# bibtab

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: https://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 =          "https://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: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=565589
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://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 =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=565589",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://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: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=589230
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://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 =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=589230",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: 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: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=620478
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://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 =          "https://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 =  "https://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: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=599900
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://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 =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=599900",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://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 FasMath 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 FasMath 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 FasMath 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: https://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",
  CODEN =        "ITCOB4",
  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 =  "https://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: https://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",
  DOI =          "https://doi.org/10.1109/12.565590",
  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 =  "https://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;
                 http://link.springer-ny.com/link/service/series/0558/papers/1233/12330363.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Pan:1997:SPE
author: Victor Y. Pan
title: Solving a Polynomial Equation: Some History and Recent Progress
journal: j-SIAM-REVIEW
volume: 39
number: 2
pages: 187--220
month: jun
monthnumber: 6
year: 1997
CODEN: SIREAD
DOI: https://doi.org/10.1137/S0036144595288554
ISSN: 0036-1445 (print), 1095-7200 (electronic) OR 00361445 (print), 10957200 (electronic)
ISSNL: 0036-1445 OR 00361445
MRclass: 65Hxx (01A99 65-03)
MRnumber: 1 453 318
bibdate: Sat Mar 29 09:55:49 MDT 2014
bibtimestamp: 2014.03.29 09:55:49 MDT
URL: http://epubs.siam.org/sam-bin/dbq/article/28855
fjournal: SIAM Review
acknowledgement: ack-nhfb
ajournal: SIAM Rev.
journalURL: http://epubs.siam.org/sirev
onlinedate: January 1997
rawauthor: Victor Y. Pan
rawtitle: Solving a Polynomial Equation: Some History and Recent Progress
bibsource:
http://epubs.siam.org/toc/siread/39/2; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib

entry:
@Article{Pan:1997:SPE,
  author =       "Victor Y. Pan",
  title =        "Solving a Polynomial Equation: Some History and Recent
                 Progress",
  journal =      j-SIAM-REVIEW,
  volume =       "39",
  number =       "2",
  pages =        "187--220",
  month =        jun,
  year =         "1997",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/S0036144595288554",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  MRclass =      "65Hxx (01A99 65-03)",
  MRnumber =     "1 453 318",
  bibdate =      "Sat Mar 29 09:55:49 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/39/2;
                 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/28855",
  acknowledgement = ack-nhfb,
  ajournal =     "SIAM Rev.",
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "January 1997",
}


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: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=589237
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://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 =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=589237",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://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: https://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 =  "https://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: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=559806
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://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 =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=559806",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: 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: https://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 =  "https://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: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=565588
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://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 =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=565588",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Wang:1997:MSM
author: Shaoyun Wang and V. Piuri and E. E. Swartzlander
booktitle: 1997 IEEE International Symposium on Circuits and Systems (ISCAS)
title: Merged scaling multiplication CORDIC algorithm
volume: 4
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 2581--2584 (vol. 4)
year: 1997
DOI: https://doi.org/10.1109/ISCAS.1997.612852
bibdate: Mon Oct 27 10:32:44 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2025.10.27 10:32:44 ???
acknowledgement: ack-nhfb
rawauthor: Shaoyun Wang and V. Piuri and E. E. Swartzlander
rawbooktitle: {1997 IEEE International Symposium on Circuits and Systems (ISCAS)}
rawtitle: Merged scaling multiplication {CORDIC} algorithm
keywords:
Application software; Arithmetic; Clocks; Complexity theory; Computer applications; Control system synthesis; Iterative algorithms; Signal processing algorithms; Throughput; Very large scale integration

entry:
@InProceedings{Wang:1997:MSM,
  author =       "Shaoyun Wang and V. Piuri and E. E. Swartzlander",
  booktitle =    "{1997 IEEE International Symposium on Circuits and
                 Systems (ISCAS)}",
  title =        "Merged scaling multiplication {CORDIC} algorithm",
  volume =       "4",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "2581--2584 (vol. 4)",
  year =         "1997",
  DOI =          "https://doi.org/10.1109/ISCAS.1997.612852",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Application software; Arithmetic; Clocks; Complexity
                 theory; Computer applications; Control system
                 synthesis; Iterative algorithms; Signal processing
                 algorithms; Throughput; Very large scale integration",
}


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: https://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: https://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 =          "https://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 =  "https://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 =    "Fri Nov 14 09:44:49 2025",
}


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: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=736430
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://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 =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=736430",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: 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: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=709371
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://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 =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=709371",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: 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: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=663761
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://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 =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=663761",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://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: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=709377
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://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 =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=709377",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: 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: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=709376
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://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 =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=709376",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: 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: https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=14431
fjournal: IEEE Transactions on Signal Processing
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
journalURL: https://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 =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=14431",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "https://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: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=713313
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://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 =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=713313",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: 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: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=729800
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://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 =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=729800",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: 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: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=713312
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: R. M. 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 =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=713312",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://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
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{}",
}


bibtype: book
filename: fparith.bib
label: Knuth:1998:SA
author: Donald E. Knuth
title: Seminumerical Algorithms
volume: 2
publisher: pub-AW
address: pub-AW:adr
edition: Third
pages: xiii + 762
year: 1998
ISBN: 0-201-89684-2 OR 0201896842
ISBN13: 978-0-201-89684-8 OR 9780201896848
LCCN: QA76.6 .K64 1997
bibdate: Fri Jul 11 15:41:22 1997
bibtimestamp: 1997.07.11 15:41:22 ???
note: See section 4.2.4V, The Fraction Parts, pages 254--262, for a discussion of Benford's Law.
series: The Art of Computer Programming
acknowledgement: ack-nhfb
rawauthor: Donald E. Knuth
rawnote: See section 4.2.4V, The Fraction Parts, pages 254--262, for a discussion of Benford's Law.
rawtitle: Seminumerical Algorithms
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/css.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/prng.bib; https://www.math.utah.edu/pub/tex/bib/texbook2.bib

remark:
Knuth comments on page 255: ``The fact that the leading digits tend to be small makes the most obvious techniques of ``average error'' estimation for floating point calculations invalid. The relative error due to rounding is usually a little more than expected.

TOC:
3: Random Numbers / 1 3.1. Introduction / 1 3.2. Generating Uniform Random Numbers / 10 3.2.1. The Linear Congruential Method / 10 3.2 1.1. Choice of modulus / 12 3.2.1.2 Choice of multiplier / 16 3.2.1.3. Potency / 23 3.2.2. Other Methods / 26 3.3. Statistical Tests / 41 3.3.1. General Test Procedures for Studying Random Data / 41 3.3.2. Empirical Tests / 61 *3.3.3. Theoretical Tests / 80 3.3.4. The Spectral Test / 93 3.4. Other Types of Random Quantities / 119 3.4 1. Numerical Distributions / 119 3.4.2. Random Sampling and Shuffling / 142 *3.5. What Is a Random Sequence? / 149 3.6. Summary / 184 4: Arithmetic / 194 4.1. Positional Number Systems / 195 4.2. Floating Point Arithmetic / 214 4.2.1. Single-Precision Calculations / 214 4.2 2. Accuracy of Floating Point Arithmetic / 229 *4.2.3. Double-Precision Calculations / 246 4.2.4. Distribution of Floating Point Numbers / 253 4.3 Multiple Precision Arithmetic / 265 4.3.1. The Classical Algorithms / 265 *4.3.2. Modular Arithmetic / 284 *4.3.3. How Fast Can We Multiply? / 294 4.4. Radix Conversion / 319 4.5. Rational Arithmetic / 330 4.5.1. Fractions / 330 4.5.2. The Greatest Common Divisor / 333 *4.5.3. Analysis of Euclid's Algorithm / 356 4.5.4. Factoring into Primes / 379 4.6. Polynomial Arithmetic / 418 4.6.1. Division of Polynomials / 420 *4.6.2. Factorization of Polynomials / 439 4.6.3. Evaluation of Powers / 461 4.6.4. Evaluation of Polynomials / 485 *4.7. Manipulation of Power Series / 525 Answers to Exercises / 538 Appendix A: Tables of Numerical Quantities / 726 1. Fundamental Constants (decimal) / 726 2; Fundamental Constants ( octal) / 727 3. Harmonic Numbers, Bernoulli Numbers, Fibonacci Numbers / 728 Appendix B: Index to Notations / 730 Index and Glossary / 735

rawTOC:
3: Random Numbers / 1 \\ 3.1. Introduction / 1 \\ 3.2. Generating Uniform Random Numbers / 10 \\ 3.2.1. The Linear Congruential Method / 10 \\ 3.2 1.1. Choice of modulus / 12 \\ 3.2.1.2 Choice of multiplier / 16 \\ 3.2.1.3. Potency / 23 \\ 3.2.2. Other Methods / 26 \\ 3.3. Statistical Tests / 41 \\ 3.3.1. General Test Procedures for Studying Random Data / 41 \\ 3.3.2. Empirical Tests / 61 \\ *3.3.3. Theoretical Tests / 80 \\ 3.3.4. The Spectral Test / 93 \\ 3.4. Other Types of Random Quantities / 119 \\ 3.4 1. Numerical Distributions / 119 \\ 3.4.2. Random Sampling and Shuffling / 142 \\ *3.5. What Is a Random Sequence? / 149 \\ 3.6. Summary / 184 \\ 4: Arithmetic / 194 \\ 4.1. Positional Number Systems / 195 \\ 4.2. Floating Point Arithmetic / 214 \\ 4.2.1. Single-Precision Calculations / 214 \\ 4.2 2. Accuracy of Floating Point Arithmetic / 229 \\ *4.2.3. Double-Precision Calculations / 246 \\ 4.2.4. Distribution of Floating Point Numbers / 253 \\ 4.3 Multiple Precision Arithmetic / 265 \\ 4.3.1. The Classical Algorithms / 265 \\ *4.3.2. Modular Arithmetic / 284 \\ *4.3.3. How Fast Can We Multiply? / 294 \\ 4.4. Radix Conversion / 319 \\ 4.5. Rational Arithmetic / 330 \\ 4.5.1. Fractions / 330 \\ 4.5.2. The Greatest Common Divisor / 333 \\ *4.5.3. Analysis of Euclid's Algorithm / 356 \\ 4.5.4. Factoring into Primes / 379 \\ 4.6. Polynomial Arithmetic / 418 \\ 4.6.1. Division of Polynomials / 420 \\ *4.6.2. Factorization of Polynomials / 439 \\ 4.6.3. Evaluation of Powers / 461 \\ 4.6.4. Evaluation of Polynomials / 485 \\ *4.7. Manipulation of Power Series / 525 \\ Answers to Exercises / 538 \\ Appendix A: Tables of Numerical Quantities / 726 \\ 1. Fundamental Constants (decimal) / 726 \\ 2; Fundamental Constants ( octal) / 727 \\ 3. Harmonic Numbers, Bernoulli Numbers, Fibonacci Numbers / 728 \\ Appendix B: Index to Notations / 730 \\ Index and Glossary / 735

