se/BIT/contents/bit36.html; http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=36&issue=2&spage=395

entry:
@Article{Kalantari:1996:HOI,
  author =       "B. Kalantari and I. Kalantari",
  title =        "High order iterative methods for approximating square
                 roots",
  journal =      j-BIT-NUM-MATH,
  volume =       "36",
  number =       "2",
  pages =        "395--399",
  month =        jun,
  year =         "1996",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01731991",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65D15 (65H99)",
  MRnumber =     "97k:65039",
  bibdate =      "Wed Jan 4 18:52:24 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=36&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.mai.liu.se/BIT/contents/bit36.html;
                 http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=36&issue=2&spage=395",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
}


bibtype: article
filename: fparith.bib
label: Kalliojarvi:1996:REB
author: K. Kalliojarvi and J. Astola
title: Roundoff errors in block-floating-point systems
journal: j-IEEE-TRANS-SIG-PROC
volume: 44
number: 4
pages: 783--790
month: apr
monthnumber: 4
year: 1996
CODEN: ITPRED
ISSN: 1053-587X (print), 1941-0476 (electronic) OR 1053587X (print), 19410476 (electronic)
ISSNL: 1053-587X OR 1053587X
bibdate: Sat Jul 16 08:40:52 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:52 MDT
fjournal: IEEE Transactions on Signal Processing
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78
rawauthor: K. Kalliojarvi and J. Astola
rawtitle: Roundoff errors in block-floating-point systems
entry:
@Article{Kalliojarvi:1996:REB,
  author =       "K. Kalliojarvi and J. Astola",
  title =        "Roundoff errors in block-floating-point systems",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "44",
  number =       "4",
  pages =        "783--790",
  month =        apr,
  year =         "1996",
  CODEN =        "ITPRED",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  summary =      "Block-floating-point representation is a special case
                 of floating-point representation, where several numbers
                 have a joint exponent term. In this paper, roundoff
                 errors in signal processing systems utilizing
                 block-floating-point representation are \ldots{}",
}


bibtype: book
filename: fparith.bib
label: Kane:1996:PRA
author: Gerry Kane
title: PA-RISC 2.0 Architecture
publisher: pub-PHPTR
address: pub-PHPTR:adr
pages: various
year: 1996
ISBN: 0-13-182734-0 OR 0131827340
ISBN13: 978-0-13-182734-9 OR 9780131827349
LCCN: QA76.8.H48K36 1996
bibdate: Tue Jan 09 12:34:37 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/master.bib
bibtimestamp: 2001.01.09 12:34:37 ???
keywords: Hewlett--Packard computers; PA-RISC microprocessors
acknowledgement: ack-nhfb
rawauthor: Gerry Kane
rawtitle: {PA-RISC 2.0} Architecture
URL:
http://devresource.hp.com/devresource/Docs/Refs/PA2_0/index.html; http://devresource.hp.com/devresource/Docs/Refs/PA2_0/updates/index.html

abstract:
This is the authoritative definition of Hewlett-Packard's 2.0 PA-RISC architecture, one of the most mature and efficient RISC (Reduced Instruction Set Computer) processor architectures in the industry. PA-RISC is the foundation for machines proving especially well-suited for such markets as high performance graphics, mission critical transaction processing, and emerging multimedia applications such as interactive video services.

TOC:
1: Overview 2: Processing Resources 3: Addressing and Access Control 4: Control Flow 5: Interruptions 6: Instruction Set Overview 7: Instruction Descriptions 8: Floating-point Coprocessor 9: Floating-Point Instruction Set 10: Floating-Point Exceptions 11: Performance Monitor Coprocessor B: Instruction Formats C: Operation Codes D: Conditions E: Instruction Notation Control Structures F: TLB and Cache Control G: Memory Ordering Model H: Address Formation Details I: Programming Notes PA-RISC 2 Instruction Completers and Pseudo-Ops

rawabstract:
This is the authoritative definition of Hewlett-Packard's 2.0 PA-RISC architecture, one of the most mature and efficient RISC (Reduced Instruction Set Computer) processor architectures in the industry. PA-RISC is the foundation for machines proving especially well-suited for such markets as high performance graphics, mission critical transaction processing, and emerging multimedia applications such as interactive video services.

rawTOC:
1: Overview \\ 2: Processing Resources \\ 3: Addressing and Access Control \\ 4: Control Flow \\ 5: Interruptions \\ 6: Instruction Set Overview \\ 7: Instruction Descriptions \\ 8: Floating-point Coprocessor \\ 9: Floating-Point Instruction Set \\ 10: Floating-Point Exceptions \\ 11: Performance Monitor Coprocessor \\ B: Instruction Formats \\ C: Operation Codes \\ D: Conditions \\ E: Instruction Notation Control Structures \\ F: TLB and Cache Control \\ G: Memory Ordering Model \\ H: Address Formation Details \\ I: Programming Notes \\ PA-RISC 2 Instruction Completers and Pseudo-Ops

entry:
@Book{Kane:1996:PRA,
  author =       "Gerry Kane",
  title =        "{PA-RISC 2.0} Architecture",
  publisher =    pub-PHPTR,
  address =      pub-PHPTR:adr,
  pages =        "various",
  year =         "1996",
  ISBN =         "0-13-182734-0",
  ISBN-13 =      "978-0-13-182734-9",
  LCCN =         "QA76.8.H48K36 1996",
  bibdate =      "Tue Jan 09 12:34:37 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  price =        "US\$34.40",
  URL =          "http://devresource.hp.com/devresource/Docs/Refs/PA2_0/index.html;
                 http://devresource.hp.com/devresource/Docs/Refs/PA2_0/updates/index.html",
  abstract =     "This is the authoritative definition of
                 Hewlett-Packard's 2.0 PA-RISC architecture, one of the
                 most mature and efficient RISC (Reduced Instruction Set
                 Computer) processor architectures in the industry.
                 PA-RISC is the foundation for machines proving
                 especially well-suited for such markets as high
                 performance graphics, mission critical transaction
                 processing, and emerging multimedia applications such
                 as interactive video services.",
  acknowledgement = ack-nhfb,
  keywords =     "Hewlett--Packard computers; PA-RISC microprocessors",
  tableofcontents = "1: Overview \\
                 2: Processing Resources \\
                 3: Addressing and Access Control \\
                 4: Control Flow \\
                 5: Interruptions \\
                 6: Instruction Set Overview \\
                 7: Instruction Descriptions \\
                 8: Floating-point Coprocessor \\
                 9: Floating-Point Instruction Set \\
                 10: Floating-Point Exceptions \\
                 11: Performance Monitor Coprocessor \\
                 B: Instruction Formats \\
                 C: Operation Codes \\
                 D: Conditions \\
                 E: Instruction Notation Control Structures \\
                 F: TLB and Cache Control \\
                 G: Memory Ordering Model \\
                 H: Address Formation Details \\
                 I: Programming Notes \\
                 PA-RISC 2 Instruction Completers and Pseudo-Ops",
}


bibtype: article
filename: fparith.bib
label: Katti:1996:NRA
author: Rajendra S. Katti
title: A new residue arithmetic error correction scheme
journal: j-IEEE-TRANS-COMPUT
volume: 45
number: 1
pages: 13--19
month: jan
monthnumber: 1
year: 1996
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.481482
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
MRclass: 68M07
MRnumber: MR1372160 (96j:68011)
bibdate: Wed Jul 6 19:47:08 MDT 2011
bibtimestamp: 2011.07.06 19:47:08 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=481482
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Rajendra S. Katti
rawtitle: A new residue arithmetic error correction scheme
entry:
@Article{Katti:1996:NRA,
  author =       "Rajendra S. Katti",
  title =        "A new residue arithmetic error correction scheme",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "45",
  number =       "1",
  pages =        "13--19",
  month =        jan,
  year =         "1996",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.481482",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  MRclass =      "68M07",
  MRnumber =     "MR1372160 (96j:68011)",
  bibdate =      "Wed Jul 6 19:47:08 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=481482",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Kearfott:1996:OPI
author: R. B. Kearfott and X. Shi
title: Optimal Preconditioners for Interval Gauss--Seidel Methods
crossref: Alefeld:1996:SCV
pages: 173--178
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: R. B. Kearfott and X. Shi
rawtitle: Optimal Preconditioners for Interval {Gauss--Seidel} Methods
entry:
@InProceedings{Kearfott:1996:OPI,
  author =       "R. B. Kearfott and X. Shi",
  title =        "Optimal Preconditioners for Interval {Gauss--Seidel}
                 Methods",
  crossref =     "Alefeld:1996:SCV",
  pages =        "173--178",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Kearfott:1996:TNS
author: R. B. Kearfott
crossref: Alefeld:1996:SCV
pages: 160--172
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: R. B. Kearfott
title:
Treating Non-Smooth Functions as Smooth Functions in Global Optimization and Nonlinear Systems Solvers

rawtitle:
Treating Non-Smooth Functions as Smooth Functions in Global Optimization and Nonlinear Systems Solvers

entry:
@InProceedings{Kearfott:1996:TNS,
  author =       "R. B. Kearfott",
  title =        "Treating Non-Smooth Functions as Smooth Functions in
                 Global Optimization and Nonlinear Systems Solvers",
  crossref =     "Alefeld:1996:SCV",
  pages =        "160--172",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Koeber:1996:IIF
author: M. Koeber
title: Inclusion of the Inverse of a Functions in $n$ Variables
crossref: Alefeld:1996:SCV
pages: 179--185
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: M. Koeber
rawtitle: Inclusion of the Inverse of a Functions in $n$ Variables
entry:
@InProceedings{Koeber:1996:IIF,
  author =       "M. Koeber",
  title =        "Inclusion of the Inverse of a Functions in $n$
                 Variables",
  crossref =     "Alefeld:1996:SCV",
  pages =        "179--185",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Kowaleski:1996:DEP
title: A dual execution pipelined floating-point CMOS processor
crossref: Wuorinen:1996:DTP
pages: 358--359
year: 1996
bibdate: Thu Apr 2 08:38:35 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.04.02 08:38:35 ???
acknowledgement: ack-sfo
rawtitle: A dual execution pipelined floating-point {CMOS} processor
author:
J. A. Kowaleski and G. M. Wolrich and T. C. Fischer and R. J. Dupcak and P. L. Kroesen and T. Pham and A. Olesin

rawauthor:
J. A. Kowaleski and G. M. Wolrich and T. C. Fischer and R. J. Dupcak and P. L. Kroesen and T. Pham and A. Olesin

entry:
@InProceedings{Kowaleski:1996:DEP,
  author =       "J. A. Kowaleski and G. M. Wolrich and T. C. Fischer
                 and R. J. Dupcak and P. L. Kroesen and T. Pham and A.
                 Olesin",
  title =        "A dual execution pipelined floating-point {CMOS}
                 processor",
  crossref =     "Wuorinen:1996:DTP",
  pages =        "358--359",
  year =         "1996",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Kraemer:1996:CNI
author: W. Kraemer and S. Wedner
title: Computing Narrow Inclusions for Cauchy Principal Value Integrals
crossref: Alefeld:1996:SCV
pages: 45--51
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: W. Kraemer and S. Wedner
rawtitle: Computing Narrow Inclusions for {Cauchy} Principal Value Integrals
entry:
@InProceedings{Kraemer:1996:CNI,
  author =       "W. Kraemer and S. Wedner",
  title =        "Computing Narrow Inclusions for {Cauchy} Principal
                 Value Integrals",
  crossref =     "Alefeld:1996:SCV",
  pages =        "45--51",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Kreinovich:1996:CCI
author: V. Kreinovich and A. Lakeyev and J. Rohn
crossref: Alefeld:1996:SCV
pages: 293--306
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: V. Kreinovich and A. Lakeyev and J. Rohn
title:
Computational Complexity of Interval Algebraic Problems: Some Are Feasible and Some Are Computationally Intractable --- a Survey

rawtitle:
Computational Complexity of Interval Algebraic Problems: Some Are Feasible and Some Are Computationally Intractable --- a Survey

entry:
@InProceedings{Kreinovich:1996:CCI,
  author =       "V. Kreinovich and A. Lakeyev and J. Rohn",
  title =        "Computational Complexity of Interval Algebraic
                 Problems: Some Are Feasible and Some Are
                 Computationally Intractable --- a Survey",
  crossref =     "Alefeld:1996:SCV",
  pages =        "293--306",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Ley:1996:PDU
author: Eduardo Ley
title: On the Peculiar Distribution of the U.S. Stock Indexes' Digits
journal: j-AMER-STAT
volume: 50
number: 4
pages: 311--313
month: nov
monthnumber: 11
year: 1996
CODEN: ASTAAJ
ISSN: 0003-1305 (print), 1537-2731 (electronic) OR 00031305 (print), 15372731 (electronic)
ISSNL: 0003-1305 OR 00031305
bibdate: Mon Nov 14 15:09:04 2011
bibtimestamp: 2011.11.14 15:09:04 ???
URL: http://www.jstor.org/stable/2684926
fjournal: The American Statistician
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/utas20
rawauthor: Eduardo Ley
rawtitle: On the Peculiar Distribution of the {U.S.} Stock Indexes' Digits
bibsource:
https://www.math.utah.edu/pub/tex/bib/amstat.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Ley:1996:PDU,
  author =       "Eduardo Ley",
  title =        "On the Peculiar Distribution of the {U.S.} Stock
                 Indexes' Digits",
  journal =      j-AMER-STAT,
  volume =       "50",
  number =       "4",
  pages =        "311--313",
  month =        nov,
  year =         "1996",
  CODEN =        "ASTAAJ",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  bibdate =      "Mon Nov 14 15:09:04 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/amstat.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.jstor.org/stable/2684926",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
}


bibtype: inproceedings
filename: fparith.bib
label: Li:1996:NNR
author: Yamin Li and Wanming Chu
title: A new non-restoring square root algorithm and its VLSI implementations
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 538--544
year: 1996
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: Yamin Li and Wanming Chu
rawtitle: A new non-restoring square root algorithm and its {VLSI} implementations
booktitle:
Proceedings of the IEEE International Conference on Computer Design: VLSI in Computers and Processors: ICCD '96

rawbooktitle:
Proceedings of the {IEEE} International Conference on Computer Design: {VLSI} in Computers and Processors: {ICCD '96}

entry:
@InProceedings{Li:1996:NNR,
  author =       "Yamin Li and Wanming Chu",
  booktitle =    "Proceedings of the {IEEE} International Conference on
                 Computer Design: {VLSI} in Computers and Processors:
                 {ICCD '96}",
  title =        "A new non-restoring square root algorithm and its
                 {VLSI} implementations",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "538--544",
  year =         "1996",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "We present a new non-restoring square root algorithm
                 that is very efficient to implement. The new algorithm
                 presented here has the following features unlike other
                 square root algorithms. First, the focus of the
                 ``non-restoring'' is on the {\&} \ldots{}",
}


bibtype: techreport
filename: fparith.bib
label: Lions:1996:AFF
title: Ariane 5 Flight 501 failure, report by the Inquiry Board
type: Technical Report
institution: European Space Agency
address: Paris, France
pages: 538--544
year: 1996
bibdate: Sat Apr 01 07:39:11 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2017.04.01 07:39:11 ???
URL: http://sunnyday.mit.edu/accidents/Ariane5accidentreport.html
acknowledgement: ack-nhfb
rawtitle: {Ariane 5 Flight 501} failure, report by the {Inquiry Board}
author:
Jacques-Louis Lions and Mauro Balduccini and Yvan Choquer and Remy Hergott and Bernard Humbert and Eric Lefort

note:
From the foreword: ``On 4 June 1996, the maiden flight of the Ariane 5 launcher ended in a failure. Only about 40 seconds after initiation of the flight sequence, at an altitude of about 3700 m, the launcher veered off its flight path, broke up and exploded. Engineers from the Ariane 5 project teams of CNES and Industry immediately started to investigate the failure.'' From the report: ``The internal SRI software exception was caused during execution of a data conversion from 64-bit floating point to 16-bit signed integer value. The floating point number which was converted had a value greater than what could be represented by a 16-bit signed integer. This resulted in an Operand Error. The data conversion instructions (in Ada code) were not protected from causing an Operand Error, although other conversions of comparable variables in the same place in the code were protected.''

remark:
Report of an arithmetic error that put an expensive space missile off course, requiring its destruction in the air. Presumably-reliable code in Ada adapted from an earlier missile generated had not been updated for the new design.

rawauthor:
Jacques-Louis Lions and Mauro Balduccini and Yvan Choquer and Remy Hergott and Bernard Humbert and Eric Lefort

rawnote:
From the foreword: ``On 4 June 1996, the maiden flight of the Ariane 5 launcher ended in a failure. Only about 40 seconds after initiation of the flight sequence, at an altitude of about 3700 m, the launcher veered off its flight path, broke up and exploded. Engineers from the Ariane 5 project teams of CNES and Industry immediately started to investigate the failure.'' From the report: ``The internal SRI software exception was caused during execution of a data conversion from 64-bit floating point to 16-bit signed integer value. The floating point number which was converted had a value greater than what could be represented by a 16-bit signed integer. This resulted in an Operand Error. The data conversion instructions (in Ada code) were not protected from causing an Operand Error, although other conversions of comparable variables in the same place in the code were protected.''

