# bibtab

bibtype: inproceedings
filename: fparith.bib
label: Parhami:2000:PER
author: B. Parhami
booktitle: Conference Record of the Thirty-Fourth Asilomar Conference on Signals, Systems and Computers, 2000
title: On producing exactly rounded results in digit-serial on-line arithmetic
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 889--893
year: 2000
bibdate: Sat Jul 16 11:25:05 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:05 MDT
acknowledgement: ack-nhfb
rawauthor: B. Parhami
rawbooktitle: Conference Record of the Thirty-Fourth Asilomar Conference on Signals, Systems and Computers, 2000
rawtitle: On producing exactly rounded results in digit-serial on-line arithmetic
entry:
@InProceedings{Parhami:2000:PER,
  author =       "B. Parhami",
  booktitle =    "Conference Record of the Thirty-Fourth Asilomar
                 Conference on Signals, Systems and Computers, 2000",
  title =        "On producing exactly rounded results in digit-serial
                 on-line arithmetic",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "889--893",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:05 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "The input and output of an on-line computation
                 involving redundant numbers must generally be
                 compatible with standard nonredundant formats. When
                 rounding of a result is required in the last
                 computation step, the process can be combined with
                 on-the- \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Park:2000:ESR
author: Woo-Chan Park and Tack-Don Han and Shin-Dug Kim
booktitle: Proceedings of the Second IEEE Asia Pacific Conference on ASICs 2000: AP-ASIC 2000
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 223--226
year: 2000
bibdate: Sat Jul 16 11:25:05 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:05 MDT
acknowledgement: ack-nhfb
rawauthor: Woo-Chan Park and Tack-Don Han and Shin-Dug Kim
rawbooktitle: Proceedings of the Second {IEEE} Asia Pacific Conference on {ASICs 2000}: {AP-ASIC 2000}
title:
Efficient simultaneous rounding method removing sticky-bit from critical path for floating point addition

rawtitle:
Efficient simultaneous rounding method removing sticky-bit from critical path for floating point addition

entry:
@InProceedings{Park:2000:ESR,
  author =       "Woo-Chan Park and Tack-Don Han and Shin-Dug Kim",
  booktitle =    "Proceedings of the Second {IEEE} Asia Pacific
                 Conference on {ASICs 2000}: {AP-ASIC 2000}",
  title =        "Efficient simultaneous rounding method removing
                 sticky-bit from critical path for floating point
                 addition",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "223--226",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:05 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Processing flow of the conventional floating point
                 addition/subtraction operation consists of several
                 steps, i.e., alignment, addition/subtraction,
                 normalization, and rounding stages in this order. A
                 floating adder/subtractor performing addition/
                 \ldots{}",
}


bibtype: techreport
filename: fparith.bib
label: Parker:2000:MCAa
author: D. Stott Parker and Brad Pierce and Paul R. Eggert
title: Monte Carlo arithmetic: a framework for the statistical analysis of roundoff error
number: CSD 970014
institution: Department of Computer Science, University of California, Los Angeles
address: Los Angeles, CA, USA
pages: 18
month: mar
monthnumber: 3
year: 2000
LCCN: QA75.5 .R46 no.970002 1997
bibdate: Mon Aug 25 15:03:13 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.08.25 15:03:13 ???
URL: http://www.cs.ucla.edu/~stott/mca/CSD-970014.ps.gz
acknowledgement: ack-nhfb
rawauthor: D. Stott Parker and Brad Pierce and Paul R. Eggert
rawtitle: {Monte Carlo} arithmetic: a framework for the statistical analysis of roundoff error
entry:
@TechReport{Parker:2000:MCAa,
  author =       "D. Stott Parker and Brad Pierce and Paul R. Eggert",
  title =        "{Monte Carlo} arithmetic: a framework for the
                 statistical analysis of roundoff error",
  number =       "CSD 970014",
  institution =  "Department of Computer Science, University of
                 California, Los Angeles",
  address =      "Los Angeles, CA, USA",
  pages =        "18",
  month =        mar,
  year =         "2000",
  LCCN =         "QA75.5 .R46 no.970002 1997",
  bibdate =      "Mon Aug 25 15:03:13 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.ucla.edu/~stott/mca/CSD-970014.ps.gz",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Parker:2000:MCAb
author: D. Stott Parker and Brad Pierce and Paul R. Eggert
title: Monte Carlo Arithmetic: How to Gamble with Floating Point and Win
journal: j-COMPUT-SCI-ENG
volume: 2
number: 4
pages: 58--68
month: jul
monthnumber: 7
year: 2000
CODEN: CSENFA
ISSN: 1521-9615 (print), 1558-366X (electronic) OR 15219615 (print), 1558366X (electronic)
ISSNL: 1521-9615 OR 15219615
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: Computing in Science and Engineering
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5992
rawauthor: D. Stott Parker and Brad Pierce and Paul R. Eggert
rawtitle: {Monte Carlo} Arithmetic: How to Gamble with Floating Point and Win
URL:
http://dlib.computer.org/cs/books/cs2000/pdf/c4058.pdf; http://www.computer.org/cse/cs1999/c4058abs.htm

entry:
@Article{Parker:2000:MCAb,
  author =       "D. Stott Parker and Brad Pierce and Paul R. Eggert",
  title =        "{Monte Carlo} Arithmetic: How to Gamble with Floating
                 Point and Win",
  journal =      j-COMPUT-SCI-ENG,
  volume =       "2",
  number =       "4",
  pages =        "58--68",
  month =        jul # "\slash " # aug,
  year =         "2000",
  CODEN =        "CSENFA",
  ISSN =         "1521-9615 (print), 1558-366X (electronic)",
  ISSN-L =       "1521-9615",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://dlib.computer.org/cs/books/cs2000/pdf/c4058.pdf;
                 http://www.computer.org/cse/cs1999/c4058abs.htm",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing in Science and Engineering",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5992",
  summary =      "How sensitive to rounding errors are the results
                 generated from a particular code running on a
                 particular machine applied to a particular input? Monte
                 Carlo arithmetic illustrates the potential for tools to
                 support new kinds of a posteriori round-off analysis.",
}


bibtype: article
filename: fparith.bib
label: Parks:2000:NTT
author: M. Parks
title: Number-Theoretic Test Generation for Directed Rounding
journal: j-IEEE-TRANS-COMPUT
volume: 49
number: 7
pages: 651--658
month: jul
monthnumber: 7
year: 2000
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.863034
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 5 10:35:24 MDT 2011
bibtimestamp: 2011.07.05 10:35:24 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=863034
fjournal: IEEE Transactions on Computers
keywords: ARITH-14; floating-point testing
remark: Selected papers from ARITH'14 cite Koren:1999:ISC.
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: M. Parks
rawtitle: Number-Theoretic Test Generation for Directed Rounding
entry:
@Article{Parks:2000:NTT,
  author =       "M. Parks",
  title =        "Number-Theoretic Test Generation for Directed
                 Rounding",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "49",
  number =       "7",
  pages =        "651--658",
  month =        jul,
  year =         "2000",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.863034",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 10:35:24 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib;
                 OCLC Proceedings database",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=863034",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-14; floating-point testing",
  remark =       "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.",
  summary =      "We present methods to systematically generate the
                 hardest test cases for multiplication, division, and
                 square root subject to directed rounding, essentially
                 extending previous work on number-theoretic
                 floating-point testing to rounding modes other than
                 to-nearest. The algorithms focus upon the rounding
                 boundaries of the modes truncate, to-minus-infinity,
                 and to-infinity, and programs based on them require
                 little beyond exact arithmetic in the working precision
                 to create billions of edge cases. We will show that the
                 amount of work required to calculate trial
                 multiplicands pays off in the form of free extra tests
                 due to an interconnection among the operations
                 considered herein. Although these tests do not replace
                 proofs of correctness, they can be used to gain a high
                 degree of confidence that the accuracy requirements as
                 mandated by IEEE Standard 754 have been satisfied.",
}


bibtype: article
filename: fparith.bib
label: Philippsen:2000:CNJ
author: Michael Philippsen and Edwin Gunthner
title: Complex numbers for Java
journal: j-CPE
volume: 12
number: 6
pages: 477--491
month: may
monthnumber: 5
year: 2000
CODEN: CPEXEI
DOI: https://doi.org/10.1002/1096-9128(200005)12:6<477::AID-CPE486>3.0.CO;2-W
ISSN: 1040-3108 (print), 1096-9128 (electronic) OR 10403108 (print), 10969128 (electronic)
ISSNL: 1040-3108 OR 10403108
bibdate: Sun Oct 29 16:57:06 MST 2000
bibtimestamp: 2000.10.29 16:57:06 MST
fjournal: Concurrency, practice and experience
acknowledgement: ack-nhfb
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-0634/issues
rawauthor: Michael Philippsen and Edwin G{\"u}nthner
rawtitle: Complex numbers for {Java}
bibsource:
http://www.interscience.wiley.com/jpages/1040-3108; http://www3.interscience.wiley.com/journalfinder.html; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://www3.interscience.wiley.com/cgi-bin/abstract/72515730/START; http://www3.interscience.wiley.com/cgi-bin/fulltext?ID=72515730&PLACEBO=IE.pdf

entry:
@Article{Philippsen:2000:CNJ,
  author =       "Michael Philippsen and Edwin G{\"u}nthner",
  title =        "Complex numbers for {Java}",
  journal =      j-CPE,
  volume =       "12",
  number =       "6",
  pages =        "477--491",
  month =        may,
  year =         "2000",
  CODEN =        "CPEXEI",
  DOI =          "https://doi.org/10.1002/1096-9128(200005)12:6<477::AID-CPE486>3.0.CO;2-W",
  ISSN =         "1040-3108 (print), 1096-9128 (electronic)",
  ISSN-L =       "1040-3108",
  bibdate =      "Sun Oct 29 16:57:06 MST 2000",
  bibsource =    "http://www.interscience.wiley.com/jpages/1040-3108;
                 http://www3.interscience.wiley.com/journalfinder.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.interscience.wiley.com/cgi-bin/abstract/72515730/START;
                 http://www3.interscience.wiley.com/cgi-bin/fulltext?ID=72515730&PLACEBO=IE.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Concurrency, practice and experience",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-0634/issues",
}


bibtype: article
filename: fparith.bib
label: Pillai:2000:LPA
author: R. V. Pillai and D. Al-Khalili and A. J. Al-Khalili
title: Low Power Architecture for Floating-Point MAC Fusion
journal: j-IEE-PROC-COMPUT-DIGIT-TECH
volume: 147
pages: 288--296
year: 2000
CODEN: ICDTEA
ISSN: 1350-2387 (print), 1359-7027 (electronic) OR 13502387 (print), 13597027 (electronic)
ISSNL: 1350-2387 OR 13502387
bibdate: Fri Jun 24 10:52:39 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.06.24 10:52:39 ???
fjournal: IEE Proceedings. Computers and Digital Techniques
acknowledgement: ack-nhfb
rawauthor: R. V. Pillai and D. Al-Khalili and A. J. Al-Khalili
rawtitle: Low Power Architecture for Floating-Point {MAC} Fusion
entry:
@Article{Pillai:2000:LPA,
  author =       "R. V. Pillai and D. Al-Khalili and A. J. Al-Khalili",
  title =        "Low Power Architecture for Floating-Point {MAC}
                 Fusion",
  journal =      j-IEE-PROC-COMPUT-DIGIT-TECH,
  volume =       "147",
  pages =        "288--296",
  year =         "2000",
  CODEN =        "ICDTEA",
  ISSN =         "1350-2387 (print), 1359-7027 (electronic)",
  ISSN-L =       "1350-2387",
  bibdate =      "Fri Jun 24 10:52:39 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEE Proceedings. Computers and Digital Techniques",
}


bibtype: inproceedings
filename: fparith.bib
label: Ploog:2000:MPB
author: H. Ploog and D. Timmermann
booktitle: Proceedings of the 2000 International Conference on Computer Design
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 589--590
year: 2000
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: H. Ploog and D. Timmermann
rawbooktitle: Proceedings of the 2000 International Conference on Computer Design
title:
On multiple precision based Montgomery multiplication without precomputation of $ N'_0 = - N_0^-1 bmod W $

rawtitle:
On multiple precision based {Montgomery} multiplication without precomputation of {$ N'_0 = - N_0^{-1} \bmod W $}

entry:
@InProceedings{Ploog:2000:MPB,
  author =       "H. Ploog and D. Timmermann",
  booktitle =    "Proceedings of the 2000 International Conference on
                 Computer Design",
  title =        "On multiple precision based {Montgomery}
                 multiplication without precomputation of {$ N'_0 = -
                 N_0^{-1} \bmod W $}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "589--590",
  year =         "2000",
  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 =      "An efficient implementation of modular exponentiation,
                 i.e., the main building block of many public key
                 cryptographic devices, is achieved by algorithmic
                 optimization of the Montgomery modular multiplication
                 algorithm based on multiple precision \ldots{}",
}


bibtype: book
filename: fparith.bib
label: Poitras:2000:EHF
author: Geoffrey Poitras
publisher: Edward Elgar
address: Cheltenham, UK
pages: x + 522
year: 2000
ISBN: 1-84064-455-9 OR 1840644559
ISBN13: 978-1-84064-455-5 OR 9781840644555
LCCN: HG101 .P65 2000
bibdate: Sat Aug 12 14:42:20 MDT 2023
bibsource: fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.08.12 14:42:20 MDT
acknowledgement: ack-nhfb
authordates: 1954--
rawauthor: Geoffrey Poitras
title:
The Early History of Financial Economics, 1478--1776: from Commercial Arithmetic to Life Annuities and Joint Stocks

abstract:
Geoffrey Poitras provides an exhaustive account of the early development of the subject and, in so doing, provides a sound basis for the study of modern financial economics.

subject:
Finance; History; Economics; Business mathematics; Life annuities; Stocks; Finances; Histoire; Economie politique; Mathematiques financieres; Rentes viageres; Actions (Titres de societe); Business mathematics; Economics; Finance; Life annuities; Stocks; Finanzierungstheorie; Finanzwirtschaft; Finanzwissenschaft; Kredittheorie; Financien.

TOC:
1: Introduction 2: History of Commerce and Finance 3: The Scholastic Analysis of Usury and Other Subjects 4: The Evolution of Commercial Arithmetic 5: Simple Interest and Compound Interest 6: The Valuation of Life Annuities 7: Foreign Exchange and the Bill Market 8: The Analysis of Joint Stocks 9: Development of Derivative Securities 10: Manias, Manipulations and Institutional Failures 11: English Debates over Interest Rates and Public Credit 12: Maritime Insurance, Life Insurance and Other Subjects 13: Some Speculative Conclusions

rawabstract:
Geoffrey Poitras provides an exhaustive account of the early development of the subject and, in so doing, provides a sound basis for the study of modern financial economics.

rawtitle:
The Early History of Financial Economics, 1478--1776: from Commercial Arithmetic to Life Annuities and Joint Stocks

rawTOC:
1: Introduction \\ 2: History of Commerce and Finance \\ 3: The Scholastic Analysis of Usury and Other Subjects \\ 4: The Evolution of Commercial Arithmetic \\ 5: Simple Interest and Compound Interest \\ 6: The Valuation of Life Annuities \\ 7: Foreign Exchange and the Bill Market \\ 8: The Analysis of Joint Stocks \\ 9: Development of Derivative Securities \\ 10: Manias, Manipulations and Institutional Failures \\ 11: English Debates over Interest Rates and Public Credit \\ 12: Maritime Insurance, Life Insurance and Other Subjects \\ 13: Some Speculative Conclusions

entry:
@Book{Poitras:2000:EHF,
  author =       "Geoffrey Poitras",
  title =        "The Early History of Financial Economics, 1478--1776:
                 from Commercial Arithmetic to Life Annuities and Joint
                 Stocks",
  publisher =    "Edward Elgar",
  address =      "Cheltenham, UK",
  pages =        "x + 522",
  year =         "2000",
  ISBN =         "1-84064-455-9",
  ISBN-13 =      "978-1-84064-455-5",
  LCCN =         "HG101 .P65 2000",
  bibdate =      "Sat Aug 12 14:42:20 MDT 2023",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Geoffrey Poitras provides an exhaustive account of the
                 early development of the subject and, in so doing,
                 provides a sound basis for the study of modern
                 financial economics.",
  acknowledgement = ack-nhfb,
  author-dates = "1954--",
  subject =      "Finance; History; Economics; Business mathematics;
                 Life annuities; Stocks; Finances; Histoire;
                 {\'E}conomie politique; Math{\'e}matiques
                 financi{\`e}res; Rentes viag{\`e}res; Actions (Titres
                 de soci{\'e}t{\'e}); Business mathematics; Economics;
                 Finance; Life annuities; Stocks; Finanzierungstheorie;
                 Finanzwirtschaft; Finanzwissenschaft; Kredittheorie;
                 Financi{\"e}n.",
  tableofcontents = "1: Introduction \\
                 2: History of Commerce and Finance \\
                 3: The Scholastic Analysis of Usury and Other Subjects
                 \\
                 4: The Evolution of Commercial Arithmetic \\
                 5: Simple Interest and Compound Interest \\
                 6: The Valuation of Life Annuities \\
                 7: Foreign Exchange and the Bill Market \\
                 8: The Analysis of Joint Stocks \\
                 9: Development of Derivative Securities \\
                 10: Manias, Manipulations and Institutional Failures
                 \\
                 11: English Debates over Interest Rates and Public
                 Credit \\
                 12: Maritime Insurance, Life Insurance and Other
                 Subjects \\
                 13: Some Speculative Conclusions",
}


bibtype: inproceedings
filename: fparith.bib
label: Premkumar:2000:CLB
author: A. B. Premkumar and M. Bhardwaj
title: Combinatorial logic based forward converters in residue number systems
volume: 5
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 317--320
year: 2000
DOI: https://doi.org/10.1109/ISCAS.2000.857428
bibdate: Fri Nov 9 11:38:59 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:59 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: A. B. Premkumar and M. Bhardwaj
rawtitle: Combinatorial logic based forward converters in residue number systems
booktitle:
The 2000 IEEE International Symposium on Circuits and Systems, Proceedings, ISCAS 2000 Geneva, 28--31 May 2000

rawbooktitle:
The 2000 {IEEE} International Symposium on Circuits and Systems, Proceedings, {ISCAS 2000} Geneva, 28--31 May 2000

entry:
@InProceedings{Premkumar:2000:CLB,
  author =       "A. B. Premkumar and M. Bhardwaj",
  booktitle =    "The 2000 {IEEE} International Symposium on Circuits
                 and Systems, Proceedings, {ISCAS 2000} Geneva, 28--31
                 May 2000",
  title =        "Combinatorial logic based forward converters in
                 residue number systems",
  volume =       "5",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "317--320",
  year =         "2000",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.2000.857428",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 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) offers unlimited
                 opportunities for high performance arithmetic provided
                 efficient forward and reverse converters could be
                 constructed for the moduli set at hand. All forward
                 conversion proposals to date, require some \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Ramirez:2000:NAC
author: J. Ramirez and A. Garcia and P. G. Fernandez and L. Parrilla and A. Lloris
volume: 5
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 321--324
year: 2000
DOI: https://doi.org/10.1109/ISCAS.2000.857429
bibdate: Fri Nov 9 11:38:59 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:59 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: J. Ramirez and A. Garcia and P. G. Fernandez and L. Parrilla and A. Lloris
booktitle:
Proceedings, ISCAS 2000 Geneva, The 2000 IEEE International Symposium on Circuits and Systems, 28--31 May 2000

title:
A new architecture to compute the discrete cosine transform using the quadratic residue number system

rawbooktitle:
Proceedings, {ISCAS 2000} Geneva, The 2000 {IEEE} International Symposium on Circuits and Systems, 28--31 May 2000

rawtitle:
A new architecture to compute the discrete cosine transform using the quadratic residue number system

entry:
@InProceedings{Ramirez:2000:NAC,
  author =       "J. Ramirez and A. Garcia and P. G. Fernandez and L.
                 Parrilla and A. Lloris",
  booktitle =    "Proceedings, {ISCAS 2000} Geneva, The 2000 {IEEE}
                 International Symposium on Circuits and Systems, 28--31
                 May 2000",
  title =        "A new architecture to compute the discrete cosine
                 transform using the quadratic residue number system",
  volume =       "5",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "321--324",
  year =         "2000",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.2000.857429",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 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 methodology to compute the N-point DCT (Discrete
                 Cosine Transform) in the QRNS (Quadratic Residue Number
                 System) is presented, with a significant improvement in
                 complexity and speed compared to the corresponding
                 binary version. This reduction \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Reyhani-Masoleh:2000:ENB
author: A. Reyhani-Masoleh and M. A. Hasan
title: On Efficient Normal Basis Multiplication
journal: j-LECT-NOTES-COMP-SCI
volume: 1977
pages: 213--??
year: 2000
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Tue Sep 10 19:08:57 MDT 2002
bibtimestamp: 2002.09.10 19:08:57 MDT
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: A. Reyhani-Masoleh and M. A. Hasan
rawtitle: On Efficient Normal Basis Multiplication
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t1977.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/1977/19770213.htm; http://link.springer-ny.com/link/service/series/0558/papers/1977/19770213.pdf

entry:
@Article{Reyhani-Masoleh:2000:ENB,
  author =       "A. Reyhani-Masoleh and M. A. Hasan",
  title =        "On Efficient Normal Basis Multiplication",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1977",
  pages =        "213--??",
  year =         "2000",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:08:57 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1977.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1977/19770213.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/1977/19770213.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Russinoff:2000:CSF
author: David M. Russinoff
journal: j-LECT-NOTES-COMP-SCI
volume: 1954
pages: 3--36
year: 2000
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Thu Sep 12 09:02:10 2002
bibtimestamp: 2002.09.12 09:02:10 ???
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: David M. Russinoff
title:
A Case Study in Formal Verification of Register-Transfer Logic with ACL2: The Floating Point Adder of the AMD Athlon Processor

bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t1954.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/1954/19540003.htm; http://link.springer-ny.com/link/service/series/0558/papers/1954/19540003.pdf

rawtitle:
A Case Study in Formal Verification of Register-Transfer Logic with {ACL2}: The Floating Point Adder of the {AMD Athlon} Processor

entry:
@Article{Russinoff:2000:CSF,
  author =       "David M. Russinoff",
  title =        "A Case Study in Formal Verification of
                 Register-Transfer Logic with {ACL2}: The Floating Point
                 Adder of the {AMD Athlon} Processor",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1954",
  pages =        "3--36",
  year =         "2000",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Thu Sep 12 09:02:10 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1954.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1954/19540003.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/1954/19540003.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Savas:2000:MMI
author: E. Savas and C. K. Koc
title: The Montgomery Modular Inverse---Revisited
journal: j-IEEE-TRANS-COMPUT
volume: 49
number: 7
pages: 763--766
month: jul
monthnumber: 7
year: 2000
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.863048
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 5 10:35:25 MDT 2011
bibtimestamp: 2011.07.05 10:35:25 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=863048
fjournal: IEEE Transactions on Computers
keywords: ARITH-14
remark: Selected papers from ARITH'14 cite Koren:1999:ISC.
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: E. Savas and {\c{C}}. K. Ko{\c{c}}
rawtitle: The {Montgomery} Modular Inverse---Revisited
abstract:
We modify an algorithm given by Kaliski to compute the Montgomery inverse of an integer modulo a prime number. We also give a new definition of the Montgomery inverse, and introduce efficient algorithms for computing the classical modular inverse, the Kaliski-Montgomery inverse, and the new Montgomery inverse. The proposed algorithms are suitable for software implementations on general-purpose microprocessors

rawabstract:
We modify an algorithm given by Kaliski to compute the Montgomery inverse of an integer modulo a prime number. We also give a new definition of the Montgomery inverse, and introduce efficient algorithms for computing the classical modular inverse, the Kaliski-Montgomery inverse, and the new Montgomery inverse. The proposed algorithms are suitable for software implementations on general-purpose microprocessors

entry:
@Article{Savas:2000:MMI,
  author =       "E. Savas and {\c{C}}. K. Ko{\c{c}}",
  title =        "The {Montgomery} Modular Inverse---Revisited",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "49",
  number =       "7",
  pages =        "763--766",
  month =        jul,
  year =         "2000",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.863048",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 10:35:25 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib;
                 OCLC Proceedings database",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=863048",
  abstract =     "We modify an algorithm given by Kaliski to compute the
                 Montgomery inverse of an integer modulo a prime number.
                 We also give a new definition of the Montgomery
                 inverse, and introduce efficient algorithms for
                 computing the classical modular inverse, the
                 Kaliski-Montgomery inverse, and the new Montgomery
                 inverse. The proposed algorithms are suitable for
                 software implementations on general-purpose
                 microprocessors",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-14",
  remark =       "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.",
}


bibtype: inproceedings
filename: fparith.bib
label: Schulte:2000:CUT
author: M. Schulte and M. Gok and P. Balzola and R. Brocato
title: Combined Unsigned and Two's Complement Saturating Multipliers
crossref: Luk:2000:PSA
pages: 185--196
year: 2000
bibdate: Sun Mar 04 11:31:05 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.03.04 11:31:05 ???
URL: http://mesa.ece.wisc.edu/publications/cp_2000-05.pdf
acknowledgement: ack-nhfb
rawauthor: M. Schulte and M. Gok and P. Balzola and R. Brocato
rawtitle: Combined Unsigned and Two's Complement Saturating Multipliers
entry:
@InProceedings{Schulte:2000:CUT,
  author =       "M. Schulte and M. Gok and P. Balzola and R. Brocato",
  title =        "Combined Unsigned and Two's Complement Saturating
                 Multipliers",
  crossref =     "Luk:2000:PSA",
  pages =        "185--196",
  year =         "2000",
  bibdate =      "Sun Mar 04 11:31:05 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2000-05.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Schulte:2000:FVP
author: M. J. Schulte and E. E. Swartzlander, Jr.
title: A Family of Variable-Precision, Interval Arithmetic Processors
journal: j-IEEE-TRANS-COMPUT
volume: 49
number: 5
pages: 387--398
month: may
monthnumber: 5
year: 2000
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.859535
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 5 10:35:24 MDT 2011
bibtimestamp: 2011.07.05 10:35:24 MDT
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: M. J. Schulte and E. E. {Swartzlander, Jr.}
rawtitle: A Family of Variable-Precision, Interval Arithmetic Processors
URL:
http://mesa.ece.wisc.edu/publications/cp_2000-09.pdf; https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=859535

entry:
@Article{Schulte:2000:FVP,
  author =       "M. J. Schulte and E. E. {Swartzlander, Jr.}",
  title =        "A Family of Variable-Precision, Interval Arithmetic
                 Processors",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "49",
  number =       "5",
  pages =        "387--398",
  month =        may,
  year =         "2000",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.859535",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 10:35:24 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2000-09.pdf;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=859535",
  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: Schulte:2000:IMO
author: M. J. Schulte and P. I. Balzola and A. Akkas and R. W. Brocato
title: Integer Multiplication with Overflow Detection or Saturation
journal: j-IEEE-TRANS-COMPUT
volume: 49
number: 7
pages: 681--691
month: jul
monthnumber: 7
year: 2000
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.863038
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 5 10:35:24 MDT 2011
bibtimestamp: 2011.07.05 10:35:24 MDT
fjournal: IEEE Transactions on Computers
keywords: ARITH-14
remark: Selected papers from ARITH'14 cite Koren:1999:ISC.
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: M. J. Schulte and P. I. Balzola and A. Akkas and R. W. Brocato
rawtitle: Integer Multiplication with Overflow Detection or Saturation
URL:
http://home.ku.edu.tr/~ahakkas/publications/overflow.pdf; http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=863038; http://mesa.ece.wisc.edu/publications/cp_2000-08.pdf

entry:
@Article{Schulte:2000:IMO,
  author =       "M. J. Schulte and P. I. Balzola and A. Akkas and R. W.
                 Brocato",
  title =        "Integer Multiplication with Overflow Detection or
                 Saturation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "49",
  number =       "7",
  pages =        "681--691",
  month =        jul,
  year =         "2000",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.863038",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 10:35:24 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib;
                 OCLC Proceedings database",
  URL =          "http://home.ku.edu.tr/~ahakkas/publications/overflow.pdf;
                 http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=863038;
                 http://mesa.ece.wisc.edu/publications/cp_2000-08.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-14",
  remark =       "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.",
}


bibtype: inproceedings
filename: fparith.bib
label: Schulte:2000:PSM
author: M. J. Schulte and P. I. Balzola and J. Ruan and J. Glossner
title: Parallel Saturating Multioperand Adders
crossref: ACM:2000:PIC
pages: 172--179
year: 2000
DOI: https://doi.org/10.1145/354880.354904
bibdate: Sun Mar 04 11:32:39 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.03.04 11:32:39 ???
URL: http://mesa.ece.wisc.edu/publications/cp_2000-06.pdf
acknowledgement: ack-nhfb
rawauthor: M. J. Schulte and P. I. Balzola and J. Ruan and J. Glossner
rawtitle: Parallel Saturating Multioperand Adders
entry:
@InProceedings{Schulte:2000:PSM,
  author =       "M. J. Schulte and P. I. Balzola and J. Ruan and J.
                 Glossner",
  title =        "Parallel Saturating Multioperand Adders",
  crossref =     "ACM:2000:PIC",
  pages =        "172--179",
  year =         "2000",
  DOI =          "https://doi.org/10.1145/354880.354904",
  bibdate =      "Sun Mar 04 11:32:39 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2000-06.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: phdthesis
filename: fparith.bib
label: Seidel:2000:DIC
author: Peter-Michael Seidel
title: On the Design of IEEE Compliant Floating-point Units and their Quantitative Analysis
type: Ph.D. thesis
school: Computer Science Department, University of Saarland
address: Saarbrucken, Germany
pages: xii + 188
year: 2000
bibdate: Tue Mar 13 10:27:30 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.03.13 10:27:30 ???
remark: Cited in cite Mueller:2000:CAC.
acknowledgement: ack-nhfb
rawauthor: Peter-Michael Seidel
rawtitle: On the Design of {IEEE} Compliant Floating-point Units and their Quantitative Analysis
entry:
@PhdThesis{Seidel:2000:DIC,
  author =       "Peter-Michael Seidel",
  title =        "On the Design of {IEEE} Compliant Floating-point Units
                 and their Quantitative Analysis",
  type =         "{Ph.D.} thesis",
  school =       "Computer Science Department, University of Saarland",
  address =      "Saarbr{\"u}cken, Germany",
  pages =        "xii + 188",
  year =         "2000",
  bibdate =      "Tue Mar 13 10:27:30 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Mueller:2000:CAC}.",
}


bibtype: book
filename: fparith.bib
label: Seife:2000:ZBD
author: Charles Seife
title: Zero: The Biography of a Dangerous Idea
publisher: pub-VIKING
address: pub-VIKING:adr
pages: vi + 248
year: 2000
ISBN: 0-670-88457-X, 0-14-029647-6 (paperback) OR 067088457X, 0140296476 (paperback)
ISBN13: 978-0-670-88457-5, 978-0-14-029647-1 (paperback) OR 9780670884575, 9780140296471 (paperback)
LCCN: QA141 .S45 2000
bibdate: Fri Nov 28 19:15:01 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 19:15:01 ???
acknowledgement: ack-mfc
rawauthor: Charles Seife
rawtitle: Zero: The Biography of a Dangerous Idea
entry:
@Book{Seife:2000:ZBD,
  author =       "Charles Seife",
  title =        "Zero: The Biography of a Dangerous Idea",
  publisher =    pub-VIKING,
  address =      pub-VIKING:adr,
  pages =        "vi + 248",
  year =         "2000",
  ISBN =         "0-670-88457-X, 0-14-029647-6 (paperback)",
  ISBN-13 =      "978-0-670-88457-5, 978-0-14-029647-1 (paperback)",
  LCCN =         "QA141 .S45 2000",
  bibdate =      "Fri Nov 28 19:15:01 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Shin:2000:HSC
author: Kyung-Wook Shin and Heung-Woo Jeon
journal: j-INT-J-ELECTRON
volume: 87
number: 6
pages: 683--702
month: jun
monthnumber: 6
year: 2000
CODEN: IJELA2
DOI: https://doi.org/10.1080/002072100131887
ISSN: 1362-3060 OR 13623060
ISSNL: 0020-7217 OR 00207217
bibdate: Tue Nov 11 14:51:59 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2025.11.11 14:51:59 ???
fjournal: International Journal of Electronics Theoretical & Experimental
acknowledgement: ack-nhfb
rawauthor: Kyung-Wook Shin and Heung-Woo Jeon
title:
High-speed complex-number multiplications based on redundant binary representation of partial products

rawtitle:
High-speed complex-number multiplications based on redundant binary representation of partial products

entry:
@Article{Shin:2000:HSC,
  author =       "Kyung-Wook Shin and Heung-Woo Jeon",
  title =        "High-speed complex-number multiplications based on
                 redundant binary representation of partial products",
  journal =      j-INT-J-ELECTRON,
  volume =       "87",
  number =       "6",
  pages =        "683--702",
  month =        jun,
  year =         "2000",
  CODEN =        "IJELA2",
  DOI =          "https://doi.org/10.1080/002072100131887",
  ISSN =         "1362-3060",
  ISSN-L =       "0020-7217",
  bibdate =      "Tue Nov 11 14:51:59 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Electronics Theoretical \&
                 Experimental",
}


bibtype: article
filename: fparith.bib
label: Sleijpen:2000:DER
author: Gerard L. G. Sleijpen and Henk A. van der Vorst and Jan Modersitzki
journal: j-SIAM-J-MAT-ANA-APPL
volume: 22
number: 3
pages: 726--751 (electronic)
year: 2000
CODEN: SJMAEL
DOI: https://doi.org/10.1137/S0895479897323087
ISSN: 0895-4798 (print), 1095-7162 (electronic) OR 08954798 (print), 10957162 (electronic)
ISSNL: 0895-4798 OR 08954798
MRclass: 65F10 (65N12)
MRnumber: MR1785632 (2001j:65058)
MRreviewer: Larisa V. Maslovskaya
bibdate: Sat Dec 31 06:28:14 2005
bibtimestamp: 2005.12.31 06:28:14 ???
URL: http://epubs.siam.org/sam-bin/dbq/article/32308; http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/22/3
fjournal: SIAM Journal on Matrix Analysis and Applications
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/simax
rawauthor: Gerard L. G. Sleijpen and Henk A. van der Vorst and Jan Modersitzki
title:
Differences in the Effects of Rounding Errors in Krylov Solvers for Symmetric Indefinite Linear Systems

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib; MathSciNet database

rawtitle:
Differences in the Effects of Rounding Errors in {Krylov} Solvers for Symmetric Indefinite Linear Systems

entry:
@Article{Sleijpen:2000:DER,
  author =       "Gerard L. G. Sleijpen and Henk A. van der Vorst and
                 Jan Modersitzki",
  title =        "Differences in the Effects of Rounding Errors in
                 {Krylov} Solvers for Symmetric Indefinite Linear
                 Systems",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "22",
  number =       "3",
  pages =        "726--751 (electronic)",
  year =         "2000",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/S0895479897323087",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "65F10 (65N12)",
  MRnumber =     "MR1785632 (2001j:65058)",
  MRreviewer =   "Larisa V. Maslovskaya",
  bibdate =      "Sat Dec 31 06:28:14 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib;
                 MathSciNet database",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/32308;
                 http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/22/3",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}


bibtype: article
filename: fparith.bib
label: Swider:2000:FPR
author: Zbigniew Swider
title: Floating-point roundoff errors of second-order state-space digital filters
journal: Systems Sci.
volume: 26
number: 1
pages: 67--81
year: 2000
CODEN: SYSCDP
ISSN: 0137-1223 OR 01371223
MRclass: 93E11 (65G20)
MRnumber: MR1787396
bibdate: Thu Nov 8 19:32:19 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.08 19:32:19 ???
fjournal: Wrocl aw University of Technology. Systems Science
keywords: rounding errors
acknowledgement: ack-nhfb
rawauthor: Zbigniew {\'S}wider
rawtitle: Floating-point roundoff errors of second-order state-space digital filters
entry:
@Article{Swider:2000:FPR,
  author =       "Zbigniew {\'S}wider",
  title =        "Floating-point roundoff errors of second-order
                 state-space digital filters",
  journal =      "Systems Sci.",
  volume =       "26",
  number =       "1",
  pages =        "67--81",
  year =         "2000",
  CODEN =        "SYSCDP",
  ISSN =         "0137-1223",
  MRclass =      "93E11 (65G20)",
  MRnumber =     "MR1787396",
  bibdate =      "Thu Nov 8 19:32:19 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Wroc\l aw University of Technology. Systems Science",
  keywords =     "rounding errors",
}


bibtype: inproceedings
filename: fparith.bib
label: Takahashi:2000:IMP
author: D. Takahashi
booktitle: Proceedings of the 2000 International Workshops on Parallel Processing
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 229--235
year: 2000
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: D. Takahashi
rawbooktitle: Proceedings of the 2000 International Workshops on Parallel Processing
title:
Implementation of multiple-precision parallel division and square root on distributed-memory parallel computers

rawtitle:
Implementation of multiple-precision parallel division and square root on distributed-memory parallel computers

entry:
@InProceedings{Takahashi:2000:IMP,
  author =       "D. Takahashi",
  booktitle =    "Proceedings of the 2000 International Workshops on
                 Parallel Processing",
  title =        "Implementation of multiple-precision parallel division
                 and square root on distributed-memory parallel
                 computers",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "229--235",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "We present efficient parallel algorithms for
                 multiple-precision division and square root operation
                 of more than several million decimal digits on
                 distributed-memory parallel computers. It is well known
                 that multiple-precision division and square \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Talahmeh:2000:ADR
author: S. Talahmeh and P. Siy
title: Arithmetic division in RNS using Galois Field GF($p$)
journal: j-COMPUT-MATH-APPL
volume: 39
number: 5--6
pages: 227--238
month: mar
monthnumber: 3
year: 2000
CODEN: CMAPDK
DOI: https://doi.org/10.1016/S0898-1221(00)00056-0
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Thu Nov 18 09:47:08 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.11.18 09:47:08 ???
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: S. Talahmeh and P. Siy
rawtitle: Arithmetic division in {RNS} using {Galois Field GF($p$) }
abstract:
This paper develops an enhanced algorithm for the arithmetic division problem in the Residue Number System. The proposed algorithm is based on Galois Field Theory GF($p$). Mapping the arithmetic division problem over the Galois Field GF($p$) eliminates many of the limitations of existing algorithms. The advantage of the proposed algorithm is that it has no restriction on the dividend and the divisor, no mixed radix conversion, no quotient estimation before division, no reciprocal estimation of the divisor, and no based extension operation.