entry:
@Book{Knuth:1998:SA,
  author =       "Donald E. Knuth",
  title =        "Seminumerical Algorithms",
  volume =       "2",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  edition =      "Third",
  pages =        "xiii + 762",
  year =         "1998",
  ISBN =         "0-201-89684-2",
  ISBN-13 =      "978-0-201-89684-8",
  LCCN =         "QA76.6 .K64 1997",
  bibdate =      "Fri Jul 11 15:41:22 1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/css.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/prng.bib;
                 https://www.math.utah.edu/pub/tex/bib/texbook2.bib",
  note =         "See section 4.2.4V, The Fraction Parts, pages
                 254--262, for a discussion of Benford's Law.",
  price =        "US\$52.75",
  series =       "The Art of Computer Programming",
  acknowledgement = ack-nhfb,
  remark =       "Knuth comments on page 255: ``The fact that the
                 leading digits tend to be small makes the most obvious
                 techniques of ``average error'' estimation for floating
                 point calculations invalid. The relative error due to
                 rounding is usually a little more than expected.",
  tableofcontents = "3: Random Numbers / 1 \\
                 3.1. Introduction / 1 \\
                 3.2. Generating Uniform Random Numbers / 10 \\
                 3.2.1. The Linear Congruential Method / 10 \\
                 3.2 1.1. Choice of modulus / 12 \\
                 3.2.1.2 Choice of multiplier / 16 \\
                 3.2.1.3. Potency / 23 \\
                 3.2.2. Other Methods / 26 \\
                 3.3. Statistical Tests / 41 \\
                 3.3.1. General Test Procedures for Studying Random Data
                 / 41 \\
                 3.3.2. Empirical Tests / 61 \\
                 *3.3.3. Theoretical Tests / 80 \\
                 3.3.4. The Spectral Test / 93 \\
                 3.4. Other Types of Random Quantities / 119 \\
                 3.4 1. Numerical Distributions / 119 \\
                 3.4.2. Random Sampling and Shuffling / 142 \\
                 *3.5. What Is a Random Sequence? / 149 \\
                 3.6. Summary / 184 \\
                 4: Arithmetic / 194 \\
                 4.1. Positional Number Systems / 195 \\
                 4.2. Floating Point Arithmetic / 214 \\
                 4.2.1. Single-Precision Calculations / 214 \\
                 4.2 2. Accuracy of Floating Point Arithmetic / 229 \\
                 *4.2.3. Double-Precision Calculations / 246 \\
                 4.2.4. Distribution of Floating Point Numbers / 253 \\
                 4.3 Multiple Precision Arithmetic / 265 \\
                 4.3.1. The Classical Algorithms / 265 \\
                 *4.3.2. Modular Arithmetic / 284 \\
                 *4.3.3. How Fast Can We Multiply? / 294 \\
                 4.4. Radix Conversion / 319 \\
                 4.5. Rational Arithmetic / 330 \\
                 4.5.1. Fractions / 330 \\
                 4.5.2. The Greatest Common Divisor / 333 \\
                 *4.5.3. Analysis of Euclid's Algorithm / 356 \\
                 4.5.4. Factoring into Primes / 379 \\
                 4.6. Polynomial Arithmetic / 418 \\
                 4.6.1. Division of Polynomials / 420 \\
                 *4.6.2. Factorization of Polynomials / 439 \\
                 4.6.3. Evaluation of Powers / 461 \\
                 4.6.4. Evaluation of Polynomials / 485 \\
                 *4.7. Manipulation of Power Series / 525 \\
                 Answers to Exercises / 538 \\
                 Appendix A: Tables of Numerical Quantities / 726 \\
                 1. Fundamental Constants (decimal) / 726 \\
                 2; Fundamental Constants ( octal) / 727 \\
                 3. Harmonic Numbers, Bernoulli Numbers, Fibonacci
                 Numbers / 728 \\
                 Appendix B: Index to Notations / 730 \\
                 Index and Glossary / 735",
}


bibtype: article
filename: fparith.bib
label: Koc:1998:LCB
author: C. K. Koc and B. Sunar
title: Low-complexity bit-parallel canonical and normal basis multipliers for a class of finite fields
journal: j-IEEE-TRANS-COMPUT
volume: 47
number: 3
pages: 353--356
month: mar
monthnumber: 3
year: 1998
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.660172
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 09:35:54 MDT 2011
bibtimestamp: 2011.07.06 09:35:54 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=660172
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: C. K. Koc and B. Sunar
rawtitle: Low-complexity bit-parallel canonical and normal basis multipliers for a class of finite fields
entry:
@Article{Koc:1998:LCB,
  author =       "C. K. Koc and B. Sunar",
  title =        "Low-complexity bit-parallel canonical and normal basis
                 multipliers for a class of finite fields",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "3",
  pages =        "353--356",
  month =        mar,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.660172",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 09:35:54 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=660172",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Kramer:1998:PWC
author: W. Kramer
title: A priori worst case error bounds for floating-point computations
journal: j-IEEE-TRANS-COMPUT
volume: 47
number: 7
pages: 750--756
month: jul
monthnumber: 7
year: 1998
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.709374
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
note: See cite Tang:1992:TDI.
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=709374
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: W. Kramer
rawnote: See \cite{Tang:1992:TDI}.
rawtitle: A priori worst case error bounds for floating-point computations
abstract:
A new technique for the a priori calculation of rigorous error bounds for floating-point computations is introduced. The theorems given in the paper combined with interval arithmetic lead to the implementation of reliable software routines, which enable the user to compute the desired error bounds automatically by a suitable computer program. As a prominent example, a table-lookup algorithm for calculating the function $ rm exp(x) - 1 $ that has been published by P. T. P. Tang (1992) is analyzed using these new tools. The result shows the high quality of the new approach

rawabstract:
A new technique for the a priori calculation of rigorous error bounds for floating-point computations is introduced. The theorems given in the paper combined with interval arithmetic lead to the implementation of reliable software routines, which enable the user to compute the desired error bounds automatically by a suitable computer program. As a prominent example, a table-lookup algorithm for calculating the function $ {\rm exp}(x) - 1 $ that has been published by P. T. P. Tang (1992) is analyzed using these new tools. The result shows the high quality of the new approach

entry:
@Article{Kramer:1998:PWC,
  author =       "W. Kramer",
  title =        "A priori worst case error bounds for floating-point
                 computations",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "7",
  pages =        "750--756",
  month =        jul,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.709374",
  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",
  note =         "See \cite{Tang:1992:TDI}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=709374",
  abstract =     "A new technique for the a priori calculation of
                 rigorous error bounds for floating-point computations
                 is introduced. The theorems given in the paper combined
                 with interval arithmetic lead to the implementation of
                 reliable software routines, which enable the user to
                 compute the desired error bounds automatically by a
                 suitable computer program. As a prominent example, a
                 table-lookup algorithm for calculating the function $
                 {\rm exp}(x) - 1 $ that has been published by P. T. P.
                 Tang (1992) is analyzed using these new tools. The
                 result shows the high quality of the new approach",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Kuhlmann:1998:FLP
author: M. Kuhlmann and K. K. Parhi
title: Fast low-power shared division and square-root architecture
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 128--135
year: 1998
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: M. Kuhlmann and K. K. Parhi
rawtitle: Fast low-power shared division and square-root architecture
booktitle:
Proceedings of the 1998 International Conference on Computer Design: VLSI in Computers and Processors. ICCD '98

rawbooktitle:
Proceedings of the 1998 International Conference on Computer Design: {VLSI} in Computers and Processors. {ICCD '98}

entry:
@InProceedings{Kuhlmann:1998:FLP,
  author =       "M. Kuhlmann and K. K. Parhi",
  booktitle =    "Proceedings of the 1998 International Conference on
                 Computer Design: {VLSI} in Computers and Processors.
                 {ICCD '98}",
  title =        "Fast low-power shared division and square-root
                 architecture",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "128--135",
  year =         "1998",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "This paper addresses a fast low-power implementation
                 of a shared division and square-root architecture. Two
                 approaches are considered in this paper; these include
                 the SRT (Sweeney, Robertson and Tocher) approach which
                 does not require prescaling and \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Kwak:1998:ILI
author: Jae-Hyuek Kwak and E. E. Swartzlander
title: An implementation of level-index arithmetic based on the low latency CORDIC system
volume: 1
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 208--212 (vol. 1)
year: 1998
DOI: https://doi.org/10.1109/ACSSC.1998.750855
bibdate: Mon Oct 27 10:32:44 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2025.10.27 10:32:44 ???
acknowledgement: ack-nhfb
rawauthor: Jae-Hyuek Kwak and E. E. Swartzlander
rawtitle: An implementation of level-index arithmetic based on the low latency {CORDIC} system
booktitle:
Conference Record of Thirty-Second Asilomar Conference on Signals, Systems and Computers (Cat. No. 98CH36284)

keywords:
Calculators; Computer architecture; Concurrent computing; Costs; Delay; Digital arithmetic; Equations; Hardware; Parallel processing; Timing

rawbooktitle:
{Conference Record of Thirty-Second Asilomar Conference on Signals, Systems and Computers (Cat. No. 98CH36284)}

entry:
@InProceedings{Kwak:1998:ILI,
  author =       "Jae-Hyuek Kwak and E. E. Swartzlander",
  booktitle =    "{Conference Record of Thirty-Second Asilomar
                 Conference on Signals, Systems and Computers (Cat. No.
                 98CH36284)}",
  title =        "An implementation of level-index arithmetic based on
                 the low latency {CORDIC} system",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "208--212 (vol. 1)",
  year =         "1998",
  DOI =          "https://doi.org/10.1109/ACSSC.1998.750855",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Calculators; Computer architecture; Concurrent
                 computing; Costs; Delay; Digital arithmetic; Equations;
                 Hardware; Parallel processing; Timing",
}


bibtype: article
filename: fparith.bib
label: Labrosse:1998:FPA
author: Jean J. Labrosse
title: Fixed-Point Arithmetic for Embedded Systems
journal: j-CCCUJ
volume: 16
number: 2
pages: ??--??
month: feb
monthnumber: 2
year: 1998
CODEN: CCUJEX
ISSN: 1075-2838 OR 10752838
bibdate: Tue May 14 18:09:14 MDT 2002
bibtimestamp: 2002.05.14 18:09:14 MDT
abstract: Fixed-point arithmetic is fast: you just have to worry more about overflow and significance loss.
fjournal: C/C++ Users Journal
acknowledgement: ack-nhfb
rawabstract: Fixed-point arithmetic is fast: you just have to worry more about overflow and significance loss.
rawauthor: Jean J. Labrosse
rawtitle: Fixed-Point Arithmetic for Embedded Systems
bibsource:
http://www.cuj.com/articles/1998/9802/9802toc.htm?topic=articles; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Labrosse:1998:FPA,
  author =       "Jean J. Labrosse",
  title =        "Fixed-Point Arithmetic for Embedded Systems",
  journal =      j-CCCUJ,
  volume =       "16",
  number =       "2",
  pages =        "??--??",
  month =        feb,
  year =         "1998",
  CODEN =        "CCUJEX",
  ISSN =         "1075-2838",
  bibdate =      "Tue May 14 18:09:14 MDT 2002",
  bibsource =    "http://www.cuj.com/articles/1998/9802/9802toc.htm?topic=articles;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Fixed-point arithmetic is fast: you just have to worry
                 more about overflow and significance loss.",
  acknowledgement = ack-nhfb,
  fjournal =     "C/C++ Users Journal",
}


bibtype: article
filename: fparith.bib
label: Langer:1998:CFP
author: Steven H. Langer and Paul F. Dubois
title: A comparison of the floating-point performance of current computers
journal: j-COMPUT-PHYS
volume: 12
number: 4
pages: 338--??
month: jul
monthnumber: 7
year: 1998
CODEN: CPHYE2
DOI: https://doi.org/10.1063/1.168693
ISSN: 0894-1866 (print), 1558-4208 (electronic) OR 08941866 (print), 15584208 (electronic)
ISSNL: 0894-1866 OR 08941866
bibdate: Wed Apr 10 08:46:15 MDT 2019
bibtimestamp: 2019.04.10 08:46:15 MDT
URL: https://aip.scitation.org/doi/10.1063/1.168693
fjournal: Computers in Physics
acknowledgement: ack-nhfb
ajournal: Comput. Phys
journalURL: https://aip.scitation.org/journal/cip
rawauthor: Steven H. Langer and Paul F. Dubois
rawtitle: A comparison of the floating-point performance of current computers
bibsource:
https://www.math.utah.edu/pub/tex/bib/computphys.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Langer:1998:CFP,
  author =       "Steven H. Langer and Paul F. Dubois",
  title =        "A comparison of the floating-point performance of
                 current computers",
  journal =      j-COMPUT-PHYS,
  volume =       "12",
  number =       "4",
  pages =        "338--??",
  month =        jul,
  year =         "1998",
  CODEN =        "CPHYE2",
  DOI =          "https://doi.org/10.1063/1.168693",
  ISSN =         "0894-1866 (print), 1558-4208 (electronic)",
  ISSN-L =       "0894-1866",
  bibdate =      "Wed Apr 10 08:46:15 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computphys.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://aip.scitation.org/doi/10.1063/1.168693",
  acknowledgement = ack-nhfb,
  ajournal =     "Comput. Phys",
  fjournal =     "Computers in Physics",
  journal-URL =  "https://aip.scitation.org/journal/cip",
}