entry:
@TechReport{Lions:1996:AFF,
  author =       "Jacques-Louis Lions and Mauro Balduccini and Yvan
                 Choquer and Remy Hergott and Bernard Humbert and Eric
                 Lefort",
  title =        "{Ariane 5 Flight 501} failure, report by the {Inquiry
                 Board}",
  type =         "Technical Report",
  institution =  "European Space Agency",
  address =      "Paris, France",
  year =         "1996",
  bibdate =      "Sat Apr 01 07:39:11 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "From the foreword: ``On 4 June 1996, the maiden flight
                 of the Ariane 5 launcher ended in a failure. Only about
                 40 seconds after initiation of the flight sequence, at
                 an altitude of about 3700 m, the launcher veered off
                 its flight path, broke up and exploded. Engineers from
                 the Ariane 5 project teams of CNES and Industry
                 immediately started to investigate the failure.'' From
                 the report: ``The internal SRI software exception was
                 caused during execution of a data conversion from
                 64-bit floating point to 16-bit signed integer value.
                 The floating point number which was converted had a
                 value greater than what could be represented by a
                 16-bit signed integer. This resulted in an Operand
                 Error. The data conversion instructions (in Ada code)
                 were not protected from causing an Operand Error,
                 although other conversions of comparable variables in
                 the same place in the code were protected.''",
  URL =          "http://sunnyday.mit.edu/accidents/Ariane5accidentreport.html",
  acknowledgement = ack-nhfb,
  remark =       "Report of an arithmetic error that put an expensive
                 space missile off course, requiring its destruction in
                 the air. Presumably-reliable code in Ada adapted from
                 an earlier missile generated had not been updated for
                 the new design.",
}


bibtype: article
filename: fparith.bib
label: Lo:1996:CBC
author: Jien-Chung Lo and S. Thanawastien and T. R. N. Rao
title: Correction to ``Berger Check Prediction for Array Multipliers and Array Dividers''
journal: j-IEEE-TRANS-COMPUT
volume: 45
number: 3
pages: 383--383
month: mar
monthnumber: 3
year: 1996
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1996.485579
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 19:47:10 MDT 2011
bibtimestamp: 2011.07.06 19:47:10 MDT
note: See cite Lo:1993:BCP.
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=485579
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Jien-Chung Lo and S. Thanawastien and T. R. N. Rao
rawnote: See \cite{Lo:1993:BCP}.
rawtitle: Correction to {``Berger Check Prediction for Array Multipliers and Array Dividers''}
entry:
@Article{Lo:1996:CBC,
  author =       "Jien-Chung Lo and S. Thanawastien and T. R. N. Rao",
  title =        "Correction to {``Berger Check Prediction for Array
                 Multipliers and Array Dividers''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "45",
  number =       "3",
  pages =        "383--383",
  month =        mar,
  year =         "1996",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1996.485579",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 19:47:10 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  note =         "See \cite{Lo:1993:BCP}.",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=485579",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Louca:1996:IIS
author: L. Louca and T. A. Cook and W. H. Johnson
title: Implementation of IEEE single precision floating point addition and multiplication on FPGAs
crossref: Pocek:1996:ISF
pages: 107--116
year: 1996
DOI: https://doi.org/10.1109/FPGA.1996.564761
bibdate: Sat Oct 9 12:52:57 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.09 12:52:57 ???
acknowledgement: ack-nhfb
rawauthor: L. Louca and T. A. Cook and W. H. Johnson
rawtitle: Implementation of {IEEE} single precision floating point addition and multiplication on {FPGAs}
abstract:
Floating point operations are hard to implement on FPGAs because of the complexity of their algorithms. On the other hand, many scientific problems require floating point arithmetic with high levels of accuracy in their calculations. Therefore, we have explored FPGA implementations of addition and multiplication for IEEE single precision floating-point numbers. Customizations were performed where this was possible in order to save chip area, or get the most out of our prototype board. The implementations tradeoff area and speed for accuracy. The adder is a bit-parallel adder, and the multiplier is a digit-serial multiplier. Prototypes have been implemented on Altera FLEX8000s, and peak rates of 7 MFlops for 32-bit addition and 2.3 MFlops for 32-bit multiplication have been obtained.

rawabstract:
Floating point operations are hard to implement on FPGAs because of the complexity of their algorithms. On the other hand, many scientific problems require floating point arithmetic with high levels of accuracy in their calculations. Therefore, we have explored FPGA implementations of addition and multiplication for IEEE single precision floating-point numbers. Customizations were performed where this was possible in order to save chip area, or get the most out of our prototype board. The implementations tradeoff area and speed for accuracy. The adder is a bit-parallel adder, and the multiplier is a digit-serial multiplier. Prototypes have been implemented on Altera FLEX8000s, and peak rates of 7 MFlops for 32-bit addition and 2.3 MFlops for 32-bit multiplication have been obtained.

entry:
@InProceedings{Louca:1996:IIS,
  author =       "L. Louca and T. A. Cook and W. H. Johnson",
  title =        "Implementation of {IEEE} single precision floating
                 point addition and multiplication on {FPGAs}",
  crossref =     "Pocek:1996:ISF",
  pages =        "107--116",
  year =         "1996",
  DOI =          "https://doi.org/10.1109/FPGA.1996.564761",
  bibdate =      "Sat Oct 9 12:52:57 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Floating point operations are hard to implement on
                 FPGAs because of the complexity of their algorithms. On
                 the other hand, many scientific problems require
                 floating point arithmetic with high levels of accuracy
                 in their calculations. Therefore, we have explored FPGA
                 implementations of addition and multiplication for IEEE
                 single precision floating-point numbers. Customizations
                 were performed where this was possible in order to save
                 chip area, or get the most out of our prototype board.
                 The implementations tradeoff area and speed for
                 accuracy. The adder is a bit-parallel adder, and the
                 multiplier is a digit-serial multiplier. Prototypes
                 have been implemented on Altera FLEX8000s, and peak
                 rates of 7 MFlops for 32-bit addition and 2.3 MFlops
                 for 32-bit multiplication have been obtained.",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Lozier:1996:EBL
author: Daniel W. Lozier and P. R. Turner
title: Error-Bounding in Level-Index Computer Arithmetic
crossref: Alefeld:1996:NME
pages: 138--145
year: 1996
bibdate: Fri Jul 09 07:20:57 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.07.09 07:20:57 ???
URL: http://math.nist.gov/acmd/Staff/DLozier/publications/oldenburg95.ps.Z
acknowledgement: ack-nhfb
rawauthor: Daniel W. Lozier and P. R. Turner
rawtitle: Error-Bounding in Level-Index Computer Arithmetic
entry:
@InProceedings{Lozier:1996:EBL,
  author =       "Daniel W. Lozier and P. R. Turner",
  title =        "Error-Bounding in Level-Index Computer Arithmetic",
  crossref =     "Alefeld:1996:NME",
  pages =        "138--145",
  year =         "1996",
  bibdate =      "Fri Jul 09 07:20:57 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://math.nist.gov/acmd/Staff/DLozier/publications/oldenburg95.ps.Z",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Luther:1996:CAG
author: W. Luther and W. Otten
title: The Complex Arithmetic-Geometric Mean and Multiple-Precision Matrix Functions
crossref: Alefeld:1996:SCV
pages: 52--58
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: W. Luther and W. Otten
rawtitle: The Complex Arithmetic-Geometric Mean and Multiple-Precision Matrix Functions
entry:
@InProceedings{Luther:1996:CAG,
  author =       "W. Luther and W. Otten",
  title =        "The Complex Arithmetic-Geometric Mean and
                 Multiple-Precision Matrix Functions",
  crossref =     "Alefeld:1996:SCV",
  pages =        "52--58",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: MacDonald:1996:NSS
author: D. A. MacDonald
title: A note on the summation of slowly convergent alternating series
journal: j-BIT-NUM-MATH
volume: 36
number: 4
pages: 766--774
month: dec
monthnumber: 12
year: 1996
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01733790
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
MRclass: 40A25 (65B10 65B15)
MRnumber: 98c:40001
MRreviewer: Vanna Zanelli
bibdate: Wed Jan 4 18:52:24 MST 2006
bibtimestamp: 2006.01.04 18:52:24 MST
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: D. A. MacDonald
rawtitle: A note on the summation of slowly convergent alternating series
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=36&issue=4; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://www.mai.liu.se/BIT/contents/bit36.html; http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=36&issue=4&spage=766

abstract:
The kth term of the infinite series $ sum nolimits _k = 0^infty ( - 1)^k [ln (k + 2)]^ - 0.1 $ is larger than $ 0.5 $ whenever $ k < k_0 $, where $ k_0 + 1 = e^1024 $. To sum this series correct to order $ 10^-1 $ using direct summation seems an impossible task, notwithstanding the power of modern computers. This note will present an alternative approach to those classical methods (the Euler transformation is one) which can accurately sum such series. The theory to be presented has the added advantage of providing accurate bounds for the error in the approximate result. The method used will be Euler--Maclaurin summation, revitalised by computer algebra.

keywords:
accurate floating-point summation; Euler--Maclaurin formula; slowly convergent alternating series; summation

rawabstract:
The kth term of the infinite series $ \sum \nolimits_{k = 0}^\infty {( - 1)^k [\ln (k + 2)]^{ - 0.1} } $ is larger than $ 0.5 $ whenever $ k < k_0 $, where $ k_0 + 1 = e^{1024} $. To sum this series correct to order $ 10^{-1} $ using direct summation seems an impossible task, notwithstanding the power of modern computers. This note will present an alternative approach to those classical methods (the Euler transformation is one) which can accurately sum such series. The theory to be presented has the added advantage of providing accurate bounds for the error in the approximate result. The method used will be Euler--Maclaurin summation, revitalised by computer algebra.

entry:
@Article{MacDonald:1996:NSS,
  author =       "D. A. MacDonald",
  title =        "A note on the summation of slowly convergent
                 alternating series",
  journal =      j-BIT-NUM-MATH,
  volume =       "36",
  number =       "4",
  pages =        "766--774",
  month =        dec,
  year =         "1996",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01733790",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "40A25 (65B10 65B15)",
  MRnumber =     "98c:40001",
  MRreviewer =   "Vanna Zanelli",
  bibdate =      "Wed Jan 4 18:52:24 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=36&issue=4;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.mai.liu.se/BIT/contents/bit36.html;
                 http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=36&issue=4&spage=766",
  abstract =     "The kth term of the infinite series $ \sum
                 \nolimits_{k = 0}^\infty {( - 1)^k [\ln (k + 2)]^{ -
                 0.1} } $ is larger than $ 0.5 $ whenever $ k < k_0 $,
                 where $ k_0 + 1 = e^{1024} $. To sum this series
                 correct to order $ 10^{-1} $ using direct summation
                 seems an impossible task, notwithstanding the power of
                 modern computers. This note will present an alternative
                 approach to those classical methods (the Euler
                 transformation is one) which can accurately sum such
                 series. The theory to be presented has the added
                 advantage of providing accurate bounds for the error in
                 the approximate result. The method used will be
                 Euler--Maclaurin summation, revitalised by computer
                 algebra.",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "accurate floating-point summation; Euler--Maclaurin
                 formula; slowly convergent alternating series;
                 summation",
}


bibtype: article
filename: fparith.bib
label: Macpherson:1996:RAP
author: George W. Macpherson
title: A reusable Ada package for scientific dimensional integrity
journal: j-SIGADA-LETTERS
volume: 16
number: 3
pages: 56--69
month: may
monthnumber: 5
year: 1996
CODEN: AALEE5
ISSN: 1094-3641 (print), 1557-9476 (electronic) OR 10943641 (print), 15579476 (electronic)
ISSNL: 1094-3641 OR 10943641
bibdate: Sat Aug 9 09:05:57 MDT 2003
bibtimestamp: 2003.08.09 09:05:57 MDT
fjournal: ACM SIGAda Ada Letters
acknowledgement: ack-nhfb
corpsource: CACI Inc.-Federal, Colorado Springs, CO, USA
journalURL: http://portal.acm.org/citation.cfm?id=J32
treatment: P Practical
rawauthor: George W. Macpherson
rawtitle: A reusable {Ada} package for scientific dimensional integrity
keywords:
Ada; Ada programming language; arithmetic operations; ASSIGN function; checking; computational reliability; data integrity; declaration; digital arithmetic; entries; exponents; floating point numeric value; fundamental physical units; generic package; information hiding; integer; length; limited private; mass; multiplication operation; numeric; operator; overloading; PHYSICAL QUANTITY type; physics computing; relational operations; reusability; reusable Ada package; scientific dimensional integrity; software; software modifiability; software packages; software reliability; software reusability; strong typing; symbol creation; time; types; units; units (measurement); values; variables

classcodes:
A0650M (Computing devices and techniques); A0620F (Measurement units); C7320 (Physics and chemistry computing); C6130 (Data handling techniques); C5230 (Digital arithmetic methods)

entry:
@Article{Macpherson:1996:RAP,
  author =       "George W. Macpherson",
  title =        "A reusable {Ada} package for scientific dimensional
                 integrity",
  journal =      j-SIGADA-LETTERS,
  volume =       "16",
  number =       "3",
  pages =        "56--69",
  month =        may # "\slash " # jun,
  year =         "1996",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Sat Aug 9 09:05:57 MDT 2003",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigada.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "A0650M (Computing devices and techniques); A0620F
                 (Measurement units); C7320 (Physics and chemistry
                 computing); C6130 (Data handling techniques); C5230
                 (Digital arithmetic methods)",
  corpsource =   "CACI Inc.-Federal, Colorado Springs, CO, USA",
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "Ada; Ada programming language; arithmetic operations;
                 ASSIGN function; checking; computational reliability;
                 data integrity; declaration; digital arithmetic;
                 entries; exponents; floating point numeric value;
                 fundamental physical units; generic package;
                 information hiding; integer; length; limited private;
                 mass; multiplication operation; numeric; operator;
                 overloading; PHYSICAL QUANTITY type; physics computing;
                 relational operations; reusability; reusable Ada
                 package; scientific dimensional integrity; software;
                 software modifiability; software packages; software
                 reliability; software reusability; strong typing;
                 symbol creation; time; types; units; units
                 (measurement); values; variables",
  treatment =    "P Practical",
}


bibtype: article
filename: fparith.bib
label: Maeder:1996:MPLa
author: Roman E. Maeder
title: The Mathematica Programmer: Long Integers: Basic Arithmetic and Data Types
journal: j-MATHEMATICA-J
volume: 6
number: 2
pages: 32--40
month: Spring
year: 1996
ISSN: 1047-5974 (print), 1097-1610 (electronic) OR 10475974 (print), 10971610 (electronic)
ISSNL: 1047-5974 OR 10475974
bibdate: Sat Nov 6 13:34:10 MDT 2010
bibsource: http://www.mathematica-journal.com/issue/v6i2/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.11.06 13:34:10 MDT
fjournal: Mathematica Journal
acknowledgement: ack-nhfb
journalURL: http://www.mathematica-journal.com/
rawauthor: Roman E. Maeder
rawtitle: The {Mathematica} Programmer: Long Integers: Basic Arithmetic and Data Types
URL:
http://www.mathematica-journal.com/issue/v6i2/columns/maeder/index.html; http://www.mathematica-journal.com/issue/v6i2/columns/maeder/maeder62.pdf

abstract:
Long-integer arithmetic is a fundamental part of symbolic computation. This article introduces the fundamentals of long-integer calculations by implementing a prototype system in Mathematica. Our code is strictly procedural and could be translated into C or assembler easily. The tools needed are arrays that behave like arrays in procedural languages, as well as tools for software testing and debugging.

rawabstract:
Long-integer arithmetic is a fundamental part of symbolic computation. This article introduces the fundamentals of long-integer calculations by implementing a prototype system in Mathematica. Our code is strictly procedural and could be translated into C or assembler easily. The tools needed are arrays that behave like arrays in procedural languages, as well as tools for software testing and debugging.

entry:
@Article{Maeder:1996:MPLa,
  author =       "Roman E. Maeder",
  title =        "The {Mathematica} Programmer: Long Integers: Basic
                 Arithmetic and Data Types",
  journal =      j-MATHEMATICA-J,
  volume =       "6",
  number =       "2",
  pages =        "32--40",
  month =        "Spring",
  year =         "1996",
  CODEN =        "????",
  ISSN =         "1047-5974 (print), 1097-1610 (electronic)",
  ISSN-L =       "1047-5974",
  bibdate =      "Sat Nov 6 13:34:10 MDT 2010",
  bibsource =    "http://www.mathematica-journal.com/issue/v6i2/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.mathematica-journal.com/issue/v6i2/columns/maeder/index.html;
                 http://www.mathematica-journal.com/issue/v6i2/columns/maeder/maeder62.pdf",
  abstract =     "Long-integer arithmetic is a fundamental part of
                 symbolic computation. This article introduces the
                 fundamentals of long-integer calculations by
                 implementing a prototype system in Mathematica. Our
                 code is strictly procedural and could be translated
                 into C or assembler easily. The tools needed are arrays
                 that behave like arrays in procedural languages, as
                 well as tools for software testing and debugging.",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematica Journal",
  journal-URL =  "http://www.mathematica-journal.com/",
}


bibtype: article
filename: fparith.bib
label: Maeder:1996:MPLb
author: Roman E. Maeder
title: The Mathematica Programmer: Long Integers: Efficient Algorithms
journal: j-MATHEMATICA-J
volume: 6
number: 3
pages: 37--43
month: Summer
year: 1996
ISSN: 1047-5974 (print), 1097-1610 (electronic) OR 10475974 (print), 10971610 (electronic)
ISSNL: 1047-5974 OR 10475974
bibdate: Sat Nov 6 13:34:12 MDT 2010
bibsource: http://www.mathematica-journal.com/issue/v6i3/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.11.06 13:34:12 MDT
fjournal: Mathematica Journal
acknowledgement: ack-nhfb
journalURL: http://www.mathematica-journal.com/
rawauthor: Roman E. Maeder
rawtitle: The {Mathematica} Programmer: Long Integers: Efficient Algorithms
URL:
http://www.mathematica-journal.com/issue/v6i3/columns/maeder/contents/63maeder.pdf; http://www.mathematica-journal.com/issue/v6i3/columns/maeder/index.html

abstract:
This is the second part of an article on long-integer arithmetic. It discusses the data type for long integers and investigates a few asymptotically efficient algorithms for multiplication and division. We will not discuss all our code in detail, but point out a few important ideas.

rawabstract:
This is the second part of an article on long-integer arithmetic. It discusses the data type for long integers and investigates a few asymptotically efficient algorithms for multiplication and division. We will not discuss all our code in detail, but point out a few important ideas.

