# bibtab

bibtype: inproceedings
filename: fparith.bib
label: Beaumont-Smith:1997:GBA
author: Andrew Beaumont-Smith and Neil Burgess
title: A GaAs 32-Bit Adder
crossref: Lang:1997:ISC
pages: 10--17
year: 1997
bibdate: Mon May 20 05:45:32 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 05:45:32 MDT
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Beaumont_Smith.pdf
keywords: ARITH-13
acknowledgement: ack-nhfb
rawauthor: Andrew Beaumont-Smith and Neil Burgess
rawtitle: A {GaAs} 32-Bit Adder
entry:
@InProceedings{Beaumont-Smith:1997:GBA,
  author =       "Andrew Beaumont-Smith and Neil Burgess",
  title =        "A {GaAs} 32-Bit Adder",
  crossref =     "Lang:1997:ISC",
  pages =        "10--17",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Beaumont_Smith.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}


bibtype: article
filename: fparith.bib
label: Blackford:1997:PEN
title: Practical Experience in the Numerical Dangers of Heterogeneous Computing
journal: j-TOMS
volume: 23
number: 2
pages: 133--147
month: jun
monthnumber: 6
year: 1997
CODEN: ACMSCU
DOI: https://doi.org/10.1145/264029.264030
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Thu Nov 8 14:50:37 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.08 14:50:37 ???
URL: http://www.acm.org/pubs/citations/journals/toms/1997-23-2/p133-blackford/
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-rfb
journalURL: https://dl.acm.org/loi/toms
rawtitle: Practical Experience in the Numerical Dangers of Heterogeneous Computing
author:
L. S. Blackford and A. Cleary and A. Petitet and R. C. Whaley and J. Demmel and I. Dhillon and H. Ren and K. Stanley and J. Dongarra and S. Hammarling

abstract:
Special challenges exist in writing reliable numerical library software for heterogeneous computing environments. Although a lot of software for distributed-memory parallel computers has been written, porting this software to a network of workstations requires careful consideration. The symptoms of heterogeneous computing failures can range from erroneous results without warning to deadlock. Some of the problems are straightforward to solve, but for others the solutions are not so obvious, or incur an unacceptable overhead. Making software robust on heterogeneous systems often requires additional communication. We describe and illustrate the problems encountered during the development of ScaLAPACK and the NAG Numerical PVM Library. Where possible, we suggest ways to avoid potential pitfalls, or if that is not possible, we recommend that the software not be used on heterogeneous networks.

keywords:
distributed-memory systems, floating-point arithmetic, heterogeneous processor networks, message passing, numerical software, reliability

subject:
bf D.1.3 Software, PROGRAMMING TECHNIQUES, Concurrent Programming, Distributed programming. bf G.1.0 Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic. bf G.1.0 Mathematics of Computing, NUMERICAL ANALYSIS, General, Parallel algorithms.

rawabstract:
Special challenges exist in writing reliable numerical library software for heterogeneous computing environments. Although a lot of software for distributed-memory parallel computers has been written, porting this software to a network of workstations requires careful consideration. The symptoms of heterogeneous computing failures can range from erroneous results without warning to deadlock. Some of the problems are straightforward to solve, but for others the solutions are not so obvious, or incur an unacceptable overhead. Making software robust on heterogeneous systems often requires additional communication. We describe and illustrate the problems encountered during the development of ScaLAPACK and the NAG Numerical PVM Library. Where possible, we suggest ways to avoid potential pitfalls, or if that is not possible, we recommend that the software not be used on heterogeneous networks.

rawauthor:
L. S. Blackford and A. Cleary and A. Petitet and R. C. Whaley and J. Demmel and I. Dhillon and H. Ren and K. Stanley and J. Dongarra and S. Hammarling

entry:
@Article{Blackford:1997:PEN,
  author =       "L. S. Blackford and A. Cleary and A. Petitet and R. C.
                 Whaley and J. Demmel and I. Dhillon and H. Ren and K.
                 Stanley and J. Dongarra and S. Hammarling",
  title =        "Practical Experience in the Numerical Dangers of
                 Heterogeneous Computing",
  journal =      j-TOMS,
  volume =       "23",
  number =       "2",
  pages =        "133--147",
  month =        jun,
  year =         "1997",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/264029.264030",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Nov 8 14:50:37 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1997-23-2/p133-blackford/",
  abstract =     "Special challenges exist in writing reliable numerical
                 library software for heterogeneous computing
                 environments. Although a lot of software for
                 distributed-memory parallel computers has been written,
                 porting this software to a network of workstations
                 requires careful consideration. The symptoms of
                 heterogeneous computing failures can range from
                 erroneous results without warning to deadlock. Some of
                 the problems are straightforward to solve, but for
                 others the solutions are not so obvious, or incur an
                 unacceptable overhead. Making software robust on
                 heterogeneous systems often requires additional
                 communication. We describe and illustrate the problems
                 encountered during the development of ScaLAPACK and the
                 NAG Numerical PVM Library. Where possible, we suggest
                 ways to avoid potential pitfalls, or if that is not
                 possible, we recommend that the software not be used on
                 heterogeneous networks.",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "distributed-memory systems, floating-point arithmetic,
                 heterogeneous processor networks, message passing,
                 numerical software, reliability",
  subject =      "{\bf D.1.3} Software, PROGRAMMING TECHNIQUES,
                 Concurrent Programming, Distributed programming. {\bf
                 G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS,
                 General, Computer arithmetic. {\bf G.1.0} Mathematics
                 of Computing, NUMERICAL ANALYSIS, General, Parallel
                 algorithms.",
}


bibtype: article
filename: fparith.bib
label: Blinn:1997:JBC
author: James F. Blinn
title: Jim Blinn's Corner: Floating-Point Tricks
journal: j-IEEE-CGA
volume: 17
number: 4
pages: 80--84
month: jul
monthnumber: 7
year: 1997
CODEN: ICGADZ
DOI: https://doi.org/10.1109/38.595279
ISSN: 0272-1716 (print), 1558-1756 (electronic) OR 02721716 (print), 15581756 (electronic)
ISSNL: 0272-1716 OR 02721716
bibdate: Sat Jul 16 08:40:52 MDT 2005
bibtimestamp: 2005.07.16 08:40:52 MDT
fjournal: IEEE Computer Graphics and Applications
acknowledgement: ack-nhfb
journalURL: http://www.computer.org/portal/web/csdl/magazines/cga
rawauthor: James F. Blinn
rawtitle: {Jim Blinn}'s Corner: Floating-Point Tricks
note:
Discusses use of IEEE 754 single-precision floating-point bit patterns as integers for implementations of fast, but low-accuracy, functions useful in computer graphics.

rawnote:
Discusses use of IEEE 754 single-precision floating-point bit patterns as integers for implementations of fast, but low-accuracy, functions useful in computer graphics.

entry:
@Article{Blinn:1997:JBC,
  author =       "James F. Blinn",
  title =        "{Jim Blinn}'s Corner: Floating-Point Tricks",
  journal =      j-IEEE-CGA,
  volume =       "17",
  number =       "4",
  pages =        "80--84",
  month =        jul # "\slash " # aug,
  year =         "1997",
  CODEN =        "ICGADZ",
  DOI =          "https://doi.org/10.1109/38.595279",
  ISSN =         "0272-1716 (print), 1558-1756 (electronic)",
  ISSN-L =       "0272-1716",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Discusses use of IEEE 754 single-precision
                 floating-point bit patterns as integers for
                 implementations of fast, but low-accuracy, functions
                 useful in computer graphics.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Computer Graphics and Applications",
  journal-URL =  "http://www.computer.org/portal/web/csdl/magazines/cga",
  summary =      "The author discusses IEEE floating point
                 representation that stores numbers in what amounts to
                 scientific notation. He considers the sign bit, the
                 logarithm function, function approximations, errors and
                 refinements \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Bomar:1997:RNA
author: B. W. Bomar and L. M. Smith and R. D. Joseph
journal: j-IEEE-TRANS-CIRCUITS-SYST-2
volume: 44
number: 11
pages: 952--955
month: nov
monthnumber: 11
year: 1997
CODEN: ICSPE5
DOI: https://doi.org/10.1109/82.644048
ISSN: 1057-7130 (print), 1558-125X (electronic) OR 10577130 (print), 1558125X (electronic)
ISSNL: 1057-7130 OR 10577130
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 Circuits and Systems. 2, Analog and Digital Signal Processing
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82
rawauthor: B. W. Bomar and L. M. Smith and R. D. Joseph
title:
Roundoff noise analysis of state-space digital filters implemented on floating-point digital signal processors

rawtitle:
Roundoff noise analysis of state-space digital filters implemented on floating-point digital signal processors

entry:
@Article{Bomar:1997:RNA,
  author =       "B. W. Bomar and L. M. Smith and R. D. Joseph",
  title =        "Roundoff noise analysis of state-space digital filters
                 implemented on floating-point digital signal
                 processors",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-2,
  volume =       "44",
  number =       "11",
  pages =        "952--955",
  month =        nov,
  year =         "1997",
  CODEN =        "ICSPE5",
  DOI =          "https://doi.org/10.1109/82.644048",
  ISSN =         "1057-7130 (print), 1558-125X (electronic)",
  ISSN-L =       "1057-7130",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems. 2, Analog
                 and Digital Signal Processing",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
  summary =      "An expression is obtained for the output
                 floating-point roundoff noise variance of a general
                 Nth-order state-space digital filter with zero-mean
                 white noise input signal. This expression is then
                 simplified for the case there the filter is implemented
                 \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Bshouty:1997:TBA
author: Nader H. Bshouty and Yishay Mansour and Baruch Schieber and Prasoon Tiwari
title: A tight bound for approximating the square root
journal: j-INFO-PROC-LETT
volume: 63
number: 4
pages: 211--213
day: 10
month: sep
monthnumber: 9
year: 1997
CODEN: IFPLAT
ISSN: 0020-0190 (print), 1872-6119 (electronic) OR 00200190 (print), 18726119 (electronic)
ISSNL: 0020-0190 OR 00200190
MRclass: 68Q25 (65B15 68Q40)
MRnumber: 1 477 306
bibdate: Sat Nov 7 17:55:54 MST 1998
bibtimestamp: 1998.11.07 17:55:54 MST
fjournal: Information Processing Letters
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00200190
rawauthor: Nader H. Bshouty and Yishay Mansour and Baruch Schieber and Prasoon Tiwari
rawtitle: A tight bound for approximating the square root
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{Bshouty:1997:TBA,
  author =       "Nader H. Bshouty and Yishay Mansour and Baruch
                 Schieber and Prasoon Tiwari",
  title =        "A tight bound for approximating the square root",
  journal =      j-INFO-PROC-LETT,
  volume =       "63",
  number =       "4",
  pages =        "211--213",
  day =          "10",
  month =        sep,
  year =         "1997",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  MRclass =      "68Q25 (65B15 68Q40)",
  MRnumber =     "1 477 306",
  bibdate =      "Sat Nov 7 17:55:54 MST 1998",
  bibsource =    "http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
}


bibtype: inproceedings
filename: fparith.bib
label: Burgess:1997:SUR
author: Neil Burgess
title: Scaled and unscaled residue number system to binary conversion techniques using the core function
crossref: Lang:1997:ISC
pages: 250--257
year: 1997
DOI: https://doi.org/10.1109/ARITH.1997.614902
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Burgess.pdf
keywords: ARITH-13; residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: Neil Burgess
rawtitle: Scaled and unscaled residue number system to binary conversion techniques using the core function
entry:
@InProceedings{Burgess:1997:SUR,
  author =       "Neil Burgess",
  title =        "Scaled and unscaled residue number system to binary
                 conversion techniques using the core function",
  crossref =     "Lang:1997:ISC",
  pages =        "250--257",
  year =         "1997",
  DOI =          "https://doi.org/10.1109/ARITH.1997.614902",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Burgess.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13; residue arithmetic; residue number system",
  summary =      "The paper presents related techniques for converting a
                 residue number system (RNS) number to binary, with and
                 without scaling, that use the core function. The
                 techniques remove the difficulties associated with
                 conversion procedures based on the \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Callaway:1997:PDC
author: Thomas K. Callaway and Earl E. Swartzlander, Jr.
title: Power-Delay Characteristics of CMOS Multipliers
crossref: Lang:1997:ISC
pages: 26--33
year: 1997
bibdate: Mon May 20 05:45:32 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 05:45:32 MDT
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Callaway.pdf
keywords: ARITH-13
acknowledgement: ack-nhfb
rawauthor: Thomas K. Callaway and Earl E. {Swartzlander, Jr.}
rawtitle: Power-Delay Characteristics of {CMOS} Multipliers
entry:
@InProceedings{Callaway:1997:PDC,
  author =       "Thomas K. Callaway and Earl E. {Swartzlander, Jr.}",
  title =        "Power-Delay Characteristics of {CMOS} Multipliers",
  crossref =     "Lang:1997:ISC",
  pages =        "26--33",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Callaway.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}


bibtype: inproceedings
filename: fparith.bib
label: Cao:1997:HPH
author: Jun Cao and Belle W. Y. Wei
title: High-Performance Hardware for Function Generation
crossref: Lang:1997:ISC
pages: 184--189
year: 1997
bibdate: Mon May 20 05:45:32 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 05:45:32 MDT
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Cao.pdf
keywords: ARITH-13
acknowledgement: ack-nhfb
rawauthor: Jun Cao and Belle W. Y. Wei
rawtitle: High-Performance Hardware for Function Generation
entry:
@InProceedings{Cao:1997:HPH,
  author =       "Jun Cao and Belle W. Y. Wei",
  title =        "High-Performance Hardware for Function Generation",
  crossref =     "Lang:1997:ISC",
  pages =        "184--189",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Cao.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}


bibtype: inproceedings
filename: fparith.bib
label: Cena:1997:QCA
author: Gianluca Cena and Paolo Montuschi and Luigi Ciminiera and Andrea Sanna
title: A Q-Coder Algorithm with Carry Free Addition
crossref: Lang:1997:ISC
pages: 282
year: 1997
bibdate: Sat Nov 17 12:22:42 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.17 12:22:42 ???
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Cena.pdf
keywords: ARITH-13
acknowledgement: ack-nhfb
rawauthor: Gianluca Cena and Paolo Montuschi and Luigi Ciminiera and Andrea Sanna
rawtitle: A {Q}-Coder Algorithm with Carry Free Addition
entry:
@InProceedings{Cena:1997:QCA,
  author =       "Gianluca Cena and Paolo Montuschi and Luigi Ciminiera
                 and Andrea Sanna",
  title =        "A {Q}-Coder Algorithm with Carry Free Addition",
  crossref =     "Lang:1997:ISC",
  pages =        "282",
  year =         "1997",
  bibdate =      "Sat Nov 17 12:22:42 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Cena.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}


bibtype: techreport
filename: fparith.bib
label: Chen:1997:PEG
author: Yirng-An Chen and Randal E. Bryant
title: PBHD: an efficient graph representation for floating point circuit verification
type: Report
number: CMU-CS-97-134
institution: Department of Computer Science, Carnegie-Mellon University
address: Pittsburgh, PA, USA
pages: 282
year: 1997
bibdate: Thu May 09 08:39:56 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.09 08:39:56 ???
acknowledgement: ack-nhfb
rawauthor: Yirng-An Chen and Randal E. Bryant
rawtitle: {PBHD}: an efficient graph representation for floating point circuit verification
entry:
@TechReport{Chen:1997:PEG,
  author =       "Yirng-An Chen and Randal E. Bryant",
  title =        "{PBHD}: an efficient graph representation for floating
                 point circuit verification",
  type =         "Report",
  number =       "CMU-CS-97-134",
  institution =  "Department of Computer Science, Carnegie-Mellon
                 University",
  address =      "Pittsburgh, PA, USA",
  year =         "1997",
  bibdate =      "Thu May 09 08:39:56 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Collins:1997:IPI
author: Robert C. Collins
title: Inside the Pentium II Math Bug
journal: j-DDJ
volume: 22
number: 8
pages: 52, 55--57
month: aug
monthnumber: 8
year: 1997
CODEN: DDJOEB
ISSN: 1044-789X OR 1044789X
bibdate: Sat Mar 07 08:27:48 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.03.07 08:27:48 ???
note: See letters cite Atkinson-Barr:1997:LEP,Baker:1997:LEP.
fjournal: Dr. Dobb's Journal of Software Tools
acknowledgement: ack-nhfb
rawauthor: Robert C. Collins
rawnote: See letters \cite{Atkinson-Barr:1997:LEP,Baker:1997:LEP}.
rawtitle: Inside the {Pentium II} Math Bug
abstract:
Two days before Intel's biggest processor announcement in years, a math bug in the Pentium Pro and Pentium II came to light. Robert takes you inside the Dan-0411 flag erratum,' and tells how the story unfolded.

rawabstract:
Two days before Intel's biggest processor announcement in years, a math bug in the Pentium Pro and Pentium II came to light. Robert takes you inside the Dan-0411 flag erratum,' and tells how the story unfolded.

entry:
@Article{Collins:1997:IPI,
  author =       "Robert C. Collins",
  title =        "Inside the {Pentium II} Math Bug",
  journal =      j-DDJ,
  volume =       "22",
  number =       "8",
  pages =        "52, 55--57",
  month =        aug,
  year =         "1997",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Sat Mar 07 08:27:48 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See letters
                 \cite{Atkinson-Barr:1997:LEP,Baker:1997:LEP}.",
  abstract =     "Two days before Intel's biggest processor announcement
                 in years, a math bug in the Pentium Pro and Pentium II
                 came to light. Robert takes you inside the Dan-0411
                 flag erratum,' and tells how the story unfolded.",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}


bibtype: article
filename: fparith.bib
label: Compagner:1997:RER
author: A. Compagner and A. S. Berdnikov and S. B. Turtia and A. Larionov
title: Rounding errors in random number generators
journal: j-COMP-PHYS-COMM
volume: 106
number: 3
pages: 207--218
month: nov
monthnumber: 11
year: 1997
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/S0010-4655(97)00070-2
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Thu Dec 29 21:19:40 MST 2011
bibtimestamp: 2011.12.29 21:19:40 MST
URL: http://www.sciencedirect.com/science/article/pii/S0010465597000702
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: A. Compagner and A. S. Berdnikov and S. B. Turtia and A. Larionov
rawtitle: Rounding errors in random number generators
bibsource:
https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib

abstract:
The deviations of the cumulative distribution function from the uniform one for the pseudorandom floating point values produced by integer arithmetics are discussed. It is shown that the conversion from fixed point values into floating point values introduces specific artefacts even when the integer arithmetics guarantees ideal uniformity. Two type of defects are considered: the appearance of the value 1.0 among pseudorandom values, and the sharp jumps of uniformity at the level of discreteness which corresponds to the computer representation of the floating point values. The non-uniformity at small level of discreteness can be neglected in most cases, but the appearance of the parasitic value 1.0 where nobody expects it can be very dangerous if special precautions are not taken by the user. Both defects are demonstrated using the random number generator from the system library of the Microsoft Power Station Fortran 1.0.

rawabstract:
The deviations of the cumulative distribution function from the uniform one for the pseudorandom floating point values produced by integer arithmetics are discussed. It is shown that the conversion from fixed point values into floating point values introduces specific artefacts even when the integer arithmetics guarantees ideal uniformity. Two type of defects are considered: the appearance of the value 1.0 among pseudorandom values, and the sharp jumps of uniformity at the level of discreteness which corresponds to the computer representation of the floating point values. The non-uniformity at small level of discreteness can be neglected in most cases, but the appearance of the parasitic value 1.0 where nobody expects it can be very dangerous if special precautions are not taken by the user. Both defects are demonstrated using the random number generator from the system library of the Microsoft Power Station Fortran 1.0.

entry:
@Article{Compagner:1997:RER,
  author =       "A. Compagner and A. S. Berdnikov and S. B. Turtia and
                 A. Larionov",
  title =        "Rounding errors in random number generators",
  journal =      j-COMP-PHYS-COMM,
  volume =       "106",
  number =       "3",
  pages =        "207--218",
  month =        nov,
  year =         "1997",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(97)00070-2",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Thu Dec 29 21:19:40 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465597000702",
  abstract =     "The deviations of the cumulative distribution function
                 from the uniform one for the pseudorandom floating
                 point values produced by integer arithmetics are
                 discussed. It is shown that the conversion from fixed
                 point values into floating point values introduces
                 specific artefacts even when the integer arithmetics
                 guarantees ideal uniformity. Two type of defects are
                 considered: the appearance of the value 1.0 among
                 pseudorandom values, and the sharp jumps of uniformity
                 at the level of discreteness which corresponds to the
                 computer representation of the floating point values.
                 The non-uniformity at small level of discreteness can
                 be neglected in most cases, but the appearance of the
                 parasitic value 1.0 where nobody expects it can be very
                 dangerous if special precautions are not taken by the
                 user. Both defects are demonstrated using the random
                 number generator from the system library of the
                 Microsoft Power Station Fortran 1.0.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: article
filename: fparith.bib
label: Cuyt:1997:FPV
author: A. Cuyt
title: Floating-point versus Symbolic Computations in the QD-algorithm
journal: j-J-SYMBOLIC-COMP
volume: 24
number: 6
publisher: Academic Press, Harcourt Place, 32 Jamestown Road, London, NW1 7BY, U.K.
pages: 695--703
month: dec
monthnumber: 12
year: 1997
CODEN: JSYCEH
ISSN: 0747-7171 (print), 1095-855X (electronic) OR 07477171 (print), 1095855X (electronic)
ISSNL: 0747-7171 OR 07477171
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: Journal of Symbolic Computation
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/07477171
rawauthor: A. Cuyt
rawtitle: Floating-point versus Symbolic Computations in the {QD}-algorithm
entry:
@Article{Cuyt:1997:FPV,
  author =       "A. Cuyt",
  title =        "Floating-point versus Symbolic Computations in the
                 {QD}-algorithm",
  journal =      j-J-SYMBOLIC-COMP,
  volume =       "24",
  number =       "6",
  publisher =    "Academic Press, Harcourt Place, 32 Jamestown Road,
                 London, NW1 7BY, U.K.",
  pages =        "695--703",
  month =        dec,
  year =         "1997",
  CODEN =        "JSYCEH",
  ISSN =         "0747-7171 (print), 1095-855X (electronic)",
  ISSN-L =       "0747-7171",
  bibdate =      "Fri Nov 8 05:39:32 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 Ingenta database",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Symbolic Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07477171",
  pagecount =    "9",
}


bibtype: article
filename: fparith.bib
label: Daumas:1997:VRD
author: M. Daumas and D. W. Matula
title: Validated roundings of dot products by sticky accumulation
journal: j-IEEE-TRANS-COMPUT
volume: 46
number: 5
pages: 623--629
month: may
monthnumber: 5
year: 1997
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.589241
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 10:06:23 MDT 2011
bibtimestamp: 2011.07.06 10:06:23 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=589241
fjournal: IEEE Transactions on Computers
keywords: floating-point arithmetic
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: M. Daumas and D. W. Matula
rawtitle: Validated roundings of dot products by sticky accumulation
abstract:
The dot product operation is very prevalent in scientific computation and has therefore been incorporated as a primitive operation in some languages. The implementation of the dot product operation by a sequence of IEEE standard multiplications and additions does not prevent a substantial accumulation of the round-off errors or warn the user about a catastrophic cancellation. We present the design of a double precision dot product operation employing sticky accumulation, where the final rounded result is validated by raising a new exception flag if the result incurred catastrophic cancellation. Sticky accumulation can be implemented in a pipeline or parallel environment to sustain double precision with an extended control of the error. Our design allows that, in the absence of catastrophic cancellation, one ulp accuracy is guaranteed

rawabstract:
The dot product operation is very prevalent in scientific computation and has therefore been incorporated as a primitive operation in some languages. The implementation of the dot product operation by a sequence of IEEE standard multiplications and additions does not prevent a substantial accumulation of the round-off errors or warn the user about a catastrophic cancellation. We present the design of a double precision dot product operation employing sticky accumulation, where the final rounded result is validated by raising a new exception flag if the result incurred catastrophic cancellation. Sticky accumulation can be implemented in a pipeline or parallel environment to sustain double precision with an extended control of the error. Our design allows that, in the absence of catastrophic cancellation, one ulp accuracy is guaranteed

entry:
@Article{Daumas:1997:VRD,
  author =       "M. Daumas and D. W. Matula",
  title =        "Validated roundings of dot products by sticky
                 accumulation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "46",
  number =       "5",
  pages =        "623--629",
  month =        may,
  year =         "1997",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.589241",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 10:06:23 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=589241",
  abstract =     "The dot product operation is very prevalent in
                 scientific computation and has therefore been
                 incorporated as a primitive operation in some
                 languages. The implementation of the dot product
                 operation by a sequence of IEEE standard
                 multiplications and additions does not prevent a
                 substantial accumulation of the round-off errors or
                 warn the user about a catastrophic cancellation. We
                 present the design of a double precision dot product
                 operation employing sticky accumulation, where the
                 final rounded result is validated by raising a new
                 exception flag if the result incurred catastrophic
                 cancellation. Sticky accumulation can be implemented in
                 a pipeline or parallel environment to sustain double
                 precision with an extended control of the error. Our
                 design allows that, in the absence of catastrophic
                 cancellation, one ulp accuracy is guaranteed",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "floating-point arithmetic",
}


bibtype: inproceedings
filename: fparith.bib
label: Dimitrov:1997:AME
author: V. S. Dimitrov and G. A. Jullien and W. C. Miller
title: Algorithms for Multi-Exponentiation Based on Complex Arithmetic
crossref: Lang:1997:ISC
pages: 208--217
year: 1997
bibdate: Mon May 20 05:45:32 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 05:45:32 MDT
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Dimitrov_algorithms.pdf
keywords: ARITH-13
acknowledgement: ack-nhfb
rawauthor: V. S. Dimitrov and G. A. Jullien and W. C. Miller
rawtitle: Algorithms for Multi-Exponentiation Based on Complex Arithmetic
entry:
@InProceedings{Dimitrov:1997:AME,
  author =       "V. S. Dimitrov and G. A. Jullien and W. C. Miller",
  title =        "Algorithms for Multi-Exponentiation Based on Complex
                 Arithmetic",
  crossref =     "Lang:1997:ISC",
  pages =        "208--217",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Dimitrov_algorithms.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}


bibtype: inproceedings
filename: fparith.bib
label: Dimitrov:1997:ERN
author: V. Dimitrov and G. A. Jullien and W. C. Miller
booktitle: Proceedings of the 40th Midwest Symposium on Circuits and Systems, 1997
title: Eisenstein residue number system with applications to DSP
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 675--678
year: 1997
DOI: https://doi.org/10.1109/MWSCAS.1997.662165
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. Dimitrov and G. A. Jullien and W. C. Miller
rawbooktitle: Proceedings of the 40th Midwest Symposium on Circuits and Systems, 1997
rawtitle: {Eisenstein} residue number system with applications to {DSP}
entry:
@InProceedings{Dimitrov:1997:ERN,
  author =       "V. Dimitrov and G. A. Jullien and W. C. Miller",
  booktitle =    "Proceedings of the 40th Midwest Symposium on Circuits
                 and Systems, 1997",
  title =        "{Eisenstein} residue number system with applications
                 to {DSP}",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "675--678",
  year =         "1997",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/MWSCAS.1997.662165",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A new approach for processing complex numbers has been
                 proposed, Basically, it is aimed at the implementation
                 of radix-3 FFTs, but it can be used in any situation
                 where the requirement to process Eisenstein integers
                 arises, The comparison between \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Dimitrov:1997:TAD
author: V. S. Dimitrov and G. A. Jullien and W. C. Miller
title: Theory and Applications for a Double-Base Number System
crossref: Lang:1997:ISC
pages: 44--53
year: 1997
bibdate: Mon May 20 05:45:32 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 05:45:32 MDT
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Dimitrov_theory.pdf
keywords: ARITH-13
acknowledgement: ack-nhfb
rawauthor: V. S. Dimitrov and G. A. Jullien and W. C. Miller
rawtitle: Theory and Applications for a Double-Base Number System
entry:
@InProceedings{Dimitrov:1997:TAD,
  author =       "V. S. Dimitrov and G. A. Jullien and W. C. Miller",
  title =        "Theory and Applications for a Double-Base Number
                 System",
  crossref =     "Lang:1997:ISC",
  pages =        "44--53",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Dimitrov_theory.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}


bibtype: article
filename: fparith.bib
label: Doring:1997:DAL
author: Andreas Doring and Wolfgang J. Paul
title: Decimal adjustment of long numbers in constant time
journal: j-INFO-PROC-LETT
volume: 62
number: 3
pages: 161--163
day: 4
month: jun
monthnumber: 6
year: 1997
CODEN: IFPLAT
ISSN: 0020-0190 (print), 1872-6119 (electronic) OR 00200190 (print), 18726119 (electronic)
ISSNL: 0020-0190 OR 00200190
MRclass: 68M07 (68M20)
MRnumber: 1 453 700
bibdate: Sat Nov 7 17:55:52 MST 1998
bibtimestamp: 1998.11.07 17:55:52 MST
fjournal: Information Processing Letters
keywords: decimal floating-point arithmetic
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00200190
rawauthor: Andreas D{\"o}ring and Wolfgang J. Paul
rawtitle: Decimal adjustment of long numbers in constant time
entry:
@Article{Doring:1997:DAL,
  author =       "Andreas D{\"o}ring and Wolfgang J. Paul",
  title =        "Decimal adjustment of long numbers in constant time",
  journal =      j-INFO-PROC-LETT,
  volume =       "62",
  number =       "3",
  pages =        "161--163",
  day =          "4",
  month =        jun,
  year =         "1997",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  MRclass =      "68M07 (68M20)",
  MRnumber =     "1 453 700",
  bibdate =      "Sat Nov 7 17:55:52 MST 1998",
  bibsource =    "http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
  keywords =     "decimal floating-point arithmetic",
}


bibtype: article
filename: fparith.bib
label: Drmac:1997:IJR
author: Zlatko Drmac
journal: j-SIAM-J-SCI-COMP
volume: 18
number: 4
pages: 1200--1222
month: jul
monthnumber: 7
year: 1997
CODEN: SJOCE3
DOI: https://doi.org/10.1137/S1064827594265095
ISSN: 1064-8275 (print), 1095-7197 (electronic) OR 10648275 (print), 10957197 (electronic)
ISSNL: 1064-8275 OR 10648275
MRclass: 65F15 (65G10)
MRnumber: 98e:65027; 1 453 565
MRreviewer: Ljiljana Petkovi{\'c}
bibdate: Fri Dec 4 14:47:53 MST 1998
bibsource: http://epubs.siam.org/sam-bin/dbq/toc/SISC/18/4; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.12.04 14:47:53 MST
URL: http://epubs.siam.org/sam-bin/dbq/article/26509
fjournal: SIAM Journal on Scientific Computing
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sisc
rawauthor: Zlatko Drma{\v{c}}
title:
Implementation of Jacobi Rotations for Accurate Singular Value Computation in Floating Point Arithmetic

rawtitle:
Implementation of {Jacobi} Rotations for Accurate Singular Value Computation in Floating Point Arithmetic

entry:
@Article{Drmac:1997:IJR,
  author =       "Zlatko Drma{\v{c}}",
  title =        "Implementation of {Jacobi} Rotations for Accurate
                 Singular Value Computation in Floating Point
                 Arithmetic",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "18",
  number =       "4",
  pages =        "1200--1222",
  month =        jul,
  year =         "1997",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/S1064827594265095",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  MRclass =      "65F15 (65G10)",
  MRnumber =     "98e:65027; 1 453 565",
  MRreviewer =   "Ljiljana Petkovi{\'c}",
  bibdate =      "Fri Dec 4 14:47:53 MST 1998",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SISC/18/4;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/26509",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
}


bibtype: inproceedings
filename: fparith.bib
label: Drolshagen:1997:PES
author: A. Drolshagen and H. Henkelmann and W. Anheier
title: Processor elements for the standard cell implementation of residue number systems
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 116--123
year: 1997
DOI: https://doi.org/10.1109/ASAP.1997.606818
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. Drolshagen and H. Henkelmann and W. Anheier
rawtitle: Processor elements for the standard cell implementation of residue number systems
booktitle:
IEEE International Conference on Application-Specific Systems, Architectures and Processors, Proceedings, 14--16 July 1997

rawbooktitle:
{IEEE} International Conference on Application-Specific Systems, Architectures and Processors, Proceedings, 14--16 July 1997

entry:
@InProceedings{Drolshagen:1997:PES,
  author =       "A. Drolshagen and H. Henkelmann and W. Anheier",
  booktitle =    "{IEEE} International Conference on
                 Application-Specific Systems, Architectures and
                 Processors, Proceedings, 14--16 July 1997",
  title =        "Processor elements for the standard cell
                 implementation of residue number systems",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "116--123",
  year =         "1997",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ASAP.1997.606818",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "In this article processor elements for the effective
                 implementation of standard cell circuits based on
                 residue number systems (RNS) are presented. Two new
                 processors are proposed helping to reduce the hardware
                 requirements of the implementations. \ldots{}",
}


bibtype: manual
filename: fparith.bib
label: EC:1997:IER
author: European Commission
title: The Introduction of the Euro and the Rounding of Currency Amounts
organization: European Commission Directorate General II Economic and Financial Affairs
address: Brussels, Belgium
pages: 29
year: 1997
bibdate: Fri Nov 28 11:18:05 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 11:18:05 ???
acknowledgement: ack-nhfb
rawauthor: {European Commission}
rawtitle: The Introduction of the Euro and the Rounding of Currency Amounts
entry:
@Manual{EC:1997:IER,
  author =       "{European Commission}",
  title =        "The Introduction of the Euro and the Rounding of
                 Currency Amounts",
  organization = "European Commission Directorate General II Economic
                 and Financial Affairs",
  address =      "Brussels, Belgium",
  pages =        "29",
  year =         "1997",
  bibdate =      "Fri Nov 28 11:18:05 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Edelman:1997:MPD
author: Alan Edelman
title: The Mathematics of the Pentium Division Bug
journal: j-SIAM-REVIEW
volume: 39
number: 1
pages: 54--67
month: mar
monthnumber: 3
year: 1997
CODEN: SIREAD
DOI: https://doi.org/10.1137/S0036144595293959
ISSN: 0036-1445 (print), 1095-7200 (electronic) OR 00361445 (print), 10957200 (electronic)
ISSNL: 0036-1445 OR 00361445
MRclass: 68M07
MRnumber: 1 439 485
bibdate: Sat Mar 29 09:55:47 MDT 2014
bibtimestamp: 2014.03.29 09:55:47 MDT
fjournal: SIAM Review
keywords: Intel Pentium divide flaw; Thomas R. Nicely
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sirev
onlinedate: January 1997
rawauthor: Alan Edelman
rawtitle: The Mathematics of the {Pentium} Division Bug
bibsource:
http://epubs.siam.org/sam-bin/dbq/toc/SIREV/39/1; http://epubs.siam.org/toc/siread/39/1; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib

URL:
http://epubs.siam.org/sam-bin/dbq/article/29395; http://www-math.mit.edu/~edelman/homepage/papers/pentiumbug.pdf; http://www.siam.org/journals/sirev/sirev391.htm

abstract:
Despite all of the publicity surrounding the Pentium bug of 1994, the mathematical details of the bug are poorly understood. We discuss these details and supply a new proof of the Coe--Tang result that the at-risk divisors have six consecutive ones in positions 5 through 10. Also, we prove that the worst-case absolute error for arguments in $ [1, 2) $ is on the order of 1e-5.

rawabstract:
Despite all of the publicity surrounding the Pentium bug of 1994, the mathematical details of the bug are poorly understood. We discuss these details and supply a new proof of the Coe--Tang result that the at-risk divisors have six consecutive ones in positions 5 through 10. Also, we prove that the worst-case absolute error for arguments in $ [1, 2) $ is on the order of 1e-5.