rawabstract:
This paper develops an enhanced algorithm for the arithmetic division problem in the Residue Number System. The proposed algorithm is based on Galois Field Theory GF($p$). Mapping the arithmetic division problem over the Galois Field GF($p$) eliminates many of the limitations of existing algorithms. The advantage of the proposed algorithm is that it has no restriction on the dividend and the divisor, no mixed radix conversion, no quotient estimation before division, no reciprocal estimation of the divisor, and no based extension operation.

entry:
@Article{Talahmeh:2000:ADR,
  author =       "S. Talahmeh and P. Siy",
  title =        "Arithmetic division in {RNS} using {Galois Field
                 GF($p$) }",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "39",
  number =       "5--6",
  pages =        "227--238",
  month =        mar,
  year =         "2000",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/S0898-1221(00)00056-0",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Thu Nov 18 09:47:08 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper develops an enhanced algorithm for the
                 arithmetic division problem in the Residue Number
                 System. The proposed algorithm is based on Galois Field
                 Theory GF($p$). Mapping the arithmetic division problem
                 over the Galois Field GF($p$) eliminates many of the
                 limitations of existing algorithms. The advantage of
                 the proposed algorithm is that it has no restriction on
                 the dividend and the divisor, no mixed radix
                 conversion, no quotient estimation before division, no
                 reciprocal estimation of the divisor, and no based
                 extension operation.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: inproceedings
filename: fparith.bib
label: Tchoumatchenko:2000:FBS
author: V. Tchoumatchenko and T. Vassileva and P. Gurov
title: A FPGA based square-root coprocessor
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 520--525
year: 2000
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: V. Tchoumatchenko and T. Vassileva and P. Gurov
rawtitle: A {FPGA} based square-root coprocessor
booktitle:
Proceedings of the 22nd EUROMICRO Conference EUROMICRO 96. 'Beyond 2000: Hardware and Software Design Strategies'

rawbooktitle:
Proceedings of the 22nd {EUROMICRO} Conference {EUROMICRO 96}. 'Beyond 2000: Hardware and Software Design Strategies'

entry:
@InProceedings{Tchoumatchenko:2000:FBS,
  author =       "V. Tchoumatchenko and T. Vassileva and P. Gurov",
  booktitle =    "Proceedings of the 22nd {EUROMICRO} Conference
                 {EUROMICRO 96}. 'Beyond 2000: Hardware and Software
                 Design Strategies'",
  title =        "A {FPGA} based square-root coprocessor",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "520--525",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "We present an FPGA implementation of a non-restoring
                 integer square-root algorithm, that uses estimates for
                 result-digit selection and radix-$2$ redundant addition
                 in recurrence. On-the-fly conversion of the
                 result-digit and signed-digit adder/ \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Thimbleby:2000:CNB
author: Harold Thimbleby
title: Calculators are needlessly bad
journal: International Journal of Human-Computer Studies
volume: 52
number: 6
pages: 1031--1069
month: jun
monthnumber: 6
year: 2000
DOI: https://doi.org/10.1006/ijhc.1999.0341
bibdate: Mon Jan 14 21:51:22 MST 2013
bibtimestamp: 2013.01.14 21:51:22 MST
URL: http://www.sciencedirect.com/science/article/pii/S1071581999903415
keywords: Charles Babbage
acknowledgement: ack-nhfb
rawauthor: Harold Thimbleby
rawtitle: Calculators are needlessly bad
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{Thimbleby:2000:CNB,
  author =       "Harold Thimbleby",
  title =        "Calculators are needlessly bad",
  journal =      "International Journal of Human-Computer Studies",
  volume =       "52",
  number =       "6",
  pages =        "1031--1069",
  month =        jun,
  year =         "2000",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1006/ijhc.1999.0341",
  ISSN =         "????",
  bibdate =      "Mon Jan 14 21:51:22 MST 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://www.sciencedirect.com/science/article/pii/S1071581999903415",
  acknowledgement = ack-nhfb,
  keywords =     "Charles Babbage",
}


bibtype: inproceedings
filename: fparith.bib
label: Tommiska:2000:AEI
author: M. T. Tommiska
title: Area-efficient implementation of a fast square root algorithm
publisher: pub-IEEE
address: pub-IEEE:adr
pages: S18/1--S18/4
year: 2000
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. T. Tommiska
rawtitle: Area-efficient implementation of a fast square root algorithm
booktitle:
Proceedings of the 2000 Third IEEE International Caracas Conference on Devices, Circuits and Systems, 15--17 March 2000

rawbooktitle:
Proceedings of the 2000 Third {IEEE} International Caracas Conference on Devices, Circuits and Systems, 15--17 March 2000

entry:
@InProceedings{Tommiska:2000:AEI,
  author =       "M. T. Tommiska",
  booktitle =    "Proceedings of the 2000 Third {IEEE} International
                 Caracas Conference on Devices, Circuits and Systems,
                 15--17 March 2000",
  title =        "Area-efficient implementation of a fast square root
                 algorithm",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "S18/1--S18/4",
  year =         "2000",
  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 area-efficient implementation of a fast-converging
                 square-root algorithm is presented. The design of
                 special arithmetic operations differs in many ways from
                 the traditional tasks that digital designers are used
                 to, and the role of \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Tong:2000:RPO
author: J. Y. F. Tong and D. Nagle and R. A. Rutenbar
title: Reducing power by optimizing the necessary precision / range of floating-point arithmetic
journal: j-IEEE-TRANS-VLSI-SYST
volume: 8
number: 3
pages: 273--286
month: jun
monthnumber: 6
year: 2000
CODEN: IEVSE9
DOI: https://doi.org/10.1109/92.845894
ISSN: 1063-8210 (print), 1557-9999 (electronic) OR 10638210 (print), 15579999 (electronic)
ISSNL: 1063-8210 OR 10638210
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 Very Large Scale Integration (VLSI) Systems
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/issues?punumber=92
rawauthor: J. Y. F. Tong and D. Nagle and R. A. Rutenbar
rawtitle: Reducing power by optimizing the necessary precision\slash range of floating-point arithmetic
entry:
@Article{Tong:2000:RPO,
  author =       "J. Y. F. Tong and D. Nagle and R. A. Rutenbar",
  title =        "Reducing power by optimizing the necessary
                 precision\slash range of floating-point arithmetic",
  journal =      j-IEEE-TRANS-VLSI-SYST,
  volume =       "8",
  number =       "3",
  pages =        "273--286",
  month =        jun,
  year =         "2000",
  CODEN =        "IEVSE9",
  DOI =          "https://doi.org/10.1109/92.845894",
  ISSN =         "1063-8210 (print), 1557-9999 (electronic)",
  ISSN-L =       "1063-8210",
  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 Very Large Scale Integration
                 (VLSI) Systems",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=92",
  summary =      "Low-power systems often find the power cost of
                 floating-point (FP) hardware prohibitively expensive.
                 This paper explores ways of reducing FP power
                 consumption by minimizing the bitwidth representation
                 of FP data. Analysis of several FP programs that
                 \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Tsuji:2000:REO
author: Kumiko Tsuji
booktitle: Proceedings of the Second ISAAC Congress, Vol. 2 (Fukuoka, 1999)
title: Round-off error of optimal control problems in floating-point number systems
volume: 8
publisher: Kluwer Acad. Publ.
address: Dordrecht
pages: 929--944
year: 2000
MRclass: 49M30 (65G50)
MRnumber: MR1940881
bibdate: Thu Nov 8 19:32:25 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.08 19:32:25 ???
series: Int. Soc. Anal. Appl. Comput.
keywords: rounding errors
acknowledgement: ack-nhfb
rawauthor: Kumiko Tsuji
rawbooktitle: Proceedings of the Second {ISAAC} Congress, Vol. 2 (Fukuoka, 1999)
rawtitle: Round-off error of optimal control problems in floating-point number systems
entry:
@InProceedings{Tsuji:2000:REO,
  author =       "Kumiko Tsuji",
  booktitle =    "Proceedings of the Second {ISAAC} Congress, Vol. 2
                 (Fukuoka, 1999)",
  title =        "Round-off error of optimal control problems in
                 floating-point number systems",
  volume =       "8",
  publisher =    "Kluwer Acad. Publ.",
  address =      "Dordrecht",
  pages =        "929--944",
  year =         "2000",
  MRclass =      "49M30 (65G50)",
  MRnumber =     "MR1940881",
  bibdate =      "Thu Nov 8 19:32:25 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Int. Soc. Anal. Appl. Comput.",
  acknowledgement = ack-nhfb,
  keywords =     "rounding errors",
}


bibtype: article
filename: fparith.bib
label: vanderKolk:2000:FPV
author: K. J. van der Kolk and J. A. Lee and E. F. A. Deprettere
title: A Floating Point Vectoring Algorithm Based on Fast Rotations
journal: j-J-VLSI-SIGNAL-PROC
volume: 25
number: 2
pages: 125--139
month: jun
monthnumber: 6
year: 2000
CODEN: JVSPED
DOI: https://doi.org/10.1023/A:1008166822333
ISSN: 0922-5773 (print), 1573-109x (electronic) OR 09225773 (print), 1573109x (electronic)
ISSNL: 0922-5773 OR 09225773
bibdate: Thu May 09 09:46:25 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.09 09:46:25 ???
fjournal: Journal of VLSI Signal Processing
acknowledgement: ack-nhfb
rawauthor: K. J. van der Kolk and J. A. Lee and E. F. A. Deprettere
rawtitle: A Floating Point Vectoring Algorithm Based on Fast Rotations
abstract:
The idea of approximate rotations has been introduced by J. Gotze and G. Hekstra. G. Hekstra and E. Deprettere extended the concept to orthogonal fast rotations and formalized the concept by providing a fast rotation theory. In this theory, the emphasis has been on fast rotation, whereas fast rotation-based vectorization has only been considered in an approximating sense in examples published by J. Gotze and G. Hekstra. The formalization of fast rotation-based vectorization is the subject of this paper. The few known approximate fast vectorization algorithms are special cases of the generic fast rotation-based vectorization algorithm proposed in this paper.

rawabstract:
The idea of approximate rotations has been introduced by J. G{\"o}tze and G. Hekstra. G. Hekstra and E. Deprettere extended the concept to orthogonal fast rotations and formalized the concept by providing a fast rotation theory. In this theory, the emphasis has been on fast rotation, whereas fast rotation-based vectorization has only been considered in an approximating sense in examples published by J. G{\"o}tze and G. Hekstra. The formalization of fast rotation-based vectorization is the subject of this paper. The few known approximate fast vectorization algorithms are special cases of the generic fast rotation-based vectorization algorithm proposed in this paper.

entry:
@Article{vanderKolk:2000:FPV,
  author =       "K. J. van der Kolk and J. A. Lee and E. F. A.
                 Deprettere",
  title =        "A Floating Point Vectoring Algorithm Based on Fast
                 Rotations",
  journal =      j-J-VLSI-SIGNAL-PROC,
  volume =       "25",
  number =       "2",
  pages =        "125--139",
  month =        jun,
  year =         "2000",
  CODEN =        "JVSPED",
  DOI =          "https://doi.org/10.1023/A:1008166822333",
  ISSN =         "0922-5773 (print), 1573-109x (electronic)",
  ISSN-L =       "0922-5773",
  bibdate =      "Thu May 09 09:46:25 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The idea of approximate rotations has been introduced
                 by J. G{\"o}tze and G. Hekstra. G. Hekstra and E.
                 Deprettere extended the concept to orthogonal fast
                 rotations and formalized the concept by providing a
                 fast rotation theory. In this theory, the emphasis has
                 been on fast rotation, whereas fast rotation-based
                 vectorization has only been considered in an
                 approximating sense in examples published by J.
                 G{\"o}tze and G. Hekstra. The formalization of fast
                 rotation-based vectorization is the subject of this
                 paper. The few known approximate fast vectorization
                 algorithms are special cases of the generic fast
                 rotation-based vectorization algorithm proposed in this
                 paper.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of VLSI Signal Processing",
}


bibtype: article
filename: fparith.bib
label: Wang:2000:NSA
author: Chin-Liang Wang and Jyh-Huei Guo
title: New systolic arrays for $ C + A B^2 $, inversion, and division in $ mathrm GF(2^m) $
journal: j-IEEE-TRANS-COMPUT
volume: 49
number: 10
pages: 1120--1125
month: oct
monthnumber: 10
year: 2000
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.888047
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 5 10:35:26 MDT 2011
bibtimestamp: 2011.07.05 10:35:26 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=888047
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Chin-Liang Wang and Jyh-Huei Guo
rawtitle: New systolic arrays for {$ C + A B^2 $}, inversion, and division in {$ \mathrm {GF}(2^m) $}
entry:
@Article{Wang:2000:NSA,
  author =       "Chin-Liang Wang and Jyh-Huei Guo",
  title =        "New systolic arrays for {$ C + A B^2 $}, inversion,
                 and division in {$ \mathrm {GF}(2^m) $}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "49",
  number =       "10",
  pages =        "1120--1125",
  month =        oct,
  year =         "2000",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.888047",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 10:35:26 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=888047",
  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: Wires:2000:VCT
author: K. E. Wires and M. J. Schulte and J. E. Stine
title: Variable-Correction Truncated Floating Point Multipliers
crossref: Matthews:2000:CRT
pages: 1344--1348
year: 2000
bibdate: Sun Mar 04 11:34:32 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.03.04 11:34:32 ???
URL: http://mesa.ece.wisc.edu/publications/cp_2000-07.pdf
acknowledgement: ack-nhfb
rawauthor: K. E. Wires and M. J. Schulte and J. E. Stine
rawtitle: Variable-Correction Truncated Floating Point Multipliers
entry:
@InProceedings{Wires:2000:VCT,
  author =       "K. E. Wires and M. J. Schulte and J. E. Stine",
  title =        "Variable-Correction Truncated Floating Point
                 Multipliers",
  crossref =     "Matthews:2000:CRT",
  pages =        "1344--1348",
  year =         "2000",
  bibdate =      "Sun Mar 04 11:34:32 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2000-07.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Yang:2000:EPG
author: Chia-Lin Yang and B. Sano and A. R. Lebeck
journal: j-IEEE-TRANS-COMPUT
volume: 49
number: 9
pages: 934--946
month: sep
monthnumber: 9
year: 2000
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.869324
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 5 10:35:25 MDT 2011
bibtimestamp: 2011.07.05 10:35:25 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=869324
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Chia-Lin Yang and B. Sano and A. R. Lebeck
title:
Exploiting parallelism in geometry processing with general purpose processors and floating-point SIMD instructions

rawtitle:
Exploiting parallelism in geometry processing with general purpose processors and floating-point {SIMD} instructions

entry:
@Article{Yang:2000:EPG,
  author =       "Chia-Lin Yang and B. Sano and A. R. Lebeck",
  title =        "Exploiting parallelism in geometry processing with
                 general purpose processors and floating-point {SIMD}
                 instructions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "49",
  number =       "9",
  pages =        "934--946",
  month =        sep,
  year =         "2000",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.869324",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 10:35:25 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=869324",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "Three-dimensional (3D) graphics applications have
                 become very important workloads running on today's
                 computer systems. A cost-effective graphics solution is
                 to perform geometry processing of 3D graphics on the
                 host CPU and have specialized hardware \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Yeh:2000:HSB
author: Wen-Chang Yeh and Chein-Wei Jen
title: High-Speed Booth Encoded Parallel Multiplier Design
journal: j-IEEE-TRANS-COMPUT
volume: 49
number: 7
pages: 692--701
month: jul
monthnumber: 7
year: 2000
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.863039
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 5 10:35:24 MDT 2011
bibtimestamp: 2011.07.05 10:35:24 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=863039
fjournal: IEEE Transactions on Computers
keywords: ARITH-14
remark: Selected papers from ARITH'14 cite Koren:1999:ISC.
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Wen-Chang Yeh and Chein-Wei Jen
rawtitle: High-Speed {Booth} Encoded Parallel Multiplier Design
entry:
@Article{Yeh:2000:HSB,
  author =       "Wen-Chang Yeh and Chein-Wei Jen",
  title =        "High-Speed {Booth} Encoded Parallel Multiplier
                 Design",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "49",
  number =       "7",
  pages =        "692--701",
  month =        jul,
  year =         "2000",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.863039",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 10:35:24 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib;
                 OCLC Proceedings database",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=863039",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-14",
  remark =       "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.",
}


bibtype: techreport
filename: fparith.bib
label: Zimmermann:2000:PGF
author: Paul Zimmermann
title: A proof of GMP fast division and square root implementations
type: Technical report
institution: inst-LORIA-INRIA-LORRAINE
address: inst-LORIA-INRIA-LORRAINE:adr
pages: 14
month: sep
monthnumber: 9
year: 2000
bibdate: Sun Sep 10 08:48:46 2006
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2006.09.10 08:48:46 ???
URL: http://www.loria.fr/~zimmerma/papers/proof-div-sqrt.ps.gz
acknowledgement: ack-nhfb
rawauthor: Paul Zimmermann
rawtitle: A proof of {GMP} fast division and square root implementations
abstract:
This short note gives a detailed correctness proof of fast (i.e., subquadratic) versions of the GNU MP tt mpn_bz_divrem_n and tt mpn_sqrtrem functions, together with complete GMP code. The tt mpn_bz_divrem_n function divides (with remainder) a number of $ 2 n $ limbs by a divisor of $n$ limbs in $ 2 K(n) $, where $ K(n) $ is the time spent in a $ (n times n) $ multiplication, using the Moenck--Borodin--Jebelean--Burnikel--Ziegler algorithm. The tt mpn_sqrtrem computes the square root and the remainder of a number of $ 2 n $ limbs (square root and remainder have about $n$ limbs each) in time $ 3 K(n) / 2 $; it uses Karatsuba Square Root.

rawabstract:
This short note gives a detailed correctness proof of fast (i.e., subquadratic) versions of the GNU MP {\tt mpn\_bz\_divrem\_n} and {\tt mpn\_sqrtrem} functions, together with complete GMP code. The {\tt mpn\_bz\_divrem\_n} function divides (with remainder) a number of $ 2 n $ limbs by a divisor of $n$ limbs in $ 2 K(n) $, where $ K(n) $ is the time spent in a $ (n \times n) $ multiplication, using the Moenck--Borodin--Jebelean--Burnikel--Ziegler algorithm. The {\tt mpn\_sqrtrem} computes the square root and the remainder of a number of $ 2 n $ limbs (square root and remainder have about $n$ limbs each) in time $ 3 K(n) / 2 $; it uses Karatsuba Square Root.

entry:
@TechReport{Zimmermann:2000:PGF,
  author =       "Paul Zimmermann",
  title =        "A proof of {GMP} fast division and square root
                 implementations",
  type =         "Technical report",
  institution =  inst-LORIA-INRIA-LORRAINE,
  address =      inst-LORIA-INRIA-LORRAINE:adr,
  pages =        "14",
  month =        sep,
  year =         "2000",
  bibdate =      "Sun Sep 10 08:48:46 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.loria.fr/~zimmerma/papers/proof-div-sqrt.ps.gz",
  abstract =     "This short note gives a detailed correctness proof of
                 fast (i.e., subquadratic) versions of the GNU MP {\tt
                 mpn\_bz\_divrem\_n} and {\tt mpn\_sqrtrem} functions,
                 together with complete GMP code. The {\tt
                 mpn\_bz\_divrem\_n} function divides (with remainder) a
                 number of $ 2 n $ limbs by a divisor of $n$ limbs in $
                 2 K(n) $, where $ K(n) $ is the time spent in a $ (n
                 \times n) $ multiplication, using the
                 Moenck--Borodin--Jebelean--Burnikel--Ziegler algorithm.
                 The {\tt mpn\_sqrtrem} computes the square root and the
                 remainder of a number of $ 2 n $ limbs (square root and
                 remainder have about $n$ limbs each) in time $ 3 K(n) /
                 2 $; it uses Karatsuba Square Root.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Akishita:2001:FSS
author: Toru Akishita
title: Fast Simultaneous Scalar Multiplication on Elliptic Curve with Montgomery Form
journal: j-LECT-NOTES-COMP-SCI
volume: 2259
pages: 255--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:07:44 MST 2002
bibtimestamp: 2002.02.02 13:07:44 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Toru Akishita
rawtitle: Fast Simultaneous Scalar Multiplication on Elliptic Curve with {Montgomery} Form
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2259.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2259/22590255.htm; http://link.springer-ny.com/link/service/series/0558/papers/2259/22590255.pdf

entry:
@Article{Akishita:2001:FSS,
  author =       "Toru Akishita",
  title =        "Fast Simultaneous Scalar Multiplication on Elliptic
                 Curve with {Montgomery} Form",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2259",
  pages =        "255--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:07:44 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2259.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2259/22590255.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2259/22590255.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: phdthesis
filename: fparith.bib
label: Akkas:2001:ISE
author: Ahmet Akkas
title: Instruction set enhancements for reliable computations
type: Ph.D. Thesis
school: Lehigh University
address: Bethlehem, PA, USA
pages: 159
year: 2001
ISBN: 0-493-49369-7 OR 0493493697
ISBN13: 978-0-493-49369-5 OR 9780493493695
bibdate: Fri Oct 25 17:09:55 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.10.25 17:09:55 ???
acknowledgement: ack-nhfb
rawauthor: Ahmet Akkas
rawtitle: Instruction set enhancements for reliable computations
URL:
http://wwwlib.umi.com/dissertations/fullcit/3036247; http://wwwlib.umi.com/dissertations/preview/3036247

abstract:
Although there have been significant advances in VLSI technology and numerical computing, floating-point computations still suffer from undetected errors due to rounding and catastrophic cancellation. Fast computers let programmers write numerically intensive programs, but computed results can be far from the true results due to the accumulation of errors in arithmetic operations. Therefore, accurate and reliable computations have become more important. Interval arithmetic is one technique for accurate and reliable computing. With interval arithmetic, each data value is represented by two floating-point numbers which correspond to the endpoints of an interval, such that the true result is guaranteed to lie on this interval. Since interval arithmetic represents ranges of numbers, it also provides the ability to solve problems that cannot be efficiently solved using floating-point arithmetic. Although interval arithmetic provides an efficient method for monitoring and controlling errors in floating-point computations, it is not yet used widely because it is not sufficiently fast. This dissertation investigates instruction set enhancements for interval arithmetic. Existing interval arithmetic programs are examined to determine bottlenecks in interval computations. Then, a variety of instruction set enhancements are pro posed to overcome these bottlenecks. The efficiency of the proposed enhancements are evaluated using an interval-enhanced compiler and a superscalar processor simulator. Hardware modifications to support these enhancements are evaluated, and a novel design for a combined Interval and Floating-point Comparator is presented. This dissertation also investigates instruction set enhancements for extended precision arithmetic. In particular, instruction set support for quadruple precision arithmetic is examined. Hardware modifications needed to support quadruple precision arithmetic on superscalar processor is evaluated to determine which extensions can be most efficiently incorporated into superscalar processor designs. Furthermore, a technique for performing parallel double precision multiplication using quadruple precision hardware is proposed.

rawabstract:
Although there have been significant advances in VLSI technology and numerical computing, floating-point computations still suffer from undetected errors due to rounding and catastrophic cancellation. Fast computers let programmers write numerically intensive programs, but computed results can be far from the true results due to the accumulation of errors in arithmetic operations. Therefore, accurate and reliable computations have become more important. Interval arithmetic is one technique for accurate and reliable computing. With interval arithmetic, each data value is represented by two floating-point numbers which correspond to the endpoints of an interval, such that the true result is guaranteed to lie on this interval. Since interval arithmetic represents ranges of numbers, it also provides the ability to solve problems that cannot be efficiently solved using floating-point arithmetic. Although interval arithmetic provides an efficient method for monitoring and controlling errors in floating-point computations, it is not yet used widely because it is not sufficiently fast. This dissertation investigates instruction set enhancements for interval arithmetic. Existing interval arithmetic programs are examined to determine bottlenecks in interval computations. Then, a variety of instruction set enhancements are pro posed to overcome these bottlenecks. The efficiency of the proposed enhancements are evaluated using an interval-enhanced compiler and a superscalar processor simulator. Hardware modifications to support these enhancements are evaluated, and a novel design for a combined Interval and Floating-point Comparator is presented. This dissertation also investigates instruction set enhancements for extended precision arithmetic. In particular, instruction set support for quadruple precision arithmetic is examined. Hardware modifications needed to support quadruple precision arithmetic on superscalar processor is evaluated to determine which extensions can be most efficiently incorporated into superscalar processor designs. Furthermore, a technique for performing parallel double precision multiplication using quadruple precision hardware is proposed.

entry:
@PhdThesis{Akkas:2001:ISE,
  author =       "Ahmet Akkas",
  title =        "Instruction set enhancements for reliable
                 computations",
  type =         "{Ph.D.} Thesis",
  school =       "Lehigh University",
  address =      "Bethlehem, PA, USA",
  pages =        "159",
  year =         "2001",
  ISBN =         "0-493-49369-7",
  ISBN-13 =      "978-0-493-49369-5",
  bibdate =      "Fri Oct 25 17:09:55 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://wwwlib.umi.com/dissertations/fullcit/3036247;
                 http://wwwlib.umi.com/dissertations/preview/3036247",
  abstract =     "Although there have been significant advances in VLSI
                 technology and numerical computing, floating-point
                 computations still suffer from undetected errors due to
                 rounding and catastrophic cancellation. Fast computers
                 let programmers write numerically intensive programs,
                 but computed results can be far from the true results
                 due to the accumulation of errors in arithmetic
                 operations. Therefore, accurate and reliable
                 computations have become more important. Interval
                 arithmetic is one technique for accurate and reliable
                 computing. With interval arithmetic, each data value is
                 represented by two floating-point numbers which
                 correspond to the endpoints of an interval, such that
                 the true result is guaranteed to lie on this interval.
                 Since interval arithmetic represents ranges of numbers,
                 it also provides the ability to solve problems that
                 cannot be efficiently solved using floating-point
                 arithmetic. Although interval arithmetic provides an
                 efficient method for monitoring and controlling errors
                 in floating-point computations, it is not yet used
                 widely because it is not sufficiently fast. This
                 dissertation investigates instruction set enhancements
                 for interval arithmetic. Existing interval arithmetic
                 programs are examined to determine bottlenecks in
                 interval computations. Then, a variety of instruction
                 set enhancements are pro posed to overcome these
                 bottlenecks. The efficiency of the proposed
                 enhancements are evaluated using an interval-enhanced
                 compiler and a superscalar processor simulator.
                 Hardware modifications to support these enhancements
                 are evaluated, and a novel design for a combined
                 Interval and Floating-point Comparator is presented.
                 This dissertation also investigates instruction set
                 enhancements for extended precision arithmetic. In
                 particular, instruction set support for quadruple
                 precision arithmetic is examined. Hardware
                 modifications needed to support quadruple precision
                 arithmetic on superscalar processor is evaluated to
                 determine which extensions can be most efficiently
                 incorporated into superscalar processor designs.
                 Furthermore, a technique for performing parallel double
                 precision multiplication using quadruple precision
                 hardware is proposed.",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: fparith.bib
label: Alefeld:2001:SAM
editor: Gotz Alefeld and Jiri Rohn and Siegfried Rump and Tetsuro Yamamoto
title: Symbolic algebraic methods and verification methods
publisher: pub-SV
address: pub-SV:adr
pages: ix + 266
year: 2001
ISBN: 3-211-83593-8 OR 3211835938
ISBN13: 978-3-211-83593-7 OR 9783211835937
LCCN: QA76.9.M35 S92 2001
bibdate: Thu May 09 07:34:15 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.09 07:34:15 ???
series: Springer mathematics
URL: http://www.springer-ny.com/detail.tpl?cart=10209516271260963&isbn=3211835938
keywords: Computer arithmetic; Floating-point arithmetic; Numerical calculations--Verification
acknowledgement: ack-nhfb
raweditor: G{\"o}tz Alefeld and Ji{\v{r}}i Rohn and Siegfried Rump and Tetsuro Yamamoto
rawtitle: Symbolic algebraic methods and verification methods
remark:
From the publisher: ``The usual `implementation' of real numbers as floating point numbers on existing computers has the well-known disadvantage that most of the real numbers are not exactly representable in floating point. Also the four basic arithmetic operations can usually not be performed exactly. During the last years research in different areas has been intensified in order to overcome these problems. (em LEDA-Library, by K. Mehlhorn et al., em Exact arithmetic with real numbers, by A. Edalat et al., Symbolic algebraic methods, verification methods). The latest development is the combination of symbolic-algebraic methods and verification methods to so-called hybrid methods. This book contains a collection of worked out talks on these subjects given during a Dagstuhl seminar at the Forschungszentrum fuer Informatik, Schloss Dagstuhl, Germany, presenting the state of the art.''

entry:
@Book{Alefeld:2001:SAM,
  editor =       "G{\"o}tz Alefeld and Ji{\v{r}}i Rohn and Siegfried
                 Rump and Tetsuro Yamamoto",
  title =        "Symbolic algebraic methods and verification methods",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "ix + 266",
  year =         "2001",
  ISBN =         "3-211-83593-8",
  ISBN-13 =      "978-3-211-83593-7",
  LCCN =         "QA76.9.M35 S92 2001",
  bibdate =      "Thu May 09 07:34:15 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$69.95",
  series =       "Springer mathematics",
  URL =          "http://www.springer-ny.com/detail.tpl?cart=10209516271260963&isbn=3211835938",
  acknowledgement = ack-nhfb,
  contents =     "\begin{itemize}

                 \item Introduction (G. Alefeld, J. Rohn, S. Rump, T.
                 Yamamoto).

                 \item Topological Concepts for Hierarchies of
                 Variables, Types and Controls (R. Albrecht).

                 \item Modifications of the Oettli-Prager Theorem with
                 Application to the Eigenvalue Problem (G. Alefeld, V.
                 Kreinovich, G. Mayer).

                 \item Symbolic-Numeric Algorithms for Polynomials: Some
                 Recent Results (R. Corless).

                 \item Symbolic-Numeric QD-Algorithms with Applications
                 in Function Theory and Linear Algebra (A. Cuyt).

                 \item On the Isoefficiency of the Parallel Descartes
                 Method (Th. Decker, W. Krandick).

                 \item Matrix Methods for Solving Algebraic Systems (I.
                 Z. Emiris).

                 \item A Feasibility Result for Interval Gaussian
                 Elimination Relying on Graph Structure (A.
                 Frommer).

                 \item Solution of Systems of Polynomial Equations by
                 Using Bernstein Expansion (J. Garloff, A. P.
                 Smith).

                 \item Symbolic-Algebraic Computations in Modeling
                 Language for Mathematical Programming (D. M.
                 Gay).

                 \item Translation of Taylor Series into LFT Expansions
                 (R. Heckmann).

                 \item Quasi Convex-Concave Extensions (Chr.
                 Jansson).

                 \item Rewriting, Induction and Decision Procedures: A
                 Case Study of Presburger Arithmetic (D. Kapur).

                 \item Derivative-Based Subdivision in Multi-dimensional
                 Verified Gaussian Quadrature (B. Lang).

                 \item On the Shape of the Fixed Points of
                 $\overline{A}f\overline{U}(\overline{A}x\overline{U}) =
                 \overline{A}A\overline{U}\overline{A}x\overline{U} +
                 \overline{A}b\overline{U}$ (G. Mayer, I. Warnke).

                 \item Exact Computation with leda real --- Theory and
                 Geometric Applications (K. Mehlhorn, St.
                 Schirra).

                 \item Numerical Verification Method for Solutions of
                 Nonlinear Hyperbolic Equations (T. Minamoto).

                 \item Geometric Series Bounds for the Local Errors of
                 Taylor Methods for Linear $n$-th-Order ODEs (M.
                 Neher).

                 \item Save Numerical Error Bounds for Solutions of
                 Nonlinear Elliptic Boundary Value Problems (M.
                 Plum).

                 \item Fast Verification Algorithms in MATLAB (S.
                 Rump).

                 \item The Linear Complementarity Problem with Interval
                 Data (U. Sch{\"a}fer).

                 \item Some Numerical Methods for Nonlinear Least
                 Squares Problems (St. Shakhno).

                 \item A New Insight of the Shortley--Weller
                 Approximation for Dirichlet Problems (T.
                 Yamamoto).