entry:
@Article{Maeder:1996:MPLb,
  author =       "Roman E. Maeder",
  title =        "The {Mathematica} Programmer: Long Integers: Efficient
                 Algorithms",
  journal =      j-MATHEMATICA-J,
  volume =       "6",
  number =       "3",
  pages =        "37--43",
  month =        "Summer",
  year =         "1996",
  CODEN =        "????",
  ISSN =         "1047-5974 (print), 1097-1610 (electronic)",
  ISSN-L =       "1047-5974",
  bibdate =      "Sat Nov 6 13:34:12 MDT 2010",
  bibsource =    "http://www.mathematica-journal.com/issue/v6i3/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.mathematica-journal.com/issue/v6i3/columns/maeder/contents/63maeder.pdf;
                 http://www.mathematica-journal.com/issue/v6i3/columns/maeder/index.html",
  abstract =     "This is the second part of an article on long-integer
                 arithmetic. It discusses the data type for long
                 integers and investigates a few asymptotically
                 efficient algorithms for multiplication and division.
                 We will not discuss all our code in detail, but point
                 out a few important ideas.",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematica Journal",
  journal-URL =  "http://www.mathematica-journal.com/",
}


bibtype: article
filename: fparith.bib
label: Makino:1996:MBF
author: H. Makino and H. Suzuki and H. Morinaka and Y. Nakase and K. Mashiko and T. Sumi
title: A 286 MHz 64-b floating point multiplier with enhanced CG operation
journal: j-IEEE-J-SOLID-STATE-CIRCUITS
volume: 31
number: 4
pages: 504--513
month: apr
monthnumber: 4
year: 1996
CODEN: IJSCBC
ISSN: 0018-9200 (print), 1558-173X (electronic) OR 00189200 (print), 1558173X (electronic)
ISSNL: 0018-9200 OR 00189200
bibdate: Sat Jul 16 08:40:52 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:52 MDT
fjournal: IEEE Journal of Solid-State Circuits
acknowledgement: ack-nhfb
rawauthor: H. Makino and H. Suzuki and H. Morinaka and Y. Nakase and K. Mashiko and T. Sumi
rawtitle: A {286 MHz} 64-b floating point multiplier with enhanced {CG} operation
entry:
@Article{Makino:1996:MBF,
  author =       "H. Makino and H. Suzuki and H. Morinaka and Y. Nakase
                 and K. Mashiko and T. Sumi",
  title =        "A {286 MHz} 64-b floating point multiplier with
                 enhanced {CG} operation",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "31",
  number =       "4",
  pages =        "504--513",
  month =        apr,
  year =         "1996",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  summary =      "This paper presents a high speed 64-b floating point
                 (FP) multiplier that has a useful function for computer
                 graphics (CG). The critical path delay is minimized by
                 using high speed logic gates and limiting the stage
                 number of series transmission gate \ldots{}",
}


bibtype: mastersthesis
filename: fparith.bib
label: Manickavasagam:1996:ATI
author: SenthilKumar Manickavasagam
title: ``$ a + b $'' arithmetic: theory and implementation
type: Thesis (M.S.)
school: Electrical Engineering and Computer Science, Ohio University
address: Athens, OH, USA
pages: xi + 152
year: 1996
bibdate: Mon Mar 05 14:33:56 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.03.05 14:33:56 ???
acknowledgement: ack-nhfb
rawauthor: SenthilKumar Manickavasagam
rawtitle: ``$ a + b $'' arithmetic: theory and implementation
entry:
@MastersThesis{Manickavasagam:1996:ATI,
  author =       "SenthilKumar Manickavasagam",
  title =        "``$ a + b $'' arithmetic: theory and implementation",
  type =         "Thesis ({M.S.})",
  school =       "Electrical Engineering and Computer Science, Ohio
                 University",
  address =      "Athens, OH, USA",
  pages =        "xi + 152",
  year =         "1996",
  bibdate =      "Mon Mar 05 14:33:56 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Manning:1996:FS
author: Evan Manning
title: Floating-point Summation
journal: j-CCCUJ
volume: 14
number: 9
pages: 51--??
month: sep
monthnumber: 9
year: 1996
CODEN: CCUJEX
ISSN: 1075-2838 OR 10752838
bibdate: Wed Nov 6 07:30:58 MST 1996
bibsource: http://www.cuj.com/cbklist.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.11.06 07:30:58 MST
fjournal: C/C++ Users Journal
keywords: accurate floating-point summation
acknowledgement: ack-nhfb
rawauthor: Evan Manning
rawtitle: Floating-point Summation
entry:
@Article{Manning:1996:FS,
  author =       "Evan Manning",
  title =        "Floating-point Summation",
  journal =      j-CCCUJ,
  volume =       "14",
  number =       "9",
  pages =        "51--??",
  month =        sep,
  year =         "1996",
  CODEN =        "CCUJEX",
  ISSN =         "1075-2838",
  bibdate =      "Wed Nov 6 07:30:58 MST 1996",
  bibsource =    "http://www.cuj.com/cbklist.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "C/C++ Users Journal",
  keywords =     "accurate floating-point summation",
}


bibtype: inproceedings
filename: fparith.bib
label: Markov:1996:FIA
author: S. M. Markov
title: On the Foundations of Interval Arithmetic
crossref: Alefeld:1996:SCV
pages: 307--313
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: S. M. Markov
rawtitle: On the Foundations of Interval Arithmetic
entry:
@InProceedings{Markov:1996:FIA,
  author =       "S. M. Markov",
  title =        "On the Foundations of Interval Arithmetic",
  crossref =     "Alefeld:1996:SCV",
  pages =        "307--313",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Mayer:1996:SEI
author: G. Mayer
title: Success in Epsilon-Inflation
crossref: Alefeld:1996:SCV
pages: 98--104
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: G. Mayer
rawtitle: Success in Epsilon-Inflation
entry:
@InProceedings{Mayer:1996:SEI,
  author =       "G. Mayer",
  title =        "Success in Epsilon-Inflation",
  crossref =     "Alefeld:1996:SCV",
  pages =        "98--104",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Mikov:1996:LSA
author: Alexander I. Mikov
title: Large-scale addition of machine real numbers: Accuracy estimates
journal: j-THEOR-COMP-SCI
volume: 162
number: 1
pages: 151--170
day: 05
month: aug
monthnumber: 8
year: 1996
CODEN: TCSCDI
ISSN: 0304-3975 (print), 1879-2294 (electronic) OR 03043975 (print), 18792294 (electronic)
ISSNL: 0304-3975 OR 03043975
bibdate: Mon Jul 19 22:20:05 MDT 1999
bibtimestamp: 1999.07.19 22:20:05 MDT
fjournal: Theoretical Computer Science
acknowledgement: ack-nhfb
corpsource: Department of Computer Science, Perm State University, Russia
journalURL: http://www.sciencedirect.com/science/journal/03043975/
treatment: T Theoretical or Mathematical
rawauthor: Alexander I. Mikov
rawtitle: Large-scale addition of machine real numbers: {Accuracy} estimates
bibsource:
http://www.elsevier.com/cgi-bin/cas/tree/store/tcs/cas_free/browse/browse.cgi?year=1996&volume=162&issue=1; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/tcs1995.bib

URL:
http://www.elsevier.com/cgi-bin/cas/tree/store/tcs/cas_sub/browse/browse.cgi?year=1996&volume=162&issue=1&aid=2194

keywords:
accuracy estimates; digital arithmetic; floating-point arithmetic; large-scale addition; machine real numbers; positive independent random variables; random variables; real distribution interval; roundoff error

entry:
@Article{Mikov:1996:LSA,
  author =       "Alexander I. Mikov",
  title =        "Large-scale addition of machine real numbers:
                 {Accuracy} estimates",
  journal =      j-THEOR-COMP-SCI,
  volume =       "162",
  number =       "1",
  pages =        "151--170",
  day =          "05",
  month =        aug,
  year =         "1996",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Mon Jul 19 22:20:05 MDT 1999",
  bibsource =    "http://www.elsevier.com/cgi-bin/cas/tree/store/tcs/cas_free/browse/browse.cgi?year=1996&volume=162&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/tcs1995.bib",
  URL =          "http://www.elsevier.com/cgi-bin/cas/tree/store/tcs/cas_sub/browse/browse.cgi?year=1996&volume=162&issue=1&aid=2194",
  acknowledgement = ack-nhfb,
  classification = "C5230 (Digital arithmetic methods)",
  corpsource =   "Department of Computer Science, Perm State University,
                 Russia",
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975/",
  keywords =     "accuracy estimates; digital arithmetic; floating-point
                 arithmetic; large-scale addition; machine real numbers;
                 positive independent random variables; random
                 variables; real distribution interval; roundoff error",
  pubcountry =   "Netherlands",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: inproceedings
filename: fparith.bib
label: Miner:1996:VIC
author: Paul S. Miner and James F. Leathrum, Jr.
title: Verification of IEEE Compliant Subtractive Division Algorithms
crossref: Srivas:1996:FMC
pages: 64--78
year: 1996
bibdate: Wed Nov 24 12:01:07 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.24 12:01:07 ???
URL: http://www.ece.odu.edu/~leathrum/Formal_Methods/computer_arithmetic/fmcad.ps
acknowledgement: ack-nhfb
rawauthor: Paul S. Miner and James F. {Leathrum, Jr.}
rawtitle: Verification of {IEEE} Compliant Subtractive Division Algorithms
remark:
fmcad.ps actually contains two separate versions of this article, and must be split manually before printing.

entry:
@InProceedings{Miner:1996:VIC,
  author =       "Paul S. Miner and James F. {Leathrum, Jr.}",
  title =        "Verification of {IEEE} Compliant Subtractive Division
                 Algorithms",
  crossref =     "Srivas:1996:FMC",
  pages =        "64--78",
  year =         "1996",
  bibdate =      "Wed Nov 24 12:01:07 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.ece.odu.edu/~leathrum/Formal_Methods/computer_arithmetic/fmcad.ps",
  acknowledgement = ack-nhfb,
  remark =       "fmcad.ps actually contains two separate versions of
                 this article, and must be split manually before
                 printing.",
}


bibtype: techreport
filename: fparith.bib
label: Moler:1996:CCF
author: Cleve B. Moler
title: Cleve's Corner: Floating points: IEEE Standard unifies arithmetic model
type: Technical note
institution: inst-MATHWORKS
address: inst-MATHWORKS:adr
pages: 3
month: Fall
year: 1996
bibdate: Thu Oct 24 07:16:21 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.10.24 07:16:21 ???
URL: http://www.mathworks.com/company/newsletter/pdf/Fall96Cleve.pdf
keywords: Matlab
acknowledgement: ack-nhfb
rawauthor: Cleve B. Moler
rawtitle: {Cleve}'s Corner: {Floating} points: {IEEE Standard} unifies arithmetic model
entry:
@TechReport{Moler:1996:CCF,
  author =       "Cleve B. Moler",
  title =        "{Cleve}'s Corner: {Floating} points: {IEEE Standard}
                 unifies arithmetic model",
  type =         "Technical note",
  institution =  inst-MATHWORKS,
  address =      inst-MATHWORKS:adr,
  pages =        "3",
  month =        "Fall",
  year =         "1996",
  bibdate =      "Thu Oct 24 07:16:21 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.mathworks.com/company/newsletter/pdf/Fall96Cleve.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "Matlab",
}


bibtype: inproceedings
filename: fparith.bib
label: Mraz:1996:ELB
author: F. Mraz
title: The Exact Lower Bound of Optimal Values in Interval LP
crossref: Alefeld:1996:SCV
pages: 214--220
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: F. Mraz
rawtitle: The Exact Lower Bound of Optimal Values in Interval {LP}
entry:
@InProceedings{Mraz:1996:ELB,
  author =       "F. Mraz",
  title =        "The Exact Lower Bound of Optimal Values in Interval
                 {LP}",
  crossref =     "Alefeld:1996:SCV",
  pages =        "214--220",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Mrozek:1996:IPC
author: M. Mrozek
title: Inheritable Properties and Computer Assisted Proofs in Dynamics
crossref: Alefeld:1996:SCV
pages: 245--257
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: M. Mrozek
rawtitle: Inheritable Properties and Computer Assisted Proofs in Dynamics
entry:
@InProceedings{Mrozek:1996:IPC,
  author =       "M. Mrozek",
  title =        "Inheritable Properties and Computer Assisted Proofs in
                 Dynamics",
  crossref =     "Alefeld:1996:SCV",
  pages =        "245--257",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Muller:1996:CES
author: Michael Muller and Christine Rub and Wolfgang Rulling
title: A circuit for exact summation of floating-point numbers
journal: j-INFO-PROC-LETT
volume: 57
number: 3
pages: 159--163
day: 12
month: feb
monthnumber: 2
year: 1996
CODEN: IFPLAT
ISSN: 0020-0190 (print), 1872-6119 (electronic) OR 00200190 (print), 18726119 (electronic)
ISSNL: 0020-0190 OR 00200190
bibdate: Sat Nov 7 17:55:43 MST 1998
bibtimestamp: 1998.11.07 17:55:43 MST
fjournal: Information Processing Letters
keywords: accurate floating-point summation
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00200190
rawauthor: Michael M{\"u}ller and Christine R{\"u}b and Wolfgang R{\"u}lling
rawtitle: A circuit for exact summation of floating-point numbers
bibsource:
http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Muller:1996:CES,
  author =       "Michael M{\"u}ller and Christine R{\"u}b and Wolfgang
                 R{\"u}lling",
  title =        "A circuit for exact summation of floating-point
                 numbers",
  journal =      j-INFO-PROC-LETT,
  volume =       "57",
  number =       "3",
  pages =        "159--163",
  day =          "12",
  month =        feb,
  year =         "1996",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  bibdate =      "Sat Nov 7 17:55:43 MST 1998",
  bibsource =    "http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
  keywords =     "accurate floating-point summation",
}


bibtype: inproceedings
filename: fparith.bib
label: Muller:1996:TER
author: Jean-Michel Muller and A. Tisserand
title: Towards Exact Rounding of the Elementary Functions
crossref: Alefeld:1996:SCV
pages: 59--71
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: Jean-Michel Muller and A. Tisserand
rawtitle: Towards Exact Rounding of the Elementary Functions
entry:
@InProceedings{Muller:1996:TER,
  author =       "Jean-Michel Muller and A. Tisserand",
  title =        "Towards Exact Rounding of the Elementary Functions",
  crossref =     "Alefeld:1996:SCV",
  pages =        "59--71",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Nakao:1996:GEB
author: M. T. Nakao and N. Yamamoto and Y. Watanabe
title: Guaranteed Error Bounds for Finite Element Solutions of the Stokes Problem
crossref: Alefeld:1996:SCV
pages: 258--264
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: M. T. Nakao and N. Yamamoto and Y. Watanabe
rawtitle: Guaranteed Error Bounds for Finite Element Solutions of the {Stokes} Problem
entry:
@InProceedings{Nakao:1996:GEB,
  author =       "M. T. Nakao and N. Yamamoto and Y. Watanabe",
  title =        "Guaranteed Error Bounds for Finite Element Solutions
                 of the {Stokes} Problem",
  crossref =     "Alefeld:1996:SCV",
  pages =        "258--264",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Nonnenmacher:1996:LCS
author: A. Nonnenmacher and D. A. Mlynski
title: Liquid Crystal Simulation Using Automatic Differentiation and Interval Arithmetic
crossref: Alefeld:1996:SCV
pages: 334--340
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: A. Nonnenmacher and D. A. Mlynski
rawtitle: Liquid Crystal Simulation Using Automatic Differentiation and Interval Arithmetic
entry:
@InProceedings{Nonnenmacher:1996:LCS,
  author =       "A. Nonnenmacher and D. A. Mlynski",
  title =        "Liquid Crystal Simulation Using Automatic
                 Differentiation and Interval Arithmetic",
  crossref =     "Alefeld:1996:SCV",
  pages =        "334--340",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: phdthesis
filename: fparith.bib
label: Oberman:1996:DIH
author: Stuart Franklin Oberman
title: Design Issues in High Performance Floating Point Arithmetic Units
type: Thesis (Ph.D.)
school: Department of Electrical Engineering, Stanford University
address: Stanford, CA, USA
pages: xiv + 151
month: nov
monthnumber: 11
year: 1996
bibdate: Fri Mar 27 10:14:18 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.03.27 10:14:18 ???
URL: ftp://umunhum.stanford.edu/tr/oberman.nov96.thesis.ps.Z
acknowledgement: ack-nhfb
rawauthor: Stuart Franklin Oberman
rawtitle: Design Issues in High Performance Floating Point Arithmetic Units
entry:
@PhdThesis{Oberman:1996:DIH,
  author =       "Stuart Franklin Oberman",
  title =        "Design Issues in High Performance Floating Point
                 Arithmetic Units",
  type =         "Thesis ({Ph.D.})",
  school =       "Department of Electrical Engineering, Stanford
                 University",
  address =      "Stanford, CA, USA",
  pages =        "xiv + 151",
  month =        nov,
  year =         "1996",
  bibdate =      "Fri Mar 27 10:14:18 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://umunhum.stanford.edu/tr/oberman.nov96.thesis.ps.Z",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: fparith.bib
label: Oberman:1996:FIR
author: Stuart F. Oberman and Michael J. Flynn
title: Fast IEEE Rounding for Division by Functional Iteration
type: Technical Report
number: CSL-TR-96-700
institution: Stanford University
address: Stanford, CA, USA
pages: v + 16
month: jul
monthnumber: 7
year: 1996
bibdate: Sun Dec 10 13:50:59 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.10 13:50:59 ???
URL: http://i.stanford.edu/pub/cstr/reports/csl/tr/96/700/CSL-TR-96-700.pdf
keywords: division, Goldschmidt's algorithm, IEEE rounding, Newton--Raphson, variable latency
acknowledgement: ack-nhfb
rawauthor: Stuart F. Oberman and Michael J. Flynn
rawtitle: Fast {IEEE} Rounding for Division by Functional Iteration
abstract:
A class of high performance division algorithms is functional iteration. Division by functional iteration uses multiplication as the fundamental operator. The main advantage of division by functional iteration is quadratic convergence to the quotient. However, unlike non-restoring division algorithms such as SRT division, functional iteration does not directly provide a final remainder. This makes fast and exact rounding difficult. This paper clarifies the methodology for correct IEEE compliant rounding for quadratically-converging division algorithms. It proposes an extension to previously reported techniques of using extended precision in the computation to reduce the frequency of back multiplications required to obtain the final remainder. Further, a technique applicable to all IEEE rounding modes is presented which replaces the final subtraction for remainder computation with very simple combinational logic.

rawabstract:
A class of high performance division algorithms is functional iteration. Division by functional iteration uses multiplication as the fundamental operator. The main advantage of division by functional iteration is quadratic convergence to the quotient. However, unlike non-restoring division algorithms such as SRT division, functional iteration does not directly provide a final remainder. This makes fast and exact rounding difficult. This paper clarifies the methodology for correct IEEE compliant rounding for quadratically-converging division algorithms. It proposes an extension to previously reported techniques of using extended precision in the computation to reduce the frequency of back multiplications required to obtain the final remainder. Further, a technique applicable to all IEEE rounding modes is presented which replaces the final subtraction for remainder computation with very simple combinational logic.