entry:
@Article{Edelman:1997:MPD,
  author =       "Alan Edelman",
  title =        "The Mathematics of the {Pentium} Division Bug",
  journal =      j-SIAM-REVIEW,
  volume =       "39",
  number =       "1",
  pages =        "54--67",
  month =        mar,
  year =         "1997",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/S0036144595293959",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  MRclass =      "68M07",
  MRnumber =     "1 439 485",
  bibdate =      "Sat Mar 29 09:55:47 MDT 2014",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIREV/39/1;
                 http://epubs.siam.org/toc/siread/39/1;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/29395;
                 http://www-math.mit.edu/~edelman/homepage/papers/pentiumbug.pdf;
                 http://www.siam.org/journals/sirev/sirev391.htm",
  abstract =     "Despite all of the publicity surrounding the Pentium
                 bug of 1994, the mathematical details of the bug are
                 poorly understood. We discuss these details and supply
                 a new proof of the Coe--Tang result that the at-risk
                 divisors have six consecutive ones in positions 5
                 through 10. Also, we prove that the worst-case absolute
                 error for arguments in $ [1, 2) $ is on the order of
                 1e-5.",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  keywords =     "Intel Pentium divide flaw; Thomas R. Nicely",
  onlinedate =   "January 1997",
}


bibtype: inproceedings
filename: fparith.bib
label: Even:1997:DIC
author: Guy Even and Wolfgang Paul
title: On the Design of IEEE Compliant Floating Point Units
crossref: Lang:1997:ISC
pages: 54--63
year: 1997
bibdate: Mon May 20 05:45:32 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 05:45:32 MDT
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Even.pdf
keywords: ARITH-13
remark: Cited in cite Mueller:2000:CAC.
acknowledgement: ack-nhfb
rawauthor: Guy Even and Wolfgang Paul
rawtitle: On the Design of {IEEE} Compliant Floating Point Units
entry:
@InProceedings{Even:1997:DIC,
  author =       "Guy Even and Wolfgang Paul",
  title =        "On the Design of {IEEE} Compliant Floating Point
                 Units",
  crossref =     "Lang:1997:ISC",
  pages =        "54--63",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Even.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
  remark =       "Cited in \cite{Mueller:2000:CAC}.",
}


bibtype: article
filename: fparith.bib
label: Fitzpatrick:1997:EBE
author: P. Fitzpatrick
title: Extending backward error assertions to tolerance of large errors in floating point computations
journal: j-IEEE-TRANS-COMPUT
volume: 46
number: 4
pages: 505--510
month: apr
monthnumber: 4
year: 1997
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.588072
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 10:06:22 MDT 2011
bibtimestamp: 2011.07.06 10:06:22 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=588072
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: P. Fitzpatrick
rawtitle: Extending backward error assertions to tolerance of large errors in floating point computations
entry:
@Article{Fitzpatrick:1997:EBE,
  author =       "P. Fitzpatrick",
  title =        "Extending backward error assertions to tolerance of
                 large errors in floating point computations",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "46",
  number =       "4",
  pages =        "505--510",
  month =        apr,
  year =         "1997",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.588072",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 10:06:22 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=588072",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "The use of backward error assertions combined with
                 iterative refinement has been suggested for the
                 correction of small fault induced errors in the
                 floating point solution of linear systems. We extend
                 this to the correction of large errors, typically
                 \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Frougny:1997:FAS
author: Christiane Frougny
title: On-the-Fly Algorithms and Sequential Machines
crossref: Lang:1997:ISC
pages: 260--265
year: 1997
bibdate: Wed Nov 14 18:57:13 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 18:57:13 ???
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Frougny.pdf
keywords: ARITH-13
acknowledgement: ack-nhfb
rawauthor: Christiane Frougny
rawtitle: On-the-Fly Algorithms and Sequential Machines
entry:
@InProceedings{Frougny:1997:FAS,
  author =       "Christiane Frougny",
  title =        "On-the-Fly Algorithms and Sequential Machines",
  crossref =     "Lang:1997:ISC",
  pages =        "260--265",
  year =         "1997",
  bibdate =      "Wed Nov 14 18:57:13 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Frougny.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}


bibtype: article
filename: fparith.bib
label: Garber:1997:NBB
author: Lee Garber
journal: j-COMPUTER
volume: 30
number: 4
pages: 25--27
month: apr
monthnumber: 4
year: 1997
CODEN: CPTRB4
ISSN: 0018-9162 (print), 1558-0814 (electronic) OR 00189162 (print), 15580814 (electronic)
ISSNL: 0018-9162 OR 00189162
bibdate: Tue May 06 16:51:53 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.05.06 16:51:53 ???
fjournal: Computer
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2
rawauthor: Lee Garber
title:
News Briefs: Binary Version Could Bring VRML into the Mainstream. FCC Jumps Into Internet Fray. Java and Floating-Point Math. Intel to Design NDRAM. Battle over Net Telephony. Vendors Seek Fast Modems. US Permits Export of Strong Encryption. E-commerce Nears $1 Billion. Chasing the Blue Light. Personal E-mail Use Will Soar

rawtitle:
News Briefs: Binary Version Could Bring {VRML} into the Mainstream. {FCC} Jumps Into {Internet} Fray. {Java} and Floating-Point Math. {Intel} to Design {NDRAM}. Battle over Net Telephony. Vendors Seek Fast Modems. {US} Permits Export of Strong Encryption. {E}-commerce Nears \$1 Billion. Chasing the Blue Light. Personal {E}-mail Use Will Soar

entry:
@Article{Garber:1997:NBB,
  author =       "Lee Garber",
  title =        "News Briefs: Binary Version Could Bring {VRML} into
                 the Mainstream. {FCC} Jumps Into {Internet} Fray.
                 {Java} and Floating-Point Math. {Intel} to Design
                 {NDRAM}. Battle over Net Telephony. Vendors Seek Fast
                 Modems. {US} Permits Export of Strong Encryption.
                 {E}-commerce Nears \$1 Billion. Chasing the Blue Light.
                 Personal {E}-mail Use Will Soar",
  journal =      j-COMPUTER,
  volume =       "30",
  number =       "4",
  pages =        "25--27",
  month =        apr,
  year =         "1997",
  CODEN =        "CPTRB4",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Tue May 06 16:51:53 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}


bibtype: inproceedings
filename: fparith.bib
label: Garjanov:1997:CRE
author: A. E. Garjanov
booktitle: Proceedings of the 1st International Conference on Control of Oscillations and Chaos, 1997
title: Controlled round-off error oscillations for initial value problem numerical solution
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 333--334
year: 1997
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. E. Garjanov
rawbooktitle: Proceedings of the 1st International Conference on Control of Oscillations and Chaos, 1997
rawtitle: Controlled round-off error oscillations for initial value problem numerical solution
entry:
@InProceedings{Garjanov:1997:CRE,
  author =       "A. E. Garjanov",
  booktitle =    "Proceedings of the 1st International Conference on
                 Control of Oscillations and Chaos, 1997",
  title =        "Controlled round-off error oscillations for initial
                 value problem numerical solution",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "333--334",
  year =         "1997",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:04 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "A new methodology of a computer simulation is desired
                 for the accumulated round-off error elimination to be
                 possible. It is well known that the propagation of
                 round-off error in the numerical integration of
                 differential equations may be crucial \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Giachetti:1997:PRF
author: Ronald E. Giachetti and Robert E. Young
title: A Parametric Representation of Fuzzy Numbers and Their Arithmetic Operators
journal: j-FUZZY-SETS-SYSTEMS
volume: 92
number: 2
pages: ??--??
day: 1
month: sep
monthnumber: 9
year: 1997
CODEN: FSSYD8
ISSN: 0165-0114 (print), 1872-6801 (electronic) OR 01650114 (print), 18726801 (electronic)
ISSNL: 0165-0114 OR 01650114
bibdate: Tue Nov 05 15:22:41 2019
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2019.11.05 15:22:41 ???
fjournal: Fuzzy Sets and Systems
keywords: arithmetic approximations; Fuzzy arithmetic; membership functions; triangular fuzzy numbers
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01650114
rawauthor: Ronald E. Giachetti and Robert E. Young
rawtitle: A Parametric Representation of Fuzzy Numbers and Their Arithmetic Operators
URL:
https://www.nist.gov/publications/parametric-representation-fuzzy-numbers-and-their-arithmetic-operators

abstract:
Direct implementation of extended arithmetic operators on fuzzy numbers is computationally complex. Implementation of the extension principle is equivalent to solving a nonlinear programming problem. To overcome this difficulty many applications limit the membership functions to certain shapes, usually either triangular fuzzy numbers (TFN) or trapezoidal fuzzy numbers (TrFN). Then calculation of the extended operators can be performed on the parameters defining the fuzzy numbers, thus making the calculations trivial. Unfortunately the TFN shape is not closed under multiplication and division. The result of these operators is a polynomial membership function and the triangular shape only approximates the actual result.The linear approximation can be quite poor and may lead to incorrect results when used in engineering applications. We analyze this problem and propose six parameters which define parameterized fuzzy numbers (PFN), of which TFNs are a special case. We provide the methods for performing fuzzy arithmetic and show that the PFN representation is closed under the arithmetic operations. The new representation in conjunction with the arithmetic operators obeys many of the same arithmetic properties as TFNs. The new method has better accuracy and similar computational speed to using TFNs and appears to have benefits when used in engineering applications.

rawabstract:
Direct implementation of extended arithmetic operators on fuzzy numbers is computationally complex. Implementation of the extension principle is equivalent to solving a nonlinear programming problem. To overcome this difficulty many applications limit the membership functions to certain shapes, usually either triangular fuzzy numbers (TFN) or trapezoidal fuzzy numbers (TrFN). Then calculation of the extended operators can be performed on the parameters defining the fuzzy numbers, thus making the calculations trivial. Unfortunately the TFN shape is not closed under multiplication and division. The result of these operators is a polynomial membership function and the triangular shape only approximates the actual result.The linear approximation can be quite poor and may lead to incorrect results when used in engineering applications. We analyze this problem and propose six parameters which define parameterized fuzzy numbers (PFN), of which TFNs are a special case. We provide the methods for performing fuzzy arithmetic and show that the PFN representation is closed under the arithmetic operations. The new representation in conjunction with the arithmetic operators obeys many of the same arithmetic properties as TFNs. The new method has better accuracy and similar computational speed to using TFNs and appears to have benefits when used in engineering applications.

entry:
@Article{Giachetti:1997:PRF,
  author =       "Ronald E. Giachetti and Robert E. Young",
  title =        "A Parametric Representation of Fuzzy Numbers and Their
                 Arithmetic Operators",
  journal =      j-FUZZY-SETS-SYSTEMS,
  volume =       "92",
  number =       "2",
  pages =        "??--??",
  day =          "1",
  month =        sep,
  year =         "1997",
  CODEN =        "FSSYD8",
  ISSN =         "0165-0114 (print), 1872-6801 (electronic)",
  ISSN-L =       "0165-0114",
  bibdate =      "Tue Nov 05 15:22:41 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.nist.gov/publications/parametric-representation-fuzzy-numbers-and-their-arithmetic-operators",
  abstract =     "Direct implementation of extended arithmetic operators
                 on fuzzy numbers is computationally complex.
                 Implementation of the extension principle is equivalent
                 to solving a nonlinear programming problem. To overcome
                 this difficulty many applications limit the membership
                 functions to certain shapes, usually either triangular
                 fuzzy numbers (TFN) or trapezoidal fuzzy numbers
                 (TrFN). Then calculation of the extended operators can
                 be performed on the parameters defining the fuzzy
                 numbers, thus making the calculations trivial.
                 Unfortunately the TFN shape is not closed under
                 multiplication and division. The result of these
                 operators is a polynomial membership function and the
                 triangular shape only approximates the actual
                 result.The linear approximation can be quite poor and
                 may lead to incorrect results when used in engineering
                 applications. We analyze this problem and propose six
                 parameters which define parameterized fuzzy numbers
                 (PFN), of which TFNs are a special case. We provide the
                 methods for performing fuzzy arithmetic and show that
                 the PFN representation is closed under the arithmetic
                 operations. The new representation in conjunction with
                 the arithmetic operators obeys many of the same
                 arithmetic properties as TFNs. The new method has
                 better accuracy and similar computational speed to
                 using TFNs and appears to have benefits when used in
                 engineering applications.",
  acknowledgement = ack-nhfb,
  fjournal =     "Fuzzy Sets and Systems",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01650114",
  keywords =     "arithmetic approximations; Fuzzy arithmetic;
                 membership functions; triangular fuzzy numbers",
}


bibtype: misc
filename: fparith.bib
label: Gosling:1997:ENC
author: James A. Gosling
title: The Evolution of Numerical Computing in Java
pages: ??--??
year: 1997
bibdate: Mon May 06 17:11:19 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.06 17:11:19 ???
URL: http://java.sun.com/people/jag/FP.html
acknowledgement: ack-nhfb
howpublished: World Wide Web document.
rawauthor: James A. Gosling
rawtitle: The Evolution of Numerical Computing in {Java}
entry:
@Misc{Gosling:1997:ENC,
  author =       "James A. Gosling",
  title =        "The Evolution of Numerical Computing in {Java}",
  howpublished = "World Wide Web document.",
  year =         "1997",
  bibdate =      "Mon May 06 17:11:19 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://java.sun.com/people/jag/FP.html",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Grosse:1997:RI
author: Eric Grosse
title: Real Inferno
crossref: Boisvert:1997:QNS
pages: 270--279
year: 1997
bibdate: Tue Jul 21 11:18:48 1998
bibtimestamp: 1998.07.21 11:18:48 ???
URL: ftp://cm.bell-labs.com/inferno/real.ps
acknowledgement: ack-nhfb
rawauthor: Eric Grosse
rawtitle: Real {Inferno}
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/g/grosse-eric.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

remark:
From cite Steele:2004:RHP: ``the language Limbo adopted accurate base conversion as one of its improvements over C (p. 271 of this article)''.

entry:
@InProceedings{Grosse:1997:RI,
  author =       "Eric Grosse",
  title =        "Real {Inferno}",
  crossref =     "Boisvert:1997:QNS",
  pages =        "270--279",
  year =         "1997",
  bibdate =      "Tue Jul 21 11:18:48 1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/g/grosse-eric.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://cm.bell-labs.com/inferno/real.ps",
  acknowledgement = ack-nhfb,
  remark =       "From \cite{Steele:2004:RHP}: ``the language Limbo
                 adopted accurate base conversion as one of its
                 improvements over C (p. 271 of this article)''.",
}


bibtype: book
filename: fparith.bib
label: Guedj:1997:NUL
author: Denis Guedj
title: Numbers: The Universal Language
publisher: Harry N. Abrams, Inc.
address: New York, NY, USA
pages: 175
year: 1997
ISBN: 0-8109-2845-0 OR 0810928450
ISBN13: 978-0-8109-2845-9 OR 9780810928459
LCCN: QA141.G8413 1997
bibdate: Fri Nov 28 17:05:12 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 17:05:12 ???
note: Translated from the French edition cite Guedj:1996:EN by Lory Frankel.
acknowledgement: ack-mfc
rawauthor: Denis Guedj
rawnote: Translated from the French edition \cite{Guedj:1996:EN} by Lory Frankel.
rawtitle: Numbers: The Universal Language
entry:
@Book{Guedj:1997:NUL,
  author =       "Denis Guedj",
  title =        "Numbers: The Universal Language",
  publisher =    "Harry N. Abrams, Inc.",
  address =      "New York, NY, USA",
  pages =        "175",
  year =         "1997",
  ISBN =         "0-8109-2845-0",
  ISBN-13 =      "978-0-8109-2845-9",
  LCCN =         "QA141.G8413 1997",
  bibdate =      "Fri Nov 28 17:05:12 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Translated from the French edition
                 \cite{Guedj:1996:EN} by Lory Frankel.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Hagihara:1997:FPD
author: Y. Hagihara and S. Inui and F. Okamoto and M. Nishida and T. Nakamura and H. Yamada
title: Floating-point datapaths with online built-in self speed test
journal: j-IEEE-J-SOLID-STATE-CIRCUITS
volume: 32
number: 3
pages: 444--449
month: mar
monthnumber: 3
year: 1997
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: Y. Hagihara and S. Inui and F. Okamoto and M. Nishida and T. Nakamura and H. Yamada
rawtitle: Floating-point datapaths with online built-in self speed test
entry:
@Article{Hagihara:1997:FPD,
  author =       "Y. Hagihara and S. Inui and F. Okamoto and M. Nishida
                 and T. Nakamura and H. Yamada",
  title =        "Floating-point datapaths with online built-in self
                 speed test",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "32",
  number =       "3",
  pages =        "444--449",
  month =        mar,
  year =         "1997",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  summary =      "This paper describes floating-point (FP) datapaths
                 developed for graphics and simulation applications. The
                 datapaths are fabricated using 0.35 $\mu$m CMOS
                 technology and embedded in a 125 MHz, 291 MFLOPS vector
                 pipelined processor for use in supercomputers
                 \ldots{}",
}


bibtype: book
filename: fparith.bib
label: Hanson:1997:CII
author: David R. Hanson
title: C Interfaces and Implementations: Techniques for Creating Reusable Software
publisher: pub-AW
address: pub-AW:adr
pages: xvii + 519
year: 1997
ISBN: 0-201-49841-3 OR 0201498413
ISBN13: 978-0-201-49841-7 OR 9780201498417
LCCN: QA76.73.C15H37 1997
bibdate: Fri Feb 27 16:08:11 1998
bibtimestamp: 1998.02.27 16:08:11 ???
series: Addison-Wesley Professional Computing Series
URL: http://www.cs.princeton.edu/software/cii/
subject: C (Computer program language); Computer software; Reusability; Literate Programming
acknowledgement: ack-nhfb
rawauthor: David R. Hanson
rawtitle: {C} Interfaces and Implementations: Techniques for Creating Reusable Software
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/litprog.bib

TOC:
1. Introduction 2. Interfaces and Implementations 3. Atoms 4. Exceptions and Assertions 5. Memory Management 6. More Memory Management 7. Lists 8. Tables 9. Sets 10. Dynamic Arrays 11. Sequences 12. Rings 13. Bit Vectors 14. Formatting 15. Low-Level Strings 16. High-Level Strings 17. Extended-Precision Arithmetic 18. Arbitrary-Precision Arithmetic 19. Multiple-Precision Arithmetic 20. Threads

rawTOC:
1. Introduction \\ 2. Interfaces and Implementations \\ 3. Atoms \\ 4. Exceptions and Assertions \\ 5. Memory Management \\ 6. More Memory Management \\ 7. Lists \\ 8. Tables \\ 9. Sets \\ 10. Dynamic Arrays \\ 11. Sequences \\ 12. Rings \\ 13. Bit Vectors \\ 14. Formatting \\ 15. Low-Level Strings \\ 16. High-Level Strings \\ 17. Extended-Precision Arithmetic \\ 18. Arbitrary-Precision Arithmetic \\ 19. Multiple-Precision Arithmetic \\ 20. Threads

entry:
@Book{Hanson:1997:CII,
  author =       "David R. Hanson",
  title =        "{C} Interfaces and Implementations: Techniques for
                 Creating Reusable Software",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  pages =        "xvii + 519",
  year =         "1997",
  ISBN =         "0-201-49841-3",
  ISBN-13 =      "978-0-201-49841-7",
  LCCN =         "QA76.73.C15H37 1997",
  bibdate =      "Fri Feb 27 16:08:11 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/litprog.bib",
  price =        "US\$37.95",
  series =       "Addison-Wesley Professional Computing Series",
  URL =          "http://www.cs.princeton.edu/software/cii/",
  acknowledgement = ack-nhfb,
  subject =      "C (Computer program language); Computer software;
                 Reusability; Literate Programming",
  tableofcontents = "1. Introduction \\
                 2. Interfaces and Implementations \\
                 3. Atoms \\
                 4. Exceptions and Assertions \\
                 5. Memory Management \\
                 6. More Memory Management \\
                 7. Lists \\
                 8. Tables \\
                 9. Sets \\
                 10. Dynamic Arrays \\
                 11. Sequences \\
                 12. Rings \\
                 13. Bit Vectors \\
                 14. Formatting \\
                 15. Low-Level Strings \\
                 16. High-Level Strings \\
                 17. Extended-Precision Arithmetic \\
                 18. Arbitrary-Precision Arithmetic \\
                 19. Multiple-Precision Arithmetic \\
                 20. Threads",
}


bibtype: techreport
filename: fparith.bib
label: Hanson:1997:ECR
author: Kenton L. Hanson
title: Economical Correctly Rounded Binary Decimal Conversion
type: Report
pages: xvii + 519
day: 19
month: dec
monthnumber: 12
year: 1997
bibdate: Sat May 07 09:46:31 2022
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2022.05.07 09:46:31 ???
acknowledgement: ack-nhfb
rawauthor: Kenton L. Hanson
rawtitle: Economical Correctly Rounded Binary Decimal Conversion
note:
Cited in cite [p. 134, reference 4]Hack:2004:IPR, and reported there to be now inaccessible. Further queries in May 2022 to four search engines fail to find this document, or its institution and address.

rawnote:
Cited in \cite[p. 134, reference 4]{Hack:2004:IPR}, and reported there to be now inaccessible. Further queries in May 2022 to four search engines fail to find this document, or its institution and address.

entry:
@TechReport{Hanson:1997:ECR,
  author =       "Kenton L. Hanson",
  title =        "Economical Correctly Rounded Binary Decimal
                 Conversion",
  type =         "Report",
  number =       "??",
  institution =  "????",
  address =      "????",
  day =          "19",
  month =        dec,
  year =         "1997",
  bibdate =      "Sat May 07 09:46:31 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Cited in \cite[p. 134, reference 4]{Hack:2004:IPR},
                 and reported there to be now inaccessible. Further
                 queries in May 2022 to four search engines fail to find
                 this document, or its institution and address.",
  acknowledgement = ack-nhfb,
}


bibtype: misc
filename: fparith.bib
label: Hanson:1997:MAD
author: Kenton L. Hanson
pages: xvii + 519
day: 29
month: jul
monthnumber: 7
year: 1997
bibdate: Thu Oct 14 14:54:45 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.14 14:54:45 ???
URL: http://www.patentgenius.com/patent/5652862.html
remark: Patent held by Apple Computer, Inc., Cupertino, CA, USA.
acknowledgement: ack-nhfb
howpublished: US Patent 5652862
rawauthor: Kenton L. Hanson
title:
Method and apparatus for determining a precision of an intermediate arithmetic for converting values between a first numeric format and a second numeric format

abstract:
A method and apparatus for efficient allocation of temporary storage for performing accurate and correct numeric base conversions on a computer system is provided. Numeric base conversions are common because computers operate in binary whereas the values that are input into computers are based on a decimal system. A common source of error occurs when converted values are rounded. The intermediate arithmetic used to perform the conversion requires greater precision than the target floating point format. It is known that to always insure correctly rounded results, an extremely high precision intermediate arithmetic may be used. However, in many case this is a waste of system memory. To efficiently allocate system memory to this task, the most difficult rounding case is determined. The precision needed to correctly round the most difficult case is then derived. This information is then stored and subsequently used to allocate an efficient amount of storage whenever a numeric base conversion is to take place.

rawabstract:
A method and apparatus for efficient allocation of temporary storage for performing accurate and correct numeric base conversions on a computer system is provided. Numeric base conversions are common because computers operate in binary whereas the values that are input into computers are based on a decimal system. A common source of error occurs when converted values are rounded. The intermediate arithmetic used to perform the conversion requires greater precision than the target floating point format. It is known that to always insure correctly rounded results, an extremely high precision intermediate arithmetic may be used. However, in many case this is a waste of system memory. To efficiently allocate system memory to this task, the most difficult rounding case is determined. The precision needed to correctly round the most difficult case is then derived. This information is then stored and subsequently used to allocate an efficient amount of storage whenever a numeric base conversion is to take place.

rawtitle:
Method and apparatus for determining a precision of an intermediate arithmetic for converting values between a first numeric format and a second numeric format

entry:
@Misc{Hanson:1997:MAD,
  author =       "Kenton L. Hanson",
  title =        "Method and apparatus for determining a precision of an
                 intermediate arithmetic for converting values between a
                 first numeric format and a second numeric format",
  howpublished = "US Patent 5652862",
  day =          "29",
  month =        jul,
  year =         "1997",
  bibdate =      "Thu Oct 14 14:54:45 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.patentgenius.com/patent/5652862.html",
  abstract =     "A method and apparatus for efficient allocation of
                 temporary storage for performing accurate and correct
                 numeric base conversions on a computer system is
                 provided. Numeric base conversions are common because
                 computers operate in binary whereas the values that are
                 input into computers are based on a decimal system. A
                 common source of error occurs when converted values are
                 rounded. The intermediate arithmetic used to perform
                 the conversion requires greater precision than the
                 target floating point format. It is known that to
                 always insure correctly rounded results, an extremely
                 high precision intermediate arithmetic may be used.
                 However, in many case this is a waste of system memory.
                 To efficiently allocate system memory to this task, the
                 most difficult rounding case is determined. The
                 precision needed to correctly round the most difficult
                 case is then derived. This information is then stored
                 and subsequently used to allocate an efficient amount
                 of storage whenever a numeric base conversion is to
                 take place.",
  acknowledgement = ack-nhfb,
  remark =       "Patent held by Apple Computer, Inc., Cupertino, CA,
                 USA.",
}


bibtype: inproceedings
filename: fparith.bib
label: Harris:1997:SDA
author: David L. Harris and Stuart F. Oberman and Mark A. Horowitz
title: SRT Division Architectures and Implementations
crossref: Lang:1997:ISC
pages: 18--25
year: 1997
bibdate: Mon May 20 05:45:32 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 05:45:32 MDT
keywords: ARITH-13
acknowledgement: ack-nhfb
rawauthor: David L. Harris and Stuart F. Oberman and Mark A. Horowitz
rawtitle: {SRT} Division Architectures and Implementations
URL:
ftp://arith.stanford.edu/tr/srtcircuits.ps.Z; http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Harris.pdf

entry:
@InProceedings{Harris:1997:SDA,
  author =       "David L. Harris and Stuart F. Oberman and Mark A.
                 Horowitz",
  title =        "{SRT} Division Architectures and Implementations",
  crossref =     "Lang:1997:ISC",
  pages =        "18--25",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "ftp://arith.stanford.edu/tr/srtcircuits.ps.Z;
                 http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Harris.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}


bibtype: techreport
filename: fparith.bib
label: Harrison:1997:FPV
author: John Robert Harrison
title: Floating point verification in HOL Light: the exponential function
type: Technical Report
number: 428
institution: University of Cambridge Computer Laboratory
address: Cambridge, UK
pages: ii + 110
month: jun
monthnumber: 6
year: 1997
LCCN: QA76.9.A96 H367 1997
bibdate: Thu Oct 24 14:30:40 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.10.24 14:30:40 ???
URL: http://www.cl.cam.ac.uk/users/jrh/papers/tang.ps.gz
keywords: automatic theorem proving; floating-point arithmetic; proof theory
acknowledgement: ack-nhfb
rawauthor: John Robert Harrison
rawtitle: Floating point verification in {HOL Light}: the exponential function
entry:
@TechReport{Harrison:1997:FPV,
  author =       "John Robert Harrison",
  title =        "Floating point verification in {HOL Light}: the
                 exponential function",
  type =         "Technical Report",
  number =       "428",
  institution =  "University of Cambridge Computer Laboratory",
  address =      "Cambridge, UK",
  pages =        "ii + 110",
  month =        jun,
  year =         "1997",
  LCCN =         "QA76.9.A96 H367 1997",
  bibdate =      "Thu Oct 24 14:30:40 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cl.cam.ac.uk/users/jrh/papers/tang.ps.gz",
  acknowledgement = ack-nhfb,
  keywords =     "automatic theorem proving; floating-point arithmetic;
                 proof theory",
}


bibtype: article
filename: fparith.bib
label: Hasan:1997:DA
author: M. A. Hasan
title: Division-and-accumulation over $ mathrm GF(2^m) $
journal: j-IEEE-TRANS-COMPUT
volume: 46
number: 6
pages: 705--708
month: jun
monthnumber: 6
year: 1997
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.600829
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 10:06:23 MDT 2011
bibtimestamp: 2011.07.06 10:06:23 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=600829
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: M. A. Hasan
rawtitle: Division-and-accumulation over {$ \mathrm {GF}(2^m) $}
entry:
@Article{Hasan:1997:DA,
  author =       "M. A. Hasan",
  title =        "Division-and-accumulation over {$ \mathrm {GF}(2^m)
                 $}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "46",
  number =       "6",
  pages =        "705--708",
  month =        jun,
  year =         "1997",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.600829",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 10:06:23 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=600829",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Hekstra:1997:FRL
author: Gerber J. Hekstra and Ed F. A. Deprettere
title: Fast Rotations: Low-Cost Arithmetic Methods for Orthonormal Rotation
crossref: Lang:1997:ISC
pages: 116--125
year: 1997
bibdate: Mon May 20 05:45:32 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 05:45:32 MDT
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Hekstra.pdf
keywords: ARITH-13
acknowledgement: ack-nhfb
rawauthor: Gerber J. Hekstra and Ed F. A. Deprettere
rawtitle: Fast Rotations: Low-Cost Arithmetic Methods for Orthonormal Rotation
entry:
@InProceedings{Hekstra:1997:FRL,
  author =       "Gerber J. Hekstra and Ed F. A. Deprettere",
  title =        "Fast Rotations: Low-Cost Arithmetic Methods for
                 Orthonormal Rotation",
  crossref =     "Lang:1997:ISC",
  pages =        "116--125",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Hekstra.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}


bibtype: inproceedings
filename: fparith.bib
label: Hiasat:1997:DIR
author: Ahmad A. Hiasat and Hoda S. Abdel-Aty-Zohdy
title: Design and Implementation of an RNS Division Algorithm
crossref: Lang:1997:ISC
pages: 240--249
year: 1997
bibdate: Wed Nov 14 18:57:54 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 18:57:54 ???
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Hiasat.pdf
keywords: ARITH-13; residue number system
acknowledgement: ack-nhfb
rawauthor: Ahmad A. Hiasat and Hoda S. Abdel-Aty-Zohdy
rawtitle: Design and Implementation of an {RNS} Division Algorithm
entry:
@InProceedings{Hiasat:1997:DIR,
  author =       "Ahmad A. Hiasat and Hoda S. Abdel-Aty-Zohdy",
  title =        "Design and Implementation of an {RNS} Division
                 Algorithm",
  crossref =     "Lang:1997:ISC",
  pages =        "240--249",
  year =         "1997",
  bibdate =      "Wed Nov 14 18:57:54 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Hiasat.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13; residue number system",
}


bibtype: mastersthesis
filename: fparith.bib
label: Hix:1997:CTV
author: Robert W. Hix
title: A comparison of two VHDL design environments for FPGA-based computer arithmetic
type: Thesis (M.S.)
school: Tennessee Technological University
address: Cookeville, TN, USA
pages: x + 301
year: 1997
bibdate: Mon Mar 05 14:38:08 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.03.05 14:38:08 ???
acknowledgement: ack-nhfb
rawauthor: Robert W. Hix
rawtitle: A comparison of two {VHDL} design environments for {FPGA}-based computer arithmetic
entry:
@MastersThesis{Hix:1997:CTV,
  author =       "Robert W. Hix",
  title =        "A comparison of two {VHDL} design environments for
                 {FPGA}-based computer arithmetic",
  type =         "Thesis ({M.S.})",
  school =       "Tennessee Technological University",
  address =      "Cookeville, TN, USA",
  pages =        "x + 301",
  year =         "1997",
  bibdate =      "Mon Mar 05 14:38:08 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Holmes:1997:CAP
author: W. Neville Holmes
title: Composite Arithmetic: Proposal for a New Standard
journal: j-COMPUTER
volume: 30
number: 3
pages: 65--73
month: mar
monthnumber: 3
year: 1997
CODEN: CPTRB4
ISSN: 0018-9162 (print), 1558-0814 (electronic) OR 00189162 (print), 15580814 (electronic)
ISSNL: 0018-9162 OR 00189162
bibdate: Fri May 9 17:30:55 MDT 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.05.09 17:30:55 MDT
fjournal: Computer
acknowledgement: ack-nhfb
corpsource: Department of Comput., Tasmania University, Launceston, Tas., Australia
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2
treatment: P Practical
rawauthor: W. Neville Holmes
rawtitle: Composite Arithmetic: Proposal for a New Standard
URL:
ftp://ftp.comp.utas.edu.au/pub/nholmes/ca/dsdf.ps; ftp://ftp.comp.utas.edu.au/pub/nholmes/ca/dsrf.ps; ftp://ftp.comp.utas.edu.au/pub/nholmes/ca/dssf.ps

keywords:
composite arithmetic; digital arithmetic; exact numbers; extended arithmetic; floating point arithmetic; formatting scheme; general computation; general-purpose arithmetic standard; inexact numbers; number display; number format; number storage; reliability; stability; standards

entry:
@Article{Holmes:1997:CAP,
  author =       "W. Neville Holmes",
  title =        "Composite Arithmetic: Proposal for a New Standard",
  journal =      j-COMPUTER,
  volume =       "30",
  number =       "3",
  pages =        "65--73",
  month =        mar,
  year =         "1997",
  CODEN =        "CPTRB4",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Fri May 9 17:30:55 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://ftp.comp.utas.edu.au/pub/nholmes/ca/dsdf.ps;
                 ftp://ftp.comp.utas.edu.au/pub/nholmes/ca/dsrf.ps;
                 ftp://ftp.comp.utas.edu.au/pub/nholmes/ca/dssf.ps",
  acknowledgement = ack-nhfb,
  classification = "C5230 (Digital arithmetic methods)",
  corpsource =   "Department of Comput., Tasmania University,
                 Launceston, Tas., Australia",
  fjournal =     "Computer",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
  keywords =     "composite arithmetic; digital arithmetic; exact
                 numbers; extended arithmetic; floating point
                 arithmetic; formatting scheme; general computation;
                 general-purpose arithmetic standard; inexact numbers;
                 number display; number format; number storage;
                 reliability; stability; standards",
  treatment =    "P Practical",
}


bibtype: article
filename: fparith.bib
label: Irmay:1997:RBZ
author: Shragga Irmay
title: The relationship between Zipf's law and the distribution of first digits
journal: j-J-APPL-STAT
volume: 24
number: 4
pages: 383--393
day: 1
month: aug
monthnumber: 8
year: 1997
ISSN: 0266-4763 (print), 1360-0532 (electronic) OR 02664763 (print), 13600532 (electronic)
ISSNL: 0266-4763 OR 02664763
MRclass: 62E15
MRnumber: 98h:62015
bibdate: Sat Apr 13 11:27:31 MDT 2002
bibtimestamp: 2002.04.13 11:27:31 MDT
fjournal: Journal of Applied Statistics
keywords: Benford's Law; Zipf's Law
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/cjas20
rawauthor: Shragga Irmay
rawtitle: The relationship between {Zipf}'s law and the distribution of first digits
bibsource:
http://www.catchword.co.uk/titles/carfax/02664763/; http://www.tandf.co.uk/journals/routledge/02664763.html; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://www.catchword.co.uk/cgi-bin/cgi?ini=carfax&body=linker&reqidx=/catchword/carfax/13600532/v24n4/s2/p383

entry:
@Article{Irmay:1997:RBZ,
  author =       "Shragga Irmay",
  title =        "The relationship between {Zipf}'s law and the
                 distribution of first digits",
  journal =      j-J-APPL-STAT,
  volume =       "24",
  number =       "4",
  pages =        "383--393",
  day =          "1",
  month =        aug,
  year =         "1997",
  CODEN =        "????",
  ISSN =         "0266-4763 (print), 1360-0532 (electronic)",
  ISSN-L =       "0266-4763",
  MRclass =      "62E15",
  MRnumber =     "98h:62015",
  bibdate =      "Sat Apr 13 11:27:31 MDT 2002",
  bibsource =    "http://www.catchword.co.uk/titles/carfax/02664763/;
                 http://www.tandf.co.uk/journals/routledge/02664763.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.catchword.co.uk/cgi-bin/cgi?ini=carfax&body=linker&reqidx=/catchword/carfax/13600532/v24n4/s2/p383",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Statistics",
  journal-URL =  "http://www.tandfonline.com/loi/cjas20",
  keywords =     "Benford's Law; Zipf's Law",
  xxpages =      "383--394",
}


bibtype: article
filename: fparith.bib
label: Ito:1997:EIA
author: M. Ito and N. Takagi and S. Yajima
journal: j-IEEE-TRANS-COMPUT
volume: 46
number: 4
pages: 495--498
month: apr
monthnumber: 4
year: 1997
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.588066
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 10:06:22 MDT 2011
bibtimestamp: 2011.07.06 10:06:22 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=588066
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: M. Ito and N. Takagi and S. Yajima
title:
Efficient initial approximation for multiplicative division and square root by a multiplication with operand modification

rawtitle:
Efficient initial approximation for multiplicative division and square root by a multiplication with operand modification

entry:
@Article{Ito:1997:EIA,
  author =       "M. Ito and N. Takagi and S. Yajima",
  title =        "Efficient initial approximation for multiplicative
                 division and square root by a multiplication with
                 operand modification",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "46",
  number =       "4",
  pages =        "495--498",
  month =        apr,
  year =         "1997",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.588066",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 10:06:22 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=588066",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "An efficient initial approximation method for
                 multiplicative division and square root is proposed. It
                 is a modification of the piecewise linear
                 approximation. The multiplication and the addition
                 required for the linear approximation are replaced by
                 \ldots{}",
}


bibtype: misc
filename: fparith.bib
label: Kahan:1997:JNL
author: W. Kahan
title: The John von Neumann lecture at the SIAM 45th annual meeting
pages: 495--498
year: 1997
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/SIAMjvnl.ps
acknowledgement: ack-nhfb
howpublished: World-Wide Web document.
rawauthor: W. Kahan
rawtitle: The {John von Neumann} lecture at the {SIAM} 45th annual meeting
entry:
@Misc{Kahan:1997:JNL,
  author =       "W. Kahan",
  title =        "The {John von Neumann} lecture at the {SIAM} 45th
                 annual meeting",
  howpublished = "World-Wide Web document.",
  year =         "1997",
  bibdate =      "Sat Apr 28 18:52:17 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/SIAMjvnl.ps",
  acknowledgement = ack-nhfb,
}


bibtype: misc
filename: fparith.bib
label: Kahan:1997:LNS
author: W. Kahan
title: Lecture Notes on the Status of IEEE Standard 754 for Binary Floating-Point Arithmetic
pages: 30
day: 1
month: oct
monthnumber: 10
year: 1997
bibdate: Mon Apr 25 17:54:35 2005
bibtimestamp: 2005.04.25 17:54:35 ???
URL: http://www.cs.berkeley.edu/~wkahan/ieee754status/IEEE754.PDF
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:1997:LNS,
  author =       "W. Kahan",
  title =        "Lecture Notes on the Status of {IEEE Standard 754 for
                 Binary Floating-Point Arithmetic}",
  howpublished = "World-Wide Web document",
  pages =        "30",
  day =          "1",
  month =        oct,
  year =         "1997",
  bibdate =      "Mon Apr 25 17:54:35 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/ieee754status/IEEE754.PDF",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: fparith.bib
label: Kahan:1997:RDI
author: W. Kahan and Melody Y. Ivory
title: Roundoff Degrades an Idealized Cantilever
type: Technical report
address: Berkeley, CA, USA
pages: 11
day: 3
month: jul
monthnumber: 7
year: 1997
bibdate: Fri May 03 12:15:09 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.03 12:15:09 ???
URL: http://www.cs.berkeley.edu/~wkahan/Cantilever.pdf; http://www.cs.berkeley.edu/~wkahan/Cantilever.ps
acknowledgement: ack-nhfb
rawauthor: W. Kahan and Melody Y. Ivory
rawtitle: Roundoff Degrades an Idealized Cantilever
institution:
Department of Mathematics and Department of Electrical Engineering and Computer Science, University of California, Berkeley

entry:
@TechReport{Kahan:1997:RDI,
  author =       "W. Kahan and Melody Y. Ivory",
  title =        "Roundoff Degrades an Idealized Cantilever",
  type =         "Technical report",
  institution =  "Department of Mathematics and Department of Electrical
                 Engineering and Computer Science, University of
                 California, Berkeley",
  address =      "Berkeley, CA, USA",
  pages =        "11",
  day =          "3",
  month =        jul,
  year =         "1997",
  bibdate =      "Fri May 03 12:15:09 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Cantilever.pdf;
                 http://www.cs.berkeley.edu/~wkahan/Cantilever.ps",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Kako:1997:PEF
author: Fujio Kako and Tateaki Sasaki
title: Proposal of ``Effective Floating-Point Number'' for Approximate Algebraic Computation
journal: j-SIGSAM
volume: 31
number: 3
pages: 31--31
month: sep
monthnumber: 9
year: 1997
CODEN: SIGSBZ
ISSN: 0163-5824 (print), 1557-9492 (electronic) OR 01635824 (print), 15579492 (electronic)
ISSNL: 0163-5824 OR 01635824
bibdate: Wed Dec 17 07:49:58 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.12.17 07:49:58 ???
note: Poster abstract only. Discusses fuzzy and interval floating-point arithmetic.
fjournal: SIGSAM Bulletin
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J1000
rawauthor: Fujio Kako and Tateaki Sasaki
rawnote: Poster abstract only. Discusses fuzzy and interval floating-point arithmetic.
rawtitle: Proposal of {``Effective} Floating-Point Number'' for Approximate Algebraic Computation
entry:
@Article{Kako:1997:PEF,
  author =       "Fujio Kako and Tateaki Sasaki",
  title =        "Proposal of {``Effective} Floating-Point Number'' for
                 Approximate Algebraic Computation",
  journal =      j-SIGSAM,
  volume =       "31",
  number =       "3",
  pages =        "31--31",
  month =        sep,
  year =         "1997",
  CODEN =        "SIGSBZ",
  ISSN =         "0163-5824 (print), 1557-9492 (electronic)",
  ISSN-L =       "0163-5824",
  bibdate =      "Wed Dec 17 07:49:58 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Poster abstract only. Discusses fuzzy and interval
                 floating-point arithmetic.",
  acknowledgement = ack-nhfb,
  fjournal =     "SIGSAM Bulletin",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}


bibtype: article
filename: fparith.bib
label: Kapur:1997:MVA
author: Deepak Kapur and M. Subramaniam
title: Mechanizing Verification of Arithmetic Circuits: SRT Division
journal: j-LECT-NOTES-COMP-SCI
volume: 1346
pages: 103--??
year: 1997
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Tue Feb 5 11:51:29 MST 2002
bibtimestamp: 2002.02.05 11:51:29 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Deepak Kapur and M. Subramaniam
rawtitle: Mechanizing Verification of Arithmetic Circuits: {SRT} Division
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t1346.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/1346/13460103.htm; http://link.springer-ny.com/link/service/series/0558/papers/1346/13460103.pdf

entry:
@Article{Kapur:1997:MVA,
  author =       "Deepak Kapur and M. Subramaniam",
  title =        "Mechanizing Verification of Arithmetic Circuits: {SRT}
                 Division",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1346",
  pages =        "103--??",
  year =         "1997",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Feb 5 11:51:29 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1346.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1346/13460103.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/1346/13460103.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Karp:1997:HPD
author: Alan H. Karp and Peter Markstein
title: High-Precision Division and Square Root
journal: j-TOMS
volume: 23
number: 4
pages: 561--589
month: dec
monthnumber: 12
year: 1997
CODEN: ACMSCU
DOI: https://doi.org/10.1145/279232.279237
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Thu Nov 8 14:50:37 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.08 14:50:37 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms, performance, division, quad precision, square root.
acknowledgement: ack-rfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Alan H. Karp and Peter Markstein
rawtitle: High-Precision Division and Square Root
URL:
http://www.acm.org/pubs/articles/journals/toms/forthcoming/a0-karp/a0-karp.ps; http://www.acm.org/pubs/citations/journals/toms/1997-23-4/p561-karp/

abstract:
We present division and square root algorithms for calculation with more bits than are handled by the floating-point hardware. These algorithms avoid the need to multiply two high-precision numbers, speeding up the last iteration by as much as a factor of 10. We also show how to produce the floating-point number closest to the exact result with relatively few additional operations.