                 \item How Orthogonality is Lost in Krylov Methods
                 (\ldots{})

                 \end{itemize}",
  keywords =     "Computer arithmetic; Floating-point arithmetic;
                 Numerical calculations--Verification",
  remark =       "From the publisher: ``The usual `implementation' of
                 real numbers as floating point numbers on existing
                 computers has the well-known disadvantage that most of
                 the real numbers are not exactly representable in
                 floating point. Also the four basic arithmetic
                 operations can usually not be performed exactly. During
                 the last years research in different areas has been
                 intensified in order to overcome these problems. ({\em
                 LEDA-Library}, by K. Mehlhorn et al., {\em Exact
                 arithmetic with real numbers}, by A. Edalat et al.,
                 Symbolic algebraic methods, verification methods). The
                 latest development is the combination of
                 symbolic-algebraic methods and verification methods to
                 so-called hybrid methods. This book contains a
                 collection of worked out talks on these subjects given
                 during a Dagstuhl seminar at the Forschungszentrum fuer
                 Informatik, Schlo{\ss} Dagstuhl, Germany, presenting
                 the state of the art.''",
}


bibtype: inproceedings
filename: fparith.bib
label: Ammar:2001:SIC
author: A. Ammar and A. Al Kabbany and M. Youssef and A. Amam
booktitle: NRSC 2001, Proceedings of the Eighteenth National Radio Science Conference, 27--29 March 2001
title: A secure image coding scheme using residue number system
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 399--405
year: 2001
DOI: https://doi.org/10.1109/NRSC.2001.929397
bibdate: Fri Nov 9 11:38:59 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:59 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: A. Ammar and A. Al Kabbany and M. Youssef and A. Amam
rawbooktitle: {NRSC 2001}, Proceedings of the Eighteenth National Radio Science Conference, 27--29 March 2001
rawtitle: A secure image coding scheme using residue number system
entry:
@InProceedings{Ammar:2001:SIC,
  author =       "A. Ammar and A. Al Kabbany and M. Youssef and A.
                 Amam",
  booktitle =    "{NRSC 2001}, Proceedings of the Eighteenth National
                 Radio Science Conference, 27--29 March 2001",
  title =        "A secure image coding scheme using residue number
                 system",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "399--405",
  year =         "2001",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/NRSC.2001.929397",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A secure image coding scheme using the residue number
                 system (RNS) is presented and tested. The proposed
                 scheme can be also used as the base for a full security
                 multiple access image communication system. Using RNS
                 with multiple look-up tables for \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Aoki:2001:ECA
author: Kazumaro Aoki and Fumitaka Hoshino and Tetsutaro Kobayashi and Hiroaki Oguro
title: Elliptic Curve Arithmetic Using SIMD
journal: j-LECT-NOTES-COMP-SCI
volume: 2200
pages: 235--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:06:44 MST 2002
bibtimestamp: 2002.02.02 13:06:44 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Kazumaro Aoki and Fumitaka Hoshino and Tetsutaro Kobayashi and Hiroaki Oguro
rawtitle: Elliptic Curve Arithmetic Using {SIMD}
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2200.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2200/22000235.htm; http://link.springer-ny.com/link/service/series/0558/papers/2200/22000235.pdf

entry:
@Article{Aoki:2001:ECA,
  author =       "Kazumaro Aoki and Fumitaka Hoshino and Tetsutaro
                 Kobayashi and Hiroaki Oguro",
  title =        "Elliptic Curve Arithmetic Using {SIMD}",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2200",
  pages =        "235--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:06:44 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2200.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2200/22000235.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2200/22000235.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Armando:2001:PEM
author: A. Armando and S. Ranise
journal: j-J-UCS
volume: 7
number: 2
pages: 124--??
day: 28
month: feb
monthnumber: 2
year: 2001
ISSN: 0948-6968 OR 09486968
ISSNL: 0948-6968 OR 09486968
bibdate: Wed Feb 20 07:23:08 MST 2002
bibsource: http://www.jucs.org/jucs; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.02.20 07:23:08 MST
URL: http://www.jucs.org/jucs_7_2/a_practical_extension_mechanism
fjournal: J.UCS: Journal of Universal Computer Science
acknowledgement: ack-nhfb
journalURL: http://www.jucs.org/jucs
rawauthor: A. Armando and S. Ranise
title:
A Practical Extension Mechanism for Decision Procedures: the Case Study of Universal Presburger Arithmetic

rawtitle:
A Practical Extension Mechanism for Decision Procedures: the Case Study of Universal {Presburger} Arithmetic

entry:
@Article{Armando:2001:PEM,
  author =       "A. Armando and S. Ranise",
  title =        "A Practical Extension Mechanism for Decision
                 Procedures: the Case Study of Universal {Presburger}
                 Arithmetic",
  journal =      j-J-UCS,
  volume =       "7",
  number =       "2",
  pages =        "124--??",
  day =          "28",
  month =        feb,
  year =         "2001",
  CODEN =        "????",
  ISSN =         "0948-6968",
  ISSN-L =       "0948-6968",
  bibdate =      "Wed Feb 20 07:23:08 MST 2002",
  bibsource =    "http://www.jucs.org/jucs;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.jucs.org/jucs_7_2/a_practical_extension_mechanism",
  acknowledgement = ack-nhfb,
  fjournal =     "J.UCS: Journal of Universal Computer Science",
  journal-URL =  "http://www.jucs.org/jucs",
}


bibtype: inproceedings
filename: fparith.bib
label: Arnold:2001:ACL
author: M. Arnold and T. Bailey and J. Cowles and C. Walter
booktitle: 2001 IEEE Workshop on Signal Processing Systems
title: Analysis of complex LNS FFTs
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 58--69
year: 2001
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: M. Arnold and T. Bailey and J. Cowles and C. Walter
rawbooktitle: 2001 {IEEE} Workshop on Signal Processing Systems
rawtitle: Analysis of complex {LNS} {FFTs}
entry:
@InProceedings{Arnold:2001:ACL,
  author =       "M. Arnold and T. Bailey and J. Cowles and C. Walter",
  booktitle =    "2001 {IEEE} Workshop on Signal Processing Systems",
  title =        "Analysis of complex {LNS} {FFTs}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "58--69",
  year =         "2001",
  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 =      "The complex-logarithmic number system (CLNS), which
                 represents each complex point in log/polar coordinates,
                 may be practical to implement the fast Fourier
                 transform (FFT). The roots of unity needed by the FFT
                 have exact representations in CLNS and \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Arnold:2001:DFL
author: M. G. Arnold
booktitle: Proceedings of the Euromicro Symposium on Digital Systems, Design, 2001
title: Design of a faithful LNS interpolator
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 336--345
year: 2001
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: M. G. Arnold
rawbooktitle: Proceedings of the Euromicro Symposium on Digital Systems, Design, 2001
rawtitle: Design of a faithful {LNS} interpolator
entry:
@InProceedings{Arnold:2001:DFL,
  author =       "M. G. Arnold",
  booktitle =    "Proceedings of the Euromicro Symposium on Digital
                 Systems, Design, 2001",
  title =        "Design of a faithful {LNS} interpolator",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "336--345",
  year =         "2001",
  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 =      "A design is given for a quadratic interpolator needed
                 by the logarithmic number system (LNS). Unlike previous
                 LNS designs that have attempted to produce results
                 consistently better than a floating-paint
                 representation of the same word size (32 bits),
                 \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Arnold:2001:PLA
author: M. G. Arnold
booktitle: Proceedings of the IEEE Computer Society Workshop on VLSI, 19--20 April 2001
title: A pipelined LNS ALU
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 155--161
year: 2001
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: M. G. Arnold
rawbooktitle: Proceedings of the {IEEE} Computer Society Workshop on {VLSI, 19--20} April 2001
rawtitle: A pipelined {LNS} {ALU}
entry:
@InProceedings{Arnold:2001:PLA,
  author =       "M. G. Arnold",
  booktitle =    "Proceedings of the {IEEE} Computer Society Workshop on
                 {VLSI, 19--20} April 2001",
  title =        "A pipelined {LNS} {ALU}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "155--161",
  year =         "2001",
  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 =      "A new ALU design is proposed that is more economical
                 than a conventional Logarithmic Number System (LNS) ALU
                 for pipelined multiply-accumulate applications (such as
                 FIR filters). A novel interpolator that accepts both
                 positive and negative arguments \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Arnold:2001:SMQ
author: M. G. Arnold and M. D. Winkel
title: A Single-Multiplier Quadratic Interpolator for LNS Arithmetic
crossref: IEEE:2001:PII
pages: 178--183
year: 2001
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
keywords: logarithmic number system (LNS)
acknowledgement: ack-nhfb
rawauthor: M. G. Arnold and M. D. Winkel
rawtitle: A Single-Multiplier Quadratic Interpolator for {LNS} Arithmetic
entry:
@InProceedings{Arnold:2001:SMQ,
  author =       "M. G. Arnold and M. D. Winkel",
  title =        "A Single-Multiplier Quadratic Interpolator for {LNS}
                 Arithmetic",
  crossref =     "IEEE:2001:PII",
  pages =        "178--183",
  year =         "2001",
  bibdate =      "Sat Jul 16 16:14:38 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "logarithmic number system (LNS)",
  summary =      "Linear interpolation requires a single multiplication
                 but is significantly less accurate than quadratic
                 interpolation. The latter requires two multiplications.
                 Two novel quadratic interpolation schemes are shown
                 that approximate the functions \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Arnold:2001:UFR
author: Mark G. Arnold and Colin Walter
title: Unrestricted Faithful Rounding is Good Enough for Some LNS Applications
crossref: Burgess:2001:ISC
pages: 237--246
year: 2001
bibdate: Sat Jul 16 16:14:38 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2005.07.16 16:14:38 MDT
URL: http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Arnold.pdf
keywords: ARITH-15
acknowledgement: ack-nhfb
rawauthor: Mark G. Arnold and Colin Walter
rawtitle: Unrestricted Faithful Rounding is Good Enough for Some {LNS} Applications
entry:
@InProceedings{Arnold:2001:UFR,
  author =       "Mark G. Arnold and Colin Walter",
  title =        "Unrestricted Faithful Rounding is Good Enough for Some
                 {LNS} Applications",
  crossref =     "Burgess:2001:ISC",
  pages =        "237--246",
  year =         "2001",
  bibdate =      "Sat Jul 16 16:14:38 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Arnold.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
  summary =      "We propose to relax the restricted form of faithful
                 rounding used in prior 32 bit logarithmic number system
                 (LNS) implementations. Unrestricted faithful rounding
                 yields three- to six-fold savings in VLSI ROM size (or
                 four- to six-fold savings in \ldots{}).",
}


bibtype: article
filename: fparith.bib
label: Atlamazoglou:2001:ALP
author: P. E. Atlamazoglou and H. T. Anastassiu and D. I. Kaklamani
journal: j-IEEE-APM
volume: 43
number: 4
pages: 104--114
month: aug
monthnumber: 8
year: 2001
CODEN: IAPMEZ
DOI: https://doi.org/10.1109/74.951564
ISSN: 1045-9243 (print), 1558-4143 (electronic) OR 10459243 (print), 15584143 (electronic)
ISSNL: 1045-9243 OR 10459243
bibdate: Mon Jul 5 14:39:37 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.07.05 14:39:37 ???
fjournal: IEEE Antennas and Propagation Magazine
acknowledgement: ack-nhfb
rawauthor: P. E. Atlamazoglou and H. T. Anastassiu and D. I. Kaklamani
title:
Application of literate-programming principles for the description of a FORTRAN 90 extension to quaternion arithmetic

abstract:
In an effort to effectively annotate and document a FORTRAN 90 module that extends the language's mathematical capabilities to the performance of quaternion operations, the literate-programming paradigm is adopted. The basic principles of this paradigm are discussed through a short introduction to the features of a specific literate-programming system known as FWEB. This system is then employed for the efficient presentation of the FORTRAN 90 quaternion arithmetic module

rawabstract:
In an effort to effectively annotate and document a FORTRAN 90 module that extends the language's mathematical capabilities to the performance of quaternion operations, the literate-programming paradigm is adopted. The basic principles of this paradigm are discussed through a short introduction to the features of a specific literate-programming system known as FWEB. This system is then employed for the efficient presentation of the FORTRAN 90 quaternion arithmetic module

rawtitle:
Application of literate-programming principles for the description of a {FORTRAN 90} extension to quaternion arithmetic

entry:
@Article{Atlamazoglou:2001:ALP,
  author =       "P. E. Atlamazoglou and H. T. Anastassiu and D. I.
                 Kaklamani",
  title =        "Application of literate-programming principles for the
                 description of a {FORTRAN 90} extension to quaternion
                 arithmetic",
  journal =      j-IEEE-APM,
  volume =       "43",
  number =       "4",
  pages =        "104--114",
  month =        aug,
  year =         "2001",
  CODEN =        "IAPMEZ",
  DOI =          "https://doi.org/10.1109/74.951564",
  ISSN =         "1045-9243 (print), 1558-4143 (electronic)",
  ISSN-L =       "1045-9243",
  bibdate =      "Mon Jul 5 14:39:37 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In an effort to effectively annotate and document a
                 FORTRAN 90 module that extends the language's
                 mathematical capabilities to the performance of
                 quaternion operations, the literate-programming
                 paradigm is adopted. The basic principles of this
                 paradigm are discussed through a short introduction to
                 the features of a specific literate-programming system
                 known as FWEB. This system is then employed for the
                 efficient presentation of the FORTRAN 90 quaternion
                 arithmetic module",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Antennas and Propagation Magazine",
}


bibtype: article
filename: fparith.bib
label: Baidas:2001:FPB
author: Z. Baidas and A. D. Brown and A. C. Williams
title: Floating-point behavioral synthesis
journal: j-IEEE-TRANS-CAD-ICS
volume: 20
number: 7
pages: 828--839
month: jul
monthnumber: 7
year: 2001
CODEN: ITCSDI
ISSN: 0278-0070 (print), 1937-4151 (electronic) OR 02780070 (print), 19374151 (electronic)
ISSNL: 0278-0070 OR 02780070
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 Computer-Aided Design of Integrated Circuits and Systems
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=43
rawauthor: Z. Baidas and A. D. Brown and A. C. Williams
rawtitle: Floating-point behavioral synthesis
entry:
@Article{Baidas:2001:FPB,
  author =       "Z. Baidas and A. D. Brown and A. C. Williams",
  title =        "Floating-point behavioral synthesis",
  journal =      j-IEEE-TRANS-CAD-ICS,
  volume =       "20",
  number =       "7",
  pages =        "828--839",
  month =        jul,
  year =         "2001",
  CODEN =        "ITCSDI",
  ISSN =         "0278-0070 (print), 1937-4151 (electronic)",
  ISSN-L =       "0278-0070",
  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 Computer-Aided Design of
                 Integrated Circuits and Systems",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=43",
  summary =      "Traditionally, the data processed by a synthesized
                 digital design is fixed (occasionally variable) width
                 integer, and the functional units available are
                 concomitantly simple ladders, subtractors, multipliers,
                 multiplexers, and so on. The aims of \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Bajard:2001:MMB
author: Jean-Claude Bajard and Laurent-Stephane Didier and Peter Kornerup
title: Modular Multiplication and Base Extensions in Residue Number Systems
crossref: Burgess:2001:ISC
pages: 59--65
year: 2001
DOI: https://doi.org/10.1109/ARITH.2001.930104
bibdate: Fri Nov 9 11:38:59 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2007.11.09 11:38:59 MST
URL: http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Bajard.pdf
keywords: ARITH-15; residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: Jean-Claude Bajard and Laurent-Stephane Didier and Peter Kornerup
rawtitle: Modular Multiplication and Base Extensions in Residue Number Systems
entry:
@InProceedings{Bajard:2001:MMB,
  author =       "Jean-Claude Bajard and Laurent-Stephane Didier and
                 Peter Kornerup",
  title =        "Modular Multiplication and Base Extensions in Residue
                 Number Systems",
  crossref =     "Burgess:2001:ISC",
  pages =        "59--65",
  year =         "2001",
  DOI =          "https://doi.org/10.1109/ARITH.2001.930104",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Bajard.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15; residue arithmetic; residue number system",
  summary =      "We present a new RNS modular multiplication for very
                 large operands. The algorithm is based on Montgomery's
                 (1985) method adapted to residue arithmetic. By
                 choosing the moduli of the RNS system reasonably large,
                 an effect corresponding to a \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Balzola:2001:DAP
author: P. I. Balzola and M. J. Schulte and J. Ruan and J. Glossner and E. Hokenek
title: Design Alternatives for Parallel Saturating Multioperand Adders
crossref: IEEE:2001:PII
pages: 172--177
year: 2001
bibdate: Sun Mar 04 11:43:43 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.03.04 11:43:43 ???
URL: http://mesa.ece.wisc.edu/publications/cp_2001-06.pdf
acknowledgement: ack-nhfb
rawauthor: P. I. Balzola and M. J. Schulte and J. Ruan and J. Glossner and E. Hokenek
rawtitle: Design Alternatives for Parallel Saturating Multioperand Adders
entry:
@InProceedings{Balzola:2001:DAP,
  author =       "P. I. Balzola and M. J. Schulte and J. Ruan and J.
                 Glossner and E. Hokenek",
  title =        "Design Alternatives for Parallel Saturating
                 Multioperand Adders",
  crossref =     "IEEE:2001:PII",
  pages =        "172--177",
  year =         "2001",
  bibdate =      "Sun Mar 04 11:43:43 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2001-06.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: incollection
filename: fparith.bib
label: Barraud:2001:SAR
author: Alain Barraud and Suzanne Lesecq and Nicolai Christov
booktitle: Numerical analysis and its applications (Rousse, 2000)
title: From sensitivity analysis to random floating point arithmetics---application to Sylvester equations
volume: 1988
publisher: pub-SV
address: pub-SV:adr
pages: 35--41
year: 2001
MRclass: 65F35 (93B40)
MRnumber: MR1938402
bibdate: Thu Nov 8 19:16:07 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.08 19:16:07 ???
series: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
rawauthor: Alain Barraud and Suzanne Lesecq and Nicolai Christov
rawbooktitle: Numerical analysis and its applications (Rousse, 2000)
rawtitle:
From sensitivity analysis to random floating point arithmetics---application to {Sylvester} equations

entry:
@InCollection{Barraud:2001:SAR,
  author =       "Alain Barraud and Suzanne Lesecq and Nicolai
                 Christov",
  booktitle =    "Numerical analysis and its applications (Rousse,
                 2000)",
  title =        "From sensitivity analysis to random floating point
                 arithmetics---application to {Sylvester} equations",
  volume =       "1988",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "35--41",
  year =         "2001",
  MRclass =      "65F35 (93B40)",
  MRnumber =     "MR1938402",
  bibdate =      "Thu Nov 8 19:16:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Lecture Notes in Computer Science",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Bashagha:2001:NRS
author: A. E. Bashagha
title: Novel radix-$2$ $k$ square root module
volume: 148
number: 4
pages: 190--196
month: aug
monthnumber: 8
year: 2001
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
acknowledgement: ack-nhfb
rawauthor: A. E. Bashagha
rawtitle: Novel radix-$2$ $k$ square root module
entry:
@Article{Bashagha:2001:NRS,
  author =       "A. E. Bashagha",
  title =        "Novel radix-$2$ $k$ square root module",
  journal =      "Circuits, Devices and Systems, IEE Proceedings [see
                 also IEE Proceedings G- Circuits, Devices and
                 Systems]",
  volume =       "148",
  number =       "4",
  pages =        "190--196",
  month =        aug,
  year =         "2001",
  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,
  summary =      "The conventional two's complement radix-$2$ k square
                 root algorithm requires a set of 2 k full precision
                 comparisons to generate all the 2 k possible values of
                 the partial remainder. The correct remainder is the
                 minimum \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Beaumont-Smith:2001:PPA
author: Andrew Beaumont-Smith and Cheng-Chew Lim
title: Parallel Prefix Adder Design
crossref: Burgess:2001:ISC
pages: 218--228
year: 2001
bibdate: Fri May 3 13:58:18 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.03 13:58:18 MDT
URL: http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Beaumont_Smith.pdf
keywords: ARITH-15
acknowledgement: ack-nhfb
rawauthor: Andrew Beaumont-Smith and Cheng-Chew Lim
rawtitle: Parallel Prefix Adder Design
entry:
@InProceedings{Beaumont-Smith:2001:PPA,
  author =       "Andrew Beaumont-Smith and Cheng-Chew Lim",
  title =        "Parallel Prefix Adder Design",
  crossref =     "Burgess:2001:ISC",
  pages =        "218--228",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Beaumont_Smith.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}


bibtype: misc
filename: fparith.bib
label: Beebe:2001:IFP
author: Nelson H. F. Beebe
title: IEEE 754 floating-point test software
pages: 17
day: 1
month: dec
monthnumber: 12
year: 2001
bibdate: Sat Dec 01 16:34:39 2001
bibtimestamp: 2001.12.01 16:34:39 ???
URL: https://www.math.utah.edu/~beebe/software/ieee/
keywords: floating-point testing
acknowledgement: ack-nhfb
howpublished: World-Wide Web document.
rawauthor: Nelson H. F. Beebe
rawtitle: {IEEE 754} floating-point test software
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/beebe-nelson-h-f.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Misc{Beebe:2001:IFP,
  author =       "Nelson H. F. Beebe",
  title =        "{IEEE 754} floating-point test software",
  howpublished = "World-Wide Web document.",
  pages =        "17",
  day =          "1",
  month =        dec,
  year =         "2001",
  bibdate =      "Sat Dec 01 16:34:39 2001",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/beebe-nelson-h-f.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.math.utah.edu/~beebe/software/ieee/",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point testing",
}


bibtype: article
filename: fparith.bib
label: Berg:2001:FVV
author: Christoph Berg and Christian Jacobi
title: Formal Verification of the VAMP Floating Point Unit
journal: j-LECT-NOTES-COMP-SCI
volume: 2144
pages: 325--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:05:47 MST 2002
bibtimestamp: 2002.02.02 13:05:47 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Christoph Berg and Christian Jacobi
rawtitle: Formal Verification of the {VAMP} Floating Point Unit
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2144.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2144/21440325.htm; http://link.springer-ny.com/link/service/series/0558/papers/2144/21440325.pdf

entry:
@Article{Berg:2001:FVV,
  author =       "Christoph Berg and Christian Jacobi",
  title =        "Formal Verification of the {VAMP} Floating Point
                 Unit",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2144",
  pages =        "325--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:05:47 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2144.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2144/21440325.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2144/21440325.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: inproceedings
filename: fparith.bib
label: Bickerstaff:2001:ACC
author: K'Andrea C. Bickerstaff and Earl E. Swartzlander, Jr. and Michael J. Schulte
title: Analysis of Column Compression Multipliers
crossref: Burgess:2001:ISC
pages: 33--39
year: 2001
bibdate: Fri May 3 13:52:01 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.03 13:52:01 MDT
keywords: ARITH-15
acknowledgement: ack-nhfb
rawauthor: K'Andrea C. Bickerstaff and Earl E. {Swartzlander, Jr.} and Michael J. Schulte
rawtitle: Analysis of Column Compression Multipliers
URL:
http://mesa.ece.wisc.edu/publications/cp_2001-02.pdf; http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Bickerstaff.pdf

entry:
@InProceedings{Bickerstaff:2001:ACC,
  author =       "K'Andrea C. Bickerstaff and Earl E. {Swartzlander,
                 Jr.} and Michael J. Schulte",
  title =        "Analysis of Column Compression Multipliers",
  crossref =     "Burgess:2001:ISC",
  pages =        "33--39",
  year =         "2001",
  bibdate =      "Fri May 3 13:52:01 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2001-02.pdf;
                 http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Bickerstaff.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}


bibtype: article
filename: fparith.bib
label: Blanck:2001:ERA
author: Jens Blanck
title: Exact Real Arithmetic Systems: Results of Competition
journal: j-LECT-NOTES-COMP-SCI
volume: 2064
pages: 389--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:04:19 MST 2002
bibtimestamp: 2002.02.02 13:04:19 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Jens Blanck
rawtitle: Exact Real Arithmetic Systems: Results of Competition
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2064.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2064/20640389.htm; http://link.springer-ny.com/link/service/series/0558/papers/2064/20640389.pdf

entry:
@Article{Blanck:2001:ERA,
  author =       "Jens Blanck",
  title =        "Exact Real Arithmetic Systems: Results of
                 Competition",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2064",
  pages =        "389--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:04:19 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2064.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2064/20640389.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2064/20640389.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Blum:2001:HRM
author: T. Blum and C. Paar
title: High-radix Montgomery modular exponentiation on reconfigurable hardware
journal: j-IEEE-TRANS-COMPUT
volume: 50
number: 7
pages: 759--764
month: jul
monthnumber: 7
year: 2001
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.936241
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 10:36:33 MDT 2011
bibtimestamp: 2011.07.06 10:36:33 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=936241
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: T. Blum and C. Paar
rawtitle: High-radix {Montgomery} modular exponentiation on reconfigurable hardware
entry:
@Article{Blum:2001:HRM,
  author =       "T. Blum and C. Paar",
  title =        "High-radix {Montgomery} modular exponentiation on
                 reconfigurable hardware",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "50",
  number =       "7",
  pages =        "759--764",
  month =        jul,
  year =         "2001",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.936241",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 10:36:33 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=936241",
  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: Boldo:2001:FAP
author: Sylvie Boldo
type: Master's thesis
school: Ecole Normale Superieure de Lyon
address: 69364 Lyon Cedex 07, France
pages: ix + 42
day: 27
month: jun
monthnumber: 6
year: 2001
bibdate: Tue Nov 23 09:48:04 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.23 09:48:04 ???
note: Also issued as Report DEA No. 2001-03.
URL: ftp://ftp.ens-lyon.fr/pub/LIP/Rapports/DEA/DEA2001/DEA2001-03.ps.Z
language: French
acknowledgement: ack-nhfb
rawauthor: Sylvie Boldo
rawnote: Also issued as Report DEA No. 2001-03.
title:
Formalisation, amelioration et preuves d'algorithmes en arithmetique flottante. (French) [Formalization, improvement, and proofs of algorithms in floating-point arithmetic]

rawtitle:
Formalisation, am{\'e}lioration et preuves d'algorithmes en arithm{\'e}tique flottante. ({French}) [Formalization, improvement, and proofs of algorithms in floating-point arithmetic]

entry:
@MastersThesis{Boldo:2001:FAP,
  author =       "Sylvie Boldo",
  title =        "Formalisation, am{\'e}lioration et preuves
                 d'algorithmes en arithm{\'e}tique flottante. ({French})
                 [Formalization, improvement, and proofs of algorithms
                 in floating-point arithmetic]",
  type =         "{Master}'s thesis",
  school =       "{\'E}cole Normale Sup{\'e}rieure de Lyon",
  address =      "69364 Lyon Cedex 07, France",
  pages =        "ix + 42",
  day =          "27",
  month =        jun,
  year =         "2001",
  bibdate =      "Tue Nov 23 09:48:04 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Also issued as Report DEA No. 2001-03.",
  URL =          "ftp://ftp.ens-lyon.fr/pub/LIP/Rapports/DEA/DEA2001/DEA2001-03.ps.Z",
  acknowledgement = ack-nhfb,
  language =     "French",
}


bibtype: inproceedings
filename: fparith.bib
label: Boldo:2001:MVT
author: Sylvie Boldo and Marc Daumas
title: A mechanically validated technique for extending the available precision
crossref: Matthews:2001:CRT
pages: 1299--1303
year: 2001
bibdate: Tue Nov 23 10:22:31 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.23 10:22:31 ???
URL: http://perso.ens-lyon.fr/marc.daumas/SoftArith/BolDau01b.pdf
acknowledgement: ack-nhfb
rawauthor: Sylvie Boldo and Marc Daumas
rawtitle: A mechanically validated technique for extending the available precision
entry:
@InProceedings{Boldo:2001:MVT,
  author =       "Sylvie Boldo and Marc Daumas",
  title =        "A mechanically validated technique for extending the
                 available precision",
  crossref =     "Matthews:2001:CRT",
  pages =        "1299--1303",
  year =         "2001",
  bibdate =      "Tue Nov 23 10:22:31 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://perso.ens-lyon.fr/marc.daumas/SoftArith/BolDau01b.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Boldo:2001:PIA
author: Sylvie Boldo and Marc Daumas
pages: ??--??
year: 2001
bibdate: Tue Nov 23 10:28:39 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.23 10:28:39 ???
URL: http://www.laria.u-picardie.fr/~cerin/paris2001.html
language: French
acknowledgement: ack-nhfb
rawauthor: Sylvie Boldo and Marc Daumas
booktitle:
ASTI '2001 / SYMPA 7: 7eme Symposium en Architectures Nouvelles de Machines, La Villette, Paris, 24--27 avril, 2001

title:
Performances d'implantations de l'addition en precision quad-double sur differentes machines. (French) [Performance of implantations of quad-double precision on different machines]

rawbooktitle:
{ASTI '2001\slash} {SYMPA 7}: 7{\`e}me Symposium en Architectures Nouvelles de Machines, La Villette, Paris, 24--27 avril, 2001

rawtitle:
Performances d'implantations de l'addition en pr{\'e}cision quad-double sur diff{\'e}rentes machines. ({French}) [Performance of implantations of quad-double precision on different machines]

entry:
@InProceedings{Boldo:2001:PIA,
  author =       "Sylvie Boldo and Marc Daumas",
  editor =       "????",
  booktitle =    "{ASTI '2001\slash} {SYMPA 7}: 7{\`e}me Symposium en
                 Architectures Nouvelles de Machines, La Villette,
                 Paris, 24--27 avril, 2001",
  title =        "Performances d'implantations de l'addition en
                 pr{\'e}cision quad-double sur diff{\'e}rentes machines.
                 ({French}) [Performance of implantations of quad-double
                 precision on different machines]",
  publisher =    "????",
  address =      "????",
  pages =        "??--??",
  year =         "2001",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Tue Nov 23 10:28:39 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.laria.u-picardie.fr/~cerin/paris2001.html",
  acknowledgement = ack-nhfb,
  language =     "French",
}


bibtype: article
filename: fparith.bib
label: Breyer:2001:NGE
author: Laird Breyer and Gareth O. Roberts and Jeffrey S. Rosenthal
title: A note on geometric ergodicity and floating-point roundoff error
journal: j-STAT-PROB-LETT
volume: 53
number: 2
pages: 123--127
day: 1
month: jun
monthnumber: 6
year: 2001
CODEN: SPLTDC
ISSN: 0167-7152 (print), 1879-2103 (electronic) OR 01677152 (print), 18792103 (electronic)
ISSNL: 0167-7152 OR 01677152
MRclass: 60J10 (65C40)
MRnumber: MR1843871 (2002f:60138)
MRreviewer: Denis Talay
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: Statistics & Probability Letters
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01677152
rawauthor: Laird Breyer and Gareth O. Roberts and Jeffrey S. Rosenthal
rawtitle: A note on geometric ergodicity and floating-point roundoff error
entry:
@Article{Breyer:2001:NGE,
  author =       "Laird Breyer and Gareth O. Roberts and Jeffrey S.
                 Rosenthal",
  title =        "A note on geometric ergodicity and floating-point
                 roundoff error",
  journal =      j-STAT-PROB-LETT,
  volume =       "53",
  number =       "2",
  pages =        "123--127",
  day =          "1",
  month =        jun,
  year =         "2001",
  CODEN =        "SPLTDC",
  ISSN =         "0167-7152 (print), 1879-2103 (electronic)",
  ISSN-L =       "0167-7152",
  MRclass =      "60J10 (65C40)",
  MRnumber =     "MR1843871 (2002f:60138)",
  MRreviewer =   "Denis Talay",
  bibdate =      "Fri Nov 8 05:39:32 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 Ingenta database",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistics \& Probability Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01677152",
  pagecount =    "5",
}


bibtype: misc
filename: fparith.bib
label: Briggs:2001:XER
author: Keith Briggs and Yannis Smaragdakis
title: XR --- Exact Real Arithmetic
pages: 123--127
day: 01
month: mar
monthnumber: 3
year: 2001
bibdate: Sat Apr 28 10:07:59 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.04.28 10:07:59 ???
URL: http://www.btexact.com/people/briggsk2/XR.html
acknowledgement: ack-nhfb
howpublished: World-Wide Web document and software package.
rawauthor: Keith Briggs and Yannis Smaragdakis
rawtitle: {XR} --- Exact Real Arithmetic
note:
From the overview: ``This is an implementation of exact (or constructive) real arithmetic, as an alternative to multiple-precision floating-point (MPFP). An important distinction is that in MPFP one sets the precision before starting a computation, and then one cannot be sure of the final result. Interval arithmetic is an improvement on this, but still not an ideal solution because if the final interval is larger than desired, there is no simple way to restart the computation at higher precision. By contrast, in XR no precision level is set in advance, and no computation takes place until a final request takes place for some output. Despite this, programming with XR is no different from MPFP, except for the declaration of critical variables as type `XR'.par The main aim is to produce a usably efficient implementation, which can be easily interfaced with existing C++ code. This contrasts with previous implementations in functional languages (Haskell, Miranda etc.), which, although theoretically important, seem to be rather too slow for real use.par This code is designed as an add-on to Victor Shoup's arbitrary-precision arithmetic package NTL, and implements a new type XR, to complement NTL's ZZ and RR integer and real types.

rawnote:
From the overview: ``This is an implementation of exact (or constructive) real arithmetic, as an alternative to multiple-precision floating-point (MPFP). An important distinction is that in MPFP one sets the precision before starting a computation, and then one cannot be sure of the final result. Interval arithmetic is an improvement on this, but still not an ideal solution because if the final interval is larger than desired, there is no simple way to restart the computation at higher precision. By contrast, in XR no precision level is set in advance, and no computation takes place until a final request takes place for some output. Despite this, programming with XR is no different from MPFP, except for the declaration of critical variables as type `XR'.\par The main aim is to produce a usably efficient implementation, which can be easily interfaced with existing C++ code. This contrasts with previous implementations in functional languages (Haskell, Miranda etc.), which, although theoretically important, seem to be rather too slow for real use.\par This code is designed as an add-on to Victor Shoup's arbitrary-precision arithmetic package NTL, and implements a new type XR, to complement NTL's ZZ and RR integer and real types.

entry:
@Misc{Briggs:2001:XER,
  author =       "Keith Briggs and Yannis Smaragdakis",
  title =        "{XR} --- Exact Real Arithmetic",
  howpublished = "World-Wide Web document and software package.",
  day =          "01",
  month =        mar,
  year =         "2001",
  bibdate =      "Sat Apr 28 10:07:59 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "From the overview: ``This is an implementation of
                 exact (or constructive) real arithmetic, as an
                 alternative to multiple-precision floating-point
                 (MPFP). An important distinction is that in MPFP one
                 sets the precision before starting a computation, and
                 then one cannot be sure of the final result. Interval
                 arithmetic is an improvement on this, but still not an
                 ideal solution because if the final interval is larger
                 than desired, there is no simple way to restart the
                 computation at higher precision. By contrast, in XR no
                 precision level is set in advance, and no computation
                 takes place until a final request takes place for some
                 output. Despite this, programming with XR is no
                 different from MPFP, except for the declaration of
                 critical variables as type `XR'.\par

                 The main aim is to produce a usably efficient
                 implementation, which can be easily interfaced with
                 existing C++ code. This contrasts with previous
                 implementations in functional languages (Haskell,
                 Miranda etc.), which, although theoretically important,
                 seem to be rather too slow for real use.\par

                 This code is designed as an add-on to Victor Shoup's
                 arbitrary-precision arithmetic package NTL, and
                 implements a new type XR, to complement NTL's ZZ and RR
                 integer and real types.",
  URL =          "http://www.btexact.com/people/briggsk2/XR.html",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Bruguera:2001:URC
author: Javier D. Bruguera and Tomas Lang
title: Using the Reverse-Carry Approach for Double-Datapath Floating-Point Addition
crossref: Burgess:2001:ISC
pages: 203--210
year: 2001
bibdate: Fri May 3 13:58:18 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.03 13:58:18 MDT
URL: http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Bruguera.pdf
keywords: ARITH-15
acknowledgement: ack-nhfb
rawauthor: Javier D. Bruguera and Tom{\'a}s Lang
rawtitle: Using the Reverse-Carry Approach for Double-Datapath Floating-Point Addition
entry:
@InProceedings{Bruguera:2001:URC,
  author =       "Javier D. Bruguera and Tom{\'a}s Lang",
  title =        "Using the Reverse-Carry Approach for Double-Datapath
                 Floating-Point Addition",
  crossref =     "Burgess:2001:ISC",
  pages =        "203--210",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Bruguera.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}


bibtype: article
filename: fparith.bib
label: Bryant:2001:VAC
author: Randal E. Bryant and Yirng-An Chen
title: Verification of arithmetic circuits using binary moment diagrams
journal: j-INT-J-SOFTW-TOOLS-TECHNOL-TRANSFER
volume: 3
number: 2
pages: 137--155
month: may
monthnumber: 5
year: 2001
ISSN: 1433-2779 (print), 1433-2787 (electronic) OR 14332779 (print), 14332787 (electronic)
ISSNL: 1433-2779 OR 14332779
bibdate: Tue Nov 23 15:01:40 MST 2004
bibtimestamp: 2004.11.23 15:01:40 MST
fjournal: International Journal on Software Tools for Technology Transfer: STTT
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10009
rawauthor: Randal E. Bryant and Yirng-An Chen
rawtitle: Verification of arithmetic circuits using binary moment diagrams
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=journal&issn=1433-2779; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Bryant:2001:VAC,
  author =       "Randal E. Bryant and Yirng-An Chen",
  title =        "Verification of arithmetic circuits using binary
                 moment diagrams",
  journal =      j-INT-J-SOFTW-TOOLS-TECHNOL-TRANSFER,
  volume =       "3",
  number =       "2",
  pages =        "137--155",
  month =        may,
  year =         "2001",
  CODEN =        "????",
  ISSN =         "1433-2779 (print), 1433-2787 (electronic)",
  ISSN-L =       "1433-2779",
  bibdate =      "Tue Nov 23 15:01:40 MST 2004",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=journal&issn=1433-2779;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal on Software Tools for Technology
                 Transfer: STTT",
  journal-URL =  "http://link.springer.com/journal/10009",
}


bibtype: inproceedings
filename: fparith.bib
label: Burgess:2001:DIR
author: N. Burgess and C. Hinds
booktitle: Conference Record of the Thirty-Fifth Asilomar Conference on Signals, Systems and Computers, 2001
title: Design issues in radix-$4$ SRT square root & divide unit
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1646--1650
year: 2001
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: N. Burgess and C. Hinds
rawbooktitle: Conference Record of the Thirty-Fifth Asilomar Conference on Signals, Systems and Computers, 2001
rawtitle: Design issues in radix-$4$ {SRT} square root {\&} divide unit
entry:
@InProceedings{Burgess:2001:DIR,
  author =       "N. Burgess and C. Hinds",
  booktitle =    "Conference Record of the Thirty-Fifth Asilomar
                 Conference on Signals, Systems and Computers, 2001",
  title =        "Design issues in radix-$4$ {SRT} square root {\&}
                 divide unit",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1646--1650",
  year =         "2001",
  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 introduces a number of design issues not
                 covered in the open literature that arose during the
                 design of a radix-$4$ SRT divide/square root unit for a
                 vector processing chip. These include compression of
                 the partial remainder's m.s.b.'s, \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Busaba:2001:IZD
title: The IBM z900 Decimal Arithmetic Unit
crossref: Matthews:2001:CRT
volume: 2
pages: 1335--1339
year: 2001
DOI: https://doi.org/10.1109/ACSSC.2001.987708
bibdate: Fri Nov 28 16:15:49 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 16:15:49 ???
keywords: decimal floating-point arithmetic
acknowledgement: ack-mfc
rawtitle: The {IBM z900} Decimal Arithmetic Unit
author:
Fadi Y. Busaba and Christopher A. Krygowski and Wen H. Li and Eric M. Schwarz and Steven R. Carlough

abstract:
As the cost for adding functions to a processor continues to decline, processor designs are including many additional features. An example of this trend is the appearance of graphics engines and compression engines on midrange and even low end microprocessors. One area that has the potential to capture chip real estate is the decimal arithmetic engine because of its importance in financial and business applications. Studies show that 55% of the numeric data stored on commercial databases are in decimal format. Although decimal arithmetic is supported in many software languages it is not yet available on many microprocessors. This paper details the decimal arithmetic engine in the recently announced z900 microprocessor.