entry:
@TechReport{Oberman:1996:FIR,
  author =       "Stuart F. Oberman and Michael J. Flynn",
  title =        "Fast {IEEE} Rounding for Division by Functional
                 Iteration",
  type =         "Technical Report",
  number =       "CSL-TR-96-700",
  institution =  "Stanford University",
  address =      "Stanford, CA, USA",
  pages =        "v + 16",
  month =        jul,
  year =         "1996",
  bibdate =      "Sun Dec 10 13:50:59 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://i.stanford.edu/pub/cstr/reports/csl/tr/96/700/CSL-TR-96-700.pdf",
  abstract =     "A class of high performance division algorithms is
                 functional iteration. Division by functional iteration
                 uses multiplication as the fundamental operator. The
                 main advantage of division by functional iteration is
                 quadratic convergence to the quotient. However, unlike
                 non-restoring division algorithms such as SRT division,
                 functional iteration does not directly provide a final
                 remainder. This makes fast and exact rounding
                 difficult. This paper clarifies the methodology for
                 correct IEEE compliant rounding for
                 quadratically-converging division algorithms. It
                 proposes an extension to previously reported techniques
                 of using extended precision in the computation to
                 reduce the frequency of back multiplications required
                 to obtain the final remainder. Further, a technique
                 applicable to all IEEE rounding modes is presented
                 which replaces the final subtraction for remainder
                 computation with very simple combinational logic.",
  acknowledgement = ack-nhfb,
  keywords =     "division, Goldschmidt's algorithm, IEEE rounding,
                 Newton--Raphson, variable latency",
}


bibtype: inproceedings
filename: fparith.bib
label: Oberman:1996:IDO
author: Stuart F. Oberman and Michael J. Flynn
title: Implementing Division and Other Floating-Point Operations: a System Perspective
crossref: Alefeld:1996:SCV
pages: 18--24
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
URL: ftp://arith.stanford.edu/tr/scan_system.ps.Z
acknowledgement: ack-nhfb
rawauthor: Stuart F. Oberman and Michael J. Flynn
rawtitle: Implementing Division and Other Floating-Point Operations: a System Perspective
entry:
@InProceedings{Oberman:1996:IDO,
  author =       "Stuart F. Oberman and Michael J. Flynn",
  title =        "Implementing Division and Other Floating-Point
                 Operations: a System Perspective",
  crossref =     "Alefeld:1996:SCV",
  pages =        "18--24",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "ftp://arith.stanford.edu/tr/scan_system.ps.Z",
  acknowledgement = ack-nhfb,
  summary =      "Modern computer applications have increased in their
                 computation complexity in recent years. The
                 industry-wide usage of performance benchmarks, such as
                 SPECmarks forces processor designers to pay particular
                 attention to floating-point (FP) computation.
                 Furthermore, special purpose applications, such as high
                 performance graphics rendering systems, have placed
                 further demands on processors. The development of high
                 speed FP hardware is a requirement to meet these
                 increasing computation demands.",
}


bibtype: article
filename: fparith.bib
label: Oberman:1996:RDL
author: S. F. Oberman and M. J. Flynn
title: Reducing division latency with reciprocal caches
journal: j-RELIABLE-COMPUTING
volume: 2
number: 2
pages: 147--153
month: apr
monthnumber: 4
year: 1996
CODEN: RCOMF8
ISSN: 1385-3139 (print), 1573-1340 (electronic) OR 13853139 (print), 15731340 (electronic)
ISSNL: 1385-3139 OR 13853139
bibdate: Thu Apr 2 08:38:35 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.04.02 08:38:35 ???
URL: ftp://arith.stanford.edu/tr/scan_recip.ps.Z
fjournal: Reliable Computing = Nadezhnye vychisleniia
acknowledgement: ack-sfo
journalURL: http://link.springer.com/journal/11155
rawauthor: S. F. Oberman and M. J. Flynn
rawtitle: Reducing division latency with reciprocal caches
entry:
@Article{Oberman:1996:RDL,
  author =       "S. F. Oberman and M. J. Flynn",
  title =        "Reducing division latency with reciprocal caches",
  journal =      j-RELIABLE-COMPUTING,
  volume =       "2",
  number =       "2",
  pages =        "147--153",
  month =        apr,
  year =         "1996",
  CODEN =        "RCOMF8",
  ISSN =         "1385-3139 (print), 1573-1340 (electronic)",
  ISSN-L =       "1385-3139",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://arith.stanford.edu/tr/scan_recip.ps.Z",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  fjournal =     "Reliable Computing = Nadezhnye vychisleniia",
  journal-URL =  "http://link.springer.com/journal/11155",
}


bibtype: article
filename: fparith.bib
label: Oberman:1996:VLP
author: S. F. Oberman and M. J. Flynn
title: A Variable Latency Pipelined Floating-Point Adder
journal: j-LECT-NOTES-COMP-SCI
volume: 1124
pages: 183--192
year: 1996
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Fri Mar 27 10:07:13 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.03.27 10:07:13 ???
URL: ftp://arith.stanford.edu/tr/fpadd_euro.ps.Z
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: S. F. Oberman and M. J. Flynn
rawtitle: A Variable Latency Pipelined Floating-Point Adder
entry:
@Article{Oberman:1996:VLP,
  author =       "S. F. Oberman and M. J. Flynn",
  title =        "A Variable Latency Pipelined Floating-Point Adder",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1124",
  pages =        "183--192",
  year =         "1996",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Fri Mar 27 10:07:13 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://arith.stanford.edu/tr/fpadd_euro.ps.Z",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Oklobdzija:1996:MSO
author: V. G. Oklobdzija and D. Villeger and S. S. Liu
journal: j-IEEE-TRANS-COMPUT
volume: 45
number: 3
pages: 294--306
month: mar
monthnumber: 3
year: 1996
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.485568
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 19:47:09 MDT 2011
bibtimestamp: 2011.07.06 19:47:09 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=485568
fjournal: IEEE Transactions on Computers
acknowledgement: ack-sfo
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: V. G. Oklobdzija and D. Villeger and S. S. Liu
title:
A method for speed optimized partial product reduction and generation of fast parallel multipliers using an algorithmic approach

rawtitle:
A method for speed optimized partial product reduction and generation of fast parallel multipliers using an algorithmic approach

entry:
@Article{Oklobdzija:1996:MSO,
  author =       "V. G. Oklobdzija and D. Villeger and S. S. Liu",
  title =        "A method for speed optimized partial product reduction
                 and generation of fast parallel multipliers using an
                 algorithmic approach",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "45",
  number =       "3",
  pages =        "294--306",
  month =        mar,
  year =         "1996",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.485568",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 19:47:09 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=485568",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Paar:1996:NAP
author: C. Paar
journal: j-IEEE-TRANS-COMPUT
volume: 45
number: 7
pages: 856--861
month: jul
monthnumber: 7
year: 1996
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.508323
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 19:47:12 MDT 2011
bibtimestamp: 2011.07.06 19:47:12 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=508323
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: C. Paar
title:
A new architecture for a parallel finite field multiplier with low complexity based on composite fields

rawtitle:
A new architecture for a parallel finite field multiplier with low complexity based on composite fields

entry:
@Article{Paar:1996:NAP,
  author =       "C. Paar",
  title =        "A new architecture for a parallel finite field
                 multiplier with low complexity based on composite
                 fields",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "45",
  number =       "7",
  pages =        "856--861",
  month =        jul,
  year =         "1996",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.508323",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 19:47:12 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=508323",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Parhami:1996:CHS
author: B. Parhami and S. Kawahito and M. Ishida and T. Nakamura and M. Kameyama and T. Higuchi
journal: j-IEEE-TRANS-COMPUT
volume: 45
number: 5
pages: 637--639
month: may
monthnumber: 5
year: 1996
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.509918
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 19:47:11 MDT 2011
bibtimestamp: 2011.07.06 19:47:11 MDT
note: See cite Kawahito:1994:HSA.
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=509918
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: B. Parhami and S. Kawahito and M. Ishida and T. Nakamura and M. Kameyama and T. Higuchi
rawnote: See \cite{Kawahito:1994:HSA}.
title:
Comments on ``High-speed area-efficient multiplier design using multiple-valued current-mode circuits''

rawtitle:
Comments on {``High-speed area-efficient multiplier design using multiple-valued current-mode circuits''}

entry:
@Article{Parhami:1996:CHS,
  author =       "B. Parhami and S. Kawahito and M. Ishida and T.
                 Nakamura and M. Kameyama and T. Higuchi",
  title =        "Comments on {``High-speed area-efficient multiplier
                 design using multiple-valued current-mode circuits''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "45",
  number =       "5",
  pages =        "637--639",
  month =        may,
  year =         "1996",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.509918",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 19:47:11 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  note =         "See \cite{Kawahito:1994:HSA}.",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=509918",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Park:1996:OHW
author: Edwards Park
journal: j-SMITHSONIAN
volume: 26
number: 11
pages: 20--??
day: 01
month: feb
monthnumber: 2
year: 1996
CODEN: SMSNA5
ISSN: 0037-7333 (print), 1930-5508 (electronic) OR 00377333 (print), 19305508 (electronic)
ISSNL: 0037-7333 OR 00377333
bibdate: Fri Jun 21 14:38:22 MDT 1996
bibtimestamp: 1996.06.21 14:38:22 MDT
fjournal: Smithsonian
acknowledgement: ack-nhfb
rawauthor: Edwards Park
title:
The Object at Hand: What a difference the Difference Engine made: from Charles Babbage's calculator emerged today's computer

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/babbage-charles.bib; https://www.math.utah.edu/pub/tex/bib/adabooks.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

rawtitle:
The Object at Hand: What a difference the {Difference Engine} made: from {Charles Babbage}'s calculator emerged today's computer

entry:
@Article{Park:1996:OHW,
  author =       "Edwards Park",
  title =        "The Object at Hand: What a difference the {Difference
                 Engine} made: from {Charles Babbage}'s calculator
                 emerged today's computer",
  journal =      j-SMITHSONIAN,
  volume =       "26",
  number =       "11",
  pages =        "20--??",
  day =          "01",
  month =        feb,
  year =         "1996",
  CODEN =        "SMSNA5",
  ISSN =         "0037-7333 (print), 1930-5508 (electronic)",
  ISSN-L =       "0037-7333",
  bibdate =      "Fri Jun 21 14:38:22 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/babbage-charles.bib;
                 https://www.math.utah.edu/pub/tex/bib/adabooks.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Smithsonian",
}


bibtype: article
filename: fparith.bib
label: Park:1996:PAG
author: Taegeun Park
title: A Parallel Algorithm for Global Routing Using an Associative Processor
journal: j-J-PAR-DIST-COMP
volume: 38
number: 1
pages: 51--62
day: 10
month: oct
monthnumber: 10
year: 1996
CODEN: JPDCER
DOI: https://doi.org/10.1006/jpdc.1996.0128
ISSN: 0743-7315 (print), 1096-0848 (electronic) OR 07437315 (print), 10960848 (electronic)
ISSNL: 0743-7315 OR 07437315
bibdate: Thu Mar 9 09:19:01 MST 2000
bibtimestamp: 2000.03.09 09:19:01 MST
fjournal: Journal of Parallel and Distributed Computing
acknowledgement: ack-nhfb
corpsource: Design Lab., Hyundai Electron. Ind., Kyoungki, South Korea
journalURL: http://www.sciencedirect.com/science/journal/07437315
treatment: A Application; P Practical
rawauthor: Taegeun Park
rawtitle: A Parallel Algorithm for Global Routing Using an Associative Processor
URL:
http://www.idealibrary.com/links/doi/10.1006/jpdc.1996.0128/production; http://www.idealibrary.com/links/doi/10.1006/jpdc.1996.0128/production/pdf

keywords:
addressable storage; array; associative processing; associative processor; benchmark problems; computational complexity; content-; content-addressable memory; control section; digital arithmetic; global routing; layout process; matching; minimisation; minimum-; multiple data device; O(d) complexity; parallel algorithm; parallel algorithms; parallel arithmetic; problem; processing elements; randomly generated data; row logic; rudimentary logic; search-oriented applications; selective; single instruction; weight path

entry:
@Article{Park:1996:PAG,
  author =       "Taegeun Park",
  title =        "A Parallel Algorithm for Global Routing Using an
                 Associative Processor",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "38",
  number =       "1",
  pages =        "51--62",
  day =          "10",
  month =        oct,
  year =         "1996",
  CODEN =        "JPDCER",
  DOI =          "https://doi.org/10.1006/jpdc.1996.0128",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Thu Mar 9 09:19:01 MST 2000",
  bibsource =    "http://www.idealibrary.com/servlet/useragent?func=showAllIssues&curIssueID=jpdc;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.idealibrary.com/links/doi/10.1006/jpdc.1996.0128/production;
                 http://www.idealibrary.com/links/doi/10.1006/jpdc.1996.0128/production/pdf",
  acknowledgement = ack-nhfb,
  classification = "C1180 (Optimisation techniques); C4240C
                 (Computational complexity); C4240P (Parallel
                 programming and algorithm theory); C5230 (Digital
                 arithmetic methods); C5340 (Associative storage)",
  corpsource =   "Design Lab., Hyundai Electron. Ind., Kyoungki, South
                 Korea",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  keywords =     "addressable storage; array; associative processing;
                 associative processor; benchmark problems;
                 computational complexity; content-; content-addressable
                 memory; control section; digital arithmetic; global
                 routing; layout process; matching; minimisation;
                 minimum-; multiple data device; O(d) complexity;
                 parallel algorithm; parallel algorithms; parallel
                 arithmetic; problem; processing elements; randomly
                 generated data; row logic; rudimentary logic;
                 search-oriented applications; selective; single
                 instruction; weight path",
  treatment =    "A Application; P Practical",
}


bibtype: inproceedings
filename: fparith.bib
label: Petunin:1996:UMI
author: D. Petunin and A. Semenov
title: The Use of Multi-Intervals in the UniCalc Solver
crossref: Alefeld:1996:SCV
pages: 91--97
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: D. Petunin and A. Semenov
rawtitle: The Use of Multi-Intervals in the {UniCalc} Solver
entry:
@InProceedings{Petunin:1996:UMI,
  author =       "D. Petunin and A. Semenov",
  title =        "The Use of Multi-Intervals in the {UniCalc} Solver",
  crossref =     "Alefeld:1996:SCV",
  pages =        "91--97",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Plum:1996:ETP
author: M. Plum
title: Enclosure for Two-Point Boundary Value Problems Near Bifurcation Points
crossref: Alefeld:1996:SCV
pages: 265--279
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: M. Plum
rawtitle: Enclosure for Two-Point Boundary Value Problems Near Bifurcation Points
entry:
@InProceedings{Plum:1996:ETP,
  author =       "M. Plum",
  title =        "Enclosure for Two-Point Boundary Value Problems Near
                 Bifurcation Points",
  crossref =     "Alefeld:1996:SCV",
  pages =        "265--279",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Popova:1996:IOI
author: E. D. Popova
title: Interval operations involving NaNs
journal: j-RELIABLE-COMPUTING
volume: 2
number: 2
pages: 161--166
month: jun
monthnumber: 6
year: 1996
CODEN: RCOMF8
ISSN: 1385-3139 (print), 1573-1340 (electronic) OR 13853139 (print), 15731340 (electronic)
ISSNL: 1385-3139 OR 13853139
bibdate: Sat Feb 4 17:45:55 2012
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2012.02.04 17:45:55 ???
fjournal: Reliable Computing = Nadezhnye vychisleniia
acknowledgement: ack-vk
journalURL: http://link.springer.com/journal/11155
rawauthor: E. D. Popova
rawtitle: Interval operations involving {NaNs}
entry:
@Article{Popova:1996:IOI,
  author =       "E. D. Popova",
  title =        "Interval operations involving {NaNs}",
  journal =      j-RELIABLE-COMPUTING,
  volume =       "2",
  number =       "2",
  pages =        "161--166",
  month =        jun,
  year =         "1996",
  CODEN =        "RCOMF8",
  ISSN =         "1385-3139 (print), 1573-1340 (electronic)",
  ISSN-L =       "1385-3139",
  bibdate =      "Sat Feb 4 17:45:55 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-vk,
  fjournal =     "Reliable Computing = Nadezhnye vychisleniia",
  journal-URL =  "http://link.springer.com/journal/11155",
}


bibtype: article
filename: fparith.bib
label: Posch:1996:DRN
author: K. C. Posch and R. Posch
title: Division in residue number systems involving length indicators
journal: j-J-COMPUT-APPL-MATH
volume: 66
number: 1--2
pages: 411--419
day: 31
month: jan
monthnumber: 1
year: 1996
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:27:48 MST 2017
bibtimestamp: 2017.02.25 12:27:48 MST
URL: http://www.sciencedirect.com/science/article/pii/0377042795001646
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: K. C. Posch and R. Posch
rawtitle: Division in residue number systems involving length indicators
entry:
@Article{Posch:1996:DRN,
  author =       "K. C. Posch and R. Posch",
  title =        "Division in residue number systems involving length
                 indicators",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "66",
  number =       "1--2",
  pages =        "411--419",
  day =          "31",
  month =        jan,
  year =         "1996",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:27:48 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042795001646",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: fparith.bib
label: Price:1996:RA
author: David T. Price
title: Remark on Algorithm 715
journal: j-TOMS
volume: 22
number: 2
pages: 258--258
month: jun
monthnumber: 6
year: 1996
CODEN: ACMSCU
DOI: https://doi.org/10.1145/229473.236186
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sat Feb 8 10:28:55 2020
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2020.02.08 10:28:55 ???
note: See cite Cody:1993:ASE
URL: http://www.acm.org/pubs/citations/journals/toms/1996-22-2/p258-price/
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: David T. Price
rawnote: See \cite{Cody:1993:ASE}
rawtitle: Remark on {Algorithm 715}
entry:
@Article{Price:1996:RA,
  author =       "David T. Price",
  title =        "Remark on {Algorithm 715}",
  journal =      j-TOMS,
  volume =       "22",
  number =       "2",
  pages =        "258--258",
  month =        jun,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/229473.236186",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Feb 8 10:28:55 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Cody:1993:ASE}",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1996-22-2/p258-price/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: inproceedings
filename: fparith.bib
label: Rao:1996:NHS
author: Vishwas M. Rao and Behrouz Nowrouzian
title: Novel high-speed bit-parallel multiply accumulate arithmetic architecture
crossref: Luk:1996:PSC
pages: 26--38
year: 1996
DOI: https://doi.org/10.1117/12.255442
bibdate: Tue Jun 14 18:26:06 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2011.06.14 18:26:06 ???
acknowledgement: ack-nhfb
rawauthor: Vishwas M. Rao and Behrouz Nowrouzian
rawtitle: Novel high-speed bit-parallel multiply accumulate arithmetic architecture
entry:
@InProceedings{Rao:1996:NHS,
  author =       "Vishwas M. Rao and Behrouz Nowrouzian",
  title =        "Novel high-speed bit-parallel multiply accumulate
                 arithmetic architecture",
  crossref =     "Luk:1996:PSC",
  pages =        "26--38",
  year =         "1996",
  DOI =          "https://doi.org/10.1117/12.255442",
  bibdate =      "Tue Jun 14 18:26:06 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Rao:1996:RTS
author: V. M. Rao and B. Nowrouzian
booktitle: Canadian Conference on Electrical and Computer Engineering. 26--29 May 1996
title: Rounding techniques for signed binary arithmetic
volume: 1
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 294--297
year: 1996
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: V. M. Rao and B. Nowrouzian
rawbooktitle: Canadian Conference on Electrical and Computer Engineering. 26--29 May 1996
rawtitle: Rounding techniques for signed binary arithmetic
abstract:
This paper is concerned with the derivation of the relationship that exists between the number truncation in two's complement (TC) arithmetic and the corresponding truncation in signed-binary (SB) arithmetic. The resulting relationship is subsequently exploited and applied to the development of a pair of novel techniques for SB rounding. These techniques are then translated into algorithm suitable for two-level logic implementation. Finally, the resulting algorithms are applied to the design and implementation of a high-speed SB-kernel based TC multiply-accumulate arithmetic architecture.

rawabstract:
This paper is concerned with the derivation of the relationship that exists between the number truncation in two's complement (TC) arithmetic and the corresponding truncation in signed-binary (SB) arithmetic. The resulting relationship is subsequently exploited and applied to the development of a pair of novel techniques for SB rounding. These techniques are then translated into algorithm suitable for two-level logic implementation. Finally, the resulting algorithms are applied to the design and implementation of a high-speed SB-kernel based TC multiply-accumulate arithmetic architecture.