subject:
G.1.0 [Numerical Analysis]: General -- computer arithmetic. G.4 [Mathematics of Computing]: Mathematical Software.

rawabstract:
We present division and square root algorithms for calculation with more bits than are handled by the floating-point hardware. These algorithms avoid the need to multiply two high-precision numbers, speeding up the last iteration by as much as a factor of 10. We also show how to produce the floating-point number closest to the exact result with relatively few additional operations.

entry:
@Article{Karp:1997:HPD,
  author =       "Alan H. Karp and Peter Markstein",
  title =        "High-Precision Division and Square Root",
  journal =      j-TOMS,
  volume =       "23",
  number =       "4",
  pages =        "561--589",
  month =        dec,
  year =         "1997",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/279232.279237",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Nov 8 14:50:37 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/articles/journals/toms/forthcoming/a0-karp/a0-karp.ps;
                 http://www.acm.org/pubs/citations/journals/toms/1997-23-4/p561-karp/",
  abstract =     "We present division and square root algorithms for
                 calculation with more bits than are handled by the
                 floating-point hardware. These algorithms avoid the
                 need to multiply two high-precision numbers, speeding
                 up the last iteration by as much as a factor of 10. We
                 also show how to produce the floating-point number
                 closest to the exact result with relatively few
                 additional operations.",
  accepted =     "June 1997",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms, performance, division, quad precision,
                 square root.",
  subject =      "G.1.0 [Numerical Analysis]: General -- computer
                 arithmetic. G.4 [Mathematics of Computing]:
                 Mathematical Software.",
}


bibtype: book
filename: fparith.bib
label: Khinchin:1997:CF
author: Aleksandr Iakovlevich Khinchin
title: Continued fractions
publisher: pub-DOVER
address: pub-DOVER:adr
pages: xi + 95
year: 1997
ISBN: 0-486-69630-8 (paperback) OR 0486696308 (paperback)
ISBN13: 978-0-486-69630-0 (paperback) OR 9780486696300 (paperback)
LCCN: QA295 .K513 1997
bibdate: Fri Nov 30 06:55:53 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2007.11.30 06:55:53 MST
acknowledgement: ack-nhfb
authordates: 1894--1959
rawauthor: Aleksandr Iakovlevich Khinchin
rawtitle: Continued fractions
URL:
http://www.loc.gov/catdir/description/dover032/97008056.html; http://www.loc.gov/catdir/toc/dover031/97008056.html

remark:
Translated from the Russian by Scripta Technica, Inc. Originally published: Chicago : University of Chicago Press, 1964. Edited by Herbert Eagle.

entry:
@Book{Khinchin:1997:CF,
  author =       "Aleksandr Iakovlevich Khinchin",
  title =        "Continued fractions",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "xi + 95",
  year =         "1997",
  ISBN =         "0-486-69630-8 (paperback)",
  ISBN-13 =      "978-0-486-69630-0 (paperback)",
  LCCN =         "QA295 .K513 1997",
  bibdate =      "Fri Nov 30 06:55:53 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/description/dover032/97008056.html;
                 http://www.loc.gov/catdir/toc/dover031/97008056.html",
  acknowledgement = ack-nhfb,
  author-dates = "1894--1959",
  remark =       "Translated from the Russian by Scripta Technica, Inc.
                 Originally published: Chicago : University of Chicago
                 Press, 1964. Edited by Herbert Eagle.",
}


bibtype: inproceedings
filename: fparith.bib
label: King:1997:DDT
author: E. J. King and E. E. Swartzlander, Jr.
title: Data-Dependent Truncation Scheme for Parallel Multipliers
crossref: Fargues:1997:CRT
pages: 1178--1182
year: 1997
bibdate: Fri Jun 24 20:50:14 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.06.24 20:50:14 ???
acknowledgement: ack-nhfb
rawauthor: E. J. King and E. E. {Swartzlander, Jr.}
rawtitle: Data-Dependent Truncation Scheme for Parallel Multipliers
entry:
@InProceedings{King:1997:DDT,
  author =       "E. J. King and E. E. {Swartzlander, Jr.}",
  title =        "Data-Dependent Truncation Scheme for Parallel
                 Multipliers",
  crossref =     "Fargues:1997:CRT",
  pages =        "1178--1182",
  year =         "1997",
  bibdate =      "Fri Jun 24 20:50:14 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Kinoshita:1997:RAE
author: Eisuke Kinoshita and Ki-Ja Lee
title: A Residue Arithmetic Extension for Reliable Scientific Computation
journal: j-IEEE-TRANS-COMPUT
volume: 46
number: 2
pages: 129--138
month: feb
monthnumber: 2
year: 1997
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.565587
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
MRclass: 65G10 (65Y99)
MRnumber: MR1434396 (97j:65080)
bibdate: Wed Jul 6 10:06:20 MDT 2011
bibtimestamp: 2011.07.06 10:06:20 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=565587
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Eisuke Kinoshita and Ki-Ja Lee
rawtitle: A Residue Arithmetic Extension for Reliable Scientific Computation
entry:
@Article{Kinoshita:1997:RAE,
  author =       "Eisuke Kinoshita and Ki-Ja Lee",
  title =        "A Residue Arithmetic Extension for Reliable Scientific
                 Computation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "46",
  number =       "2",
  pages =        "129--138",
  month =        feb,
  year =         "1997",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.565587",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  MRclass =      "65G10 (65Y99)",
  MRnumber =     "MR1434396 (97j:65080)",
  bibdate =      "Wed Jul 6 10:06:20 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=565587",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Koc:1997:FSE
author: C. K. Koc and T. Acar
title: Fast Software Exponentiation in $ mathrm GF(2^k) $
crossref: Lang:1997:ISC
pages: 225--231
year: 1997
bibdate: Sat Nov 17 12:22:42 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.17 12:22:42 ???
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Koc.pdf
keywords: ARITH-13
acknowledgement: ack-nhfb
rawauthor: {\c{C}}. K. Ko{\c{c}} and T. Acar
rawtitle: Fast Software Exponentiation in {$ \mathrm {GF}(2^k) $}
entry:
@InProceedings{Koc:1997:FSE,
  author =       "{\c{C}}. K. Ko{\c{c}} and T. Acar",
  title =        "Fast Software Exponentiation in {$ \mathrm {GF}(2^k)
                 $}",
  crossref =     "Lang:1997:ISC",
  pages =        "225--231",
  year =         "1997",
  bibdate =      "Sat Nov 17 12:22:42 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Koc.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}


bibtype: inproceedings
filename: fparith.bib
label: Kramer:1997:PWC
author: Walter Kramer
title: A Priori Worst-Case Error Bounds for Floating-Point Computations
crossref: Lang:1997:ISC
pages: 64--73
year: 1997
bibdate: Mon May 20 05:45:32 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 05:45:32 MDT
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Kramer.pdf
keywords: ARITH-13
acknowledgement: ack-nhfb
authordates: 1952--2014
rawauthor: Walter Kr{\"a}mer
rawtitle: A Priori Worst-Case Error Bounds for Floating-Point Computations
entry:
@InProceedings{Kramer:1997:PWC,
  author =       "Walter Kr{\"a}mer",
  title =        "A Priori Worst-Case Error Bounds for Floating-Point
                 Computations",
  crossref =     "Lang:1997:ISC",
  pages =        "64--73",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Kramer.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "1952--2014",
  keywords =     "ARITH-13",
}


bibtype: article
filename: fparith.bib
label: Kravchenko:1997:AEP
author: Yu. P. Kravchenko and M. A. Liberman
title: On the Application of Extended Precision Arithmetic to Quantum Mechanical Calculations
journal: j-IJQC
volume: 62
number: 6
pages: 593--601
year: 1997
CODEN: IJQCB2
DOI: https://doi.org/10.1002/(SICI)1097-461X(1997)62:6<593::AID-QUA3>3.0.CO;2-R
ISSN: 0020-7608 (print), 1097-461X (electronic) OR 00207608 (print), 1097461X (electronic)
ISSNL: 0020-7608 OR 00207608
bibdate: Tue Oct 4 06:59:08 MDT 2011
bibtimestamp: 2011.10.04 06:59:08 MDT
fjournal: International Journal of Quantum Chemistry
acknowledgement: ack-nhfb
ajournal: Int. J. Quantum Chem.
journalURL: http://www.interscience.wiley.com/jpages/0020-7608/
journalabr: Int J Quant Chem
onlinedate: 6 Dec 1998
rawauthor: Yu. P. Kravchenko and M. A. Liberman
rawtitle: On the Application of Extended Precision Arithmetic to Quantum Mechanical Calculations
bibsource:
Compendex database; http://www3.interscience.wiley.com/journalfinder.html; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ijqc1990.bib

URL:
http://www3.interscience.wiley.com/cgi-bin/abstract?ID=42544; http://www3.interscience.wiley.com/cgi-bin/fulltext?ID=42544&PLACEBO=IE.pdf

entry:
@Article{Kravchenko:1997:AEP,
  author =       "Yu. P. Kravchenko and M. A. Liberman",
  title =        "On the Application of Extended Precision Arithmetic to
                 Quantum Mechanical Calculations",
  journal =      j-IJQC,
  volume =       "62",
  number =       "6",
  pages =        "593--601",
  month =        "????",
  year =         "1997",
  CODEN =        "IJQCB2",
  DOI =          "https://doi.org/10.1002/(SICI)1097-461X(1997)62:6<593::AID-QUA3>3.0.CO;2-R",
  ISSN =         "0020-7608 (print), 1097-461X (electronic)",
  ISSN-L =       "0020-7608",
  bibdate =      "Tue Oct 4 06:59:08 MDT 2011",
  bibsource =    "Compendex database;
                 http://www3.interscience.wiley.com/journalfinder.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ijqc1990.bib",
  URL =          "http://www3.interscience.wiley.com/cgi-bin/abstract?ID=42544;
                 http://www3.interscience.wiley.com/cgi-bin/fulltext?ID=42544&PLACEBO=IE.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Int. J. Quantum Chem.",
  fjournal =     "International Journal of Quantum Chemistry",
  journal-URL =  "http://www.interscience.wiley.com/jpages/0020-7608/",
  journalabr =   "Int J Quant Chem",
  onlinedate =   "6 Dec 1998",
}


bibtype: inproceedings
filename: fparith.bib
label: Lang:1997:CVA
author: Tomas Lang and Elisardo Antelo
title: CORDIC Vectoring with Arbitrary Target Value
crossref: Lang:1997:ISC
pages: 108--115
year: 1997
bibdate: Mon May 20 05:45:32 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 05:45:32 MDT
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Lang.pdf
keywords: ARITH-13
acknowledgement: ack-nhfb
rawauthor: Tom{\'a}s Lang and Elisardo Antelo
rawtitle: {CORDIC} Vectoring with Arbitrary Target Value
entry:
@InProceedings{Lang:1997:CVA,
  author =       "Tom{\'a}s Lang and Elisardo Antelo",
  title =        "{CORDIC} Vectoring with Arbitrary Target Value",
  crossref =     "Lang:1997:ISC",
  pages =        "108--115",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Lang.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}


bibtype: inproceedings
filename: fparith.bib
label: Lang:1997:FIS
author: Tomas Lang and Jean-Michel Muller and Naofumi Takagi
title: Foreword: 13th IEEE Symposium on Computer Arithmetic, July 6--9, 1997, Asilomar, California, USA
crossref: Lang:1997:ISC
pages: viii--viii
year: 1997
bibdate: Sat Nov 17 12:22:42 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.17 12:22:42 ???
keywords: ARITH-13
acknowledgement: ack-nhfb
rawauthor: Tom{\'a}s Lang and Jean-Michel Muller and Naofumi Takagi
rawtitle: Foreword: {13th IEEE Symposium on Computer Arithmetic, July 6--9, 1997, Asilomar, California, USA}
URL:
http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_contents.pdf; http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_foreword.pdf; http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_preface.pdf

entry:
@InProceedings{Lang:1997:FIS,
  author =       "Tom{\'a}s Lang and Jean-Michel Muller and Naofumi
                 Takagi",
  title =        "Foreword: {13th IEEE Symposium on Computer Arithmetic,
                 July 6--9, 1997, Asilomar, California, USA}",
  crossref =     "Lang:1997:ISC",
  pages =        "viii--viii",
  year =         "1997",
  bibdate =      "Sat Nov 17 12:22:42 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_contents.pdf;
                 http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_foreword.pdf;
                 http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_preface.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}


bibtype: inproceedings
filename: fparith.bib
label: Lee:1997:SSA
author: Choong Ho Lee and M. Kawamata and T. Higuchi
title: State-space approach to roundoff error analysis of fractal image coding
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1341--1344
year: 1997
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: Choong Ho Lee and M. Kawamata and T. Higuchi
rawtitle: State-space approach to roundoff error analysis of fractal image coding
booktitle:
Proceedings of 1997 IEEE International Symposium on Circuits and Systems: ISCAS '97, 9--12 June 1997

rawbooktitle:
Proceedings of 1997 {IEEE} International Symposium on Circuits and Systems: {ISCAS '97}, 9--12 June 1997

entry:
@InProceedings{Lee:1997:SSA,
  author =       "Choong Ho Lee and M. Kawamata and T. Higuchi",
  booktitle =    "Proceedings of 1997 {IEEE} International Symposium on
                 Circuits and Systems: {ISCAS '97}, 9--12 June 1997",
  title =        "State-space approach to roundoff error analysis of
                 fractal image coding",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1341--1344",
  year =         "1997",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:07 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Roundoff error due to iterative computation with
                 finite wordlength degrades the quality of decoded
                 images in fractal image coding that employs a
                 deterministic iterated function system. This paper
                 presents a state-space approach to roundoff error
                 \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Lee:1997:VDA
author: Inseop Lee and W. K. Jenkins
booktitle: Proceedings of the 40th Midwest Symposium on Circuits and Systems, 1997
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 782--785
year: 1997
DOI: https://doi.org/10.1109/MWSCAS.1997.662191
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: Inseop Lee and W. K. Jenkins
rawbooktitle: Proceedings of the 40th Midwest Symposium on Circuits and Systems, 1997
title:
VLSI design for an adaptive equalizer using a residue number system architecture for magnetic channels

rawtitle:
{VLSI} design for an adaptive equalizer using a residue number system architecture for magnetic channels

entry:
@InProceedings{Lee:1997:VDA,
  author =       "Inseop Lee and W. K. Jenkins",
  booktitle =    "Proceedings of the 40th Midwest Symposium on Circuits
                 and Systems, 1997",
  title =        "{VLSI} design for an adaptive equalizer using a
                 residue number system architecture for magnetic
                 channels",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "782--785",
  year =         "1997",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/MWSCAS.1997.662191",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "This paper presents the design of an experimental ASIC
                 for an all-digital adaptive equalizer for magnetic
                 channels. The equalizer design, which is based on an
                 RNS chip architecture, is presented at a system level,
                 with particular attention to \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Lefevre:1997:TCR
author: Vincent Lefevre and Jean-Michel Muller and Arnaud Tisserand
title: Towards Correctly Rounded Transcendentals
crossref: Lang:1997:ISC
pages: 132--139
year: 1997
bibdate: Mon May 20 05:45:32 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 05:45:32 MDT
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Lefevre.pdf
keywords: ARITH-13; correct rounding; floating-point arithmetic
acknowledgement: ack-nhfb
rawauthor: Vincent Lef{\`e}vre and Jean-Michel Muller and Arnaud Tisserand
rawtitle: Towards Correctly Rounded Transcendentals
entry:
@InProceedings{Lefevre:1997:TCR,
  author =       "Vincent Lef{\`e}vre and Jean-Michel Muller and Arnaud
                 Tisserand",
  title =        "Towards Correctly Rounded Transcendentals",
  crossref =     "Lang:1997:ISC",
  pages =        "132--139",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Lefevre.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13; correct rounding; floating-point
                 arithmetic",
  summary =      "The Table Maker's Dilemma is the problem of always
                 getting exactly rounded results when computing the
                 elementary functions. After a brief presentation of
                 this problem, we present new developments that helped
                 us to solve this problem for the double \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: LeLann:1997:AAF
author: Gerard Le Lann
booktitle: Proceedings of the International Conference and Workshop on Engineering of Computer-Based Systems
title: An Analysis of the Ariane 5 Flight 501 Failure --- A System Engineering Perspective
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 339--346
year: 1997
DOI: https://doi.org/10.1109/ECBS.1997.581900
bibdate: Sat Apr 01 08:29:32 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2017.04.01 08:29:32 ???
URL: http://ieeexplore.ieee.org/document/581900/
acknowledgement: ack-nhfb
rawauthor: G{\'e}rard {Le Lann}
rawbooktitle: {Proceedings of the International Conference and Workshop on Engineering of Computer-Based Systems}
rawtitle: An Analysis of the {Ariane 5 Flight 501} Failure --- A System Engineering Perspective
note:
From the article: ``The SRI S/W exception was raised during a conversion from a 64-bit floating point number F to a 16-bit signed integer number. F had a value greater than what can be represented by a 16-bit signed integer, which caused an Operand Error (data conversion --- in Ada code --- was not protected, for the reason that a maximum workload target of 80% had been set for the SRI computer). ldots The value of BH was much higher than expected because the early part of the trajectory of Ariane 5 differs from that of Ariane 4, which results in considerably higher horizontal velocity values.''

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.

rawnote:
From the article: ``The SRI S/W exception was raised during a conversion from a 64-bit floating point number F to a 16-bit signed integer number. F had a value greater than what can be represented by a 16-bit signed integer, which caused an Operand Error (data conversion --- in Ada code --- was not protected, for the reason that a maximum workload target of 80\% had been set for the SRI computer). \ldots{} The value of BH was much higher than expected because the early part of the trajectory of Ariane 5 differs from that of Ariane 4, which results in considerably higher horizontal velocity values.''

entry:
@InProceedings{LeLann:1997:AAF,
  author =       "G{\'e}rard {Le Lann}",
  booktitle =    "{Proceedings of the International Conference and
                 Workshop on Engineering of Computer-Based Systems}",
  title =        "An Analysis of the {Ariane 5 Flight 501} Failure --- A
                 System Engineering Perspective",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "339--346",
  year =         "1997",
  DOI =          "https://doi.org/10.1109/ECBS.1997.581900",
  bibdate =      "Sat Apr 01 08:29:32 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "From the article: ``The SRI S/W exception was raised
                 during a conversion from a 64-bit floating point number
                 F to a 16-bit signed integer number. F had a value
                 greater than what can be represented by a 16-bit signed
                 integer, which caused an Operand Error (data conversion
                 --- in Ada code --- was not protected, for the reason
                 that a maximum workload target of 80\% had been set for
                 the SRI computer). \ldots{} The value of BH was much
                 higher than expected because the early part of the
                 trajectory of Ariane 5 differs from that of Ariane 4,
                 which results in considerably higher horizontal
                 velocity values.''",
  URL =          "http://ieeexplore.ieee.org/document/581900/",
  acknowledgement = ack-nhfb,
  remark =       "Report of an arithmetic error that put an expensive
                 space missile off course, requiring its destruction in
                 the air. Presumably-reliable code in Ada adapted from
                 an earlier missile generated had not been updated for
                 the new design.",
}


bibtype: inproceedings
filename: fparith.bib
label: Li:1997:ISP
author: Yamin Li and Wanming Chu
title: Implementation of single precision floating point square root on FPGAs
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 226--232
year: 1997
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: Implementation of single precision floating point square root on {FPGAs}
booktitle:
Proceedings of the 5th Annual IEEE Symposium on FPGAs for Custom Computing Machines, 16--18 April 1997

rawbooktitle:
Proceedings of the 5th Annual {IEEE} Symposium on {FPGAs} for Custom Computing Machines, 16--18 April 1997

entry:
@InProceedings{Li:1997:ISP,
  author =       "Yamin Li and Wanming Chu",
  booktitle =    "Proceedings of the 5th Annual {IEEE} Symposium on
                 {FPGAs} for Custom Computing Machines, 16--18 April
                 1997",
  title =        "Implementation of single precision floating point
                 square root on {FPGAs}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "226--232",
  year =         "1997",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "The square root operation is hard to implement on
                 FPGAs because of the complexity of the algorithms. In
                 this paper, we present a non-restoring square root
                 algorithm and two very simple single precision floating
                 point square root implementations \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Li:1997:PAI
author: Yamin Li and Wanming Chu
title: Parallel-array implementations of a non-restoring square root algorithm
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 690--695
year: 1997
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: Parallel-array implementations of a non-restoring square root algorithm
booktitle:
Proceedings of the 1997 IEEE International Conference on Computer Design: VLSI in Computers and Processors: ICCD '97

rawbooktitle:
Proceedings of the 1997 {IEEE} International Conference on Computer Design: {VLSI} in Computers and Processors: {ICCD '97}

entry:
@InProceedings{Li:1997:PAI,
  author =       "Yamin Li and Wanming Chu",
  booktitle =    "Proceedings of the 1997 {IEEE} International
                 Conference on Computer Design: {VLSI} in Computers and
                 Processors: {ICCD '97}",
  title =        "Parallel-array implementations of a non-restoring
                 square root algorithm",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "690--695",
  year =         "1997",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "In this paper we present a parallel-array
                 implementation of a new non-restoring square root
                 algorithm (PASQRT). The carry-save adder (CSA) is used
                 in the parallel array. The PASQRT has several features
                 unlike other implementations. First, it does \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Lin:1997:DOA
author: Ming-Bo Lin and A. Y. Oruc
title: The design of an optoelectronic arithmetic processor based on permutation networks
journal: j-IEEE-TRANS-COMPUT
volume: 46
number: 2
pages: 142--153
month: feb
monthnumber: 2
year: 1997
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.565589
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 10:06:20 MDT 2011
bibtimestamp: 2011.07.06 10:06:20 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=565589
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Ming-Bo Lin and A. Y. Oruc
rawtitle: The design of an optoelectronic arithmetic processor based on permutation networks
entry:
@Article{Lin:1997:DOA,
  author =       "Ming-Bo Lin and A. Y. Oruc",
  title =        "The design of an optoelectronic arithmetic processor
                 based on permutation networks",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "46",
  number =       "2",
  pages =        "142--153",
  month =        feb,
  year =         "1997",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.565589",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 10:06:20 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=565589",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: phdthesis
filename: fparith.bib
label: Lin:1997:HSN
author: Lei Lin
title: High-speed nonlinear computer arithmetic: algorithms, VLSI design, and accuracy prediction
type: Thesis (Ph.D.)
school: University of South Florida
address: Tampa, FL, USA
pages: xv + 204
year: 1997
bibdate: Mon Mar 05 14:36:45 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.03.05 14:36:45 ???
acknowledgement: ack-nhfb
rawauthor: Lei Lin
rawtitle: High-speed nonlinear computer arithmetic: algorithms, {VLSI} design, and accuracy prediction
entry:
@PhdThesis{Lin:1997:HSN,
  author =       "Lei Lin",
  title =        "High-speed nonlinear computer arithmetic: algorithms,
                 {VLSI} design, and accuracy prediction",
  type =         "Thesis ({Ph.D.})",
  school =       "University of South Florida",
  address =      "Tampa, FL, USA",
  pages =        "xv + 204",
  year =         "1997",
  bibdate =      "Mon Mar 05 14:36:45 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Lu:1997:SMK
author: Chung-Chin Lu
title: A search of minimal key functions for normal basis multipliers
journal: j-IEEE-TRANS-COMPUT
volume: 46
number: 5
pages: 588--592
month: may
monthnumber: 5
year: 1997
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.589230
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 10:06:22 MDT 2011
bibtimestamp: 2011.07.06 10:06:22 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=589230
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Chung-Chin Lu
rawtitle: A search of minimal key functions for normal basis multipliers
entry:
@Article{Lu:1997:SMK,
  author =       "Chung-Chin Lu",
  title =        "A search of minimal key functions for normal basis
                 multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "46",
  number =       "5",
  pages =        "588--592",
  month =        may,
  year =         "1997",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.589230",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 10:06:22 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=589230",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Lutz:1997:HAF
author: David R. Lutz and D. N. Jayasimha
title: The Half-Adder Form and Early Branch Condition Resolution
crossref: Lang:1997:ISC
pages: 266--273
year: 1997
bibdate: Sat Nov 17 12:22:42 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.17 12:22:42 ???
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Lutz.pdf
keywords: ARITH-13
acknowledgement: ack-nhfb
rawauthor: David R. Lutz and D. N. Jayasimha
rawtitle: The Half-Adder Form and Early Branch Condition Resolution
entry:
@InProceedings{Lutz:1997:HAF,
  author =       "David R. Lutz and D. N. Jayasimha",
  title =        "The Half-Adder Form and Early Branch Condition
                 Resolution",
  crossref =     "Lang:1997:ISC",
  pages =        "266--273",
  year =         "1997",
  bibdate =      "Sat Nov 17 12:22:42 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Lutz.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}


bibtype: inproceedings
filename: fparith.bib
label: Matsubara:1997:LPZ
author: G. Matsubara and N. Ide
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 198--209
year: 1997
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: G. Matsubara and N. Ide
booktitle:
Proceedings of the Third International Symposium on Advanced Research in Asynchronous Circuits and Systems, 7--10 April 1997

title:
A low power zero-overhead self-timed division and square root unit combining a single-rail static circuit with a dual-rail dynamic circuit

rawbooktitle:
Proceedings of the Third International Symposium on Advanced Research in Asynchronous Circuits and Systems, 7--10 April 1997

rawtitle:
A low power zero-overhead self-timed division and square root unit combining a single-rail static circuit with a dual-rail dynamic circuit

entry:
@InProceedings{Matsubara:1997:LPZ,
  author =       "G. Matsubara and N. Ide",
  booktitle =    "Proceedings of the Third International Symposium on
                 Advanced Research in Asynchronous Circuits and Systems,
                 7--10 April 1997",
  title =        "A low power zero-overhead self-timed division and
                 square root unit combining a single-rail static circuit
                 with a dual-rail dynamic circuit",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "198--209",
  year =         "1997",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "An asynchronous pipeline scheme that combines a low
                 power static circuit with a high-speed dual-rail
                 dynamic circuit is proposed. The scheme utilizes a
                 dual-rail circuit only in the critical path of an SRT
                 division and square root calculation unit. \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Matula:1997:PPF
author: David W. Matula and Asger Munk Nielsen
title: Pipelined Packet-Forwarding Floating Point: I. Foundations and a Rounder
crossref: Lang:1997:ISC
pages: 140--147
year: 1997
bibdate: Mon May 20 05:45:32 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 05:45:32 MDT
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Matula.pdf
keywords: ARITH-13
acknowledgement: ack-nhfb
rawauthor: David W. Matula and Asger Munk Nielsen
rawtitle: Pipelined Packet-Forwarding Floating Point: {I}. Foundations and a Rounder
entry:
@InProceedings{Matula:1997:PPF,
  author =       "David W. Matula and Asger Munk Nielsen",
  title =        "Pipelined Packet-Forwarding Floating Point: {I}.
                 Foundations and a Rounder",
  crossref =     "Lang:1997:ISC",
  pages =        "140--147",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Matula.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
  summary =      "The paper presents the foundations for a packet
                 forwarding floating point format and the design of a
                 rounder ensuring compatibility between packet
                 forwarding format and the standard binary IEEE 754
                 floating point format. The packet forwarding format
                 \ldots{}",
}


bibtype: article
filename: fparith.bib
label: McClain:1997:EC
author: Dylan Loeb McClain
title: The Evolution of the Calculator
journal: j-NY-TIMES
pages: D3--D3
day: 1
month: sep
monthnumber: 9
year: 1997
CODEN: NYTIAO
ISSN: 0362-4331 (print), 1542-667X, 1553-8095 OR 03624331 (print), 1542667X, 15538095
ISSNL: 0362-4331 OR 03624331
bibdate: Sat Aug 17 16:58:52 2013
bibtimestamp: 2013.08.17 16:58:52 ???
URL: http://search.proquest.com/docview/109786292
fjournal: New York Times
keywords: Charles Babbage: Difference Engine
acknowledgement: ack-nhfb
journalURL: http://www.nytimes.com/
rawauthor: Dylan Loeb McClain
rawtitle: The Evolution of the Calculator
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

entry:
@Article{McClain:1997:EC,
  author =       "Dylan Loeb McClain",
  title =        "The Evolution of the Calculator",
  journal =      j-NY-TIMES,
  volume =       "??",
  number =       "??",
  pages =        "D3--D3",
  day =          "1",
  month =        sep,
  year =         "1997",
  CODEN =        "NYTIAO",
  ISSN =         "0362-4331 (print), 1542-667X, 1553-8095",
  ISSN-L =       "0362-4331",
  bibdate =      "Sat Aug 17 16:58:52 2013",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/babbage-charles.bib;
                 https://www.math.utah.edu/pub/tex/bib/adabooks.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://search.proquest.com/docview/109786292",
  acknowledgement = ack-nhfb,
  fjournal =     "New York Times",
  journal-URL =  "http://www.nytimes.com/",
  keywords =     "Charles Babbage: Difference Engine",
}


bibtype: article
filename: fparith.bib
label: Michelucci:1997:LA
author: D. Michelucci and J.-M. Moreau
title: Lazy arithmetic
journal: j-IEEE-TRANS-COMPUT
volume: 46
number: 9
pages: 961--975
month: sep
monthnumber: 9
year: 1997
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.620478
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 10:06:24 MDT 2011
bibtimestamp: 2011.07.06 10:06:24 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=620478
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: D. Michelucci and J.-M. Moreau
rawtitle: Lazy arithmetic
abstract:
Finite-precision leads to many problems in geometric methods from CAD or Computational Geometry. Until now, using exact rational arithmetic was a simple, yet much too slow, solution to be of any practical use in real-scale applications. A recent optimization-the lazy rational arithmetic-seems promising: It defers exact computations until they become either unnecessary (in most cases) or unavoidable; in such a context, only indispensable computations are performed exactly, that is, those without which any given decision cannot be reached safely using only floating-point arithmetic. This paper takes stock of the lazy arithmetic paradigm: principles, functionalities and limits, speed, possible variants and extensions, difficulties, problems solved or left unresolved

rawabstract:
Finite-precision leads to many problems in geometric methods from CAD or Computational Geometry. Until now, using exact rational arithmetic was a simple, yet much too slow, solution to be of any practical use in real-scale applications. A recent optimization-the lazy rational arithmetic-seems promising: It defers exact computations until they become either unnecessary (in most cases) or unavoidable; in such a context, only indispensable computations are performed exactly, that is, those without which any given decision cannot be reached safely using only floating-point arithmetic. This paper takes stock of the lazy arithmetic paradigm: principles, functionalities and limits, speed, possible variants and extensions, difficulties, problems solved or left unresolved

entry:
@Article{Michelucci:1997:LA,
  author =       "D. Michelucci and J.-M. Moreau",
  title =        "Lazy arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "46",
  number =       "9",
  pages =        "961--975",
  month =        sep,
  year =         "1997",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.620478",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 10:06:24 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=620478",
  abstract =     "Finite-precision leads to many problems in geometric
                 methods from CAD or Computational Geometry. Until now,
                 using exact rational arithmetic was a simple, yet much
                 too slow, solution to be of any practical use in
                 real-scale applications. A recent optimization-the lazy
                 rational arithmetic-seems promising: It defers exact
                 computations until they become either unnecessary (in
                 most cases) or unavoidable; in such a context, only
                 indispensable computations are performed exactly, that
                 is, those without which any given decision cannot be
                 reached safely using only floating-point arithmetic.
                 This paper takes stock of the lazy arithmetic paradigm:
                 principles, functionalities and limits, speed, possible
                 variants and extensions, difficulties, problems solved
                 or left unresolved",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: mastersthesis
filename: fparith.bib
label: Mizukami:1997:AFP
author: Etsuko Mizukami
title: The Accuracy of Floating Point Summations for CG-Like Methods
type: Master's Thesis
school: Department of Computer Science, Indiana University-Bloomington
address: Bloomington, IN, USA
pages: v + 55
year: 1997
bibdate: Tue Nov 22 07:27:31 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.11.22 07:27:31 ???
note: Also issued as Technical report 486.
keywords: accurate floating-point summation
acknowledgement: ack-nhfb
rawauthor: Etsuko Mizukami
rawnote: Also issued as Technical report 486.
rawtitle: The Accuracy of Floating Point Summations for {CG}-Like Methods
URL:
ftp://ftp.cs.indiana.edu/pub/techreports/TR486.pdf; ftp://ftp.cs.indiana.edu/pub/techreports/TR486.ps; ftp://ftp.cs.indiana.edu/pub/techreports/TR486.ps.Z; http://www.cs.indiana.edu/cgi-bin/techreports/TRNNN.cgi?trnum=TR486

abstract:
It is well known that different ordering of summations in floating point arithmetic can give different sums due to rounding error. This dissertation reviews classic analytic error bounds. A new accurate algorithm is explained thoroughly along with its analytic error bound. These summation algorithms were implemented as dotproducts in an iterative solver to determine which summation ordering is more accurate in practice. Another issue is the relationship between dotproduct accuracy and the convergence of iterative solvers. Analysis and experiments indicate there are two primary sources of errors, and show which summation methods are better for reducing these errors. Results also indicate little correlation between dotproduct accuracy and numbers of iterations required by a solver, within a wide range of accuracies.

rawabstract:
It is well known that different ordering of summations in floating point arithmetic can give different sums due to rounding error. This dissertation reviews classic analytic error bounds. A new accurate algorithm is explained thoroughly along with its analytic error bound. These summation algorithms were implemented as dotproducts in an iterative solver to determine which summation ordering is more accurate in practice. Another issue is the relationship between dotproduct accuracy and the convergence of iterative solvers. Analysis and experiments indicate there are two primary sources of errors, and show which summation methods are better for reducing these errors. Results also indicate little correlation between dotproduct accuracy and numbers of iterations required by a solver, within a wide range of accuracies.

entry:
@MastersThesis{Mizukami:1997:AFP,
  author =       "Etsuko Mizukami",
  title =        "The Accuracy of Floating Point Summations for
                 {CG}-Like Methods",
  type =         "{Master's Thesis}",
  school =       "Department of Computer Science, Indiana
                 University-Bloomington",
  address =      "Bloomington, IN, USA",
  pages =        "v + 55",
  year =         "1997",
  bibdate =      "Tue Nov 22 07:27:31 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Also issued as Technical report 486.",
  URL =          "ftp://ftp.cs.indiana.edu/pub/techreports/TR486.pdf;
                 ftp://ftp.cs.indiana.edu/pub/techreports/TR486.ps;
                 ftp://ftp.cs.indiana.edu/pub/techreports/TR486.ps.Z;
                 http://www.cs.indiana.edu/cgi-bin/techreports/TRNNN.cgi?trnum=TR486",
  abstract =     "It is well known that different ordering of summations
                 in floating point arithmetic can give different sums
                 due to rounding error. This dissertation reviews
                 classic analytic error bounds. A new accurate algorithm
                 is explained thoroughly along with its analytic error
                 bound. These summation algorithms were implemented as
                 dotproducts in an iterative solver to determine which
                 summation ordering is more accurate in practice.
                 Another issue is the relationship between dotproduct
                 accuracy and the convergence of iterative solvers.
                 Analysis and experiments indicate there are two primary
                 sources of errors, and show which summation methods are
                 better for reducing these errors. Results also indicate
                 little correlation between dotproduct accuracy and
                 numbers of iterations required by a solver, within a
                 wide range of accuracies.",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation",
}


bibtype: article
filename: fparith.bib
label: MRaihi:1997:XFO
author: David M'Raihi and David Naccache and Jacques Stern and Serge Vaudenay
title: XMX: a Firmware-Oriented Block Cipher Based on Modular Multiplications
journal: j-LECT-NOTES-COMP-SCI
volume: 1267
pages: 166--??
year: 1997
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Tue Feb 5 11:51:07 MST 2002
bibtimestamp: 2002.02.05 11:51:07 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: David M'Ra{\"\i}hi and David Naccache and Jacques Stern and Serge Vaudenay
rawtitle: {XMX}: a Firmware-Oriented Block Cipher Based on Modular Multiplications
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t1267.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/1267/12670166.htm; http://link.springer-ny.com/link/service/series/0558/papers/1267/12670166.pdf

entry:
@Article{MRaihi:1997:XFO,
  author =       "David M'Ra{\"\i}hi and David Naccache and Jacques
                 Stern and Serge Vaudenay",
  title =        "{XMX}: a Firmware-Oriented Block Cipher Based on
                 Modular Multiplications",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1267",
  pages =        "166--??",
  year =         "1997",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Feb 5 11:51:07 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1267.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1267/12670166.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/1267/12670166.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Mukherjee:1997:DTM
author: N. Mukherjee and J. Rajski and J. Tyszer
title: Design of testable multipliers for fixed-width data paths
journal: j-IEEE-TRANS-COMPUT
volume: 46
number: 7
pages: 795--810
month: jul
monthnumber: 7
year: 1997
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.599900
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 10:06:23 MDT 2011
bibtimestamp: 2011.07.06 10:06:23 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=599900
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: N. Mukherjee and J. Rajski and J. Tyszer
rawtitle: Design of testable multipliers for fixed-width data paths
entry:
@Article{Mukherjee:1997:DTM,
  author =       "N. Mukherjee and J. Rajski and J. Tyszer",
  title =        "Design of testable multipliers for fixed-width data
                 paths",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "46",
  number =       "7",
  pages =        "795--810",
  month =        jul,
  year =         "1997",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.599900",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 10:06:23 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=599900",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: book
filename: fparith.bib
label: Muller:1997:EFA
author: Jean-Michel Muller
title: Elementary Functions: Algorithms and Implementation
publisher: pub-BIRKHAUSER
address: pub-BIRKHAUSER:adr
pages: xv + 204
year: 1997
ISBN: 0-8176-3990-X OR 081763990X
ISBN13: 978-0-8176-3990-7 OR 9780817639907
LCCN: QA331.M866 1997
bibdate: Fri Jul 25 12:00:55 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/master.bib
bibtimestamp: 1997.07.25 12:00:55 ???
acknowledgement: ack-nhfb
rawauthor: Jean-Michel Muller
rawtitle: Elementary Functions: Algorithms and Implementation
URL:
http://www.birkhauser.com/cgi-win/ISBN/0-8176-3990-X; http://www.ens-lyon.fr/~jmmuller/book_functions.html

abstract:
The elementary functions (sine, cosine, tan, exponentials, and logarithms) are the most commonly used mathematical functions in science and engineering. Computing these functions quickly and accurately is a major goal in computer arithmetic. This new book gives the concepts and background necessary to understand and build algorithms for computing these functions, presenting and structuring the algorithms (hardware-oriented as well as software-oriented), and discusses issues related to the accurate floating-point implementation. The purpose is not to give ``cookbook recipes'' that allow one to implement some given function, but to provide the reader with the knowledge that is necessary to build, or adapt, algorithms to their specific computing environment. The book provides an up-to-date presentation of the information needed to understand and accurately use mathematical functions and algorithms in computational work and design. Graduates, professionals and researchers in scientific computing, software engineering and computer engineering will find the book a useful reference and resource.