rawabstract:
As the cost for adding functions to a processor continues to decline, processor designs are including many additional features. An example of this trend is the appearance of graphics engines and compression engines on midrange and even low end microprocessors. One area that has the potential to capture chip real estate is the decimal arithmetic engine because of its importance in financial and business applications. Studies show that 55\% of the numeric data stored on commercial databases are in decimal format. Although decimal arithmetic is supported in many software languages it is not yet available on many microprocessors. This paper details the decimal arithmetic engine in the recently announced z900 microprocessor.

rawauthor:
Fadi Y. Busaba and Christopher A. Krygowski and Wen H. Li and Eric M. Schwarz and Steven R. Carlough

entry:
@InProceedings{Busaba:2001:IZD,
  author =       "Fadi Y. Busaba and Christopher A. Krygowski and Wen H.
                 Li and Eric M. Schwarz and Steven R. Carlough",
  title =        "The {IBM z900} Decimal Arithmetic Unit",
  crossref =     "Matthews:2001:CRT",
  volume =       "2",
  pages =        "1335--1339",
  year =         "2001",
  DOI =          "https://doi.org/10.1109/ACSSC.2001.987708",
  bibdate =      "Fri Nov 28 16:15:49 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "As the cost for adding functions to a processor
                 continues to decline, processor designs are including
                 many additional features. An example of this trend is
                 the appearance of graphics engines and compression
                 engines on midrange and even low end microprocessors.
                 One area that has the potential to capture chip real
                 estate is the decimal arithmetic engine because of its
                 importance in financial and business applications.
                 Studies show that 55\% of the numeric data stored on
                 commercial databases are in decimal format. Although
                 decimal arithmetic is supported in many software
                 languages it is not yet available on many
                 microprocessors. This paper details the decimal
                 arithmetic engine in the recently announced z900
                 microprocessor.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}


bibtype: inproceedings
filename: fparith.bib
label: Cao:2001:HPA
author: Jun Cao and Belle W. Y. Wei and Jie Cheng
title: High-Performance Architectures for Elementary Function Generation
crossref: Burgess:2001:ISC
pages: 136--144
year: 2001
bibdate: Fri May 3 13:58:18 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.03 13:58:18 MDT
URL: http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Cao.pdf
keywords: ARITH-15
acknowledgement: ack-nhfb
rawauthor: Jun Cao and Belle W. Y. Wei and Jie Cheng
rawtitle: High-Performance Architectures for Elementary Function Generation
entry:
@InProceedings{Cao:2001:HPA,
  author =       "Jun Cao and Belle W. Y. Wei and Jie Cheng",
  title =        "High-Performance Architectures for Elementary Function
                 Generation",
  crossref =     "Burgess:2001:ISC",
  pages =        "136--144",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Cao.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}


bibtype: inproceedings
filename: fparith.bib
label: Chen:2001:ADF
author: Chichyang Chen and Liang-An Chen and Jih-Ren Cheng
crossref: IEEE:2001:PES
pages: 346--353
year: 2001
DOI: https://doi.org/10.1109/DSD.2001.952324
bibdate: Fri Jun 24 10:45:22 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.06.24 10:45:22 ???
acknowledgement: ack-nhfb
rawauthor: Chichyang Chen and Liang-An Chen and Jih-Ren Cheng
title:
Architectural Design of a Fast Floating-Point Multiplication-Add Fused Unit Using Signed-Digit Addition

abstract:
Signed digit (SD) addition is applied to the design of a new floating-point (FLP) multiplication-add fused (MAF) unit. This adoption, together with the proposed two-step normalization method, can reduce the three-word-length addition that is required in the conventional FLP MAF unit to two-word-length addition. Furthermore, the sign reversion of the intermediate mantissa that requires three-word-length carry propagation in the conventional MAF unit is replaced by only single-word sign detection. These two improvements can enhance the speed and cost of the MAF unit significantly. With the use of the SD addition, the circuit of the unit can be designed in a more regular and simple manner, which is a property that is desired in VLSI design. The proposed FLP MAF unit has been designed and simulated by using Verilog hardware description language. The functions of the deigned unit are verified to be correct.

rawabstract:
Signed digit (SD) addition is applied to the design of a new floating-point (FLP) multiplication-add fused (MAF) unit. This adoption, together with the proposed two-step normalization method, can reduce the three-word-length addition that is required in the conventional FLP MAF unit to two-word-length addition. Furthermore, the sign reversion of the intermediate mantissa that requires three-word-length carry propagation in the conventional MAF unit is replaced by only single-word sign detection. These two improvements can enhance the speed and cost of the MAF unit significantly. With the use of the SD addition, the circuit of the unit can be designed in a more regular and simple manner, which is a property that is desired in VLSI design. The proposed FLP MAF unit has been designed and simulated by using Verilog hardware description language. The functions of the deigned unit are verified to be correct.

rawtitle:
Architectural Design of a Fast Floating-Point Multiplication-Add Fused Unit Using Signed-Digit Addition

entry:
@InProceedings{Chen:2001:ADF,
  author =       "Chichyang Chen and Liang-An Chen and Jih-Ren Cheng",
  title =        "Architectural Design of a Fast Floating-Point
                 Multiplication-Add Fused Unit Using Signed-Digit
                 Addition",
  crossref =     "IEEE:2001:PES",
  pages =        "346--353",
  year =         "2001",
  DOI =          "https://doi.org/10.1109/DSD.2001.952324",
  bibdate =      "Fri Jun 24 10:45:22 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Signed digit (SD) addition is applied to the design of
                 a new floating-point (FLP) multiplication-add fused
                 (MAF) unit. This adoption, together with the proposed
                 two-step normalization method, can reduce the
                 three-word-length addition that is required in the
                 conventional FLP MAF unit to two-word-length addition.
                 Furthermore, the sign reversion of the intermediate
                 mantissa that requires three-word-length carry
                 propagation in the conventional MAF unit is replaced by
                 only single-word sign detection. These two improvements
                 can enhance the speed and cost of the MAF unit
                 significantly. With the use of the SD addition, the
                 circuit of the unit can be designed in a more regular
                 and simple manner, which is a property that is desired
                 in VLSI design. The proposed FLP MAF unit has been
                 designed and simulated by using Verilog hardware
                 description language. The functions of the deigned unit
                 are verified to be correct.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Coppersmith:2001:FSS
author: Don Coppersmith
title: Finding Small Solutions to Small Degree Polynomials
journal: j-LECT-NOTES-COMP-SCI
volume: 2146
pages: 20--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:05:49 MST 2002
bibtimestamp: 2002.02.02 13:05:49 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Don Coppersmith
rawtitle: Finding Small Solutions to Small Degree Polynomials
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2146.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2146/21460020.htm; http://link.springer-ny.com/link/service/series/0558/papers/2146/21460020.pdf

entry:
@Article{Coppersmith:2001:FSS,
  author =       "Don Coppersmith",
  title =        "Finding Small Solutions to Small Degree Polynomials",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2146",
  pages =        "20--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:05:49 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2146.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2146/21460020.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2146/21460020.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: techreport
filename: fparith.bib
label: Cowlishaw:2001:DAJ
author: Mike Cowlishaw
title: Decimal Arithmetic for tt java.math: JSR 13 Public Review Draft
type: Technical Report
number: Version 1.33
institution: IBM UK Laboratories
address: Hursley, UK
pages: iii + 60
day: 16
month: jul
monthnumber: 7
year: 2001
bibdate: Fri May 20 14:37:16 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.05.20 14:37:16 ???
URL: http://www2.hursley.ibm.com/jsr13/jsr13spec.pdf
keywords: decimal floating-point arithmetic
remark: Describes a proposal for arbitrary-precision decimal floating-point arithmetic in Java.
acknowledgement: ack-nhfb
rawauthor: Mike Cowlishaw
rawtitle: Decimal Arithmetic for {\tt java.math}: {JSR 13} Public Review Draft
entry:
@TechReport{Cowlishaw:2001:DAJ,
  author =       "Mike Cowlishaw",
  title =        "Decimal Arithmetic for {\tt java.math}: {JSR 13}
                 Public Review Draft",
  type =         "Technical Report",
  number =       "Version 1.33",
  institution =  "IBM UK Laboratories",
  address =      "Hursley, UK",
  pages =        "iii + 60",
  day =          "16",
  month =        jul,
  year =         "2001",
  bibdate =      "Fri May 20 14:37:16 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www2.hursley.ibm.com/jsr13/jsr13spec.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
  remark =       "Describes a proposal for arbitrary-precision decimal
                 floating-point arithmetic in Java.",
}


bibtype: inproceedings
filename: fparith.bib
label: Cowlishaw:2001:DFP
author: Michael F. Cowlishaw and Eric M. Schwarz and Ronald M. Smith and Charles F. Webb
title: A Decimal Floating-Point Specification
crossref: Burgess:2001:ISC
pages: 147--154
year: 2001
bibdate: Fri May 3 13:58:18 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.03 13:58:18 MDT
keywords: ARITH-15; decimal floating-point arithmetic
acknowledgement: ack-nhfb
rawauthor: Michael F. Cowlishaw and Eric M. Schwarz and Ronald M. Smith and Charles F. Webb
rawtitle: A Decimal Floating-Point Specification
URL:
http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Cowlishaw.pdf; http://www2.hursley.ibm.com/decimal/arith15-foils.pdf

entry:
@InProceedings{Cowlishaw:2001:DFP,
  author =       "Michael F. Cowlishaw and Eric M. Schwarz and Ronald M.
                 Smith and Charles F. Webb",
  title =        "A Decimal Floating-Point Specification",
  crossref =     "Burgess:2001:ISC",
  pages =        "147--154",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Cowlishaw.pdf;
                 http://www2.hursley.ibm.com/decimal/arith15-foils.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15; decimal floating-point arithmetic",
}


bibtype: misc
filename: fparith.bib
label: Cuyt:2001:ARI
author: A. Cuyt and P. Kuterna and B. Verdonk and J. Vervloet
title: Arithmos: a reliable integrated computational environment
pages: 147--154
year: 2001
bibdate: Wed Nov 24 07:50:59 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.24 07:50:59 ???
URL: http://win-www.uia.ac.be/u/cant/arithmos/index.html
acknowledgement: ack-nhfb
howpublished: World Wide Web document.
rawauthor: A. Cuyt and P. Kuterna and B. Verdonk and J. Vervloet
rawtitle: {Arithmos}: a reliable integrated computational environment
entry:
@Misc{Cuyt:2001:ARI,
  author =       "A. Cuyt and P. Kuterna and B. Verdonk and J.
                 Vervloet",
  title =        "{Arithmos}: a reliable integrated computational
                 environment",
  howpublished = "World Wide Web document.",
  year =         "2001",
  bibdate =      "Wed Nov 24 07:50:59 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://win-www.uia.ac.be/u/cant/arithmos/index.html",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Cuyt:2001:REC
author: Annie Cuyt and Brigitte Verdonk and S. Becuwe and Peter Kuterna
title: A Remarkable Example of Catastrophic Cancellation Unraveled
journal: j-COMPUTING
volume: 66
number: 3
pages: 309--320
year: 2001
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
MRclass: 65-04 65G10 65Y99
bibdate: Thu Jul 12 05:20:09 MDT 2001
bibtimestamp: 2001.07.12 05:20:09 MDT
fjournal: Computing: Archiv fur informatik und numerik
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/607
rawauthor: Annie Cuyt and Brigitte Verdonk and S. Becuwe and Peter Kuterna
rawtitle: A Remarkable Example of Catastrophic Cancellation Unraveled
bibsource:
http://link.springer-ny.com/link/service/journals/00607/tocs/t1066003.htm; http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/journals/00607/bibs/1066003/10660309.htm; http://link.springer-ny.com/link/service/journals/00607/papers/1066003/10660309.pdf

abstract:
In this paper we reinvestigate a well-known expression first published in [7], which is often used to illustrate catastrophic cancellation as well as the fact that identical output in different precisions does not imply reliability. The purpose of revisiting this expression is twofold. First, we show in Section 2 that the effect of the cancellation is very different on different IEEE 754 compliant platforms, and we unravel the underlying (hardware) reasons which are unknown to many numerical analysts. Besides illustrating cancellation, this expression also counters the common misbelief among many numerical analysts that a same program will deliver identical results on all IEEE conforming systems. Second, in Section 3 we use, illustrate and comment upon the cross-platform didactical tool Arithmetic Explorer developed at the University of Antwerp, by means of which we performed the bit level analysis of the expression evaluation under investigation on the different machines. We believe that this tool, which is freely available from the authors, can be of use to all of us teaching a first numerical analysis course.

rawabstract:
In this paper we reinvestigate a well-known expression first published in [7], which is often used to illustrate catastrophic cancellation as well as the fact that identical output in different precisions does not imply reliability. The purpose of revisiting this expression is twofold. First, we show in Section 2 that the effect of the cancellation is very different on different IEEE 754 compliant platforms, and we unravel the underlying (hardware) reasons which are unknown to many numerical analysts. Besides illustrating cancellation, this expression also counters the common misbelief among many numerical analysts that a same program will deliver identical results on all IEEE conforming systems. Second, in Section 3 we use, illustrate and comment upon the cross-platform didactical tool Arithmetic Explorer developed at the University of Antwerp, by means of which we performed the bit level analysis of the expression evaluation under investigation on the different machines. We believe that this tool, which is freely available from the authors, can be of use to all of us teaching a first numerical analysis course.

entry:
@Article{Cuyt:2001:REC,
  author =       "Annie Cuyt and Brigitte Verdonk and S. Becuwe and
                 Peter Kuterna",
  title =        "A Remarkable Example of Catastrophic Cancellation
                 Unraveled",
  journal =      j-COMPUTING,
  volume =       "66",
  number =       "3",
  pages =        "309--320",
  year =         "2001",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65-04 65G10 65Y99",
  bibdate =      "Thu Jul 12 05:20:09 MDT 2001",
  bibsource =    "http://link.springer-ny.com/link/service/journals/00607/tocs/t1066003.htm;
                 http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/journals/00607/bibs/1066003/10660309.htm;
                 http://link.springer-ny.com/link/service/journals/00607/papers/1066003/10660309.pdf",
  abstract =     "In this paper we reinvestigate a well-known expression
                 first published in [7], which is often used to
                 illustrate catastrophic cancellation as well as the
                 fact that identical output in different precisions does
                 not imply reliability. The purpose of revisiting this
                 expression is twofold. First, we show in Section 2 that
                 the effect of the cancellation is very different on
                 different IEEE 754 compliant platforms, and we unravel
                 the underlying (hardware) reasons which are unknown to
                 many numerical analysts. Besides illustrating
                 cancellation, this expression also counters the common
                 misbelief among many numerical analysts that a same
                 program will deliver identical results on all IEEE
                 conforming systems. Second, in Section 3 we use,
                 illustrate and comment upon the cross-platform
                 didactical tool Arithmetic Explorer developed at the
                 University of Antwerp, by means of which we performed
                 the bit level analysis of the expression evaluation
                 under investigation on the different machines. We
                 believe that this tool, which is freely available from
                 the authors, can be of use to all of us teaching a
                 first numerical analysis course.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
}


bibtype: misc
filename: fparith.bib
label: Darcy:2001:BLH
author: Joseph D. Darcy
title: Borneo Language Homepage
pages: 309--320
year: 2001
bibdate: Mon May 06 09:06:04 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.06 09:06:04 ???
URL: http://www.jddarcy.org/Borneo
keywords: floating-point arithmetic; IEEE 754; Java
acknowledgement: ack-nhfb
howpublished: World Wide Web site.
rawauthor: Joseph D. Darcy
rawtitle: {Borneo} Language Homepage
entry:
@Misc{Darcy:2001:BLH,
  author =       "Joseph D. Darcy",
  title =        "{Borneo} Language Homepage",
  howpublished = "World Wide Web site.",
  year =         "2001",
  bibdate =      "Mon May 06 09:06:04 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.jddarcy.org/Borneo",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point arithmetic; IEEE 754; Java",
}


bibtype: misc
filename: fparith.bib
label: Darcy:2001:DLS
author: Joseph D. Darcy
title: Designing Language Support for IEEE 754
pages: 309--320
year: 2001
bibdate: Mon May 06 09:16:52 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.06 09:16:52 ???
note: 50 slides.
URL: http://grouper.ieee.org/groups/754/meeting-materials/2001-10-18-langdesign.pdf
acknowledgement: ack-nhfb
howpublished: IEEE 754 Revision Committee meeting, October 18, 2001.
rawauthor: Joseph D. Darcy
rawnote: 50 slides.
rawtitle: Designing Language Support for {IEEE 754}
entry:
@Misc{Darcy:2001:DLS,
  author =       "Joseph D. Darcy",
  title =        "Designing Language Support for {IEEE 754}",
  howpublished = "IEEE 754 Revision Committee meeting, October 18,
                 2001.",
  year =         "2001",
  bibdate =      "Mon May 06 09:16:52 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "50 slides.",
  URL =          "http://grouper.ieee.org/groups/754/meeting-materials/2001-10-18-langdesign.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Darcy:2001:WEU
author: Joseph D. Darcy
title: What Everybody Using the JavaTM Programming Language Should Know About Floating-Point Arithmetic
crossref: Anonymous:2001:JJ
pages: ??--??
year: 2001
bibdate: Mon May 06 09:14:05 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.06 09:14:05 ???
note: 51 slides.
URL: http://java.sun.com/people/darcy/JavaOne/2001/1789darcy.pdf
acknowledgement: ack-nhfb
rawauthor: Joseph D. Darcy
rawnote: 51 slides.
rawtitle: What Everybody Using the {Java\TM} Programming Language Should Know About Floating-Point Arithmetic
entry:
@InProceedings{Darcy:2001:WEU,
  author =       "Joseph D. Darcy",
  title =        "What Everybody Using the {Java\TM} Programming
                 Language Should Know About Floating-Point Arithmetic",
  crossref =     "Anonymous:2001:JJ",
  pages =        "??--??",
  year =         "2001",
  bibdate =      "Mon May 06 09:14:05 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "51 slides.",
  URL =          "http://java.sun.com/people/darcy/JavaOne/2001/1789darcy.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: fparith.bib
label: Daumas:2001:CVP
author: Marc Daumas and Claire Moreau-Finot and Laurent Thery
title: Computer validated proofs of a toolset for adaptable arithmetic
type: Research report
number: 4095
institution: Institut National de Recherche en Informatique et en Automatique
address: Le Chesnay, France
pages: ??--??
year: 2001
bibdate: Wed Nov 24 10:50:24 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.24 10:50:24 ???
acknowledgement: ack-nhfb
rawauthor: Marc Daumas and Claire Moreau-Finot and Laurent Thery
rawtitle: Computer validated proofs of a toolset for adaptable arithmetic
entry:
@TechReport{Daumas:2001:CVP,
  author =       "Marc Daumas and Claire Moreau-Finot and Laurent
                 Thery",
  title =        "Computer validated proofs of a toolset for adaptable
                 arithmetic",
  type =         "Research report",
  number =       "4095",
  institution =  "Institut National de Recherche en Informatique et en
                 Automatique",
  address =      "Le Chesnay, France",
  year =         "2001",
  bibdate =      "Wed Nov 24 10:50:24 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Daumas:2001:GLF
author: Marc Daumas and Laurence Rideau and Laurent Thery
title: A Generic Library for Floating-Point Numbers and Its Application to Exact Computing
journal: j-LECT-NOTES-COMP-SCI
volume: 2152
pages: 169--184
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
MRclass: 68T15 (65G50)
MRnumber: MR1907603
bibdate: Sat Feb 2 13:05:56 MST 2002
bibtimestamp: 2002.02.02 13:05:56 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Marc Daumas and Laurence Rideau and Laurent Th{\'e}ry
rawtitle: A Generic Library for Floating-Point Numbers and Its Application to Exact Computing
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2152.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2152/21520169.htm; http://link.springer-ny.com/link/service/series/0558/papers/2152/21520169.pdf; https://hal.archives-ouvertes.fr/hal-00157285

entry:
@Article{Daumas:2001:GLF,
  author =       "Marc Daumas and Laurence Rideau and Laurent
                 Th{\'e}ry",
  title =        "A Generic Library for Floating-Point Numbers and Its
                 Application to Exact Computing",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2152",
  pages =        "169--184",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  MRclass =      "68T15 (65G50)",
  MRnumber =     "MR1907603",
  bibdate =      "Sat Feb 2 13:05:56 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2152.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2152/21520169.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2152/21520169.pdf;
                 https://hal.archives-ouvertes.fr/hal-00157285",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: inproceedings
filename: fparith.bib
label: deDinechin:2001:SIM
author: Florent de Dinechin and Arnaud Tisserand
title: Some Improvements on Multipartite Table Methods
crossref: Burgess:2001:ISC
pages: 128--135
year: 2001
bibdate: Fri May 3 13:58:18 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.03 13:58:18 MDT
URL: http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Dinechin.pdf
keywords: ARITH-15
acknowledgement: ack-nhfb
rawauthor: Florent de Dinechin and Arnaud Tisserand
rawtitle: Some Improvements on Multipartite Table Methods
entry:
@InProceedings{deDinechin:2001:SIM,
  author =       "Florent de Dinechin and Arnaud Tisserand",
  title =        "Some Improvements on Multipartite Table Methods",
  crossref =     "Burgess:2001:ISC",
  pages =        "128--135",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Dinechin.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}


bibtype: techreport
filename: fparith.bib
label: Defour:2001:CREa
author: David Defour and Florent de Dinechin and Jean-Michel Muller
title: Correctly rounded exponential function in double precision arithmetic
type: Rapport de recherche
number: RR-4231
institution: INRIA Rhone-Alpes
address: ZIRST, 655 Avenue de l'Europe, Montbonnot, 38334 Saint Ismier cedex, France
pages: 128--135
month: jul
monthnumber: 7
year: 2001
bibdate: Sat Jun 25 11:10:46 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.06.25 11:10:46 ???
acknowledgement: ack-nhfb
rawauthor: David Defour and Florent de Dinechin and Jean-Michel Muller
rawtitle: Correctly rounded exponential function in double precision arithmetic
URL:
ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-4231.pdf; ftp://ftp.inria.fr/INRIA/publication/publi-ps-gz/RR/RR-4231.ps.gz; http://www.inria.fr/rrrt/rr-4231.html

abstract:
We present an algorithm for implementing correctly rounded exponentials in double-precision floating point arithmetic. This algorithm is based on floating-point operations in the widespread IEEE-754 standard, and is therefore more efficient than those using multiprecision arithmetic, while being fully portable. It requires a table of reasonable size and IEEE-754 double precision multiplications and additions. In a preliminary implementation, the overhead due to correct rounding is a 2.3 times slowdown when compared to the standard library function.

rawabstract:
We present an algorithm for implementing correctly rounded exponentials in double-precision floating point arithmetic. This algorithm is based on floating-point operations in the widespread IEEE-754 standard, and is therefore more efficient than those using multiprecision arithmetic, while being fully portable. It requires a table of reasonable size and IEEE-754 double precision multiplications and additions. In a preliminary implementation, the overhead due to correct rounding is a 2.3 times slowdown when compared to the standard library function.

entry:
@TechReport{Defour:2001:CREa,
  author =       "David Defour and Florent de Dinechin and Jean-Michel
                 Muller",
  title =        "Correctly rounded exponential function in double
                 precision arithmetic",
  type =         "Rapport de recherche",
  number =       "RR-4231",
  institution =  "INRIA Rhone-Alpes",
  address =      "ZIRST, 655 Avenue de l'Europe, Montbonnot, 38334 Saint
                 Ismier cedex, France",
  month =        jul,
  year =         "2001",
  bibdate =      "Sat Jun 25 11:10:46 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-4231.pdf;
                 ftp://ftp.inria.fr/INRIA/publication/publi-ps-gz/RR/RR-4231.ps.gz;
                 http://www.inria.fr/rrrt/rr-4231.html",
  abstract =     "We present an algorithm for implementing correctly
                 rounded exponentials in double-precision floating point
                 arithmetic. This algorithm is based on floating-point
                 operations in the widespread IEEE-754 standard, and is
                 therefore more efficient than those using
                 multiprecision arithmetic, while being fully portable.
                 It requires a table of reasonable size and IEEE-754
                 double precision multiplications and additions. In a
                 preliminary implementation, the overhead due to correct
                 rounding is a 2.3 times slowdown when compared to the
                 standard library function.",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Defour:2001:CREb
author: David Defour and Florida de Dinechin and Jean-Michel Muller
title: Correctly rounded exponential function in double precision arithmetic
crossref: Luk:2001:ASP
pages: 156--167
year: 2001
bibdate: Fri Jun 24 14:43:41 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.06.24 14:43:41 ???
URL: http://bookstore.spie.org/index.cfm?fuseaction=DetailPaper&ProductId=448644&coden=PSISDG
acknowledgement: ack-nhfb
rawauthor: David Defour and Florida de Dinechin and Jean-Michel Muller
rawtitle: Correctly rounded exponential function in double precision arithmetic
abstract:
We present an algorithm for implementing correctly rounded exponentials in double-precision floating point arithmetic. This algorithm is based on floating-point operations in the widespread EEE-754 standard, and is therefore more efficient than those using multiprecision arithmetic, while being fully portable. It requires a table of reasonable size and IEEE-754 double precision multiplications and additions. In a preliminary implementation, the overhead due to correct rounding is a 6 times slowdown when compared to the standard library function.

rawabstract:
We present an algorithm for implementing correctly rounded exponentials in double-precision floating point arithmetic. This algorithm is based on floating-point operations in the widespread EEE-754 standard, and is therefore more efficient than those using multiprecision arithmetic, while being fully portable. It requires a table of reasonable size and IEEE-754 double precision multiplications and additions. In a preliminary implementation, the overhead due to correct rounding is a 6 times slowdown when compared to the standard library function.

entry:
@InProceedings{Defour:2001:CREb,
  author =       "David Defour and Florida de Dinechin and Jean-Michel
                 Muller",
  title =        "Correctly rounded exponential function in double
                 precision arithmetic",
  crossref =     "Luk:2001:ASP",
  pages =        "156--167",
  year =         "2001",
  bibdate =      "Fri Jun 24 14:43:41 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://bookstore.spie.org/index.cfm?fuseaction=DetailPaper&ProductId=448644&coden=PSISDG",
  abstract =     "We present an algorithm for implementing correctly
                 rounded exponentials in double-precision floating point
                 arithmetic. This algorithm is based on floating-point
                 operations in the widespread EEE-754 standard, and is
                 therefore more efficient than those using
                 multiprecision arithmetic, while being fully portable.
                 It requires a table of reasonable size and IEEE-754
                 double precision multiplications and additions. In a
                 preliminary implementation, the overhead due to correct
                 rounding is a 6 times slowdown when compared to the
                 standard library function.",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: fparith.bib
label: Defour:2001:NRRa
author: David Defour and Peter Kornerup and Jean-Michel Muller and Nathalie Revol
title: A new range reduction algorithm
type: Research Report
number: {LIP RR 2001-33, INRIA RR-4267}
institution: LIP, Ecole Normale Superieure de Lyon
address: Lyon, France
pages: 13
year: 2001
bibdate: Sat Jun 25 08:52:06 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.06.25 08:52:06 ???
keywords: range reduction
acknowledgement: ack-nhfb
rawauthor: David Defour and Peter Kornerup and Jean-Michel Muller and Nathalie Revol
rawtitle: A new range reduction algorithm
URL:
ftp://ftp.ens-lyon.fr/pub/LIP/Rapports/RR/RR2001/RR2001-33.ps.Z; ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-4267.pdf; ftp://ftp.inria.fr/INRIA/publication/publi-ps-gz/RR/RR-4267.ps.gz; http://www.inria.fr/rrrt/rr-4267.html

abstract:
Range reduction is a key point for getting accurate elementary function routines. We introduce a new algorithm that is fast for input arguments belonging to the most common domains, yet accurate over the full double precision range.

rawabstract:
Range reduction is a key point for getting accurate elementary function routines. We introduce a new algorithm that is fast for input arguments belonging to the most common domains, yet accurate over the full double precision range.

entry:
@TechReport{Defour:2001:NRRa,
  author =       "David Defour and Peter Kornerup and Jean-Michel Muller
                 and Nathalie Revol",
  title =        "A new range reduction algorithm",
  type =         "Research Report",
  number =       "{LIP RR 2001-33, INRIA RR-4267}",
  institution =  "LIP, {\'E}cole Normale Sup{\'e}rieure de Lyon",
  address =      "Lyon, France",
  pages =        "13",
  year =         "2001",
  bibdate =      "Sat Jun 25 08:52:06 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://ftp.ens-lyon.fr/pub/LIP/Rapports/RR/RR2001/RR2001-33.ps.Z;
                 ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-4267.pdf;
                 ftp://ftp.inria.fr/INRIA/publication/publi-ps-gz/RR/RR-4267.ps.gz;
                 http://www.inria.fr/rrrt/rr-4267.html",
  abstract =     "Range reduction is a key point for getting accurate
                 elementary function routines. We introduce a new
                 algorithm that is fast for input arguments belonging to
                 the most common domains, yet accurate over the full
                 double precision range.",
  acknowledgement = ack-nhfb,
  keywords =     "range reduction",
}


bibtype: inproceedings
filename: fparith.bib
label: Defour:2001:NRRb
author: David Defour and Peter Kornerup and Jean-Michel Muller and Nathalie Revol
title: A new range reduction algorithm
crossref: Matthews:2001:CRT
pages: ??--??
year: 2001
bibdate: Fri Jun 24 12:12:10 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.06.24 12:12:10 ???
URL: http://www.imada.sdu.dk/~kornerup/papers/RR2.pdf
keywords: range reduction
acknowledgement: ack-nhfb
rawauthor: David Defour and Peter Kornerup and Jean-Michel Muller and Nathalie Revol
rawtitle: A new range reduction algorithm
abstract:
Range reduction is a key point for getting accurate elementary function routines. We introduce a new algorithm that is fast for input arguments belonging to the most common domains, yet accurate over the full double precision range.

entry:
@InProceedings{Defour:2001:NRRb,
  author =       "David Defour and Peter Kornerup and Jean-Michel Muller
                 and Nathalie Revol",
  title =        "A new range reduction algorithm",
  crossref =     "Matthews:2001:CRT",
  pages =        "??--??",
  year =         "2001",
  bibdate =      "Fri Jun 24 12:12:10 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.imada.sdu.dk/~kornerup/papers/RR2.pdf",
  abstract =     "Range reduction is a key point for getting accurate
                 elementary function routines. We introduce a new
                 algorithm that is fast for input arguments belonging to
                 the most common domains, yet accurate over the full
                 double precision range.",
  acknowledgement = ack-nhfb,
  keywords =     "range reduction",
  pagecount =    "11",
}


bibtype: inproceedings
filename: fparith.bib
label: DelRe:2001:IDF
author: A. Del Re and A. Nannarelli and M. Re
booktitle: Conference Record of the Thirty-Fifth Asilomar Conference on Signals, Systems and Computers, 2001
title: Implementation of digital filters in carry-save residue number system
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1309--1313
year: 2001
DOI: https://doi.org/10.1109/ACSSC.2001.987702
bibdate: Fri Nov 9 11:38:59 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:59 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: A. {Del Re} and A. Nannarelli and M. Re
rawbooktitle: Conference Record of the Thirty-Fifth Asilomar Conference on Signals, Systems and Computers, 2001
rawtitle: Implementation of digital filters in carry-save residue number system
entry:
@InProceedings{DelRe:2001:IDF,
  author =       "A. {Del Re} and A. Nannarelli and M. Re",
  booktitle =    "Conference Record of the Thirty-Fifth Asilomar
                 Conference on Signals, Systems and Computers, 2001",
  title =        "Implementation of digital filters in carry-save
                 residue number system",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1309--1313",
  year =         "2001",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ACSSC.2001.987702",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "In this work, we present the implementation of a
                 finite impulse response (FIR) filter in the residue
                 number system (RNS), in which we use a carry-save
                 scheme in the binary representation of the residues to
                 speed-up modular additions. We compare the \ldots{}",
}


bibtype: unpublished
filename: fparith.bib
label: Demmel:2001:CAF
pages: 31
year: 2001
bibdate: Mon Apr 25 06:47:21 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.04.25 06:47:21 ???
note: Lecture slides
URL: http://www.cs.berkeley.edu/~demmel/ISSAC2001_2.pdf
acknowledgement: ack-nhfb
rawnote: Lecture slides
author:
J. Demmel and Ben Diament and W. Kahan and Plamen Koev and Ming Gu and Stan Eisenstat and Ivan Slapnicar and Kresimir Veselic and Zlatko Drmac

title:
The Complexity of Accurate Floating Point Computation and Symbolic Computing, or, Can we do Numerical Linear Algebra In Polynomial Time?

rawauthor:
J. Demmel and Ben Diament and W. Kahan and Plamen Koev and Ming Gu and Stan Eisenstat and Ivan Slapni{\v{c}}ar and Kresimir Veseli{\'c} and Zlatko Drma{\v{c}}

rawtitle:
The Complexity of Accurate Floating Point Computation and Symbolic Computing, or, Can we do Numerical Linear Algebra In Polynomial Time?

entry:
@Unpublished{Demmel:2001:CAF,
  author =       "J. Demmel and Ben Diament and W. Kahan and Plamen Koev
                 and Ming Gu and Stan Eisenstat and Ivan Slapni{\v{c}}ar
                 and Kresimir Veseli{\'c} and Zlatko Drma{\v{c}}",
  title =        "The Complexity of Accurate Floating Point Computation
                 and Symbolic Computing, or, Can we do Numerical Linear
                 Algebra In Polynomial Time?",
  pages =        "31",
  year =         "2001",
  bibdate =      "Mon Apr 25 06:47:21 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Lecture slides",
  URL =          "http://www.cs.berkeley.edu/~demmel/ISSAC2001_2.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: misc
filename: fparith.bib
label: Dhong:2001:ACR
pages: 31
day: 04
month: dec
monthnumber: 12
year: 2001
bibdate: Tue Dec 23 15:06:47 2008
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2008.12.23 15:06:47 ???
URL: http://www.patentstorm.us/patents/7444367/fulltext.html
acknowledgement: ack-nhfb
howpublished: US Patent 7447725
author:
Sang Hoo Dhong and Harm Peter Hofstee and Christian Jacobi and Silvia Melitta Mueller and Hwa-Joon Oh

title:
Apparatus for controlling rounding modes in single instruction multiple data (SIMD) floating-point units

abstract:
An apparatus for controlling rounding modes in a single instruction multiple data (SIMD) floating-point unit is disclosed. The SIMD floating-point unit includes a floating-point status-and-control register (FPSCR) having a first rounding mode bit field and a second rounding mode bit field. The SIMD floating-point unit also includes means for generating a first slice and a second slice. During a floating-point operation, the SIMD floating-point unit concurrently performs a first rounding operation on the first slice and a second rounding operation on the second slice according to a bit in the first rounding mode bit field and a bit in the second rounding mode bit field within the FPSCR, respectively.

rawabstract:
An apparatus for controlling rounding modes in a single instruction multiple data (SIMD) floating-point unit is disclosed. The SIMD floating-point unit includes a floating-point status-and-control register (FPSCR) having a first rounding mode bit field and a second rounding mode bit field. The SIMD floating-point unit also includes means for generating a first slice and a second slice. During a floating-point operation, the SIMD floating-point unit concurrently performs a first rounding operation on the first slice and a second rounding operation on the second slice according to a bit in the first rounding mode bit field and a bit in the second rounding mode bit field within the FPSCR, respectively.