entry:
@InProceedings{Rao:1996:RTS,
  author =       "V. M. Rao and B. Nowrouzian",
  booktitle =    "Canadian Conference on Electrical and Computer
                 Engineering. 26--29 May 1996",
  title =        "Rounding techniques for signed binary arithmetic",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "294--297",
  year =         "1996",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:04 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper is concerned with the derivation of the
                 relationship that exists between the number truncation
                 in two's complement (TC) arithmetic and the
                 corresponding truncation in signed-binary (SB)
                 arithmetic. The resulting relationship is subsequently
                 exploited and applied to the development of a pair of
                 novel techniques for SB rounding. These techniques are
                 then translated into algorithm suitable for two-level
                 logic implementation. Finally, the resulting algorithms
                 are applied to the design and implementation of a
                 high-speed SB-kernel based TC multiply-accumulate
                 arithmetic architecture.",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Ratz:1996:BRS
author: D. Ratz
title: On Branching Rules in Second-Order Branch-and-Bound Methods for Global Optimization
crossref: Alefeld:1996:SCV
pages: 221--227
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: D. Ratz
rawtitle: On Branching Rules in Second-Order Branch-and-Bound Methods for Global Optimization
entry:
@InProceedings{Ratz:1996:BRS,
  author =       "D. Ratz",
  title =        "On Branching Rules in Second-Order Branch-and-Bound
                 Methods for Global Optimization",
  crossref =     "Alefeld:1996:SCV",
  pages =        "221--227",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Reid:1996:RFF
author: J. K. Reid
title: Remark on ``Fast Floating-Point Processing in Common Lisp''
journal: j-TOMS
volume: 22
number: 4
pages: 496--497
month: dec
monthnumber: 12
year: 1996
CODEN: ACMSCU
DOI: https://doi.org/10.1145/235815.235824
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Mar 9 10:21:08 1999
bibsource: Compendex database; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1999.03.09 10:21:08 ???
note: See cite Fateman:1995:FFP.
URL: http://www.acm.org/pubs/citations/journals/toms/1996-22-4/p496-reid/
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
affiliation: Rutherford Appleton Lab
journalURL: https://dl.acm.org/loi/toms
journalabr: ACM Trans Math Software
rawauthor: J. K. Reid
rawnote: See \cite{Fateman:1995:FFP}.
rawtitle: Remark on ``{Fast Floating-Point Processing in Common Lisp}''
abstract:
We explain why we feel that the comparison between Common Lisp and Fortran in a recent article by Fateman et al. in this journal is not entirely fair.

keywords:
Common Lisp language; Control structures; Digital arithmetic; Floating point computation; fortran (programming language); Lisp (programming language); Standards

subject:
bf D.3.2: Software, PROGRAMMING LANGUAGES, General, Standards. bf D.3.3: Software, PROGRAMMING LANGUAGES, Language Constructs and Features, Modules, packages.

rawabstract:
We explain why we feel that the comparison between Common Lisp and Fortran in a recent article by Fateman et al. in this journal is not entirely fair.

entry:
@Article{Reid:1996:RFF,
  author =       "J. K. Reid",
  title =        "Remark on ``{Fast Floating-Point Processing in Common
                 Lisp}''",
  journal =      j-TOMS,
  volume =       "22",
  number =       "4",
  pages =        "496--497",
  month =        dec,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/235815.235824",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 9 10:21:08 1999",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Fateman:1995:FFP}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1996-22-4/p496-reid/",
  abstract =     "We explain why we feel that the comparison between
                 Common Lisp and Fortran in a recent article by Fateman
                 et al. in this journal is not entirely fair.",
  acknowledgement = ack-nhfb # " and " # ack-rfb,
  affiliation =  "Rutherford Appleton Lab",
  classification = "721.1; 723.1.1; 902.2; 921.6",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  journalabr =   "ACM Trans Math Software",
  keywords =     "Common Lisp language; Control structures; Digital
                 arithmetic; Floating point computation; fortran
                 (programming language); Lisp (programming language);
                 Standards",
  subject =      "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, General,
                 Standards. {\bf D.3.3}: Software, PROGRAMMING
                 LANGUAGES, Language Constructs and Features, Modules,
                 packages.",
}


bibtype: inproceedings
filename: fparith.bib
label: Rump:1996:DBR
author: Siegfried M. Rump
title: The Distance Between Regularity and Strong Regularity
crossref: Alefeld:1996:SCV
pages: 105--117
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: Siegfried M. Rump
rawtitle: The Distance Between Regularity and Strong Regularity
entry:
@InProceedings{Rump:1996:DBR,
  author =       "Siegfried M. Rump",
  title =        "The Distance Between Regularity and Strong
                 Regularity",
  crossref =     "Alefeld:1996:SCV",
  pages =        "105--117",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Sarma:1996:HRT
author: D. Das Sarma and D. W. Matula
title: Hardware Reciprocal Table Compression / Decompression Techniques
crossref: Alefeld:1996:SCV
pages: 11--17
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: D. Das Sarma and D. W. Matula
rawtitle: Hardware Reciprocal Table Compression\slash Decompression Techniques
entry:
@InProceedings{Sarma:1996:HRT,
  author =       "D. Das Sarma and D. W. Matula",
  title =        "Hardware Reciprocal Table Compression\slash
                 Decompression Techniques",
  crossref =     "Alefeld:1996:SCV",
  pages =        "11--17",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: fparith.bib
label: Saunders:1996:TGF
author: Kevin Saunders
title: Third generation floating point DSP design
type: Report
number: 800 XY/N-1
institution: University of Bristol. Department of Aerospace Engineering
address: Bristol, UK
pages: 11--17
year: 1996
bibdate: Thu May 09 08:52:59 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.09 08:52:59 ???
acknowledgement: ack-nhfb
rawauthor: Kevin Saunders
rawtitle: Third generation floating point {DSP} design
entry:
@TechReport{Saunders:1996:TGF,
  author =       "Kevin Saunders",
  title =        "Third generation floating point {DSP} design",
  type =         "Report",
  number =       "800 XY/N-1",
  institution =  "University of Bristol. Department of Aerospace
                 Engineering",
  address =      "Bristol, UK",
  year =         "1996",
  bibdate =      "Thu May 09 08:52:59 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Schatzman:1996:ADF
author: James C. Schatzman
title: Accuracy of the discrete Fourier transform and the fast Fourier transform
journal: j-SIAM-J-SCI-COMP
volume: 17
number: 5
pages: 1150--1166
month: sep
monthnumber: 9
year: 1996
CODEN: SJOCE3
DOI: https://doi.org/10.1137/S1064827593247023
ISSN: 1064-8275 (print), 1095-7197 (electronic) OR 10648275 (print), 10957197 (electronic)
ISSNL: 1064-8275 OR 10648275
MRclass: 65T20 (42A65 42C10 68Q25)
MRnumber: 97e:65155
bibdate: Fri Dec 4 14:47:53 MST 1998
bibtimestamp: 1998.12.04 14:47:53 MST
URL: http://epubs.siam.org/sam-bin/dbq/article/24702
fjournal: SIAM Journal on Scientific Computing
acknowledgement: ack-nhfb
ajournal: SIAM J. Sci. Comput.
journalURL: http://epubs.siam.org/sisc
rawauthor: James C. Schatzman
rawtitle: Accuracy of the discrete {Fourier} transform and the fast {Fourier} transform
bibsource:
http://epubs.siam.org/toc/sjoce3/17/5; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib

remark:
This article analyzes errors in computing one-dimensional Fourier transforms, the fast way (FFT) and the slow way. The author identifies two main causes of accuracy loss in the computed transforms: (1) inaccurate sine and cosine functions, and (2) failure to use accurate summation methods, such as Kahan's compensated summation.

entry:
@Article{Schatzman:1996:ADF,
  author =       "James C. Schatzman",
  title =        "Accuracy of the discrete {Fourier} transform and the
                 fast {Fourier} transform",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "17",
  number =       "5",
  pages =        "1150--1166",
  month =        sep,
  year =         "1996",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/S1064827593247023",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  MRclass =      "65T20 (42A65 42C10 68Q25)",
  MRnumber =     "97e:65155",
  bibdate =      "Fri Dec 4 14:47:53 MST 1998",
  bibsource =    "http://epubs.siam.org/toc/sjoce3/17/5;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/24702",
  acknowledgement = ack-nhfb,
  ajournal =     "SIAM J. Sci. Comput.",
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  remark =       "This article analyzes errors in computing
                 one-dimensional Fourier transforms, the fast way (FFT)
                 and the slow way. The author identifies two main causes
                 of accuracy loss in the computed transforms:
                 (1) inaccurate sine and cosine functions, and (2)
                 failure to use accurate summation methods, such as
                 Kahan's compensated summation.",
}


bibtype: inproceedings
filename: fparith.bib
label: Schulte:1996:HDI
author: M. J. Schulte and K. C. Bickerstaff and E. E. Swartzlander, Jr.
title: Hardware Designs for Interval Multiplication
pages: 85--87
year: 1996
bibdate: Sun Mar 04 10:51:30 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.03.04 10:51:30 ???
acknowledgement: ack-nhfb
rawauthor: M. J. Schulte and K. C. Bickerstaff and E. E. {Swartzlander, Jr.}
rawtitle: Hardware Designs for Interval Multiplication
booktitle:
Proceedings of the II Workshop on Computer Arithmetic, Interval and Symbolic Computation, Recife, Brazil, August, 1996

rawbooktitle:
Proceedings of the {II} Workshop on Computer Arithmetic, Interval and Symbolic Computation, Recife, Brazil, August, 1996

entry:
@InProceedings{Schulte:1996:HDI,
  author =       "M. J. Schulte and K. C. Bickerstaff and E. E.
                 {Swartzlander, Jr.}",
  editor =       "????",
  booktitle =    "Proceedings of the {II} Workshop on Computer
                 Arithmetic, Interval and Symbolic Computation, Recife,
                 Brazil, August, 1996",
  title =        "Hardware Designs for Interval Multiplication",
  publisher =    "????",
  address =      "????",
  pages =        "85--87",
  year =         "1996",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sun Mar 04 10:51:30 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Schulte:1996:PAS
author: M. J. Schulte and E. E. Swartzlander
title: A Processor for Accurate, Self-Validating Computing
crossref: Alefeld:1996:SCV
pages: 25--31
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: M. J. Schulte and E. E. Swartzlander
rawtitle: A Processor for Accurate, Self-Validating Computing
entry:
@InProceedings{Schulte:1996:PAS,
  author =       "M. J. Schulte and E. E. Swartzlander",
  title =        "A Processor for Accurate, Self-Validating Computing",
  crossref =     "Alefeld:1996:SCV",
  pages =        "25--31",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Schwandt:1996:GCI
author: H. Schwandt
crossref: Alefeld:1996:SCV
pages: 280--286
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: H. Schwandt
title:
Globally Convergent Iterative Domain Decomposition Methods for the Parallel Solution of a Class of Nonlinear Systems of Equations

rawtitle:
Globally Convergent Iterative Domain Decomposition Methods for the Parallel Solution of a Class of Nonlinear Systems of Equations

entry:
@InProceedings{Schwandt:1996:GCI,
  author =       "H. Schwandt",
  title =        "Globally Convergent Iterative Domain Decomposition
                 Methods for the Parallel Solution of a Class of
                 Nonlinear Systems of Equations",
  crossref =     "Alefeld:1996:SCV",
  pages =        "280--286",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Schwarz:1996:HSA
author: Eric M. Schwarz and Michael J. Flynn
title: Hardware Starting Approximation Method and Its Application to the Square Root Operation
journal: j-IEEE-TRANS-COMPUT
volume: 45
number: 12
pages: 1356--1369
month: dec
monthnumber: 12
year: 1996
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.545966
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 19:47:15 MDT 2011
bibtimestamp: 2011.07.06 19:47:15 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=545966
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Eric M. Schwarz and Michael J. Flynn
rawtitle: Hardware Starting Approximation Method and Its Application to the Square Root Operation
entry:
@Article{Schwarz:1996:HSA,
  author =       "Eric M. Schwarz and Michael J. Flynn",
  title =        "Hardware Starting Approximation Method and Its
                 Application to the Square Root Operation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "45",
  number =       "12",
  pages =        "1356--1369",
  month =        dec,
  year =         "1996",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.545966",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 19:47:15 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=545966",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "Quadratically converging algorithms for high-order
                 arithmetic operations typically are accelerated by a
                 starting approximation. The higher the precision of the
                 starting approximation, the less number of iterations
                 required for convergence. \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Sezgin:1996:SIR
author: F. Sezgin
title: Some improvements for a random number generator with single-precision floating-point arithmetic
journal: j-COMP-GEOSCI
volume: 22
number: 4
publisher: Elsevier Science
pages: 453--455
month: may
monthnumber: 5
year: 1996
CODEN: CGEODT, CGOSDN
ISSN: 0098-3004 (print), 1873-7803 (electronic) OR 00983004 (print), 18737803 (electronic)
ISSNL: 0098-3004 OR 00983004
bibdate: Fri Nov 8 05:39:32 MST 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; Ingenta database
bibtimestamp: 2002.11.08 05:39:32 MST
fjournal: Computers and Geosciences
acknowledgement: ack-nhfb
rawauthor: F. Sezgin
rawtitle: Some improvements for a random number generator with single-precision floating-point arithmetic
entry:
@Article{Sezgin:1996:SIR,
  author =       "F. Sezgin",
  title =        "Some improvements for a random number generator with
                 single-precision floating-point arithmetic",
  journal =      j-COMP-GEOSCI,
  volume =       "22",
  number =       "4",
  publisher =    "Elsevier Science",
  pages =        "453--455",
  month =        may,
  year =         "1996",
  CODEN =        "CGEODT, CGOSDN",
  ISSN =         "0098-3004 (print), 1873-7803 (electronic)",
  ISSN-L =       "0098-3004",
  bibdate =      "Fri Nov 8 05:39:32 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 Ingenta database",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Geosciences",
  pagecount =    "3",
}


bibtype: inproceedings
filename: fparith.bib
label: Shary:1996:NAA
author: S. P. Shary
title: A New Approach to the Analysis of Static Systems Under Internal Uncertainty
crossref: Alefeld:1996:SCV
pages: 118--132
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: S. P. Shary
rawtitle: A New Approach to the Analysis of Static Systems Under Internal Uncertainty
entry:
@InProceedings{Shary:1996:NAA,
  author =       "S. P. Shary",
  title =        "A New Approach to the Analysis of Static Systems Under
                 Internal Uncertainty",
  crossref =     "Alefeld:1996:SCV",
  pages =        "118--132",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: fparith.bib
label: Shewchuk:1996:APF
author: Jonathan Richard Shewchuk
title: Adaptive precision floating-point arithmetic and fast robust geometric predicates
type: Report
number: CMU-CS-96-140
institution: Department of Computer Science, Carnegie-Mellon University
address: Pittsburgh, PA, USA
pages: 53
year: 1996
bibdate: Fri Jan 06 11:59:17 2006
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2006.01.06 11:59:17 ???
keywords: floating-point arithmetic; multiple-precision arithmetic
acknowledgement: ack-nhfb
rawauthor: Jonathan Richard Shewchuk
rawtitle: Adaptive precision floating-point arithmetic and fast robust geometric predicates
abstract:
Exact computer arithmetic has a variety of uses including, but not limited to, the robust implementation of geometric algorithms. This report has three purposes. The first is to offer fast software-level algorithms for exact addition and multiplication of arbitrary precision floating-point values. The second is to propose a technique for adaptive-precision arithmetic that can often speed these algorithms when one wishes to perform multiprecision calculations that do not always require exact arithmetic, but must satisfy some error bound. The third is to provide a practical demonstration of these techniques, in the form of implementations of several common geometric calculations whose required degree of accuracy depends on their inputs. These robust geometric predicates are adaptive; their running time depends on the degree of uncertainty of the result, and is usually small.par These algorithms work on computers whose floating-point arithmetic uses radix two and exact rounding, including machines complying with the IEEE 754 standard. The inputs to the predicates may be arbitrary single or double precision floating-point numbers. C code is publicly available for the 2D and 3D orientation and incircle tests, and robust Delaunay triangulation using these tests. Timings of the implementations demonstrate their effectiveness.

rawabstract:
Exact computer arithmetic has a variety of uses including, but not limited to, the robust implementation of geometric algorithms. This report has three purposes. The first is to offer fast software-level algorithms for exact addition and multiplication of arbitrary precision floating-point values. The second is to propose a technique for adaptive-precision arithmetic that can often speed these algorithms when one wishes to perform multiprecision calculations that do not always require exact arithmetic, but must satisfy some error bound. The third is to provide a practical demonstration of these techniques, in the form of implementations of several common geometric calculations whose required degree of accuracy depends on their inputs. These robust geometric predicates are adaptive; their running time depends on the degree of uncertainty of the result, and is usually small.\par These algorithms work on computers whose floating-point arithmetic uses radix two and exact rounding, including machines complying with the IEEE 754 standard. The inputs to the predicates may be arbitrary single or double precision floating-point numbers. C code is publicly available for the 2D and 3D orientation and incircle tests, and robust Delaunay triangulation using these tests. Timings of the implementations demonstrate their effectiveness.

entry:
@TechReport{Shewchuk:1996:APF,
  author =       "Jonathan Richard Shewchuk",
  title =        "Adaptive precision floating-point arithmetic and fast
                 robust geometric predicates",
  type =         "Report",
  number =       "CMU-CS-96-140",
  institution =  "Department of Computer Science, Carnegie-Mellon
                 University",
  address =      "Pittsburgh, PA, USA",
  pages =        "53",
  year =         "1996",
  bibdate =      "Fri Jan 06 11:59:17 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Exact computer arithmetic has a variety of uses
                 including, but not limited to, the robust
                 implementation of geometric algorithms. This report has
                 three purposes. The first is to offer fast
                 software-level algorithms for exact addition and
                 multiplication of arbitrary precision floating-point
                 values. The second is to propose a technique for
                 adaptive-precision arithmetic that can often speed
                 these algorithms when one wishes to perform
                 multiprecision calculations that do not always require
                 exact arithmetic, but must satisfy some error bound.
                 The third is to provide a practical demonstration of
                 these techniques, in the form of implementations of
                 several common geometric calculations whose required
                 degree of accuracy depends on their inputs. These
                 robust geometric predicates are adaptive; their running
                 time depends on the degree of uncertainty of the
                 result, and is usually small.\par