bibtype: article
filename: fparith.bib
label: Langlois:1998:RBR
author: Ph. Langlois and F. Nativel
title: Reduction and bounding of the rounding error in floating-point arithmetic
journal: j-C-R-ACAD-SCI-PARIS-SER-I-MATH
volume: 327
pages: 781--786
year: 1998
CODEN: CASMEI
ISSN: 0249-6291 OR 02496291
bibdate: Thu May 27 07:37:54 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.05.27 07:37:54 ???
fjournal: Comptes Rendus des Seances de l'Academie des Sciences. Serie I. Mathematique
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/1631073X
rawauthor: Ph. Langlois and F. Nativel
rawtitle: Reduction and bounding of the rounding error in floating-point arithmetic
entry:
@Article{Langlois:1998:RBR,
  author =       "Ph. Langlois and F. Nativel",
  title =        "Reduction and bounding of the rounding error in
                 floating-point arithmetic",
  journal =      j-C-R-ACAD-SCI-PARIS-SER-I-MATH,
  volume =       "327",
  number =       "??",
  pages =        "781--786",
  year =         "1998",
  CODEN =        "CASMEI",
  ISSN =         "0249-6291",
  bibdate =      "Thu May 27 07:37:54 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Comptes Rendus des S{\'e}ances de l'Acad{\'e}mie des
                 Sciences. S{\'e}rie I. Math{\'e}matique",
  journal-URL =  "http://www.sciencedirect.com/science/journal/1631073X",
}


bibtype: inproceedings
filename: fparith.bib
label: Lee:1998:DRN
author: I. Lee and W. K. Jenkins
booktitle: Proceedings of the 8th Great Lakes Symposium on VLSI, 1998
title: The design of residue number system arithmetic units for a VLSI adaptive equalizer
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 179--184
year: 1998
DOI: https://doi.org/10.1109/GLSV.1998.665222
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: I. Lee and W. K. Jenkins
rawbooktitle: Proceedings of the 8th Great Lakes Symposium on {VLSI, 1998}
rawtitle: The design of residue number system arithmetic units for a {VLSI} adaptive equalizer
entry:
@InProceedings{Lee:1998:DRN,
  author =       "I. Lee and W. K. Jenkins",
  booktitle =    "Proceedings of the 8th Great Lakes Symposium on {VLSI,
                 1998}",
  title =        "The design of residue number system arithmetic units
                 for a {VLSI} adaptive equalizer",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "179--184",
  year =         "1998",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/GLSV.1998.665222",
  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 details of an
                 experimental ASIC for an all-digital adaptive
                 equalizer. In this design, the LMS algorithm is chosen
                 because of its simplicity. The adaptive equalizer
                 design, which is based on an RNS architecture,
                 \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Lefevre:1998:TCR
author: Vincent Lefevre and Jean-Michel Muller and Arnaud Tisserand
title: Toward correctly rounded transcendentals
journal: j-IEEE-TRANS-COMPUT
volume: 47
number: 11
pages: 1235--1243
month: nov
monthnumber: 11
year: 1998
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.736435
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 16 11:25:04 MDT 2005
bibtimestamp: 2005.07.16 11:25:04 MDT
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Vincent Lef{\`e}vre and Jean-Michel Muller and Arnaud Tisserand
rawtitle: Toward correctly rounded transcendentals
entry:
@Article{Lefevre:1998:TCR,
  author =       "Vincent Lef{\`e}vre and Jean-Michel Muller and Arnaud
                 Tisserand",
  title =        "Toward correctly rounded transcendentals",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "11",
  pages =        "1235--1243",
  month =        nov,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.736435",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 11:25:04 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "The Table Maker's Dilemma is the problem of always
                 getting correctly rounded results when computing the
                 elementary functions. After a brief presentation of
                 this problem, we present new developments that have
                 helped us to solve this problem for the
                 double-precision exponential function in a small
                 domain. These new results show that this problem can be
                 solved, at least for the double-precision format, for
                 the most usual functions.",
}


bibtype: inproceedings
filename: fparith.bib
label: Ligon:1998:REP
author: W. B. Ligon III and S. McMillan and G. Monn and K. Schoonover and F. Stivers and K. D. Underwood
title: A re-evaluation of the practicality of floating-point operations on FPGAs
crossref: Pocek:1998:PIS
pages: 206--215
year: 1998
DOI: https://doi.org/10.1109/FPGA.1998.707898
bibdate: Sat Oct 9 12:51:26 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.09 12:51:26 ???
acknowledgement: ack-nhfb
rawauthor: W. B. {Ligon III} and S. McMillan and G. Monn and K. Schoonover and F. Stivers and K. D. Underwood
rawtitle: A re-evaluation of the practicality of floating-point operations on {FPGAs}
abstract:
The use of reconfigurable hardware to perform high precision operations such as IEEE floating point operations has been limited in the past by FPGA resources. We discuss the implementation of IEEE single precision floating-point multiplication and addition. Then, we assess the practical implications of using these operations in the Xilinx 4000 series FPGAs considering densities available now and scheduled for the near future. For each operation, we present space requirements and performance information. This is followed by a discussion of an algorithm, matrix multiplication, based on these operations, which achieves performance comparable to conventional microprocessors. Algorithm implementation options and their performance implications are discussed and corresponding measured results are given

rawabstract:
The use of reconfigurable hardware to perform high precision operations such as IEEE floating point operations has been limited in the past by FPGA resources. We discuss the implementation of IEEE single precision floating-point multiplication and addition. Then, we assess the practical implications of using these operations in the Xilinx 4000 series FPGAs considering densities available now and scheduled for the near future. For each operation, we present space requirements and performance information. This is followed by a discussion of an algorithm, matrix multiplication, based on these operations, which achieves performance comparable to conventional microprocessors. Algorithm implementation options and their performance implications are discussed and corresponding measured results are given

entry:
@InProceedings{Ligon:1998:REP,
  author =       "W. B. {Ligon III} and S. McMillan and G. Monn and K.
                 Schoonover and F. Stivers and K. D. Underwood",
  title =        "A re-evaluation of the practicality of floating-point
                 operations on {FPGAs}",
  crossref =     "Pocek:1998:PIS",
  pages =        "206--215",
  year =         "1998",
  DOI =          "https://doi.org/10.1109/FPGA.1998.707898",
  bibdate =      "Sat Oct 9 12:51:26 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The use of reconfigurable hardware to perform high
                 precision operations such as IEEE floating point
                 operations has been limited in the past by FPGA
                 resources. We discuss the implementation of IEEE single
                 precision floating-point multiplication and addition.
                 Then, we assess the practical implications of using
                 these operations in the Xilinx 4000 series FPGAs
                 considering densities available now and scheduled for
                 the near future. For each operation, we present space
                 requirements and performance information. This is
                 followed by a discussion of an algorithm, matrix
                 multiplication, based on these operations, which
                 achieves performance comparable to conventional
                 microprocessors. Algorithm implementation options and
                 their performance implications are discussed and
                 corresponding measured results are given",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Looye:1998:MMF
author: A. Looye and G. Hekstra and E. Deprettere
title: Multiport memory and floating-point CORDIC pipeline in Jacobium processing elements
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 406--416
year: 1998
DOI: https://doi.org/10.1109/SIPS.1998.715803
bibdate: Mon Oct 27 10:32:44 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2025.10.27 10:32:44 ???
acknowledgement: ack-nhfb
rawauthor: A. Looye and G. Hekstra and E. Deprettere
rawtitle: Multiport memory and floating-point {CORDIC} pipeline in {Jacobium} processing elements
booktitle:
1998 IEEE Workshop on Signal Processing Systems. SIPS 98. Design and Implementation (Cat. No. 98TH8374)

keywords:
Data analysis; Jacobian matrices; Jacobium dataflow processor; Pipelines; Process design; Symmetric matrices

rawbooktitle:
{1998 IEEE Workshop on Signal Processing Systems. SIPS 98. Design and Implementation (Cat. No. 98TH8374)}

entry:
@InProceedings{Looye:1998:MMF,
  author =       "A. Looye and G. Hekstra and E. Deprettere",
  booktitle =    "{1998 IEEE Workshop on Signal Processing Systems. SIPS
                 98. Design and Implementation (Cat. No. 98TH8374)}",
  title =        "Multiport memory and floating-point {CORDIC} pipeline
                 in {Jacobium} processing elements",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "406--416",
  year =         "1998",
  DOI =          "https://doi.org/10.1109/SIPS.1998.715803",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Data analysis; Jacobian matrices; Jacobium dataflow
                 processor; Pipelines; Process design; Symmetric
                 matrices",
}


bibtype: misc
filename: fparith.bib
label: LPT:1998:SC
author: Log Point Technologies
title: Soft CoProcessor
pages: 406--416
month: jun
monthnumber: 6
year: 1998
bibdate: Tue Jun 16 13:12:58 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.06.16 13:12:58 ???
URL: http://www.logpoint.com/; http://www.logpoint.com/prelimi.htm
acknowledgement: ack-nhfb
howpublished: World-Wide Web document.
rawauthor: {Log Point Technologies}
rawtitle: Soft {CoProcessor}
note:
This product provides software emulation of a logarithmic floating-point representation. Programming support is provided by a drop-in module for the GNU C compiler, tt gcc, and user-callable library support is available for several commercial compilers.

rawnote:
This product provides software emulation of a logarithmic floating-point representation. Programming support is provided by a drop-in module for the GNU C compiler, {\tt gcc}, and user-callable library support is available for several commercial compilers.

entry:
@Misc{LPT:1998:SC,
  author =       "{Log Point Technologies}",
  title =        "Soft {CoProcessor}",
  howpublished = "World-Wide Web document.",
  month =        jun,
  year =         "1998",
  bibdate =      "Tue Jun 16 13:12:58 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "This product provides software emulation of a
                 logarithmic floating-point representation. Programming
                 support is provided by a drop-in module for the GNU C
                 compiler, {\tt gcc}, and user-callable library support
                 is available for several commercial compilers.",
  URL =          "http://www.logpoint.com/;
                 http://www.logpoint.com/prelimi.htm",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Ma:1998:SAM
author: Yutai Ma
title: A simplified architecture for modulo $ (2^n + 1) $ multiplication
journal: j-IEEE-TRANS-COMPUT
volume: 47
number: 3
pages: 333--337
month: mar
monthnumber: 3
year: 1998
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.660169
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 09:35:54 MDT 2011
bibtimestamp: 2011.07.06 09:35:54 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=660169
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Yutai Ma
rawtitle: A simplified architecture for modulo $ (2^n + 1) $ multiplication
entry:
@Article{Ma:1998:SAM,
  author =       "Yutai Ma",
  title =        "A simplified architecture for modulo $ (2^n + 1) $
                 multiplication",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "3",
  pages =        "333--337",
  month =        mar,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.660169",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 09:35:54 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=660169",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: McCullough:1998:ARS
author: B. D. McCullough
title: Assessing the Reliability of Statistical Software: Part I
journal: j-AMER-STAT
volume: 52
number: 4
pages: 358--366
month: nov
monthnumber: 11
year: 1998
CODEN: ASTAAJ
ISSN: 0003-1305 (print), 1537-2731 (electronic) OR 00031305 (print), 15372731 (electronic)
ISSNL: 0003-1305 OR 00031305
bibdate: Fri Jan 27 14:51:25 MST 2012
bibtimestamp: 2012.01.27 14:51:25 MST
URL: http://www.jstor.org/stable/2685442
fjournal: The American Statistician
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/utas20
rawauthor: B. D. McCullough
rawtitle: Assessing the Reliability of Statistical Software: {Part I}
bibsource:
http://www.jstor.org/journals/00031305.html; http://www.jstor.org/stable/i326502; https://www.math.utah.edu/pub/tex/bib/amstat1990.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{McCullough:1998:ARS,
  author =       "B. D. McCullough",
  title =        "Assessing the Reliability of Statistical Software:
                 {Part I}",
  journal =      j-AMER-STAT,
  volume =       "52",
  number =       "4",
  pages =        "358--366",
  month =        nov,
  year =         "1998",
  CODEN =        "ASTAAJ",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  bibdate =      "Fri Jan 27 14:51:25 MST 2012",
  bibsource =    "http://www.jstor.org/journals/00031305.html;
                 http://www.jstor.org/stable/i326502;
                 https://www.math.utah.edu/pub/tex/bib/amstat1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.jstor.org/stable/2685442",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
}