rawauthor:
Sang Hoo Dhong and Harm Peter Hofstee and Christian Jacobi and Silvia Melitta Mueller and Hwa-Joon Oh

rawtitle:
Apparatus for controlling rounding modes in single instruction multiple data ({SIMD}) floating-point units

entry:
@Misc{Dhong:2001:ACR,
  author =       "Sang Hoo Dhong and Harm Peter Hofstee and Christian
                 Jacobi and Silvia Melitta Mueller and Hwa-Joon Oh",
  title =        "Apparatus for controlling rounding modes in single
                 instruction multiple data ({SIMD}) floating-point
                 units",
  howpublished = "US Patent 7447725",
  day =          "04",
  month =        dec,
  year =         "2001",
  bibdate =      "Tue Dec 23 15:06:47 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.patentstorm.us/patents/7444367/fulltext.html",
  abstract =     "An apparatus for controlling rounding modes in a
                 single instruction multiple data (SIMD) floating-point
                 unit is disclosed. The SIMD floating-point unit
                 includes a floating-point status-and-control register
                 (FPSCR) having a first rounding mode bit field and a
                 second rounding mode bit field. The SIMD floating-point
                 unit also includes means for generating a first slice
                 and a second slice. During a floating-point operation,
                 the SIMD floating-point unit concurrently performs a
                 first rounding operation on the first slice and a
                 second rounding operation on the second slice according
                 to a bit in the first rounding mode bit field and a bit
                 in the second rounding mode bit field within the FPSCR,
                 respectively.",
  acknowledgement = ack-nhfb,
}


bibtype: misc
filename: fparith.bib
label: Dickinson:2001:IRB
author: Patrick Dickinson
title: Instant Replay: Building a Game Engine with Reproducible Behavior
pages: 31
day: 13
month: jul
monthnumber: 7
year: 2001
bibdate: Mon Dec 04 07:04:15 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.04 07:04:15 ???
acknowledgement: ack-nhfb
howpublished: Web site
rawauthor: Patrick Dickinson
rawtitle: Instant Replay: Building a Game Engine with Reproducible Behavior
URL:
https://www.gamedeveloper.com/design/instant-replay-building-a-game-engine-with-reproducible-behavior#close-modal

remark:
Comments on problems of rerunning games on different platforms where floating-point issues produce differing outcomes, See also cite Fiedler:2010:GGF.

entry:
@Misc{Dickinson:2001:IRB,
  author =       "Patrick Dickinson",
  title =        "Instant Replay: Building a Game Engine with
                 Reproducible Behavior",
  howpublished = "Web site",
  day =          "13",
  month =        jul,
  year =         "2001",
  bibdate =      "Mon Dec 04 07:04:15 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.gamedeveloper.com/design/instant-replay-building-a-game-engine-with-reproducible-behavior#close-modal",
  acknowledgement = ack-nhfb,
  remark =       "Comments on problems of rerunning games on different
                 platforms where floating-point issues produce differing
                 outcomes, See also \cite{Fiedler:2010:GGF}.",
}


bibtype: inproceedings
filename: fparith.bib
label: Dimitrov:2001:UMD
author: V. S. Dimitrov and J. Eskritt and L. Imbert and G. A. Jullien and W. C. Miller
title: The Use of the Multi-Dimensional Logarithmic Number System in DSP Applications
crossref: Burgess:2001:ISC
pages: 247--256
year: 2001
bibdate: Fri May 3 13:58:18 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.03 13:58:18 MDT
URL: http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Dimitrov.pdf
keywords: ARITH-15
acknowledgement: ack-nhfb
rawauthor: V. S. Dimitrov and J. Eskritt and L. Imbert and G. A. Jullien and W. C. Miller
rawtitle: The Use of the Multi-Dimensional Logarithmic Number System in {DSP} Applications
entry:
@InProceedings{Dimitrov:2001:UMD,
  author =       "V. S. Dimitrov and J. Eskritt and L. Imbert and G. A.
                 Jullien and W. C. Miller",
  title =        "The Use of the Multi-Dimensional Logarithmic Number
                 System in {DSP} Applications",
  crossref =     "Burgess:2001:ISC",
  pages =        "247--256",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Dimitrov.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}


bibtype: article
filename: fparith.bib
label: Drmac:2001:AQS
author: Zlatko Drmac and Elizabeth R. Jessup
title: On Accurate Quotient Singular Value Computation in Floating-Point Arithmetic
journal: j-SIAM-J-MAT-ANA-APPL
volume: 22
number: 3
pages: 853--873
month: jul
monthnumber: 7
year: 2001
CODEN: SJMAEL
ISSN: 0895-4798 (print), 1095-7162 (electronic) OR 08954798 (print), 10957162 (electronic)
ISSNL: 0895-4798 OR 08954798
bibdate: Wed Oct 23 08:36:30 MDT 2002
bibsource: http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/22/3; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.10.23 08:36:30 MDT
URL: http://epubs.siam.org/sam-bin/dbq/article/31054
fjournal: SIAM Journal on Matrix Analysis and Applications
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/simax
rawauthor: Zlatko Drmac and Elizabeth R. Jessup
rawtitle: On Accurate Quotient Singular Value Computation in Floating-Point Arithmetic
entry:
@Article{Drmac:2001:AQS,
  author =       "Zlatko Drmac and Elizabeth R. Jessup",
  title =        "On Accurate Quotient Singular Value Computation in
                 Floating-Point Arithmetic",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "22",
  number =       "3",
  pages =        "853--873",
  month =        jul,
  year =         "2001",
  CODEN =        "SJMAEL",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  bibdate =      "Wed Oct 23 08:36:30 MDT 2002",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/22/3;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/31054",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}


bibtype: inproceedings
filename: fparith.bib
label: Fernandez:2001:IOD
author: P. G. Fernandez and J. Ramirez and A. Garcia and L. Parrilla and A. Lloris
booktitle: The 8th IEEE International Conference on Electronics, Circuits and Systems, ICECS 2001
title: Implementation of the one dimensional discrete cosine transform using the residue number system
volume: 1
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 433--436
year: 2001
DOI: https://doi.org/10.1109/ICECS.2001.957772
bibdate: Fri Nov 9 11:38:59 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:59 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: P. G. Fernandez and J. Ramirez and A. Garcia and L. Parrilla and A. Lloris
rawbooktitle: The 8th {IEEE} International Conference on Electronics, Circuits and Systems, {ICECS 2001}
rawtitle: Implementation of the one dimensional discrete cosine transform using the residue number system
entry:
@InProceedings{Fernandez:2001:IOD,
  author =       "P. G. Fernandez and J. Ramirez and A. Garcia and L.
                 Parrilla and A. Lloris",
  booktitle =    "The 8th {IEEE} International Conference on
                 Electronics, Circuits and Systems, {ICECS 2001}",
  title =        "Implementation of the one dimensional discrete cosine
                 transform using the residue number system",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "433--436",
  year =         "2001",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ICECS.2001.957772",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 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 shows the implementation of the one
                 dimensional discrete cosine transform (1D-DCT) based on
                 the residue number system (RNS). The 1D-DCT has been
                 derived by,the application of a previously developed
                 scaled fast cosine transform (FCT) \ldots{}",
}


bibtype: phdthesis
filename: fparith.bib
label: Finot-Moreau:2001:PAU
author: Claire Finot-Moreau
title: Preuves et algorithmes utilisant l'arithmetique flottante normalisee IEEE
type: Ph.D. thesis
school: Ecole Normale Superieure de Lyon
address: Lyon, France
pages: 433--436
month: jul
monthnumber: 7
year: 2001
bibdate: Sat Apr 01 08:46:03 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2017.04.01 08:46:03 ???
acknowledgement: ack-nhfb
rawauthor: Claire Finot-Moreau
rawtitle: Preuves et algorithmes utilisant l'arithm{\'e}tique flottante normalis{\'e}e {IEEE}
entry:
@PhdThesis{Finot-Moreau:2001:PAU,
  author =       "Claire Finot-Moreau",
  title =        "Preuves et algorithmes utilisant l'arithm{\'e}tique
                 flottante normalis{\'e}e {IEEE}",
  type =         "{Ph.D.} thesis",
  school =       "{\'E}cole Normale Sup{\'e}rieure de Lyon",
  address =      "Lyon, France",
  month =        jul,
  year =         "2001",
  bibdate =      "Sat Apr 01 08:46:03 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: fparith.bib
label: Flynn:2001:ACA
author: Michael J. Flynn and Stuart F. Oberman
title: Advanced computer arithmetic design
publisher: pub-WILEY
address: pub-WILEY:adr
pages: xv + 325
year: 2001
ISBN: 0-471-41209-0 OR 0471412090
ISBN13: 978-0-471-41209-0 OR 9780471412090
LCCN: TK7895.A65 F59 2001
bibdate: Tue May 07 05:20:32 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.07 05:20:32 ???
acknowledgement: ack-nhfb
rawauthor: Michael J. Flynn and Stuart F. Oberman
rawtitle: Advanced computer arithmetic design
remark:
From the preface: ``The book is not written as a textbook, but rather, it is written with computer designers and researchers in mind. Therefore its focus is on em design, not on other aspects of computer arithmetic, such as number systems, representation, or precision.'' Chapter 12, Rational Arithmetic, treats the application of continued fractions to the computation of elementary functions.

TOC:
Preface Acknowledgments Notation 1. Integer Addition 2. Floating-Point Addition 3. Multiplication with Partially Redundant Multiples 4. Multiplier Topologies 5. Technology Scaling Effects on Multipliers 6. Design Issues in Division 7. Minimizing the Complexity of SRT Tables 8. Very High-Radix Division 9. Using a Multiplier for Function Approximation 10. FUPA [Floating-point unit-cost performance analysis metric] 11. High-Speed Clocking Using Wave Pipelining 12. Rational Arithmetic Bibliography Index

rawTOC:
Preface \\ Acknowledgments \\ Notation \\ 1. Integer Addition \\ 2. Floating-Point Addition \\ 3. Multiplication with Partially Redundant Multiples \\ 4. Multiplier Topologies \\ 5. Technology Scaling Effects on Multipliers \\ 6. Design Issues in Division \\ 7. Minimizing the Complexity of SRT Tables \\ 8. Very High-Radix Division \\ 9. Using a Multiplier for Function Approximation \\ 10. FUPA [Floating-point unit-cost performance analysis metric] \\ 11. High-Speed Clocking Using Wave Pipelining \\ 12. Rational Arithmetic \\ Bibliography \\ Index

entry:
@Book{Flynn:2001:ACA,
  author =       "Michael J. Flynn and Stuart F. Oberman",
  title =        "Advanced computer arithmetic design",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xv + 325",
  year =         "2001",
  ISBN =         "0-471-41209-0",
  ISBN-13 =      "978-0-471-41209-0",
  LCCN =         "TK7895.A65 F59 2001",
  bibdate =      "Tue May 07 05:20:32 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "From the preface: ``The book is not written as a
                 textbook, but rather, it is written with computer
                 designers and researchers in mind. Therefore its focus
                 is on {\em design}, not on other aspects of computer
                 arithmetic, such as number systems, representation, or
                 precision.'' Chapter 12, Rational Arithmetic, treats
                 the application of continued fractions to the
                 computation of elementary functions.",
  tableofcontents = "Preface \\
                 Acknowledgments \\
                 Notation \\
                 1. Integer Addition \\
                 2. Floating-Point Addition \\
                 3. Multiplication with Partially Redundant Multiples
                 \\
                 4. Multiplier Topologies \\
                 5. Technology Scaling Effects on Multipliers \\
                 6. Design Issues in Division \\
                 7. Minimizing the Complexity of SRT Tables \\
                 8. Very High-Radix Division \\
                 9. Using a Multiplier for Function Approximation \\
                 10. FUPA [Floating-point unit-cost performance analysis
                 metric] \\
                 11. High-Speed Clocking Using Wave Pipelining \\
                 12. Rational Arithmetic \\
                 Bibliography \\
                 Index",
}


bibtype: article
filename: fparith.bib
label: Galan-Simon:2001:MLD
author: F. Javier Galan-Simon and Edgar Martinez-Moro and Juan G. Tena-Ayuso
title: Majority-Logic-Decodable Cyclic Arithmetic-Modular AN-Codes in $1$, $2$, and $L$ Steps
journal: j-LECT-NOTES-COMP-SCI
volume: 2260
pages: 128--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:07:45 MST 2002
bibtimestamp: 2002.02.02 13:07:45 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: F. Javier Gal{\'a}n-Sim{\'o}n and Edgar Mart{\'\i}nez-Moro and Juan G. Tena-Ayuso
rawtitle: Majority-Logic-Decodable Cyclic Arithmetic-Modular {AN}-Codes in $1$, $2$, and {$L$} Steps
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2260.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2260/22600128.htm; http://link.springer-ny.com/link/service/series/0558/papers/2260/22600128.pdf

entry:
@Article{Galan-Simon:2001:MLD,
  author =       "F. Javier Gal{\'a}n-Sim{\'o}n and Edgar
                 Mart{\'\i}nez-Moro and Juan G. Tena-Ayuso",
  title =        "Majority-Logic-Decodable Cyclic Arithmetic-Modular
                 {AN}-Codes in $1$, $2$, and {$L$} Steps",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2260",
  pages =        "128--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:07:45 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2260.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2260/22600128.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2260/22600128.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Gallant:2001:FPM
author: Robert P. Gallant and Robert J. Lambert and Scott A. Vanstone
title: Faster Point Multiplication on Elliptic Curves with Efficient Endomorphisms
journal: j-LECT-NOTES-COMP-SCI
volume: 2139
pages: 190--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:05:41 MST 2002
bibtimestamp: 2002.02.02 13:05:41 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Robert P. Gallant and Robert J. Lambert and Scott A. Vanstone
rawtitle: Faster Point Multiplication on Elliptic Curves with Efficient Endomorphisms
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2139.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2139/21390190.htm; http://link.springer-ny.com/link/service/series/0558/papers/2139/21390190.pdf

entry:
@Article{Gallant:2001:FPM,
  author =       "Robert P. Gallant and Robert J. Lambert and Scott A.
                 Vanstone",
  title =        "Faster Point Multiplication on Elliptic Curves with
                 Efficient Endomorphisms",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2139",
  pages =        "190--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:05:41 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2139.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2139/21390190.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2139/21390190.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Gelbukh:2001:ZHL
author: Alexander Gelbukh and Grigori Sidorov
title: Zipf and Heaps Laws' Coefficients Depend on Language
journal: j-LECT-NOTES-COMP-SCI
volume: 2004
pages: 332--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:03:22 MST 2002
bibtimestamp: 2002.02.02 13:03:22 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Alexander Gelbukh and Grigori Sidorov
rawtitle: {Zipf} and {Heaps Laws}' Coefficients Depend on Language
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2004.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2004/20040332.htm; http://link.springer-ny.com/link/service/series/0558/papers/2004/20040332.pdf

entry:
@Article{Gelbukh:2001:ZHL,
  author =       "Alexander Gelbukh and Grigori Sidorov",
  title =        "{Zipf} and {Heaps Laws}' Coefficients Depend on
                 Language",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2004",
  pages =        "332--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:03:22 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2004.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2004/20040332.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2004/20040332.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Gil:2001:SAT
author: Joseph (Yossi) Gil
title: Subtyping arithmetical types
journal: j-SIGPLAN
volume: 36
number: 3
pages: 276--289
month: mar
monthnumber: 3
year: 2001
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 09:18:23 MST 2003
bibtimestamp: 2003.12.14 09:18:23 MST
fjournal: ACM SIGPLAN Notices
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J706
rawauthor: Joseph (Yossi) Gil
rawtitle: Subtyping arithmetical types
bibsource:
http://portal.acm.org/; http://www.acm.org/pubs/contents/proceedings/series/popl/; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://www.acm.org/pubs/articles/proceedings/plan/360204/p276-gil/p276-gil.pdf; http://www.acm.org/pubs/citations/proceedings/plan/360204/p276-gil/

entry:
@Article{Gil:2001:SAT,
  author =       "Joseph (Yossi) Gil",
  title =        "Subtyping arithmetical types",
  journal =      j-SIGPLAN,
  volume =       "36",
  number =       "3",
  pages =        "276--289",
  month =        mar,
  year =         "2001",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sun Dec 14 09:18:23 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.acm.org/pubs/contents/proceedings/series/popl/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/articles/proceedings/plan/360204/p276-gil/p276-gil.pdf;
                 http://www.acm.org/pubs/citations/proceedings/plan/360204/p276-gil/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
}


bibtype: inproceedings
filename: fparith.bib
label: Gok:2001:EIM
author: M. Gok and M. J. Schulte and P. I. Balzola
title: Efficient Integer Multiplication Overflow Detection Circuits
crossref: Matthews:2001:CRT
pages: 1661--1665
year: 2001
bibdate: Sun Mar 04 11:45:08 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.03.04 11:45:08 ???
URL: http://mesa.ece.wisc.edu/publications/cp_2001-07.pdf
acknowledgement: ack-nhfb
rawauthor: M. Gok and M. J. Schulte and P. I. Balzola
rawtitle: Efficient Integer Multiplication Overflow Detection Circuits
entry:
@InProceedings{Gok:2001:EIM,
  author =       "M. Gok and M. J. Schulte and P. I. Balzola",
  title =        "Efficient Integer Multiplication Overflow Detection
                 Circuits",
  crossref =     "Matthews:2001:CRT",
  pages =        "1661--1665",
  year =         "2001",
  bibdate =      "Sun Mar 04 11:45:08 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2001-07.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Goubault:2001:SAP
author: Eric Goubault
title: Static Analyses of the Precision of Floating-Point Operations
journal: j-LECT-NOTES-COMP-SCI
volume: 2126
pages: 234--259
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
MRnumber: MR2051233
bibdate: Sat Feb 2 13:05:28 MST 2002
bibtimestamp: 2002.02.02 13:05:28 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Eric Goubault
rawtitle: Static Analyses of the Precision of Floating-Point Operations
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2126.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2126/21260234.htm; http://link.springer-ny.com/link/service/series/0558/papers/2126/21260234.pdf

entry:
@Article{Goubault:2001:SAP,
  author =       "Eric Goubault",
  title =        "Static Analyses of the Precision of Floating-Point
                 Operations",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2126",
  pages =        "234--259",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  MRnumber =     "MR2051233",
  bibdate =      "Sat Feb 2 13:05:28 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2126.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2126/21260234.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2126/21260234.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Gowland:2001:SEA
author: Paul Gowland and David Lester
title: A Survey of Exact Arithmetic Implementations
journal: j-LECT-NOTES-COMP-SCI
volume: 2064
pages: 30--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:04:19 MST 2002
bibtimestamp: 2002.02.02 13:04:19 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Paul Gowland and David Lester
rawtitle: A Survey of Exact Arithmetic Implementations
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2064.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2064/20640030.htm; http://link.springer-ny.com/link/service/series/0558/papers/2064/20640030.pdf

entry:
@Article{Gowland:2001:SEA,
  author =       "Paul Gowland and David Lester",
  title =        "A Survey of Exact Arithmetic Implementations",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2064",
  pages =        "30--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:04:19 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2064.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2064/20640030.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2064/20640030.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Grossschadl:2001:BSU
author: J. Gross schadl
title: A Bit-Serial Unified Multiplier Architecture for Finite Fields GF$ (p) $ and GF$ (2^m) $
journal: j-LECT-NOTES-COMP-SCI
volume: 2162
pages: 202--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:06:06 MST 2002
bibtimestamp: 2002.02.02 13:06:06 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: J. Gro{\ss}sch{\"a}dl
rawtitle: A Bit-Serial Unified Multiplier Architecture for Finite Fields {GF$ (p) $} and {GF$ (2^m) $}
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2162.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2162/21620202.htm; http://link.springer-ny.com/link/service/series/0558/papers/2162/21620202.pdf

entry:
@Article{Grossschadl:2001:BSU,
  author =       "J. Gro{\ss}sch{\"a}dl",
  title =        "A Bit-Serial Unified Multiplier Architecture for
                 Finite Fields {GF$ (p) $} and {GF$ (2^m) $}",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2162",
  pages =        "202--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:06:06 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2162.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2162/21620202.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2162/21620202.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Groza:2001:HRF
author: V. Z. Groza
title: High-resolution floating-point ADC
journal: j-IEEE-TRANS-INSTRUM-MEAS
volume: 50
number: 6
pages: 1822--1829
month: dec
monthnumber: 12
year: 2001
CODEN: IEIMAO
ISSN: 0018-9456 (print), 1557-9662 (electronic) OR 00189456 (print), 15579662 (electronic)
ISSNL: 0018-9456 OR 00189456
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 Instrumentation and Measurement
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=19
rawauthor: V. Z. Groza
rawtitle: High-resolution floating-point {ADC}
entry:
@Article{Groza:2001:HRF,
  author =       "V. Z. Groza",
  title =        "High-resolution floating-point {ADC}",
  journal =      j-IEEE-TRANS-INSTRUM-MEAS,
  volume =       "50",
  number =       "6",
  pages =        "1822--1829",
  month =        dec,
  year =         "2001",
  CODEN =        "IEIMAO",
  ISSN =         "0018-9456 (print), 1557-9662 (electronic)",
  ISSN-L =       "0018-9456",
  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 Instrumentation and Measurement",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=19",
  summary =      "Floating-point analog-to-digital converters (FP-ADC)
                 are used for acquiring signals within a high dynamic
                 range. The quantization range of FP-ADCs is several
                 orders of magnitude higher than that of a fixed-point
                 analog-to-digital converter (ADC). \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Gunther:2001:SAK
author: Christian Gunther and Tanja Lange and Andreas Stein
title: Speeding up the Arithmetic on Koblitz Curves of Genus Two
journal: j-LECT-NOTES-COMP-SCI
volume: 2012
pages: 106--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:03:30 MST 2002
bibtimestamp: 2002.02.02 13:03:30 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Christian G{\"u}nther and Tanja Lange and Andreas Stein
rawtitle: Speeding up the Arithmetic on {Koblitz} Curves of Genus Two
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2012.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2012/20120106.htm; http://link.springer-ny.com/link/service/series/0558/papers/2012/20120106.pdf

entry:
@Article{Gunther:2001:SAK,
  author =       "Christian G{\"u}nther and Tanja Lange and Andreas
                 Stein",
  title =        "Speeding up the Arithmetic on {Koblitz} Curves of
                 Genus Two",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2012",
  pages =        "106--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:03:30 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2012.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2012/20120106.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2012/20120106.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: inproceedings
filename: fparith.bib
label: Hasan:2001:ECM
author: M. A. Hasan
title: Efficient Computation of Multiplicative Inverses for Cryptographic Applications
crossref: Burgess:2001:ISC
pages: 66--72
year: 2001
bibdate: Fri May 3 13:58:18 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.03 13:58:18 MDT
URL: http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Hasan.pdf
keywords: ARITH-15
acknowledgement: ack-nhfb
rawauthor: M. A. Hasan
rawtitle: Efficient Computation of Multiplicative Inverses for Cryptographic Applications
entry:
@InProceedings{Hasan:2001:ECM,
  author =       "M. A. Hasan",
  title =        "Efficient Computation of Multiplicative Inverses for
                 Cryptographic Applications",
  crossref =     "Burgess:2001:ISC",
  pages =        "66--72",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Hasan.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}


bibtype: article
filename: fparith.bib
label: Hayes:2001:TB
author: Brian Hayes
title: Third Base
journal: j-AM-SCI
volume: 89
number: 6
pages: 490--495
month: nov
monthnumber: 11
year: 2001
CODEN: AMSCAC
ISSN: 0003-0996 (print), 1545-2786 (electronic) OR 00030996 (print), 15452786 (electronic)
ISSNL: 0003-0996 OR 00030996
bibdate: Tue Nov 08 08:06:17 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.11.08 08:06:17 ???
URL: http://www.americanscientist.org/content/AMSCI/AMSCI/ArticleAltFormat/20035214317_146.pdf
fjournal: American Scientist
keywords: ternary arithmetic
acknowledgement: ack-nhfb
journalURL: http://www.americanscientist.org/issues/past.aspx
rawauthor: Brian Hayes
rawtitle: Third Base
abstract:
People count by tens and machines count by twos that pretty much sums up the way we do arithmetic on this planet. But there are countless other ways to count. Here I want to offer three cheers for base 3, the ternary system. The numerals in this sequence beginning 0, 1, 2, 10, 11, 12, 20, 21, 22, 100, 101 are not as widely known or widely used as their decimal and binary cousins, but they have charms all their own. They are the Goldilocks choice among numbering systems: When base 2 is too small and base 10 is too big, base 3 is just right.

rawabstract:
People count by tens and machines count by twos that pretty much sums up the way we do arithmetic on this planet. But there are countless other ways to count. Here I want to offer three cheers for base 3, the ternary system. The numerals in this sequence beginning 0, 1, 2, 10, 11, 12, 20, 21, 22, 100, 101 are not as widely known or widely used as their decimal and binary cousins, but they have charms all their own. They are the Goldilocks choice among numbering systems: When base 2 is too small and base 10 is too big, base 3 is just right.

entry:
@Article{Hayes:2001:TB,
  author =       "Brian Hayes",
  title =        "Third Base",
  journal =      j-AM-SCI,
  volume =       "89",
  number =       "6",
  pages =        "490--495",
  month =        nov # "\slash " # dec,
  year =         "2001",
  CODEN =        "AMSCAC",
  ISSN =         "0003-0996 (print), 1545-2786 (electronic)",
  ISSN-L =       "0003-0996",
  bibdate =      "Tue Nov 08 08:06:17 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.americanscientist.org/content/AMSCI/AMSCI/ArticleAltFormat/20035214317_146.pdf",
  abstract =     "People count by tens and machines count by twos that
                 pretty much sums up the way we do arithmetic on this
                 planet. But there are countless other ways to count.
                 Here I want to offer three cheers for base 3, the
                 ternary system. The numerals in this sequence beginning
                 0, 1, 2, 10, 11, 12, 20, 21, 22, 100, 101 are not as
                 widely known or widely used as their decimal and binary
                 cousins, but they have charms all their own. They are
                 the Goldilocks choice among numbering systems: When
                 base 2 is too small and base 10 is too big, base 3 is
                 just right.",
  acknowledgement = ack-nhfb,
  fjournal =     "American Scientist",
  journal-URL =  "http://www.americanscientist.org/issues/past.aspx",
  keywords =     "ternary arithmetic",
}


bibtype: article
filename: fparith.bib
label: He:2001:UAA
author: Yun He and Chris H. Q. Ding
journal: j-J-SUPERCOMPUTING
volume: 18
number: 3
pages: 259--277
month: mar
monthnumber: 3
year: 2001
CODEN: JOSUED
DOI: https://doi.org/10.1023/A:1008153532043
ISSN: 0920-8542 (print), 1573-0484 (electronic) OR 09208542 (print), 15730484 (electronic)
ISSNL: 0920-8542 OR 09208542
bibdate: Wed Jul 6 12:13:17 MDT 2005
bibtimestamp: 2005.07.06 12:13:17 MDT
fjournal: The Journal of Supercomputing
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/11227
rawauthor: Yun He and Chris H. Q. Ding
title:
Using Accurate Arithmetics to Improve Numerical Reproducibility and Stability in Parallel Applications

bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0920-8542&volume=18&issue=3; http://www.wkap.nl/issuetoc.htm/0920-8542+18+3+2001; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://www.springerlink.com/openurl.asp?genre=article&issn=0920-8542&volume=18&issue=3&spage=259; http://www.wkap.nl/oasis.htm/323815

rawtitle:
Using Accurate Arithmetics to Improve Numerical Reproducibility and Stability in Parallel Applications

entry:
@Article{He:2001:UAA,
  author =       "Yun He and Chris H. Q. Ding",
  title =        "Using Accurate Arithmetics to Improve Numerical
                 Reproducibility and Stability in Parallel
                 Applications",
  journal =      j-J-SUPERCOMPUTING,
  volume =       "18",
  number =       "3",
  pages =        "259--277",
  month =        mar,
  year =         "2001",
  CODEN =        "JOSUED",
  DOI =          "https://doi.org/10.1023/A:1008153532043",
  ISSN =         "0920-8542 (print), 1573-0484 (electronic)",
  ISSN-L =       "0920-8542",
  bibdate =      "Wed Jul 6 12:13:17 MDT 2005",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0920-8542&volume=18&issue=3;
                 http://www.wkap.nl/issuetoc.htm/0920-8542+18+3+2001;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0920-8542&volume=18&issue=3&spage=259;
                 http://www.wkap.nl/oasis.htm/323815",
  acknowledgement = ack-nhfb,
  fjournal =     "The Journal of Supercomputing",
  journal-URL =  "http://link.springer.com/journal/11227",
}


bibtype: article
filename: fparith.bib
label: Hesse:2001:DUT
author: William Hesse
title: Division Is in Uniform TC$^0$
journal: j-LECT-NOTES-COMP-SCI
volume: 2076
pages: 104--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Fri Feb 1 09:17:25 MST 2002
bibtimestamp: 2002.02.01 09:17:25 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: William Hesse
rawtitle: Division Is in Uniform {TC$^0$}
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2076.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2076/20760104.htm; http://link.springer-ny.com/link/service/series/0558/papers/2076/20760104.pdf

entry:
@Article{Hesse:2001:DUT,
  author =       "William Hesse",
  title =        "Division Is in Uniform {TC$^0$}",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2076",
  pages =        "104--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Fri Feb 1 09:17:25 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2076.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2076/20760104.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2076/20760104.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: inproceedings
filename: fparith.bib
label: Hida:2001:AQD
author: Yozo Hida and Xiaoye S. Li and David H. Bailey
title: Algorithms for Quad-Double Precision Floating Point Arithmetic
crossref: Burgess:2001:ISC
pages: 155--162
year: 2001
DOI: https://doi.org/10.1109/ARITH.2001.930115
bibdate: Fri May 3 13:58:18 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.03 13:58:18 MDT
URL: http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Hida.pdf
keywords: ARITH-15
acknowledgement: ack-nhfb
rawauthor: Yozo Hida and Xiaoye S. Li and David H. Bailey
rawtitle: Algorithms for Quad-Double Precision Floating Point Arithmetic
entry:
@InProceedings{Hida:2001:AQD,
  author =       "Yozo Hida and Xiaoye S. Li and David H. Bailey",
  title =        "Algorithms for Quad-Double Precision Floating Point
                 Arithmetic",
  crossref =     "Burgess:2001:ISC",
  pages =        "155--162",
  year =         "2001",
  DOI =          "https://doi.org/10.1109/ARITH.2001.930115",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Hida.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}


bibtype: techreport
filename: fparith.bib
label: Hlavacs:2001:IAN
author: H. Hlavacs and C. W. Ueberhuber
title: Improving the Accuracy of Numerical Integration
type: Technical report
number: TR 2001-06
institution: Aurora: Advanced Models, Applications and Software Systems for High Performance Computing
address: European Centre for Parallel Computing at Vienna Nordbergstrass e 15/C/3, A-1090 Vienna, Austria
pages: i + 14
year: 2001
bibdate: Tue Nov 22 06:22:21 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.11.22 06:22:21 ???
keywords: accurate floating-point summation
acknowledgement: ack-nhfb
rawauthor: H. Hlavacs and C. W. Ueberhuber
rawtitle: Improving the Accuracy of Numerical Integration
URL:
ftp://ftp.vcpc.univie.ac.at/projects/aurora/reports/auroratr2001-06.ps.gz; http://citeseer.ist.psu.edu/hlavacs01improving.html

abstract:
In this report, a method for reducing the effect of round-off errors occurring in one-dimensional integration is presented. The new method, applicable to uneven integrand functions, is based on an extended version of Kahan--Babuska summation.

rawabstract:
In this report, a method for reducing the effect of round-off errors occurring in one-dimensional integration is presented. The new method, applicable to uneven integrand functions, is based on an extended version of Kahan--Babuska summation.

entry:
@TechReport{Hlavacs:2001:IAN,
  author =       "H. Hlavacs and C. W. Ueberhuber",
  title =        "Improving the Accuracy of Numerical Integration",
  type =         "Technical report",
  number =       "TR 2001-06",
  institution =  "Aurora: Advanced Models, Applications and Software
                 Systems for High Performance Computing",
  address =      "European Centre for Parallel Computing at Vienna
                 Nordbergstra{\ss}e 15/C/3, A-1090 Vienna, Austria",
  pages =        "i + 14",
  year =         "2001",
  bibdate =      "Tue Nov 22 06:22:21 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://ftp.vcpc.univie.ac.at/projects/aurora/reports/auroratr2001-06.ps.gz;
                 http://citeseer.ist.psu.edu/hlavacs01improving.html",
  abstract =     "In this report, a method for reducing the effect of
                 round-off errors occurring in one-dimensional
                 integration is presented. The new method, applicable to
                 uneven integrand functions, is based on an extended
                 version of Kahan--Babuska summation.",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation",
}


bibtype: book
filename: fparith.bib
label: Hsu:2001:CAS
author: John Y. Hsu
title: Computer Architecture: Software Aspects, Coding, Hardware
publisher: pub-CRC
address: pub-CRC:adr
pages: 427
year: 2001
ISBN: 0-8493-1026-1, 1-351-83604-8, 1-4200-4110-X (e-book) OR 0849310261, 1351836048, 142004110X (ebook)
LCCN: A76.9.A73 H758 2001
bibdate: Fri Jan 19 15:47:59 2001
bibtimestamp: 2001.01.19 15:47:59 ???
acknowledgement: ack-nhfb
rawauthor: John Y. Hsu
rawtitle: Computer Architecture: Software Aspects, Coding, Hardware
ISBN13:
978-0-8493-1026-3, 978-1-351-83604-3, 978-1-4200-4110-1 (e-book) OR 9780849310263, 9781351836043, 9781420041101 (ebook)

bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/java2000.bib; https://www.math.utah.edu/pub/tex/bib/master.bib; https://www.math.utah.edu/pub/tex/bib/microchip.bib; https://www.math.utah.edu/pub/tex/bib/virtual-machines.bib; https://www.math.utah.edu/pub/tex/bib/visual-instruction-set.bib

abstract:
With the new developments in computer architecture, fairly recent publications can quickly become outdated. Computer Architecture: Software Aspects, Coding, and Hardware takes a modern approach. This comprehensive, practical text provides that critical understanding of a central processor by clearly detailing fundamentals, and cutting edge design features. With its balanced software/hardware perspective and its description of Pentium processors, the book allows readers to acquire practical PC software experience. The text presents a foundation-level set of ideas, design concepts, and applications that fully meet the requirements of computer organization and architecture courses. The book features a ``bottom up'' computer design approach, based upon the author's thirty years experience in both academe and industry. By combining computer engineering with electrical engineering, the author describes how logic circuits are designed in a CPU. The extensive coverage of a microprogrammed CPU and new processor design features gives the insight of current computer development. Computer Architecture: Software Aspects, Coding, and Hardware presents a comprehensive review of the subject, from beginner to advanced levels. Topics include: * Two's complement numbers * Integer overflow * Exponent overflow and underflow * Looping * Addressing modes * Indexing * Subroutine linking * I/O structures * Memory mapped I/O * Cycle stealing * Interrupts * Multitasking * Microprogrammed CPU * Multiplication tree * Instruction queue * Multimedia instructions * Instruction cache * Virtual memory * Data cache * Alpha chip * Interprocessor communications * Branch prediction * Speculative loading * Register stack * JAVA virtual machine * Stack machine principles.

keywords:
Compaq/DEC Alpha; floating-point arithmetic; Intel x86; Java Virtual Machine; multimedia instructions; Pentium

TOC:
Number Systems Basic Computer Principles Assembly Language Principles Computer Architecture--General Features Microprogrammed CPU Design Superscalar Machine Principles Vector and Multiple-Processor Machines Processor Design Case Studies Stack Machine Principles

rawabstract:
With the new developments in computer architecture, fairly recent publications can quickly become outdated. Computer Architecture: Software Aspects, Coding, and Hardware takes a modern approach. This comprehensive, practical text provides that critical understanding of a central processor by clearly detailing fundamentals, and cutting edge design features. With its balanced software/hardware perspective and its description of Pentium processors, the book allows readers to acquire practical PC software experience. The text presents a foundation-level set of ideas, design concepts, and applications that fully meet the requirements of computer organization and architecture courses. The book features a ``bottom up'' computer design approach, based upon the author's thirty years experience in both academe and industry. By combining computer engineering with electrical engineering, the author describes how logic circuits are designed in a CPU. The extensive coverage of a microprogrammed CPU and new processor design features gives the insight of current computer development. Computer Architecture: Software Aspects, Coding, and Hardware presents a comprehensive review of the subject, from beginner to advanced levels. Topics include: * Two's complement numbers * Integer overflow * Exponent overflow and underflow * Looping * Addressing modes * Indexing * Subroutine linking * I/O structures * Memory mapped I/O * Cycle stealing * Interrupts * Multitasking * Microprogrammed CPU * Multiplication tree * Instruction queue * Multimedia instructions * Instruction cache * Virtual memory * Data cache * Alpha chip * Interprocessor communications * Branch prediction * Speculative loading * Register stack * JAVA virtual machine * Stack machine principles.