TOC:
1 Introduction / 1 2 Computer Arithmetic / 9 2.1 Floating-Point Arithmetic / 9 2.1.1 Floating-point formats / 9 2.1.2 Rounding modes / 10 2.1.3 Subnormal numbers and exceptions / 12 2.1.4 ULPs / 13 2.1.5 Testing your computational environment / 13 2.2 Redundant Number Systems / 13 2.2.1 Signed-digit number systems / 14 2.2.2 Radix-2 redundant number systems / 15 I Algorithms Based on Polynomial Approximation and/or Table Lookup / 19 3 Polynomial Approximations / 21 3.1 Least Squares Polynomial Approximations / 22 3.1.1 Legendre polynomials / 23 3.1.2 Chebyshev polynomials / 23 3.1.3 Jacobi polynomials / 23 3.2 Least Maximum Approximations / 24 3.3 Speed of Convergence / 31 3.4 Rational Approximations / 34 3.5 Actual Computation / 38 3.6 Example: the Cyrix FastMath Processor / 41 3.7 Algorithms and Architectures / 43 3.7.1 The E-Method / 45 3.7.2 Estrin's Method / 47 3.8 Miscellaneous / 47 4 Table-Based Methods / 51 4.1 Introduction / 51 4.2 Table-Driven Algorithms / 53 4.2.1 Tang's algorithm for $exp (x)$ in IEEE floating-point arithmetic / 55 4.2.2 $ln (x)$ on $[1,2]$ / 57 4.2.3 $sin (x)$ on $[0,pi /4]$ / 58 4.3 Gal's Accurate Tables Method / 58 4.4 Methods Requiring Specialized Hardware / 62 4.4.1 Wong and Goto, logarithm / 62 4.4.2 Wong and Goto, exponential / 65 II Shift-and-Add Algorithms / 69 5 Shift-and-Add algorithms / 71 5.1 The Restoring and Nonrestoring Algorithms / 73 5.2 Simple Algorithms for Exponentials and Logarithms / 77 5.2.1 The restoring algorithm for exponentials / 77 5.2.2 The restoring algorithm for logarithms / 79 5.3 Faster Algorithms / 81 5.3.1 Faster computation of exponentials / 81 5.3.2 Faster computation of logarithms / 87 5.4 Baker's Predictive Algorithm / 90 5.5 Bibliographic notes / 98 6 The CORDIC Algorithm / 101 6.1 Introduction / 101 6.2 The Conventional Iteration / 101 6.3 Scale Factor Compensation / 107 6.4 CORDIC With Redundant Number Systems / 109 6.4.1 Signed-digit implementation / 111 6.4.2 Carry-save implementation / 111 6.4.3 The variable scale factor problem / 112 6.5 The Double Rotation Method / 112 6.6 Branching CORDIC / 115 6.7 Differential CORDIC / 118 6.8 Computation of $cos ^-1$ and $sin ^-1$ / 122 6.9 Variations on CORDIC / 124 7 Other Shift-and-Add Algorithms / 127 7.1 High-Radix Algorithms / 127 7.1.1 Ercegovac's radix-16 algorithms / 127 7.2 The BKM Algorithm / 131 7.2.1 The BKM iteration / 133 7.2.2 Computation of the exponential function (E-mode) / 133 7.2.3 Computation of the logarithm function (L-mode) / 137 7.2.4 Application to the computation of elementary functions / 138 III Range Reduction, Final Rounding and Exceptions / 141 8 Range Reduction / 143 8.1 Introduction / 143 8.2 Cody and Waite's Method for Range Reduction / 148 8.3 Worst Cases for Range Reduction / 149 8.3.1 A few basic notions on continued fractions / 149 8.3.2 Finding worst cases using continued fractions / 151 8.4 The Payne and Hanek Algorithm / 154 8.5 The Modular Algorithm / 158 8.5.1 Fixed-point reduction / 158 8.5.2 Floating-point reduction / 161 8.5.3 Architectures for Modular Reduction / 161 9 Final Rounding / 163 9.1 Introduction / 163 9.2 Monotonicity / 164 9.3 Exact Rounding: Presentation of the Problem / 165 9.4 Some Experiments / 168 9.5 A ``Probabilistic'' Approach / 168 9.6 Upper Bounds on $m$ / 171 9.6.1 Frequency of failures / 173 9.6.2 Computing with one million bits / 173 10 Miscellaneous / 175 10.1 Exceptions / 175 10.1.1 NaNs / 176 10.1.2 Exact results / 177 10.2 Notes on $x^y$ / 178 10.3 Multiple Precision / 180

rawabstract:
The elementary functions (sine, cosine, tan, exponentials, and logarithms) are the most commonly used mathematical functions in science and engineering. Computing these functions quickly and accurately is a major goal in computer arithmetic. This new book gives the concepts and background necessary to understand and build algorithms for computing these functions, presenting and structuring the algorithms (hardware-oriented as well as software-oriented), and discusses issues related to the accurate floating-point implementation. The purpose is not to give ``cookbook recipes'' that allow one to implement some given function, but to provide the reader with the knowledge that is necessary to build, or adapt, algorithms to their specific computing environment. The book provides an up-to-date presentation of the information needed to understand and accurately use mathematical functions and algorithms in computational work and design. Graduates, professionals and researchers in scientific computing, software engineering and computer engineering will find the book a useful reference and resource.

shortTOC:
1: Introduction 2: Computer arithmetic I: Algorithms based on polynomial approximation and/or table lookup 3: Polynomial approximations 4: Table-based methods II: Shift-and-Add algorithms 5: Shift-and-Add algorithms 6: The CORDIC algorithm 7: Other shift-and-add algorithms III: Range reduction, final rounding and exceptions 8: Range reduction 9: Final rounding 10: Miscellaneous

rawshortTOC:
1: Introduction \\ 2: Computer arithmetic \\ I: Algorithms based on polynomial approximation and/or table lookup \\ 3: Polynomial approximations \\ 4: Table-based methods \\ II: Shift-and-Add algorithms \\ 5: Shift-and-Add algorithms 6: The CORDIC algorithm \\ 7: Other shift-and-add algorithms \\ III: Range reduction, final rounding and exceptions \\ 8: Range reduction \\ 9: Final rounding \\ 10: Miscellaneous

rawTOC:
1 Introduction / 1 \\ 2 Computer Arithmetic / 9 \\ 2.1 Floating-Point Arithmetic / 9 \\ 2.1.1 Floating-point formats / 9 \\ 2.1.2 Rounding modes / 10 \\ 2.1.3 Subnormal numbers and exceptions / 12 \\ 2.1.4 ULPs / 13 \\ 2.1.5 Testing your computational environment / 13 \\ 2.2 Redundant Number Systems / 13 \\ 2.2.1 Signed-digit number systems / 14 \\ 2.2.2 Radix-2 redundant number systems / 15 \\ I Algorithms Based on Polynomial Approximation and/or Table Lookup / 19 \\ 3 Polynomial Approximations / 21 \\ 3.1 Least Squares Polynomial Approximations / 22 \\ 3.1.1 Legendre polynomials / 23 \\ 3.1.2 Chebyshev polynomials / 23 \\ 3.1.3 Jacobi polynomials / 23 \\ 3.2 Least Maximum Approximations / 24 \\ 3.3 Speed of Convergence / 31 \\ 3.4 Rational Approximations / 34 \\ 3.5 Actual Computation / 38 \\ 3.6 Example: the Cyrix FastMath Processor / 41 \\ 3.7 Algorithms and Architectures / 43 \\ 3.7.1 The E-Method / 45 \\ 3.7.2 Estrin's Method / 47 \\ 3.8 Miscellaneous / 47 \\ 4 Table-Based Methods / 51 \\ 4.1 Introduction / 51 \\ 4.2 Table-Driven Algorithms / 53 \\ 4.2.1 Tang's algorithm for $\exp(x)$ in IEEE floating-point arithmetic / 55 \\ 4.2.2 $\ln(x)$ on $[1,2]$ / 57 \\ 4.2.3 $\sin(x)$ on $[0,\pi/4]$ / 58 \\ 4.3 Gal's Accurate Tables Method / 58 \\ 4.4 Methods Requiring Specialized Hardware / 62 \\ 4.4.1 Wong and Goto, logarithm / 62 \\ 4.4.2 Wong and Goto, exponential / 65 \\ II Shift-and-Add Algorithms / 69 \\ 5 Shift-and-Add algorithms / 71 \\ 5.1 The Restoring and Nonrestoring Algorithms / 73 \\ 5.2 Simple Algorithms for Exponentials and Logarithms / 77 \\ 5.2.1 The restoring algorithm for exponentials / 77 \\ 5.2.2 The restoring algorithm for logarithms / 79 \\ 5.3 Faster Algorithms / 81 \\ 5.3.1 Faster computation of exponentials / 81 \\ 5.3.2 Faster computation of logarithms / 87 \\ 5.4 Baker's Predictive Algorithm / 90 \\ 5.5 Bibliographic notes / 98 \\ 6 The CORDIC Algorithm / 101 \\ 6.1 Introduction / 101 \\ 6.2 The Conventional Iteration / 101 \\ 6.3 Scale Factor Compensation / 107 \\ 6.4 CORDIC With Redundant Number Systems / 109 \\ 6.4.1 Signed-digit implementation / 111 \\ 6.4.2 Carry-save implementation / 111 \\ 6.4.3 The variable scale factor problem / 112 \\ 6.5 The Double Rotation Method / 112 \\ 6.6 Branching CORDIC / 115 \\ 6.7 Differential CORDIC / 118 \\ 6.8 Computation of $\cos^{-1}$ and $\sin^{-1}$ / 122 \\ 6.9 Variations on CORDIC / 124 \\ 7 Other Shift-and-Add Algorithms / 127 \\ 7.1 High-Radix Algorithms / 127 \\ 7.1.1 Ercegovac's radix-16 algorithms / 127 \\ 7.2 The BKM Algorithm / 131 \\ 7.2.1 The BKM iteration / 133 \\ 7.2.2 Computation of the exponential function (E-mode) / 133 \\ 7.2.3 Computation of the logarithm function (L-mode) / 137 \\ 7.2.4 Application to the computation of elementary functions / 138 \\ III Range Reduction, Final Rounding and Exceptions / 141 \\ 8 Range Reduction / 143 \\ 8.1 Introduction / 143 \\ 8.2 Cody and Waite's Method for Range Reduction / 148 \\ 8.3 Worst Cases for Range Reduction / 149 \\ 8.3.1 A few basic notions on continued fractions / 149 \\ 8.3.2 Finding worst cases using continued fractions / 151 \\ 8.4 The Payne and Hanek Algorithm / 154 \\ 8.5 The Modular Algorithm / 158 \\ 8.5.1 Fixed-point reduction / 158 \\ 8.5.2 Floating-point reduction / 161 \\ 8.5.3 Architectures for Modular Reduction / 161 \\ 9 Final Rounding / 163 \\ 9.1 Introduction / 163 \\ 9.2 Monotonicity / 164 \\ 9.3 Exact Rounding: Presentation of the Problem / 165 \\ 9.4 Some Experiments / 168 \\ 9.5 A ``Probabilistic'' Approach / 168 \\ 9.6 Upper Bounds on $m$ / 171 \\ 9.6.1 Frequency of failures / 173 \\ 9.6.2 Computing with one million bits / 173 \\ 10 Miscellaneous / 175 \\ 10.1 Exceptions / 175 \\ 10.1.1 NaNs / 176 \\ 10.1.2 Exact results / 177 \\ 10.2 Notes on $x^y$ / 178 \\ 10.3 Multiple Precision / 180

entry:
@Book{Muller:1997:EFA,
  author =       "Jean-Michel Muller",
  title =        "Elementary Functions: Algorithms and Implementation",
  publisher =    pub-BIRKHAUSER,
  address =      pub-BIRKHAUSER:adr,
  pages =        "xv + 204",
  year =         "1997",
  ISBN =         "0-8176-3990-X",
  ISBN-13 =      "978-0-8176-3990-7",
  LCCN =         "QA331.M866 1997",
  bibdate =      "Fri Jul 25 12:00:55 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  price =        "US\$59.95",
  URL =          "http://www.birkhauser.com/cgi-win/ISBN/0-8176-3990-X;
                 http://www.ens-lyon.fr/~jmmuller/book_functions.html",
  abstract =     "The elementary functions (sine, cosine, tan,
                 exponentials, and logarithms) are the most commonly
                 used mathematical functions in science and engineering.
                 Computing these functions quickly and accurately is a
                 major goal in computer arithmetic. This new book gives
                 the concepts and background necessary to understand and
                 build algorithms for computing these functions,
                 presenting and structuring the algorithms
                 (hardware-oriented as well as software-oriented), and
                 discusses issues related to the accurate floating-point
                 implementation. The purpose is not to give ``cookbook
                 recipes'' that allow one to implement some given
                 function, but to provide the reader with the knowledge
                 that is necessary to build, or adapt, algorithms to
                 their specific computing environment. The book provides
                 an up-to-date presentation of the information needed to
                 understand and accurately use mathematical functions
                 and algorithms in computational work and design.
                 Graduates, professionals and researchers in scientific
                 computing, software engineering and computer
                 engineering will find the book a useful reference and
                 resource.",
  acknowledgement = ack-nhfb,
  shorttableofcontents = "1: Introduction \\
                 2: Computer arithmetic \\
                 I: Algorithms based on polynomial approximation and/or
                 table lookup \\
                 3: Polynomial approximations \\
                 4: Table-based methods \\
                 II: Shift-and-Add algorithms \\
                 5: Shift-and-Add algorithms 6: The CORDIC algorithm \\
                 7: Other shift-and-add algorithms \\
                 III: Range reduction, final rounding and exceptions \\
                 8: Range reduction \\
                 9: Final rounding \\
                 10: Miscellaneous",
  tableofcontents = "1 Introduction / 1 \\
                 2 Computer Arithmetic / 9 \\
                 2.1 Floating-Point Arithmetic / 9 \\
                 2.1.1 Floating-point formats / 9 \\
                 2.1.2 Rounding modes / 10 \\
                 2.1.3 Subnormal numbers and exceptions / 12 \\
                 2.1.4 ULPs / 13 \\
                 2.1.5 Testing your computational environment / 13 \\
                 2.2 Redundant Number Systems / 13 \\
                 2.2.1 Signed-digit number systems / 14 \\
                 2.2.2 Radix-2 redundant number systems / 15 \\
                 I Algorithms Based on Polynomial Approximation and/or
                 Table Lookup / 19 \\
                 3 Polynomial Approximations / 21 \\
                 3.1 Least Squares Polynomial Approximations / 22 \\
                 3.1.1 Legendre polynomials / 23 \\
                 3.1.2 Chebyshev polynomials / 23 \\
                 3.1.3 Jacobi polynomials / 23 \\
                 3.2 Least Maximum Approximations / 24 \\
                 3.3 Speed of Convergence / 31 \\
                 3.4 Rational Approximations / 34 \\
                 3.5 Actual Computation / 38 \\
                 3.6 Example: the Cyrix FastMath Processor / 41 \\
                 3.7 Algorithms and Architectures / 43 \\
                 3.7.1 The E-Method / 45 \\
                 3.7.2 Estrin's Method / 47 \\
                 3.8 Miscellaneous / 47 \\
                 4 Table-Based Methods / 51 \\
                 4.1 Introduction / 51 \\
                 4.2 Table-Driven Algorithms / 53 \\
                 4.2.1 Tang's algorithm for $\exp(x)$ in IEEE
                 floating-point arithmetic / 55 \\
                 4.2.2 $\ln(x)$ on $[1,2]$ / 57 \\
                 4.2.3 $\sin(x)$ on $[0,\pi/4]$ / 58 \\
                 4.3 Gal's Accurate Tables Method / 58 \\
                 4.4 Methods Requiring Specialized Hardware / 62 \\
                 4.4.1 Wong and Goto, logarithm / 62 \\
                 4.4.2 Wong and Goto, exponential / 65 \\
                 II Shift-and-Add Algorithms / 69 \\
                 5 Shift-and-Add algorithms / 71 \\
                 5.1 The Restoring and Nonrestoring Algorithms / 73 \\
                 5.2 Simple Algorithms for Exponentials and Logarithms /
                 77 \\
                 5.2.1 The restoring algorithm for exponentials / 77 \\
                 5.2.2 The restoring algorithm for logarithms / 79 \\
                 5.3 Faster Algorithms / 81 \\
                 5.3.1 Faster computation of exponentials / 81 \\
                 5.3.2 Faster computation of logarithms / 87 \\
                 5.4 Baker's Predictive Algorithm / 90 \\
                 5.5 Bibliographic notes / 98 \\
                 6 The CORDIC Algorithm / 101 \\
                 6.1 Introduction / 101 \\
                 6.2 The Conventional Iteration / 101 \\
                 6.3 Scale Factor Compensation / 107 \\
                 6.4 CORDIC With Redundant Number Systems / 109 \\
                 6.4.1 Signed-digit implementation / 111 \\
                 6.4.2 Carry-save implementation / 111 \\
                 6.4.3 The variable scale factor problem / 112 \\
                 6.5 The Double Rotation Method / 112 \\
                 6.6 Branching CORDIC / 115 \\
                 6.7 Differential CORDIC / 118 \\
                 6.8 Computation of $\cos^{-1}$ and $\sin^{-1}$ / 122
                 \\
                 6.9 Variations on CORDIC / 124 \\
                 7 Other Shift-and-Add Algorithms / 127 \\
                 7.1 High-Radix Algorithms / 127 \\
                 7.1.1 Ercegovac's radix-16 algorithms / 127 \\
                 7.2 The BKM Algorithm / 131 \\
                 7.2.1 The BKM iteration / 133 \\
                 7.2.2 Computation of the exponential function (E-mode)
                 / 133 \\
                 7.2.3 Computation of the logarithm function (L-mode) /
                 137 \\
                 7.2.4 Application to the computation of elementary
                 functions / 138 \\
                 III Range Reduction, Final Rounding and Exceptions /
                 141 \\
                 8 Range Reduction / 143 \\
                 8.1 Introduction / 143 \\
                 8.2 Cody and Waite's Method for Range Reduction / 148
                 \\
                 8.3 Worst Cases for Range Reduction / 149 \\
                 8.3.1 A few basic notions on continued fractions / 149
                 \\
                 8.3.2 Finding worst cases using continued fractions /
                 151 \\
                 8.4 The Payne and Hanek Algorithm / 154 \\
                 8.5 The Modular Algorithm / 158 \\
                 8.5.1 Fixed-point reduction / 158 \\
                 8.5.2 Floating-point reduction / 161 \\
                 8.5.3 Architectures for Modular Reduction / 161 \\
                 9 Final Rounding / 163 \\
                 9.1 Introduction / 163 \\
                 9.2 Monotonicity / 164 \\
                 9.3 Exact Rounding: Presentation of the Problem / 165
                 \\
                 9.4 Some Experiments / 168 \\
                 9.5 A ``Probabilistic'' Approach / 168 \\
                 9.6 Upper Bounds on $m$ / 171 \\
                 9.6.1 Frequency of failures / 173 \\
                 9.6.2 Computing with one million bits / 173 \\
                 10 Miscellaneous / 175 \\
                 10.1 Exceptions / 175 \\
                 10.1.1 NaNs / 176 \\
                 10.1.2 Exact results / 177 \\
                 10.2 Notes on $x^y$ / 178 \\
                 10.3 Multiple Precision / 180",
}


bibtype: inproceedings
filename: fparith.bib
label: Nielsen:1997:PPF
author: Asger Munk Nielsen and David Matula and C. Lyu and Guy Even
title: Pipelined Packet-Forwarding Floating Point: II. An Adder
crossref: Lang:1997:ISC
pages: 148--155
year: 1997
bibdate: Mon May 20 05:45:32 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 05:45:32 MDT
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Nielsen_Matula.pdf
keywords: ARITH-13
acknowledgement: ack-nhfb
rawauthor: Asger Munk Nielsen and David Matula and C. Lyu and Guy Even
rawtitle: Pipelined Packet-Forwarding Floating Point: {II}. An Adder
entry:
@InProceedings{Nielsen:1997:PPF,
  author =       "Asger Munk Nielsen and David Matula and C. Lyu and Guy
                 Even",
  title =        "Pipelined Packet-Forwarding Floating Point: {II}. An
                 Adder",
  crossref =     "Lang:1997:ISC",
  pages =        "148--155",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Nielsen_Matula.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}


bibtype: inproceedings
filename: fparith.bib
label: Nielsen:1997:RRR
author: Asger Munk Nielsen and Peter Kornerup
title: On Radix Representation of Rings
crossref: Lang:1997:ISC
pages: 34--43
year: 1997
bibdate: Mon May 20 05:45:32 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 05:45:32 MDT
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Nielsen.pdf
keywords: ARITH-13
acknowledgement: ack-nhfb
rawauthor: Asger Munk Nielsen and Peter Kornerup
rawtitle: On Radix Representation of Rings
entry:
@InProceedings{Nielsen:1997:RRR,
  author =       "Asger Munk Nielsen and Peter Kornerup",
  title =        "On Radix Representation of Rings",
  crossref =     "Lang:1997:ISC",
  pages =        "34--43",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Nielsen.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}


bibtype: article
filename: fparith.bib
label: Oberman:1997:DAI
author: S. F. Oberman and M. J. Flynn
title: Division Algorithms and Implementations
journal: j-IEEE-TRANS-COMPUT
volume: 46
number: 8
pages: 833--854
month: aug
monthnumber: 8
year: 1997
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.609274
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 10:06:24 MDT 2011
bibtimestamp: 2011.07.06 10:06:24 MDT
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: S. F. Oberman and M. J. Flynn
rawtitle: Division Algorithms and Implementations
URL:
ftp://arith.stanford.edu/tr/divalgo_TOC.pdf; http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=609274

entry:
@Article{Oberman:1997:DAI,
  author =       "S. F. Oberman and M. J. Flynn",
  title =        "Division Algorithms and Implementations",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "46",
  number =       "8",
  pages =        "833--854",
  month =        aug,
  year =         "1997",
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  DOI =          "https://doi.org/10.1109/12.609274",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 10:06:24 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "ftp://arith.stanford.edu/tr/divalgo_TOC.pdf;
                 http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=609274",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Oberman:1997:DID
author: S. F. Oberman and M. J. Flynn
title: Design Issues in Division and Other Floating-Point Operations
journal: j-IEEE-TRANS-COMPUT
volume: 46
number: 2
pages: 154--161
month: feb
monthnumber: 2
year: 1997
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.565590
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 10:06:20 MDT 2011
bibtimestamp: 2011.07.06 10:06:20 MDT
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: S. F. Oberman and M. J. Flynn
rawtitle: Design Issues in Division and Other Floating-Point Operations
URL:
ftp://arith.stanford.edu/tr/desissues_TOC.pdf; http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=565590

abstract:
Floating-point division is generally regarded as a low frequency, high latency operation in typical floating-point applications. However, in the worst case, a high latency hardware floating-point divider can contribute an additional 0.50 CPI to a system executing SPECfp92 applications. This paper presents the system performance impact of floating-point division latency for varying instruction issue rates. It also examines the performance implications of shared multiplication hardware, shared square root, on-the-fly rounding and conversion, and fused functional units. Using a system level study as a basis, it is shown how typical floating-point applications can guide the designer in making implementation decisions and trade-offs.

rawabstract:
Floating-point division is generally regarded as a low frequency, high latency operation in typical floating-point applications. However, in the worst case, a high latency hardware floating-point divider can contribute an additional 0.50 CPI to a system executing SPECfp92 applications. This paper presents the system performance impact of floating-point division latency for varying instruction issue rates. It also examines the performance implications of shared multiplication hardware, shared square root, on-the-fly rounding and conversion, and fused functional units. Using a system level study as a basis, it is shown how typical floating-point applications can guide the designer in making implementation decisions and trade-offs.

entry:
@Article{Oberman:1997:DID,
  author =       "S. F. Oberman and M. J. Flynn",
  title =        "Design Issues in Division and Other Floating-Point
                 Operations",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "46",
  number =       "2",
  pages =        "154--161",
  month =        feb,
  year =         "1997",
  CODEN =        "ITCOB4",
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  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 10:06:20 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "ftp://arith.stanford.edu/tr/desissues_TOC.pdf;
                 http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=565590",
  abstract =     "Floating-point division is generally regarded as a low
                 frequency, high latency operation in typical
                 floating-point applications. However, in the worst
                 case, a high latency hardware floating-point divider
                 can contribute an additional 0.50 CPI to a system
                 executing SPECfp92 applications. This paper presents
                 the system performance impact of floating-point
                 division latency for varying instruction issue rates.
                 It also examines the performance implications of shared
                 multiplication hardware, shared square root, on-the-fly
                 rounding and conversion, and fused functional units.
                 Using a system level study as a basis, it is shown how
                 typical floating-point applications can guide the
                 designer in making implementation decisions and
                 trade-offs.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "Floating-point division is generally regarded as a low
                 frequency, high latency operation in typical
                 floating-point applications. However, in the worst
                 case, a high latency hardware floating-point divider
                 can contribute an additional 0.50 CPI to a \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Oberman:1997:SPD
author: Stuart F. Oberman and Hesham Al-Twaijry and Michael J. Flynn
title: The SNAP Project: Design of Floating Point Arithmetic Units
crossref: Lang:1997:ISC
pages: 156--165
year: 1997
DOI: https://doi.org/10.1109/ARITH.1997.614891
bibdate: Mon May 27 09:39:18 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.27 09:39:18 ???
keywords: ARITH-13
remark: Pages 166--167 left blank.
acknowledgement: ack-nhfb
rawauthor: Stuart F. Oberman and Hesham Al-Twaijry and Michael J. Flynn
rawtitle: The {SNAP} Project: Design of Floating Point Arithmetic Units
URL:
ftp://arith.stanford.edu/tr/snap13.ps.Z; http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Oberman.pdf

abstract:
In recent years computer applications have increased in their computational complexity. The industry wide usage of performance benchmarks, such as SPECmarks, and the popularity of 3D graphics applications forces processor designers to pay particular attention to implementation of the floating point unit, or FPU. The paper presents results of the Stanford subnanosecond arithmetic processor (SNAP) research effort in the design of hardware for floating point addition, multiplication and division. We show that one cycle FP addition is achievable 32% of the time using a variable latency algorithm. For multiplication, a binary tree is often inferior to a Wallace tree designed using an algorithmic layout approach for contemporary feature sizes (0.3 $ mu $ m). Further, in most cases two bit Booth encoding of the multiplier is preferable to non Booth encoding for partial product generation. It appears that for division, optimum area performance is achieved using functional iteration, and we present two techniques to further reduce average division latency.

rawabstract:
In recent years computer applications have increased in their computational complexity. The industry wide usage of performance benchmarks, such as SPECmarks, and the popularity of 3D graphics applications forces processor designers to pay particular attention to implementation of the floating point unit, or FPU. The paper presents results of the Stanford subnanosecond arithmetic processor (SNAP) research effort in the design of hardware for floating point addition, multiplication and division. We show that one cycle FP addition is achievable 32\% of the time using a variable latency algorithm. For multiplication, a binary tree is often inferior to a Wallace tree designed using an algorithmic layout approach for contemporary feature sizes (0.3 $ \mu $ m). Further, in most cases two bit Booth encoding of the multiplier is preferable to non Booth encoding for partial product generation. It appears that for division, optimum area performance is achieved using functional iteration, and we present two techniques to further reduce average division latency.

entry:
@InProceedings{Oberman:1997:SPD,
  author =       "Stuart F. Oberman and Hesham Al-Twaijry and Michael J.
                 Flynn",
  title =        "The {SNAP} Project: Design of Floating Point
                 Arithmetic Units",
  crossref =     "Lang:1997:ISC",
  pages =        "156--165",
  year =         "1997",
  DOI =          "https://doi.org/10.1109/ARITH.1997.614891",
  bibdate =      "Mon May 27 09:39:18 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "ftp://arith.stanford.edu/tr/snap13.ps.Z;
                 http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Oberman.pdf",
  abstract =     "In recent years computer applications have increased
                 in their computational complexity. The industry wide
                 usage of performance benchmarks, such as SPECmarks, and
                 the popularity of 3D graphics applications forces
                 processor designers to pay particular attention to
                 implementation of the floating point unit, or FPU. The
                 paper presents results of the Stanford subnanosecond
                 arithmetic processor (SNAP) research effort in the
                 design of hardware for floating point addition,
                 multiplication and division. We show that one cycle FP
                 addition is achievable 32\% of the time using a
                 variable latency algorithm. For multiplication, a
                 binary tree is often inferior to a Wallace tree
                 designed using an algorithmic layout approach for
                 contemporary feature sizes (0.3 $ \mu $ m). Further, in
                 most cases two bit Booth encoding of the multiplier is
                 preferable to non Booth encoding for partial product
                 generation. It appears that for division, optimum area
                 performance is achieved using functional iteration, and
                 we present two techniques to further reduce average
                 division latency.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
  remark =       "Pages 166--167 left blank.",
}


bibtype: article
filename: fparith.bib
label: Oklobdzija:1997:CLZ
author: V. Oklobdzija and H. Suzuki and H. Morinaka and H. Makino and Y. Nakase and K. Mashiko and T. Sumi
title: Comments on ``Leading-zero anticipatory logic for high-speed floating point addition'' [with reply]
journal: j-IEEE-J-SOLID-STATE-CIRCUITS
volume: 32
number: 2
pages: 292--292
month: feb
monthnumber: 2
year: 1997
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 cite Suzuki:1996:LZA.
fjournal: IEEE Journal of Solid-State Circuits
acknowledgement: ack-nhfb
rawauthor: V. Oklobdzija and H. Suzuki and H. Morinaka and H. Makino and Y. Nakase and K. Mashiko and T. Sumi
rawnote: See \cite{Suzuki:1996:LZA}.
rawtitle:
Comments on {``Leading-zero anticipatory logic for high-speed floating point addition''} [with reply]

entry:
@Article{Oklobdzija:1997:CLZ,
  author =       "V. Oklobdzija and H. Suzuki and H. Morinaka and H.
                 Makino and Y. Nakase and K. Mashiko and T. Sumi",
  title =        "Comments on {``Leading-zero anticipatory logic for
                 high-speed floating point addition''} [with reply]",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "32",
  number =       "2",
  pages =        "292--292",
  month =        feb,
  year =         "1997",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Suzuki:1996:LZA}.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  summary =      "For original article see H. Suzuki, H. Morinaka, H.
                 Makino, Y. Nakase, K. Mashiko and T. Sumi, ibid.,
                 vol.31, pp.1157-69 (Aug. 1996). I have read with a
                 great interest the article by H. Suzuki et al. I am
                 familiar with their work, and I found their \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Paar:1997:FAA
author: Christof Paar and Pedro Soria-Rodriguez
title: Fast Arithmetic Architectures for Public-Key Algorithms over Galois Fields em GF$ ((2^n)^m) $
journal: j-LECT-NOTES-COMP-SCI
volume: 1233
pages: 363--??
year: 1997
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Mon Feb 4 12:02:26 MST 2002
bibtimestamp: 2002.02.04 12:02:26 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Christof Paar and Pedro Soria-Rodriguez
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t1233.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/1233/12330363.htm; http://link.springer-ny.com/link/service/series/0558/papers/1233/12330363.pdf

rawtitle:
Fast Arithmetic Architectures for Public-Key Algorithms over {Galois} Fields {{\em GF\/}$ ((2^n)^m) $}

entry:
@Article{Paar:1997:FAA,
  author =       "Christof Paar and Pedro Soria-Rodriguez",
  title =        "Fast Arithmetic Architectures for Public-Key
                 Algorithms over {Galois} Fields {{\em GF\/}$ ((2^n)^m)
                 $}",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1233",
  pages =        "363--??",
  year =         "1997",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Mon Feb 4 12:02:26 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1233.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1233/12330363.htm;
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  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Parker:1997:MAU
author: M. G. Parker and M. Benaissa
title: Modular arithmetic using low order redundant bases
journal: j-IEEE-TRANS-COMPUT
volume: 46
number: 5
pages: 611--616
month: may
monthnumber: 5
year: 1997
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.589237
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 10:06:22 MDT 2011
bibtimestamp: 2011.07.06 10:06:22 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=589237
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: M. G. Parker and M. Benaissa
rawtitle: Modular arithmetic using low order redundant bases
entry:
@Article{Parker:1997:MAU,
  author =       "M. G. Parker and M. Benaissa",
  title =        "Modular arithmetic using low order redundant bases",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "46",
  number =       "5",
  pages =        "611--616",
  month =        may,
  year =         "1997",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.589237",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 10:06:22 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=589237",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: techreport
filename: fparith.bib
label: Parker:1997:MCAa
author: Douglass Stott Parker
title: Monte Carlo arithmetic: exploiting randomness in floating-point arithmetic
number: CSD 970002
institution: Department of Computer Science, University of California, Los Angeles
address: Los Angeles, CA, USA
pages: 86
year: 1997
LCCN: QA75.5 .R46 no.970002 1997
bibdate: Thu Oct 24 14:31:00 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.10.24 14:31:00 ???
URL: http://www.cs.ucla.edu/~stott/mca/CSD-970002.ps.gz
acknowledgement: ack-nhfb
rawauthor: Douglass Stott Parker
rawtitle: {Monte Carlo} arithmetic: exploiting randomness in floating-point arithmetic
entry:
@TechReport{Parker:1997:MCAa,
  author =       "Douglass Stott Parker",
  title =        "{Monte Carlo} arithmetic: exploiting randomness in
                 floating-point arithmetic",
  number =       "CSD 970002",
  institution =  "Department of Computer Science, University of
                 California, Los Angeles",
  address =      "Los Angeles, CA, USA",
  pages =        "86",
  year =         "1997",
  LCCN =         "QA75.5 .R46 no.970002 1997",
  bibdate =      "Thu Oct 24 14:31:00 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.ucla.edu/~stott/mca/CSD-970002.ps.gz",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: fparith.bib
label: Parker:1997:MCAb
author: Douglass Stott Parker and Paul R. Eggert and Brad Pierce
title: Monte Carlo arithmetic: a framework for the statistical analysis of roundoff error
type: Technical report
number: CSD-970014
institution: Computer Science Department, University of California, Los Angeles
address: Los Angeles, CA 90095-1596, USA
pages: 23
day: 30
month: mar
monthnumber: 3
year: 1997
bibdate: Sun Jun 17 18:24:01 2018
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2018.06.17 18:24:01 ???
acknowledgement: ack-nhfb
rawauthor: Douglass Stott Parker and Paul R. Eggert and Brad Pierce
rawtitle: {Monte Carlo} arithmetic: a framework for the statistical analysis of roundoff error
URL:
http://fmdb.cs.ucla.edu/treports/970014.pdf; https://pdfs.semanticscholar.org/b728/afdb230aa1869f79bdc21ff7a6252d3be9ab.pdf

keywords:
ANSI / IEEE floating-point standards; floating-point arithmetic; floating-point rounding; Monte Carlo methods; random rounding; roundoff error; significance arithmetic

entry:
@TechReport{Parker:1997:MCAb,
  author =       "Douglass Stott Parker and Paul R. Eggert and Brad
                 Pierce",
  title =        "{Monte Carlo} arithmetic: a framework for the
                 statistical analysis of roundoff error",
  type =         "Technical report",
  number =       "CSD-970014",
  institution =  "Computer Science Department, University of California,
                 Los Angeles",
  address =      "Los Angeles, CA 90095-1596, USA",
  pages =        "23",
  day =          "30",
  month =        mar,
  year =         "1997",
  bibdate =      "Sun Jun 17 18:24:01 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://fmdb.cs.ucla.edu/treports/970014.pdf;
                 https://pdfs.semanticscholar.org/b728/afdb230aa1869f79bdc21ff7a6252d3be9ab.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ANSI\slash IEEE floating-point standards;
                 floating-point arithmetic; floating-point rounding;
                 Monte Carlo methods; random rounding; roundoff error;
                 significance arithmetic",
}


bibtype: phdthesis
filename: fparith.bib
label: Pierce:1997:ARF
author: Brad Pierce
title: Applications of randomization to floating-point arithmetic and to linear systems solution
type: Thesis (Ph.D.)
school: Department of Computer Science, University of California, Los Angeles
address: Los Angeles, CA, USA
pages: 23
year: 1997
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 -- Computer Science
acknowledgement: ack-nhfb
rawauthor: Brad Pierce
rawtitle: Applications of randomization to floating-point arithmetic and to linear systems solution
entry:
@PhdThesis{Pierce:1997:ARF,
  author =       "Brad Pierce",
  title =        "Applications of randomization to floating-point
                 arithmetic and to linear systems solution",
  type =         "Thesis ({Ph.D.})",
  school =       "Department of Computer Science, University of
                 California, Los Angeles",
  address =      "Los Angeles, CA, USA",
  year =         "1997",
  bibdate =      "Thu Oct 24 14:19:35 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "dissertations, academic -- UCLA -- Computer Science",
}


bibtype: inproceedings
filename: fparith.bib
label: Priest:1997:FTD
author: Douglas M. Priest
title: Fast Table-Driven Algorithms for Interval Elementary Functions
crossref: Lang:1997:ISC
pages: 168--174
year: 1997
bibdate: Mon May 20 05:45:32 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 05:45:32 MDT
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Priest.pdf
keywords: ARITH-13
acknowledgement: ack-nhfb
rawauthor: Douglas M. Priest
rawtitle: Fast Table-Driven Algorithms for Interval Elementary Functions
entry:
@InProceedings{Priest:1997:FTD,
  author =       "Douglas M. Priest",
  title =        "Fast Table-Driven Algorithms for Interval Elementary
                 Functions",
  crossref =     "Lang:1997:ISC",
  pages =        "168--174",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Priest.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}


bibtype: article
filename: fparith.bib
label: Rederlechner:1997:NCP
author: B. Rederlechner and J. Keller
title: A Note on Correctness Proofs for Overflow Detection Logic in Adders for $d$-th Complement Numbers
journal: j-J-UCS
volume: 3
number: 10
pages: 1121--1125
day: 28
month: oct
monthnumber: 10
year: 1997
ISSN: 0948-6968 OR 09486968
ISSNL: 0948-6968 OR 09486968
bibdate: Wed Mar 4 15:32:49 MST 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.03.04 15:32:49 MST
URL: http://medoc.springer.de:8000/jucs/jucs_3_10/a_note_on_correctness
fjournal: J.UCS: Journal of Universal Computer Science
acknowledgement: ack-nhfb
journalURL: http://www.jucs.org/jucs
rawauthor: B. Rederlechner and J. Keller
rawtitle: A Note on Correctness Proofs for Overflow Detection Logic in Adders for $d$-th Complement Numbers
entry:
@Article{Rederlechner:1997:NCP,
  author =       "B. Rederlechner and J. Keller",
  title =        "A Note on Correctness Proofs for Overflow Detection
                 Logic in Adders for $d$-th Complement Numbers",
  journal =      j-J-UCS,
  volume =       "3",
  number =       "10",
  pages =        "1121--1125",
  day =          "28",
  month =        oct,
  year =         "1997",
  CODEN =        "????",
  ISSN =         "0948-6968",
  ISSN-L =       "0948-6968",
  bibdate =      "Wed Mar 4 15:32:49 MST 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://medoc.springer.de:8000/jucs/jucs_3_10/a_note_on_correctness",
  acknowledgement = ack-nhfb,
  fjournal =     "J.UCS: Journal of Universal Computer Science",
  journal-URL =  "http://www.jucs.org/jucs",
}


bibtype: misc
filename: fparith.bib
label: Reppy:1997:EAH
author: John H. Reppy and others
title: The Standard ML Basis Library
pages: 1121--1125
month: oct
monthnumber: 10
year: 1997
bibdate: Wed Jan 29 16:52:50 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.01.29 16:52:50 ???
note: To be published in/as cite Gansner:2003:SMB.
URL: http://cm.bell-labs.com/cm/cs/what/smlnj/doc/basis/pages/real.html
keywords: decimal floating-point arithmetic
acknowledgement: ack-nhfb
howpublished: World-Wide Web document
rawauthor: John H. Reppy and others
rawnote: To be published in/as \cite{Gansner:2003:SMB}.
rawtitle: The {Standard ML} Basis Library
remark:
From cite Steele:2004:RHP: ``toDecimal should produce only as many digits as are necessary for fromDecimal to convert back to the same number, i.e., for any Normal or SubNormal real value r, we have: fromDecimal (toDecimal r) = r ldots Algorithms for accurately and efficiently converting between binary and decimal real representations are readily available, e.g., see the technical report cite Gay:1990:CRB.''