bibtype: article
filename: fparith.bib
label: Mohan:1998:EFC
author: P. V. Ananda Mohan
title: Evaluation of fast conversion techniques for binary-residue number systems
journal: j-IEEE-TRANS-CIRCUITS-SYST-I-FUNDAM-THEORY-APPL
volume: 45
number: 10
pages: 1107--1109
month: oct
monthnumber: 10
year: 1998
CODEN: ITCAEX
DOI: https://doi.org/10.1109/81.728866
ISSNL: 1057-7122 OR 10577122
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: https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=15711
fjournal: IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=81
rawauthor: P. V. Ananda Mohan
rawtitle: Evaluation of fast conversion techniques for binary-residue number systems
entry:
@Article{Mohan:1998:EFC,
  author =       "P. V. Ananda Mohan",
  title =        "Evaluation of fast conversion techniques for
                 binary-residue number systems",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-I-FUNDAM-THEORY-APPL,
  volume =       "45",
  number =       "10",
  pages =        "1107--1109",
  month =        oct,
  year =         "1998",
  CODEN =        "ITCAEX",
  DOI =          "https://doi.org/10.1109/81.728866",
  ISSN =         "????",
  ISSN-L =       "1057-7122",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=15711",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems I:
                 Fundamental Theory and Applications",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=81",
  keywords =     "residue arithmetic; residue number system",
  summary =      "Vinnakota and Rao's RNS-to-binary converter proposed
                 recently (see ibid., vol. CAS-41, p. 927-9, 1994) for
                 the moduli set {2 n -1, 2 n and 2 n +1} is shown to be
                 a simple modification of the well-known Mixed Radix
                 \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Montalvo:1998:NST
author: L. A. Montalvo and K. K. Parhi and A. Guyot
title: New Svoboda--Tung division
journal: j-IEEE-TRANS-COMPUT
volume: 47
number: 9
pages: 1014--1020
month: sep
monthnumber: 9
year: 1998
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.713319
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: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=713319
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: L. A. Montalvo and K. K. Parhi and A. Guyot
rawtitle: New {Svoboda--Tung} division
entry:
@Article{Montalvo:1998:NST,
  author =       "L. A. Montalvo and K. K. Parhi and A. Guyot",
  title =        "New {Svoboda--Tung} division",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "9",
  pages =        "1014--1020",
  month =        sep,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.713319",
  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 =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=713319",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Moore:1998:CMC
author: G. E. Moore
title: Cramming More Components Onto Integrated Circuits
journal: j-PROC-IEEE
volume: 86
number: 1
pages: 82--85
month: jan
monthnumber: 1
year: 1998
CODEN: IEEPAD
DOI: https://doi.org/10.1109/jproc.1998.658762
ISSN: 0018-9219 (print), 1558-2256 (electronic) OR 00189219 (print), 15582256 (electronic)
ISSNL: 0018-9219 OR 00189219
bibdate: Fri Nov 14 07:42:34 2025
bibtimestamp: 2025.11.14 07:42:34 ???
fjournal: Proceedings of the IEEE
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5
rawauthor: G. E. Moore
rawtitle: Cramming More Components Onto Integrated Circuits
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/intel-ia-64.bib

remark:
Reprint of cite Moore:1965:CMC, with layout changes, and addition of roman numbering on section headings.

entry:
@Article{Moore:1998:CMC,
  author =       "G. E. Moore",
  title =        "Cramming More Components Onto Integrated Circuits",
  journal =      j-PROC-IEEE,
  volume =       "86",
  number =       "1",
  pages =        "82--85",
  month =        jan,
  year =         "1998",
  CODEN =        "IEEPAD",
  DOI =          "https://doi.org/10.1109/jproc.1998.658762",
  ISSN =         "0018-9219 (print), 1558-2256 (electronic)",
  ISSN-L =       "0018-9219",
  bibdate =      "Fri Nov 14 07:42:34 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/intel-ia-64.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the IEEE",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
  remark =       "Reprint of \cite{Moore:1965:CMC}, with layout changes,
                 and addition of roman numbering on section headings.",
}


bibtype: article
filename: fparith.bib
label: Moore:1998:MCP
author: J. S. Moore and T. W. Lynch and M. Kaufmann
title: A mechanically checked proof of the AMD5 K 86TM floating-point division program
journal: j-IEEE-TRANS-COMPUT
volume: 47
number: 9
pages: 913--926
month: sep
monthnumber: 9
year: 1998
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.713311
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: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=713311
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: J. S. Moore and T. W. Lynch and M. Kaufmann
rawtitle: A mechanically checked proof of the {AMD5 K 86{\TM}} floating-point division program
entry:
@Article{Moore:1998:MCP,
  author =       "J. S. Moore and T. W. Lynch and M. Kaufmann",
  title =        "A mechanically checked proof of the {AMD5 K 86{\TM}}
                 floating-point division program",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "9",
  pages =        "913--926",
  month =        sep,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.713311",
  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 =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=713311",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "We report on the successful application of a
                 mechanical theorem prover to the problem of verifying
                 the division microcode program used on the AMD5$_K$ 86
                 microprocessor. The division algorithm is an iterative
                 shift and subtract type. It was \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Murabayashi:1998:WBP
author: F. Murabayashi and T. Yamauchi and R. Yamagata and T. Shimizu
crossref: Huijsing:1998:EPE
pages: 440--443
year: 1998
bibdate: Sat Jun 02 08:21:00 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.06.02 08:21:00 ???
acknowledgement: ack-nhfb
rawauthor: F. Murabayashi and T. Yamauchi and R. Yamagata and T. Shimizu
title:
A 400MHz 160-Word $ times $ 64-Bit 14-Port Floating-point Register File Macrocell for a Superscalar RISC Processor

rawtitle:
A {400MHz} 160-Word $ \times $ 64-Bit 14-Port Floating-point Register File Macrocell for a Superscalar {RISC} Processor

entry:
@InProceedings{Murabayashi:1998:WBP,
  author =       "F. Murabayashi and T. Yamauchi and R. Yamagata and T.
                 Shimizu",
  title =        "A {400MHz} 160-Word $ \times $ 64-Bit 14-Port
                 Floating-point Register File Macrocell for a
                 Superscalar {RISC} Processor",
  crossref =     "Huijsing:1998:EPE",
  pages =        "440--443",
  year =         "1998",
  bibdate =      "Sat Jun 02 08:21:00 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: misc
filename: fparith.bib
label: Naffziger:1998:MAB
author: S. D. Naffziger and R. G. Beraha
pages: 440--443
day: 26
month: may
monthnumber: 5
year: 1998
bibdate: Fri Nov 28 15:35:29 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 15:35:29 ???
note: U.S. Patent No. 5,757,687.
acknowledgement: ack-nhfb
rawauthor: S. D. Naffziger and R. G. Beraha
rawnote: U.S. Patent No. 5,757,687.
title:
Method and apparatus for bounding alignment shifts to enable at speed denormalized result generation in an FMAC

rawtitle:
Method and apparatus for bounding alignment shifts to enable at speed denormalized result generation in an {FMAC}

entry:
@Misc{Naffziger:1998:MAB,
  author =       "S. D. Naffziger and R. G. Beraha",
  title =        "Method and apparatus for bounding alignment shifts to
                 enable at speed denormalized result generation in an
                 {FMAC}",
  day =          "26",
  month =        may,
  year =         "1998",
  bibdate =      "Fri Nov 28 15:35:29 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "U.S. Patent No. 5,757,687.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Nguyen:1998:MLS
author: Phong Nguyen
title: A Montgomery-Like Square Root for the Number Field Sieve
journal: j-LECT-NOTES-COMP-SCI
volume: 1423
pages: 151--??
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 11:52:18 MST 2002
bibtimestamp: 2002.02.05 11:52:18 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Phong Nguyen
rawtitle: A {Montgomery}-Like Square Root for the Number Field Sieve
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t1423.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/1423/14230151.htm; http://link.springer-ny.com/link/service/series/0558/papers/1423/14230151.pdf

entry:
@Article{Nguyen:1998:MLS,
  author =       "Phong Nguyen",
  title =        "A {Montgomery}-Like Square Root for the Number Field
                 Sieve",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1423",
  pages =        "151--??",
  year =         "1998",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Feb 5 11:52:18 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1423.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1423/14230151.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/1423/14230151.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: inproceedings
filename: fparith.bib
label: Oberman:1998:ATK
author: Stuart Oberman and Fred Weber and Norbert Juffa and Greg Favor
title: AMD 3DNow! Technology and the K6-2 Microprocessor
crossref: IEEE:1998:HCC
pages: 245--254
year: 1998
bibdate: Mon Jan 08 17:02:55 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.01.08 17:02:55 ???
acknowledgement: ack-nhfb
rawauthor: Stuart Oberman and Fred Weber and Norbert Juffa and Greg Favor
rawtitle: {AMD 3DNow!} Technology and the {K6-2} Microprocessor
entry:
@InProceedings{Oberman:1998:ATK,
  author =       "Stuart Oberman and Fred Weber and Norbert Juffa and
                 Greg Favor",
  title =        "{AMD 3DNow!} Technology and the {K6-2}
                 Microprocessor",
  crossref =     "IEEE:1998:HCC",
  pages =        "245--254",
  year =         "1998",
  bibdate =      "Mon Jan 08 17:02:55 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Oberman:1998:MCS
author: S. F. Oberman and M. J. Flynn
title: Minimizing the Complexity of SRT Tables
journal: j-IEEE-TRANS-VLSI-SYST
volume: 6
number: 1
pages: 141--149
year: 1998
CODEN: IEVSE9
DOI: https://doi.org/10.1109/92.661256
ISSN: 1063-8210 (print), 1557-9999 (electronic) OR 10638210 (print), 15579999 (electronic)
ISSNL: 1063-8210 OR 10638210
bibdate: Fri Mar 27 09:56:17 MST 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.03.27 09:56:17 MST
fjournal: IEEE Transactions on Very Large Scale Integration (VLSI) Systems
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/issues?punumber=92
rawauthor: S. F. Oberman and M. J. Flynn
rawtitle: Minimizing the Complexity of {SRT} Tables
entry:
@Article{Oberman:1998:MCS,
  author =       "S. F. Oberman and M. J. Flynn",
  title =        "Minimizing the Complexity of {SRT} Tables",
  journal =      j-IEEE-TRANS-VLSI-SYST,
  volume =       "6",
  number =       "1",
  pages =        "141--149",
  month =        "????",
  year =         "1998",
  CODEN =        "IEVSE9",
  DOI =          "https://doi.org/10.1109/92.661256",
  ISSN =         "1063-8210 (print), 1557-9999 (electronic)",
  ISSN-L =       "1063-8210",
  bibdate =      "Fri Mar 27 09:56:17 MST 1998",
  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",
}


bibtype: article
filename: fparith.bib
label: Oberman:1998:RML
author: S. F. Oberman and M. J. Flynn
title: Reducing the mean latency of floating-point addition
journal: j-THEOR-COMP-SCI
volume: 196
number: 1-2
pages: 201--214
day: 6
month: apr
monthnumber: 4
year: 1998
CODEN: TCSCDI
ISSN: 0304-3975 (print), 1879-2294 (electronic) OR 03043975 (print), 18792294 (electronic)
ISSNL: 0304-3975 OR 03043975
bibdate: Wed May 27 07:21:35 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.05.27 07:21:35 MDT
fjournal: Theoretical Computer Science
acknowledgement: ack-nhfb
corpsource: Comput. Syst. Lab., Stanford University, CA, USA
journalURL: http://www.sciencedirect.com/science/journal/03043975
treatment: P Practical
rawauthor: S. F. Oberman and M. J. Flynn
rawtitle: Reducing the mean latency of floating-point addition
keywords:
adders; floating point arithmetic; floating-point adder; floating-point addition; maximum throughput; mean addition latency; mean latency; microprocessors; shift-add-shift-round data flow; single-cycle throughput