rawTOC:
Number Systems \\ Basic Computer Principles \\ Assembly Language Principles \\ Computer Architecture--General Features \\ Microprogrammed CPU Design \\ Superscalar Machine Principles \\ Vector and Multiple-Processor Machines \\ Processor Design Case Studies \\ Stack Machine Principles

entry:
@Book{Hsu:2001:CAS,
  author =       "John Y. Hsu",
  title =        "Computer Architecture: Software Aspects, Coding,
                 Hardware",
  publisher =    pub-CRC,
  address =      pub-CRC:adr,
  pages =        "427",
  year =         "2001",
  ISBN =         "0-8493-1026-1, 1-351-83604-8, 1-4200-4110-X (e-book)",
  ISBN-13 =      "978-0-8493-1026-3, 978-1-351-83604-3,
                 978-1-4200-4110-1 (e-book)",
  LCCN =         "A76.9.A73 H758 2001",
  bibdate =      "Fri Jan 19 15:47:59 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/java2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/microchip.bib;
                 https://www.math.utah.edu/pub/tex/bib/virtual-machines.bib;
                 https://www.math.utah.edu/pub/tex/bib/visual-instruction-set.bib",
  price =        "US\$89.95, UK\pounds 59.99",
  abstract =     "With the new developments in computer architecture,
                 fairly recent publications can quickly become outdated.
                 Computer Architecture: Software Aspects, Coding, and
                 Hardware takes a modern approach. This comprehensive,
                 practical text provides that critical understanding of
                 a central processor by clearly detailing fundamentals,
                 and cutting edge design features. With its balanced
                 software/hardware perspective and its description of
                 Pentium processors, the book allows readers to acquire
                 practical PC software experience. The text presents a
                 foundation-level set of ideas, design concepts, and
                 applications that fully meet the requirements of
                 computer organization and architecture courses. The
                 book features a ``bottom up'' computer design approach,
                 based upon the author's thirty years experience in both
                 academe and industry. By combining computer engineering
                 with electrical engineering, the author describes how
                 logic circuits are designed in a CPU. The extensive
                 coverage of a microprogrammed CPU and new processor
                 design features gives the insight of current computer
                 development. Computer Architecture: Software Aspects,
                 Coding, and Hardware presents a comprehensive review of
                 the subject, from beginner to advanced levels. Topics
                 include: * Two's complement numbers * Integer overflow
                 * Exponent overflow and underflow * Looping *
                 Addressing modes * Indexing * Subroutine linking * I/O
                 structures * Memory mapped I/O * Cycle stealing *
                 Interrupts * Multitasking * Microprogrammed CPU *
                 Multiplication tree * Instruction queue * Multimedia
                 instructions * Instruction cache * Virtual memory *
                 Data cache * Alpha chip * Interprocessor communications
                 * Branch prediction * Speculative loading * Register
                 stack * JAVA virtual machine * Stack machine
                 principles.",
  acknowledgement = ack-nhfb,
  keywords =     "Compaq/DEC Alpha; floating-point arithmetic; Intel
                 x86; Java Virtual Machine; multimedia instructions;
                 Pentium",
  libnote =      "Not yet in my library.",
  tableofcontents = "Number Systems \\
                 Basic Computer Principles \\
                 Assembly Language Principles \\
                 Computer Architecture--General Features \\
                 Microprogrammed CPU Design \\
                 Superscalar Machine Principles \\
                 Vector and Multiple-Processor Machines \\
                 Processor Design Case Studies \\
                 Stack Machine Principles",
}


bibtype: article
filename: fparith.bib
label: Hur:2001:GRO
author: Namhyun Hur and James H. Davenport
title: A Generic Root Operation for Exact Real Arithmetic
journal: j-LECT-NOTES-COMP-SCI
volume: 2064
pages: 82--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:04:19 MST 2002
bibtimestamp: 2002.02.02 13:04:19 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Namhyun Hur and James H. Davenport
rawtitle: A Generic Root Operation for Exact Real Arithmetic
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2064.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2064/20640082.htm; http://link.springer-ny.com/link/service/series/0558/papers/2064/20640082.pdf

entry:
@Article{Hur:2001:GRO,
  author =       "Namhyun Hur and James H. Davenport",
  title =        "A Generic Root Operation for Exact Real Arithmetic",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2064",
  pages =        "82--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:04:19 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2064.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2064/20640082.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2064/20640082.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: book
filename: fparith.bib
label: ISO:2001:IIIc
author: ISO
publisher: pub-ISO
address: pub-ISO:adr
pages: x + 177
day: 15
month: aug
monthnumber: 8
year: 2001
bibdate: Sun Mar 15 11:09:44 2009
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2009.03.15 11:09:44 ???
acknowledgement: ack-nhfb
rawauthor: {ISO}
title:
ISO / IEC 10967-2: Information technology --- Language independent arithmetic --- Part 2: Elementary numerical functions

URL:
http://standards.iso.org/ittf/PubliclyAvailableStandards/c024427_ISO_IEC_10967-2_2001(E).zip; http://www.iso.ch/cate/d24427.html

rawtitle:
{ISO\slash IEC 10967-2}: {Information} technology --- {Language} independent arithmetic --- {Part} 2: {Elementary} numerical functions

entry:
@Book{ISO:2001:IIIc,
  author =       "{ISO}",
  title =        "{ISO\slash IEC 10967-2}: {Information} technology ---
                 {Language} independent arithmetic --- {Part} 2:
                 {Elementary} numerical functions",
  publisher =    pub-ISO,
  address =      pub-ISO:adr,
  pages =        "x + 177",
  day =          "15",
  month =        aug,
  year =         "2001",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sun Mar 15 11:09:44 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://standards.iso.org/ittf/PubliclyAvailableStandards/c024427_ISO_IEC_10967-2_2001(E).zip;
                 http://www.iso.ch/cate/d24427.html",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Jacobi:2001:FVT
author: Christian Jacobi
title: Formal verification of a theory of IEEE rounding
crossref: Boulton:2001:TPH
pages: 239--254
year: 2001
bibdate: Wed Nov 24 11:55:24 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.24 11:55:24 ???
URL: http://www.informatics.ed.ac.uk/publications/online/0046/b239.pdf
acknowledgement: ack-nhfb
rawauthor: Christian Jacobi
rawtitle: Formal verification of a theory of {IEEE} rounding
entry:
@InProceedings{Jacobi:2001:FVT,
  author =       "Christian Jacobi",
  title =        "Formal verification of a theory of {IEEE} rounding",
  crossref =     "Boulton:2001:TPH",
  pages =        "239--254",
  year =         "2001",
  bibdate =      "Wed Nov 24 11:55:24 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.informatics.ed.ac.uk/publications/online/0046/b239.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Jamil:2001:CBN
author: T. Jamil
title: The complex binary number system
journal: j-IEEE-POT
volume: 20
number: 5
pages: 39--41
month: dec
monthnumber: 12
year: 2001
CODEN: IEPTDF
DOI: https://doi.org/10.1109/45.983342
ISSN: 0278-6648 (print), 1558-1772 (electronic) OR 02786648 (print), 15581772 (electronic)
ISSNL: 0278-6648 OR 02786648
bibdate: Sat Dec 04 10:43:52 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.12.04 10:43:52 ???
fjournal: IEEE Potentials
acknowledgement: ack-nhfb
rawauthor: T. Jamil
rawtitle: The complex binary number system
abstract:
Conversion algorithms and arithmetic procedures for a $ ( - 1 + j) $-base binary number allow a given complex number to be represented as one unit. This should simplify the operations involving complex numbers in today's microprocessors. With the division process secure, we can implement the usual algorithms for calculating functions and processes such as logarithms, exponentials and trigonometric functions Currently, work is underway to write Java applets for the algorithms. We are planning to design an arithmetic unit based on the new binary system which will then be implemented using field programmable gate arrays

rawabstract:
Conversion algorithms and arithmetic procedures for a $ ( - 1 + j) $-base binary number allow a given complex number to be represented as one unit. This should simplify the operations involving complex numbers in today's microprocessors. With the division process secure, we can implement the usual algorithms for calculating functions and processes such as logarithms, exponentials and trigonometric functions Currently, work is underway to write Java applets for the algorithms. We are planning to design an arithmetic unit based on the new binary system which will then be implemented using field programmable gate arrays

entry:
@Article{Jamil:2001:CBN,
  author =       "T. Jamil",
  title =        "The complex binary number system",
  journal =      j-IEEE-POT,
  volume =       "20",
  number =       "5",
  pages =        "39--41",
  month =        dec,
  year =         "2001",
  CODEN =        "IEPTDF",
  DOI =          "https://doi.org/10.1109/45.983342",
  ISSN =         "0278-6648 (print), 1558-1772 (electronic)",
  ISSN-L =       "0278-6648",
  bibdate =      "Sat Dec 04 10:43:52 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Conversion algorithms and arithmetic procedures for a
                 $ ( - 1 + j) $-base binary number allow a given complex
                 number to be represented as one unit. This should
                 simplify the operations involving complex numbers in
                 today's microprocessors. With the division process
                 secure, we can implement the usual algorithms for
                 calculating functions and processes such as logarithms,
                 exponentials and trigonometric functions Currently,
                 work is underway to write Java applets for the
                 algorithms. We are planning to design an arithmetic
                 unit based on the new binary system which will then be
                 implemented using field programmable gate arrays",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Potentials",
}


bibtype: inproceedings
filename: fparith.bib
label: Jeong:2001:OIO
author: Cheol-Ho Jeong and Woo-Chan Park and Tack-Don Han and Sang-Woo Kim and Moon-Key Lee
title: In-Order Issue Out-of-Order Execution Floating-Point Coprocessor for CalmRISC32
crossref: Burgess:2001:ISC
pages: 195--202
year: 2001
bibdate: Fri May 3 13:58:18 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.03 13:58:18 MDT
URL: http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Jeong.pdf
keywords: ARITH-15
acknowledgement: ack-nhfb
rawauthor: Cheol-Ho Jeong and Woo-Chan Park and Tack-Don Han and Sang-Woo Kim and Moon-Key Lee
rawtitle: In-Order Issue Out-of-Order Execution Floating-Point Coprocessor for {CalmRISC32}
entry:
@InProceedings{Jeong:2001:OIO,
  author =       "Cheol-Ho Jeong and Woo-Chan Park and Tack-Don Han and
                 Sang-Woo Kim and Moon-Key Lee",
  title =        "In-Order Issue Out-of-Order Execution Floating-Point
                 Coprocessor for {CalmRISC32}",
  crossref =     "Burgess:2001:ISC",
  pages =        "195--202",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Jeong.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}


bibtype: techreport
filename: fparith.bib
label: Kahan:2001:NSF
author: W. Kahan
title: Names for Standardized Floating-Point Formats
address: Berkeley, CA, USA
pages: 4
day: 17
month: may
monthnumber: 5
year: 2001
bibdate: Fri May 03 12:23:25 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.03 12:23:25 ???
URL: http://www.cs.berkeley.edu/~wkahan/ieee754status/Names.pdf
acknowledgement: ack-nhfb
rawauthor: W. Kahan
rawtitle: Names for Standardized Floating-Point Formats
institution:
Mathematics Department and Electrical Engineering and Computer Science Department, University of California, Berkeley

entry:
@TechReport{Kahan:2001:NSF,
  author =       "W. Kahan",
  title =        "Names for Standardized Floating-Point Formats",
  institution =  "Mathematics Department and Electrical Engineering and
                 Computer Science Department, University of California,
                 Berkeley",
  address =      "Berkeley, CA, USA",
  pages =        "4",
  day =          "17",
  month =        may,
  year =         "2001",
  bibdate =      "Fri May 03 12:23:25 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/ieee754status/Names.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: unpublished
filename: fparith.bib
label: Kahan:2001:PDA
author: William Kahan
title: Pseudo-Division Algorithms for Floating-Point Logarithms and Exponentials
pages: 8
day: 20
month: may
monthnumber: 5
year: 2001
bibdate: Sat Aug 23 06:17:04 2025
bibtimestamp: 2025.08.23 06:17:04 ???
URL: https://ieeemilestones.ethw.org/w/images/3/30/Wk_pseudo_division_log_exp_may01.pdf
acknowledgement: ack-nhfb
rawauthor: William Kahan
rawtitle: Pseudo-Division Algorithms for Floating-Point Logarithms and Exponentials
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
Among the CORDIC-like algorithms for computing elementary transcendental functions like log and exp, certain pseudo-division algorithms are peculiarly well suited to implementation in microcode or in conjunction with software-implemented floating-point arithmetic. These algorithms need tables of comparatively modest size; they are almost as fast as the fastest digit-by-digit algorithms known; and they can achieve accuracy to within a unit or two in the last sig. bit carried. Algorithms like these are used by the Intel 8087 family of numeric coprocessors. This document is for people who wish to imitate or surpass them.

rawabstract:
Among the CORDIC-like algorithms for computing elementary transcendental functions like log and exp, certain pseudo-division algorithms are peculiarly well suited to implementation in microcode or in conjunction with software-implemented floating-point arithmetic. These algorithms need tables of comparatively modest size; they are almost as fast as the fastest digit-by-digit algorithms known; and they can achieve accuracy to within a unit or two in the last sig. bit carried. Algorithms like these are used by the Intel 8087 family of numeric coprocessors. This document is for people who wish to imitate or surpass them.

entry:
@Unpublished{Kahan:2001:PDA,
  author =       "William Kahan",
  title =        "Pseudo-Division Algorithms for Floating-Point
                 Logarithms and Exponentials",
  pages =        "8",
  day =          "20",
  month =        may,
  year =         "2001",
  bibdate =      "Sat Aug 23 06:17:04 2025",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeemilestones.ethw.org/w/images/3/30/Wk_pseudo_division_log_exp_may01.pdf",
  abstract =     "Among the CORDIC-like algorithms for computing
                 elementary transcendental functions like log and exp,
                 certain pseudo-division algorithms are peculiarly well
                 suited to implementation in microcode or in conjunction
                 with software-implemented floating-point arithmetic.
                 These algorithms need tables of comparatively modest
                 size; they are almost as fast as the fastest
                 digit-by-digit algorithms known; and they can achieve
                 accuracy to within a unit or two in the last sig. bit
                 carried. Algorithms like these are used by the Intel
                 8087 family of numeric coprocessors. This document is
                 for people who wish to imitate or surpass them.",
  acknowledgement = ack-nhfb,
}


bibtype: misc
filename: fparith.bib
label: Kahan:2001:SFP
author: W. Kahan
title: SRTEST: a Fortran program to test any SRT divider's logic for quotient-digit selection
pages: 8
day: 6
month: aug
monthnumber: 8
year: 2001
bibdate: Mon Apr 25 17:47:53 2005
bibtimestamp: 2005.04.25 17:47:53 ???
URL: http://www.cs.berkeley.edu/~wkahan/srtest/
keywords: floating-point testing
acknowledgement: ack-nhfb
howpublished: World-Wide Web document
rawauthor: W. Kahan
rawtitle: {SRTEST}: a {Fortran} program to test any {SRT} divider's logic for quotient-digit selection
entry:
@Misc{Kahan:2001:SFP,
  author =       "W. Kahan",
  title =        "{SRTEST}: a {Fortran} program to test any {SRT}
                 divider's logic for quotient-digit selection",
  howpublished = "World-Wide Web document",
  day =          "6",
  month =        aug,
  year =         "2001",
  bibdate =      "Mon Apr 25 17:47:53 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/srtest/",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point testing",
}


bibtype: techreport
filename: fparith.bib
label: Kahan:2001:WVT
author: W. Kahan
title: What has the Volume of a Tetrahedron to do with Computer Programming Languages?
address: Berkeley, CA, USA
pages: 8
day: 20
month: apr
monthnumber: 4
year: 2001
bibdate: Fri May 03 13:36:17 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.03 13:36:17 ???
URL: http://www.cs.berkeley.edu/~wkahan/VtetLang.pdf
acknowledgement: ack-nhfb
rawauthor: W. Kahan
rawtitle: What has the Volume of a Tetrahedron to do with Computer Programming Languages?
entry:
@TechReport{Kahan:2001:WVT,
  author =       "W. Kahan",
  title =        "What has the Volume of a Tetrahedron to do with
                 Computer Programming Languages?",
  institution =  "Department of Mathematics and Department of Electrical
                 Engineering and Computer Science, University of
                 California, Berkeley",
  address =      "Berkeley, CA, USA",
  day =          "20",
  month =        apr,
  year =         "2001",
  bibdate =      "Fri May 03 13:36:17 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/VtetLang.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Kaivola:2001:PEL
author: Roope Kaivola and Katherine Kohatsu
title: Proof Engineering in the Large: Formal Verification of Pentiumreg 4 Floating-Point Divider
journal: j-LECT-NOTES-COMP-SCI
volume: 2144
pages: 196--211
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:05:47 MST 2002
bibtimestamp: 2002.02.02 13:05:47 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Roope Kaivola and Katherine Kohatsu
rawtitle: Proof Engineering in the Large: Formal Verification of {Pentium\reg4} Floating-Point Divider
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2144.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2144/21440196.htm; http://link.springer-ny.com/link/service/series/0558/papers/2144/21440196.pdf

entry:
@Article{Kaivola:2001:PEL,
  author =       "Roope Kaivola and Katherine Kohatsu",
  title =        "Proof Engineering in the Large: Formal Verification of
                 {Pentium\reg4} Floating-Point Divider",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2144",
  pages =        "196--211",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:05:47 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2144.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2144/21440196.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2144/21440196.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Kao:2001:MRE
author: Ming-Yang Kao and Jie Wang
title: Minimizing roundoff errors of prefix sums via dynamic construction of Huffman trees
journal: j-THEOR-COMP-SCI
volume: 262
number: 1--2
pages: 101--115
day: 6
month: jul
monthnumber: 7
year: 2001
CODEN: TCSCDI
ISSN: 0304-3975 (print), 1879-2294 (electronic) OR 03043975 (print), 18792294 (electronic)
ISSNL: 0304-3975 OR 03043975
bibdate: Wed Jul 25 18:49:25 MDT 2001
bibsource: http://www.elsevier.com/locate/issn/03043975; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.07.25 18:49:25 MDT
fjournal: Theoretical Computer Science
keywords: accurate floating-point summation
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03043975
rawauthor: Ming-Yang Kao and Jie Wang
rawtitle: Minimizing roundoff errors of prefix sums via dynamic construction of {Huffman} trees
URL:
http://www.elsevier.nl/gej-ng/10/41/16/204/21/26/abstract.html; http://www.elsevier.nl/gej-ng/10/41/16/204/21/26/article.pdf

entry:
@Article{Kao:2001:MRE,
  author =       "Ming-Yang Kao and Jie Wang",
  title =        "Minimizing roundoff errors of prefix sums via dynamic
                 construction of {Huffman} trees",
  journal =      j-THEOR-COMP-SCI,
  volume =       "262",
  number =       "1--2",
  pages =        "101--115",
  day =          "6",
  month =        jul,
  year =         "2001",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Wed Jul 25 18:49:25 MDT 2001",
  bibsource =    "http://www.elsevier.com/locate/issn/03043975;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.elsevier.nl/gej-ng/10/41/16/204/21/26/abstract.html;
                 http://www.elsevier.nl/gej-ng/10/41/16/204/21/26/article.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975",
  keywords =     "accurate floating-point summation",
}


bibtype: article
filename: fparith.bib
label: Khachatrian:2001:FMI
author: Gurgen H. Khachatrian and Melsik K. Kuregian and Karen R. Ispiryan and James L. Massey
title: Fast Multiplication of Integers for Public-Key Applications
journal: j-LECT-NOTES-COMP-SCI
volume: 2259
pages: 245--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:07:44 MST 2002
bibtimestamp: 2002.02.02 13:07:44 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Gurgen H. Khachatrian and Melsik K. Kuregian and Karen R. Ispiryan and James L. Massey
rawtitle: Fast Multiplication of Integers for Public-Key Applications
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2259.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2259/22590245.htm; http://link.springer-ny.com/link/service/series/0558/papers/2259/22590245.pdf

entry:
@Article{Khachatrian:2001:FMI,
  author =       "Gurgen H. Khachatrian and Melsik K. Kuregian and Karen
                 R. Ispiryan and James L. Massey",
  title =        "Fast Multiplication of Integers for Public-Key
                 Applications",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2259",
  pages =        "245--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:07:44 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2259.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2259/22590245.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2259/22590245.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Kim:2001:AEE
author: Hyun-Sung Kim and Kee-Young Yoo
title: Area Efficient Exponentiation Using Modular Multiplier / Squarer in GF$ (2^m) $
journal: j-LECT-NOTES-COMP-SCI
volume: 2108
pages: 262--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:05:08 MST 2002
bibtimestamp: 2002.02.02 13:05:08 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Hyun-Sung Kim and Kee-Young Yoo
rawtitle: Area Efficient Exponentiation Using Modular Multiplier\slash Squarer in {GF$ (2^m) $}
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2108.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2108/21080262.htm; http://link.springer-ny.com/link/service/series/0558/papers/2108/21080262.pdf

entry:
@Article{Kim:2001:AEE,
  author =       "Hyun-Sung Kim and Kee-Young Yoo",
  title =        "Area Efficient Exponentiation Using Modular
                 Multiplier\slash Squarer in {GF$ (2^m) $}",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2108",
  pages =        "262--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:05:08 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2108.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2108/21080262.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2108/21080262.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: King:2001:IIE
author: Brian King
title: An Improved Implementation of Elliptic Curves over GF (2) when Using Projective Point Arithmetic
journal: j-LECT-NOTES-COMP-SCI
volume: 2259
pages: 134--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:07:44 MST 2002
bibtimestamp: 2002.02.02 13:07:44 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Brian King
rawtitle: An Improved Implementation of Elliptic Curves over {GF} (2) when Using Projective Point Arithmetic
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2259.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2259/22590134.htm; http://link.springer-ny.com/link/service/series/0558/papers/2259/22590134.pdf

entry:
@Article{King:2001:IIE,
  author =       "Brian King",
  title =        "An Improved Implementation of Elliptic Curves over
                 {GF} (2) when Using Projective Point Arithmetic",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2259",
  pages =        "134--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:07:44 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2259.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2259/22590134.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2259/22590134.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Kistermann:2001:CHU
author: Friedrich W. Kistermann
title: Calculators: How to Use the Schickard Calculator
journal: j-IEEE-ANN-HIST-COMPUT
volume: 23
number: 1
pages: 80--85
month: jan
monthnumber: 1
year: 2001
CODEN: IAHCEX
DOI: https://doi.org/10.1109/85.929917
ISSN: 1058-6180 (print), 1934-1547 (electronic) OR 10586180 (print), 19341547 (electronic)
ISSNL: 1058-6180 OR 10586180
bibdate: Thu Jul 12 06:23:02 MDT 2001
bibtimestamp: 2001.07.12 06:23:02 MDT
URL: http://dlib.computer.org/an/books/an2001/pdf/a1080.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: Friedrich W. Kistermann
rawtitle: Calculators: How to Use the {Schickard} Calculator
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeeannhistcomput.bib; https://www.math.utah.edu/pub/tex/bib/scicontext.bib

entry:
@Article{Kistermann:2001:CHU,
  author =       "Friedrich W. Kistermann",
  title =        "Calculators: How to Use the {Schickard} Calculator",
  journal =      j-IEEE-ANN-HIST-COMPUT,
  volume =       "23",
  number =       "1",
  pages =        "80--85",
  month =        jan # "\slash " # mar,
  year =         "2001",
  CODEN =        "IAHCEX",
  DOI =          "https://doi.org/10.1109/85.929917",
  ISSN =         "1058-6180 (print), 1934-1547 (electronic)",
  ISSN-L =       "1058-6180",
  bibdate =      "Thu Jul 12 06:23:02 MDT 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeeannhistcomput.bib;
                 https://www.math.utah.edu/pub/tex/bib/scicontext.bib",
  URL =          "http://dlib.computer.org/an/books/an2001/pdf/a1080.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: inproceedings
filename: fparith.bib
label: Knowles:2001:FA
author: Simon Knowles
title: A Family of Adders
crossref: Burgess:2001:ISC
pages: 277--284
year: 2001
bibdate: Fri May 3 13:58:18 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.03 13:58:18 MDT
URL: http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Knowles.pdf
keywords: ARITH-15
acknowledgement: ack-nhfb
rawauthor: Simon Knowles
rawtitle: A Family of Adders
entry:
@InProceedings{Knowles:2001:FA,
  author =       "Simon Knowles",
  title =        "A Family of Adders",
  crossref =     "Burgess:2001:ISC",
  pages =        "277--284",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Knowles.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}


bibtype: inproceedings
filename: fparith.bib
label: Koc-Sahan:2001:STA
author: N. Koc-Sahan and J. Schlessman and M. J. Schulte
title: Symmetric Table Addition Methods for Neural Network Approximations
crossref: Luk:2001:ASP
pages: 126--133
year: 2001
bibdate: Sun Mar 04 11:40:20 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.03.04 11:40:20 ???
URL: http://mesa.ece.wisc.edu/publications/cp_2001-03.pdf
acknowledgement: ack-nhfb
rawauthor: N. Koc-Sahan and J. Schlessman and M. J. Schulte
rawtitle: Symmetric Table Addition Methods for Neural Network Approximations
entry:
@InProceedings{Koc-Sahan:2001:STA,
  author =       "N. Koc-Sahan and J. Schlessman and M. J. Schulte",
  title =        "Symmetric Table Addition Methods for Neural Network
                 Approximations",
  crossref =     "Luk:2001:ASP",
  pages =        "126--133",
  year =         "2001",
  bibdate =      "Sun Mar 04 11:40:20 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2001-03.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Kosaraju:2001:MAM
author: S. Rao Kosaraju
title: Mesh Algorithms for Multiplication and Division
journal: j-LECT-NOTES-COMP-SCI
volume: 2228
pages: 17--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:07:14 MST 2002
bibtimestamp: 2002.02.02 13:07:14 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: S. Rao Kosaraju
rawtitle: Mesh Algorithms for Multiplication and Division
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2228.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2228/22280017.htm; http://link.springer-ny.com/link/service/series/0558/papers/2228/22280017.pdf

entry:
@Article{Kosaraju:2001:MAM,
  author =       "S. Rao Kosaraju",
  title =        "Mesh Algorithms for Multiplication and Division",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2228",
  pages =        "17--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:07:14 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2228.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2228/22280017.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2228/22280017.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Koy:2001:SLRb
author: Henrik Koy and Claus Peter Schnorr
title: Segment LLL-Reduction with Floating Point Orthogonalization
journal: j-LECT-NOTES-COMP-SCI
volume: 2146
pages: 81--96
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
MRclass: 11H55 (11Y16)
MRnumber: MR1903889 (2003f:11096)
bibdate: Sat Feb 2 13:05:49 MST 2002
bibtimestamp: 2002.02.02 13:05:49 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Henrik Koy and Claus Peter Schnorr
rawtitle: Segment {LLL}-Reduction with Floating Point Orthogonalization
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2146.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2146/21460081.htm; http://link.springer-ny.com/link/service/series/0558/papers/2146/21460081.pdf

entry:
@Article{Koy:2001:SLRb,
  author =       "Henrik Koy and Claus Peter Schnorr",
  title =        "Segment {LLL}-Reduction with Floating Point
                 Orthogonalization",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2146",
  pages =        "81--96",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  MRclass =      "11H55 (11Y16)",
  MRnumber =     "MR1903889 (2003f:11096)",
  bibdate =      "Sat Feb 2 13:05:49 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2146.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2146/21460081.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2146/21460081.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Kramer:2001:AFE
author: Walter Kramer and Armin Bantle
title: Automatic forward error analysis for floating point algorithms
journal: j-RELIABLE-COMPUTING
volume: 7
number: 4
pages: 321--340
year: 2001
CODEN: RCOMF8
ISSN: 1385-3139 (print), 1573-1340 (electronic) OR 13853139 (print), 15731340 (electronic)
ISSNL: 1385-3139 OR 13853139
MRclass: 65G40 (65G50)
MRnumber: MR1843023 (2002d:65046)
bibdate: Thu Nov 8 19:16:14 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.08 19:16:14 ???
acknowledgement: ack-nhfb
authordates: 1952--2014 (WK)
journalURL: http://link.springer.com/journal/11155
rawauthor: Walter Kr{\"a}mer and Armin Bantle
rawtitle: Automatic forward error analysis for floating point algorithms
fjournal:
Reliable Computing. An International Journal Devoted to Reliable Mathematical Computations Based on Finite Representations and Guaranteed Accuracy

entry:
@Article{Kramer:2001:AFE,
  author =       "Walter Kr{\"a}mer and Armin Bantle",
  title =        "Automatic forward error analysis for floating point
                 algorithms",
  journal =      j-RELIABLE-COMPUTING,
  volume =       "7",
  number =       "4",
  pages =        "321--340",
  year =         "2001",
  CODEN =        "RCOMF8",
  ISSN =         "1385-3139 (print), 1573-1340 (electronic)",
  ISSN-L =       "1385-3139",
  MRclass =      "65G40 (65G50)",
  MRnumber =     "MR1843023 (2002d:65046)",
  bibdate =      "Thu Nov 8 19:16:14 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  author-dates = "1952--2014 (WK)",
  fjournal =     "Reliable Computing. An International Journal Devoted
                 to Reliable Mathematical Computations Based on Finite
                 Representations and Guaranteed Accuracy",
  journal-URL =  "http://link.springer.com/journal/11155",
}


bibtype: article
filename: fparith.bib
label: Kreinovich:2001:INB
author: Vladik Kreinovich
journal: j-SIGACT
volume: 32
number: 1
pages: 115--117
year: 2001
CODEN: SIGNDM
ISSN: 0163-5700 (print), 1943-5827 (electronic) OR 01635700 (print), 19435827 (electronic)
ISSNL: 0163-5700 OR 01635700
bibdate: Sat Dec 06 15:20:39 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.12.06 15:20:39 ???
URL: http://www.cs.utep.edu/vladik/2000/tr00-42.pdf; http://www.cs.utep.edu/vladik/2000/tr00-42.ps.gz
fjournal: ACM SIGACT News
acknowledgement: ack-nhfb
journalURL: http://dl.acm.org/citation.cfm?id=J697
issue: 118
rawauthor: Vladik Kreinovich
title:
Itanium's New Basic Operation of Fused Multiply-Add: Theoretical Explanation and Theoretical Challenge

rawtitle:
{Itanium}'s New Basic Operation of Fused Multiply-Add: Theoretical Explanation and Theoretical Challenge

entry:
@Article{Kreinovich:2001:INB,
  author =       "Vladik Kreinovich",
  title =        "{Itanium}'s New Basic Operation of Fused Multiply-Add:
                 Theoretical Explanation and Theoretical Challenge",
  journal =      j-SIGACT,
  volume =       "32",
  number =       "1",
  pages =        "115--117",
  year =         "2001",
  CODEN =        "SIGNDM",
  ISSN =         "0163-5700 (print), 1943-5827 (electronic)",
  ISSN-L =       "0163-5700",
  bibdate =      "Sat Dec 06 15:20:39 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.utep.edu/vladik/2000/tr00-42.pdf;
                 http://www.cs.utep.edu/vladik/2000/tr00-42.ps.gz",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGACT News",
  issue =        "118",
  journal-URL =  "http://dl.acm.org/citation.cfm?id=J697",
}


bibtype: inproceedings
filename: fparith.bib
label: Krishnan:2001:PEM
author: Shankar Krishnan and Mark Foskey and Tim Culver and John Keyser and Dinesh Manocha
crossref: ACM:2001:PSA
pages: 274--283
year: 2001
DOI: https://doi.org/10.1145/378583.378693
bibdate: Fri Jan 06 07:53:04 2006
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2006.01.06 07:53:04 ???
keywords: floating-point arithmetic; interval arithmetic; multiple-precision arithmetic; PRECISE
acknowledgement: ack-nhfb
rawauthor: Shankar Krishnan and Mark Foskey and Tim Culver and John Keyser and Dinesh Manocha
title:
PRECISE: efficient multiprecision evaluation of algebraic roots and predicates for reliable geometric computation

abstract:
Many geometric problems like generalized Voronoi diagrams, medial axis computations and boundary evaluation involve computation and manipulation of non-linear algebraic primitives like curves and surfaces. The algorithms designed for these problems make decisions based on signs of geometric predicates or on the roots of polynomials characterizing the problem. The reliability of the algorithm depends on the accurate evaluation of these signs and roots. In this paper, we present a em naive precision-driven computational model to perform these computations reliably and demonstrate its effectiveness on a certain class of problems like sign of determinants with rational entries, boundary evaluation and curve arrangements. We also present a novel algorithm to compute all the roots of a univariate polynomial to any desired accuracy. The computational model along with the underlying number representation, precision-driven arithmetic and all the algorithms are implemented as part of a stand-alone software library, PRECISE.

rawabstract:
Many geometric problems like generalized Voronoi diagrams, medial axis computations and boundary evaluation involve computation and manipulation of non-linear algebraic primitives like curves and surfaces. The algorithms designed for these problems make decisions based on signs of geometric predicates or on the roots of polynomials characterizing the problem. The reliability of the algorithm depends on the accurate evaluation of these signs and roots. In this paper, we present a {\em naive precision-driven computational model\/} to perform these computations reliably and demonstrate its effectiveness on a certain class of problems like sign of determinants with rational entries, boundary evaluation and curve arrangements. We also present a novel algorithm to compute all the roots of a univariate polynomial to any desired accuracy. The computational model along with the underlying number representation, precision-driven arithmetic and all the algorithms are implemented as part of a stand-alone software library, PRECISE.

rawtitle:
{PRECISE}: efficient multiprecision evaluation of algebraic roots and predicates for reliable geometric computation

entry:
@InProceedings{Krishnan:2001:PEM,
  author =       "Shankar Krishnan and Mark Foskey and Tim Culver and
                 John Keyser and Dinesh Manocha",
  title =        "{PRECISE}: efficient multiprecision evaluation of
                 algebraic roots and predicates for reliable geometric
                 computation",
  crossref =     "ACM:2001:PSA",
  pages =        "274--283",
  year =         "2001",
  DOI =          "https://doi.org/10.1145/378583.378693",
  bibdate =      "Fri Jan 06 07:53:04 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Many geometric problems like generalized Voronoi
                 diagrams, medial axis computations and boundary
                 evaluation involve computation and manipulation of
                 non-linear algebraic primitives like curves and
                 surfaces. The algorithms designed for these problems
                 make decisions based on signs of geometric predicates
                 or on the roots of polynomials characterizing the
                 problem. The reliability of the algorithm depends on
                 the accurate evaluation of these signs and roots. In
                 this paper, we present a {\em naive precision-driven
                 computational model\/} to perform these computations
                 reliably and demonstrate its effectiveness on a certain
                 class of problems like sign of determinants with
                 rational entries, boundary evaluation and curve
                 arrangements. We also present a novel algorithm to
                 compute all the roots of a univariate polynomial to any
                 desired accuracy. The computational model along with
                 the underlying number representation, precision-driven
                 arithmetic and all the algorithms are implemented as
                 part of a stand-alone software library, PRECISE.",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point arithmetic; interval arithmetic;
                 multiple-precision arithmetic; PRECISE",
}


bibtype: inproceedings
filename: fparith.bib
label: Lang:2001:BRZ
author: Tomas Lang and Jean-Michel Muller
title: Bounds on Runs of Zeros and Ones for Algebraic Functions
crossref: Burgess:2001:ISC
pages: 13--22
year: 2001
bibdate: Fri May 3 13:52:01 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.03 13:52:01 MDT
URL: http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Lang.pdf
keywords: ARITH-15
acknowledgement: ack-nhfb
rawauthor: Tom{\'a}s Lang and Jean-Michel Muller
rawtitle: Bounds on Runs of Zeros and Ones for Algebraic Functions
entry:
@InProceedings{Lang:2001:BRZ,
  author =       "Tom{\'a}s Lang and Jean-Michel Muller",
  title =        "Bounds on Runs of Zeros and Ones for Algebraic
                 Functions",
  crossref =     "Burgess:2001:ISC",
  pages =        "13--22",
  year =         "2001",
  bibdate =      "Fri May 3 13:52:01 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Lang.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}


bibtype: inproceedings
filename: fparith.bib
label: Lang:2001:CRR
author: Tomas Lang and Elisardo Antelo
title: Correctly Rounded Reciprocal Square-Root by Digit Recurrence and Radix-$4$ Implementation
crossref: Burgess:2001:ISC
pages: 83--93
year: 2001
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2005.07.16 15:28:14 MDT
URL: http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Lang_Antelo.pdf
keywords: ARITH-15; correct rounding; floating-point arithmetic
acknowledgement: ack-nhfb
rawauthor: Tom{\'a}s Lang and Elisardo Antelo
rawtitle: Correctly Rounded Reciprocal Square-Root by Digit Recurrence and Radix-$4$ Implementation
entry:
@InProceedings{Lang:2001:CRR,
  author =       "Tom{\'a}s Lang and Elisardo Antelo",
  title =        "Correctly Rounded Reciprocal Square-Root by Digit
                 Recurrence and Radix-$4$ Implementation",
  crossref =     "Burgess:2001:ISC",
  pages =        "83--93",
  year =         "2001",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Lang_Antelo.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15; correct rounding; floating-point
                 arithmetic",
  summary =      "We present a reciprocal square-root algorithm by digit
                 recurrence and selection by a staircase function, and
                 the radix-$4$ implementation. As similar algorithms for
                 division and square-root, the results are obtained
                 correctly rounded in a \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Langlois:2001:ALC
author: Philippe Langlois
title: Automatic Linear Correction of Rounding Errors
journal: j-BIT-NUM-MATH
volume: 41
number: 3
pages: 515--539
month: jun
monthnumber: 6
year: 2001
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1023/A:1021919329342
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
bibdate: Wed Jan 4 15:06:04 MST 2006
bibtimestamp: 2006.01.04 15:06:04 MST
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=41&issue=3&spage=515
keywords: automatic error analysis; correct rounding; floating-point arithmetic; rounding errors
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: Philippe Langlois
rawtitle: Automatic Linear Correction of Rounding Errors
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=41&issue=3; http://www.mai.liu.se/BIT/contents/bit41.html; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
A new automatic method to correct the first-order effect of floating point rounding errors on the result of a numerical algorithm is presented. A correcting term and a confidence threshold are computed using algorithmic differentiation, computation of elementary rounding error and running error analysis. Algorithms for which the accuracy of the result is not affected by higher order terms are identified. The correction is applied to the final result or to sensitive intermediate results to improve the accuracy of the computed result and / or the stability of the algorithm.