entry:
@Misc{Reppy:1997:EAH,
  author =       "John H. Reppy and others",
  title =        "The {Standard ML} Basis Library",
  howpublished = "World-Wide Web document",
  month =        oct,
  year =         "1997",
  bibdate =      "Wed Jan 29 16:52:50 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "To be published in/as \cite{Gansner:2003:SMB}.",
  URL =          "http://cm.bell-labs.com/cm/cs/what/smlnj/doc/basis/pages/real.html",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
  remark =       "From \cite{Steele:2004:RHP}: ``toDecimal should
                 produce only as many digits as are necessary for
                 fromDecimal to convert back to the same number, i.e.,
                 for any Normal or SubNormal real value r, we have:
                 fromDecimal (toDecimal r) = r \ldots{} Algorithms for
                 accurately and efficiently converting between binary
                 and decimal real representations are readily available,
                 e.g., see the technical report \cite{Gay:1990:CRB}.''",
}


bibtype: inproceedings
filename: fparith.bib
label: Rice:1997:MDB
author: Eric Rice and Richard Hughey
title: Multiprecision Division on an 8-Bit Processor
crossref: Lang:1997:ISC
pages: 74--81
year: 1997
bibdate: Mon May 20 05:45:32 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 05:45:32 MDT
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Rice.pdf
keywords: ARITH-13
acknowledgement: ack-nhfb
rawauthor: Eric Rice and Richard Hughey
rawtitle: Multiprecision Division on an 8-Bit Processor
entry:
@InProceedings{Rice:1997:MDB,
  author =       "Eric Rice and Richard Hughey",
  title =        "Multiprecision Division on an 8-Bit Processor",
  crossref =     "Lang:1997:ISC",
  pages =        "74--81",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Rice.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}


bibtype: inproceedings
filename: fparith.bib
label: Sanz-Gonzalez:1997:TBR
author: J. L. Sanz-Gonzalez
title: Tradeoff between roundoff and overflow errors in digital filter realizations
volume: 3
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 2189--2192
year: 1997
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: J. L. Sanz-Gonzalez
rawtitle: Tradeoff between roundoff and overflow errors in digital filter realizations
booktitle:
Acoustics, Speech, and Signal Processing, 1997. ICASSP-97., 1997 IEEE International Conference on. 21--24 April 1997

rawbooktitle:
Acoustics, Speech, and Signal Processing, 1997. {ICASSP-97., 1997} {IEEE} International Conference on. 21--24 April 1997

entry:
@InProceedings{Sanz-Gonzalez:1997:TBR,
  author =       "J. L. Sanz-Gonzalez",
  booktitle =    "Acoustics, Speech, and Signal Processing, 1997.
                 {ICASSP-97., 1997} {IEEE} International Conference on.
                 21--24 April 1997",
  title =        "Tradeoff between roundoff and overflow errors in
                 digital filter realizations",
  volume =       "3",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "2189--2192",
  year =         "1997",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:07 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "This paper is concerned with a linked analysis of
                 overflow and roundoff errors in fixed-point digital
                 filter realizations. Upper bounds for the overflow
                 error power are obtained, having considered the
                 saturation quantizer characteristics. Also, \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Sarma:1997:FIR
author: Debjit Das Sarma and David W. Matula
title: Faithful Interpolation in Reciprocal Tables
crossref: Lang:1997:ISC
pages: 82--91
year: 1997
bibdate: Mon May 20 05:45:32 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 05:45:32 MDT
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Sarma.pdf
keywords: ARITH-13
acknowledgement: ack-nhfb
rawauthor: Debjit Das Sarma and David W. Matula
rawtitle: Faithful Interpolation in Reciprocal Tables
entry:
@InProceedings{Sarma:1997:FIR,
  author =       "Debjit Das Sarma and David W. Matula",
  title =        "Faithful Interpolation in Reciprocal Tables",
  crossref =     "Lang:1997:ISC",
  pages =        "82--91",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Sarma.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}


bibtype: inproceedings
filename: fparith.bib
label: Schulte:1997:AFA
author: M. J. Schulte and James E. Stine
title: Accurate Function Approximations by Symmetric Table Lookup and Addition
crossref: Thiele:1997:IIC
pages: 144--153
year: 1997
bibdate: Sun Mar 04 10:55:40 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.03.04 10:55:40 ???
URL: http://mesa.ece.wisc.edu/publications/cp_1997-02.pdf
acknowledgement: ack-nhfb
rawauthor: M. J. Schulte and James E. Stine
rawtitle: Accurate Function Approximations by Symmetric Table Lookup and Addition
entry:
@InProceedings{Schulte:1997:AFA,
  author =       "M. J. Schulte and James E. Stine",
  title =        "Accurate Function Approximations by Symmetric Table
                 Lookup and Addition",
  crossref =     "Thiele:1997:IIC",
  pages =        "144--153",
  year =         "1997",
  bibdate =      "Sun Mar 04 10:55:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1997-02.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Schulte:1997:HSR
author: M. J. Schulte and J. E. Stine and K. E. Wires
title: High-Speed Reciprocal Approximations
crossref: Fargues:1997:CRT
pages: 1183--1187
year: 1997
bibdate: Sun Mar 04 10:53:45 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.03.04 10:53:45 ???
URL: http://mesa.ece.wisc.edu/publications/cp_1997-03.pdf
acknowledgement: ack-nhfb
rawauthor: M. J. Schulte and J. E. Stine and K. E. Wires
rawtitle: High-Speed Reciprocal Approximations
entry:
@InProceedings{Schulte:1997:HSR,
  author =       "M. J. Schulte and J. E. Stine and K. E. Wires",
  title =        "High-Speed Reciprocal Approximations",
  crossref =     "Fargues:1997:CRT",
  pages =        "1183--1187",
  year =         "1997",
  bibdate =      "Sun Mar 04 10:53:45 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1997-03.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Schulte:1997:SBT
author: Michael J. Schulte and James E. Stine
title: Symmetric Bipartite Tables for Accurate Function Approximation
crossref: Lang:1997:ISC
pages: 175--183
year: 1997
bibdate: Mon May 20 05:45:32 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 05:45:32 MDT
keywords: ARITH-13
acknowledgement: ack-nhfb
rawauthor: Michael J. Schulte and James E. Stine
rawtitle: Symmetric Bipartite Tables for Accurate Function Approximation
URL:
http://mesa.ece.wisc.edu/publications/cp_1997-01.pdf; http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Schulte.pdf

entry:
@InProceedings{Schulte:1997:SBT,
  author =       "Michael J. Schulte and James E. Stine",
  title =        "Symmetric Bipartite Tables for Accurate Function
                 Approximation",
  crossref =     "Lang:1997:ISC",
  pages =        "175--183",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1997-01.pdf;
                 http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Schulte.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}


bibtype: article
filename: fparith.bib
label: Schwarz:1997:CFP
author: E. M. Schwarz and L. Sigal and T. J. McPherson
title: CMOS floating-point unit for the S/390 Parallel Enterprise Server G4
journal: j-IBM-JRD
volume: 41
number: 4/5
pages: 475--488
year: 1997
CODEN: IBMJAE
ISSN: 0018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)
ISSNL: 0018-8646 OR 00188646
bibdate: Mon Feb 12 08:10:59 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.02.12 08:10:59 ???
URL: http://www.almaden.ibm.com/journal/rd/414/schwarz.html
fjournal: IBM Journal of Research and Development
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520
rawauthor: E. M. Schwarz and L. Sigal and T. J. McPherson
rawtitle: {CMOS} floating-point unit for the {S/390 Parallel Enterprise Server G4}
entry:
@Article{Schwarz:1997:CFP,
  author =       "E. M. Schwarz and L. Sigal and T. J. McPherson",
  title =        "{CMOS} floating-point unit for the {S/390 Parallel
                 Enterprise Server G4}",
  journal =      j-IBM-JRD,
  volume =       "41",
  number =       "4/5",
  pages =        "475--488",
  month =        "????",
  year =         "1997",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Mon Feb 12 08:10:59 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.almaden.ibm.com/journal/rd/414/schwarz.html",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}


bibtype: inproceedings
filename: fparith.bib
label: Schwarz:1997:RCM
author: Eric M. Schwarz and Robert M. Averill III and Leon J. Sigal
title: A Radix-8 CMOS S/390 Multiplier
crossref: Lang:1997:ISC
pages: 2--9
year: 1997
bibdate: Mon May 20 05:45:32 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 05:45:32 MDT
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Schwarz.pdf
keywords: ARITH-13
acknowledgement: ack-nhfb
rawauthor: Eric M. Schwarz and Robert M. {Averill III} and Leon J. Sigal
rawtitle: A Radix-8 {CMOS S/390} Multiplier
entry:
@InProceedings{Schwarz:1997:RCM,
  author =       "Eric M. Schwarz and Robert M. {Averill III} and Leon
                 J. Sigal",
  title =        "A Radix-8 {CMOS S/390} Multiplier",
  crossref =     "Lang:1997:ISC",
  pages =        "2--9",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Schwarz.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}


bibtype: article
filename: fparith.bib
label: Shewchuk:1997:APF
author: Jonathan Richard Shewchuk
title: Adaptive precision floating-point arithmetic and fast robust geometric predicates
journal: j-DISCRETE-COMPUT-GEOM
volume: 18
number: 3
pages: 305--363
year: 1997
CODEN: DCGEER
DOI: https://doi.org/10.1007/PL00009321
ISSN: 0179-5376 (print), 1432-0444 (electronic) OR 01795376 (print), 14320444 (electronic)
ISSNL: 0179-5376 OR 01795376
bibdate: Sat Apr 28 19:08:39 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.04.28 19:08:39 ???
URL: http://www.cs.cmu.edu/~quake/robust.html
fjournal: Discrete and Computational Geometry
keywords: accurate floating-point summation
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/454
rawauthor: Jonathan Richard Shewchuk
rawtitle: Adaptive precision floating-point arithmetic and fast robust geometric predicates
entry:
@Article{Shewchuk:1997:APF,
  author =       "Jonathan Richard Shewchuk",
  title =        "Adaptive precision floating-point arithmetic and fast
                 robust geometric predicates",
  journal =      j-DISCRETE-COMPUT-GEOM,
  volume =       "18",
  number =       "3",
  pages =        "305--363",
  year =         "1997",
  CODEN =        "DCGEER",
  DOI =          "https://doi.org/10.1007/PL00009321",
  ISSN =         "0179-5376 (print), 1432-0444 (electronic)",
  ISSN-L =       "0179-5376",
  bibdate =      "Sat Apr 28 19:08:39 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.cmu.edu/~quake/robust.html",
  acknowledgement = ack-nhfb,
  fjournal =     "Discrete and Computational Geometry",
  journal-URL =  "http://link.springer.com/journal/454",
  keywords =     "accurate floating-point summation",
}


bibtype: article
filename: fparith.bib
label: Soderquist:1997:DSR
author: Peter Soderquist and Miriam Leeser
journal: j-IEEE-MICRO
volume: 17
number: 4
pages: 56--66
month: jul
monthnumber: 7
year: 1997
CODEN: IEMIDZ
DOI: https://doi.org/10.1109/40.612224
ISSN: 0272-1732 (print), 1937-4143 (electronic) OR 02721732 (print), 19374143 (electronic)
ISSNL: 0272-1732 OR 02721732
bibdate: Thu Dec 14 06:08:58 MST 2000
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; Science Citation Index database (1980--2000)
bibtimestamp: 2000.12.14 06:08:58 MST
URL: http://pascal.computer.org/mi/books/mi1997/pdf/m4056.pdf
fjournal: IEEE Micro
acknowledgement: ack-nhfb
journalURL: http://www.computer.org/csdl/mags/mi/index.html
rawauthor: Peter Soderquist and Miriam Leeser
title:
Division and Square Root: Choosing the Right Implementation: Exploring the major design choices for microprocessor implementations of floating-point division and square root

rawtitle:
Division and Square Root: Choosing the Right Implementation: Exploring the major design choices for microprocessor implementations of floating-point division and square root

entry:
@Article{Soderquist:1997:DSR,
  author =       "Peter Soderquist and Miriam Leeser",
  title =        "Division and Square Root: Choosing the Right
                 Implementation: Exploring the major design choices for
                 microprocessor implementations of floating-point
                 division and square root",
  journal =      j-IEEE-MICRO,
  volume =       "17",
  number =       "4",
  pages =        "56--66",
  month =        jul # "\slash " # aug,
  year =         "1997",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/40.612224",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Thu Dec 14 06:08:58 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 Science Citation Index database (1980--2000)",
  URL =          "http://pascal.computer.org/mi/books/mi1997/pdf/m4056.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
}


bibtype: article
filename: fparith.bib
label: Solinas:1997:IAA
author: Jerome A. Solinas
title: An Improved Algorithm for Arithmetic on a Family of Elliptic Curves
journal: j-LECT-NOTES-COMP-SCI
volume: 1294
pages: 357--??
year: 1997
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Tue Feb 5 11:51:15 MST 2002
bibtimestamp: 2002.02.05 11:51:15 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Jerome A. Solinas
rawtitle: An Improved Algorithm for Arithmetic on a Family of Elliptic Curves
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t1294.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/1294/12940357.htm; http://link.springer-ny.com/link/service/series/0558/papers/1294/12940357.pdf

entry:
@Article{Solinas:1997:IAA,
  author =       "Jerome A. Solinas",
  title =        "An Improved Algorithm for Arithmetic on a Family of
                 Elliptic Curves",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1294",
  pages =        "357--??",
  year =         "1997",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Feb 5 11:51:15 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1294.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1294/12940357.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/1294/12940357.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Srinivas:1997:RDR
author: H. R. Srinivas and K. K. Parhi and L. A. Montalvo
title: Radix $2$ division with over-redundant quotient selection
journal: j-IEEE-TRANS-COMPUT
volume: 46
number: 1
pages: 85--92
month: jan
monthnumber: 1
year: 1997
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.559806
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 10:06:20 MDT 2011
bibtimestamp: 2011.07.06 10:06:20 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=559806
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: H. R. Srinivas and K. K. Parhi and L. A. Montalvo
rawtitle: Radix $2$ division with over-redundant quotient selection
entry:
@Article{Srinivas:1997:RDR,
  author =       "H. R. Srinivas and K. K. Parhi and L. A. Montalvo",
  title =        "Radix $2$ division with over-redundant quotient
                 selection",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "46",
  number =       "1",
  pages =        "85--92",
  month =        jan,
  year =         "1997",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.559806",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 10:06:20 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=559806",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Stan:1997:SUC
author: Mircea R. Stan
title: Synchronous Up / Down Counter with Clock Period Independent of Counter Size
crossref: Lang:1997:ISC
pages: 274--281
year: 1997
bibdate: Sat Nov 17 12:22:42 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.17 12:22:42 ???
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Stan.pdf
keywords: ARITH-13
acknowledgement: ack-nhfb
rawauthor: Mircea R. Stan
rawtitle: Synchronous Up\slash Down Counter with Clock Period Independent of Counter Size
entry:
@InProceedings{Stan:1997:SUC,
  author =       "Mircea R. Stan",
  title =        "Synchronous Up\slash Down Counter with Clock Period
                 Independent of Counter Size",
  crossref =     "Lang:1997:ISC",
  pages =        "274--281",
  year =         "1997",
  bibdate =      "Sat Nov 17 12:22:42 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Stan.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}


bibtype: article
filename: fparith.bib
label: Stankovic:1997:ASM
author: M. Stankovic and J. Madic and P. Stanimirovic
journal: Math. Balkanica (N.S.)
volume: 11
number: 1--2
pages: 11--23
year: 1997
ISSN: 0205-3217 OR 02053217
MRclass: 11Y55 (11A67 68R99)
MRnumber: MR1606580 (98m:11141)
MRreviewer: Marc Del{\'e}glise
bibdate: Thu Nov 8 14:50:38 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.08 14:50:38 ???
fjournal: Mathematica Balkanica. New Series
acknowledgement: ack-nhfb
rawauthor: M. Stankovi{\'c} and J. Madi{\'c} and P. Stanimirovi{\'c}
title:
Addition, subtraction and multiplication of sequences of fractions by means of residue arithmetic and mathematical spectra

rawtitle:
Addition, subtraction and multiplication of sequences of fractions by means of residue arithmetic and mathematical spectra

entry:
@Article{Stankovic:1997:ASM,
  author =       "M. Stankovi{\'c} and J. Madi{\'c} and P.
                 Stanimirovi{\'c}",
  title =        "Addition, subtraction and multiplication of sequences
                 of fractions by means of residue arithmetic and
                 mathematical spectra",
  journal =      "Math. Balkanica (N.S.)",
  volume =       "11",
  number =       "1--2",
  pages =        "11--23",
  year =         "1997",
  ISSN =         "0205-3217",
  MRclass =      "11Y55 (11A67 68R99)",
  MRnumber =     "MR1606580 (98m:11141)",
  MRreviewer =   "Marc Del{\'e}glise",
  bibdate =      "Thu Nov 8 14:50:38 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematica Balkanica. New Series",
}


bibtype: inproceedings
filename: fparith.bib
label: Stelling:1997:IMA
author: Paul F. Stelling and Voji. G. Oklobdzija
title: Implementing Multiply-Accumulate Operation In Multiplication Time
crossref: Lang:1997:ISC
pages: 99--107
year: 1997
bibdate: Mon May 20 05:45:32 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 05:45:32 MDT
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Stelling.pdf
keywords: ARITH-13
acknowledgement: ack-nhfb
rawauthor: Paul F. Stelling and Voji. G. Oklobdzija
rawtitle: Implementing Multiply-Accumulate Operation In Multiplication Time
entry:
@InProceedings{Stelling:1997:IMA,
  author =       "Paul F. Stelling and Voji. G. Oklobdzija",
  title =        "Implementing Multiply-Accumulate Operation In
                 Multiplication Time",
  crossref =     "Lang:1997:ISC",
  pages =        "99--107",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Stelling.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}


bibtype: article
filename: fparith.bib
label: Strzebonski:1997:CFC
author: Adam Wojciech Strzebonski
title: Computing in the Field of Complex Algebraic Numbers
journal: j-J-SYMBOLIC-COMP
volume: 24
number: 6
pages: 647--656
month: dec
monthnumber: 12
year: 1997
CODEN: JSYCEH
ISSN: 0747-7171 (print), 1095-855X (electronic) OR 07477171 (print), 1095855X (electronic)
ISSNL: 0747-7171 OR 07477171
MRclass: 68Q40
MRnumber: 98h:68125
bibdate: Tue Nov 10 06:53:22 MST 1998
bibtimestamp: 1998.11.10 06:53:22 MST
fjournal: Journal of Symbolic Computation
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/07477171/
rawauthor: Adam Wojciech Strzebo{\'n}ski
rawtitle: Computing in the Field of Complex Algebraic Numbers
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/jsymcomp.bib

entry:
@Article{Strzebonski:1997:CFC,
  author =       "Adam Wojciech Strzebo{\'n}ski",
  title =        "Computing in the Field of Complex Algebraic Numbers",
  journal =      j-J-SYMBOLIC-COMP,
  volume =       "24",
  number =       "6",
  pages =        "647--656",
  month =        dec,
  year =         "1997",
  CODEN =        "JSYCEH",
  ISSN =         "0747-7171 (print), 1095-855X (electronic)",
  ISSN-L =       "0747-7171",
  MRclass =      "68Q40",
  MRnumber =     "98h:68125",
  bibdate =      "Tue Nov 10 06:53:22 MST 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jsymcomp.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Symbolic Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07477171/",
}


bibtype: inproceedings
filename: fparith.bib
label: Szabo:1997:REAa
author: T. Szabo and G. Horvath
title: A roundoff error analysis of the Oja's subspace rule
volume: 4
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 3297--3300
year: 1997
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: T. Szabo and G. Horvath
rawtitle: A roundoff error analysis of the {Oja}'s subspace rule
booktitle:
Acoustics, Speech, and Signal Processing, 1997. ICASSP-97., 1997 IEEE International Conference on. 21--24 April 1997

rawbooktitle:
Acoustics, Speech, and Signal Processing, 1997. {ICASSP-97., 1997} {IEEE} International Conference on. 21--24 April 1997

entry:
@InProceedings{Szabo:1997:REAa,
  author =       "T. Szabo and G. Horvath",
  booktitle =    "Acoustics, Speech, and Signal Processing, 1997.
                 {ICASSP-97., 1997} {IEEE} International Conference on.
                 21--24 April 1997",
  title =        "A roundoff error analysis of the {Oja}'s subspace
                 rule",
  volume =       "4",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "3297--3300",
  year =         "1997",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:07 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "This paper deals with the effects of finite precision
                 data representation and arithmetic in principal
                 component analysis (PCA) networks. PCA or Karhunen
                 Loeve transform (KLT) is a statistical method that
                 determines an optimal linear transformation \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Szabo:1997:REAb
author: T. Szabo and G. Horvath
title: Roundoff error analysis of the PCA networks
volume: 1
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 263--268
year: 1997
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: T. Szabo and G. Horvath
rawtitle: Roundoff error analysis of the {PCA} networks
booktitle:
Instrumentation and Measurement Technology Conference, 1997. IMTC/97. Proceedings. 'Sensing, Processing, Networking'., IEEE. 19--21 May 1997

rawbooktitle:
Instrumentation and Measurement Technology Conference, 1997. {IMTC/97}. Proceedings. 'Sensing, Processing, Networking'., {IEEE. 19--21} May 1997

entry:
@InProceedings{Szabo:1997:REAb,
  author =       "T. Szabo and G. Horvath",
  booktitle =    "Instrumentation and Measurement Technology Conference,
                 1997. {IMTC/97}. Proceedings. 'Sensing, Processing,
                 Networking'., {IEEE. 19--21} May 1997",
  title =        "Roundoff error analysis of the {PCA} networks",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "263--268",
  year =         "1997",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:07 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "This paper deals with some of the effects of finite
                 precision data representation and arithmetics in
                 principal component analysis (PCA) neural networks. The
                 PCA networks are single layer linear neural networks
                 that use some versions of Oja's \ldots{}",
}


bibtype: misc
filename: fparith.bib
label: Taborn:1997:DSM
author: M. P. Taborn and S. M. Burchfiel and D. T. Matheny
title: Denormalization system and method of operation
pages: 263--268
day: 8
month: jul
monthnumber: 7
year: 1997
bibdate: Fri Nov 28 15:28:39 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 15:28:39 ???
note: U.S. Patent No. 5,646,875.
acknowledgement: ack-nhfb
rawauthor: M. P. Taborn and S. M. Burchfiel and D. T. Matheny
rawnote: U.S. Patent No. 5,646,875.
rawtitle: Denormalization system and method of operation
entry:
@Misc{Taborn:1997:DSM,
  author =       "M. P. Taborn and S. M. Burchfiel and D. T. Matheny",
  title =        "Denormalization system and method of operation",
  day =          "8",
  month =        jul,
  year =         "1997",
  bibdate =      "Fri Nov 28 15:28:39 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "U.S. Patent No. 5,646,875.",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Takagi:1997:GPO
author: Naofumi Takagi
title: Generating a Power of an Operand by a Table Look-Up and a Multiplication
crossref: Lang:1997:ISC
pages: 126--131
year: 1997
bibdate: Mon May 20 05:45:32 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 05:45:32 MDT
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Takagi.pdf
keywords: ARITH-13
acknowledgement: ack-nhfb
rawauthor: Naofumi Takagi
rawtitle: Generating a Power of an Operand by a Table Look-Up and a Multiplication
entry:
@InProceedings{Takagi:1997:GPO,
  author =       "Naofumi Takagi",
  title =        "Generating a Power of an Operand by a Table Look-Up
                 and a Multiplication",
  crossref =     "Lang:1997:ISC",
  pages =        "126--131",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Takagi.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}


bibtype: manual
filename: fparith.bib
label: TI:1997:TUG
title: TMS320C3x User's Guide
organization: Texas Instruments
address: Post Office box 655303, Dallas, TX 75265, USA
pages: 126--131
year: 1997
bibdate: Wed Nov 24 09:20:17 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.24 09:20:17 ???
keywords: digital signal processor (DSP)
remark: No longer accessible at the first URL. A 2004 edition is at the second URL.
acknowledgement: ack-nhfb
rawtitle: {TMS320C3x} User's Guide
URL:
http://www-s.ti.com/sc/psheets/spru031e/spru031e.pdf; http://www-s.ti.com/sc/psheets/spru031f/spru031f.pdf

entry:
@Manual{TI:1997:TUG,
  title =        "{TMS320C3x} User's Guide",
  organization = "Texas Instruments",
  address =      "Post Office box 655303, Dallas, TX 75265, USA",
  year =         "1997",
  bibdate =      "Wed Nov 24 09:20:17 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www-s.ti.com/sc/psheets/spru031e/spru031e.pdf;
                 http://www-s.ti.com/sc/psheets/spru031f/spru031f.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "digital signal processor (DSP)",
  remark =       "No longer accessible at the first URL. A 2004 edition
                 is at the second URL.",
}


bibtype: inproceedings
filename: fparith.bib
label: Tomabechi:1997:WOD
author: N. Tomabechi
title: WSI oriented design for noise-tolerant systems based on the residue number system
volume: 4
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 2733--2736
year: 1997
DOI: https://doi.org/10.1109/ISCAS.1997.612890
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: N. Tomabechi
rawtitle: {WSI} oriented design for noise-tolerant systems based on the residue number system
booktitle:
Proceedings of 1997 IEEE International Symposium on Circuits and Systems, ISCAS '97, 9--12 June 1997

rawbooktitle:
Proceedings of 1997 {IEEE} International Symposium on Circuits and Systems, {ISCAS '97}, 9--12 June 1997

entry:
@InProceedings{Tomabechi:1997:WOD,
  author =       "N. Tomabechi",
  booktitle =    "Proceedings of 1997 {IEEE} International Symposium on
                 Circuits and Systems, {ISCAS '97}, 9--12 June 1997",
  title =        "{WSI} oriented design for noise-tolerant systems based
                 on the residue number system",
  volume =       "4",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "2733--2736",
  year =         "1997",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.1997.612890",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "This paper presents a design method for noise-tolerant
                 WSI systems in which the features of the residue number
                 system and multiple clock pulses are effectively
                 combined. The analysis shows that the reliability of
                 the presented system is greatly \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Tsai:1997:FPR
author: Chimin Tsai
title: Floating-point roundoff noises of first- and second-order sections in parallel form digital filters
journal: j-IEEE-TRANS-CIRCUITS-SYST-2
volume: 44
number: 9
pages: 774--779
month: sep
monthnumber: 9
year: 1997
CODEN: ICSPE5
DOI: https://doi.org/10.1109/82.625021
ISSN: 1057-7130 (print), 1558-125X (electronic) OR 10577130 (print), 1558125X (electronic)
ISSNL: 1057-7130 OR 10577130
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 Circuits and Systems. 2, Analog and Digital Signal Processing
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82
rawauthor: Chimin Tsai
rawtitle: Floating-point roundoff noises of first- and second-order sections in parallel form digital filters
entry:
@Article{Tsai:1997:FPR,
  author =       "Chimin Tsai",
  title =        "Floating-point roundoff noises of first- and
                 second-order sections in parallel form digital
                 filters",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-2,
  volume =       "44",
  number =       "9",
  pages =        "774--779",
  month =        sep,
  year =         "1997",
  CODEN =        "ICSPE5",
  DOI =          "https://doi.org/10.1109/82.625021",
  ISSN =         "1057-7130 (print), 1558-125X (electronic)",
  ISSN-L =       "1057-7130",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems. 2, Analog
                 and Digital Signal Processing",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
  summary =      "Assuming wide-sense stationary white noise input, we
                 investigated the floating-point roundoff noises of
                 first- and second order digital subfilters. For
                 first-order subfilters, the roundoff noise of parallel
                 form 3P realization is invariably smaller \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Turner:1997:FFR
author: Peter R. Turner
title: Fraction-Free RNS Algorithms for Solving Linear Systems
crossref: Lang:1997:ISC
pages: 218--224
year: 1997
bibdate: Mon May 20 05:45:32 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 05:45:32 MDT
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Turner.pdf
keywords: ARITH-13
acknowledgement: ack-nhfb
rawauthor: Peter R. Turner
rawtitle: Fraction-Free {RNS} Algorithms for Solving Linear Systems
entry:
@InProceedings{Turner:1997:FFR,
  author =       "Peter R. Turner",
  title =        "Fraction-Free {RNS} Algorithms for Solving Linear
                 Systems",
  crossref =     "Lang:1997:ISC",
  pages =        "218--224",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Turner.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}


bibtype: book
filename: fparith.bib
label: Ueberhuber:1997:NCM
author: Christoph W. Ueberhuber
title: Numerical Computation: Methods, Software, and Analysis
publisher: pub-SV
address: pub-SV:adr
pages: xvi + 474 (vol. 1), xvi + 495 (vol. 2)
year: 1997
DOI: https://doi.org/10.1007/978-3-642-59118-1
LCCN: QA297 .U2413 1997
bibdate: Thu Oct 28 15:17:48 1999
bibtimestamp: 1999.10.28 15:17:48 ???
acknowledgement: ack-nhfb
rawauthor: Christoph W. Ueberhuber
rawtitle: Numerical Computation: Methods, Software, and Analysis
ISBN:
3-540-62058-3 (vol. 1: softcover), 3-540-62057-5 (vol. 2: softcover), 3-642-59118-3 (e-book) OR 3540620583 (vol. 1: softcover), 3540620575 (vol. 2: softcover), 3642591183 (ebook)

ISBN13:
978-3-540-62058-7 (vol. 1: softcover), 978-3-540-62057-0 (vol. 2: softcover), 978-3-642-59118-1 (e-book) OR 9783540620587 (vol. 1: softcover), 9783540620570 (vol. 2: softcover), 9783642591181 (ebook)

bibsource:
https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/master.bib; https://www.math.utah.edu/pub/tex/bib/numana1990.bib

abstract:
This book is the first part of a modern, two-volume introduction to numerical computation, which strongly emphasizes software aspects. It can serve as a textbook for courses on numerical analysis, particularly for engineers. The book can also be used as a reference book and it includes an extensive bibliography. The author is a well-known specialist in numerical analysis who was involved in the creation of the software package QUADPACK.

TOC:
1 Scientific Modeling 1.1 Reality Versus Model 1.2 The Model Subject and the Model 1.3 The Model Subject and Reality 1.4 Model Building 2 Fundamental Principles of Numerical Methods 2.1 From Application Problems to their Numerical Solution 2.2 Numerical Problems 2.3 Types of Errors in Numerics 2.4 The Condition of Mathematical Problems 2.5 The Condition of Application Problems 2.6 The Mathematical Elements of Condition Estimation 2.7 Validation of Numerical Computations 3 Computers for Numerical Data Processing 3.1 Processors 3.2 Memory 3.3 Performance Quantification 3.4 Analytical Performance Assessment 3.5 Empirical Performance Assessment 4 Numerical Data and Numerical Operations 4.1 Mathematical Data 4.2 Numerical Data on Computers 4.3 Operations on Numerical Data 4.4 Number Systems on Computers 4.5 Structure of Floating-Point Systems 4.6 Standardization of Floating-Point Number Systems 4.7 Arithmetics for Floating-Point Systems 4.8 Inquiry Functions and Manipulation of Numbers in Fortran 90 4.9 Operations with Algebraic Data 4.10 Operations with Arrays 4.11 Operations with Analytic Data 5 Numerical Algorithms 5.1 The Intuitive Notion of an Algorithm 5.2 Properties of Algorithms 5.3 Existence of Algorithms 5.4 Practical Solvability of Problems 5.5 Complexity of Algorithms 5.6 Representation of Algorithms 5.7 Influence of Rounding Errors on Numerical Algorithms 5.8 Case Study: Floating-Point Summation 6 Numerical Programs 6.1 The Quality of Numerical Programs 6.2 Reasons for Poor Efficiency 6.3 The Measurement of Performance Indices 6.4 Performance Optimization 6.5 Architecture Independent Optimizations 6.6 Loop Optimizations 6.7 Blocked Memory Access 6.8 Case Study: Multiplication of Matrices 7 Available Numerical Software 7.1 The Cost of Software 7.2 Sources of Numerical Software 7.3 Software and the Internet 7.4 Interactive Multifunctional Systems 7.5 Problem Solving Environments 7.6 Case Study: Software for Elliptic PDEs 8 Using Approximation in Mathematical Model Building 8.1 Analytic Models 8.2 Information and Data 8.3 Discrete Approximation 8.4 Function Approximation 8.5 Choosing a Model Function 8.6 Choice of the Distance Function 8.7 Transformation of the Problem 9 Interpolation 9.1 Interpolation Problems 9.2 Mathematical Foundations 9.3 Univariate Polynomial Interpolation 9.4 Univariate, Piecewise, Polynomial Interpolation 9.5 Polynomial Splines 9.6 B-Splines 9.7 Cubic Spline Interpolation 9.8 Splines Without Undesirable Oscillations 9.9 Multivariate Interpolation 9.10 Multivariate Polynomial Interpolation 9.11 Multivariate (Sub-) Spline Interpolation 9.12 Related Problems and Methods Glossary of Notation Author Index

rawabstract:
This book is the first part of a modern, two-volume introduction to numerical computation, which strongly emphasizes software aspects. It can serve as a textbook for courses on numerical analysis, particularly for engineers. The book can also be used as a reference book and it includes an extensive bibliography. The author is a well-known specialist in numerical analysis who was involved in the creation of the software package QUADPACK.