entry:
@Article{Oberman:1998:RML,
  author =       "S. F. Oberman and M. J. Flynn",
  title =        "Reducing the mean latency of floating-point addition",
  journal =      j-THEOR-COMP-SCI,
  volume =       "196",
  number =       "1-2",
  pages =        "201--214",
  day =          "6",
  month =        apr,
  year =         "1998",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Wed May 27 07:21:35 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C5230 (Digital arithmetic methods)",
  corpsource =   "Comput. Syst. Lab., Stanford University, CA, USA",
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975",
  keywords =     "adders; floating point arithmetic; floating-point
                 adder; floating-point addition; maximum throughput;
                 mean addition latency; mean latency; microprocessors;
                 shift-add-shift-round data flow; single-cycle
                 throughput",
  pubcountry =   "Netherlands",
  treatment =    "P Practical",
}


bibtype: article
filename: fparith.bib
label: Paar:1998:EMA
author: C. Paar and P. Fleischmann and P. Roeise
title: Efficient multiplier architectures for Galois fields $ mathrm GF(2^4n) $
journal: j-IEEE-TRANS-COMPUT
volume: 47
number: 2
pages: 162--170
month: feb
monthnumber: 2
year: 1998
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.663762
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: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=663762
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: C. Paar and P. Fleischmann and P. Roeise
rawtitle: Efficient multiplier architectures for {Galois} fields {$ \mathrm {GF}(2^{4n}) $}
entry:
@Article{Paar:1998:EMA,
  author =       "C. Paar and P. Fleischmann and P. Roeise",
  title =        "Efficient multiplier architectures for {Galois} fields
                 {$ \mathrm {GF}(2^{4n}) $}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "2",
  pages =        "162--170",
  month =        feb,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.663762",
  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 =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=663762",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Paul:1998:CBR
author: Wolfgang J. Paul and Peter-Michael Seidel
title: On the complexity of Booth recoding
crossref: Chesneaux:1998:PCR
pages: 199--218
year: 1998
bibdate: Tue Mar 13 10:23:30 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.03.13 10:23:30 ???
remark: Cited in cite Mueller:2000:CAC.
acknowledgement: ack-nhfb
rawauthor: Wolfgang J. Paul and Peter-Michael Seidel
rawtitle: On the complexity of {Booth} recoding
entry:
@InProceedings{Paul:1998:CBR,
  author =       "Wolfgang J. Paul and Peter-Michael Seidel",
  title =        "On the complexity of {Booth} recoding",
  crossref =     "Chesneaux:1998:PCR",
  pages =        "199--218",
  year =         "1998",
  bibdate =      "Tue Mar 13 10:23:30 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Mueller:2000:CAC}.",
}


bibtype: article
filename: fparith.bib
label: Paulus:1998:CRI
author: Sachar Paulus and Andreas Stein
title: Comparing Real and Imaginary Arithmetics for Divisor Class Groups of Hyperelliptic Curves
journal: j-LECT-NOTES-COMP-SCI
volume: 1423
pages: 576--??
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 11:52:18 MST 2002
bibtimestamp: 2002.02.05 11:52:18 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Sachar Paulus and Andreas Stein
rawtitle: Comparing Real and Imaginary Arithmetics for Divisor Class Groups of Hyperelliptic Curves
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t1423.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/1423/14230576.htm; http://link.springer-ny.com/link/service/series/0558/papers/1423/14230576.pdf

entry:
@Article{Paulus:1998:CRI,
  author =       "Sachar Paulus and Andreas Stein",
  title =        "Comparing Real and Imaginary Arithmetics for Divisor
                 Class Groups of Hyperelliptic Curves",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1423",
  pages =        "576--??",
  year =         "1998",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Feb 5 11:52:18 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1423.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1423/14230576.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/1423/14230576.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: techreport
filename: fparith.bib
label: Pena:1998:CDI
author: J. Pena
title: Computing the Distance to Infeasibility: Theoretical and Practical Issues
type: Technical Report
institution: Center for Applied Mathematics, Cornell University
address: Ithaca, NY, USA
pages: 576--??
year: 1998
bibdate: Tue Nov 22 06:34:32 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.11.22 06:34:32 ???
keywords: accurate floating-point summation
acknowledgement: ack-nhfb
rawauthor: J. Pena
rawtitle: Computing the Distance to Infeasibility: Theoretical and Practical Issues
entry:
@TechReport{Pena:1998:CDI,
  author =       "J. Pena",
  title =        "Computing the Distance to Infeasibility: Theoretical
                 and Practical Issues",
  type =         "Technical Report",
  institution =  "Center for Applied Mathematics, Cornell University",
  address =      "Ithaca, NY, USA",
  year =         "1998",
  bibdate =      "Tue Nov 22 06:34:32 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation",
}


bibtype: inproceedings
filename: fparith.bib
label: Peuto:1998:ITM
author: Bernard L. Peuto and Leonard J. Shustek
title: An Instruction Timing Model of CPU Performance
crossref: Sohi:1998:YIS
pages: 152--163
year: 1998
bibdate: Fri Nov 28 18:36:16 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 18:36:16 ???
acknowledgement: ack-mfc
rawauthor: Bernard L. Peuto and Leonard J. Shustek
rawtitle: An Instruction Timing Model of {CPU} Performance
abstract:
A model of high-performance computers is derived from instruction timing formulas, with compensation for pipeline and cache memory effects. The model is used to predict the performance of the IBM 370/168 and the Amdahl 470 V/6 on specific programs, and the results are verified by comparison with actual performance. Data collected about program behavior is combined with the performance analysis to highlight some of the problems with high-performance implementations of such architectures.

rawabstract:
A model of high-performance computers is derived from instruction timing formulas, with compensation for pipeline and cache memory effects. The model is used to predict the performance of the IBM 370/168 and the Amdahl 470 V/6 on specific programs, and the results are verified by comparison with actual performance. Data collected about program behavior is combined with the performance analysis to highlight some of the problems with high-performance implementations of such architectures.

entry:
@InProceedings{Peuto:1998:ITM,
  author =       "Bernard L. Peuto and Leonard J. Shustek",
  title =        "An Instruction Timing Model of {CPU} Performance",
  crossref =     "Sohi:1998:YIS",
  pages =        "152--163",
  year =         "1998",
  bibdate =      "Fri Nov 28 18:36:16 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A model of high-performance computers is derived from
                 instruction timing formulas, with compensation for
                 pipeline and cache memory effects. The model is used to
                 predict the performance of the IBM 370/168 and the
                 Amdahl 470 V/6 on specific programs, and the results
                 are verified by comparison with actual performance.
                 Data collected about program behavior is combined with
                 the performance analysis to highlight some of the
                 problems with high-performance implementations of such
                 architectures.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
}


bibtype: book
filename: fparith.bib
label: Rajski:1998:ABS
author: Janusz Rajski and Jerzy Tyszer
title: Arithmetic built-in self-test for embedded systems
publisher: pub-PHPTR
address: pub-PHPTR:adr
pages: xii + 268
year: 1998
ISBN: 0-13-756438-4 OR 0137564384
ISBN13: 978-0-13-756438-5 OR 9780137564385
LCCN: TK7895.E42 R35 1998
bibdate: Mon Dec 24 09:18:51 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2007.12.24 09:18:51 MST
keywords: BIST (Built-In Self Test); DFT (Design for Testability); floating-point testing
subject: Embedded computer systems; Testing; Computer firmware
acknowledgement: ack-nhfb
rawauthor: Janusz Rajski and Jerzy Tyszer
rawtitle: Arithmetic built-in self-test for embedded systems
TOC:
1. Built-In Self-Test. Introduction. Design for Testability. Generation of Test Vectors. Compaction of Test Responses. BIST Schemes for Random Logic. BIST for Memory Arrays 2. Generation of Test Vectors. Additive Generators of Exhaustive Patterns. Other Generation Schemes. Two-Dimensional Generators 3. Test-Response Compaction. Binary Adders. 1's Complement Adders. Rotate-Carry Adders. Cascaded Compaction Scheme 4. Fault Diagnosis. Analytical Model. Experimental Validation. The Quality of Diagnostic Resolution. Fault Diagnosis in Scan-Based Designs 5. BIST of Data-Path Kernel. Testing of ALU. Testing of the MAC Unit. Testing of the Microcontroller 6. Fault Grading. Fault Simulation Framework. Functional Fault Simulation. Experimental Results 7. High-Level Synthesis. Implementation-Dependent Fault Grading. Synthesis Steps. Simulation Results 8. ABIST at Work. Testing of Random Logic. Memory Testing. Digital Integrators. Leaking Integrators 9. Epilog A. Tables of Generators B. Assembly Language Bibliography Index

rawTOC:
1. Built-In Self-Test. Introduction. Design for Testability. Generation of Test Vectors. Compaction of Test Responses. BIST Schemes for Random Logic. BIST for Memory Arrays\\ 2. Generation of Test Vectors. Additive Generators of Exhaustive Patterns. Other Generation Schemes. Two-Dimensional Generators\\ 3. Test-Response Compaction. Binary Adders. 1's Complement Adders. Rotate-Carry Adders. Cascaded Compaction Scheme\\ 4. Fault Diagnosis. Analytical Model. Experimental Validation. The Quality of Diagnostic Resolution. Fault Diagnosis in Scan-Based Designs\\ 5. BIST of Data-Path Kernel. Testing of ALU. Testing of the MAC Unit. Testing of the Microcontroller\\ 6. Fault Grading. Fault Simulation Framework. Functional Fault Simulation. Experimental Results\\ 7. High-Level Synthesis. Implementation-Dependent Fault Grading. Synthesis Steps. Simulation Results\\ 8. ABIST at Work. Testing of Random Logic. Memory Testing. Digital Integrators. Leaking Integrators\\ 9. Epilog\\ A. Tables of Generators\\ B. Assembly Language\\ Bibliography\\ Index

entry:
@Book{Rajski:1998:ABS,
  author =       "Janusz Rajski and Jerzy Tyszer",
  title =        "Arithmetic built-in self-test for embedded systems",
  publisher =    pub-PHPTR,
  address =      pub-PHPTR:adr,
  pages =        "xii + 268",
  year =         "1998",
  ISBN =         "0-13-756438-4",
  ISBN-13 =      "978-0-13-756438-5",
  LCCN =         "TK7895.E42 R35 1998",
  bibdate =      "Mon Dec 24 09:18:51 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  keywords =     "BIST (Built-In Self Test); DFT (Design for
                 Testability); floating-point testing",
  subject =      "Embedded computer systems; Testing; Computer
                 firmware",
  tableofcontents = "1. Built-In Self-Test. Introduction. Design for
                 Testability. Generation of Test Vectors. Compaction of
                 Test Responses. BIST Schemes for Random Logic. BIST for
                 Memory Arrays\\
                 2. Generation of Test Vectors. Additive Generators of
                 Exhaustive Patterns. Other Generation Schemes.
                 Two-Dimensional Generators\\
                 3. Test-Response Compaction. Binary Adders. 1's
                 Complement Adders. Rotate-Carry Adders. Cascaded
                 Compaction Scheme\\
                 4. Fault Diagnosis. Analytical Model. Experimental
                 Validation. The Quality of Diagnostic Resolution. Fault
                 Diagnosis in Scan-Based Designs\\
                 5. BIST of Data-Path Kernel. Testing of ALU. Testing of
                 the MAC Unit. Testing of the Microcontroller\\
                 6. Fault Grading. Fault Simulation Framework.
                 Functional Fault Simulation. Experimental Results\\
                 7. High-Level Synthesis. Implementation-Dependent Fault
                 Grading. Synthesis Steps. Simulation Results\\
                 8. ABIST at Work. Testing of Random Logic. Memory
                 Testing. Digital Integrators. Leaking Integrators\\
                 9. Epilog\\
                 A. Tables of Generators\\
                 B. Assembly Language\\
                 Bibliography\\
                 Index",
}