                 These algorithms work on computers whose floating-point
                 arithmetic uses radix two and exact rounding, including
                 machines complying with the IEEE 754 standard. The
                 inputs to the predicates may be arbitrary single or
                 double precision floating-point numbers. C code is
                 publicly available for the 2D and 3D orientation and
                 incircle tests, and robust Delaunay triangulation using
                 these tests. Timings of the implementations demonstrate
                 their effectiveness.",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point arithmetic; multiple-precision
                 arithmetic",
}


bibtype: inproceedings
filename: fparith.bib
label: Shewchuk:1996:RAF
author: Jonathan Richard Shewchuk
booktitle: Proceedings of the 12th Annual ACM Symposium on Computational Geometry
title: Robust Adaptive Floating-Point Geometric Predicates
publisher: pub-ACM
address: pub-ACM:adr
pages: 141--150
year: 1996
DOI: https://doi.org/10.1145/237218.237337
bibdate: Sat May 1 15:33:15 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.05.01 15:33:15 ???
URL: http://www.cs.cmu.edu/afs/cs/project/quake/public/papers/robust-predicates.ps
acknowledgement: ack-nhfb
rawauthor: Jonathan Richard Shewchuk
rawbooktitle: {Proceedings of the 12th Annual ACM Symposium on Computational Geometry}
rawtitle: Robust Adaptive Floating-Point Geometric Predicates
entry:
@InProceedings{Shewchuk:1996:RAF,
  author =       "Jonathan Richard Shewchuk",
  booktitle =    "{Proceedings of the 12th Annual ACM Symposium on
                 Computational Geometry}",
  title =        "Robust Adaptive Floating-Point Geometric Predicates",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "141--150",
  year =         "1996",
  DOI =          "https://doi.org/10.1145/237218.237337",
  bibdate =      "Sat May 1 15:33:15 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.cmu.edu/afs/cs/project/quake/public/papers/robust-predicates.ps",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Shewchuk:1996:TEQ
author: J. R. Shewchuk
editor: Ming C. Lin and Dinesh Manocha
booktitle: Applied Computational Geometry: Towards Geometric Engineering
title: Triangle: Engineering a $2$D Quality Mesh Generator and Delaunay Triangulator
journal: j-LECT-NOTES-COMP-SCI
volume: 1148
pages: 203--222
year: 1996
CODEN: LNCSD9
DOI: https://doi.org/10.1007/BFb0014497
ISBN: 3-540-61785-X (softcover), 3-540-70680-1 (e-book) OR 354061785X (softcover), 3540706801 (ebook)
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Dec 21 09:47:26 1996
bibtimestamp: 1996.12.21 09:47:26 ???
URL: https://link.springer.com/chapter/10.1007/BFb0014497
fjournal: Lecture Notes in Computer Science
keywords: Delaunay triangulation; exact arithmetic; refinement algorithm; refinement stage; roundoff error
remark: First ACM Workshop on Applied Computational Geometry.
acknowledgement: ack-nhfb
bookURL: https://link.springer.com/book/10.1007/BFb0014474
journalURL: http://link.springer.com/bookseries/558
rawauthor: J. R. Shewchuk
rawbooktitle: Applied Computational Geometry: Towards Geometric Engineering
raweditor: Ming C. Lin and Dinesh Manocha
rawtitle: {Triangle}: Engineering a {$2$D} Quality Mesh Generator and {Delaunay} Triangulator
ISBN13:
978-3-540-61785-3 (softcover), 978-3-540-70680-9 (e-book) OR 9783540617853 (softcover), 9783540706809 (ebook)

bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/lncs1996b.bib

entry:
@Article{Shewchuk:1996:TEQ,
  author =       "J. R. Shewchuk",
  editor =       "Ming C. Lin and Dinesh Manocha",
  booktitle =    "Applied Computational Geometry: Towards Geometric
                 Engineering",
  title =        "{Triangle}: Engineering a {$2$D} Quality Mesh
                 Generator and {Delaunay} Triangulator",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1148",
  pages =        "203--222",
  year =         "1996",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/BFb0014497",
  ISBN =         "3-540-61785-X (softcover), 3-540-70680-1 (e-book)",
  ISBN-13 =      "978-3-540-61785-3 (softcover), 978-3-540-70680-9
                 (e-book)",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Dec 21 09:47:26 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/lncs1996b.bib",
  URL =          "https://link.springer.com/chapter/10.1007/BFb0014497",
  acknowledgement = ack-nhfb,
  book-URL =     "https://link.springer.com/book/10.1007/BFb0014474",
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
  keywords =     "Delaunay triangulation; exact arithmetic; refinement
                 algorithm; refinement stage; roundoff error",
  remark =       "First ACM Workshop on Applied Computational
                 Geometry.",
}


bibtype: inproceedings
filename: fparith.bib
label: Shokin:1996:IPI
author: Y. I. Shokin
title: On Interval Problems, Interval Algorithms and Their Computational Complexity
crossref: Alefeld:1996:SCV
pages: 314--328
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: Y. I. Shokin
rawtitle: On Interval Problems, Interval Algorithms and Their Computational Complexity
entry:
@InProceedings{Shokin:1996:IPI,
  author =       "Y. I. Shokin",
  title =        "On Interval Problems, Interval Algorithms and Their
                 Computational Complexity",
  crossref =     "Alefeld:1996:SCV",
  pages =        "314--328",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Sinclair:1996:ORS
author: R. Sinclair
title: Optimization of reciprocals and square roots on the i860 microprocessor
journal: j-INT-J-HIGH-SPEED-COMPUTING
volume: 8
number: 1
pages: 57--64
year: 1996
CODEN: IHSCEZ
ISSN: 0129-0533 OR 01290533
bibdate: Mon Feb 25 11:19:22 MST 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Article1st database
bibtimestamp: 2002.02.25 11:19:22 MST
fjournal: International Journal of High Speed Computing
acknowledgement: ack-nhfb
journalURL: http://www.worldscientific.com/worldscinet/ijhsc
rawauthor: R. Sinclair
rawtitle: Optimization of reciprocals and square roots on the {i860} microprocessor
entry:
@Article{Sinclair:1996:ORS,
  author =       "R. Sinclair",
  title =        "Optimization of reciprocals and square roots on the
                 {i860} microprocessor",
  journal =      j-INT-J-HIGH-SPEED-COMPUTING,
  volume =       "8",
  number =       "1",
  pages =        "57--64",
  year =         "1996",
  CODEN =        "IHSCEZ",
  ISSN =         "0129-0533",
  bibdate =      "Mon Feb 25 11:19:22 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Article1st database",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of High Speed Computing",
  journal-URL =  "http://www.worldscientific.com/worldscinet/ijhsc",
}


bibtype: article
filename: fparith.bib
label: Singer:1996:EAP
author: Benjamin Singer and George Saon
title: An efficient algorithm for parallel integer multiplication
journal: j-J-NETW-COMPUT-APPL
volume: 19
number: 4
pages: 415--418
month: oct
monthnumber: 10
year: 1996
CODEN: JNCAF3
ISSN: 1084-8045 (print), 1095-8592 (electronic) OR 10848045 (print), 10958592 (electronic)
ISSNL: 1084-8045 OR 10848045
bibdate: Wed Jan 28 15:41:22 MST 2015
bibtimestamp: 2015.01.28 15:41:22 MST
URL: http://www.sciencedirect.com/science/article/pii/S1084804596900296
fjournal: Journal of Network and Computer Applications
acknowledgement: ack-nhfb
ajournal: J. Netw. Comput. Appl.
journalURL: http://www.sciencedirect.com/science/journal/10848045
rawauthor: Benjamin Singer and George Saon
rawtitle: An efficient algorithm for parallel integer multiplication
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/jnetwcomputappl.bib

entry:
@Article{Singer:1996:EAP,
  author =       "Benjamin Singer and George Saon",
  title =        "An efficient algorithm for parallel integer
                 multiplication",
  journal =      j-J-NETW-COMPUT-APPL,
  volume =       "19",
  number =       "4",
  pages =        "415--418",
  month =        oct,
  year =         "1996",
  CODEN =        "JNCAF3",
  ISSN =         "1084-8045 (print), 1095-8592 (electronic)",
  ISSN-L =       "1084-8045",
  bibdate =      "Wed Jan 28 15:41:22 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jnetwcomputappl.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1084804596900296",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Netw. Comput. Appl.",
  fjournal =     "Journal of Network and Computer Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/10848045",
}


bibtype: article
filename: fparith.bib
label: Soderquist:1996:AFT
author: Peter Soderquist and Miriam Leeser
title: Area and Performance Tradeoffs in Floating-Point Divide and Square-Root Implementations
journal: j-COMP-SURV
volume: 28
number: 3
pages: 518--564
month: sep
monthnumber: 9
year: 1996
CODEN: CMSVAN
ISSN: 0360-0300 (print), 1557-7341 (electronic) OR 03600300 (print), 15577341 (electronic)
ISSNL: 0360-0300 OR 03600300
bibdate: Wed Nov 13 06:52:01 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.11.13 06:52:01 MST
fjournal: ACM Computing Surveys
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J204
rawauthor: Peter Soderquist and Miriam Leeser
rawtitle: Area and Performance Tradeoffs in Floating-Point Divide and Square-Root Implementations
entry:
@Article{Soderquist:1996:AFT,
  author =       "Peter Soderquist and Miriam Leeser",
  title =        "Area and Performance Tradeoffs in Floating-Point
                 Divide and Square-Root Implementations",
  journal =      j-COMP-SURV,
  volume =       "28",
  number =       "3",
  pages =        "518--564",
  month =        sep,
  year =         "1996",
  CODEN =        "CMSVAN",
  ISSN =         "0360-0300 (print), 1557-7341 (electronic)",
  ISSN-L =       "0360-0300",
  bibdate =      "Wed Nov 13 06:52:01 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Computing Surveys",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J204",
}


bibtype: article
filename: fparith.bib
label: Soderquist:1996:APT
author: Peter Soderquist and Miriam Leeser
title: Area and Performance Tradeoffs in Floating-Point Divide and Square-Root Implementations
journal: j-COMP-SURV
volume: 28
number: 3
pages: 518--564
month: sep
monthnumber: 9
year: 1996
CODEN: CMSVAN
DOI: https://doi.org/10.1145/243439.243481
ISSN: 0360-0300 (print), 1557-7341 (electronic) OR 03600300 (print), 15577341 (electronic)
ISSNL: 0360-0300 OR 03600300
bibdate: Thu Jun 19 09:54:32 MDT 2008
bibtimestamp: 2008.06.19 09:54:32 MDT
URL: http://www.acm.org/pubs/citations/journals/surveys/1996-28-3/p518-soderquist/
fjournal: ACM Computing Surveys
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J204
rawauthor: Peter Soderquist and Miriam Leeser
rawtitle: Area and Performance Tradeoffs in Floating-Point Divide and Square-Root Implementations
bibsource:
http://www.acm.org/pubs/contents/journals/surveys/; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
Floating-point divide and square-root operations are essential to many scientific and engineering applications, and are required in all computer systems that support the IEEE floating-point standard. Yet many current microprocessors provide only weak support for these operations. The latency and throughput of division are typically far inferior to those of floating-point addition and multiplication, and square-root performance is often even lower. This article argues the case for high-performance division and square root. It also explains the algorithms and implementations of the primary techniques, subtractive and multiplicative methods, employed in microprocessor floating-point units with their associated area/performance tradeoffs. Case studies of representative floating-point unit configurations are presented, supported by simulation results using a carefully selected benchmark, Givens rotation, to show the dynamic performance impact of the various implementation alternatives. The topology of the implementation is found to be an important performance factor. Multiplicative algorithms, such as the Newton--Raphson method and Goldschmidt's algorithm, can achieve low latencies. However, these implementations serialize multiply, divide, and square root operations through a single pipeline, which can lead to low throughput. While this hardware sharing yields low size requirements for baseline implementations, lower-latency versions require many times more area. For these reasons, multiplicative implementations are best suited to cases where subtractive methods are precluded by area constraints, and modest performance on divide and square root operations is tolerable. Subtractive algorithms, exemplified by radix-4 SRT and radix-16 SRT, can be made to execute in parallel with other floating-point operations.

keywords:
area and performance tradeoffs; arithmetic and logic structures; computer arithmetic.; computer system implementation; design studies. bf c.5.3: computer systems organization; design styles; division; floating-point; FPU; general; microcomputers; microprocessors. bf g.1.0: mathematics of computing; numerical analysis; parallel. bf c.4: computer systems organization; performance of systems; square root; SRT; bf b.2.1: hardware

subject:
bf B.2.1: Hardware, ARITHMETIC AND LOGIC STRUCTURES, Design Styles, Parallel. bf C.4: Computer Systems Organization, PERFORMANCE OF SYSTEMS, Design studies. bf C.5.3: Computer Systems Organization, COMPUTER SYSTEM IMPLEMENTATION, Microcomputers, Microprocessors. bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic.

rawabstract:
Floating-point divide and square-root operations are essential to many scientific and engineering applications, and are required in all computer systems that support the IEEE floating-point standard. Yet many current microprocessors provide only weak support for these operations. The latency and throughput of division are typically far inferior to those of floating-point addition and multiplication, and square-root performance is often even lower. This article argues the case for high-performance division and square root. It also explains the algorithms and implementations of the primary techniques, subtractive and multiplicative methods, employed in microprocessor floating-point units with their associated area/performance tradeoffs. Case studies of representative floating-point unit configurations are presented, supported by simulation results using a carefully selected benchmark, Givens rotation, to show the dynamic performance impact of the various implementation alternatives. The topology of the implementation is found to be an important performance factor. Multiplicative algorithms, such as the Newton--Raphson method and Goldschmidt's algorithm, can achieve low latencies. However, these implementations serialize multiply, divide, and square root operations through a single pipeline, which can lead to low throughput. While this hardware sharing yields low size requirements for baseline implementations, lower-latency versions require many times more area. For these reasons, multiplicative implementations are best suited to cases where subtractive methods are precluded by area constraints, and modest performance on divide and square root operations is tolerable. Subtractive algorithms, exemplified by radix-4 SRT and radix-16 SRT, can be made to execute in parallel with other floating-point operations.

entry:
@Article{Soderquist:1996:APT,
  author =       "Peter Soderquist and Miriam Leeser",
  title =        "Area and Performance Tradeoffs in Floating-Point
                 Divide and Square-Root Implementations",
  journal =      j-COMP-SURV,
  volume =       "28",
  number =       "3",
  pages =        "518--564",
  month =        sep,
  year =         "1996",
  CODEN =        "CMSVAN",
  DOI =          "https://doi.org/10.1145/243439.243481",
  ISSN =         "0360-0300 (print), 1557-7341 (electronic)",
  ISSN-L =       "0360-0300",
  bibdate =      "Thu Jun 19 09:54:32 MDT 2008",
  bibsource =    "http://www.acm.org/pubs/contents/journals/surveys/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/surveys/1996-28-3/p518-soderquist/",
  abstract =     "Floating-point divide and square-root operations are
                 essential to many scientific and engineering
                 applications, and are required in all computer systems
                 that support the IEEE floating-point standard. Yet many
                 current microprocessors provide only weak support for
                 these operations. The latency and throughput of
                 division are typically far inferior to those of
                 floating-point addition and multiplication, and
                 square-root performance is often even lower. This
                 article argues the case for high-performance division
                 and square root. It also explains the algorithms and
                 implementations of the primary techniques, subtractive
                 and multiplicative methods, employed in microprocessor
                 floating-point units with their associated
                 area/performance tradeoffs. Case studies of
                 representative floating-point unit configurations are
                 presented, supported by simulation results using a
                 carefully selected benchmark, Givens rotation, to show
                 the dynamic performance impact of the various
                 implementation alternatives. The topology of the
                 implementation is found to be an important performance
                 factor. Multiplicative algorithms, such as the
                 Newton--Raphson method and Goldschmidt's algorithm, can
                 achieve low latencies. However, these implementations
                 serialize multiply, divide, and square root operations
                 through a single pipeline, which can lead to low
                 throughput. While this hardware sharing yields low size
                 requirements for baseline implementations,
                 lower-latency versions require many times more area.
                 For these reasons, multiplicative implementations are
                 best suited to cases where subtractive methods are
                 precluded by area constraints, and modest performance
                 on divide and square root operations is tolerable.
                 Subtractive algorithms, exemplified by radix-4 SRT and
                 radix-16 SRT, can be made to execute in parallel with
                 other floating-point operations.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Computing Surveys",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J204",
  keywords =     "area and performance tradeoffs; arithmetic and logic
                 structures; computer arithmetic.; computer system
                 implementation; design studies. {\bf c.5.3}: computer
                 systems organization; design styles; division;
                 floating-point; FPU; general; microcomputers;
                 microprocessors. {\bf g.1.0}: mathematics of computing;
                 numerical analysis; parallel. {\bf c.4}: computer
                 systems organization; performance of systems; square
                 root; SRT; {\bf b.2.1}: hardware",
  subject =      "{\bf B.2.1}: Hardware, ARITHMETIC AND LOGIC
                 STRUCTURES, Design Styles, Parallel. {\bf C.4}:
                 Computer Systems Organization, PERFORMANCE OF SYSTEMS,
                 Design studies. {\bf C.5.3}: Computer Systems
                 Organization, COMPUTER SYSTEM IMPLEMENTATION,
                 Microcomputers, Microprocessors. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Computer arithmetic.",
}


bibtype: incollection
filename: fparith.bib
label: Steele:1996:EL
author: Guy L. Steele Jr. and Richard P. Gabriel
title: The evolution of Lisp
crossref: Bergin:1996:HPL
pages: 233--330
year: 1996
bibdate: Wed Jan 29 17:01:12 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.01.29 17:01:12 ???
keywords: decimal floating-point arithmetic
acknowledgement: ack-nhfb
rawauthor: Guy L. {Steele Jr.} and Richard P. Gabriel
rawtitle: The evolution of {Lisp}
remark:
From cite Steele:2004:RHP: ``In early 1971, he [White] began to analyze the machine-language algorithm used in the implementation of MacLisp (described in this report) to convert PDP-10 floating-point numbers into decimal notation.''

entry:
@InCollection{Steele:1996:EL,
  author =       "Guy L. {Steele Jr.} and Richard P. Gabriel",
  title =        "The evolution of {Lisp}",
  crossref =     "Bergin:1996:HPL",
  pages =        "233--330",
  year =         "1996",
  bibdate =      "Wed Jan 29 17:01:12 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
  remark =       "From \cite{Steele:2004:RHP}: ``In early 1971, he
                 [White] began to analyze the machine-language algorithm
                 used in the implementation of MacLisp (described in
                 this report) to convert PDP-10 floating-point numbers
                 into decimal notation.''",
}


bibtype: book
filename: fparith.bib
label: Stewart:1996:ANA
author: G. W. (Gilbert W.) Stewart
publisher: pub-SIAM
address: pub-SIAM:adr
pages: x + 200
year: 1996
DOI: https://doi.org/10.1137/1.9781611971491
ISBN: 0-89871-362-5 (paperback) OR 0898713625 (paperback)
ISBN13: 978-0-89871-362-6 (paperback) OR 9780898713626 (paperback)
LCCN: QA297 .S785 1996
MRclass: 65-01
MRnumber: 1372060
bibdate: Tue May 27 08:35:41 MDT 2014
bibtimestamp: 2014.05.27 08:35:41 MDT
keywords: numerical analysis
subject: Numerical analysis
acknowledgement: ack-nhfb
rawauthor: G. W. (Gilbert W.) Stewart
title:
Afternotes on numerical analysis: a series of lectures on elementary numerical analysis presented at the University of Maryland at College Park and recorded after the fact