rawabstract:
A new automatic method to correct the first-order effect of floating point rounding errors on the result of a numerical algorithm is presented. A correcting term and a confidence threshold are computed using algorithmic differentiation, computation of elementary rounding error and running error analysis. Algorithms for which the accuracy of the result is not affected by higher order terms are identified. The correction is applied to the final result or to sensitive intermediate results to improve the accuracy of the computed result and\slash or the stability of the algorithm.

entry:
@Article{Langlois:2001:ALC,
  author =       "Philippe Langlois",
  title =        "Automatic Linear Correction of Rounding Errors",
  journal =      j-BIT-NUM-MATH,
  volume =       "41",
  number =       "3",
  pages =        "515--539",
  month =        jun,
  year =         "2001",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1023/A:1021919329342",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 15:06:04 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=41&issue=3;
                 http://www.mai.liu.se/BIT/contents/bit41.html;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=41&issue=3&spage=515",
  abstract =     "A new automatic method to correct the first-order
                 effect of floating point rounding errors on the result
                 of a numerical algorithm is presented. A correcting
                 term and a confidence threshold are computed using
                 algorithmic differentiation, computation of elementary
                 rounding error and running error analysis. Algorithms
                 for which the accuracy of the result is not affected by
                 higher order terms are identified. The correction is
                 applied to the final result or to sensitive
                 intermediate results to improve the accuracy of the
                 computed result and\slash or the stability of the
                 algorithm.",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "automatic error analysis; correct rounding;
                 floating-point arithmetic; rounding errors",
}


bibtype: inproceedings
filename: fparith.bib
label: Laurent:2001:UFV
author: O. Laurent and P. Michel and V. Wiels
title: Using formal verification techniques to reduce simulation and test effort
crossref: Oliveira:2001:FFM
pages: 465--477
year: 2001
DOI: https://doi.org/10.1007/3-540-45251-6_27
bibdate: Wed Nov 24 11:58:06 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.24 11:58:06 ???
URL: http://link.springer.de/link/service/series/0558/papers/2021/20210465.pdf
acknowledgement: ack-nhfb
rawauthor: O. Laurent and P. Michel and V. Wiels
rawtitle: Using formal verification techniques to reduce simulation and test effort
entry:
@InProceedings{Laurent:2001:UFV,
  author =       "O. Laurent and P. Michel and V. Wiels",
  title =        "Using formal verification techniques to reduce
                 simulation and test effort",
  crossref =     "Oliveira:2001:FFM",
  pages =        "465--477",
  year =         "2001",
  DOI =          "https://doi.org/10.1007/3-540-45251-6_27",
  bibdate =      "Wed Nov 24 11:58:06 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer.de/link/service/series/0558/papers/2021/20210465.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Lee:2001:BPS
author: Chiou-Yng Lee and Erl-Huei Lu and Jau-Yien Lee
title: Bit-Parallel Systolic Modular Multipliers for a Class of $ mathrm GF(2^m) $
crossref: Burgess:2001:ISC
pages: 51--58
year: 2001
bibdate: Fri May 3 13:58:18 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.03 13:58:18 MDT
URL: http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Chiou_Yng.pdf
keywords: ARITH-15
acknowledgement: ack-nhfb
rawauthor: Chiou-Yng Lee and Erl-Huei Lu and Jau-Yien Lee
rawtitle: Bit-Parallel Systolic Modular Multipliers for a Class of {$ \mathrm {GF}(2^m) $}
entry:
@InProceedings{Lee:2001:BPS,
  author =       "Chiou-Yng Lee and Erl-Huei Lu and Jau-Yien Lee",
  title =        "Bit-Parallel Systolic Modular Multipliers for a Class
                 of {$ \mathrm {GF}(2^m) $}",
  crossref =     "Burgess:2001:ISC",
  pages =        "51--58",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Chiou_Yng.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}


bibtype: inproceedings
filename: fparith.bib
label: Lee:2001:CAP
author: Ruby B. Lee
title: Computer Arithmetic --- a Processor Architect's Perspective
crossref: Burgess:2001:ISC
pages: 3--4
year: 2001
bibdate: Fri May 3 13:52:01 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.03 13:52:01 MDT
URL: http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Lee.pdf
keywords: ARITH-15
acknowledgement: ack-nhfb
rawauthor: Ruby B. Lee
rawtitle: Computer Arithmetic --- a Processor Architect's Perspective
entry:
@InProceedings{Lee:2001:CAP,
  author =       "Ruby B. Lee",
  title =        "Computer Arithmetic --- a Processor Architect's
                 Perspective",
  crossref =     "Burgess:2001:ISC",
  pages =        "3--4",
  year =         "2001",
  bibdate =      "Fri May 3 13:52:01 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Lee.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}


bibtype: article
filename: fparith.bib
label: Lee:2001:DLS
author: Won-Ho Lee and Keon-Jik Lee and Kee-Young Yoo
journal: j-COMPUT-MATH-APPL
volume: 42
number: 1--2
pages: 231--240
month: jul
monthnumber: 7
year: 2001
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 21:49:16 MST 2017
bibtimestamp: 2017.03.01 21:49:16 MST
URL: http://www.sciencedirect.com/science/article/pii/S089812210100147X
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: Won-Ho Lee and Keon-Jik Lee and Kee-Young Yoo
title:
Design of a linear systolic array for computing modular multiplication and squaring in $ bf GF(2^m) $

bibsource:
https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

rawtitle:
Design of a linear systolic array for computing modular multiplication and squaring in {$ {\bf GF}(2^m) $}

entry:
@Article{Lee:2001:DLS,
  author =       "Won-Ho Lee and Keon-Jik Lee and Kee-Young Yoo",
  title =        "Design of a linear systolic array for computing
                 modular multiplication and squaring in {$ {\bf GF}(2^m)
                 $}",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "42",
  number =       "1--2",
  pages =        "231--240",
  month =        jul,
  year =         "2001",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:49:16 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S089812210100147X",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: inproceedings
filename: fparith.bib
label: Lefevre:2001:WCC
author: Vincent Lefevre and Jean-Michel Muller
title: Worst Cases for Correct Rounding of the Elementary Functions in Double Precision
crossref: Burgess:2001:ISC
pages: 111--118
year: 2001
DOI: https://doi.org/10.1109/ARITH.2001.930110
bibdate: Fri May 3 13:58:18 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.03 13:58:18 MDT
URL: http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Lefevre.pdf
keywords: ARITH-15; correct rounding; floating-point arithmetic
acknowledgement: ack-nhfb
rawauthor: Vincent Lef{\`e}vre and Jean-Michel Muller
rawtitle: Worst Cases for Correct Rounding of the Elementary Functions in Double Precision
entry:
@InProceedings{Lefevre:2001:WCC,
  author =       "Vincent Lef{\`e}vre and Jean-Michel Muller",
  title =        "Worst Cases for Correct Rounding of the Elementary
                 Functions in Double Precision",
  crossref =     "Burgess:2001:ISC",
  pages =        "111--118",
  year =         "2001",
  DOI =          "https://doi.org/10.1109/ARITH.2001.930110",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Lefevre.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15; correct rounding; floating-point
                 arithmetic",
  summary =      "We give the results of a four-year search for the
                 worst cases for correct rounding of the major
                 elementary functions in double precision. These results
                 allow the design of reasonably fast routines that will
                 compute these functions with correct \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Lemieux:2001:FPM
author: Joe Lemieux
title: Fixed-Point Math in C
journal: j-EMBED-SYS-PROG
volume: 14
number: 1
pages: ??--??
month: apr
monthnumber: 4
year: 2001
CODEN: EYPRE4
ISSN: 1040-3272 OR 10403272
bibdate: Fri Nov 28 18:24:03 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 18:24:03 ???
URL: http://www.embedded.com/story/OEG20010311S0022
fjournal: Embedded Systems Programming
acknowledgement: ack-mfc
rawauthor: Joe Lemieux
rawtitle: Fixed-Point Math in {C}
abstract:
Floating-point arithmetic can be expensive if you're using an integer-only processor. But floating-point values can be manipulated as integers, as a less expensive alternative.

rawabstract:
Floating-point arithmetic can be expensive if you're using an integer-only processor. But floating-point values can be manipulated as integers, as a less expensive alternative.

entry:
@Article{Lemieux:2001:FPM,
  author =       "Joe Lemieux",
  title =        "Fixed-Point Math in {C}",
  journal =      j-EMBED-SYS-PROG,
  volume =       "14",
  number =       "1",
  pages =        "??--??",
  month =        apr,
  year =         "2001",
  CODEN =        "EYPRE4",
  ISSN =         "1040-3272",
  bibdate =      "Fri Nov 28 18:24:03 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.embedded.com/story/OEG20010311S0022",
  abstract =     "Floating-point arithmetic can be expensive if you're
                 using an integer-only processor. But floating-point
                 values can be manipulated as integers, as a less
                 expensive alternative.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  fjournal =     "Embedded Systems Programming",
}


bibtype: article
filename: fparith.bib
label: Leone:2001:NLC
author: M. Leone
title: A New Low Complexity Parallel Multiplier for a Class of Finite Fields
journal: j-LECT-NOTES-COMP-SCI
volume: 2162
pages: 160--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:06:06 MST 2002
bibtimestamp: 2002.02.02 13:06:06 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: M. Leone
rawtitle: A New Low Complexity Parallel Multiplier for a Class of Finite Fields
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2162.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2162/21620160.htm; http://link.springer-ny.com/link/service/series/0558/papers/2162/21620160.pdf

entry:
@Article{Leone:2001:NLC,
  author =       "M. Leone",
  title =        "A New Low Complexity Parallel Multiplier for a Class
                 of Finite Fields",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2162",
  pages =        "160--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:06:06 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2162.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2162/21620160.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2162/21620160.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: inproceedings
filename: fparith.bib
label: Lester:2001:ECF
author: David Lester
title: Effective Continued Fractions
crossref: Burgess:2001:ISC
pages: 163--172
year: 2001
bibdate: Fri May 3 13:58:18 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.03 13:58:18 MDT
URL: http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Lester.pdf
keywords: ARITH-15
acknowledgement: ack-nhfb
rawauthor: David Lester
rawtitle: Effective Continued Fractions
entry:
@InProceedings{Lester:2001:ECF,
  author =       "David Lester",
  title =        "Effective Continued Fractions",
  crossref =     "Burgess:2001:ISC",
  pages =        "163--172",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Lester.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}


bibtype: techreport
filename: fparith.bib
label: Li:2001:LLF
author: Ren-Cang Li and Peter Markstein and Jon P. Okada and James W. Thomas
title: The tt libm library and floating-point arithmetic for HP-UX on Itanium
type: Technical report
institution: Hewlett--Packard Company
address: Palo Alto, CA, USA
month: apr
monthnumber: 4
year: 2001
bibdate: Fri Jun 24 20:12:09 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.06.24 20:12:09 ???
acknowledgement: ack-nhfb
rawauthor: Ren-Cang Li and Peter Markstein and Jon P. Okada and James W. Thomas
rawtitle: The {\tt libm} library and floating-point arithmetic for {HP-UX} on {Itanium}
URL:
http://h21007.www2.hp.com/dspp/ddl/ddl_Download_File_TRX/1,1249,942,00.pdf; http://h21007.www2.hp.com/dspp/tech/tech_TechDocumentDetailPage_IDX/1,1701,981,00.html

entry:
@TechReport{Li:2001:LLF,
  author =       "Ren-Cang Li and Peter Markstein and Jon P. Okada and
                 James W. Thomas",
  title =        "The {\tt libm} library and floating-point arithmetic
                 for {HP-UX} on {Itanium}",
  type =         "Technical report",
  institution =  "Hewlett--Packard Company",
  address =      "Palo Alto, CA, USA",
  pages =        "??",
  month =        apr,
  year =         "2001",
  bibdate =      "Fri Jun 24 20:12:09 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://h21007.www2.hp.com/dspp/ddl/ddl_Download_File_TRX/1,1249,942,00.pdf;
                 http://h21007.www2.hp.com/dspp/tech/tech_TechDocumentDetailPage_IDX/1,1701,981,00.html",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Li:2001:PMM
author: Keqin Li and V. Y. Pan
title: Parallel matrix multiplication on a linear array with a reconfigurable pipelined bus system
journal: j-IEEE-TRANS-COMPUT
volume: 50
number: 5
pages: 519--525
month: may
monthnumber: 5
year: 2001
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.926164
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 5 10:03:10 MDT 2011
bibtimestamp: 2011.07.05 10:03:10 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=926164
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Keqin Li and V. Y. Pan
rawtitle: Parallel matrix multiplication on a linear array with a reconfigurable pipelined bus system
entry:
@Article{Li:2001:PMM,
  author =       "Keqin Li and V. Y. Pan",
  title =        "Parallel matrix multiplication on a linear array with
                 a reconfigurable pipelined bus system",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "50",
  number =       "5",
  pages =        "519--525",
  month =        may,
  year =         "2001",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.926164",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 10:03:10 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=926164",
  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: Lippert:2001:HSM
author: Th. Lippert and N. Petkov and P. Palazzari and K. Schilling
title: Hyper-systolic matrix multiplication
journal: j-PARALLEL-COMPUTING
volume: 27
number: 6
pages: 737--759
month: may
monthnumber: 5
year: 2001
CODEN: PACOEJ
ISSN: 0167-8191 (print), 1872-7336 (electronic) OR 01678191 (print), 18727336 (electronic)
ISSNL: 0167-8191 OR 01678191
bibdate: Wed Jul 18 06:31:15 MDT 2001
bibsource: http://www.elsevier.com/locate/issn/01678191; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.07.18 06:31:15 MDT
fjournal: Parallel Computing
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01678191
rawauthor: Th. Lippert and N. Petkov and P. Palazzari and K. Schilling
rawtitle: Hyper-systolic matrix multiplication
URL:
http://www.elsevier.nl/gej-ng/10/35/21/47/30/23/abstract.html; http://www.elsevier.nl/gej-ng/10/35/21/47/30/23/article.pdf

entry:
@Article{Lippert:2001:HSM,
  author =       "Th. Lippert and N. Petkov and P. Palazzari and K.
                 Schilling",
  title =        "Hyper-systolic matrix multiplication",
  journal =      j-PARALLEL-COMPUTING,
  volume =       "27",
  number =       "6",
  pages =        "737--759",
  month =        may,
  year =         "2001",
  CODEN =        "PACOEJ",
  ISSN =         "0167-8191 (print), 1872-7336 (electronic)",
  ISSN-L =       "0167-8191",
  bibdate =      "Wed Jul 18 06:31:15 MDT 2001",
  bibsource =    "http://www.elsevier.com/locate/issn/01678191;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.elsevier.nl/gej-ng/10/35/21/47/30/23/abstract.html;
                 http://www.elsevier.nl/gej-ng/10/35/21/47/30/23/article.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Parallel Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01678191",
}


bibtype: inproceedings
filename: fparith.bib
label: Madhukumar:2001:EMH
author: A. S. Madhukumar and F. Chin
booktitle: 12th IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, 2001
title: An efficient method for high-rate data transmission using residue number system based DS--CDMA
volume: 1
publisher: pub-IEEE
address: pub-IEEE:adr
pages: C-1--C-5
year: 2001
DOI: https://doi.org/10.1109/PIMRC.2001.965450
bibdate: Fri Nov 9 11:38:59 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:59 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: A. S. Madhukumar and F. Chin
rawbooktitle: 12th {IEEE} International Symposium on Personal, Indoor and Mobile Radio Communications, 2001
rawtitle: An efficient method for high-rate data transmission using residue number system based {DS--CDMA}
entry:
@InProceedings{Madhukumar:2001:EMH,
  author =       "A. S. Madhukumar and F. Chin",
  booktitle =    "12th {IEEE} International Symposium on Personal,
                 Indoor and Mobile Radio Communications, 2001",
  title =        "An efficient method for high-rate data transmission
                 using residue number system based {DS--CDMA}",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "C-1--C-5",
  year =         "2001",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/PIMRC.2001.965450",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 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 an advanced architecture for a
                 residue number system (RNS) based CDMA system for
                 high-rate data transmission by combining RNS
                 representation, PSK/QAM modulation and orthogonal
                 modulation. The proposed system uses a lesser
                 \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Madhukumar:2001:IBE
author: A. S. Madhukumar and F. Chin
booktitle: VTC 2001 Fall. IEEE VTS 54th Vehicular Technology Conference
title: Improving bandwidth efficiency for a residue number system based DS--CDMA system
volume: 1
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 247--251
year: 2001
DOI: https://doi.org/10.1109/VTC.2001.956595
bibdate: Fri Nov 9 11:38:59 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:59 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: A. S. Madhukumar and F. Chin
rawbooktitle: {VTC 2001} Fall. {IEEE} {VTS 54th} Vehicular Technology Conference
rawtitle: Improving bandwidth efficiency for a residue number system based {DS--CDMA} system
entry:
@InProceedings{Madhukumar:2001:IBE,
  author =       "A. S. Madhukumar and F. Chin",
  booktitle =    "{VTC 2001} Fall. {IEEE} {VTS 54th} Vehicular
                 Technology Conference",
  title =        "Improving bandwidth efficiency for a residue number
                 system based {DS--CDMA} system",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "247--251",
  year =         "2001",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/VTC.2001.956595",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 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 method to improve bandwidth
                 efficiency of RNS based CDMA system by combining RNS
                 representation, PSK/QAM modulation and orthogonal
                 modulation. Using the proposed method significantly
                 reduces the computational complexity of \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Madhukumar:2001:IIR
author: A. S. Madhukumar and F. Chin
booktitle: VTC 2001 Fall. IEEE VTS 54th Vehicular Technology Conference
volume: 4
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 2272--2276
year: 2001
DOI: https://doi.org/10.1109/VTC.2001.957150
bibdate: Fri Nov 9 11:38:59 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:59 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: A. S. Madhukumar and F. Chin
rawbooktitle: {VTC 2001} Fall. {IEEE} {VTS 54th} Vehicular Technology Conference
title:
Incorporating incremental redundancy and link adaptation in communication systems using residue number systems

rawtitle:
Incorporating incremental redundancy and link adaptation in communication systems using residue number systems

entry:
@InProceedings{Madhukumar:2001:IIR,
  author =       "A. S. Madhukumar and F. Chin",
  booktitle =    "{VTC 2001} Fall. {IEEE} {VTS 54th} Vehicular
                 Technology Conference",
  title =        "Incorporating incremental redundancy and link
                 adaptation in communication systems using residue
                 number systems",
  volume =       "4",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "2272--2276",
  year =         "2001",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/VTC.2001.957150",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 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 explores the use of redundant residue
                 number systems to incorporate incremental redundancy in
                 a communication system. By exploiting this property
                 further, one can design an appropriate coding scheme
                 for transmission at the currently \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Matula:2001:ITL
author: David W. Matula
title: Improved Table Lookup Algorithms for Postscaled Division
crossref: Burgess:2001:ISC
pages: 101--110
year: 2001
bibdate: Fri May 3 13:58:18 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.03 13:58:18 MDT
URL: http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Matula.pdf
keywords: ARITH-15
acknowledgement: ack-nhfb
rawauthor: David W. Matula
rawtitle: Improved Table Lookup Algorithms for Postscaled Division
entry:
@InProceedings{Matula:2001:ITL,
  author =       "David W. Matula",
  title =        "Improved Table Lookup Algorithms for Postscaled
                 Division",
  crossref =     "Burgess:2001:ISC",
  pages =        "101--110",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Matula.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}


bibtype: inproceedings
filename: fparith.bib
label: McFearin:2001:GAH
author: Lee D. McFearin and David W. Matula
title: Generation and Analysis of Hard to Round Cases for Binary Floating Point Division
crossref: Burgess:2001:ISC
pages: 119--127
year: 2001
bibdate: Fri May 3 13:58:18 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.03 13:58:18 MDT
URL: http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_McFearin.pdf
keywords: ARITH-15
acknowledgement: ack-nhfb
rawauthor: Lee D. McFearin and David W. Matula
rawtitle: Generation and Analysis of Hard to Round Cases for Binary Floating Point Division
entry:
@InProceedings{McFearin:2001:GAH,
  author =       "Lee D. McFearin and David W. Matula",
  title =        "Generation and Analysis of Hard to Round Cases for
                 Binary Floating Point Division",
  crossref =     "Burgess:2001:ISC",
  pages =        "119--127",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_McFearin.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
  summary =      "We investigate two sets of hard to round p$\times$p
                 bit fractions arising from division of a normalized p
                 bit floating point dividend by a normalized p bit
                 floating point divisor. These sets are characterized by
                 the p$\times$p bit fraction's quotient \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Michel:2001:SCF
author: Claude Michel and Michel Rueher and Yahia Lebbah
title: Solving Constraints over Floating-Point Numbers
journal: j-LECT-NOTES-COMP-SCI
volume: 2239
pages: 524--538
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
MRclass: 90C08 (65G30 68T20)
MRnumber: MR1904621
bibdate: Sat Feb 2 13:07:24 MST 2002
bibtimestamp: 2002.02.02 13:07:24 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Claude Michel and Michel Rueher and Yahia Lebbah
rawtitle: Solving Constraints over Floating-Point Numbers
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2239.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2239/22390524.htm; http://link.springer-ny.com/link/service/series/0558/papers/2239/22390524.pdf

entry:
@Article{Michel:2001:SCF,
  author =       "Claude Michel and Michel Rueher and Yahia Lebbah",
  title =        "Solving Constraints over Floating-Point Numbers",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2239",
  pages =        "524--538",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  MRclass =      "90C08 (65G30 68T20)",
  MRnumber =     "MR1904621",
  bibdate =      "Sat Feb 2 13:07:24 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2239.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2239/22390524.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2239/22390524.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: phdthesis
filename: fparith.bib
label: Mobley:2001:ICW
author: Byron Paul Mobley
title: The ingenuity of common workmen: and the invention of the computer
type: Ph.D. thesis
school: Department of History, Iowa State University
address: Ames, IA, USA
pages: 301
year: 2001
ISBN: 0-493-46949-4 OR 0493469494
ISBN13: 978-0-493-46949-2 OR 9780493469492
bibdate: Thu Nov 18 11:31:13 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.11.18 11:31:13 ???
keywords: ABC (Atanasoff-Berry Computer); ENIAC (Electronic Numerical Integrator and Computer)
acknowledgement: ack-nhfb
rawauthor: Byron Paul Mobley
rawtitle: The ingenuity of common workmen: and the invention of the computer
abstract:
Since World War II, state support for scientific research has been assumed crucial to technological and economic progress. Governments accordingly spent tremendous sums to that end. Nothing epitomizes the alleged fruits of that involvement better than the electronic digital computer. The first such computer has been widely reputed to be the ENIAC, financed by the U.S. Army for the war but finished afterwards. Vastly improved computers followed, initially paid for in good share by the Federal Government of the United States, but with the private sector then dominating, both in development and use, and computers are of major significance. Despite the supposed success of public-supported science, evidence is that computers would have evolved much the same without it but at less expense. Indeed, the foundations of modern computer theory and technology were articulated before World War II, both as a tool of applied mathematics and for information processing, and the computer was itself on the cusp of reality. Contrary to popular understanding, the ENIAC actually represented a movement backwards and a dead end.par Rather, modern computation derived more directly, for example, from the prewar work of John Vincent Atanasoff and Clifford Berry, a physics professor and graduate student, respectively, at Iowa State College (now University) in Ames, Iowa. They built the Atanasoff Berry Computer (ABC), which, although special purpose and inexpensive, heralded the efficient and elegant design of modern computers. Moreover, while no one foresaw commercialization of computers based on the ungainly and costly ENIAC, the commercial possibilities of the ABC were immediately evident, although unrealized due to war. Evidence indicates, furthermore, that the private sector was willing and able to develop computers beyond the ABC and could have done so more effectively than government, to the most sophisticated machines. A full and inclusive history of computers suggests that Adam Smith, the eighteenth century Scottish philosopher, had it right. He believed that minimal and aloof government best served society, and that the inherent genius of citizens was itself enough to ensure the general prosperity.

rawabstract:
Since World War II, state support for scientific research has been assumed crucial to technological and economic progress. Governments accordingly spent tremendous sums to that end. Nothing epitomizes the alleged fruits of that involvement better than the electronic digital computer. The first such computer has been widely reputed to be the ENIAC, financed by the U.S. Army for the war but finished afterwards. Vastly improved computers followed, initially paid for in good share by the Federal Government of the United States, but with the private sector then dominating, both in development and use, and computers are of major significance. Despite the supposed success of public-supported science, evidence is that computers would have evolved much the same without it but at less expense. Indeed, the foundations of modern computer theory and technology were articulated before World War II, both as a tool of applied mathematics and for information processing, and the computer was itself on the cusp of reality. Contrary to popular understanding, the ENIAC actually represented a movement backwards and a dead end.\par Rather, modern computation derived more directly, for example, from the prewar work of John Vincent Atanasoff and Clifford Berry, a physics professor and graduate student, respectively, at Iowa State College (now University) in Ames, Iowa. They built the Atanasoff Berry Computer (ABC), which, although special purpose and inexpensive, heralded the efficient and elegant design of modern computers. Moreover, while no one foresaw commercialization of computers based on the ungainly and costly ENIAC, the commercial possibilities of the ABC were immediately evident, although unrealized due to war. Evidence indicates, furthermore, that the private sector was willing and able to develop computers beyond the ABC and could have done so more effectively than government, to the most sophisticated machines. A full and inclusive history of computers suggests that Adam Smith, the eighteenth century Scottish philosopher, had it right. He believed that minimal and aloof government best served society, and that the inherent genius of citizens was itself enough to ensure the general prosperity.

entry:
@PhdThesis{Mobley:2001:ICW,
  author =       "Byron Paul Mobley",
  title =        "The ingenuity of common workmen: and the invention of
                 the computer",
  type =         "{Ph.D.} thesis",
  school =       "Department of History, Iowa State University",
  address =      "Ames, IA, USA",
  pages =        "301",
  year =         "2001",
  ISBN =         "0-493-46949-4",
  ISBN-13 =      "978-0-493-46949-2",
  bibdate =      "Thu Nov 18 11:31:13 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Since World War II, state support for scientific
                 research has been assumed crucial to technological and
                 economic progress. Governments accordingly spent
                 tremendous sums to that end. Nothing epitomizes the
                 alleged fruits of that involvement better than the
                 electronic digital computer. The first such computer
                 has been widely reputed to be the ENIAC, financed by
                 the U.S. Army for the war but finished afterwards.
                 Vastly improved computers followed, initially paid for
                 in good share by the Federal Government of the United
                 States, but with the private sector then dominating,
                 both in development and use, and computers are of major
                 significance. Despite the supposed success of
                 public-supported science, evidence is that computers
                 would have evolved much the same without it but at less
                 expense. Indeed, the foundations of modern computer
                 theory and technology were articulated before World War
                 II, both as a tool of applied mathematics and for
                 information processing, and the computer was itself on
                 the cusp of reality. Contrary to popular understanding,
                 the ENIAC actually represented a movement backwards and
                 a dead end.\par

                 Rather, modern computation derived more directly, for
                 example, from the prewar work of John Vincent Atanasoff
                 and Clifford Berry, a physics professor and graduate
                 student, respectively, at Iowa State College (now
                 University) in Ames, Iowa. They built the Atanasoff
                 Berry Computer (ABC), which, although special purpose
                 and inexpensive, heralded the efficient and elegant
                 design of modern computers. Moreover, while no one
                 foresaw commercialization of computers based on the
                 ungainly and costly ENIAC, the commercial possibilities
                 of the ABC were immediately evident, although
                 unrealized due to war. Evidence indicates, furthermore,
                 that the private sector was willing and able to develop
                 computers beyond the ABC and could have done so more
                 effectively than government, to the most sophisticated
                 machines. A full and inclusive history of computers
                 suggests that Adam Smith, the eighteenth century
                 Scottish philosopher, had it right. He believed that
                 minimal and aloof government best served society, and
                 that the inherent genius of citizens was itself enough
                 to ensure the general prosperity.",
  acknowledgement = ack-nhfb,
  keywords =     "ABC (Atanasoff-Berry Computer); ENIAC (Electronic
                 Numerical Integrator and Computer)",
}


bibtype: article
filename: fparith.bib
label: Moller:2001:SEC
author: Bodo Moller
title: Securing Elliptic Curve Point Multiplication against Side-Channel Attacks
journal: j-LECT-NOTES-COMP-SCI
volume: 2200
pages: 324--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:06:44 MST 2002
bibtimestamp: 2002.02.02 13:06:44 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Bodo M{\"o}ller
rawtitle: Securing Elliptic Curve Point Multiplication against Side-Channel Attacks
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2200.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2200/22000324.htm; http://link.springer-ny.com/link/service/series/0558/papers/2200/22000324.pdf

entry:
@Article{Moller:2001:SEC,
  author =       "Bodo M{\"o}ller",
  title =        "Securing Elliptic Curve Point Multiplication against
                 Side-Channel Attacks",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2200",
  pages =        "324--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:06:44 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2200.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2200/22000324.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2200/22000324.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Montuschi:2001:BVH
author: P. Montuschi and T. Lang
title: Boosting very-high radix division with prescaling and selection by rounding
journal: j-IEEE-TRANS-COMPUT
volume: 50
number: 1
pages: 13--27
month: jan
monthnumber: 1
year: 2001
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.902750
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 5 10:03:08 MDT 2011
bibtimestamp: 2011.07.05 10:03:08 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=902750
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: P. Montuschi and T. Lang
rawtitle: Boosting very-high radix division with prescaling and selection by rounding
entry:
@Article{Montuschi:2001:BVH,
  author =       "P. Montuschi and T. Lang",
  title =        "Boosting very-high radix division with prescaling and
                 selection by rounding",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "50",
  number =       "1",
  pages =        "13--27",
  month =        jan,
  year =         "2001",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.902750",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 10:03:08 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=902750",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "An extension of the very-high radix division with
                 prescaling and selection by rounding is presented. This
                 extension consists of increasing the effective radix of
                 the implementation by obtaining a few additional bits
                 of the quotient per iteration, \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Morioka:2001:TEV
author: Sumio Morioka and Yasunao Katayama and Toshiyuki Yamane
title: Towards Efficient Verification of Arithmetic Algorithms over Galois Fields $ G F(2^m) $
journal: j-LECT-NOTES-COMP-SCI
volume: 2102
pages: 465--477
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:05:02 MST 2002
bibtimestamp: 2002.02.02 13:05:02 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Sumio Morioka and Yasunao Katayama and Toshiyuki Yamane
rawtitle: Towards Efficient Verification of Arithmetic Algorithms over {Galois} Fields {$ G F(2^m) $}
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2102.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2102/21020465.htm; http://link.springer-ny.com/link/service/series/0558/papers/2102/21020465.pdf

entry:
@Article{Morioka:2001:TEV,
  author =       "Sumio Morioka and Yasunao Katayama and Toshiyuki
                 Yamane",
  title =        "Towards Efficient Verification of Arithmetic
                 Algorithms over {Galois} Fields {$ G F(2^m) $}",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2102",
  pages =        "465--477",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:05:02 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2102.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2102/21020465.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2102/21020465.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: MRaihi:2001:ACR
author: David M'Raihi and David Naccache and Michael Tunstall
title: Asymmetric Currency Rounding
journal: j-LECT-NOTES-COMP-SCI
volume: 1962
pages: 192--201
year: 2001
CODEN: LNCSD9
DOI: https://doi.org/10.1007/3-540-45472-1
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:02:55 MST 2002
bibtimestamp: 2002.02.02 13:02:55 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 Michael Tunstall
rawtitle: Asymmetric Currency Rounding
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t1962.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/1962/19620192.htm; http://link.springer-ny.com/link/service/series/0558/papers/1962/19620192.pdf

abstract:
The euro was introduced on the first of January 1999 as a common currency in fourteen European nations. EC regulations are fundamentally different from usual banking practices for they forbid fees when converting national currencies to euros (fees would otherwise deter users from adopting the euro); this creates a unique fraud context where money can be made by taking advantage of the EC's official rounding rules. This paper proposes a public-key-based protection against such attacks. In our scheme, the parties conducting a transaction can not predict whether the rounding will cause loss or gain while the expected statistical difference between an amount and its euro-equivalent decreases exponentially as the number of transactions increases.

rawabstract:
The euro was introduced on the first of January 1999 as a common currency in fourteen European nations. EC regulations are fundamentally different from usual banking practices for they forbid fees when converting national currencies to euros (fees would otherwise deter users from adopting the euro); this creates a unique fraud context where money can be made by taking advantage of the EC's official rounding rules. This paper proposes a public-key-based protection against such attacks. In our scheme, the parties conducting a transaction can not predict whether the rounding will cause loss or gain while the expected statistical difference between an amount and its euro-equivalent decreases exponentially as the number of transactions increases.