bibtype: article
filename: fparith.bib
label: Rivolo:1998:CDR
author: M. T. Rivolo and A. Simi
journal: j-ARCH-HIST-EXACT-SCI
volume: 52
number: 2
pages: 161--193
month: feb
monthnumber: 2
year: 1998
CODEN: AHESAN
DOI: https://doi.org/10.1007/s004070050015
ISSN: 0003-9519 (print), 1432-0657 (electronic) OR 00039519 (print), 14320657 (electronic)
ISSNL: 0003-9519 OR 00039519
MRclass: 01A35 (01A40)
MRnumber: 1610136 (99d:01015)
MRreviewer: Massimo Galuzzi
bibdate: Fri Feb 4 21:50:33 MST 2011
bibtimestamp: 2011.02.04 21:50:33 MST
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0003-9519&volume=52&issue=2&spage=161
fjournal: Archive for History of Exact Sciences
language: Italian
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/407
rawauthor: M. T. Rivolo and A. Simi
title:
Il Calcolo delle Radici Quadrate e Cubiche in Italia da Fibonacci a Bombelli. (Italian) [The calculation of square and cube roots in Italy from Fibonacci to Bombelli]

bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0003-9519&volume=52&issue=2; https://www.math.utah.edu/pub/tex/bib/fibquart.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

rawtitle:
Il Calcolo delle Radici Quadrate e Cubiche in {Italia} da {Fibonacci} a {Bombelli}. ({Italian}) [{The} calculation of square and cube roots in {Italy} from {Fibonacci} to {Bombelli}]

entry:
@Article{Rivolo:1998:CDR,
  author =       "M. T. Rivolo and A. Simi",
  title =        "Il Calcolo delle Radici Quadrate e Cubiche in {Italia}
                 da {Fibonacci} a {Bombelli}. ({Italian}) [{The}
                 calculation of square and cube roots in {Italy} from
                 {Fibonacci} to {Bombelli}]",
  journal =      j-ARCH-HIST-EXACT-SCI,
  volume =       "52",
  number =       "2",
  pages =        "161--193",
  month =        feb,
  year =         "1998",
  CODEN =        "AHESAN",
  DOI =          "https://doi.org/10.1007/s004070050015",
  ISSN =         "0003-9519 (print), 1432-0657 (electronic)",
  ISSN-L =       "0003-9519",
  MRclass =      "01A35 (01A40)",
  MRnumber =     "1610136 (99d:01015)",
  MRreviewer =   "Massimo Galuzzi",
  bibdate =      "Fri Feb 4 21:50:33 MST 2011",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0003-9519&volume=52&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0003-9519&volume=52&issue=2&spage=161",
  acknowledgement = ack-nhfb,
  fjournal =     "Archive for History of Exact Sciences",
  journal-URL =  "http://link.springer.com/journal/407",
  language =     "Italian",
  MRtitle =      "The computation of square and cube roots in {Italy}
                 from {Fibonacci} to {Bombelli}",
}


bibtype: misc
filename: fparith.bib
label: Russinoff:1998:MCPa
author: D. M. Russinoff
pages: 161--193
year: 1998
bibdate: Fri Nov 29 09:41:27 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.11.29 09:41:27 ???
note: See journal article cite Russinoff:1998:MCPb.
URL: http://www.onr.com/user/russ/david/k7-div-sqrt.html
remark: Cited in cite Mueller:2000:CAC.
acknowledgement: ack-nhfb
howpublished: World-Wide Web document.
rawauthor: D. M. Russinoff
rawnote: See journal article \cite{Russinoff:1998:MCPb}.
title:
A mechanically-checked proof of IEEE compliance of a register-transfer-level specification of the AMD K7 floating-point division and square root instructions

rawtitle:
A mechanically-checked proof of {IEEE} compliance of a register-transfer-level specification of the {AMD K7} floating-point division and square root instructions

entry:
@Misc{Russinoff:1998:MCPa,
  author =       "D. M. Russinoff",
  title =        "A mechanically-checked proof of {IEEE} compliance of a
                 register-transfer-level specification of the {AMD K7}
                 floating-point division and square root instructions",
  howpublished = "World-Wide Web document.",
  year =         "1998",
  bibdate =      "Fri Nov 29 09:41:27 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See journal article \cite{Russinoff:1998:MCPb}.",
  URL =          "http://www.onr.com/user/russ/david/k7-div-sqrt.html",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Mueller:2000:CAC}.",
}


bibtype: article
filename: fparith.bib
label: Russinoff:1998:MCPb
author: David M. Russinoff
journal: j-LMS-J-COMPUT-MATH
volume: 1
pages: 148--200
year: 1998
ISSN: 1461-1570 OR 14611570
MRclass: 68M07 (65Y99 68T15)
MRnumber: 99m:68015
MRreviewer: J. Michel Muller
bibdate: Wed Nov 24 09:19:02 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.24 09:19:02 ???
URL: http://www.lms.ac.uk/jcm/1/lms1998-001/; http://www.onr.com/user/russ/david/k7-div-sqrt.ps
fjournal: LMS Journal of Computation and Mathematics
acknowledgement: ack-nhfb
journalURL: http://journals.cambridge.org/action/displayJournal?jid=JCM
rawauthor: David M. Russinoff
title:
A mechanically checked proof of IEEE compliance of the floating point multiplication, division and square root algorithms of the AMD-K7TM processor

note:
Appendices A and B available to subscribers electronically (http://www.lms.ac.uk/jcm/1/lms98001/appendix-a/ and http://www.lms.ac.uk/jcm/1/lms98001/appendix-b/)

rawnote:
Appendices A and B available to subscribers electronically (http://www.lms.ac.uk/jcm/1/lms98001/appendix-a/ and http://www.lms.ac.uk/jcm/1/lms98001/appendix-b/)

rawtitle:
A mechanically checked proof of {IEEE} compliance of the floating point multiplication, division and square root algorithms of the {AMD-K7{\TM}} processor

entry:
@Article{Russinoff:1998:MCPb,
  author =       "David M. Russinoff",
  title =        "A mechanically checked proof of {IEEE} compliance of
                 the floating point multiplication, division and square
                 root algorithms of the {AMD-K7{\TM}} processor",
  journal =      j-LMS-J-COMPUT-MATH,
  volume =       "1",
  pages =        "148--200",
  year =         "1998",
  CODEN =        "????",
  ISSN =         "1461-1570",
  MRclass =      "68M07 (65Y99 68T15)",
  MRnumber =     "99m:68015",
  MRreviewer =   "J. Michel Muller",
  bibdate =      "Wed Nov 24 09:19:02 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Appendices A and B available to subscribers
                 electronically
                 (http://www.lms.ac.uk/jcm/1/lms98001/appendix-a/ and
                 http://www.lms.ac.uk/jcm/1/lms98001/appendix-b/)",
  URL =          "http://www.lms.ac.uk/jcm/1/lms1998-001/;
                 http://www.onr.com/user/russ/david/k7-div-sqrt.ps",
  acknowledgement = ack-nhfb,
  fjournal =     "LMS Journal of Computation and Mathematics",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=JCM",
}


bibtype: inproceedings
filename: fparith.bib
label: Sasaki:1998:ACE
author: Tateaki Sasaki and Satoshi Yamaguchi
crossref: Gloor:1998:IPI
pages: 1--8
year: 1998
bibdate: Wed Sep 16 17:16:31 1998
bibtimestamp: 1998.09.16 17:16:31 ???
URL: http://www.acm.org/pubs/citations/proceedings/issac/281508/p1-sasaki/
acknowledgement: ack-nhfb
rawauthor: Tateaki Sasaki and Satoshi Yamaguchi
title:
An analysis of cancellation error in multivariate Hensel construction with floating-point number arithmetic

bibsource:
http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html; https://www.math.utah.edu/pub/tex/bib/fparith.bib

rawtitle:
An analysis of cancellation error in multivariate {Hensel} construction with floating-point number arithmetic

entry:
@InProceedings{Sasaki:1998:ACE,
  author =       "Tateaki Sasaki and Satoshi Yamaguchi",
  title =        "An analysis of cancellation error in multivariate
                 {Hensel} construction with floating-point number
                 arithmetic",
  crossref =     "Gloor:1998:IPI",
  pages =        "1--8",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p1-sasaki/",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Sasaki:1998:CEM
author: Tateaki Sasaki and Tomoyuki Sato
title: Cancellation Errors in Multivariate Resultant Computation with Floating-point Numbers
journal: j-SIGSAM
volume: 32
number: 4
pages: 13--20
month: dec
monthnumber: 12
year: 1998
CODEN: SIGSBZ
ISSN: 0163-5824 (print), 1557-9492 (electronic) OR 01635824 (print), 15579492 (electronic)
ISSNL: 0163-5824 OR 01635824
bibdate: Wed Apr 14 15:21:10 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1999.04.14 15:21:10 ???
fjournal: SIGSAM Bulletin
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J1000
issue: 126
rawauthor: Tateaki Sasaki and Tomoyuki Sato
rawtitle: Cancellation Errors in Multivariate Resultant Computation with Floating-point Numbers
entry:
@Article{Sasaki:1998:CEM,
  author =       "Tateaki Sasaki and Tomoyuki Sato",
  title =        "Cancellation Errors in Multivariate Resultant
                 Computation with Floating-point Numbers",
  journal =      j-SIGSAM,
  volume =       "32",
  number =       "4",
  pages =        "13--20",
  month =        dec,
  year =         "1998",
  CODEN =        "SIGSBZ",
  ISSN =         "0163-5824 (print), 1557-9492 (electronic)",
  ISSN-L =       "0163-5824",
  bibdate =      "Wed Apr 14 15:21:10 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIGSAM Bulletin",
  issue =        "126",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}


bibtype: article
filename: fparith.bib
label: Sastry:1998:EIF
author: S. Subramanya Sastry and Subbarao Palacharla and James E. Smith
title: Exploiting Idle Floating-Point Resources for Integer Execution
journal: j-SIGPLAN
volume: 33
number: 5
pages: 118--129
month: may
monthnumber: 5
year: 1998
CODEN: SINODQ
ISBN: 0-89791-987-4 OR 0897919874
ISBN13: 978-0-89791-987-6 OR 9780897919876
ISSN: 0362-1340 (print), 1523-2867 (print), 1558-1160 OR 03621340 (print), 15232867 (print), 15581160
ISSNL: 0362-1340 OR 03621340
bibdate: Sun Dec 14 09:17:47 MST 2003
bibtimestamp: 2003.12.14 09:17:47 MST
URL: http://www.acm.org:80/pubs/citations/proceedings/pldi/277650/p118-sastry/
fjournal: ACM SIGPLAN Notices
keywords: algorithms; performance
remark: Published as part of the Proceedings of PLDI'98.
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J706
rawauthor: S. Subramanya Sastry and Subbarao Palacharla and James E. Smith
rawtitle: Exploiting Idle Floating-Point Resources for Integer Execution
bibsource:
http://portal.acm.org/; http://www.acm.org/pubs/contents/proceedings/pldi/277650/index.html; http://www.cs.virginia.edu/pldi98/program.html; https://www.math.utah.edu/pub/tex/bib/fparith.bib

subject:
bf D.3.4 Software, PROGRAMMING LANGUAGES, Processors, Compilers. bf D.3.4 Software, PROGRAMMING LANGUAGES, Processors, Optimization. bf G.1.0 Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic.