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/numana1990.bib; z3950.loc.gov:7090/Voyager

URL:
http://www.loc.gov/catdir/enhancements/fy0726/95047768-d.html; http://www.loc.gov/catdir/enhancements/fy0726/95047768-t.html

TOC:
Part I. Nonlinear Equations Lecture 1. By the Dawn's Early Light Interval Bisection Relative Error Lecture 2. Newton's Method Reciprocals and Square Roots Local Convergence Analysis Slow Death Lecture 3. A Quasi-Newton Method Rates of Convergence Iterating for a Fixed Point Multiple Zeros Ending with a Proposition Lecture 4. The Secant Method Convergence Rate of Convergence Multipoint Methods Muller's Method The Linear-Fractional Method Lecture 5. A Hybrid Method Errors, Accuracy, and Condition Numbers Part II. Computer Arithmetic: Lecture 6. Floating-Point Numbers Overflow and Underflow Rounding Error Floating-point Arithmetic Lecture 7. Computing Sums Backward Error Analysis Perturbation Analysis Cheap and Chippy Chopping Lecture 8. Cancellation The Quadratic Equation That Fatal Bit of Rounding Error Envoi Part III. Linear Equations Lecture 9. Matrices, Vectors, and Scalars Operations with Matrices Rank-One Matrices Partitioned Matrices Lecture 10. Theory of Linear Systems Computational Generalities Triangular Systems Operation Counts Lecture 11. Memory Considerations Row Oriented Algorithms A Column Oriented Algorithm General Observations on Row and Column Orientation Basic Linear Algebra Subprograms Lecture 12. Positive Definite Matrices The Cholesky Decomposition Economics Lecture 13. Inner-Product Form of the Cholesky Algorithm Gaussian Elimination Lecture 14. Pivoting BLAS Upper Hessenberg and Tridiagonal Systems Lecture 15. Vector Norms Matrix Norms Relative Error Sensitivity of Linear Systems Lecture 16. The Condition of Linear Systems Artificial Ill Conditioning Rounding Error and Gaussian Elimination Comments on the Analysis Lecture 17. The Wonderful Residual: A Project Introduction More on Norms The Wonderful Residual Matrices with Known Condition Invert and Multiply Cramer's Rule Submission Part IV. Polynomial Interpolation Lecture 18. Quadratic Interpolation Shifting Polynomial Interpolation Lagrange Polynomials and Existence Uniqueness Lecture 19. Synthetic Division The Newton Form of the Interpolant Evaluation Existence Divided Differences Lecture 20. Error in Interpolation Error Bounds Convergence Chebyshev Points Part V. Numerical Integration and Differentiation Lecture 21. Numerical Integration Change of Intervals The Trapezoidal Rule The Composite Trapezoidal Rule Newton-Cotes Formulas Undetermined Coefficients and Simpson's Rule Lecture 22. The Composite Simpson's Rule Errors in Simpson's Rule Weighting Functions Gaussian Quadrature Lecture 23. The Setting Orthogonal Polynomials Existence Zeros of Orthogonal Polynomials Gaussian Quadrature Error and Convergence Examples Lecture 24. Numerical Differentiation and Integration Formulas From Power Series Limitations Bibliography

rawtitle:
Afternotes on numerical analysis: a series of lectures on elementary numerical analysis presented at the {University of Maryland at College Park} and recorded after the fact

rawTOC:
Part I. Nonlinear Equations \\ \\ Lecture 1. By the Dawn's Early Light \\ Interval Bisection \\ Relative Error \\ \\ Lecture 2. Newton's Method \\ Reciprocals and Square Roots \\ Local Convergence Analysis \\ Slow Death \\ \\ Lecture 3. A Quasi-Newton Method \\ Rates of Convergence \\ Iterating for a Fixed Point \\ Multiple Zeros \\ Ending with a Proposition \\ \\ Lecture 4. The Secant Method \\ Convergence \\ Rate of Convergence \\ Multipoint Methods \\ Muller's Method \\ The Linear-Fractional Method \\ \\ Lecture 5. A Hybrid Method \\ Errors, Accuracy, and Condition Numbers \\ \\ Part II. Computer Arithmetic: \\ \\ Lecture 6. Floating-Point Numbers \\ Overflow and Underflow \\ Rounding Error \\ Floating-point Arithmetic \\ \\ Lecture 7. Computing Sums \\ Backward Error Analysis \\ Perturbation Analysis \\ Cheap and Chippy Chopping \\ \\ Lecture 8. Cancellation \\ The Quadratic Equation \\ That Fatal Bit of Rounding Error \\ Envoi \\ \\ Part III. Linear Equations \\ \\ Lecture 9. Matrices, Vectors, and Scalars \\ Operations with Matrices \\ Rank-One Matrices \\ Partitioned Matrices \\ \\ Lecture 10. Theory of Linear Systems \\ Computational Generalities \\ Triangular Systems \\ Operation Counts \\ \\ Lecture 11. Memory Considerations \\ Row Oriented Algorithms \\ A Column Oriented Algorithm \\ General Observations on Row and Column Orientation \\ Basic Linear Algebra Subprograms \\ \\ Lecture 12. Positive Definite Matrices \\ The Cholesky Decomposition \\ Economics \\ \\ Lecture 13. Inner-Product Form of the Cholesky Algorithm \\ Gaussian Elimination \\ \\ Lecture 14. Pivoting \\ BLAS \\ Upper Hessenberg and Tridiagonal Systems \\ \\ Lecture 15. Vector Norms \\ Matrix Norms \\ Relative Error \\ Sensitivity of Linear Systems \\ \\ Lecture 16. The Condition of Linear Systems \\ Artificial Ill Conditioning \\ Rounding Error and Gaussian Elimination \\ Comments on the Analysis \\ \\ Lecture 17. The Wonderful Residual: A Project \\ Introduction \\ More on Norms \\ The Wonderful Residual \\ Matrices with Known Condition \\ Invert and Multiply \\ Cramer's Rule \\ Submission \\ \\ Part IV. Polynomial Interpolation \\ \\ Lecture 18. Quadratic Interpolation \\ Shifting \\ Polynomial Interpolation \\ Lagrange Polynomials and Existence \\ Uniqueness \\ \\ Lecture 19. Synthetic Division \\ The Newton Form of the Interpolant \\ Evaluation \\ Existence \\ Divided Differences \\ \\ Lecture 20. Error in Interpolation \\ Error Bounds \\ Convergence \\ Chebyshev Points \\ \\ Part V. Numerical Integration and Differentiation \\ \\ Lecture 21. Numerical Integration \\ Change of Intervals \\ The Trapezoidal Rule \\ The Composite Trapezoidal Rule \\ Newton-Cotes Formulas \\ Undetermined Coefficients and Simpson's Rule \\ \\ Lecture 22. The Composite Simpson's Rule \\ Errors in Simpson's Rule \\ Weighting Functions \\ Gaussian Quadrature \\ \\ Lecture 23. The Setting \\ Orthogonal Polynomials \\ Existence \\ Zeros of Orthogonal Polynomials \\ Gaussian Quadrature \\ Error and Convergence \\ Examples \\ \\ Lecture 24. Numerical Differentiation and Integration \\ Formulas From Power Series \\ Limitations \\ Bibliography

entry:
@Book{Stewart:1996:ANA,
  author =       "G. W. (Gilbert W.) Stewart",
  title =        "Afternotes on numerical analysis: a series of lectures
                 on elementary numerical analysis presented at the
                 {University of Maryland at College Park} and recorded
                 after the fact",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "x + 200",
  year =         "1996",
  DOI =          "https://doi.org/10.1137/1.9781611971491",
  ISBN =         "0-89871-362-5 (paperback)",
  ISBN-13 =      "978-0-89871-362-6 (paperback)",
  LCCN =         "QA297 .S785 1996",
  MRclass =      "65-01",
  MRnumber =     "1372060",
  bibdate =      "Tue May 27 08:35:41 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/numana1990.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0726/95047768-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0726/95047768-t.html",
  acknowledgement = ack-nhfb,
  keywords =     "numerical analysis",
  subject =      "Numerical analysis",
  tableofcontents = "Part I. Nonlinear Equations \\
                 \\
                 Lecture 1. By the Dawn's Early Light \\
                 Interval Bisection \\
                 Relative Error \\
                 \\
                 Lecture 2. Newton's Method \\
                 Reciprocals and Square Roots \\
                 Local Convergence Analysis \\
                 Slow Death \\
                 \\
                 Lecture 3. A Quasi-Newton Method \\
                 Rates of Convergence \\
                 Iterating for a Fixed Point \\
                 Multiple Zeros \\
                 Ending with a Proposition \\
                 \\
                 Lecture 4. The Secant Method \\
                 Convergence \\
                 Rate of Convergence \\
                 Multipoint Methods \\
                 Muller's Method \\
                 The Linear-Fractional Method \\
                 \\
                 Lecture 5. A Hybrid Method \\
                 Errors, Accuracy, and Condition Numbers \\
                 \\
                 Part II. Computer Arithmetic: \\
                 \\
                 Lecture 6. Floating-Point Numbers \\
                 Overflow and Underflow \\
                 Rounding Error \\
                 Floating-point Arithmetic \\
                 \\
                 Lecture 7. Computing Sums \\
                 Backward Error Analysis \\
                 Perturbation Analysis \\
                 Cheap and Chippy Chopping \\
                 \\
                 Lecture 8. Cancellation \\
                 The Quadratic Equation \\
                 That Fatal Bit of Rounding Error \\
                 Envoi \\
                 \\
                 Part III. Linear Equations \\
                 \\
                 Lecture 9. Matrices, Vectors, and Scalars \\
                 Operations with Matrices \\
                 Rank-One Matrices \\
                 Partitioned Matrices \\
                 \\
                 Lecture 10. Theory of Linear Systems \\
                 Computational Generalities \\
                 Triangular Systems \\
                 Operation Counts \\
                 \\
                 Lecture 11. Memory Considerations \\
                 Row Oriented Algorithms \\
                 A Column Oriented Algorithm \\
                 General Observations on Row and Column Orientation \\
                 Basic Linear Algebra Subprograms \\
                 \\
                 Lecture 12. Positive Definite Matrices \\
                 The Cholesky Decomposition \\
                 Economics \\
                 \\
                 Lecture 13. Inner-Product Form of the Cholesky
                 Algorithm \\
                 Gaussian Elimination \\
                 \\
                 Lecture 14. Pivoting \\
                 BLAS \\
                 Upper Hessenberg and Tridiagonal Systems \\
                 \\
                 Lecture 15. Vector Norms \\
                 Matrix Norms \\
                 Relative Error \\
                 Sensitivity of Linear Systems \\
                 \\
                 Lecture 16. The Condition of Linear Systems \\
                 Artificial Ill Conditioning \\
                 Rounding Error and Gaussian Elimination \\
                 Comments on the Analysis \\
                 \\
                 Lecture 17. The Wonderful Residual: A Project \\
                 Introduction \\
                 More on Norms \\
                 The Wonderful Residual \\
                 Matrices with Known Condition \\
                 Invert and Multiply \\
                 Cramer's Rule \\
                 Submission \\
                 \\
                 Part IV. Polynomial Interpolation \\
                 \\
                 Lecture 18. Quadratic Interpolation \\
                 Shifting \\
                 Polynomial Interpolation \\
                 Lagrange Polynomials and Existence \\
                 Uniqueness \\
                 \\
                 Lecture 19. Synthetic Division \\
                 The Newton Form of the Interpolant \\
                 Evaluation \\
                 Existence \\
                 Divided Differences \\
                 \\
                 Lecture 20. Error in Interpolation \\
                 Error Bounds \\
                 Convergence \\
                 Chebyshev Points \\
                 \\
                 Part V. Numerical Integration and Differentiation \\
                 \\
                 Lecture 21. Numerical Integration \\
                 Change of Intervals \\
                 The Trapezoidal Rule \\
                 The Composite Trapezoidal Rule \\
                 Newton-Cotes Formulas \\
                 Undetermined Coefficients and Simpson's Rule \\
                 \\
                 Lecture 22. The Composite Simpson's Rule \\
                 Errors in Simpson's Rule \\
                 Weighting Functions \\
                 Gaussian Quadrature \\
                 \\
                 Lecture 23. The Setting \\
                 Orthogonal Polynomials \\
                 Existence \\
                 Zeros of Orthogonal Polynomials \\
                 Gaussian Quadrature \\
                 Error and Convergence \\
                 Examples \\
                 \\
                 Lecture 24. Numerical Differentiation and Integration
                 \\
                 Formulas From Power Series \\
                 Limitations \\
                 Bibliography",
}


bibtype: article
filename: fparith.bib
label: Suzuki:1996:LZA
author: H. Suzuki and H. Morinaka and H. Makino and Y. Nakase and K. Mashiko and T. Sumi
title: Leading-zero anticipatory logic for high-speed floating point addition
journal: j-IEEE-J-SOLID-STATE-CIRCUITS
volume: 31
number: 8
pages: 1157--1164
month: aug
monthnumber: 8
year: 1996
CODEN: IJSCBC
ISSN: 0018-9200 (print), 1558-173X (electronic) OR 00189200 (print), 1558173X (electronic)
ISSNL: 0018-9200 OR 00189200
bibdate: Sat Jul 16 08:40:52 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:52 MDT
note: See comments cite Oklobdzija:1997:CLZ.
fjournal: IEEE Journal of Solid-State Circuits
acknowledgement: ack-nhfb
rawauthor: H. Suzuki and H. Morinaka and H. Makino and Y. Nakase and K. Mashiko and T. Sumi
rawnote: See comments \cite{Oklobdzija:1997:CLZ}.
rawtitle: Leading-zero anticipatory logic for high-speed floating point addition
entry:
@Article{Suzuki:1996:LZA,
  author =       "H. Suzuki and H. Morinaka and H. Makino and Y. Nakase
                 and K. Mashiko and T. Sumi",
  title =        "Leading-zero anticipatory logic for high-speed
                 floating point addition",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "31",
  number =       "8",
  pages =        "1157--1164",
  month =        aug,
  year =         "1996",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See comments \cite{Oklobdzija:1997:CLZ}.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  summary =      "This paper describes a new leading-zero anticipatory
                 (LZA) logic for high-speed floating-point addition
                 (FADD). This logic carries out the pre-decoding for
                 normalization concurrently with addition for the
                 significand. It also performs the shift operation
                 \ldots{}",
}


bibtype: mastersthesis
filename: fparith.bib
label: Tan:1996:MPF
author: Kien Beng Tan
title: A micro-power, floating point analog-to-digital converter
type: Thesis (M.S.)
school: Department of Electrical Engineering, University of California, Los Angeles
address: Los Angeles, CA, USA
year: 1996
bibdate: Thu Oct 24 14:19:35 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.10.24 14:19:35 MDT
keywords: dissertations, academic -- UCLA -- Electrical Engineering
acknowledgement: ack-nhfb
rawauthor: Kien Beng Tan
rawtitle: A micro-power, floating point analog-to-digital converter
entry:
@MastersThesis{Tan:1996:MPF,
  author =       "Kien Beng Tan",
  title =        "A micro-power, floating point analog-to-digital
                 converter",
  type =         "Thesis ({M.S.})",
  school =       "Department of Electrical Engineering, University of
                 California, Los Angeles",
  address =      "Los Angeles, CA, USA",
  pages =        "????",
  year =         "1996",
  bibdate =      "Thu Oct 24 14:19:35 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "dissertations, academic -- UCLA -- Electrical
                 Engineering",
}


bibtype: inproceedings
filename: fparith.bib
label: Tatsaki:1996:AIC
author: A. Tatsaki
title: An adaptive image coder based on residue number system
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 700--703
year: 1996
DOI: https://doi.org/10.1109/ICECS.1996.584458
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: A. Tatsaki
rawtitle: An adaptive image coder based on residue number system
booktitle:
Proceedings of the Third IEEE International Conference on Electronics, Circuits, and Systems, 1996. ICECS 96

rawbooktitle:
Proceedings of the Third {IEEE} International Conference on Electronics, Circuits, and Systems, 1996. {ICECS 96}

entry:
@InProceedings{Tatsaki:1996:AIC,
  author =       "A. Tatsaki",
  booktitle =    "Proceedings of the Third {IEEE} International
                 Conference on Electronics, Circuits, and Systems, 1996.
                 {ICECS 96}",
  title =        "An adaptive image coder based on residue number
                 system",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "700--703",
  year =         "1996",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ICECS.1996.584458",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "An efficient coder for adaptive lossy compression of
                 still images is presented. It is based on a
                 computational efficient extraction of the details of
                 image blocks. The Discrete Cosine Transform and an
                 efficient Lattice Vector Quantizer based on the
                 \ldots{}",
}


bibtype: mastersthesis
filename: fparith.bib
label: Trott:1996:AWL
author: Aaron Gregory Trott
type: M.S.E.E. thesis
school: Mississippi State University
address: Mississippi State, MS 39762, USA
pages: 103
year: 1996
bibdate: Fri Feb 1 09:20:32 MST 2013
bibtimestamp: 2013.02.01 09:20:32 MST
URL: http://search.proquest.com/docview/304273691
subject: Electrical engineering; Aerospace materials
acknowledgement: ack-nhfb
advisor: Robert J. Moorhead
rawauthor: Aaron Gregory Trott
title:
The application of wavelets to lossless compression and progressive transmission of floating point data in three-dimensional curvilinear grids

bibsource:
http://search.proquest.com/; https://www.math.utah.edu/pub/tex/bib/datacompression.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

rawtitle:
The application of wavelets to lossless compression and progressive transmission of floating point data in three-dimensional curvilinear grids

entry:
@MastersThesis{Trott:1996:AWL,
  author =       "Aaron Gregory Trott",
  title =        "The application of wavelets to lossless compression
                 and progressive transmission of floating point data in
                 three-dimensional curvilinear grids",
  type =         "{M.S.E.E.} thesis",
  school =       "Mississippi State University",
  address =      "Mississippi State, MS 39762, USA",
  pages =        "103",
  year =         "1996",
  bibdate =      "Fri Feb 1 09:20:32 MST 2013",
  bibsource =    "http://search.proquest.com/;
                 https://www.math.utah.edu/pub/tex/bib/datacompression.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://search.proquest.com/docview/304273691",
  acknowledgement = ack-nhfb,
  advisor =      "Robert J. Moorhead",
  classification = "0538: Aerospace materials; 0544: Electrical
                 engineering",
  dissertation-thesis-number = "1379238",
  subject =      "Electrical engineering; Aerospace materials",
}