rawTOC:
1 Scientific Modeling \\ 1.1 Reality Versus Model \\ 1.2 The Model Subject and the Model \\ 1.3 The Model Subject and Reality \\ 1.4 Model Building \\ 2 Fundamental Principles of Numerical Methods \\ 2.1 From Application Problems to their Numerical Solution \\ 2.2 Numerical Problems \\ 2.3 Types of Errors in Numerics \\ 2.4 The Condition of Mathematical Problems \\ 2.5 The Condition of Application Problems \\ 2.6 The Mathematical Elements of Condition Estimation \\ 2.7 Validation of Numerical Computations \\ 3 Computers for Numerical Data Processing \\ 3.1 Processors \\ 3.2 Memory \\ 3.3 Performance Quantification \\ 3.4 Analytical Performance Assessment \\ 3.5 Empirical Performance Assessment \\ 4 Numerical Data and Numerical Operations \\ 4.1 Mathematical Data \\ 4.2 Numerical Data on Computers \\ 4.3 Operations on Numerical Data \\ 4.4 Number Systems on Computers \\ 4.5 Structure of Floating-Point Systems \\ 4.6 Standardization of Floating-Point Number Systems \\ 4.7 Arithmetics for Floating-Point Systems \\ 4.8 Inquiry Functions and Manipulation of Numbers in Fortran 90 \\ 4.9 Operations with Algebraic Data \\ 4.10 Operations with Arrays \\ 4.11 Operations with Analytic Data \\ 5 Numerical Algorithms \\ 5.1 The Intuitive Notion of an Algorithm \\ 5.2 Properties of Algorithms \\ 5.3 Existence of Algorithms \\ 5.4 Practical Solvability of Problems \\ 5.5 Complexity of Algorithms \\ 5.6 Representation of Algorithms \\ 5.7 Influence of Rounding Errors on Numerical Algorithms \\ 5.8 Case Study: Floating-Point Summation \\ 6 Numerical Programs \\ 6.1 The Quality of Numerical Programs \\ 6.2 Reasons for Poor Efficiency \\ 6.3 The Measurement of Performance Indices \\ 6.4 Performance Optimization \\ 6.5 Architecture Independent Optimizations \\ 6.6 Loop Optimizations \\ 6.7 Blocked Memory Access \\ 6.8 Case Study: Multiplication of Matrices \\ 7 Available Numerical Software \\ 7.1 The Cost of Software \\ 7.2 Sources of Numerical Software \\ 7.3 Software and the Internet \\ 7.4 Interactive Multifunctional Systems \\ 7.5 Problem Solving Environments \\ 7.6 Case Study: Software for Elliptic PDEs \\ 8 Using Approximation in Mathematical Model Building \\ 8.1 Analytic Models \\ 8.2 Information and Data \\ 8.3 Discrete Approximation \\ 8.4 Function Approximation \\ 8.5 Choosing a Model Function \\ 8.6 Choice of the Distance Function \\ 8.7 Transformation of the Problem \\ 9 Interpolation \\ 9.1 Interpolation Problems \\ 9.2 Mathematical Foundations \\ 9.3 Univariate Polynomial Interpolation \\ 9.4 Univariate, Piecewise, Polynomial Interpolation \\ 9.5 Polynomial Splines \\ 9.6 B-Splines \\ 9.7 Cubic Spline Interpolation \\ 9.8 Splines Without Undesirable Oscillations \\ 9.9 Multivariate Interpolation \\ 9.10 Multivariate Polynomial Interpolation \\ 9.11 Multivariate (Sub-) Spline Interpolation \\ 9.12 Related Problems and Methods \\ Glossary of Notation \\ Author Index

entry:
@Book{Ueberhuber:1997:NCM,
  author =       "Christoph W. Ueberhuber",
  title =        "Numerical Computation: Methods, Software, and
                 Analysis",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xvi + 474 (vol. 1), xvi + 495 (vol. 2)",
  year =         "1997",
  DOI =          "https://doi.org/10.1007/978-3-642-59118-1",
  ISBN =         "3-540-62058-3 (vol. 1: softcover), 3-540-62057-5 (vol.
                 2: softcover), 3-642-59118-3 (e-book)",
  ISBN-13 =      "978-3-540-62058-7 (vol. 1: softcover),
                 978-3-540-62057-0 (vol. 2: softcover),
                 978-3-642-59118-1 (e-book)",
  LCCN =         "QA297 .U2413 1997",
  bibdate =      "Thu Oct 28 15:17:48 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/numana1990.bib",
  price =        "US\$44.95 (vol. 1), US\$49.95 (vol. 2)",
  abstract =     "This book is the first part of a modern, two-volume
                 introduction to numerical computation, which strongly
                 emphasizes software aspects. It can serve as a textbook
                 for courses on numerical analysis, particularly for
                 engineers. The book can also be used as a reference
                 book and it includes an extensive bibliography. The
                 author is a well-known specialist in numerical analysis
                 who was involved in the creation of the software
                 package QUADPACK.",
  acknowledgement = ack-nhfb,
  tableofcontents = "1 Scientific Modeling \\
                 1.1 Reality Versus Model \\
                 1.2 The Model Subject and the Model \\
                 1.3 The Model Subject and Reality \\
                 1.4 Model Building \\
                 2 Fundamental Principles of Numerical Methods \\
                 2.1 From Application Problems to their Numerical
                 Solution \\
                 2.2 Numerical Problems \\
                 2.3 Types of Errors in Numerics \\
                 2.4 The Condition of Mathematical Problems \\
                 2.5 The Condition of Application Problems \\
                 2.6 The Mathematical Elements of Condition Estimation
                 \\
                 2.7 Validation of Numerical Computations \\
                 3 Computers for Numerical Data Processing \\
                 3.1 Processors \\
                 3.2 Memory \\
                 3.3 Performance Quantification \\
                 3.4 Analytical Performance Assessment \\
                 3.5 Empirical Performance Assessment \\
                 4 Numerical Data and Numerical Operations \\
                 4.1 Mathematical Data \\
                 4.2 Numerical Data on Computers \\
                 4.3 Operations on Numerical Data \\
                 4.4 Number Systems on Computers \\
                 4.5 Structure of Floating-Point Systems \\
                 4.6 Standardization of Floating-Point Number Systems
                 \\
                 4.7 Arithmetics for Floating-Point Systems \\
                 4.8 Inquiry Functions and Manipulation of Numbers in
                 Fortran 90 \\
                 4.9 Operations with Algebraic Data \\
                 4.10 Operations with Arrays \\
                 4.11 Operations with Analytic Data \\
                 5 Numerical Algorithms \\
                 5.1 The Intuitive Notion of an Algorithm \\
                 5.2 Properties of Algorithms \\
                 5.3 Existence of Algorithms \\
                 5.4 Practical Solvability of Problems \\
                 5.5 Complexity of Algorithms \\
                 5.6 Representation of Algorithms \\
                 5.7 Influence of Rounding Errors on Numerical
                 Algorithms \\
                 5.8 Case Study: Floating-Point Summation \\
                 6 Numerical Programs \\
                 6.1 The Quality of Numerical Programs \\
                 6.2 Reasons for Poor Efficiency \\
                 6.3 The Measurement of Performance Indices \\
                 6.4 Performance Optimization \\
                 6.5 Architecture Independent Optimizations \\
                 6.6 Loop Optimizations \\
                 6.7 Blocked Memory Access \\
                 6.8 Case Study: Multiplication of Matrices \\
                 7 Available Numerical Software \\
                 7.1 The Cost of Software \\
                 7.2 Sources of Numerical Software \\
                 7.3 Software and the Internet \\
                 7.4 Interactive Multifunctional Systems \\
                 7.5 Problem Solving Environments \\
                 7.6 Case Study: Software for Elliptic PDEs \\
                 8 Using Approximation in Mathematical Model Building
                 \\
                 8.1 Analytic Models \\
                 8.2 Information and Data \\
                 8.3 Discrete Approximation \\
                 8.4 Function Approximation \\
                 8.5 Choosing a Model Function \\
                 8.6 Choice of the Distance Function \\
                 8.7 Transformation of the Problem \\
                 9 Interpolation \\
                 9.1 Interpolation Problems \\
                 9.2 Mathematical Foundations \\
                 9.3 Univariate Polynomial Interpolation \\
                 9.4 Univariate, Piecewise, Polynomial Interpolation \\
                 9.5 Polynomial Splines \\
                 9.6 B-Splines \\
                 9.7 Cubic Spline Interpolation \\
                 9.8 Splines Without Undesirable Oscillations \\
                 9.9 Multivariate Interpolation \\
                 9.10 Multivariate Polynomial Interpolation \\
                 9.11 Multivariate (Sub-) Spline Interpolation \\
                 9.12 Related Problems and Methods \\
                 Glossary of Notation \\
                 Author Index",
}


bibtype: article
filename: fparith.bib
label: Verschaeren:1997:NPF
author: Dennis Verschaeren and Annie Cuyt and Brigitte Verdonk
journal: j-SIGPLAN
volume: 32
number: 3
pages: 57--64
month: mar
monthnumber: 3
year: 1997
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 09:17:30 MST 2003
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.12.14 09:17:30 MST
fjournal: ACM SIGPLAN Notices
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J706
rawauthor: Dennis Verschaeren and Annie Cuyt and Brigitte Verdonk
title:
On the Need for Predictable Floating-Point Arithmetic in the Programming Languages Fortran 90 and C / C++

rawtitle:
On the Need for Predictable Floating-Point Arithmetic in the Programming Languages {Fortran 90} and {C\slash C++}

entry:
@Article{Verschaeren:1997:NPF,
  author =       "Dennis Verschaeren and Annie Cuyt and Brigitte
                 Verdonk",
  title =        "On the Need for Predictable Floating-Point Arithmetic
                 in the Programming Languages {Fortran 90} and {C\slash
                 C++}",
  journal =      j-SIGPLAN,
  volume =       "32",
  number =       "3",
  pages =        "57--64",
  month =        mar,
  year =         "1997",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sun Dec 14 09:17:30 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
}


bibtype: inproceedings
filename: fparith.bib
label: Walter:1997:EUD
author: Colin D. Walter
title: Exponentiation using Division Chains
crossref: Lang:1997:ISC
pages: 92--98
year: 1997
bibdate: Mon May 20 05:45:32 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 05:45:32 MDT
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Walter.pdf
keywords: ARITH-13
acknowledgement: ack-nhfb
rawauthor: Colin D. Walter
rawtitle: Exponentiation using Division Chains
entry:
@InProceedings{Walter:1997:EUD,
  author =       "Colin D. Walter",
  title =        "Exponentiation using Division Chains",
  crossref =     "Lang:1997:ISC",
  pages =        "92--98",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Walter.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}


bibtype: article
filename: fparith.bib
label: Walter:1997:STT
author: C. D. Walter
title: Space / time trade-offs for higher radix modular multiplication using repeated addition
journal: j-IEEE-TRANS-COMPUT
volume: 46
number: 2
pages: 139--141
month: feb
monthnumber: 2
year: 1997
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.565588
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 10:06:20 MDT 2011
bibtimestamp: 2011.07.06 10:06:20 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=565588
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: C. D. Walter
rawtitle: Space\slash time trade-offs for higher radix modular multiplication using repeated addition
entry:
@Article{Walter:1997:STT,
  author =       "C. D. Walter",
  title =        "Space\slash time trade-offs for higher radix modular
                 multiplication using repeated addition",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "46",
  number =       "2",
  pages =        "139--141",
  month =        feb,
  year =         "1997",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.565588",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 10:06:20 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=565588",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Wilkes:1997:AE
author: M. V. Wilkes
title: Arithmetic on the EDSAC
journal: j-IEEE-ANN-HIST-COMPUT
volume: 19
number: 1
pages: 13--15
month: jan
monthnumber: 1
year: 1997
CODEN: IAHCEX
DOI: https://doi.org/10.1109/85.560726
ISSN: 1058-6180 (print), 1934-1547 (electronic) OR 10586180 (print), 19341547 (electronic)
ISSNL: 1058-6180 OR 10586180
bibdate: Thu Jul 12 08:14:44 MDT 2001
bibtimestamp: 2001.07.12 08:14:44 MDT
URL: http://ieeexplore.ieee.org/iel4/85/12228/00560726.pdf
fjournal: IEEE Annals of the History of Computing
acknowledgement: ack-nhfb
ajournal: IEEE Ann. Hist. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=85
rawauthor: M. V. Wilkes
rawtitle: Arithmetic on the {EDSAC}
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeeannhistcomput.bib

entry:
@Article{Wilkes:1997:AE,
  author =       "M. V. Wilkes",
  title =        "Arithmetic on the {EDSAC}",
  journal =      j-IEEE-ANN-HIST-COMPUT,
  volume =       "19",
  number =       "1",
  pages =        "13--15",
  month =        jan # "\slash " # mar,
  year =         "1997",
  CODEN =        "IAHCEX",
  DOI =          "https://doi.org/10.1109/85.560726",
  ISSN =         "1058-6180 (print), 1934-1547 (electronic)",
  ISSN-L =       "1058-6180",
  bibdate =      "Thu Jul 12 08:14:44 MDT 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeeannhistcomput.bib",
  URL =          "http://ieeexplore.ieee.org/iel4/85/12228/00560726.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Ann. Hist. Comput.",
  fjournal =     "IEEE Annals of the History of Computing",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=85",
}


bibtype: article
filename: fparith.bib
label: Williams:1997:IPC
author: C. Williams
title: Intel's Pentium chip crisis: an ethical analysis
journal: j-IEEE-TRANS-PROF-COMMUN
volume: 40
number: 1
pages: 13--19
month: mar
monthnumber: 3
year: 1997
CODEN: IEPCBU
DOI: https://doi.org/10.1109/47.557513
ISSN: 0361-1434 (print), 1558-1500 (electronic) OR 03611434 (print), 15581500 (electronic)
ISSNL: 0361-1434 OR 03611434
bibdate: Sat Dec 18 11:57:01 2021
bibtimestamp: 2021.12.18 11:57:01 ???
fjournal: IEEE Transactions on Professional Communication
keywords: Pentium divide flaw; Thomas Nicely
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=47
rawauthor: C. Williams
rawtitle: {Intel}'s {Pentium} chip crisis: an ethical analysis
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetransprofcommun.bib

abstract:
In October 1994 a mathematics professor informed the Intel Corporation that its Pentium chip had a flaw which caused mathematical errors. Intel's response to the professor and its customers created a backlash of anger and a public relations crisis. By analyzing Intel's actions using the work of two relevant ethical philosophies, the article shows that some of the company's errors in public relations were also ethical errors. However, it also points out that Intel has made improvements which will help it avoid future problems and which could set an ethical precedent for the semiconductor industry.

rawabstract:
In October 1994 a mathematics professor informed the Intel Corporation that its Pentium chip had a flaw which caused mathematical errors. Intel's response to the professor and its customers created a backlash of anger and a public relations crisis. By analyzing Intel's actions using the work of two relevant ethical philosophies, the article shows that some of the company's errors in public relations were also ethical errors. However, it also points out that Intel has made improvements which will help it avoid future problems and which could set an ethical precedent for the semiconductor industry.

entry:
@Article{Williams:1997:IPC,
  author =       "C. Williams",
  title =        "{Intel}'s {Pentium} chip crisis: an ethical analysis",
  journal =      j-IEEE-TRANS-PROF-COMMUN,
  volume =       "40",
  number =       "1",
  pages =        "13--19",
  month =        mar,
  year =         "1997",
  CODEN =        "IEPCBU",
  DOI =          "https://doi.org/10.1109/47.557513",
  ISSN =         "0361-1434 (print), 1558-1500 (electronic)",
  ISSN-L =       "0361-1434",
  bibdate =      "Sat Dec 18 11:57:01 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransprofcommun.bib",
  abstract =     "In October 1994 a mathematics professor informed the
                 Intel Corporation that its Pentium chip had a flaw
                 which caused mathematical errors. Intel's response to
                 the professor and its customers created a backlash of
                 anger and a public relations crisis. By analyzing
                 Intel's actions using the work of two relevant ethical
                 philosophies, the article shows that some of the
                 company's errors in public relations were also ethical
                 errors. However, it also points out that Intel has made
                 improvements which will help it avoid future problems
                 and which could set an ethical precedent for the
                 semiconductor industry.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Professional Communication",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=47",
  keywords =     "Pentium divide flaw; Thomas Nicely",
}


bibtype: article
filename: fparith.bib
label: Woehr:1997:CWK
author: Jack Woehr
title: A Conversation with William Kahan: How important is numerical accuracy?
journal: j-DDJ
volume: 22
number: 11
pages: 18--20, 22, 24, 26, 30, 32
month: nov
monthnumber: 11
year: 1997
CODEN: DDJOEB
ISSN: 1044-789X OR 1044789X
bibdate: Fri Nov 28 17:28:03 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.11.28 17:28:03 MST
fjournal: Dr. Dobb's Journal of Software Tools
acknowledgement: ack-nhfb
rawauthor: Jack Woehr
rawtitle: A Conversation with {William Kahan}: How important is numerical accuracy?
note:
Kahan, the father of the IEEE 754 floating-point standard, talks about floating-point arithmetic issues, and numerical deficiencies in Java.

abstract:
Noted mathematician and computer scientist William Kahan has played a central role in everything from the design of the 8087 math coprocessor to defining the ANSI / IEEE Standard for binary floating-point arithmetic. He takes time out of his schedule to talk with us about the current state of numeric computing.

rawabstract:
Noted mathematician and computer scientist William Kahan has played a central role in everything from the design of the 8087 math coprocessor to defining the ANSI\slash IEEE Standard for binary floating-point arithmetic. He takes time out of his schedule to talk with us about the current state of numeric computing.

rawnote:
Kahan, the father of the IEEE 754 floating-point standard, talks about floating-point arithmetic issues, and numerical deficiencies in Java.

entry:
@Article{Woehr:1997:CWK,
  author =       "Jack Woehr",
  title =        "A Conversation with {William Kahan}: How important is
                 numerical accuracy?",
  journal =      j-DDJ,
  volume =       "22",
  number =       "11",
  pages =        "18--20, 22, 24, 26, 30, 32",
  month =        nov,
  year =         "1997",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Fri Nov 28 17:28:03 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Kahan, the father of the IEEE 754 floating-point
                 standard, talks about floating-point arithmetic issues,
                 and numerical deficiencies in Java.",
  abstract =     "Noted mathematician and computer scientist William
                 Kahan has played a central role in everything from the
                 design of the 8087 math coprocessor to defining the
                 ANSI\slash IEEE Standard for binary floating-point
                 arithmetic. He takes time out of his schedule to talk
                 with us about the current state of numeric computing.",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}


bibtype: article
filename: fparith.bib
label: Xue:1997:DPK
author: Jinyun Xue and Ruth Davis
title: A Derivation and Proof of Knuth's Binary to Decimal Conversion Program
journal: j-SOFTW-CONCEPTS-TOOLS
volume: 18
number: 4
pages: 149--156
year: 1997
CODEN: SCOTE5
ISSN: 0945-8115 (print), 1432-2188 (electronic) OR 09458115 (print), 14322188 (electronic)
ISSNL: 0945-8115 OR 09458115
bibdate: Sat Jan 6 12:49:28 2024
bibtimestamp: 2024.01.06 12:49:28 ???
fjournal: Software---Concepts and Tools
acknowledgement: ack-nhfb
journalURL: https://link.springer.com/journal/378
rawauthor: Jinyun Xue and Ruth Davis
rawtitle: A Derivation and Proof of {Knuth}'s Binary to Decimal Conversion Program
bibsource:
dblp computer science bibliography; https://dblp.org; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/structprogram.bib

entry:
@Article{Xue:1997:DPK,
  author =       "Jinyun Xue and Ruth Davis",
  title =        "A Derivation and Proof of {Knuth}'s Binary to Decimal
                 Conversion Program",
  journal =      j-SOFTW-CONCEPTS-TOOLS,
  volume =       "18",
  number =       "4",
  pages =        "149--156",
  year =         "1997",
  CODEN =        "SCOTE5",
  ISSN =         "0945-8115 (print), 1432-2188 (electronic)",
  ISSN-L =       "0945-8115",
  bibdate =      "Sat Jan 6 12:49:28 2024",
  bibsource =    "dblp computer science bibliography; https://dblp.org;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/structprogram.bib",
  acknowledgement = ack-nhfb,
  biburl =       "https://dblp.org/rec/journals/stp/XueD97.bib",
  dblp-id =      "DBLP:journals/stp/XueD97",
  fjournal =     "Software---Concepts and Tools",
  journal-URL =  "https://link.springer.com/journal/378",
  timestamp =    "Mon Mar 11 11:49:37 2024",
}


bibtype: inproceedings
filename: fparith.bib
label: Zeng:1997:REA
author: Bing Zeng
title: Roundoff error analysis of floating-point paraunitary filter banks realized in lattice structure
volume: 4
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 2405--2408
year: 1997
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: Bing Zeng
rawtitle: Roundoff error analysis of floating-point paraunitary filter banks realized in lattice structure
booktitle:
Proceedings of 1997 IEEE International Symposium on Circuits and Systems: ISCAS '97, 9--12 June 1997

rawbooktitle:
Proceedings of 1997 {IEEE} International Symposium on Circuits and Systems: {ISCAS '97}, 9--12 June 1997

entry:
@InProceedings{Zeng:1997:REA,
  author =       "Bing Zeng",
  booktitle =    "Proceedings of 1997 {IEEE} International Symposium on
                 Circuits and Systems: {ISCAS '97}, 9--12 June 1997",
  title =        "Roundoff error analysis of floating-point paraunitary
                 filter banks realized in lattice structure",
  volume =       "4",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "2405--2408",
  year =         "1997",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:07 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Floating-point roundoff noise characteristics of
                 two-channel paraunitary filter banks realized in
                 lattice structure are studied in detail in this paper.
                 Under the assumption that all quantization errors are
                 independent WSS white noise with zero-mean, \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Aberbour:1998:PMF
author: M. Aberbour and A. Houelle and H. Mehrez and N. Vaucher and A. Guyot
journal: j-IEEE-TRANS-VLSI-SYST
volume: 6
number: 1
pages: 114--121
month: mar
monthnumber: 3
year: 1998
CODEN: IEVSE9
DOI: https://doi.org/10.1109/92.661253
ISSN: 1063-8210 (print), 1557-9999 (electronic) OR 10638210 (print), 15579999 (electronic)
ISSNL: 1063-8210 OR 10638210
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: IEEE Transactions on Very Large Scale Integration (VLSI) Systems
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/issues?punumber=92
rawauthor: M. Aberbour and A. Houelle and H. Mehrez and N. Vaucher and A. Guyot
title:
On portable macrocell FPU generators for division and square root operators complying to the full IEEE-754 standard

rawtitle:
On portable macrocell {FPU} generators for division and square root operators complying to the full {IEEE-754} standard

entry:
@Article{Aberbour:1998:PMF,
  author =       "M. Aberbour and A. Houelle and H. Mehrez and N.
                 Vaucher and A. Guyot",
  title =        "On portable macrocell {FPU} generators for division
                 and square root operators complying to the full
                 {IEEE-754} standard",
  journal =      j-IEEE-TRANS-VLSI-SYST,
  volume =       "6",
  number =       "1",
  pages =        "114--121",
  month =        mar,
  year =         "1998",
  CODEN =        "IEVSE9",
  DOI =          "https://doi.org/10.1109/92.661253",
  ISSN =         "1063-8210 (print), 1557-9999 (electronic)",
  ISSN-L =       "1063-8210",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Very Large Scale Integration
                 (VLSI) Systems",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=92",
  summary =      "In this paper, we investigate the design of macrocell
                 generators of division and square root floating-point
                 operators. The number representation used in our
                 operators is the IEEE-754-1985 standard for binary
                 floating-point numbers. The design and \ldots{}",
}


bibtype: book
filename: fparith.bib
label: Aberth:1998:PNM
author: Oliver Aberth
title: Precise numerical methods using C++
publisher: pub-ACADEMIC
address: pub-ACADEMIC:adr
pages: xiv + 238
year: 1998
ISBN: 0-12-041750-2 OR 0120417502
ISBN13: 978-0-12-041750-6 OR 9780120417506
LCCN: QA76.73.C153 A32 1998
bibdate: Wed Nov 3 09:30:14 MST 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1999.11.03 09:30:14 MST
keywords: C (computer program language); numerical analysis -- data processing
acknowledgement: ack-nhfb
rawauthor: Oliver Aberth
rawtitle: Precise numerical methods using {C++}
note:
Contents: I. Introduction -- II. Various Arithmetics -- III. Solvable Problems and Nonsolvable Problems -- IV. Computing Derivatives and Integrals -- V. Finding Zeros of Real Functions -- VI. Finding Zeros of Polynomials and Other Analytic Functions -- VII. Problems of Linear Algebra -- VIII. Optimization Problems -- IX. Numerical Solution of Ordinary Differential Equations -- X. The C++ System for Precise Computation.

rawnote:
Contents: I. Introduction -- II. Various Arithmetics -- III. Solvable Problems and Nonsolvable Problems -- IV. Computing Derivatives and Integrals -- V. Finding Zeros of Real Functions -- VI. Finding Zeros of Polynomials and Other Analytic Functions -- VII. Problems of Linear Algebra -- VIII. Optimization Problems -- IX. Numerical Solution of Ordinary Differential Equations -- X. The C++ System for Precise Computation.

entry:
@Book{Aberth:1998:PNM,
  author =       "Oliver Aberth",
  title =        "Precise numerical methods using {C++}",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xiv + 238",
  year =         "1998",
  ISBN =         "0-12-041750-2",
  ISBN-13 =      "978-0-12-041750-6",
  LCCN =         "QA76.73.C153 A32 1998",
  bibdate =      "Wed Nov 3 09:30:14 MST 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Contents: I. Introduction -- II. Various Arithmetics
                 -- III. Solvable Problems and Nonsolvable Problems --
                 IV. Computing Derivatives and Integrals -- V. Finding
                 Zeros of Real Functions -- VI. Finding Zeros of
                 Polynomials and Other Analytic Functions -- VII.
                 Problems of Linear Algebra -- VIII. Optimization
                 Problems -- IX. Numerical Solution of Ordinary
                 Differential Equations -- X. The C++ System for Precise
                 Computation.",
  price =        "US\$59.95",
  acknowledgement = ack-nhfb,
  keywords =     "C (computer program language); numerical analysis --
                 data processing",
}


bibtype: article
filename: fparith.bib
label: Al-Twaijry:1998:SPB
author: H. A. Al-Twaijry and S. F. Oberman and S. T. Fu and M. J. Flynn
title: The SNAP Project: Building Validated Floating Point
journal: j-J-UCS
volume: 4
number: 2
pages: 99--109
day: 28
month: feb
monthnumber: 2
year: 1998
ISSN: 0948-6968 OR 09486968
ISSNL: 0948-6968 OR 09486968
bibdate: Wed Mar 4 15:32:49 MST 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.03.04 15:32:49 MST
fjournal: J.UCS: Journal of Universal Computer Science
acknowledgement: ack-nhfb
journalURL: http://www.jucs.org/jucs
rawauthor: H. A. Al-Twaijry and S. F. Oberman and S. T. Fu and M. J. Flynn
rawtitle: The {SNAP} Project: Building Validated Floating Point
URL:
http://medoc.springer.de:8000/jucs/jucs_4_2/the_snap_project_building; http://www.jucs.org/jucs_4_2/the_snap_project_building/Al_twaijry_H_A.pdf

entry:
@Article{Al-Twaijry:1998:SPB,
  author =       "H. A. Al-Twaijry and S. F. Oberman and S. T. Fu and M.
                 J. Flynn",
  title =        "The {SNAP} Project: Building Validated Floating
                 Point",
  journal =      j-J-UCS,
  volume =       "4",
  number =       "2",
  pages =        "99--109",
  day =          "28",
  month =        feb,
  year =         "1998",
  CODEN =        "????",
  ISSN =         "0948-6968",
  ISSN-L =       "0948-6968",
  bibdate =      "Wed Mar 4 15:32:49 MST 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://medoc.springer.de:8000/jucs/jucs_4_2/the_snap_project_building;
                 http://www.jucs.org/jucs_4_2/the_snap_project_building/Al_twaijry_H_A.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "J.UCS: Journal of Universal Computer Science",
  journal-URL =  "http://www.jucs.org/jucs",
}


bibtype: article
filename: fparith.bib
label: Al-Twaijry:1998:TSE
author: H. A. Al-Twaijry and M. J. Flynn
title: Technology scaling effects on multipliers
journal: j-IEEE-TRANS-COMPUT
volume: 47
number: 11
pages: 1201--1215
month: nov
monthnumber: 11
year: 1998
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.736430
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 09:35:56 MDT 2011
bibtimestamp: 2011.07.06 09:35:56 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=736430
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: H. A. Al-Twaijry and M. J. Flynn
rawtitle: Technology scaling effects on multipliers
entry:
@Article{Al-Twaijry:1998:TSE,
  author =       "H. A. Al-Twaijry and M. J. Flynn",
  title =        "Technology scaling effects on multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "11",
  pages =        "1201--1215",
  month =        nov,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.736430",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 09:35:56 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=736430",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Althaus:1998:MNF
author: Ernst Althaus and Kurt Mehlhorn
title: Maximum network flow with floating point arithmetic
journal: j-INFO-PROC-LETT
volume: 66
number: 3
pages: 109--113
day: 15
month: may
monthnumber: 5
year: 1998
CODEN: IFPLAT
ISSN: 0020-0190 (print), 1872-6119 (electronic) OR 00200190 (print), 18726119 (electronic)
ISSNL: 0020-0190 OR 00200190
bibdate: Sat Nov 7 17:55:59 MST 1998
bibtimestamp: 1998.11.07 17:55:59 MST
fjournal: Information Processing Letters
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00200190
rawauthor: Ernst Althaus and Kurt Mehlhorn
rawtitle: Maximum network flow with floating point arithmetic
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{Althaus:1998:MNF,
  author =       "Ernst Althaus and Kurt Mehlhorn",
  title =        "Maximum network flow with floating point arithmetic",
  journal =      j-INFO-PROC-LETT,
  volume =       "66",
  number =       "3",
  pages =        "109--113",
  day =          "15",
  month =        may,
  year =         "1998",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  bibdate =      "Sat Nov 7 17:55:59 MST 1998",
  bibsource =    "http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/
                 2/; https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
}


bibtype: article
filename: fparith.bib
label: Anonymous:1998:ANO
author: Anonymous
journal: j-FORTRAN-FORUM
volume: 17
number: 3
pages: 1--2
month: dec
monthnumber: 12
year: 1998
ISSN: 1061-7264 (print), 1931-1311 (electronic) OR 10617264 (print), 19311311 (electronic)
ISSNL: 1061-7264 OR 10617264
bibdate: Thu Feb 07 13:34:54 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.02.07 13:34:54 ???
fjournal: ACM Fortran Forum
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/toc.cfm?id=J286
issue: 53
rawauthor: Anonymous
title:
Announcements: New Official Fortran Technical Reports; Working Group 5 Documents; OpenGL Fortran 95 Bindings; MPI Module Provides Enhanced Fortran Support; Variable Precision Arithmetic; Fortran Information Sites; New Fortran Compiler Versions from Lahey and Fujitsu; Downloadable Advanced Fortran Textbook; Fortran Engineering Textbook

rawtitle:
Announcements: New Official {Fortran} Technical Reports; Working Group 5 Documents; {OpenGL} {Fortran 95} Bindings; {MPI} Module Provides Enhanced {Fortran} Support; Variable Precision Arithmetic; {Fortran} Information Sites; New {Fortran} Compiler Versions from {Lahey} and {Fujitsu}; Downloadable Advanced {Fortran} Textbook; {Fortran} Engineering Textbook

entry:
@Article{Anonymous:1998:ANO,
  author =       "Anonymous",
  title =        "Announcements: New Official {Fortran} Technical
                 Reports; Working Group 5 Documents; {OpenGL} {Fortran
                 95} Bindings; {MPI} Module Provides Enhanced {Fortran}
                 Support; Variable Precision Arithmetic; {Fortran}
                 Information Sites; New {Fortran} Compiler Versions from
                 {Lahey} and {Fujitsu}; Downloadable Advanced {Fortran}
                 Textbook; {Fortran} Engineering Textbook",
  journal =      j-FORTRAN-FORUM,
  volume =       "17",
  number =       "3",
  pages =        "1--2",
  month =        dec,
  year =         "1998",
  CODEN =        "????",
  ISSN =         "1061-7264 (print), 1931-1311 (electronic)",
  ISSN-L =       "1061-7264",
  bibdate =      "Thu Feb 07 13:34:54 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Fortran Forum",
  issue =        "53",
  journal-URL =  "http://portal.acm.org/toc.cfm?id=J286",
}


bibtype: article
filename: fparith.bib
label: Anonymous:1998:PIS
author: Anonymous
title: Papers from the 13th IEEE Symposium on Computer Arithmetic
journal: j-IEEE-TRANS-COMPUT
volume: 47
number: 7
pages: 721--721
month: jul
monthnumber: 7
year: 1998
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1998.709371
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 09:35:55 MDT 2011
bibtimestamp: 2011.07.06 09:35:55 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=709371
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Anonymous
rawtitle: Papers from the {13th IEEE Symposium on Computer Arithmetic}
entry:
@Article{Anonymous:1998:PIS,
  author =       "Anonymous",
  title =        "Papers from the {13th IEEE Symposium on Computer
                 Arithmetic}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "7",
  pages =        "721--721",
  month =        jul,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1998.709371",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 09:35:55 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=709371",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Antelo:1998:CVH
author: E. Antelo and T. Lang and J. D. Bruguera
journal: j-IEEE-TRANS-COMPUT
volume: 47
number: 2
pages: 152--161
month: feb
monthnumber: 2
year: 1998
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.663761
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 09:35:53 MDT 2011
bibtimestamp: 2011.07.06 09:35:53 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=663761
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: E. Antelo and T. Lang and J. D. Bruguera
title:
Computation of $ sqrt (x / d) $ in a very high radix combined division / square-root unit with scaling and selection by rounding

rawtitle:
Computation of $ \sqrt {(x / d)} $ in a very high radix combined division\slash square-root unit with scaling and selection by rounding

entry:
@Article{Antelo:1998:CVH,
  author =       "E. Antelo and T. Lang and J. D. Bruguera",
  title =        "Computation of $ \sqrt {(x / d)} $ in a very high
                 radix combined division\slash square-root unit with
                 scaling and selection by rounding",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "2",
  pages =        "152--161",
  month =        feb,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.663761",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 09:35:53 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=663761",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "A very-high radix digit-recurrence algorithm for the
                 operation {\surd}(x/d) is developed, with residual
                 scaling and digit selection by rounding. This is an
                 extension of the division and square-root algorithms
                 presented previously, and for which a \ldots{}",
}


bibtype: book
filename: fparith.bib
label: Appel:1998:MCI
author: Andrew W. Appel
title: Modern Compiler Implementation in ML
publisher: pub-CAMBRIDGE
address: pub-CAMBRIDGE:adr
pages: x + 538
year: 1998
DOI: https://doi.org/10.1017/CBO9780511811449
ISBN: 0-521-58274-1, 0-521-60764-7 (paperback) OR 0521582741, 0521607647 (paperback)
ISBN13: 978-0-521-58274-2, 978-0-521-60764-3 (paperback) OR 9780521582742, 9780521607643 (paperback)
LCCN: QA76.76.C65 A675 1998
bibdate: Sat Apr 1 07:46:22 MDT 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2017.04.01 07:46:22 MDT
acknowledgement: ack-nhfb
authordates: 1960--
rawauthor: Andrew W. Appel
rawtitle: Modern Compiler Implementation in {ML}
URL:
http://proquest.safaribooksonline.com/9781107263826; http://www.loc.gov/catdir/description/cam028/97031091.html; http://www.loc.gov/catdir/toc/cam023/97031091.html

abstract:
This new, expanded textbook describes all phases of a modern compiler: lexical analysis, parsing, abstract syntax, semantic actions, intermediate representations, instruction selection via tree matching, dataflow analysis, graph-coloring register allocation, and runtime systems. It includes good coverage of current techniques in code generation and register allocation, as well as functional and object-oriented languages, that are missing from most books. In addition, more advanced chapters are now included so that it can be used as the basis for two-semester or graduate course. The most accepted and successful techniques are described in a concise way, rather than as an exhaustive catalog of every possible variant. Detailed descriptions of the interfaces between modules of a compiler are illustrated with actual C header files. The first part of the book, Fundamentals of Compilation, is suitable for a one-semester first course in compiler design. The second part, Advanced Topics, which includes the advanced chapters, covers the compilation of object-oriented and functional languages, garbage collection, loop optimizations, SSA form, loop scheduling, and optimization for cache-memory hierarchies.

subject:
ML (Computer program language); Compilers (Computer programs); Compilers (Computer programs); ML (Computer program language); Compiler

TOC:
Part I. Fundamentals of Compilation: 1. Introduction 2. Lexical analysis 3. Parsing 4. Abstract syntax 5. Semantic analysis 6. Activation records 7. Translation to intermediate code 8. Basic blocks and traces 9. Instruction selection 10. Liveness analysis 11. Register allocation 12. Putting it all together Part II. Advanced Topics: 13. Garbage collection 14. Object-oriented languages 15. Functional programming languages 16. Polymorphic types 17. Dataflow analysis 18. Loop optimizations 19. Static single-assignment form 20. Pipelining and scheduling 21. The memory hierarchy

rawabstract:
This new, expanded textbook describes all phases of a modern compiler: lexical analysis, parsing, abstract syntax, semantic actions, intermediate representations, instruction selection via tree matching, dataflow analysis, graph-coloring register allocation, and runtime systems. It includes good coverage of current techniques in code generation and register allocation, as well as functional and object-oriented languages, that are missing from most books. In addition, more advanced chapters are now included so that it can be used as the basis for two-semester or graduate course. The most accepted and successful techniques are described in a concise way, rather than as an exhaustive catalog of every possible variant. Detailed descriptions of the interfaces between modules of a compiler are illustrated with actual C header files. The first part of the book, Fundamentals of Compilation, is suitable for a one-semester first course in compiler design. The second part, Advanced Topics, which includes the advanced chapters, covers the compilation of object-oriented and functional languages, garbage collection, loop optimizations, SSA form, loop scheduling, and optimization for cache-memory hierarchies.

rawTOC:
Part I. Fundamentals of Compilation: \\ 1. Introduction \\ 2. Lexical analysis \\ 3. Parsing \\ 4. Abstract syntax \\ 5. Semantic analysis \\ 6. Activation records \\ 7. Translation to intermediate code \\ 8. Basic blocks and traces \\ 9. Instruction selection \\ 10. Liveness analysis \\ 11. Register allocation \\ 12. Putting it all together \\ Part II. Advanced Topics: \\ 13. Garbage collection \\ 14. Object-oriented languages \\ 15. Functional programming languages \\ 16. Polymorphic types \\ 17. Dataflow analysis \\ 18. Loop optimizations \\ 19. Static single-assignment form \\ 20. Pipelining and scheduling \\ 21. The memory hierarchy

entry:
@Book{Appel:1998:MCI,
  author =       "Andrew W. Appel",
  title =        "Modern Compiler Implementation in {ML}",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "x + 538",
  year =         "1998",
  DOI =          "https://doi.org/10.1017/CBO9780511811449",
  ISBN =         "0-521-58274-1, 0-521-60764-7 (paperback)",
  ISBN-13 =      "978-0-521-58274-2, 978-0-521-60764-3 (paperback)",
  LCCN =         "QA76.76.C65 A675 1998",
  bibdate =      "Sat Apr 1 07:46:22 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://proquest.safaribooksonline.com/9781107263826;
                 http://www.loc.gov/catdir/description/cam028/97031091.html;
                 http://www.loc.gov/catdir/toc/cam023/97031091.html",
  abstract =     "This new, expanded textbook describes all phases of a
                 modern compiler: lexical analysis, parsing, abstract
                 syntax, semantic actions, intermediate representations,
                 instruction selection via tree matching, dataflow
                 analysis, graph-coloring register allocation, and
                 runtime systems. It includes good coverage of current
                 techniques in code generation and register allocation,
                 as well as functional and object-oriented languages,
                 that are missing from most books. In addition, more
                 advanced chapters are now included so that it can be
                 used as the basis for two-semester or graduate course.
                 The most accepted and successful techniques are
                 described in a concise way, rather than as an
                 exhaustive catalog of every possible variant. Detailed
                 descriptions of the interfaces between modules of a
                 compiler are illustrated with actual C header files.
                 The first part of the book, Fundamentals of
                 Compilation, is suitable for a one-semester first
                 course in compiler design. The second part, Advanced
                 Topics, which includes the advanced chapters, covers
                 the compilation of object-oriented and functional
                 languages, garbage collection, loop optimizations, SSA
                 form, loop scheduling, and optimization for
                 cache-memory hierarchies.",
  acknowledgement = ack-nhfb,
  author-dates = "1960--",
  subject =      "ML (Computer program language); Compilers (Computer
                 programs); Compilers (Computer programs); ML (Computer
                 program language); Compiler",
  tableofcontents = "Part I. Fundamentals of Compilation: \\
                 1. Introduction \\
                 2. Lexical analysis \\
                 3. Parsing \\
                 4. Abstract syntax \\
                 5. Semantic analysis \\
                 6. Activation records \\
                 7. Translation to intermediate code \\
                 8. Basic blocks and traces \\
                 9. Instruction selection \\
                 10. Liveness analysis \\
                 11. Register allocation \\
                 12. Putting it all together \\
                 Part II. Advanced Topics: \\
                 13. Garbage collection \\
                 14. Object-oriented languages \\
                 15. Functional programming languages \\
                 16. Polymorphic types \\
                 17. Dataflow analysis \\
                 18. Loop optimizations \\
                 19. Static single-assignment form \\
                 20. Pipelining and scheduling \\
                 21. The memory hierarchy",
}


bibtype: article
filename: fparith.bib
label: Arnold:1998:ACT
author: M. G. Arnold and T. A. Bailey and J. R. Cowles and M. D. Winkel
title: Arithmetic co-transformations in the real and complex logarithmic number systems
journal: j-IEEE-TRANS-COMPUT
volume: 47
number: 7
pages: 777--786
month: jul
monthnumber: 7
year: 1998
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.709377
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 09:35:55 MDT 2011
bibtimestamp: 2011.07.06 09:35:55 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=709377
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: M. G. Arnold and T. A. Bailey and J. R. Cowles and M. D. Winkel
rawtitle: Arithmetic co-transformations in the real and complex logarithmic number systems
entry:
@Article{Arnold:1998:ACT,
  author =       "M. G. Arnold and T. A. Bailey and J. R. Cowles and M.
                 D. Winkel",
  title =        "Arithmetic co-transformations in the real and complex
                 logarithmic number systems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "7",
  pages =        "777--786",
  month =        jul,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.709377",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 09:35:55 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=709377",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Bailey:1998:OEF
author: Daniel V. Bailey and Christof Paar
title: Optimal Extension Fields for Fast Arithmetic in Public-Key Algorithms
journal: j-LECT-NOTES-COMP-SCI
volume: 1462
pages: 472--??
year: 1998
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Tue Feb 5 11:52:43 MST 2002
bibtimestamp: 2002.02.05 11:52:43 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Daniel V. Bailey and Christof Paar
rawtitle: Optimal Extension Fields for Fast Arithmetic in Public-Key Algorithms
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t1462.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/1462/14620472.htm; http://link.springer-ny.com/link/service/series/0558/papers/1462/14620472.pdf

entry:
@Article{Bailey:1998:OEF,
  author =       "Daniel V. Bailey and Christof Paar",
  title =        "Optimal Extension Fields for Fast Arithmetic in
                 Public-Key Algorithms",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1462",
  pages =        "472--??",
  year =         "1998",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Feb 5 11:52:43 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1462.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1462/14620472.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/1462/14620472.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Bajard:1998:NED
author: Jean-Claude Bajard and Laurent-Stephane Didier and Jean-Michel Muller
title: A New Euclidean Division Algorithm for Residue Number Systems
journal: j-J-VLSI-SIGNAL-PROC
volume: 19
number: 2
pages: 167--178
month: jul
monthnumber: 7
year: 1998
CODEN: JVSPED
DOI: https://doi.org/10.1023/A:1008065819322
ISSN: 0922-5773 (print), 1573-109x (electronic) OR 09225773 (print), 1573109x (electronic)
ISSNL: 0922-5773 OR 09225773
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: Journal of VLSI Signal Processing
keywords: residue number systems (RNS)
acknowledgement: ack-nhfb
rawauthor: Jean-Claude Bajard and Laurent-St{\'e}phane Didier and Jean-Michel Muller
rawtitle: A New {Euclidean} Division Algorithm for Residue Number Systems
abstract:
We propose a new algorithm and architecture for performing divisions in residue number systems (RNS). Our algorithm is suitable for RNS with large moduli, with the aim of manipulating very large integers on a parallel computer or a special-purpose architecture. The two basic features of our algorithm are the use of a high-radix division method, and the use of a floating-point arithmetic that should run in parallel with the modular arithmetic.