entry:
@Article{Sastry:1998:EIF,
  author =       "S. Subramanya Sastry and Subbarao Palacharla and James
                 E. Smith",
  title =        "Exploiting Idle Floating-Point Resources for Integer
                 Execution",
  journal =      j-SIGPLAN,
  volume =       "33",
  number =       "5",
  pages =        "118--129",
  month =        may,
  year =         "1998",
  CODEN =        "SINODQ",
  ISBN =         "0-89791-987-4",
  ISBN-13 =      "978-0-89791-987-6",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sun Dec 14 09:17:47 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.acm.org/pubs/contents/proceedings/pldi/277650/index.html;
                 http://www.cs.virginia.edu/pldi98/program.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/pldi/277650/p118-sastry/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "algorithms; performance",
  remark =       "Published as part of the Proceedings of PLDI'98.",
  subject =      "{\bf D.3.4} Software, PROGRAMMING LANGUAGES,
                 Processors, Compilers. {\bf D.3.4} Software,
                 PROGRAMMING LANGUAGES, Processors, Optimization. {\bf
                 G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS,
                 General, Computer arithmetic.",
}


bibtype: inproceedings
filename: fparith.bib
label: Seidel:1998:HHL
author: Peter-Michael Seidel
title: How to half [sic] the latency of IEEE compliant floating-point multiplication
crossref: IEEE:1998:IOM
pages: 329--332
year: 1998
bibdate: Fri Jun 24 20:55:14 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.06.24 20:55:14 ???
acknowledgement: ack-nhfb
rawauthor: Peter-Michael Seidel
rawtitle: How to half [sic] the latency of {IEEE} compliant floating-point multiplication
entry:
@InProceedings{Seidel:1998:HHL,
  author =       "Peter-Michael Seidel",
  title =        "How to half [sic] the latency of {IEEE} compliant
                 floating-point multiplication",
  crossref =     "IEEE:1998:IOM",
  pages =        "329--332",
  year =         "1998",
  bibdate =      "Fri Jun 24 20:55:14 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Seidel:1998:HSR
author: P.-M. (Peter-Michael) Seidel
booktitle: Proceedings of the 3rd Conference on Real Numbers and Computers (RNC3), Paris, April 1998
title: High-Speed Redundant Reciprocal Approximation
pages: 219--229
year: 1998
bibdate: Sat Jun 25 07:46:25 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.06.25 07:46:25 ???
acknowledgement: ack-nhfb
rawauthor: P.-M. (Peter-Michael) Seidel
rawbooktitle: Proceedings of the 3rd Conference on Real Numbers and Computers ({RNC3}), Paris, April 1998
rawtitle: High-Speed Redundant Reciprocal Approximation
entry:
@InProceedings{Seidel:1998:HSR,
  author =       "P.-M. (Peter-Michael) Seidel",
  booktitle =    "Proceedings of the 3rd Conference on Real Numbers and
                 Computers ({RNC3}), Paris, April 1998",
  title =        "High-Speed Redundant Reciprocal Approximation",
  publisher =    "????",
  address =      "????",
  pages =        "219--229",
  year =         "1998",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Jun 25 07:46:25 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: misc
filename: fparith.bib
label: Severance:1998:IOM
author: C. Severance
title: An interview with the old man of floating-point: Reminiscences elicited from William Kahan
pages: 219--229
year: 1998
bibdate: Sat Apr 28 19:05:42 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.04.28 19:05:42 ???
note: A shortened version appears in cite Severance:1998:SII.
URL: http://www.cs.berkeley.edu/~wkahan/ieee754status/754story.html
acknowledgement: ack-nhfb
howpublished: World-Wide Web document.
rawauthor: C. Severance
rawnote: A shortened version appears in \cite{Severance:1998:SII}.
rawtitle: An interview with the old man of floating-point: Reminiscences elicited from {William Kahan}
entry:
@Misc{Severance:1998:IOM,
  author =       "C. Severance",
  title =        "An interview with the old man of floating-point:
                 Reminiscences elicited from {William Kahan}",
  howpublished = "World-Wide Web document.",
  year =         "1998",
  bibdate =      "Sat Apr 28 19:05:42 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "A shortened version appears in
                 \cite{Severance:1998:SII}.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/ieee754status/754story.html",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Severance:1998:SII
author: Charles Severance
title: Standards: IEEE 754: An Interview with William Kahan
journal: j-COMPUTER
volume: 31
number: 3
pages: 114--115
month: mar
monthnumber: 3
year: 1998
CODEN: CPTRB4
ISSN: 0018-9162 (print), 1558-0814 (electronic) OR 00189162 (print), 15580814 (electronic)
ISSNL: 0018-9162 OR 00189162
bibdate: Wed Mar 4 10:07:59 MST 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.03.04 10:07:59 MST
URL: http://pdf.computer.org/co/books/co1998/pdf/r3114.pdf
fjournal: Computer
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2
rawauthor: Charles Severance
rawtitle: Standards: {IEEE 754}: An Interview with {William Kahan}
entry:
@Article{Severance:1998:SII,
  author =       "Charles Severance",
  title =        "Standards: {IEEE 754}: An Interview with {William
                 Kahan}",
  journal =      j-COMPUTER,
  volume =       "31",
  number =       "3",
  pages =        "114--115",
  month =        mar,
  year =         "1998",
  CODEN =        "CPTRB4",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Wed Mar 4 10:07:59 MST 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://pdf.computer.org/co/books/co1998/pdf/r3114.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}


bibtype: inproceedings
filename: fparith.bib
label: Simons:1998:IFP
author: N. R. S. Simons and G. E. Bridges and B. Ghosh and M. Cuhaci
booktitle: 1998. IEEE Antennas and Propagation Society International Symposium. 21--26 June 1998
volume: 1
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 260--263
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: N. R. S. Simons and G. E. Bridges and B. Ghosh and M. Cuhaci
rawbooktitle: 1998. {IEEE} Antennas and Propagation Society International Symposium. 21--26 June 1998
title:
Investigation of floating-point round-off errors within time-domain electromagnetic field computations

rawtitle:
Investigation of floating-point round-off errors within time-domain electromagnetic field computations

entry:
@InProceedings{Simons:1998:IFP,
  author =       "N. R. S. Simons and G. E. Bridges and B. Ghosh and M.
                 Cuhaci",
  booktitle =    "1998. {IEEE} Antennas and Propagation Society
                 International Symposium. 21--26 June 1998",
  title =        "Investigation of floating-point round-off errors
                 within time-domain electromagnetic field computations",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "260--263",
  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 =      "We present an investigation of floating-point
                 round-off errors within time-domain electromagnetic
                 field computations. Our eventual goal is to determine
                 the minimal computational requirements for the
                 successful implementation of algorithms for \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Skavantzos:1998:ERW
author: A. Skavantzos
booktitle: Proceedings of the 8th Great Lakes Symposium on VLSI, 1998
title: An efficient residue to weighted converter for a new residue number system
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 185--191
year: 1998
DOI: https://doi.org/10.1109/GLSV.1998.665223
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. Skavantzos
rawbooktitle: Proceedings of the 8th Great Lakes Symposium on {VLSI, 1998}
rawtitle: An efficient residue to weighted converter for a new residue number system
entry:
@InProceedings{Skavantzos:1998:ERW,
  author =       "A. Skavantzos",
  booktitle =    "Proceedings of the 8th Great Lakes Symposium on {VLSI,
                 1998}",
  title =        "An efficient residue to weighted converter for a new
                 residue number system",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "185--191",
  year =         "1998",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/GLSV.1998.665223",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "The Residue Number System (RNS) is an integer system
                 appropriate far implementing fast digital signal
                 processors since it can support parallel, carry-free,
                 high-speed arithmetic. In this paper a new RNS system
                 and an efficient implementation of its \ldots{}",
}


bibtype: misc
filename: fparith.bib
label: Slabodkin:1998:SGL
author: G. Slabodkin
title: Software glitches leave Navy Smart Ship dead in the water
pages: 185--191
day: 31
month: jul
monthnumber: 7
year: 1998
bibdate: Mon Aug 26 11:13:26 2024
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2024.08.26 11:13:26 ???
URL: https://www.rose-hulman.edu/class/cs/csse442/current/hw/homework6-story.pdf
keywords: Aegis missile cruiser USS Yorktown
acknowledgement: ack-nhfb
howpublished: Web site
rawauthor: G. Slabodkin
rawtitle: Software glitches leave {Navy Smart Ship} dead in the water
entry:
@Misc{Slabodkin:1998:SGL,
  author =       "G. Slabodkin",
  title =        "Software glitches leave {Navy Smart Ship} dead in the
                 water",
  howpublished = "Web site",
  day =          "31",
  month =        jul,
  year =         "1998",
  bibdate =      "Mon Aug 26 11:13:26 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.rose-hulman.edu/class/cs/csse442/current/hw/homework6-story.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "Aegis missile cruiser USS Yorktown",
}


bibtype: article
filename: fparith.bib
label: Smith:1998:AMP
author: David M. Smith
title: Algorithm 786: Multiple-Precision Complex Arithmetic and Functions
journal: j-TOMS
volume: 24
number: 4
pages: 359--367
month: dec
monthnumber: 12
year: 1998
CODEN: ACMSCU
DOI: https://doi.org/10.1145/293686.293687
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Mar 09 10:09:51 1999
bibtimestamp: 1999.03.09 10:09:51 ???
note: See also cite Bailey:1995:FBM,Brent:1978:AMF,Brent:1979:RMF,Brent:1980:AIB.
URL: http://www.acm.org:80/pubs/citations/journals/toms/1998-24-4/p359-smith/
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms; correct rounding; floating-point arithmetic; performance; reliability
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: David M. Smith
rawnote: See also \cite{Bailey:1995:FBM,Brent:1978:AMF,Brent:1979:RMF,Brent:1980:AIB}.
rawtitle: {Algorithm 786}: Multiple-Precision Complex Arithmetic and Functions
bibsource:
http://www.acm.org/pubs/contents/journals/toms/1998-24/; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
The article describes a collection of Fortran routines for multiple-precision complex arithmetic and elementary functions. The package provides good exception handling, flexible input and output, trace features, and results that are almost always correctly rounded. For best efficiency on different machines, the user can change the arithmetic type used to represent the multiple-precision numbers.

subject:
bf G.1.0 Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic. bf G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation. bf G.4 Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm design and analysis. bf G.4 Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency. bf G.4 Mathematics of Computing, MATHEMATICAL SOFTWARE, Portability**.

rawabstract:
The article describes a collection of Fortran routines for multiple-precision complex arithmetic and elementary functions. The package provides good exception handling, flexible input and output, trace features, and results that are almost always correctly rounded. For best efficiency on different machines, the user can change the arithmetic type used to represent the multiple-precision numbers.

entry:
@Article{Smith:1998:AMP,
  author =       "David M. Smith",
  title =        "{Algorithm 786}: Multiple-Precision Complex Arithmetic
                 and Functions",
  journal =      j-TOMS,
  volume =       "24",
  number =       "4",
  pages =        "359--367",
  month =        dec,
  year =         "1998",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/293686.293687",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 09 10:09:51 1999",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/1998-24/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See also
                 \cite{Bailey:1995:FBM,Brent:1978:AMF,Brent:1979:RMF,Brent:1980:AIB}.",
  URL =          "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-4/p359-smith/",
  abstract =     "The article describes a collection of Fortran routines
                 for multiple-precision complex arithmetic and
                 elementary functions. The package provides good
                 exception handling, flexible input and output, trace
                 features, and results that are almost always correctly
                 rounded. For best efficiency on different machines, the
                 user can change the arithmetic type used to represent
                 the multiple-precision numbers.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; correct rounding; floating-point
                 arithmetic; performance; reliability",
  subject =      "{\bf G.1.0} Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Computer arithmetic. {\bf G.1.2}
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation. {\bf
                 G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Algorithm design and analysis. {\bf G.4} Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf G.4}
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Portability**.",
}