entry:
@Article{MRaihi:2001:ACR,
  author =       "David M'Ra{\"\i}hi and David Naccache and Michael
                 Tunstall",
  title =        "Asymmetric Currency Rounding",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1962",
  pages =        "192--201",
  year =         "2001",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/3-540-45472-1",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:02:55 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1962.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1962/19620192.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/1962/19620192.pdf",
  abstract =     "The euro was introduced on the first of January 1999
                 as a common currency in fourteen European nations. EC
                 regulations are fundamentally different from usual
                 banking practices for they forbid fees when converting
                 national currencies to euros (fees would otherwise
                 deter users from adopting the euro); this creates a
                 unique fraud context where money can be made by taking
                 advantage of the EC's official rounding rules. This
                 paper proposes a public-key-based protection against
                 such attacks. In our scheme, the parties conducting a
                 transaction can not predict whether the rounding will
                 cause loss or gain while the expected statistical
                 difference between an amount and its euro-equivalent
                 decreases exponentially as the number of transactions
                 increases.",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Muller:2001:IEA
author: Norbert Th. Muller
title: The iRRAM: Exact Arithmetic in C++
journal: j-LECT-NOTES-COMP-SCI
volume: 2064
pages: 222--252
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:04:19 MST 2002
bibtimestamp: 2002.02.02 13:04:19 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Norbert Th. M{\"u}ller
rawtitle: The {iRRAM}: Exact Arithmetic in {C++}
URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2064/20640222.htm; http://link.springer-ny.com/link/service/series/0558/papers/2064/20640222.pdf

entry:
@Article{Muller:2001:IEA,
  author =       "Norbert Th. M{\"u}ller",
  title =        "The {iRRAM}: Exact Arithmetic in {C++}",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2064",
  pages =        "222--252",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:04:19 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2064.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2064/20640222.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2064/20640222.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: inproceedings
filename: fparith.bib
label: Naini:2001:GHS
author: Ajay Naini and Atul Dhablania and Warren James and Debjit Das Sarma
title: 1-GHz HAL SPARC64reg Dual Floating Point Unit with RAS Features
crossref: Burgess:2001:ISC
pages: 173--183
year: 2001
bibdate: Fri May 3 13:58:18 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.03 13:58:18 MDT
URL: http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Naini.pdf
keywords: ARITH-15
acknowledgement: ack-nhfb
rawauthor: Ajay Naini and Atul Dhablania and Warren James and Debjit Das Sarma
rawtitle: {1-GHz HAL SPARC64\reg{}} Dual Floating Point Unit with {RAS} Features
entry:
@InProceedings{Naini:2001:GHS,
  author =       "Ajay Naini and Atul Dhablania and Warren James and
                 Debjit Das Sarma",
  title =        "{1-GHz HAL SPARC64\reg{}} Dual Floating Point Unit
                 with {RAS} Features",
  crossref =     "Burgess:2001:ISC",
  pages =        "173--183",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Naini.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}


bibtype: article
filename: fparith.bib
label: Nakamura:2001:AAA
author: Yoshimasa Nakamura
title: Algorithms associated with arithmetic, geometric and harmonic means and integrable systems
journal: j-J-COMPUT-APPL-MATH
volume: 131
number: 1--2
pages: 161--174
day: 1
month: jun
monthnumber: 6
year: 2001
CODEN: JCAMDI
DOI: https://doi.org/10.1016/S0377-0427(00)00316-2
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
MRclass: 65P40 (37N30 39A10)
MRnumber: 1835710
bibdate: Sat Feb 25 12:45:18 MST 2017
bibtimestamp: 2017.02.25 12:45:18 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042700003162
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Yoshimasa Nakamura
rawtitle: Algorithms associated with arithmetic, geometric and harmonic means and integrable systems
bibsource:
https://www.math.utah.edu/pub/tex/bib/agm.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib

entry:
@Article{Nakamura:2001:AAA,
  author =       "Yoshimasa Nakamura",
  title =        "Algorithms associated with arithmetic, geometric and
                 harmonic means and integrable systems",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "131",
  number =       "1--2",
  pages =        "161--174",
  day =          "1",
  month =        jun,
  year =         "2001",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/S0377-0427(00)00316-2",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  MRclass =      "65P40 (37N30 39A10)",
  MRnumber =     "1835710",
  bibdate =      "Sat Feb 25 12:45:18 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042700003162",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: inproceedings
filename: fparith.bib
label: Nannarelli:2001:TBR
author: A. Nannarelli and M. Re and G. C. Cardarilli
booktitle: ISCAS 2001, The 2001 IEEE International Symposium on Circuits and Systems, 6--9 May 2001
title: Tradeoffs between residue number system and traditional FIR filters
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 305--308
year: 2001
DOI: https://doi.org/10.1109/ISCAS.2001.921068
bibdate: Fri Nov 9 11:38:59 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:59 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: A. Nannarelli and M. Re and G. C. Cardarilli
rawbooktitle: {ISCAS 2001}, The 2001 {IEEE} International Symposium on Circuits and Systems, 6--9 May 2001
rawtitle: Tradeoffs between residue number system and traditional {FIR} filters
entry:
@InProceedings{Nannarelli:2001:TBR,
  author =       "A. Nannarelli and M. Re and G. C. Cardarilli",
  booktitle =    "{ISCAS 2001}, The 2001 {IEEE} International Symposium
                 on Circuits and Systems, 6--9 May 2001",
  title =        "Tradeoffs between residue number system and
                 traditional {FIR} filters",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "305--308",
  year =         "2001",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.2001.921068",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "In this work, a study on the implementation of FIR
                 filters in the Residue Number System (RNS) is carried
                 out. For different configurations, RNS filters are
                 compared with filters realized in the traditional two's
                 complement system (TCS) in terms of \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Ning:2001:ESI
author: Peng Ning and Yiqun Lisa Yin
title: Efficient Software Implementation for Finite Field Multiplication in Normal Basis
journal: j-LECT-NOTES-COMP-SCI
volume: 2229
pages: 177--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:07:15 MST 2002
bibtimestamp: 2002.02.02 13:07:15 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Peng Ning and Yiqun Lisa Yin
rawtitle: Efficient Software Implementation for Finite Field Multiplication in Normal Basis
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2229.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2229/22290177.htm; http://link.springer-ny.com/link/service/series/0558/papers/2229/22290177.pdf

entry:
@Article{Ning:2001:ESI,
  author =       "Peng Ning and Yiqun Lisa Yin",
  title =        "Efficient Software Implementation for Finite Field
                 Multiplication in Normal Basis",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2229",
  pages =        "177--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:07:15 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2229.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2229/22290177.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2229/22290177.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Nozaki:2001:IRA
author: H. Nozaki and M. Motoyama and A. Shimbo and S. Kawamura
title: Implementation of RSA Algorithm Based on RNS Montgomery Multiplication
journal: j-LECT-NOTES-COMP-SCI
volume: 2162
pages: 364--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:06:06 MST 2002
bibtimestamp: 2002.02.02 13:06:06 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: H. Nozaki and M. Motoyama and A. Shimbo and S. Kawamura
rawtitle: Implementation of {RSA} Algorithm Based on {RNS Montgomery} Multiplication
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2162.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2162/21620364.htm; http://link.springer-ny.com/link/service/series/0558/papers/2162/21620364.pdf

entry:
@Article{Nozaki:2001:IRA,
  author =       "H. Nozaki and M. Motoyama and A. Shimbo and S.
                 Kawamura",
  title =        "Implementation of {RSA} Algorithm Based on {RNS
                 Montgomery} Multiplication",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2162",
  pages =        "364--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:06:06 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2162.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2162/21620364.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2162/21620364.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Oishi:2001:FEM
author: Shin'ichi Oishi
title: Fast enclosure of matrix eigenvalues and singular values via rounding mode controlled computation
journal: j-LINEAR-ALGEBRA-APPL
volume: 324
number: 1--3
pages: 133--146
day: 15
month: feb
monthnumber: 2
year: 2001
CODEN: LAAPAW
ISSN: 0024-3795 (print), 1873-1856 (electronic) OR 00243795 (print), 18731856 (electronic)
ISSNL: 0024-3795 OR 00243795
bibdate: Mon Mar 19 19:03:24 MST 2001
bibsource: http://www.elsevier.com/locate/laa; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.03.19 19:03:24 MST
fjournal: Linear Algebra and its Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00243795
rawauthor: Shin'ichi Oishi
rawtitle: Fast enclosure of matrix eigenvalues and singular values via rounding mode controlled computation
URL:
http://www.elsevier.nl/gej-ng/10/30/19/144/24/32/abstract.html; http://www.elsevier.nl/gej-ng/10/30/19/144/24/32/article.pdf

entry:
@Article{Oishi:2001:FEM,
  author =       "Shin'ichi Oishi",
  title =        "Fast enclosure of matrix eigenvalues and singular
                 values via rounding mode controlled computation",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "324",
  number =       "1--3",
  pages =        "133--146",
  day =          "15",
  month =        feb,
  year =         "2001",
  CODEN =        "LAAPAW",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  bibdate =      "Mon Mar 19 19:03:24 MST 2001",
  bibsource =    "http://www.elsevier.com/locate/laa;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.elsevier.nl/gej-ng/10/30/19/144/24/32/abstract.html;
                 http://www.elsevier.nl/gej-ng/10/30/19/144/24/32/article.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
}


bibtype: article
filename: fparith.bib
label: Okeya:2001:EEC
author: K. Okeya and K. Sakurai
journal: j-LECT-NOTES-COMP-SCI
volume: 2162
pages: 126--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:06:06 MST 2002
bibtimestamp: 2002.02.02 13:06:06 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: K. Okeya and K. Sakurai
title:
Efficient Elliptic Curve Cryptosystems from a Scalar Multiplication Algorithm with Recovery of the $y$-Coordinate on a Montgomery-Form Elliptic Curve

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2162/21620126.htm; http://link.springer-ny.com/link/service/series/0558/papers/2162/21620126.pdf

rawtitle:
Efficient Elliptic Curve Cryptosystems from a Scalar Multiplication Algorithm with Recovery of the $y$-Coordinate on a {Montgomery}-Form Elliptic Curve

entry:
@Article{Okeya:2001:EEC,
  author =       "K. Okeya and K. Sakurai",
  title =        "Efficient Elliptic Curve Cryptosystems from a Scalar
                 Multiplication Algorithm with Recovery of the
                 $y$-Coordinate on a {Montgomery}-Form Elliptic Curve",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2162",
  pages =        "126--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:06:06 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2162.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2162/21620126.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2162/21620126.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: book
filename: fparith.bib
label: Overton:2001:NCI
author: Michael L. Overton
publisher: pub-SIAM
address: pub-SIAM:adr
pages: xiv + 104
year: 2001
LCCN: QA76.9.M35 O94 2001
MRclass: 65-02 (65G30 68M07 68N99)
MRnumber: MR1828597 (2003b:65002)
MRreviewer: Jesse L. Barlow
bibdate: Fri Apr 27 16:50:46 2001
bibtimestamp: 2001.04.27 16:50:46 ???
URL: http://www.cs.nyu.edu/cs/faculty/overton/book/; http://www.siam.org/catalog/mcc07/ot76.htm
acknowledgement: ack-nhfb
rawauthor: Michael L. Overton
title:
Numerical Computing with IEEE Floating Point Arithmetic, Including One Theorem, One Rule of Thumb, and One Hundred and One Exercises

ISBN:
0-89871-482-6 (hardcover), 0-89871-571-7 (paperback), 0-89871-807-4 (ebook) OR 0898714826 (hardcover), 0898715717 (paperback), 0898718074 (ebook)

ISBN13:
978-0-89871-482-1 (hardcover), 978-0-89871-571-2 (print), 978-0-89871-807-2 (e-book) OR 9780898714821 (hardcover), 9780898715712 (print), 9780898718072 (ebook)

bibsource:
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.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/numana2000.bib

abstract:
Are you familiar with the IEEE floating point arithmetic standard? Would you like to understand it better? This book gives a broad overview of numerical computing, in a historical context, with a special focus on the IEEE standard for binary floating point arithmetic. Key ideas are developed step by step, taking the reader from floating point representation, correctly rounded arithmetic, and the IEEE philosophy on exceptions, to an understanding of the crucial concepts of conditioning and stability, explained in a simple yet rigorous context. It gives technical details that are not readily available elsewhere and includes challenging exercises that go beyond the topics covered in the text. Numerical Computing with IEEE Floating Point Arithmetic provides an easily accessible yet detailed discussion of IEEE Std 754-1985, arguably the most important standard in the computer industry. The result of an unprecedented cooperation between academic computer scientists and the cutting edge of industry, it is supported by virtually every modern computer. Other topics include the floating point architecture of the Intel microprocessors and a discussion of programming language support for the standard.

TOC:
1: Introduction 2: The real numbers 3: Computer representation of numbers 4: IEEE floating point representation 5: Rounding 6: Correctly rounded floating point operations 7: Exceptions 8: The Intel microprocessors 9: Programming languages 10: Floating point in C 11: Cancellation 12: Conditioning of problems 13: Stability of algorithms 14: Conclusion

rawabstract:
Are you familiar with the IEEE floating point arithmetic standard? Would you like to understand it better? This book gives a broad overview of numerical computing, in a historical context, with a special focus on the IEEE standard for binary floating point arithmetic. Key ideas are developed step by step, taking the reader from floating point representation, correctly rounded arithmetic, and the IEEE philosophy on exceptions, to an understanding of the crucial concepts of conditioning and stability, explained in a simple yet rigorous context. It gives technical details that are not readily available elsewhere and includes challenging exercises that go beyond the topics covered in the text. Numerical Computing with IEEE Floating Point Arithmetic provides an easily accessible yet detailed discussion of IEEE Std 754-1985, arguably the most important standard in the computer industry. The result of an unprecedented cooperation between academic computer scientists and the cutting edge of industry, it is supported by virtually every modern computer. Other topics include the floating point architecture of the Intel microprocessors and a discussion of programming language support for the standard.

rawtitle:
Numerical Computing with {IEEE} Floating Point Arithmetic, Including One Theorem, One Rule of Thumb, and One Hundred and One Exercises

rawTOC:
1: Introduction \\ 2: The real numbers \\ 3: Computer representation of numbers \\ 4: IEEE floating point representation \\ 5: Rounding \\ 6: Correctly rounded floating point operations \\ 7: Exceptions \\ 8: The Intel microprocessors \\ 9: Programming languages \\ 10: Floating point in C \\ 11: Cancellation \\ 12: Conditioning of problems \\ 13: Stability of algorithms \\ 14: Conclusion

entry:
@Book{Overton:2001:NCI,
  author =       "Michael L. Overton",
  title =        "Numerical Computing with {IEEE} Floating Point
                 Arithmetic, Including One Theorem, One Rule of Thumb,
                 and One Hundred and One Exercises",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xiv + 104",
  year =         "2001",
  ISBN =         "0-89871-482-6 (hardcover), 0-89871-571-7 (paperback),
                 0-89871-807-4 (ebook)",
  ISBN-13 =      "978-0-89871-482-1 (hardcover), 978-0-89871-571-2
                 (print), 978-0-89871-807-2 (e-book)",
  LCCN =         "QA76.9.M35 O94 2001",
  MRclass =      "65-02 (65G30 68M07 68N99)",
  MRnumber =     "MR1828597 (2003b:65002)",
  MRreviewer =   "Jesse L. Barlow",
  bibdate =      "Fri Apr 27 16:50:46 2001",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.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/numana2000.bib",
  price =        "US\$40.00",
  URL =          "http://www.cs.nyu.edu/cs/faculty/overton/book/;
                 http://www.siam.org/catalog/mcc07/ot76.htm",
  abstract =     "Are you familiar with the IEEE floating point
                 arithmetic standard? Would you like to understand it
                 better? This book gives a broad overview of numerical
                 computing, in a historical context, with a special
                 focus on the IEEE standard for binary floating point
                 arithmetic. Key ideas are developed step by step,
                 taking the reader from floating point representation,
                 correctly rounded arithmetic, and the IEEE philosophy
                 on exceptions, to an understanding of the crucial
                 concepts of conditioning and stability, explained in a
                 simple yet rigorous context. It gives technical details
                 that are not readily available elsewhere and includes
                 challenging exercises that go beyond the topics covered
                 in the text. Numerical Computing with IEEE Floating
                 Point Arithmetic provides an easily accessible yet
                 detailed discussion of IEEE Std 754-1985, arguably the
                 most important standard in the computer industry. The
                 result of an unprecedented cooperation between academic
                 computer scientists and the cutting edge of industry,
                 it is supported by virtually every modern computer.
                 Other topics include the floating point architecture of
                 the Intel microprocessors and a discussion of
                 programming language support for the standard.",
  acknowledgement = ack-nhfb,
  tableofcontents = "1: Introduction \\
                 2: The real numbers \\
                 3: Computer representation of numbers \\
                 4: IEEE floating point representation \\
                 5: Rounding \\
                 6: Correctly rounded floating point operations \\
                 7: Exceptions \\
                 8: The Intel microprocessors \\
                 9: Programming languages \\
                 10: Floating point in C \\
                 11: Cancellation \\
                 12: Conditioning of problems \\
                 13: Stability of algorithms \\
                 14: Conclusion",
}


bibtype: inproceedings
filename: fparith.bib
label: Paliouras:2001:LPP
author: V. Paliouras and T. Stouraitis
title: Low-Power Properties of the Logarithmic Number System
crossref: Burgess:2001:ISC
pages: 229--236
year: 2001
bibdate: Fri May 3 13:58:18 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.03 13:58:18 MDT
URL: http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Paliouras.pdf
keywords: ARITH-15
acknowledgement: ack-nhfb
rawauthor: V. Paliouras and T. Stouraitis
rawtitle: Low-Power Properties of the Logarithmic Number System
entry:
@InProceedings{Paliouras:2001:LPP,
  author =       "V. Paliouras and T. Stouraitis",
  title =        "Low-Power Properties of the Logarithmic Number
                 System",
  crossref =     "Burgess:2001:ISC",
  pages =        "229--236",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Paliouras.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}


bibtype: article
filename: fparith.bib
label: Park:2001:ADI
author: Young-Ho Park and Sangtae Jeong and Chang Han Kim and Jongin Lim
title: An Alternate Decomposition of an Integer for Faster Point Multiplication on Certain Elliptic Curves
journal: j-LECT-NOTES-COMP-SCI
volume: 2274
pages: 323--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Tue Sep 10 19:09:07 MDT 2002
bibtimestamp: 2002.09.10 19:09:07 MDT
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Young-Ho Park and Sangtae Jeong and Chang Han Kim and Jongin Lim
rawtitle: An Alternate Decomposition of an Integer for Faster Point Multiplication on Certain Elliptic Curves
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2274.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2274/22740323.htm; http://link.springer-ny.com/link/service/series/0558/papers/2274/22740323.pdf

entry:
@Article{Park:2001:ADI,
  author =       "Young-Ho Park and Sangtae Jeong and Chang Han Kim and
                 Jongin Lim",
  title =        "An Alternate Decomposition of an Integer for Faster
                 Point Multiplication on Certain Elliptic Curves",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2274",
  pages =        "323--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:09:07 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2274.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2274/22740323.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2274/22740323.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Park:2001:IMM
author: Young-Ho Park and Sangho Oh and Sangjin Lee and Jongin Lim and Maenghee Sung
title: An Improved Method of Multiplication on Certain Elliptic Curves
journal: j-LECT-NOTES-COMP-SCI
volume: 2274
pages: 310--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Tue Sep 10 19:09:07 MDT 2002
bibtimestamp: 2002.09.10 19:09:07 MDT
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Young-Ho Park and Sangho Oh and Sangjin Lee and Jongin Lim and Maenghee Sung
rawtitle: An Improved Method of Multiplication on Certain Elliptic Curves
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2274.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2274/22740310.htm; http://link.springer-ny.com/link/service/series/0558/papers/2274/22740310.pdf

entry:
@Article{Park:2001:IMM,
  author =       "Young-Ho Park and Sangho Oh and Sangjin Lee and Jongin
                 Lim and Maenghee Sung",
  title =        "An Improved Method of Multiplication on Certain
                 Elliptic Curves",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2274",
  pages =        "310--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:09:07 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2274.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2274/22740310.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2274/22740310.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: inproceedings
filename: fparith.bib
label: Phillips:2001:MMM
author: B. Phillips
booktitle: Conference Record of the Thirty-Fifth Asilomar Conference on Signals, Systems and Computers, 2001
title: Modular multiplication in the Montgomery residue number system
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1637--1640
year: 2001
DOI: https://doi.org/10.1109/ACSSC.2001.987762
bibdate: Fri Nov 9 11:38:59 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:59 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: B. Phillips
rawbooktitle: Conference Record of the Thirty-Fifth Asilomar Conference on Signals, Systems and Computers, 2001
rawtitle: Modular multiplication in the {Montgomery} residue number system
entry:
@InProceedings{Phillips:2001:MMM,
  author =       "B. Phillips",
  booktitle =    "Conference Record of the Thirty-Fifth Asilomar
                 Conference on Signals, Systems and Computers, 2001",
  title =        "Modular multiplication in the {Montgomery} residue
                 number system",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1637--1640",
  year =         "2001",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ACSSC.2001.987762",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 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 considers the evaluation of long wordlength
                 modular products. An algorithm is described in which
                 long wordlength (e.g. 1024-bit) integers are
                 represented by short-wordlength (e.g. 32-bit)
                 Montgomery (1985) residues. Long integer modular
                 \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Phillips:2001:MRN
author: B. J. Phillips
title: Montgomery residue number systems
journal: j-ELECT-LETTERS
volume: 37
number: 21
pages: 1286--1287
day: 11
month: oct
monthnumber: 10
year: 2001
CODEN: ELLEAK
DOI: https://doi.org/10.1049/el:20010852
ISSN: 0013-5194 (print), 1350-911X (electronic) OR 00135194 (print), 1350911X (electronic)
ISSNL: 0013-5194 OR 00135194
bibdate: Fri Nov 9 11:38:59 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:59 MST
URL: https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=20889
fjournal: Electronics Letters
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220
rawauthor: B. J. Phillips
rawtitle: {Montgomery} residue number systems
entry:
@Article{Phillips:2001:MRN,
  author =       "B. J. Phillips",
  title =        "{Montgomery} residue number systems",
  journal =      j-ELECT-LETTERS,
  volume =       "37",
  number =       "21",
  pages =        "1286--1287",
  day =          "11",
  month =        oct,
  year =         "2001",
  CODEN =        "ELLEAK",
  DOI =          "https://doi.org/10.1049/el:20010852",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=20889",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  keywords =     "residue arithmetic; residue number system",
  summary =      "The Montgomery residue number system (MRNS) for long
                 word-length arithmetic is introduced. MRNS, a
                 modification of the residue number system (RNS),
                 represents a long integer as a set of smaller
                 Montgomery residues. Long integer addition, subtraction
                 \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Phillips:2001:OSL
author: Braden Phillips
title: Optimised Squaring of Long Integers Using Precomputed Partial Products
crossref: Burgess:2001:ISC
pages: 73--82
year: 2001
bibdate: Fri May 3 13:58:18 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.03 13:58:18 MDT
URL: http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Phillips.pdf
keywords: ARITH-15
acknowledgement: ack-nhfb
rawauthor: Braden Phillips
rawtitle: Optimised Squaring of Long Integers Using Precomputed Partial Products
entry:
@InProceedings{Phillips:2001:OSL,
  author =       "Braden Phillips",
  title =        "Optimised Squaring of Long Integers Using Precomputed
                 Partial Products",
  crossref =     "Burgess:2001:ISC",
  pages =        "73--82",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Phillips.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}


bibtype: article
filename: fparith.bib
label: Pietronero:2001:EUD
author: L. Pietronero and E. Tosatti and V. Tosatti and A. Vespignani
title: Explaining the uneven distribution of numbers in nature: the laws of Benford and Zipf
journal: j-PHYSICA-A
volume: 293
pages: 297--304
year: 2001
CODEN: PHYADX
DOI: https://doi.org/10.1016/S0378-4371(00)00633-6
ISSN: 0378-4371 (print), 1873-2119 (electronic) OR 03784371 (print), 18732119 (electronic)
ISSNL: 0378-4371 OR 03784371
bibdate: Thu Feb 15 16:36:18 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.02.15 16:36:18 ???
fjournal: Physica A. Statistical Mechanics and its Applications
keywords: Benford's Law; Law of Anomalous Numbers; Zipf's Law
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03784371
rawauthor: L. Pietronero and E. Tosatti and V. Tosatti and A. Vespignani
rawtitle: Explaining the uneven distribution of numbers in nature: the laws of {Benford} and {Zipf}
abstract:
The distribution of first digits in numbers series obtained from very different origins shows a marked asymmetry in favor of small digits that goes under the name of Benford's law. We analyze in detail this property for different data sets and give a general explanation for the origin of the Benford's law in terms of multiplicative processes. We show that this law can be also generalized to series of numbers generated from more complex systems like the catalogs of seismic activity. Finally, we derive a relation between the generalized Benford's law and the popular Zipf's law which characterize the rank order statistics and has been extensively applied to many problems ranging from city population to linguistics.

rawabstract:
The distribution of first digits in numbers series obtained from very different origins shows a marked asymmetry in favor of small digits that goes under the name of Benford's law. We analyze in detail this property for different data sets and give a general explanation for the origin of the Benford's law in terms of multiplicative processes. We show that this law can be also generalized to series of numbers generated from more complex systems like the catalogs of seismic activity. Finally, we derive a relation between the generalized Benford's law and the popular Zipf's law which characterize the rank order statistics and has been extensively applied to many problems ranging from city population to linguistics.

entry:
@Article{Pietronero:2001:EUD,
  author =       "L. Pietronero and E. Tosatti and V. Tosatti and A.
                 Vespignani",
  title =        "Explaining the uneven distribution of numbers in
                 nature: the laws of {Benford} and {Zipf}",
  journal =      j-PHYSICA-A,
  volume =       "293",
  number =       "??",
  pages =        "297--304",
  month =        "????",
  year =         "2001",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/S0378-4371(00)00633-6",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Thu Feb 15 16:36:18 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The distribution of first digits in numbers series
                 obtained from very different origins shows a marked
                 asymmetry in favor of small digits that goes under the
                 name of Benford's law. We analyze in detail this
                 property for different data sets and give a general
                 explanation for the origin of the Benford's law in
                 terms of multiplicative processes. We show that this
                 law can be also generalized to series of numbers
                 generated from more complex systems like the catalogs
                 of seismic activity. Finally, we derive a relation
                 between the generalized Benford's law and the popular
                 Zipf's law which characterize the rank order statistics
                 and has been extensively applied to many problems
                 ranging from city population to linguistics.",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}


bibtype: article
filename: fparith.bib
label: Pillai:2001:LPA
author: R. V. K. Pillai and D. Al-Khalili and A. J. Al-Khalili and S. Y. A. Shah
title: A Low Power Approach to Floating Point Adder Design for DSP Applications
journal: j-J-VLSI-SIGNAL-PROC
volume: 27
number: 3
pages: 195--213
month: mar
monthnumber: 3
year: 2001
CODEN: JVSPED
DOI: https://doi.org/10.1023/A:1008140025773
ISSN: 0922-5773 (print), 1573-109x (electronic) OR 09225773 (print), 1573109x (electronic)
ISSNL: 0922-5773 OR 09225773
bibdate: Thu May 09 09:49:01 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.09 09:49:01 ???
fjournal: Journal of VLSI Signal Processing
acknowledgement: ack-nhfb
rawauthor: R. V. K. Pillai and D. Al-Khalili and A. J. Al-Khalili and S. Y. A. Shah
rawtitle: A Low Power Approach to Floating Point Adder Design for {DSP} Applications
abstract:
The demand for high performance, low power floating point adder cores has been on the rise during the recent years particularly for DSP applications. In this paper, we present a new architecture for a low power, IEEE compatible, floating point adder, that is fast and has low latency. The functional partitioning of the adder into three distinct, clock gated data paths allows activity reduction. The switching activity function of the proposed adder is represented as a three state FSM. During any given operation cycle, only one of the data paths is active, during which time, the logic assertion status of the circuit nodes of the other data paths are held at their previous states. Critical path delay and latency are reduced by incorporating speculative rounding and pseudo leading zero anticipatory logic as well as data path simplifications. In contrast to conventional high speed floating point adders that use leading zero anticipatory logic, the proposed scheme offers a worst case power reduction of 50%.

rawabstract:
The demand for high performance, low power floating point adder cores has been on the rise during the recent years particularly for DSP applications. In this paper, we present a new architecture for a low power, IEEE compatible, floating point adder, that is fast and has low latency. The functional partitioning of the adder into three distinct, clock gated data paths allows activity reduction. The switching activity function of the proposed adder is represented as a three state FSM. During any given operation cycle, only one of the data paths is active, during which time, the logic assertion status of the circuit nodes of the other data paths are held at their previous states. Critical path delay and latency are reduced by incorporating speculative rounding and pseudo leading zero anticipatory logic as well as data path simplifications. In contrast to conventional high speed floating point adders that use leading zero anticipatory logic, the proposed scheme offers a worst case power reduction of 50\%.

entry:
@Article{Pillai:2001:LPA,
  author =       "R. V. K. Pillai and D. Al-Khalili and A. J. Al-Khalili
                 and S. Y. A. Shah",
  title =        "A Low Power Approach to Floating Point Adder Design
                 for {DSP} Applications",
  journal =      j-J-VLSI-SIGNAL-PROC,
  volume =       "27",
  number =       "3",
  pages =        "195--213",
  month =        mar,
  year =         "2001",
  CODEN =        "JVSPED",
  DOI =          "https://doi.org/10.1023/A:1008140025773",
  ISSN =         "0922-5773 (print), 1573-109x (electronic)",
  ISSN-L =       "0922-5773",
  bibdate =      "Thu May 09 09:49:01 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The demand for high performance, low power floating
                 point adder cores has been on the rise during the
                 recent years particularly for DSP applications. In this
                 paper, we present a new architecture for a low power,
                 IEEE compatible, floating point adder, that is fast and
                 has low latency. The functional partitioning of the
                 adder into three distinct, clock gated data paths
                 allows activity reduction. The switching activity
                 function of the proposed adder is represented as a
                 three state FSM. During any given operation cycle, only
                 one of the data paths is active, during which time, the
                 logic assertion status of the circuit nodes of the
                 other data paths are held at their previous states.
                 Critical path delay and latency are reduced by
                 incorporating speculative rounding and pseudo leading
                 zero anticipatory logic as well as data path
                 simplifications. In contrast to conventional high speed
                 floating point adders that use leading zero
                 anticipatory logic, the proposed scheme offers a worst
                 case power reduction of 50\%.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of VLSI Signal Processing",
}


bibtype: inproceedings
filename: fparith.bib
label: Pineiro:2001:FPC
author: J. A. Pineiro and J. D. Bruguera and J.-M. Muller
title: Faithful Powering Computation Using Table Look-Up and a Fused Accumulation Tree
crossref: Burgess:2001:ISC
pages: 40--50
year: 2001
bibdate: Fri May 3 13:52:01 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.03 13:52:01 MDT
URL: http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Pineiro.pdf
keywords: ARITH-15
acknowledgement: ack-nhfb
rawauthor: J. A. Pi{\~n}eiro and J. D. Bruguera and J.-M. Muller
rawtitle: Faithful Powering Computation Using Table Look-Up and a Fused Accumulation Tree
entry:
@InProceedings{Pineiro:2001:FPC,
  author =       "J. A. Pi{\~n}eiro and J. D. Bruguera and J.-M.
                 Muller",
  title =        "Faithful Powering Computation Using Table Look-Up and
                 a Fused Accumulation Tree",
  crossref =     "Burgess:2001:ISC",
  pages =        "40--50",
  year =         "2001",
  bibdate =      "Fri May 3 13:52:01 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Pineiro.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
  xxnote =       "Check pages: one reference has 40--47??",
}


bibtype: inproceedings
filename: fparith.bib
label: Rajagopal:2001:LAD
author: Sridhar Rajagopal and Joseph R. Cavallaro
title: On-Line Arithmetic for Detection in Digital Communication Receivers
crossref: Burgess:2001:ISC
pages: 257--265
year: 2001
bibdate: Fri May 3 13:58:18 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.03 13:58:18 MDT
URL: http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Rajagopal.pdf
keywords: ARITH-15
acknowledgement: ack-nhfb
rawauthor: Sridhar Rajagopal and Joseph R. Cavallaro
rawtitle: On-Line Arithmetic for Detection in Digital Communication Receivers
entry:
@InProceedings{Rajagopal:2001:LAD,
  author =       "Sridhar Rajagopal and Joseph R. Cavallaro",
  title =        "On-Line Arithmetic for Detection in Digital
                 Communication Receivers",
  crossref =     "Burgess:2001:ISC",
  pages =        "257--265",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Rajagopal.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}


bibtype: book
filename: fparith.bib
label: Ralston:2001:FCN
author: Anthony Ralston and Philip Rabinowitz
title: A first course in numerical analysis
publisher: pub-DOVER
address: pub-DOVER:adr
edition: Second
pages: xviii + 556 + 50
year: 2001
ISBN: 0-486-41454-X (paperback) OR 048641454X (paperback)
ISBN13: 978-0-486-41454-6 (paperback) OR 9780486414546 (paperback)
LCCN: QA297 .R3 2001
bibdate: Fri Aug 20 10:13:32 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.08.20 10:13:32 MDT
subject: Numerical analysis
acknowledgement: ack-nhfb
rawauthor: Anthony Ralston and Philip Rabinowitz
rawtitle: A first course in numerical analysis
URL:
http://www.loc.gov/catdir/description/dover032/00064343.html; http://www.loc.gov/catdir/toc/dover031/00064343.html

remark:
This Dover edition, first published in 2001, is an unabridged, slightly corrected republication of the second edition of the work originally published in cite Ralston:1965:FC and issued in a revised second edition in cite Ralston:1978:FCN.

entry:
@Book{Ralston:2001:FCN,
  author =       "Anthony Ralston and Philip Rabinowitz",
  title =        "A first course in numerical analysis",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  edition =      "Second",
  pages =        "xviii + 556 + 50",
  year =         "2001",
  ISBN =         "0-486-41454-X (paperback)",
  ISBN-13 =      "978-0-486-41454-6 (paperback)",
  LCCN =         "QA297 .R3 2001",
  bibdate =      "Fri Aug 20 10:13:32 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/description/dover032/00064343.html;
                 http://www.loc.gov/catdir/toc/dover031/00064343.html",
  acknowledgement = ack-nhfb,
  remark =       "This Dover edition, first published in 2001, is an
                 unabridged, slightly corrected republication of the
                 second edition of the work originally published in
                 \cite{Ralston:1965:FC} and issued in a revised second
                 edition in \cite{Ralston:1978:FCN}.",
  subject =      "Numerical analysis",
}


bibtype: inproceedings
filename: fparith.bib
label: Rejeb:2001:IDR
author: B. Rejeb and H. Henkelmann and W. Anheier
booktitle: The 8th IEEE International Conference on Electronics, Circuits and Systems, ICECS 2001
title: Integer division in residue number system
volume: 1
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 259--262
year: 2001
DOI: https://doi.org/10.1109/ICECS.2001.957729
bibdate: Fri Nov 9 11:38:59 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:59 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: B. Rejeb and H. Henkelmann and W. Anheier
rawbooktitle: The 8th {IEEE} International Conference on Electronics, Circuits and Systems, {ICECS 2001}
rawtitle: Integer division in residue number system
entry:
@InProceedings{Rejeb:2001:IDR,
  author =       "B. Rejeb and H. Henkelmann and W. Anheier",
  booktitle =    "The 8th {IEEE} International Conference on
                 Electronics, Circuits and Systems, {ICECS 2001}",
  title =        "Integer division in residue number system",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "259--262",
  year =         "2001",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ICECS.2001.957729",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Division, sign detection and number comparison are the
                 more difficult operations in residue number systems
                 (RNS). These shortcomings limited most RNS
                 implementations to additions, subtractions and
                 multiplications. In this paper, a high level \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Reyhani-Masoleh:2001:FNB
author: Arash Reyhani-Masoleh and M. Anwar Hasan
title: Fast Normal Basis Multiplication Using General Purpose Processors
journal: j-LECT-NOTES-COMP-SCI
volume: 2259
pages: 230--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:07:44 MST 2002
bibtimestamp: 2002.02.02 13:07:44 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Arash Reyhani-Masoleh and M. Anwar Hasan
rawtitle: Fast Normal Basis Multiplication Using General Purpose Processors
URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2259/22590230.htm; http://link.springer-ny.com/link/service/series/0558/papers/2259/22590230.pdf

entry:
@Article{Reyhani-Masoleh:2001:FNB,
  author =       "Arash Reyhani-Masoleh and M. Anwar Hasan",
  title =        "Fast Normal Basis Multiplication Using General Purpose
                 Processors",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2259",
  pages =        "230--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:07:44 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2259.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2259/22590230.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2259/22590230.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Rinfret:2001:BSI
author: Denis Rinfret and Patrick O'Neil and Elizabeth O'Neil
title: Bit-sliced index arithmetic
journal: j-SIGMOD
volume: 30
number: 2
pages: 47--57
month: jun
monthnumber: 6
year: 2001
CODEN: SRECD8
ISSN: 0163-5808 (print), 1943-5835 (electronic) OR 01635808 (print), 19435835 (electronic)
ISSNL: 0163-5808 OR 01635808
bibdate: Mon Jan 12 08:46:06 MST 2004
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.01.12 08:46:06 MST
fjournal: ACM SIGMOD Record
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J689
rawauthor: Denis Rinfret and Patrick O'Neil and Elizabeth O'Neil
rawtitle: Bit-sliced index arithmetic
entry:
@Article{Rinfret:2001:BSI,
  author =       "Denis Rinfret and Patrick O'Neil and Elizabeth
                 O'Neil",
  title =        "Bit-sliced index arithmetic",
  journal =      j-SIGMOD,
  volume =       "30",
  number =       "2",
  pages =        "47--57",
  month =        jun,
  year =         "2001",
  CODEN =        "SRECD8",
  ISSN =         "0163-5808 (print), 1943-5835 (electronic)",
  ISSN-L =       "0163-5808",
  bibdate =      "Mon Jan 12 08:46:06 MST 2004",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGMOD Record",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J689",
}