rawabstract:
We propose a new algorithm and architecture for performing divisions in residue number systems (RNS). Our algorithm is suitable for RNS with large moduli, with the aim of manipulating very large integers on a parallel computer or a special-purpose architecture. The two basic features of our algorithm are the use of a high-radix division method, and the use of a floating-point arithmetic that should run in parallel with the modular arithmetic.

entry:
@Article{Bajard:1998:NED,
  author =       "Jean-Claude Bajard and Laurent-St{\'e}phane Didier and
                 Jean-Michel Muller",
  title =        "A New {Euclidean} Division Algorithm for Residue
                 Number Systems",
  journal =      j-J-VLSI-SIGNAL-PROC,
  volume =       "19",
  number =       "2",
  pages =        "167--178",
  month =        jul,
  year =         "1998",
  CODEN =        "JVSPED",
  DOI =          "https://doi.org/10.1023/A:1008065819322",
  ISSN =         "0922-5773 (print), 1573-109x (electronic)",
  ISSN-L =       "0922-5773",
  bibdate =      "Fri Nov 8 05:39:32 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 Ingenta database",
  abstract =     "We propose a new algorithm and architecture for
                 performing divisions in residue number systems (RNS).
                 Our algorithm is suitable for RNS with large moduli,
                 with the aim of manipulating very large integers on a
                 parallel computer or a special-purpose architecture.
                 The two basic features of our algorithm are the use of
                 a high-radix division method, and the use of a
                 floating-point arithmetic that should run in parallel
                 with the modular arithmetic.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of VLSI Signal Processing",
  keywords =     "residue number systems (RNS)",
  pagecount =    "12",
}


bibtype: article
filename: fparith.bib
label: Bajard:1998:RMM
author: J.-C. Bajard and L.-S. Didier and P. Kornerup
title: An RNS Montgomery modular multiplication algorithm
journal: j-IEEE-TRANS-COMPUT
volume: 47
number: 7
pages: 766--776
month: jul
monthnumber: 7
year: 1998
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.709376
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 09:35:55 MDT 2011
bibtimestamp: 2011.07.06 09:35:55 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=709376
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: J.-C. Bajard and L.-S. Didier and P. Kornerup
rawtitle: An {RNS} {Montgomery} modular multiplication algorithm
entry:
@Article{Bajard:1998:RMM,
  author =       "J.-C. Bajard and L.-S. Didier and P. Kornerup",
  title =        "An {RNS} {Montgomery} modular multiplication
                 algorithm",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "7",
  pages =        "766--776",
  month =        jul,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.709376",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 09:35:55 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=709376",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Bhardwaj:1998:RRN
author: M. Bhardwaj and B. Ljusanin
booktitle: Conference Record of the Thirty-Second Asilomar Conference on Signals, Systems & Computers, 1998
volume: 1
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 202--207
year: 1998
DOI: https://doi.org/10.1109/ACSSC.1998.750854
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: M. Bhardwaj and B. Ljusanin
rawbooktitle: Conference Record of the Thirty-Second Asilomar Conference on Signals, Systems {\&} Computers, 1998
title:
The Renaissance --- a residue number system based vector co-processor for DSP dominated embedded ASICs

rawtitle:
The {Renaissance} --- a residue number system based vector co-processor for {DSP} dominated embedded {ASICs}

entry:
@InProceedings{Bhardwaj:1998:RRN,
  author =       "M. Bhardwaj and B. Ljusanin",
  booktitle =    "Conference Record of the Thirty-Second Asilomar
                 Conference on Signals, Systems {\&} Computers, 1998",
  title =        "The {Renaissance} --- a residue number system based
                 vector co-processor for {DSP} dominated embedded
                 {ASICs}",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "202--207",
  year =         "1998",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ACSSC.1998.750854",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "This paper reports our ongoing investigation of a new
                 paradigm to realize high performance DSP architectures
                 suitable for embedded ASICs. The reasons for the
                 significant gap between achievable MAC bandwidth and
                 that delivered by current embedded DSP \ldots{}",
}


bibtype: misc
filename: fparith.bib
label: Bjorksten:1998:FFP
author: A. A. Bjorksten and J. D. G. Mikan and M. S. Schmookler
title: Fast floating point results alignment apparatus
pages: 202--207
day: 9
month: jun
monthnumber: 6
year: 1998
bibdate: Fri Nov 28 15:36:39 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 15:36:39 ???
note: U.S. Patent No. 5,764,549.
acknowledgement: ack-nhfb
rawauthor: A. A. Bjorksten and J. D. G. Mikan and M. S. Schmookler
rawnote: U.S. Patent No. 5,764,549.
rawtitle: Fast floating point results alignment apparatus
entry:
@Misc{Bjorksten:1998:FFP,
  author =       "A. A. Bjorksten and J. D. G. Mikan and M. S.
                 Schmookler",
  title =        "Fast floating point results alignment apparatus",
  day =          "9",
  month =        jun,
  year =         "1998",
  bibdate =      "Fri Nov 28 15:36:39 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "U.S. Patent No. 5,764,549.",
  acknowledgement = ack-nhfb,
}


bibtype: misc
filename: fparith.bib
label: Briggs:1998:DFP
author: Keith Briggs
title: Doubledouble floating point arithmetic
institution: Department of Plant Sciences, University of Cambridge
address: Downing Street, Cambridge CB2 3EA, UK
pages: 202--207
year: 1998
bibdate: Wed Nov 24 08:26:24 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.24 08:26:24 ???
acknowledgement: ack-nhfb
howpublished: World-Wide Web document.
rawauthor: Keith Briggs
rawtitle: Doubledouble floating point arithmetic
URL:
http://web.archive.org/web/20000520034826/http://www-epidem.plantsci.cam.ac.uk/~kbriggs/doubledouble.html; http://web.archive.org/web/20000815202251/http://www-epidem.plantsci.cam.ac.uk/~kbriggs/doubledouble.html; http://web.archive.org/web/20001207115000/http://www-epidem.plantsci.cam.ac.uk/~kbriggs/doubledouble.html; http://web.archive.org/web/20010204072400/http://web.archive.org/web/20010204072400/http://www-epidem.plantsci.cam.ac.uk/~kbriggs/doubledouble.tgz; http://web.archive.org/web/20010204072400/http://www-epidem.plantsci.cam.ac.uk/~kbriggs/doubledouble.html; http://www-epidem.plantsci.cam.ac.uk/~kbriggs/doubledouble.html

remark:
Author no longer at Cambridge, and Web page gone; however, www.archive.org has saved it (see the second URL)

entry:
@Misc{Briggs:1998:DFP,
  author =       "Keith Briggs",
  title =        "Doubledouble floating point arithmetic",
  howpublished = "World-Wide Web document.",
  institution =  "Department of Plant Sciences, University of
                 Cambridge",
  address =      "Downing Street, Cambridge CB2 3EA, UK",
  year =         "1998",
  bibdate =      "Wed Nov 24 08:26:24 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://web.archive.org/web/20000520034826/http://www-epidem.plantsci.cam.ac.uk/~kbriggs/doubledouble.html;
                 http://web.archive.org/web/20000815202251/http://www-epidem.plantsci.cam.ac.uk/~kbriggs/doubledouble.html;
                 http://web.archive.org/web/20001207115000/http://www-epidem.plantsci.cam.ac.uk/~kbriggs/doubledouble.html;
                 http://web.archive.org/web/20010204072400/http://web.archive.org/web/20010204072400/http://www-epidem.plantsci.cam.ac.uk/~kbriggs/doubledouble.tgz;
                 http://web.archive.org/web/20010204072400/http://www-epidem.plantsci.cam.ac.uk/~kbriggs/doubledouble.html;
                 http://www-epidem.plantsci.cam.ac.uk/~kbriggs/doubledouble.html",
  acknowledgement = ack-nhfb,
  remark =       "Author no longer at Cambridge, and Web page gone;
                 however, www.archive.org has saved it (see the second
                 URL)",
}


bibtype: inproceedings
filename: fparith.bib
label: Bronnimann:1998:IAY
author: Herve Bronnimann and Christoph Burnikel and Sylvain Pion
booktitle: Proc. 14th Annu. ACM Sympos. Comput. Geom. (1998)
title: Interval arithmetic yields efficient dynamic filters for computational geometry
publisher: pub-ACM
address: pub-ACM:adr
pages: 165--174
year: 1998
bibdate: Fri Jan 6 11:53:51 2006
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2006.01.06 11:53:51 ???
URL: citeseer.csail.mit.edu/onnimann98interval.html
acknowledgement: ack-nhfb
rawauthor: Herv{\'e} Br{\"o}nnimann and Christoph Burnikel and Sylvain Pion
rawbooktitle: Proc. 14th Annu. {ACM} Sympos. Comput. Geom. (1998)
rawtitle: Interval arithmetic yields efficient dynamic filters for computational geometry
abstract:
We discuss floating-point filters as a means of restricting the precision needed for arithmetic operations while still computing the exact result. We show that interval techniques can be used to speed up the exact evaluation of geometric predicates and describe an efficient implementation of interval arithmetic that is strongly influenced by the rounding modes of the widely used IEEE 754 standard. Using this approach we engineer an efficient floating-point filter for the computation of the sign of a determinant that works for arbitrary dimensions. We validate our approach experimentally, comparing it with other static, dynamic and semi-static filters.

rawabstract:
We discuss floating-point filters as a means of restricting the precision needed for arithmetic operations while still computing the exact result. We show that interval techniques can be used to speed up the exact evaluation of geometric predicates and describe an efficient implementation of interval arithmetic that is strongly influenced by the rounding modes of the widely used IEEE 754 standard. Using this approach we engineer an efficient floating-point filter for the computation of the sign of a determinant that works for arbitrary dimensions. We validate our approach experimentally, comparing it with other static, dynamic and semi-static filters.

entry:
@InProceedings{Bronnimann:1998:IAY,
  author =       "Herv{\'e} Br{\"o}nnimann and Christoph Burnikel and
                 Sylvain Pion",
  booktitle =    "Proc. 14th Annu. {ACM} Sympos. Comput. Geom. (1998)",
  title =        "Interval arithmetic yields efficient dynamic filters
                 for computational geometry",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "165--174",
  year =         "1998",
  bibdate =      "Fri Jan 6 11:53:51 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "citeseer.csail.mit.edu/onnimann98interval.html",
  abstract =     "We discuss floating-point filters as a means of
                 restricting the precision needed for arithmetic
                 operations while still computing the exact result. We
                 show that interval techniques can be used to speed up
                 the exact evaluation of geometric predicates and
                 describe an efficient implementation of interval
                 arithmetic that is strongly influenced by the rounding
                 modes of the widely used IEEE 754 standard. Using this
                 approach we engineer an efficient floating-point filter
                 for the computation of the sign of a determinant that
                 works for arbitrary dimensions. We validate our
                 approach experimentally, comparing it with other
                 static, dynamic and semi-static filters.",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Chang:1998:HPD
author: Yun-Nan Chang and Keshab K. Parhi
title: High-Performance Digit-Serial Complex-Number Multiplier-Accumulator
crossref: IEEE:1998:IIC
pages: 211--??
year: 1998
DOI: https://doi.org/10.1109/ICCD.1998.727050
bibdate: Sat Aug 22 08:31:58 2009
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2009.08.22 08:31:58 ???
keywords: complex-number; digit-serial multiplier; redundant arithmetic
acknowledgement: ack-nhfb
rawauthor: Yun-Nan Chang and Keshab K. Parhi
rawtitle: High-Performance Digit-Serial Complex-Number Multiplier-Accumulator
abstract:
This paper presents a fast highly regular digit-serial complex-number multiplier-accumulator (CMAC) architecture which is well suited for VLSI implementations. This paper makes two contributions. First, several complex-number representation schemes are discussed. It is shown that the real-imaginary alternate (RIA) scheme is the best among all representation schemes and the prior designs of CMACs based on the radix-(2j) Redundant Complex Number System (RCNS) are not efficient with respect to hardware complexity and processing speed. Second, digit-serial CMAC architectures which can be pipelined at fine-grain level to increase the throughput rate are designed based on carry-save configuration.

rawabstract:
This paper presents a fast highly regular digit-serial complex-number multiplier-accumulator (CMAC) architecture which is well suited for VLSI implementations. This paper makes two contributions. First, several complex-number representation schemes are discussed. It is shown that the real-imaginary alternate (RIA) scheme is the best among all representation schemes and the prior designs of CMACs based on the radix-(2j) Redundant Complex Number System (RCNS) are not efficient with respect to hardware complexity and processing speed. Second, digit-serial CMAC architectures which can be pipelined at fine-grain level to increase the throughput rate are designed based on carry-save configuration.

entry:
@InProceedings{Chang:1998:HPD,
  author =       "Yun-Nan Chang and Keshab K. Parhi",
  title =        "High-Performance Digit-Serial Complex-Number
                 Multiplier-Accumulator",
  crossref =     "IEEE:1998:IIC",
  pages =        "211--??",
  year =         "1998",
  DOI =          "https://doi.org/10.1109/ICCD.1998.727050",
  bibdate =      "Sat Aug 22 08:31:58 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper presents a fast highly regular digit-serial
                 complex-number multiplier-accumulator (CMAC)
                 architecture which is well suited for VLSI
                 implementations. This paper makes two contributions.
                 First, several complex-number representation schemes
                 are discussed. It is shown that the real-imaginary
                 alternate (RIA) scheme is the best among all
                 representation schemes and the prior designs of CMACs
                 based on the radix-(2j) Redundant Complex Number System
                 (RCNS) are not efficient with respect to hardware
                 complexity and processing speed. Second, digit-serial
                 CMAC architectures which can be pipelined at fine-grain
                 level to increase the throughput rate are designed
                 based on carry-save configuration.",
  acknowledgement = ack-nhfb,
  keywords =     "complex-number; digit-serial multiplier; redundant
                 arithmetic",
}


bibtype: misc
filename: fparith.bib
label: Chatterjee:1998:MMP
author: Siddhardtha Chatterjee
title: MPFUN++: a multiple precision floating point computation package in C++
pages: 211--??
year: 1998
bibdate: Thu Nov 25 10:08:42 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.25 10:08:42 ???
URL: http://www.cs.unc.edu/Research/HARPOON/mpfun++/
acknowledgement: ack-nhfb
howpublished: World Wide Web document.
rawauthor: Siddhardtha Chatterjee
rawtitle: {MPFUN++}: a multiple precision floating point computation package in {C++}
entry:
@Misc{Chatterjee:1998:MMP,
  author =       "Siddhardtha Chatterjee",
  title =        "{MPFUN++}: a multiple precision floating point
                 computation package in {C++}",
  howpublished = "World Wide Web document.",
  year =         "1998",
  bibdate =      "Thu Nov 25 10:08:42 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.unc.edu/Research/HARPOON/mpfun++/",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Chen:1998:PCL
author: Chichyang Chen and Chih-Huan Yang
booktitle: Proceedings International Conference on Computer Design: VLSI in Computers and Processors: ICCD '98
title: Pipelined computation of LNS addition / subtraction with very small lookup tables
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 292--297
year: 1998
bibdate: Sat Jul 16 16:14:38 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 16:14:38 MDT
acknowledgement: ack-nhfb
rawauthor: Chichyang Chen and Chih-Huan Yang
rawtitle: Pipelined computation of {LNS} addition\slash subtraction with very small lookup tables
rawbooktitle:
Proceedings International Conference on Computer Design: {VLSI} in Computers and Processors: {ICCD '98}

entry:
@InProceedings{Chen:1998:PCL,
  author =       "Chichyang Chen and Chih-Huan Yang",
  booktitle =    "Proceedings International Conference on Computer
                 Design: {VLSI} in Computers and Processors: {ICCD
                 '98}",
  title =        "Pipelined computation of {LNS} addition\slash
                 subtraction with very small lookup tables",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "292--297",
  year =         "1998",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 16:14:38 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Logarithmic number system (LNS) has the advantages of
                 regular data flow high speed, and high precision.
                 However, the development of LNS arithmetic is hindered
                 by the large size of the lookup tables used in LNS
                 addition/subtraction, since the size is \ldots{}",
}


bibtype: techreport
filename: fparith.bib
label: Chen:1998:VFP
author: Yirng-An Chen and Randal E. Bryant
title: Verification of floating-point adders
type: Report
number: CMU-CS-98-121
institution: Department of Computer Science, Carnegie-Mellon University
address: Pittsburgh, PA, USA
pages: 292--297
year: 1998
bibdate: Thu May 09 08:44:02 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.09 08:44:02 ???
acknowledgement: ack-nhfb
rawauthor: Yirng-An Chen and Randal E. Bryant
rawtitle: Verification of floating-point adders
entry:
@TechReport{Chen:1998:VFP,
  author =       "Yirng-An Chen and Randal E. Bryant",
  title =        "Verification of floating-point adders",
  type =         "Report",
  number =       "CMU-CS-98-121",
  institution =  "Department of Computer Science, Carnegie-Mellon
                 University",
  address =      "Pittsburgh, PA, USA",
  year =         "1998",
  bibdate =      "Thu May 09 08:44:02 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Cheon:1998:TEA
author: Jung Hee Cheon and S. M. Park and S. W. Park and D. Kim
title: Two efficient algorithms for arithmetic of elliptic curves using Frobenius map
journal: j-LECT-NOTES-COMP-SCI
volume: 1431
pages: 195--??
year: 1998
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Thu Oct 31 17:36:21 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.10.31 17:36:21 ???
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Jung Hee Cheon and S. M. Park and S. W. Park and D. Kim
rawtitle: Two efficient algorithms for arithmetic of elliptic curves using {Frobenius} map
entry:
@Article{Cheon:1998:TEA,
  author =       "Jung Hee Cheon and S. M. Park and S. W. Park and D.
                 Kim",
  title =        "Two efficient algorithms for arithmetic of elliptic
                 curves using {Frobenius} map",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1431",
  pages =        "195--??",
  year =         "1998",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Thu Oct 31 17:36:21 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Chren:1998:OHR
author: W. A. Chren
title: One-Hot Residue Coding for Low Delay Power Product CMOS Design
journal: j-IEEE-TRANS-CIRCUITS-SYST
volume: 45
number: 3
pages: 303--313
month: mar
monthnumber: 3
year: 1998
CODEN: ICSYBT
ISSN: 0098-4094 (print), 1558-1276 (electronic) OR 00984094 (print), 15581276 (electronic)
ISSNL: 0098-4094 OR 00984094
bibdate: Fri Jun 24 18:14:56 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.06.24 18:14:56 ???
fjournal: IEEE Transactions on Circuits and Systems
acknowledgement: ack-nhfb
rawauthor: W. A. Chren
rawtitle: One-Hot Residue Coding for Low Delay Power Product {CMOS} Design
entry:
@Article{Chren:1998:OHR,
  author =       "W. A. Chren",
  title =        "One-Hot Residue Coding for Low Delay Power Product
                 {CMOS} Design",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "45",
  number =       "3",
  pages =        "303--313",
  month =        mar,
  year =         "1998",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Fri Jun 24 18:14:56 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
}


bibtype: article
filename: fparith.bib
label: Citron:1998:AMM
author: Daniel Citron and Dror Feitelson and Larry Rudolph
title: Accelerating Multi-Media processing by Implementing Memoing in Multiplication and Division Units
journal: j-SIGPLAN
volume: 33
number: 11
pages: 252--261
month: nov
monthnumber: 11
year: 1998
CODEN: SINODQ
ISSN: 0362-1340 (print), 1523-2867 (print), 1558-1160 OR 03621340 (print), 15232867 (print), 15581160
ISSNL: 0362-1340 OR 03621340
bibdate: Sat May 1 15:51:26 MDT 1999
bibsource: http://www.acm.org/pubs/toc/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1999.05.01 15:51:26 MDT
URL: http://www.acm.org:80/pubs/citations/proceedings/asplos/291069/p252-citron/
fjournal: ACM SIGPLAN Notices
keywords: design; measurement; performance; theory
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J706
rawauthor: Daniel Citron and Dror Feitelson and Larry Rudolph
rawtitle: Accelerating Multi-Media processing by Implementing Memoing in Multiplication and Division Units
remark:
This paper shows how memoing of multiply and divide units in a 32-entry four-way set associative memo cache can produces cache hit ratios of 0.11 for floating-point multiply, and 0.16 for floating-point divide on the Perfect benchmarks. For SPEC95, the corresponding results are 0.20 and 0.17. For a multimedia benchmark, the figures are 0.39 and 0.47, and for integer multiply 0.59. Current architectures require 2 to 5 cycles for pipelined floating-point multiply (one result per clock, in the best case), but 22 to 40 cycles for floating-point division (not pipelined). Such a cache would require about 1KB of on-chip memory, which is currently feasible, since several architectures offer on-chip caches of up to 64KB, and could offer significant speedups for division.

subject:
bf H.5.1 Information Systems, INFORMATION INTERFACES AND PRESENTATION, Multimedia Information Systems. bf H.5.2 Information Systems, INFORMATION INTERFACES AND PRESENTATION, User Interfaces. bf B.3.2 Hardware, MEMORY STRUCTURES, Design Styles, Cache memories.

entry:
@Article{Citron:1998:AMM,
  author =       "Daniel Citron and Dror Feitelson and Larry Rudolph",
  title =        "Accelerating Multi-Media processing by Implementing
                 Memoing in Multiplication and Division Units",
  journal =      j-SIGPLAN,
  volume =       "33",
  number =       "11",
  pages =        "252--261",
  month =        nov,
  year =         "1998",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sat May 1 15:51:26 MDT 1999",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/asplos/291069/p252-citron/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "design; measurement; performance; theory",
  remark =       "This paper shows how memoing of multiply and divide
                 units in a 32-entry four-way set associative memo cache
                 can produces cache hit ratios of 0.11 for
                 floating-point multiply, and 0.16 for floating-point
                 divide on the Perfect benchmarks. For SPEC95, the
                 corresponding results are 0.20 and 0.17. For a
                 multimedia benchmark, the figures are 0.39 and 0.47,
                 and for integer multiply 0.59. Current architectures
                 require 2 to 5 cycles for pipelined floating-point
                 multiply (one result per clock, in the best case), but
                 22 to 40 cycles for floating-point division (not
                 pipelined). Such a cache would require about 1KB of
                 on-chip memory, which is currently feasible, since
                 several architectures offer on-chip caches of up to
                 64KB, and could offer significant speedups for
                 division.",
  subject =      "{\bf H.5.1} Information Systems, INFORMATION
                 INTERFACES AND PRESENTATION, Multimedia Information
                 Systems. {\bf H.5.2} Information Systems, INFORMATION
                 INTERFACES AND PRESENTATION, User Interfaces. {\bf
                 B.3.2} Hardware, MEMORY STRUCTURES, Design Styles,
                 Cache memories.",
}


bibtype: article
filename: fparith.bib
label: Collins:1998:PFB
author: Robert R. Collins
title: The Pentium F00F Bug
journal: j-DDJ
volume: 23
number: 5
pages: 62, 64--66
month: may
monthnumber: 5
year: 1998
CODEN: DDJOEB
ISSN: 1044-789X OR 1044789X
bibdate: Sat Jun 05 14:14:22 1999
bibtimestamp: 1999.06.05 14:14:22 ???
URL: http://www.ddj.com/ftp/1998/1998_05/f00fbug.txt; http://www.ddj.com/ftp/1998/1998_05/f00fbug.zip
fjournal: Dr. Dobb's Journal of Software Tools
acknowledgement: ack-nhfb
rawauthor: Robert R. Collins
rawtitle: The {Pentium F00F} Bug
bibsource:
https://www.math.utah.edu/pub/tex/bib/dr-dobbs.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
When x86 processors encounter an invalid instruction and the processor is supposed to generate an invalid opcode exception. If this mechanism fails and however and the program can bring the system down -- and that's what happens with the F00F bug. Additional resources include F00FBUG.TXT (listings) and f00fbug.zip (source code).

rawabstract:
When x86 processors encounter an invalid instruction and the processor is supposed to generate an invalid opcode exception. If this mechanism fails and however and the program can bring the system down -- and that's what happens with the F00F bug. Additional resources include F00FBUG.TXT (listings) and f00fbug.zip (source code).

entry:
@Article{Collins:1998:PFB,
  author =       "Robert R. Collins",
  title =        "The {Pentium F00F} Bug",
  journal =      j-DDJ,
  volume =       "23",
  number =       "5",
  pages =        "62, 64--66",
  month =        may,
  year =         "1998",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Sat Jun 05 14:14:22 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/dr-dobbs.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.ddj.com/ftp/1998/1998_05/f00fbug.txt;
                 http://www.ddj.com/ftp/1998/1998_05/f00fbug.zip",
  abstract =     "When x86 processors encounter an invalid instruction
                 and the processor is supposed to generate an invalid
                 opcode exception. If this mechanism fails and however
                 and the program can bring the system down -- and that's
                 what happens with the F00F bug. Additional resources
                 include F00FBUG.TXT (listings) and f00fbug.zip (source
                 code).",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}


bibtype: article
filename: fparith.bib
label: Cornea-Hasegan:1998:PIC
author: Marius Cornea-Hasegan
journal: j-INTEL-TECH-J
volume: Q2
pages: 11
year: 1998
bibdate: Fri Jun 01 06:02:08 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.06.01 06:02:08 ???
acknowledgement: ack-nhfb
rawauthor: Marius Cornea-Hasegan
title:
Proving the IEEE Correctness of Iterative Floating-Point Square Root, Divide, and Remainder Algorithms

URL:
http://developer.intel.com/technology/itj/q21998/articles/art_3.htm; http://developer.intel.com/technology/itj/q21998/pdf/ieee.pdf

rawtitle:
Proving the {IEEE} Correctness of Iterative Floating-Point Square Root, Divide, and Remainder Algorithms

entry:
@Article{Cornea-Hasegan:1998:PIC,
  author =       "Marius Cornea-Hasegan",
  title =        "Proving the {IEEE} Correctness of Iterative
                 Floating-Point Square Root, Divide, and Remainder
                 Algorithms",
  journal =      j-INTEL-TECH-J,
  volume =       "Q2",
  pages =        "11",
  year =         "1998",
  bibdate =      "Fri Jun 01 06:02:08 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://developer.intel.com/technology/itj/q21998/articles/art_3.htm;
                 http://developer.intel.com/technology/itj/q21998/pdf/ieee.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Crenshaw:1998:ISR
author: Jack W. Crenshaw
title: Integer Square Roots
journal: j-EMBED-SYS-PROG
volume: 11
number: 2
pages: 15--32
month: feb
monthnumber: 2
year: 1998
CODEN: EYPRE4
ISSN: 1040-3272 OR 10403272
bibdate: Fri Nov 28 16:31:58 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 16:31:58 ???
URL: http://www.embedded.com/98/9802fe2.htm
fjournal: Embedded Systems Programming
acknowledgement: ack-mfc
rawauthor: Jack W. Crenshaw
rawtitle: Integer Square Roots
entry:
@Article{Crenshaw:1998:ISR,
  author =       "Jack W. Crenshaw",
  title =        "Integer Square Roots",
  journal =      j-EMBED-SYS-PROG,
  volume =       "11",
  number =       "2",
  pages =        "15--32",
  month =        feb,
  year =         "1998",
  CODEN =        "EYPRE4",
  ISSN =         "1040-3272",
  bibdate =      "Fri Nov 28 16:31:58 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.embedded.com/98/9802fe2.htm",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  fjournal =     "Embedded Systems Programming",
}


bibtype: techreport
filename: fparith.bib
label: Darcy:1998:APE
author: Joseph D. Darcy and William Kahan
title: Analysis of em Proposal for Extension to Java Floating Point Semantics, Revision 1
institution: Java Grande Numerics Working Group
pages: 18
day: 7
month: aug
monthnumber: 8
year: 1998
bibdate: Mon May 06 09:08:27 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.06 09:08:27 ???
URL: http://www.sonic.net/~jddarcy/Research/jgrande.pdf
acknowledgement: ack-nhfb
rawauthor: Joseph D. Darcy and William Kahan
rawtitle: Analysis of {{\em Proposal for Extension to Java Floating Point Semantics, Revision 1}}
entry:
@TechReport{Darcy:1998:APE,
  author =       "Joseph D. Darcy and William Kahan",
  title =        "Analysis of {{\em Proposal for Extension to Java
                 Floating Point Semantics, Revision 1}}",
  institution =  "{Java Grande Numerics Working Group}",
  pages =        "18",
  day =          "7",
  month =        aug,
  year =         "1998",
  bibdate =      "Mon May 06 09:08:27 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sonic.net/~jddarcy/Research/jgrande.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: mastersthesis
filename: fparith.bib
label: Darcy:1998:BAI
author: Joseph D. Darcy
title: Borneo 1.0: adding IEEE 754 floating point support to Java
type: Master of Science, Plan II
school: University of California, Berkeley, Dept. of Electrical Engineering and Computer Sciences
address: Berkeley, CA, USA
pages: 131
year: 1998
LCCN: T7.49.1998 D27
bibdate: Mon May 06 09:01:22 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.06 09:01:22 ???
URL: http://www.sonic.net/~jddarcy/Borneo/borneo.pdf
acknowledgement: ack-nhfb
rawauthor: Joseph D. Darcy
rawtitle: {Borneo 1.0}: adding {IEEE 754} floating point support to {Java}
entry:
@MastersThesis{Darcy:1998:BAI,
  author =       "Joseph D. Darcy",
  title =        "{Borneo 1.0}: adding {IEEE 754} floating point support
                 to {Java}",
  type =         "{Master of Science, Plan II}",
  school =       "University of California, Berkeley, Dept. of
                 Electrical Engineering and Computer Sciences",
  address =      "Berkeley, CA, USA",
  pages =        "131",
  year =         "1998",
  LCCN =         "T7.49.1998 D27",
  bibdate =      "Mon May 06 09:01:22 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sonic.net/~jddarcy/Borneo/borneo.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Darcy:1998:EJF
author: Joseph D. Darcy
title: Evolving Java's Floating Point Support: The Good, The Bad, and the Ugly
crossref: MacKay:1998:PCT
pages: ??--??
year: 1998
bibdate: Mon May 06 09:11:13 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.06 09:11:13 ???
note: 31 slides.
URL: http://www.sonic.net/~jddarcy/Research/cascon.pdf
acknowledgement: ack-nhfb
rawauthor: Joseph D. Darcy
rawnote: 31 slides.
rawtitle: Evolving {Java}'s Floating Point Support: The Good, The Bad, and the Ugly
entry:
@InProceedings{Darcy:1998:EJF,
  author =       "Joseph D. Darcy",
  title =        "Evolving {Java}'s Floating Point Support: The Good,
                 The Bad, and the Ugly",
  crossref =     "MacKay:1998:PCT",
  pages =        "??--??",
  year =         "1998",
  bibdate =      "Mon May 06 09:11:13 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "31 slides.",
  URL =          "http://www.sonic.net/~jddarcy/Research/cascon.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: fparith.bib
label: Darcy:1998:WRI
author: Joseph D. Darcy
title: Writing robust IEEE recommended functions in ``100 Pure JavaTM ''
type: Report
number: UCB/CSD-98-1009
institution: University of California, Berkeley. Computer Science Division
address: Berkeley, CA, USA
pages: ??--??
month: aug
monthnumber: 8
year: 1998
bibdate: Mon May 06 09:03:35 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.06 09:03:35 ???
URL: http://sunsite.berkeley.edu/Dienst/UI/2.0/Describe/ncstrl.ucb/CSD-98-1009
acknowledgement: ack-nhfb
rawauthor: Joseph D. Darcy
rawtitle: Writing robust {IEEE} recommended functions in ``100 Pure {Java\TM}''
entry:
@TechReport{Darcy:1998:WRI,
  author =       "Joseph D. Darcy",
  title =        "Writing robust {IEEE} recommended functions in ``100
                 Pure {Java\TM}''",
  type =         "Report",
  number =       "UCB/CSD-98-1009",
  institution =  "University of California, Berkeley. Computer Science
                 Division",
  address =      "Berkeley, CA, USA",
  month =        aug,
  year =         "1998",
  bibdate =      "Mon May 06 09:03:35 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://sunsite.berkeley.edu/Dienst/UI/2.0/Describe/ncstrl.ucb/CSD-98-1009",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Daumas:1998:ELM
author: Marc Daumas
booktitle: Architecture and Arithmetic Support for Multimedia, Dagstuhl, Germany
title: Expansions: lightweight multiple precision arithmetic
pages: 14--??
year: 1998
bibdate: Wed Nov 24 07:59:30 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.24 07:59:30 ???
acknowledgement: ack-nhfb
rawauthor: Marc Daumas
rawbooktitle: Architecture and Arithmetic Support for Multimedia, Dagstuhl, Germany
rawtitle: Expansions: lightweight multiple precision arithmetic
entry:
@InProceedings{Daumas:1998:ELM,
  author =       "Marc Daumas",
  editor =       "????",
  booktitle =    "Architecture and Arithmetic Support for Multimedia,
                 Dagstuhl, Germany",
  title =        "Expansions: lightweight multiple precision
                 arithmetic",
  publisher =    "????",
  address =      "????",
  pages =        "14--??",
  year =         "1998",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Wed Nov 24 07:59:30 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Dimitrov:1998:AME
author: V. S. Dimitrov and G. A. Jullien and W. C. Miller
title: An algorithm for modular exponentiation
journal: j-INFO-PROC-LETT
volume: 66
number: 3
pages: 155--159
day: 15
month: may
monthnumber: 5
year: 1998
CODEN: IFPLAT
ISSN: 0020-0190 (print), 1872-6119 (electronic) OR 00200190 (print), 18726119 (electronic)
ISSNL: 0020-0190 OR 00200190
bibdate: Sat Nov 7 17:55:59 MST 1998
bibtimestamp: 1998.11.07 17:55:59 MST
fjournal: Information Processing Letters
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00200190
rawauthor: V. S. Dimitrov and G. A. Jullien and W. C. Miller
rawtitle: An algorithm for modular exponentiation
entry:
@Article{Dimitrov:1998:AME,
  author =       "V. S. Dimitrov and G. A. Jullien and W. C. Miller",
  title =        "An algorithm for modular exponentiation",
  journal =      j-INFO-PROC-LETT,
  volume =       "66",
  number =       "3",
  pages =        "155--159",
  day =          "15",
  month =        may,
  year =         "1998",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  bibdate =      "Sat Nov 7 17:55:59 MST 1998",
  bibsource =    "http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
}


bibtype: article
filename: fparith.bib
label: Dimitrov:1998:FRR
author: V. S. Dimitrov and G. A. Jullien and W. C. Miller
title: A fast and robust RNS algorithm for evaluating signs of determinants
journal: j-COMPUT-MATH-APPL
volume: 35
number: 8
pages: 9--14
month: apr
monthnumber: 4
year: 1998
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 21:48:48 MST 2017
bibtimestamp: 2017.03.01 21:48:48 MST
URL: http://www.sciencedirect.com/science/article/pii/S0898122198000418
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: V. S. Dimitrov and G. A. Jullien and W. C. Miller
rawtitle: A fast and robust {RNS} algorithm for evaluating signs of determinants
entry:
@Article{Dimitrov:1998:FRR,
  author =       "V. S. Dimitrov and G. A. Jullien and W. C. Miller",
  title =        "A fast and robust {RNS} algorithm for evaluating signs
                 of determinants",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "35",
  number =       "8",
  pages =        "9--14",
  month =        apr,
  year =         "1998",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:48:48 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122198000418",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: article
filename: fparith.bib
label: Dimitrov:1998:RNS
author: V. S. Dimitrov and G. A. Jullien and W. C. Miller
title: A residue number system implementation of real orthogonal transforms
journal: j-IEEE-TRANS-SIG-PROC
volume: 46
number: 3
pages: 563--570
month: mar
monthnumber: 3
year: 1998
CODEN: ITPRED
DOI: https://doi.org/10.1109/78.661325
ISSN: 1053-587X (print), 1941-0476 (electronic) OR 1053587X (print), 19410476 (electronic)
ISSNL: 1053-587X OR 1053587X
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
URL: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=14431
fjournal: IEEE Transactions on Signal Processing
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78
rawauthor: V. S. Dimitrov and G. A. Jullien and W. C. Miller
rawtitle: A residue number system implementation of real orthogonal transforms
entry:
@Article{Dimitrov:1998:RNS,
  author =       "V. S. Dimitrov and G. A. Jullien and W. C. Miller",
  title =        "A residue number system implementation of real
                 orthogonal transforms",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "46",
  number =       "3",
  pages =        "563--570",
  month =        mar,
  year =         "1998",
  CODEN =        "ITPRED",
  DOI =          "https://doi.org/10.1109/78.661325",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=14431",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  keywords =     "residue arithmetic; residue number system",
  summary =      "Previous work has focused on performing residue
                 computations that are quantized within a dense ring of
                 integers in the real domain. The aims of this paper are
                 to provide an efficient algorithm for the approximation
                 of real input signals, with \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Drolet:1998:NRE
author: G. Drolet
journal: j-IEEE-TRANS-COMPUT
volume: 47
number: 9
pages: 938--946
month: sep
monthnumber: 9
year: 1998
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.713313
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 09:35:56 MDT 2011
bibtimestamp: 2011.07.06 09:35:56 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=713313
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: G. Drolet
title:
A new representation of elements of finite fields $ mathrm GF(2^m) $ yielding small complexity arithmetic circuits

rawtitle:
A new representation of elements of finite fields {$ \mathrm {GF}(2^m) $} yielding small complexity arithmetic circuits

entry:
@Article{Drolet:1998:NRE,
  author =       "G. Drolet",
  title =        "A new representation of elements of finite fields {$
                 \mathrm {GF}(2^m) $} yielding small complexity
                 arithmetic circuits",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "9",
  pages =        "938--946",
  month =        sep,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.713313",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 09:35:56 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=713313",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Drolshagen:1998:RNA
author: A. Drolshagen and C. C. Sekhar and W. Anheier
booktitle: Eleventh International Conference on VLSI Design, 1998. Proceedings
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 122--127
year: 1998
DOI: https://doi.org/10.1109/ICVD.1998.646589
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. Drolshagen and C. C. Sekhar and W. Anheier
rawbooktitle: Eleventh International Conference on {VLSI} Design, 1998. Proceedings
title:
A residue number arithmetic based circuit for pipelined computation of autocorrelation coefficients of speech signal

rawtitle:
A residue number arithmetic based circuit for pipelined computation of autocorrelation coefficients of speech signal

entry:
@InProceedings{Drolshagen:1998:RNA,
  author =       "A. Drolshagen and C. C. Sekhar and W. Anheier",
  booktitle =    "Eleventh International Conference on {VLSI} Design,
                 1998. Proceedings",
  title =        "A residue number arithmetic based circuit for
                 pipelined computation of autocorrelation coefficients
                 of speech signal",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "122--127",
  year =         "1998",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ICVD.1998.646589",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "This paper presents a new design for module
                 multipliers suitable for moduli that are not
                 necessarily prime. The design avoids the need for
                 building special purpose look-up tables. An RNS
                 arithmetic based autocorrelator circuit that uses a
                 large \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Dunay:1998:DFP
author: Rezso Dunay and Istvan Kollar and Bernard Widrow
title: Dithering for Floating-Point Number Representation
crossref: Holub:1998:ILW
pages: 0--1--9--12
year: 1998
bibdate: Thu Sep 11 07:08:34 2003
bibsource: http://measure.feld.cvut.cz/dithering98/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.09.11 07:08:34 ???
keywords: digital signal processor; Dither; DSP; floating-point; quantization; roundoff
acknowledgement: ack-nhfb
rawauthor: Rezso Dunay and Istvan Kollar and Bernard Widrow
rawtitle: Dithering for Floating-Point Number Representation
URL:
http://citeseer.nj.nec.com/cache/papers/cs/1878/ftp:zSzzSzftp.mit.bme.huzSzpubzSzstaffzSzkollarzSzpaperszSzditherws.ps.gz/dunay98dithering.ps.gz; http://citeseer.nj.nec.com/dunay98dithering.html

abstract:
Dithering is widely used for decreasing the bias in fixed-point quantization and rounding. Since floating-point digital signal processors (DSP's) and floating-point arithmetic are becoming widely used, it is timely to investigate the necessity and possibilities of dithering for floating-point numbers. The paper introduces a simple model of dithers for floating-point, and discusses its practical use.