bibtype: article
filename: fparith.bib
label: Stelling:1998:OCP
author: P. F. Stelling and C. U. Martel and V. G. Oklobdzija and R. Ravi
title: Optimal circuits for parallel multipliers
journal: j-IEEE-TRANS-COMPUT
volume: 47
number: 3
pages: 273--285
month: mar
monthnumber: 3
year: 1998
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.660163
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 09:35:54 MDT 2011
bibtimestamp: 2011.07.06 09:35:54 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=660163
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: P. F. Stelling and C. U. Martel and V. G. Oklobdzija and R. Ravi
rawtitle: Optimal circuits for parallel multipliers
entry:
@Article{Stelling:1998:OCP,
  author =       "P. F. Stelling and C. U. Martel and V. G. Oklobdzija
                 and R. Ravi",
  title =        "Optimal circuits for parallel multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "3",
  pages =        "273--285",
  month =        mar,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.660163",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 09:35:54 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=660163",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Stine:1998:CIFa
author: J. E. Stine and M. J. Schulte
title: A Combined Interval and Floating Point Divider
crossref: Matthews:1998:CRT
pages: 218--222
year: 1998
bibdate: Sun Mar 04 10:59:12 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.03.04 10:59:12 ???
URL: http://mesa.ece.wisc.edu/publications/cp_1998-02.pdf
acknowledgement: ack-nhfb
rawauthor: J. E. Stine and M. J. Schulte
rawtitle: A Combined Interval and Floating Point Divider
entry:
@InProceedings{Stine:1998:CIFa,
  author =       "J. E. Stine and M. J. Schulte",
  title =        "A Combined Interval and Floating Point Divider",
  crossref =     "Matthews:1998:CRT",
  pages =        "218--222",
  year =         "1998",
  bibdate =      "Sun Mar 04 10:59:12 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1998-02.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Stine:1998:CIFb
author: J. E. Stine and M. J. Schulte
title: A Combined Interval and Floating Point Multiplier
crossref: IEEE:1998:PGL
pages: 208--213
year: 1998
bibdate: Sun Mar 04 10:59:12 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.03.04 10:59:12 ???
URL: http://mesa.ece.wisc.edu/publications/cp_1998-01.pdf
acknowledgement: ack-nhfb
rawauthor: J. E. Stine and M. J. Schulte
rawtitle: A Combined Interval and Floating Point Multiplier
entry:
@InProceedings{Stine:1998:CIFb,
  author =       "J. E. Stine and M. J. Schulte",
  title =        "A Combined Interval and Floating Point Multiplier",
  crossref =     "IEEE:1998:PGL",
  pages =        "208--213",
  year =         "1998",
  bibdate =      "Sun Mar 04 10:59:12 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1998-01.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Takagi:1998:PTL
author: N. Takagi
title: Powering by a table look-up and a multiplication with operand modification
journal: j-IEEE-TRANS-COMPUT
volume: 47
number: 11
pages: 1216--1222
month: nov
monthnumber: 11
year: 1998
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.736432
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: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=736432
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: N. Takagi
rawtitle: Powering by a table look-up and a multiplication with operand modification
entry:
@Article{Takagi:1998:PTL,
  author =       "N. Takagi",
  title =        "Powering by a table look-up and a multiplication with
                 operand modification",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "11",
  pages =        "1216--1222",
  month =        nov,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.736432",
  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 =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=736432",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Takashi:1998:FPN
author: Y. Takashi
title: Floating Point Number Format with Number System with Base of 1000
journal: j-IBM-TDB
volume: 01-98
pages: 609--610
month: jan
monthnumber: 1
year: 1998
CODEN: IBMTAA
ISSN: 0018-8689 OR 00188689
bibdate: Fri Nov 28 19:29:01 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 19:29:01 ???
fjournal: IBM Technical Disclosure Bulletin
acknowledgement: ack-mfc
rawauthor: Y. Takashi
rawtitle: Floating Point Number Format with Number System with Base of 1000
abstract:
Disclosed is a use number system with a base of 1000 instead of 2 at the mantissa part of a floating point number. The unit is 10 bit. Each 10 bit keeps the value between 0 and 1000. This format is superior to Binary Coded Decimal (BCD) because it can keep more decimal numbers in the same size. This format is superior to binary because 1000 is 100 times of 10, and it makes no difference when converted to/from human's decimal format.

rawabstract:
Disclosed is a use number system with a base of 1000 instead of 2 at the mantissa part of a floating point number. The unit is 10 bit. Each 10 bit keeps the value between 0 and 1000. This format is superior to Binary Coded Decimal (BCD) because it can keep more decimal numbers in the same size. This format is superior to binary because 1000 is 100 times of 10, and it makes no difference when converted to/from human's decimal format.

entry:
@Article{Takashi:1998:FPN,
  author =       "Y. Takashi",
  title =        "Floating Point Number Format with Number System with
                 Base of 1000",
  journal =      j-IBM-TDB,
  volume =       "01-98",
  pages =        "609--610",
  month =        jan,
  year =         "1998",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Fri Nov 28 19:29:01 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Disclosed is a use number system with a base of 1000
                 instead of 2 at the mantissa part of a floating point
                 number. The unit is 10 bit. Each 10 bit keeps the value
                 between 0 and 1000. This format is superior to Binary
                 Coded Decimal (BCD) because it can keep more decimal
                 numbers in the same size. This format is superior to
                 binary because 1000 is 100 times of 10, and it makes no
                 difference when converted to/from human's decimal
                 format.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  fjournal =     "IBM Technical Disclosure Bulletin",
}


bibtype: article
filename: fparith.bib
label: Thorup:1998:FIS
author: M. Thorup
title: Floats, Integers, and Single Source Shortest Paths
journal: j-LECT-NOTES-COMP-SCI
volume: 1373
pages: 14--??
year: 1998
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Tue Apr 28 08:51:33 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.04.28 08:51:33 MDT
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: M. Thorup
rawtitle: Floats, Integers, and Single Source Shortest Paths
entry:
@Article{Thorup:1998:FIS,
  author =       "M. Thorup",
  title =        "Floats, Integers, and Single Source Shortest Paths",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1373",
  pages =        "14--??",
  year =         "1998",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Apr 28 08:51:33 MDT 1998",
  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: Ulman:1998:HPF
author: Zenon D. Ulman and Maciej Czyzak
title: Highly parallel, fast scaling of numbers in nonredundant residue arithmetic
journal: j-IEEE-TRANS-SIG-PROC
volume: 46
number: 2
pages: 487--496
year: 1998
CODEN: ITPRED
ISSN: 1053-587X (print), 1941-0476 (electronic) OR 1053587X (print), 19410476 (electronic)
ISSNL: 1053-587X OR 1053587X
MRclass: 94A12 (11A67 65Y10 68W35)
MRnumber: MR1664521 (2000c:94006)
MRreviewer: Behrooz Parhami
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: IEEE Transactions on Signal Processing
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78
rawauthor: Zenon D. Ulman and Maciej Czyzak
rawtitle: Highly parallel, fast scaling of numbers in nonredundant residue arithmetic
entry:
@Article{Ulman:1998:HPF,
  author =       "Zenon D. Ulman and Maciej Czyzak",
  title =        "Highly parallel, fast scaling of numbers in
                 nonredundant residue arithmetic",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "46",
  number =       "2",
  pages =        "487--496",
  year =         "1998",
  CODEN =        "ITPRED",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  MRclass =      "94A12 (11A67 65Y10 68W35)",
  MRnumber =     "MR1664521 (2000c:94006)",
  MRreviewer =   "Behrooz Parhami",
  bibdate =      "Thu Nov 8 14:50:38 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
}


bibtype: article
filename: fparith.bib
label: Upton:1998:RH
author: Graham Upton
title: Rounding halves
journal: j-J-APPL-STAT
volume: 25
number: 6
pages: 811--816
day: 1
month: dec
monthnumber: 12
year: 1998
ISSN: 0266-4763 (print), 1360-0532 (electronic) OR 02664763 (print), 13600532 (electronic)
ISSNL: 0266-4763 OR 02664763
bibdate: Sat Apr 13 11:27:32 MDT 2002
bibtimestamp: 2002.04.13 11:27:32 MDT
fjournal: Journal of Applied Statistics
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/cjas20
rawauthor: Graham Upton
rawtitle: Rounding halves
bibsource:
http://www.carfax.co.uk/jas-con.htm; 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/v25n6/s9/p811

entry:
@Article{Upton:1998:RH,
  author =       "Graham Upton",
  title =        "Rounding halves",
  journal =      j-J-APPL-STAT,
  volume =       "25",
  number =       "6",
  pages =        "811--816",
  day =          "1",
  month =        dec,
  year =         "1998",
  CODEN =        "????",
  ISSN =         "0266-4763 (print), 1360-0532 (electronic)",
  ISSN-L =       "0266-4763",
  bibdate =      "Sat Apr 13 11:27:32 MDT 2002",
  bibsource =    "http://www.carfax.co.uk/jas-con.htm;
                 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/v25n6/s9/p811",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Statistics",
  journal-URL =  "http://www.tandfonline.com/loi/cjas20",
}


bibtype: article
filename: fparith.bib
label: Vogt:1998:FPP
author: Christopher J. Vogt
title: Floating Point Performance of Common Lisp
journal: j-SIGPLAN
volume: 33
number: 9
pages: 103--107
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: Sun Dec 14 09:17:51 MST 2003
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.12.14 09:17:51 MST
fjournal: ACM SIGPLAN Notices
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J706
rawauthor: Christopher J. Vogt
rawtitle: Floating Point Performance of {Common Lisp}
entry:
@Article{Vogt:1998:FPP,
  author =       "Christopher J. Vogt",
  title =        "Floating Point Performance of {Common Lisp}",
  journal =      j-SIGPLAN,
  volume =       "33",
  number =       "9",
  pages =        "103--107",
  month =        sep,
  year =         "1998",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sun Dec 14 09:17:51 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
}


bibtype: article
filename: fparith.bib
label: Walter:1998:EUD
author: C. D. Walter
title: Exponentiation using division chains
journal: j-IEEE-TRANS-COMPUT
volume: 47
number: 7
pages: 757--765
month: jul
monthnumber: 7
year: 1998
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.709375
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: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=709375
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: C. D. Walter
rawtitle: Exponentiation using division chains
entry:
@Article{Walter:1998:EUD,
  author =       "C. D. Walter",
  title =        "Exponentiation using division chains",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "7",
  pages =        "757--765",
  month =        jul,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.709375",
  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 =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=709375",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Walters:1998:SFF
author: A. Walters and P. Athanas
crossref: Pocek:1998:PIS
pages: 333--334
year: 1998
DOI: https://doi.org/10.1109/FPGA.1998.707941
bibdate: Sat Oct 09 15:44:51 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.09 15:44:51 ???
acknowledgement: ack-nhfb
rawauthor: A. Walters and P. Athanas
title:
A scaleable FIR filter using 32-bit floating-point complex arithmetic on a configurable computing machine

abstract:
This paper presents an approach for implementing a scalable high-performance digital filter using the WILDFORCE configurable computing platform. Although not designed specifically for signal processing, configurable computing platforms offer more flexibility for algorithms than application-specific hardware, which is often needed for instances when factors such as environment or product volume dictate alterations in computing. The added flexibility enables users to construct deep pipelines to exploit properties of specific computations. In this paper, wide 32-bit floating-point arithmetic operators have been implemented which provide compatibility with hosts machines. The filter achieves 160 MFLOPs on a single WILDFORCE configurable computing platform.

rawabstract:
This paper presents an approach for implementing a scalable high-performance digital filter using the WILDFORCE configurable computing platform. Although not designed specifically for signal processing, configurable computing platforms offer more flexibility for algorithms than application-specific hardware, which is often needed for instances when factors such as environment or product volume dictate alterations in computing. The added flexibility enables users to construct deep pipelines to exploit properties of specific computations. In this paper, wide 32-bit floating-point arithmetic operators have been implemented which provide compatibility with hosts machines. The filter achieves 160 MFLOPs on a single WILDFORCE configurable computing platform.

rawtitle:
A scaleable {FIR} filter using 32-bit floating-point complex arithmetic on a configurable computing machine

entry:
@InProceedings{Walters:1998:SFF,
  author =       "A. Walters and P. Athanas",
  title =        "A scaleable {FIR} filter using 32-bit floating-point
                 complex arithmetic on a configurable computing
                 machine",
  crossref =     "Pocek:1998:PIS",
  pages =        "333--334",
  year =         "1998",
  DOI =          "https://doi.org/10.1109/FPGA.1998.707941",
  bibdate =      "Sat Oct 09 15:44:51 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper presents an approach for implementing a
                 scalable high-performance digital filter using the
                 WILDFORCE configurable computing platform. Although not
                 designed specifically for signal processing,
                 configurable computing platforms offer more flexibility
                 for algorithms than application-specific hardware,
                 which is often needed for instances when factors such
                 as environment or product volume dictate alterations in
                 computing. The added flexibility enables users to
                 construct deep pipelines to exploit properties of
                 specific computations. In this paper, wide 32-bit
                 floating-point arithmetic operators have been
                 implemented which provide compatibility with hosts
                 machines. The filter achieves 160 MFLOPs on a single
                 WILDFORCE configurable computing platform.",
  acknowledgement = ack-nhfb,
}