bibtype: misc
filename: fparith.bib
label: Urano:1996:MAN
author: M. Urano and T. Taniguchi
title: Method and apparatus for normalization of a floating point binary number
pages: 103
day: 30
month: apr
monthnumber: 4
year: 1996
bibdate: Fri Nov 28 15:31:26 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 15:31:26 ???
note: U.S. Patent No. 5,513,362.
acknowledgement: ack-mfc
rawauthor: M. Urano and T. Taniguchi
rawnote: U.S. Patent No. 5,513,362.
rawtitle: Method and apparatus for normalization of a floating point binary number
entry:
@Misc{Urano:1996:MAN,
  author =       "M. Urano and T. Taniguchi",
  title =        "Method and apparatus for normalization of a floating
                 point binary number",
  day =          "30",
  month =        apr,
  year =         "1996",
  bibdate =      "Fri Nov 28 15:31:26 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "U.S. Patent No. 5,513,362.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Vassilladis:1996:ARA
author: S. Vassilladis and S. Contofana and K. Bertels
title: $2$-$1$ addition and related arithmetic operations with threshold logic
journal: j-IEEE-TRANS-COMPUT
volume: 45
number: 9
pages: 1062--1067
month: sep
monthnumber: 9
year: 1996
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.537130
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 19:47:13 MDT 2011
bibtimestamp: 2011.07.06 19:47:13 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=537130
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: S. Vassilladis and S. Contofana and K. Bertels
rawtitle: $2$-$1$ addition and related arithmetic operations with threshold logic
entry:
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  author =       "S. Vassilladis and S. Contofana and K. Bertels",
  title =        "$2$-$1$ addition and related arithmetic operations
                 with threshold logic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "45",
  number =       "9",
  pages =        "1062--1067",
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  bibdate =      "Wed Jul 6 19:47:13 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
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  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Venners:1996:FPA
author: Bill Venners
title: Under the Hood: Floating-point arithmetic
journal: j-JAVAWORLD
volume: 1
number: 9
pages: 1062--1067
month: nov
monthnumber: 11
year: 1996
ISSN: 1091-8906 OR 10918906
bibdate: Thu Aug 13 08:48:26 MDT 1998
bibsource: http://www.javaworld.com/javaworld/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.08.13 08:48:26 MDT
URL: http://www.javaworld.com/javaworld/jw-10-1996/jw-10-hood.htm
acknowledgement: ack-nhfb
rawauthor: Bill Venners
rawtitle: Under the Hood: Floating-point arithmetic
entry:
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  author =       "Bill Venners",
  title =        "Under the Hood: Floating-point arithmetic",
  journal =      j-JAVAWORLD,
  volume =       "1",
  number =       "9",
  month =        nov,
  year =         "1996",
  CODEN =        "????",
  ISSN =         "1091-8906",
  bibdate =      "Thu Aug 13 08:48:26 MDT 1998",
  bibsource =    "http://www.javaworld.com/javaworld/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.javaworld.com/javaworld/jw-10-1996/jw-10-hood.htm",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: vonMatt:1996:RES
author: Urs von Matt and G. W. Stewart
title: Rounding errors in solving block Hessenberg systems
journal: j-MATH-COMPUT
volume: 65
number: 213
pages: 115--135
month: jan
monthnumber: 1
year: 1996
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65F05 (65G05)
MRnumber: 96e:65019
MRreviewer: Alfonso Laratta
bibdate: Fri Jul 16 10:38:30 MDT 1999
bibtimestamp: 1999.07.16 10:38:30 MDT
URL: http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-96-00667-9&u=/mcom/1996-65-213/
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
ajournal: Math. Comput.
classcodes: C4140 (Linear algebra); C1110 (Algebra); C4240 (Programming and algorithm theory)
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Urs {von Matt} and G. W. Stewart
rawtitle: Rounding errors in solving block {Hessenberg} systems
bibsource:
http://www.ams.org/mcom/1996-65-213; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib

keywords:
algebra; algorithm; algorithm theory; block diagonally dominant; block Hessenberg; block Hessenberg system; divide and conquer methods; divide-and-conquer; linear; linear system solution; linear systems; M-matrices; matrices; matrix algebra; rounding error analysis; rounding errors; solution; stable solution

entry:
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  author =       "Urs {von Matt} and G. W. Stewart",
  title =        "Rounding errors in solving block {Hessenberg}
                 systems",
  journal =      j-MATH-COMPUT,
  volume =       "65",
  number =       "213",
  pages =        "115--135",
  month =        jan,
  year =         "1996",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65F05 (65G05)",
  MRnumber =     "96e:65019",
  MRreviewer =   "Alfonso Laratta",
  bibdate =      "Fri Jul 16 10:38:30 MDT 1999",
  bibsource =    "http://www.ams.org/mcom/1996-65-213;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
  URL =          "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-96-00667-9&u=/mcom/1996-65-213/",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  classcodes =   "C4140 (Linear algebra); C1110 (Algebra); C4240
                 (Programming and algorithm theory)",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "algebra; algorithm; algorithm theory; block diagonally
                 dominant; block Hessenberg; block Hessenberg system;
                 divide and conquer methods; divide-and-conquer; linear;
                 linear system solution; linear systems; M-matrices;
                 matrices; matrix algebra; rounding error analysis;
                 rounding errors; solution; stable solution",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: inproceedings
filename: fparith.bib
label: Vrahatis:1996:GBM
author: M. N. Vrahatis
title: A Generalized Bisection Method for Large and Imprecise Problems
crossref: Alefeld:1996:SCV
pages: 186--192
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: M. N. Vrahatis
rawtitle: A Generalized Bisection Method for Large and Imprecise Problems
entry:
@InProceedings{Vrahatis:1996:GBM,
  author =       "M. N. Vrahatis",
  title =        "A Generalized Bisection Method for Large and Imprecise
                 Problems",
  crossref =     "Alefeld:1996:SCV",
  pages =        "186--192",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Werner:1996:CIW
author: K. Werner
title: Calculations of the Inverse Weierstrass Functions in an Arbitrary Machine Arithmetic
crossref: Alefeld:1996:SCV
pages: 72--78
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: K. Werner
rawtitle: Calculations of the Inverse {Weierstrass} Functions in an Arbitrary Machine Arithmetic
entry:
@InProceedings{Werner:1996:CIW,
  author =       "K. Werner",
  title =        "Calculations of the Inverse {Weierstrass} Functions in
                 an Arbitrary Machine Arithmetic",
  crossref =     "Alefeld:1996:SCV",
  pages =        "72--78",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Wiethoff:1996:PAE
author: A. Wiethoff
title: A Parallel Algorithm for Enclosing All Zeros of a Nonlinear System of Equations
crossref: Alefeld:1996:SCV
pages: 193--199
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: A. Wiethoff
rawtitle: A Parallel Algorithm for Enclosing All Zeros of a Nonlinear System of Equations
entry:
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  author =       "A. Wiethoff",
  title =        "A Parallel Algorithm for Enclosing All Zeros of a
                 Nonlinear System of Equations",
  crossref =     "Alefeld:1996:SCV",
  pages =        "193--199",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Williams:1996:TMF
author: K. B. Williams
journal: j-CCCUJ
volume: 14
number: 12
pages: 49--54, 58--65
month: dec
monthnumber: 12
year: 1996
CODEN: CCUJEX
ISSN: 1075-2838 OR 10752838
bibdate: Mon Apr 10 06:32:36 2000
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2000.04.10 06:32:36 ???
fjournal: C/C++ Users Journal
acknowledgement: ack-nhfb
rawauthor: K. B. Williams
title:
Testing Math Functions: When requirements are tight, we must carefully examine all potential sources of error. Make sure your math library isn't the weak link in the chain

note:
Describes a package that extends the Cody-Waite-Plauger work on the ELEFUNT package for the testing of the elementary functions, including the inverse hyperbolic functions, cube root, and Bessel functions of the first and second kinds. The C++ package implements 192-bit extended precision versions of all of the functions, so that accurate results are available for comparison with the normal double-precision results.

rawnote:
Describes a package that extends the Cody-Waite-Plauger work on the ELEFUNT package for the testing of the elementary functions, including the inverse hyperbolic functions, cube root, and Bessel functions of the first and second kinds. The C++ package implements 192-bit extended precision versions of all of the functions, so that accurate results are available for comparison with the normal double-precision results.

rawtitle:
Testing Math Functions: {When} requirements are tight, we must carefully examine all potential sources of error. {Make} sure your math library isn't the weak link in the chain

entry:
@Article{Williams:1996:TMF,
  author =       "K. B. Williams",
  title =        "Testing Math Functions: {When} requirements are tight,
                 we must carefully examine all potential sources of
                 error. {Make} sure your math library isn't the weak
                 link in the chain",
  journal =      j-CCCUJ,
  volume =       "14",
  number =       "12",
  pages =        "49--54, 58--65",
  month =        dec,
  year =         "1996",
  CODEN =        "CCUJEX",
  ISSN =         "1075-2838",
  bibdate =      "Mon Apr 10 06:32:36 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Describes a package that extends the
                 Cody-Waite-Plauger work on the ELEFUNT package for the
                 testing of the elementary functions, including the
                 inverse hyperbolic functions, cube root, and Bessel
                 functions of the first and second kinds. The C++
                 package implements 192-bit extended precision versions
                 of all of the functions, so that accurate results are
                 available for comparison with the normal
                 double-precision results.",
  acknowledgement = ack-nhfb,
  fjournal =     "C/C++ Users Journal",
}


bibtype: incollection
filename: fparith.bib
label: Zachary:1996:ESD
author: Joseph L. Zachary
title: Eratosthenes: Significant Digits and Interval Arithmetic
crossref: Zachary:1996:ISP
pages: 29--43
year: 1996
DOI: https://doi.org/10.1007/978-1-4612-2366-5_3
bibdate: Sat Feb 16 15:23:11 2013
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2013.02.16 15:23:11 ???
acknowledgement: ack-nhfb
rawauthor: Joseph L. Zachary
rawtitle: {Eratosthenes}: Significant Digits and Interval Arithmetic
entry:
@InCollection{Zachary:1996:ESD,
  author =       "Joseph L. Zachary",
  title =        "{Eratosthenes}: Significant Digits and Interval
                 Arithmetic",
  crossref =     "Zachary:1996:ISP",
  pages =        "29--43",
  year =         "1996",
  DOI =          "https://doi.org/10.1007/978-1-4612-2366-5_3",
  bibdate =      "Sat Feb 16 15:23:11 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: incollection
filename: fparith.bib
label: Zachary:1996:SHA
author: Joseph L. Zachary
title: Stairway to Heaven: Accumulation of Roundoff Error
crossref: Zachary:1996:ISP
pages: 45--61
year: 1996
DOI: https://doi.org/10.1007/978-1-4612-2366-5_4
bibdate: Sat Feb 16 15:30:56 2013
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2013.02.16 15:30:56 ???
acknowledgement: ack-nhfb
rawauthor: Joseph L. Zachary
rawtitle: Stairway to Heaven: Accumulation of Roundoff Error
entry:
@InCollection{Zachary:1996:SHA,
  author =       "Joseph L. Zachary",
  title =        "Stairway to Heaven: Accumulation of Roundoff Error",
  crossref =     "Zachary:1996:ISP",
  pages =        "45--61",
  year =         "1996",
  DOI =          "https://doi.org/10.1007/978-1-4612-2366-5_4",
  bibdate =      "Sat Feb 16 15:30:56 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Zgliczynski:1996:RVC
author: P. Zgliczynski
title: Rigorous Verification of Chaos in the Roessler Equations
crossref: Alefeld:1996:SCV
pages: 287--292
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: P. Zgliczynski
rawtitle: Rigorous Verification of Chaos in the {Roessler} Equations
entry:
@InProceedings{Zgliczynski:1996:RVC,
  author =       "P. Zgliczynski",
  title =        "Rigorous Verification of Chaos in the {Roessler}
                 Equations",
  crossref =     "Alefeld:1996:SCV",
  pages =        "287--292",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: phdthesis
filename: fparith.bib
label: Al-Twaijry:1997:APO
author: Hesham Abdulaziz Al-Twaijry
title: Area And Performance Optimized CMOS Multipliers
type: Ph.D. thesis
school: Department of Electrical Engineering, Stanford University
address: Stanford, CA, USA
month: aug
monthnumber: 8
year: 1997
bibdate: Mon Dec 24 10:02:37 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.12.24 10:02:37 ???
acknowledgement: ack-nhfb
rawauthor: Hesham Abdulaziz Al-Twaijry
rawtitle: Area And Performance Optimized {CMOS} Multipliers
entry:
@PhdThesis{Al-Twaijry:1997:APO,
  author =       "Hesham Abdulaziz Al-Twaijry",
  title =        "Area And Performance Optimized {CMOS} Multipliers",
  type =         "{Ph.D.} thesis",
  school =       "Department of Electrical Engineering, Stanford
                 University",
  address =      "Stanford, CA, USA",
  pages =        "????",
  month =        aug,
  year =         "1997",
  bibdate =      "Mon Dec 24 10:02:37 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Allaart:1997:ISC
author: Pieter C. Allaart
title: An Invariant-Sum Characterization of Benford's Law
journal: j-J-APPL-PROBAB
volume: 34
number: 1
pages: 288--291
month: mar
monthnumber: 3
year: 1997
CODEN: JPRBAM
DOI: https://doi.org/10.2307/3215195
ISSN: 0021-9002 (print), 1475-6072 (electronic) OR 00219002 (print), 14756072 (electronic)
ISSNL: 0021-9002 OR 00219002
bibdate: Fri Mar 30 11:25:14 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.03.30 11:25:14 ???
fjournal: Journal of Applied Probability
keywords: Benford's Law; Law of Anomalous Numbers; Zipf's Law
acknowledgement: ack-nhfb
journalURL: http://www.jstor.org/journals/00219002.html; http://projecteuclid.org/euclid.jap/
rawauthor: Pieter C. Allaart
rawtitle: An Invariant-Sum Characterization of {Benford's Law}
URL:
http://links.jstor.org/sici?sici=0021-9002%28199703%2934%3A1%3C288%3AAICOBL%3E2.0.CO%3B2-S&size=LARGE

abstract:
The accountant Nigrini remarked that in tables of data distributed according to Benford's law, the sum of all elements with first digit $ d (d = 1, 2, cdots , 9) $ is approximately constant. In this note, a mathematical formulation of Nigrini's observation is given and it is shown that Benford's law is the unique probability distribution such that the expected sum of all elements with first digits $ d_1, cdots , d_k $ is constant for every fixed $k$.

rawabstract:
The accountant Nigrini remarked that in tables of data distributed according to Benford's law, the sum of all elements with first digit $ d (d = 1, 2, \cdots, 9) $ is approximately constant. In this note, a mathematical formulation of Nigrini's observation is given and it is shown that Benford's law is the unique probability distribution such that the expected sum of all elements with first digits $ d_1, \cdots, d_k $ is constant for every fixed $k$.

entry:
@Article{Allaart:1997:ISC,
  author =       "Pieter C. Allaart",
  title =        "An Invariant-Sum Characterization of {Benford's Law}",
  journal =      j-J-APPL-PROBAB,
  volume =       "34",
  number =       "1",
  pages =        "288--291",
  month =        mar,
  year =         "1997",
  CODEN =        "JPRBAM",
  DOI =          "https://doi.org/10.2307/3215195",
  ISSN =         "0021-9002 (print), 1475-6072 (electronic)",
  ISSN-L =       "0021-9002",
  bibdate =      "Fri Mar 30 11:25:14 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://links.jstor.org/sici?sici=0021-9002%28199703%2934%3A1%3C288%3AAICOBL%3E2.0.CO%3B2-S&size=LARGE",
  abstract =     "The accountant Nigrini remarked that in tables of data
                 distributed according to Benford's law, the sum of all
                 elements with first digit $ d (d = 1, 2, \cdots, 9) $
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                 formulation of Nigrini's observation is given and it is
                 shown that Benford's law is the unique probability
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                 every fixed $k$.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Probability",
  journal-URL =  "http://www.jstor.org/journals/00219002.html;
                 http://projecteuclid.org/euclid.jap/",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}


bibtype: techreport
filename: fparith.bib
label: Althaus:1997:MNF
author: Ernst Althaus and Kurt Mehlhorn
title: Maximum network flow with floating point arithmetic
type: Forschungsbericht
number: MPI-I-97-1-022
institution: Max-Planck-Institut fur Informatik
address: Saarbrucken, Germany
pages: 5
year: 1997
ISSN: 0946-011X OR 0946011X
bibdate: Thu May 09 08:55:36 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.09 08:55:36 ???
acknowledgement: ack-nhfb
rawauthor: Ernst Althaus and Kurt Mehlhorn
rawtitle: Maximum network flow with floating point arithmetic
entry:
@TechReport{Althaus:1997:MNF,
  author =       "Ernst Althaus and Kurt Mehlhorn",
  title =        "Maximum network flow with floating point arithmetic",
  type =         "Forschungsbericht",
  number =       "MPI-I-97-1-022",
  institution =  "Max-Planck-Institut f{\"u}r Informatik",
  address =      "Saarbr{\"u}cken, Germany",
  pages =        "5",
  year =         "1997",
  ISSN =         "0946-011X",
  bibdate =      "Thu May 09 08:55:36 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Anonymous:1997:BRPk
author: Anonymous
journal: j-COMPUT-MATH-APPL
volume: 34
number: 10
pages: 141--141
month: nov
monthnumber: 11
year: 1997
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 21:48:40 MST 2017
bibtimestamp: 2017.03.01 21:48:40 MST
URL: http://www.sciencedirect.com/science/article/pii/S0898122197902650
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: Anonymous
title:
Book Review: booktitle Primes of the form $ x^2 + n y^2 $: Fermat, class field theory, and complex multiplication: David A. Cox. John Wiley & Sons, New York. (1989). 351 pages. $49.95, pounds 29.95

rawtitle:
Book Review: {{\booktitle{Primes of the form $ x^2 + n y^2 $: Fermat, class field theory, and complex multiplication}}: David A. Cox. John Wiley \& Sons, New York. (1989). 351 pages. \$49.95, \pounds 29.95}

entry:
@Article{Anonymous:1997:BRPk,
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  title =        "Book Review: {{\booktitle{Primes of the form $ x^2 + n
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  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:48:40 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122197902650",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: article
filename: fparith.bib
label: Anonymous:1997:SIS
author: Anonymous
title: SCAN-97 International Symposium on Scientific Computing Computer Arithmetic and Validated Numerics
journal: j-J-COMPUT-APPL-MATH
volume: 81
number: 2
pages: N13--N14
day: 8
month: jul
monthnumber: 7
year: 1997
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:36:02 MST 2017
bibtimestamp: 2017.02.25 12:36:02 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042797900741
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Anonymous
rawtitle:
{SCAN-97} International Symposium on Scientific Computing Computer Arithmetic and Validated Numerics

entry:
@Article{Anonymous:1997:SIS,
  author =       "Anonymous",
  title =        "{SCAN-97} International Symposium on Scientific
                 Computing Computer Arithmetic and Validated Numerics",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "81",
  number =       "2",
  pages =        "N13--N14",
  day =          "8",
  month =        jul,
  year =         "1997",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:36:02 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042797900741",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