rawabstract:
Dithering is widely used for decreasing the bias in fixed-point quantization and rounding. Since floating-point digital signal processors (DSP's) and floating-point arithmetic are becoming widely used, it is timely to investigate the necessity and possibilities of dithering for floating-point numbers. The paper introduces a simple model of dithers for floating-point, and discusses its practical use.

entry:
@InProceedings{Dunay:1998:DFP,
  author =       "Rezso Dunay and Istvan Kollar and Bernard Widrow",
  title =        "Dithering for Floating-Point Number Representation",
  crossref =     "Holub:1998:ILW",
  pages =        "0--1--9--12",
  year =         "1998",
  bibdate =      "Thu Sep 11 07:08:34 2003",
  bibsource =    "http://measure.feld.cvut.cz/dithering98/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://citeseer.nj.nec.com/cache/papers/cs/1878/ftp:zSzzSzftp.mit.bme.huzSzpubzSzstaffzSzkollarzSzpaperszSzditherws.ps.gz/dunay98dithering.ps.gz;
                 http://citeseer.nj.nec.com/dunay98dithering.html",
  abstract =     "Dithering is widely used for decreasing the bias in
                 fixed-point quantization and rounding. Since
                 floating-point digital signal processors (DSP's) and
                 floating-point arithmetic are becoming widely used, it
                 is timely to investigate the necessity and
                 possibilities of dithering for floating-point numbers.
                 The paper introduces a simple model of dithers for
                 floating-point, and discusses its practical use.",
  acknowledgement = ack-nhfb,
  keywords =     "digital signal processor; Dither; DSP; floating-point;
                 quantization; roundoff",
}


bibtype: techreport
filename: fparith.bib
label: ECDG:1998:IER
author: European Commission Directorate General II
title: The Introduction of the Euro and the Rounding of Currency Amounts
type: II/28/99-EN Euro Papers
number: 22
institution: European Commission
pages: 32
month: mar
monthnumber: 3
year: 1998
bibdate: Wed Nov 24 12:56:20 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.24 12:56:20 ???
note: DGII/C-4-SP(99) European Commission.
acknowledgement: ack-nhfb
rawauthor: {European Commission Directorate General II}
rawnote: DGII/C-4-SP(99) European Commission.
rawtitle: The Introduction of the Euro and the Rounding of Currency Amounts
entry:
@TechReport{ECDG:1998:IER,
  author =       "{European Commission Directorate General II}",
  title =        "The Introduction of the Euro and the Rounding of
                 Currency Amounts",
  type =         "{II/28/99-EN Euro Papers}",
  number =       "22",
  institution =  "European Commission",
  pages =        "32",
  month =        mar,
  year =         "1998",
  bibdate =      "Wed Nov 24 12:56:20 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "DGII/C-4-SP(99) European Commission.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Emiris:1998:MAL
author: Ioannis Z. Emiris and Victor Y. Pan and Yanqiang Yu
title: Modular arithmetic for linear algebra computations in the real field
journal: j-J-SYMBOLIC-COMP
volume: 26
number: 1
pages: 71--87
month: jul
monthnumber: 7
year: 1998
CODEN: JSYCEH
DOI: https://doi.org/10.1006/jsco.1998.0201
ISSN: 0747-7171 (print), 1095-855X (electronic) OR 07477171 (print), 1095855X (electronic)
ISSNL: 0747-7171 OR 07477171
MRclass: 15-XX (68Q40)
MRnumber: 1 633 585
bibdate: Tue Nov 10 06:41:20 MST 1998
bibtimestamp: 1998.11.10 06:41:20 MST
fjournal: Journal of Symbolic Computation
keywords: accurate floating-point summation; floating-point arithmetic
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/07477171/
rawauthor: Ioannis Z. Emiris and Victor Y. Pan and Yanqiang Yu
rawtitle: Modular arithmetic for linear algebra computations in the real field
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/jsymcomp.bib

entry:
@Article{Emiris:1998:MAL,
  author =       "Ioannis Z. Emiris and Victor Y. Pan and Yanqiang Yu",
  title =        "Modular arithmetic for linear algebra computations in
                 the real field",
  journal =      j-J-SYMBOLIC-COMP,
  volume =       "26",
  number =       "1",
  pages =        "71--87",
  month =        jul,
  year =         "1998",
  CODEN =        "JSYCEH",
  DOI =          "https://doi.org/10.1006/jsco.1998.0201",
  ISSN =         "0747-7171 (print), 1095-855X (electronic)",
  ISSN-L =       "0747-7171",
  MRclass =      "15-XX (68Q40)",
  MRnumber =     "1 633 585",
  bibdate =      "Tue Nov 10 06:41:20 MST 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jsymcomp.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Symbolic Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07477171/",
  keywords =     "accurate floating-point summation; floating-point
                 arithmetic",
}


bibtype: inproceedings
filename: fparith.bib
label: Ercegovac:1998:BSO
author: M. Ercegovac and D. Kirovski and G. Mustafa and M. Potkonjak
title: Behavioral synthesis optimization using multiple precision arithmetic
volume: 5
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 3113--3116
year: 1998
bibdate: Sat Jul 16 16:53:44 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 16:53:44 MDT
acknowledgement: ack-nhfb
rawauthor: M. Ercegovac and D. Kirovski and G. Mustafa and M. Potkonjak
rawtitle: Behavioral synthesis optimization using multiple precision arithmetic
booktitle:
Proceedings of the 1998 IEEE International Conference on Acoustics, Speech, and Signal Processing, 1998: ICASSP '98, 12--15 May 1998

rawbooktitle:
Proceedings of the 1998 {IEEE} International Conference on Acoustics, Speech, and Signal Processing, 1998: {ICASSP '98}, 12--15 May 1998

entry:
@InProceedings{Ercegovac:1998:BSO,
  author =       "M. Ercegovac and D. Kirovski and G. Mustafa and M.
                 Potkonjak",
  booktitle =    "Proceedings of the 1998 {IEEE} International
                 Conference on Acoustics, Speech, and Signal Processing,
                 1998: {ICASSP '98}, 12--15 May 1998",
  title =        "Behavioral synthesis optimization using multiple
                 precision arithmetic",
  volume =       "5",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "3113--3116",
  year =         "1998",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 16:53:44 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Modern image and video processing applications are
                 characterized by a unique combination of arithmetic and
                 computational features: fixed point arithmetic, a
                 variety of short data types, high degree of
                 instruction-level parallelism, strict timing \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Fiore:1998:LR
author: P. D. Fiore
booktitle: IEEE Workshop on Signal Processing Systems, 1988: SIPS 98
title: Lazy rounding
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 449--458
year: 1998
bibdate: Sat Jul 16 11:25:04 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:04 MDT
acknowledgement: ack-nhfb
rawauthor: P. D. Fiore
rawbooktitle: {IEEE} Workshop on Signal Processing Systems, 1988: {SIPS 98}
rawtitle: Lazy rounding
entry:
@InProceedings{Fiore:1998:LR,
  author =       "P. D. Fiore",
  booktitle =    "{IEEE} Workshop on Signal Processing Systems, 1988:
                 {SIPS 98}",
  title =        "Lazy rounding",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "449--458",
  year =         "1998",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:04 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Intermediate results in digital signal processing
                 (DSP) hardware frequently must be truncated or rounded
                 to maintain reasonable wordlengths. Noise and bias are
                 introduced into the signal due to these operations. For
                 the addition operation, we \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Garcia:1998:PHC
author: A. Garcia and U. Meyer-Baese and F. Taylor
title: Pipelined Hogenauer CIC filters using field-programmable logic and residue number system
volume: 5
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 3085--3088
year: 1998
DOI: https://doi.org/10.1109/ICASSP.1998.678178
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. Garcia and U. Meyer-Baese and F. Taylor
rawtitle: Pipelined Hogenauer {CIC} filters using field-programmable logic and residue number system
booktitle:
Proceedings of the 1998 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 98, 12--15 May 1998

rawbooktitle:
Proceedings of the 1998 {IEEE} International Conference on Acoustics, Speech, and Signal Processing, {ICASSP 98}, 12--15 May 1998

entry:
@InProceedings{Garcia:1998:PHC,
  author =       "A. Garcia and U. Meyer-Baese and F. Taylor",
  booktitle =    "Proceedings of the 1998 {IEEE} International
                 Conference on Acoustics, Speech, and Signal Processing,
                 {ICASSP 98}, 12--15 May 1998",
  title =        "Pipelined Hogenauer {CIC} filters using
                 field-programmable logic and residue number system",
  volume =       "5",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "3085--3088",
  year =         "1998",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ICASSP.1998.678178",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Field-programmable logic (FPL) is on the verge of
                 revolutionizing digital signal processing (DSP) in the
                 manner that programmable DSP microprocessors did nearly
                 two decades ago. While FPL densities and performance
                 have steadily improved to the point \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Gordon:1998:CLF
author: Robert Gordon
title: A Calculated Look at Fixed-Point Arithmetic
journal: j-EMBED-SYS-PROG
volume: 11
number: 4
pages: 72--78
month: apr
monthnumber: 4
year: 1998
CODEN: EYPRE4
ISSN: 1040-3272 OR 10403272
bibdate: Fri Nov 28 16:54:07 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 16:54:07 ???
fjournal: Embedded Systems Programming
acknowledgement: ack-mfc
rawauthor: Robert Gordon
rawtitle: A Calculated Look at Fixed-Point Arithmetic
entry:
@Article{Gordon:1998:CLF,
  author =       "Robert Gordon",
  title =        "A Calculated Look at Fixed-Point Arithmetic",
  journal =      j-EMBED-SYS-PROG,
  volume =       "11",
  number =       "4",
  pages =        "72--78",
  month =        apr,
  year =         "1998",
  CODEN =        "EYPRE4",
  ISSN =         "1040-3272",
  bibdate =      "Fri Nov 28 16:54:07 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  fjournal =     "Embedded Systems Programming",
}


bibtype: phdthesis
filename: fparith.bib
label: Grisoni-Busca:1998:LPF
author: Louisa Grisoni-Busca
title: Low power floating point A/D converters for audio signals
type: Dissertation
school: Univ. Neuchatel
address: Neuchatel, Switzerland
pages: xii + 136
year: 1998
bibdate: Thu May 09 09:08:18 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.09 09:08:18 ???
acknowledgement: ack-nhfb
rawauthor: Louisa Grisoni-Busca
rawtitle: Low power floating point {A/D} converters for audio signals
entry:
@PhdThesis{Grisoni-Busca:1998:LPF,
  author =       "Louisa Grisoni-Busca",
  title =        "Low power floating point {A/D} converters for audio
                 signals",
  type =         "Dissertation",
  school =       "Univ. Neuch{\^a}tel",
  address =      "Neuch{\^a}tel, Switzerland",
  pages =        "xii + 136",
  year =         "1998",
  bibdate =      "Thu May 09 09:08:18 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: misc
filename: fparith.bib
label: Grushin:1998:CMA
author: A. I. Grushin and E. S. Vlasenko
pages: xii + 136
day: 24
month: may
monthnumber: 5
year: 1998
bibdate: Fri Nov 28 15:34:04 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 15:34:04 ???
note: U.S. Patent No. 5,732,007.
acknowledgement: ack-nhfb
rawauthor: A. I. Grushin and E. S. Vlasenko
rawnote: U.S. Patent No. 5,732,007.
title:
Computer methods and apparatus for eliminating leading non-significant digits in floating point computations

rawtitle:
Computer methods and apparatus for eliminating leading non-significant digits in floating point computations

entry:
@Misc{Grushin:1998:CMA,
  author =       "A. I. Grushin and E. S. Vlasenko",
  title =        "Computer methods and apparatus for eliminating leading
                 non-significant digits in floating point computations",
  day =          "24",
  month =        may,
  year =         "1998",
  bibdate =      "Fri Nov 28 15:34:04 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "U.S. Patent No. 5,732,007.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Guo:1998:SAI
author: Jyh-Huei Guo and Chin-Liang Wang
journal: j-IEEE-TRANS-COMPUT
volume: 47
number: 10
pages: 1161--1167
month: oct
monthnumber: 10
year: 1998
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.729800
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 09:35:56 MDT 2011
bibtimestamp: 2011.07.06 09:35:56 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=729800
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Jyh-Huei Guo and Chin-Liang Wang
title:
Systolic array implementation of Euclid's algorithm for inversion and division in $ mathrm GF(2^m) $

rawtitle:
Systolic array implementation of {Euclid}'s algorithm for inversion and division in {$ \mathrm {GF}(2^m) $}

entry:
@Article{Guo:1998:SAI,
  author =       "Jyh-Huei Guo and Chin-Liang Wang",
  title =        "Systolic array implementation of {Euclid}'s algorithm
                 for inversion and division in {$ \mathrm {GF}(2^m) $}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "10",
  pages =        "1161--1167",
  month =        oct,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.729800",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 09:35:56 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=729800",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Hars:1998:FCC
author: L. Hars
title: Fast Calculation of Common Mathematical Functions with Floating-Point DSPs
crossref: Anonymous:1998:PNI
pages: 521--525
year: 1998
bibdate: Sat Jun 02 08:32:02 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.06.02 08:32:02 ???
acknowledgement: ack-nhfb
rawauthor: L. Hars
rawtitle: Fast Calculation of Common Mathematical Functions with Floating-Point {DSPs}
entry:
@InProceedings{Hars:1998:FCC,
  author =       "L. Hars",
  title =        "Fast Calculation of Common Mathematical Functions with
                 Floating-Point {DSPs}",
  crossref =     "Anonymous:1998:PNI",
  pages =        "521--525",
  year =         "1998",
  bibdate =      "Sat Jun 02 08:32:02 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Heckmann:1998:ABI
author: Reinhold Heckmann
title: The Appearance of Big Integers in Exact Real Arithmetic Based on Linear Fractional Transformations
journal: j-LECT-NOTES-COMP-SCI
volume: 1378
pages: 172--??
year: 1998
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Tue Feb 5 11:51:46 MST 2002
bibtimestamp: 2002.02.05 11:51:46 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Reinhold Heckmann
rawtitle: The Appearance of Big Integers in Exact Real Arithmetic Based on Linear Fractional Transformations
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t1378.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/1378/13780172.htm; http://link.springer-ny.com/link/service/series/0558/papers/1378/13780172.pdf

entry:
@Article{Heckmann:1998:ABI,
  author =       "Reinhold Heckmann",
  title =        "The Appearance of Big Integers in Exact Real
                 Arithmetic Based on Linear Fractional Transformations",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1378",
  pages =        "172--??",
  year =         "1998",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Feb 5 11:51:46 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1378.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1378/13780172.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/1378/13780172.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Hill:1998:FDP
author: Theodore P. Hill
title: The First Digit Phenomenon
journal: j-AM-SCI
volume: 86
number: 4
pages: 358--363
month: jul
monthnumber: 7
year: 1998
CODEN: AMSCAC
DOI: https://doi.org/10.1511/1998.4.358
ISSN: 0003-0996 (print), 1545-2786 (electronic) OR 00030996 (print), 15452786 (electronic)
ISSNL: 0003-0996 OR 00030996
bibdate: Sat Dec 10 11:54:49 2011
bibtimestamp: 2011.12.10 11:54:49 ???
fjournal: American Scientist
keywords: Benford's Law; Law of Anomalous Numbers; Zipf's Law
acknowledgement: ack-nhfb
journalURL: http://www.americanscientist.org/issues/past.aspx
rawauthor: Theodore P. Hill
rawtitle: The First Digit Phenomenon
URL:
http://people.math.gatech.edu/~hill/publications/PAPER%20PDFS/TheFirstDigitPhenomenonAmericanScientist1996.pdf; http://www.math.gatech.edu/~hill/publications/cv.dir/1st-dig.pdf

abstract:
A century ago, Simon Newcomb observed an unexpected pattern in the first digits of logarithm tables: The digit $1$ is significantly more likely to occur than $2$, $2$ than $3$, and so on. More than a half-century later, Frank Benford rediscovered the first-digit phenomenon and found that it applied to many tables of numerical data, including the stock market, census statistics and accounting figures. New mathematical insights establish the empirical law developed by Newcomb and Benford as part of modern probability theory, and recent applications include testing of mathematical models, design of computers and detection of fraud in accounting.

rawabstract:
A century ago, Simon Newcomb observed an unexpected pattern in the first digits of logarithm tables: The digit $1$ is significantly more likely to occur than $2$, $2$ than $3$, and so on. More than a half-century later, Frank Benford rediscovered the first-digit phenomenon and found that it applied to many tables of numerical data, including the stock market, census statistics and accounting figures. New mathematical insights establish the empirical law developed by Newcomb and Benford as part of modern probability theory, and recent applications include testing of mathematical models, design of computers and detection of fraud in accounting.

entry:
@Article{Hill:1998:FDP,
  author =       "Theodore P. Hill",
  title =        "The First Digit Phenomenon",
  journal =      j-AM-SCI,
  volume =       "86",
  number =       "4",
  pages =        "358--363",
  month =        jul # "\slash " # aug,
  year =         "1998",
  CODEN =        "AMSCAC",
  DOI =          "https://doi.org/10.1511/1998.4.358",
  ISSN =         "0003-0996 (print), 1545-2786 (electronic)",
  ISSN-L =       "0003-0996",
  bibdate =      "Sat Dec 10 11:54:49 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://people.math.gatech.edu/~hill/publications/PAPER%20PDFS/TheFirstDigitPhenomenonAmericanScientist1996.pdf;
                 http://www.math.gatech.edu/~hill/publications/cv.dir/1st-dig.pdf",
  abstract =     "A century ago, Simon Newcomb observed an unexpected
                 pattern in the first digits of logarithm tables: The
                 digit $1$ is significantly more likely to occur than
                 $2$, $2$ than $3$, and so on. More than a half-century
                 later, Frank Benford rediscovered the first-digit
                 phenomenon and found that it applied to many tables of
                 numerical data, including the stock market, census
                 statistics and accounting figures. New mathematical
                 insights establish the empirical law developed by
                 Newcomb and Benford as part of modern probability
                 theory, and recent applications include testing of
                 mathematical models, design of computers and detection
                 of fraud in accounting.",
  acknowledgement = ack-nhfb,
  fjournal =     "American Scientist",
  journal-URL =  "http://www.americanscientist.org/issues/past.aspx",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}


bibtype: inproceedings
filename: fparith.bib
label: Huertgen:1998:TFP
author: F. Huertgen and H. Meyr and M. Willems
crossref: Anonymous:1998:PNI
pages: 630--634
year: 1998
bibdate: Sat Jun 02 08:29:37 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.06.02 08:29:37 ???
acknowledgement: ack-nhfb
rawauthor: F. Huertgen and H. Meyr and M. Willems
title:
Transformation of Floating-Point into Fixed-Point Algorithms by Interpolation Applying a Statistical Approach

rawtitle:
Transformation of Floating-Point into Fixed-Point Algorithms by Interpolation Applying a Statistical Approach

entry:
@InProceedings{Huertgen:1998:TFP,
  author =       "F. Huertgen and H. Meyr and M. Willems",
  title =        "Transformation of Floating-Point into Fixed-Point
                 Algorithms by Interpolation Applying a Statistical
                 Approach",
  crossref =     "Anonymous:1998:PNI",
  pages =        "630--634",
  year =         "1998",
  bibdate =      "Sat Jun 02 08:29:37 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Hussein:1998:LPA
author: A. E. Hussein and M. A. Hasan and M. I. Elmasry
booktitle: IEEE Canadian Conference on Electrical and Computer Engineering, 24--28 May 1998
title: A low power algorithm for division in residue number system (RNS)
volume: 1
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 205--208
year: 1998
DOI: https://doi.org/10.1109/CCECE.1998.682718
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. E. Hussein and M. A. Hasan and M. I. Elmasry
rawbooktitle: {IEEE} Canadian Conference on Electrical and Computer Engineering, 24--28 May 1998
rawtitle: A low power algorithm for division in residue number system ({RNS})
entry:
@InProceedings{Hussein:1998:LPA,
  author =       "A. E. Hussein and M. A. Hasan and M. I. Elmasry",
  booktitle =    "{IEEE} Canadian Conference on Electrical and Computer
                 Engineering, 24--28 May 1998",
  title =        "A low power algorithm for division in residue number
                 system ({RNS})",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "205--208",
  year =         "1998",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/CCECE.1998.682718",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A new algorithm for computing division in residue
                 number system (RNS) is presented. The algorithm imposes
                 no restrictions on the dividend and the divisor (except
                 zero divisor), and requires no initial quotient
                 estimation. It eliminates the need for \ldots{}",
}


bibtype: incollection
filename: fparith.bib
label: IBM:1998:DAI
author: IBM
booktitle: ESA / 390 Principles of Operation
title: Decimal Arithmetic Instructions
chapter: 8
publisher: pub-IBM
address: pub-IBM:adr
pages: 205--208
year: 1998
bibdate: Fri Nov 28 17:57:22 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 17:57:22 ???
keywords: decimal floating-point arithmetic
acknowledgement: ack-mfc
rawauthor: {IBM}
rawbooktitle: {ESA\slash 390} Principles of Operation
rawtitle: Decimal Arithmetic Instructions
abstract:
The decimal instructions of this chapter perform arithmetic and editing operations on decimal data. Additional operations on decimal data are provided by several of the instructions in Chapter 7, ``General Instructions''. Decimal operands always reside in storage, and all decimal instructions use the SS instruction format. Decimal operands occupy storage fields that can start on any byte boundary.

rawabstract:
The decimal instructions of this chapter perform arithmetic and editing operations on decimal data. Additional operations on decimal data are provided by several of the instructions in Chapter 7, ``General Instructions''. Decimal operands always reside in storage, and all decimal instructions use the SS instruction format. Decimal operands occupy storage fields that can start on any byte boundary.

entry:
@InCollection{IBM:1998:DAI,
  author =       "{IBM}",
  booktitle =    "{ESA\slash 390} Principles of Operation",
  title =        "Decimal Arithmetic Instructions",
  chapter =      "8",
  publisher =    pub-IBM,
  address =      pub-IBM:adr,
  year =         "1998",
  bibdate =      "Fri Nov 28 17:57:22 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The decimal instructions of this chapter perform
                 arithmetic and editing operations on decimal data.
                 Additional operations on decimal data are provided by
                 several of the instructions in Chapter 7, ``General
                 Instructions''. Decimal operands always reside in
                 storage, and all decimal instructions use the SS
                 instruction format. Decimal operands occupy storage
                 fields that can start on any byte boundary.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}


bibtype: book
filename: fparith.bib
label: IEC:1998:IITa
author: IEC
publisher: pub-IEC
address: pub-IEC:adr
pages: 27
year: 1998
bibdate: Mon Apr 24 06:32:09 2000
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2000.04.24 06:32:09 ???
URL: http://www.iec.ch/cgi-bin/procgi.pl/www/iecwww.p?wwwlang=E&wwwprog=cat-det.p&wartnum=023454
acknowledgement: ack-nhfb
rawauthor: {IEC}
title:
ISO / IEC / TR2 15580 (1998-12): Information technology --- Programming languages --- Fortran --- Floating-point exception handling

rawtitle:
{ISO\slash IEC\slash TR2 15580 (1998-12)}: Information technology --- Programming languages --- {Fortran} --- Floating-point exception handling

entry:
@Book{IEC:1998:IITa,
  author =       "{IEC}",
  title =        "{ISO\slash IEC\slash TR2 15580 (1998-12)}: Information
                 technology --- Programming languages --- {Fortran} ---
                 Floating-point exception handling",
  publisher =    pub-IEC,
  address =      pub-IEC:adr,
  pages =        "27",
  year =         "1998",
  bibdate =      "Mon Apr 24 06:32:09 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$56.00",
  URL =          "http://www.iec.ch/cgi-bin/procgi.pl/www/iecwww.p?wwwlang=E&wwwprog=cat-det.p&wartnum=023454",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: fparith.bib
label: ISO:1998:IITc
author: International Organization for Standardization
publisher: pub-ISO
address: pub-ISO:adr
pages: 27
year: 1998
bibdate: Tue Dec 12 06:45:58 2000
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2000.12.12 06:45:58 ???
note: Available in English only.
acknowledgement: ack-nhfb
rawauthor: {International Organization for Standardization}
rawnote: Available in English only.
title:
ISO / IEC TR 15580:1998: Information technology --- Programming languages --- Fortran --- Floating-point exception handling

URL:
http://webstore.ansi.org/ansidocstore/product.asp?sku=ISO%2FIEC+TR+15580%3A1998; http://www.iso.ch/cate/d28230.html

rawtitle:
{ISO\slash IEC TR 15580:1998}: {Information} technology --- {Programming} languages --- {Fortran} --- {Floating-point} exception handling

entry:
@Book{ISO:1998:IITc,
  author =       "{International Organization for Standardization}",
  title =        "{ISO\slash IEC TR 15580:1998}: {Information}
                 technology --- {Programming} languages --- {Fortran}
                 --- {Floating-point} exception handling",
  publisher =    pub-ISO,
  address =      pub-ISO:adr,
  pages =        "27",
  year =         "1998",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Tue Dec 12 06:45:58 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Available in English only.",
  price =        "CHF 104; US\$72.00",
  URL =          "http://webstore.ansi.org/ansidocstore/product.asp?sku=ISO%2FIEC+TR+15580%3A1998;
                 http://www.iso.ch/cate/d28230.html",
  acknowledgement = ack-nhfb,
  pricecode =    "N",
}


bibtype: article
filename: fparith.bib
label: Jessani:1998:CSD
author: R. M. Jessani and M. Putrino
title: Comparison of Single- and Dual-Pass Multiply-Add Fused Floating-Point Units
journal: j-IEEE-TRANS-COMPUT
volume: 47
number: 9
pages: 927--937
month: sep
monthnumber: 9
year: 1998
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.713312
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 09:35:56 MDT 2011
bibtimestamp: 2011.07.06 09:35:56 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=713312
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: R. M. Jessani and M. Putrino
rawtitle: Comparison of Single- and Dual-Pass Multiply-Add Fused Floating-Point Units
keywords:
alignment shifter; Booth encoding; floating-point unit; multiply array; multiply-add fused; sign encoding

entry:
@Article{Jessani:1998:CSD,
  author =       "R. M. Jessani and M. Putrino",
  title =        "Comparison of Single- and Dual-Pass Multiply-Add Fused
                 Floating-Point Units",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "9",
  pages =        "927--937",
  month =        sep,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.713312",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 09:35:56 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=713312",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "alignment shifter; Booth encoding; floating-point
                 unit; multiply array; multiply-add fused; sign
                 encoding",
  summary =      "Low power, low cost, and high performance factors
                 dictate the design of many microprocessors targeted to
                 the low power computing market. The floating point unit
                 occupies a significant percentage of the silicon area
                 in a microprocessor due its wide data bandwidth (for
                 double-precision computations) and the area occupied by
                 the multiply array. For microprocessors designed for
                 portable products, the design-size of the
                 floating-point unit plays an important role in the low
                 cost factor driven by reduced chip area. Some
                 microprocessors have multiply-add fused floating-point
                 units with a reduced multiply array, requiring two
                 passes through the array for operations involving
                 double-precision multiplies. This paper discusses the
                 design complexities around the dual-pass multiply array
                 and its effect on area and performance. Floating-point
                 unit areas and their associated multiply array areas
                 are compared for a single- and dual-pass implementation
                 in a given technology (PowerPC 604e and PowerPC 603e
                 microprocessors, respectively).",
}


bibtype: techreport
filename: fparith.bib
label: Kahan:1998:HJFa
author: W. Kahan and Joseph D. Darcy
title: How Java's Floating-Point Hurts Everyone Everywhere
type: Technical Report
address: Berkeley, CA, USA
pages: 80
day: 18
month: jun
monthnumber: 6
year: 1998
bibdate: Sat Sep 12 18:53:11 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.09.12 18:53:11 ???
URL: http://www.cs.berkeley.edu/~wkahan/JAVAhurt.pdf; http://www.cs.berkeley.edu/~wkahan/JAVAhurt.ps
acknowledgement: ack-nhfb
rawauthor: W. Kahan and Joseph D. Darcy
rawtitle: How {Java}'s Floating-Point Hurts Everyone Everywhere
institution:
Department of Mathematics and Department of Electrical Engineering and Computer Science, University of California, Berkeley

remark:
The authors deliver a biting criticism of Java for its failure to use the 80-bit temporary real format on Intel x86 architectures, failure to use multiply-add instructions when available, and failure to compute float subexpressions in double precision.

entry:
@TechReport{Kahan:1998:HJFa,
  author =       "W. Kahan and Joseph D. Darcy",
  title =        "How {Java}'s Floating-Point Hurts Everyone
                 Everywhere",
  type =         "Technical Report",
  institution =  "Department of Mathematics and Department of Electrical
                 Engineering and Computer Science, University of
                 California, Berkeley",
  address =      "Berkeley, CA, USA",
  pages =        "80",
  day =          "18",
  month =        jun,
  year =         "1998",
  bibdate =      "Sat Sep 12 18:53:11 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/JAVAhurt.pdf;
                 http://www.cs.berkeley.edu/~wkahan/JAVAhurt.ps",
  acknowledgement = ack-nhfb,
  remark =       "The authors deliver a biting criticism of Java for its
                 failure to use the 80-bit temporary real format on
                 Intel x86 architectures, failure to use multiply-add
                 instructions when available, and failure to compute
                 float subexpressions in double precision.",
}


bibtype: inproceedings
filename: fparith.bib
label: Kahan:1998:HJFb
author: William Kahan
title: How Java's Floating-Point Hurts Everyone Everywhere
crossref: ACM:1998:AWJ
pages: ??--??
year: 1998
bibdate: Sat Dec 01 07:55:27 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.12.01 07:55:27 ???
URL: http://www.cs.ucsb.edu/conferences/java98/papers/javahurt.pdf
acknowledgement: ack-nhfb
rawauthor: William Kahan
rawtitle: How {Java}'s Floating-Point Hurts Everyone Everywhere
entry:
@InProceedings{Kahan:1998:HJFb,
  author =       "William Kahan",
  title =        "How {Java}'s Floating-Point Hurts Everyone
                 Everywhere",
  crossref =     "ACM:1998:AWJ",
  pages =        "??--??",
  year =         "1998",
  bibdate =      "Sat Dec 01 07:55:27 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.ucsb.edu/conferences/java98/papers/javahurt.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: fparith.bib
label: Kahan:1998:IPE
author: W. Kahan
title: The Improbability of Probabilistic Error Analyses for Numerical Computations
address: Berkeley, CA, USA
pages: 34
day: 10
month: jun
monthnumber: 6
year: 1998
bibdate: Fri May 03 12:30:29 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.03 12:30:29 ???
URL: http://www.cs.berkeley.edu/~wkahan/improber.pdf
acknowledgement: ack-nhfb
rawauthor: W. Kahan
rawtitle: The Improbability of Probabilistic Error Analyses for Numerical Computations
entry:
@TechReport{Kahan:1998:IPE,
  author =       "W. Kahan",
  title =        "The Improbability of Probabilistic Error Analyses for
                 Numerical Computations",
  institution =  "Department of Mathematics and Department of Electrical
                 Engineering and Computer Science, University of
                 California, Berkeley",
  address =      "Berkeley, CA, USA",
  pages =        "34",
  day =          "10",
  month =        jun,
  year =         "1998",
  bibdate =      "Fri May 03 12:30:29 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/improber.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Kelsey:1998:RRA
author: Richard Kelsey and William Clinger and Jonathan Rees
title: Revised$^5$ Report on the Algorithmic Language Scheme
journal: j-SIGPLAN
volume: 33
number: 9
pages: 26--76
month: sep
monthnumber: 9
year: 1998
CODEN: SINODQ
ISSN: 0362-1340 (print), 1523-2867 (print), 1558-1160 OR 03621340 (print), 15232867 (print), 15581160
ISSNL: 0362-1340 OR 03621340
bibdate: Tue Sep 15 17:01:28 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.09.15 17:01:28 ???
fjournal: ACM SIGPLAN Notices
keywords: decimal floating-point arithmetic
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J706
rawauthor: Richard Kelsey and William Clinger and Jonathan Rees
rawtitle: Revised$^5$ Report on the Algorithmic Language {Scheme}
note:
With H. Abelson, N. I. Adams, IV, D. H. Bartley, G. Brooks, R. K. Dybvig, D. P. Friedman, R. Halstead, C. Hanson, C. T. Haynes, E. Kohlbecker, D. Oxley, K. M. Pitman, G. J. Rozas, G. L. Steele Jr., G. J. Sussman, and M. Wand.

remark:
From cite Steele:2004:RHP: ``the result [of a binary-to-decimal conversion] is expressed using the minimum number of digitsldots ''

rawnote:
With H. Abelson, N. I. {Adams, IV}, D. H. Bartley, G. Brooks, R. K. Dybvig, D. P. Friedman, R. Halstead, C. Hanson, C. T. Haynes, E. Kohlbecker, D. Oxley, K. M. Pitman, G. J. Rozas, G. L. {Steele Jr.}, G. J. Sussman, and M. Wand.

entry:
@Article{Kelsey:1998:RRA,
  author =       "Richard Kelsey and William Clinger and Jonathan Rees",
  title =        "Revised$^5$ Report on the Algorithmic Language
                 {Scheme}",
  journal =      j-SIGPLAN,
  volume =       "33",
  number =       "9",
  pages =        "26--76",
  month =        sep,
  year =         "1998",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Tue Sep 15 17:01:28 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "With H. Abelson, N. I. {Adams, IV}, D. H. Bartley, G.
                 Brooks, R. K. Dybvig, D. P. Friedman, R. Halstead, C.
                 Hanson, C. T. Haynes, E. Kohlbecker, D. Oxley, K. M.
                 Pitman, G. J. Rozas, G. L. {Steele Jr.}, G. J. Sussman,
                 and M. Wand.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "decimal floating-point arithmetic",
  remark =       "From \cite{Steele:2004:RHP}: ``the result [of a
                 binary-to-decimal conversion] is expressed using the
                 minimum number of digits\ldots{}''",
}


bibtype: article
filename: fparith.bib
label: Kiranon:1998:SRV
author: W. Kiranon and N. Kumprasert
title: Square-rooting and vector summation circuits using current conveyors
volume: 145
number: 2
pages: 139
month: apr
monthnumber: 4
year: 1998
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
keywords: accurate floating-point summation
acknowledgement: ack-nhfb
rawauthor: W. Kiranon and N. Kumprasert
rawtitle: Square-rooting and vector summation circuits using current conveyors
journal:
Circuits, Devices and Systems, IEE Proceedings [see also IEE Proceedings G- Circuits, Devices and Systems]

entry:
@Article{Kiranon:1998:SRV,
  author =       "W. Kiranon and N. Kumprasert",
  title =        "Square-rooting and vector summation circuits using
                 current conveyors",
  journal =      "Circuits, Devices and Systems, IEE Proceedings [see
                 also IEE Proceedings G- Circuits, Devices and
                 Systems]",
  volume =       "145",
  number =       "2",
  pages =        "139",
  month =        apr,
  year =         "1998",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation",
  summary =      "Recently, Lui [1995] presented a square-rooting
                 circuit using CCII, MOS transistors and a buffered
                 unity-gain inverting amplifier. It is interesting since
                 it finds various applications as described in his
                 paper. However, an error occurred in the \ldots{}",
}


