# bibtab

bibtype: inproceedings
filename: fparith.bib
label: Skavantzos:1992:TII
author: A. Skavantzos and N. Mitash
booktitle: IEEE Southeastcon '92, Proceedings, 12--15 April 1992
title: Theory and implementation issues of the 2-dimensional polynomial residue number system
volume: 1
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 226--233
year: 1992
DOI: https://doi.org/10.1109/SECON.1992.202342
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: A. Skavantzos and N. Mitash
rawbooktitle: {IEEE} Southeastcon '92, Proceedings, 12--15 April 1992
rawtitle: Theory and implementation issues of the 2-dimensional polynomial residue number system
entry:
@InProceedings{Skavantzos:1992:TII,
  author =       "A. Skavantzos and N. Mitash",
  booktitle =    "{IEEE} Southeastcon '92, Proceedings, 12--15 April
                 1992",
  title =        "Theory and implementation issues of the 2-dimensional
                 polynomial residue number system",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "226--233",
  year =         "1992",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/SECON.1992.202342",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "The authors present 2D polynomial residue number
                 system techniques for parallel polynomial
                 multiplication in modular rings and discuss array
                 implementation issues of such 2D polynomial
                 multipliers. A specific example design is presented.
                 The \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Skeel:1992:REP
author: R. Skeel
title: Roundoff error and the Patriot missile
journal: j-SIAM-NEWS
volume: 25
number: 4
pages: 11--1
month: jul
monthnumber: 7
year: 1992
ISSN: 0036-1437 OR 00361437
ISSNL: 0036-1437 OR 00361437
bibdate: Sat Apr 28 19:10:25 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.04.28 19:10:25 ???
URL: http://www.siam.org/siamnews/general/patriot.htm
fjournal: SIAM News
acknowledgement: ack-nhfb
journalURL: https://sinews.siam.org/
rawauthor: R. Skeel
rawtitle: Roundoff error and the {Patriot} missile
entry:
@Article{Skeel:1992:REP,
  author =       "R. Skeel",
  title =        "Roundoff error and the {Patriot} missile",
  journal =      j-SIAM-NEWS,
  volume =       "25",
  number =       "4",
  pages =        "11--1",
  month =        jul,
  year =         "1992",
  ISSN =         "0036-1437",
  ISSN-L =       "0036-1437",
  bibdate =      "Sat Apr 28 19:10:25 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.siam.org/siamnews/general/patriot.htm",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM News",
  journal-URL =  "https://sinews.siam.org/",
}


bibtype: article
filename: fparith.bib
label: Smith:1992:FPR
author: L. Montgomery Smith and B. W. Bomar and R. D. Joseph and G. C. J. Yang
title: Floating-Point Roundoff Noise Analysis of Second-Order State-Space Digital Filter Structures
journal: j-IEEE-TRANS-CIRCUITS-SYST-2
volume: 39
number: 2
pages: 90--98
month: feb
monthnumber: 2
year: 1992
CODEN: ICSPE5
DOI: https://doi.org/10.1109/82.205812
ISSN: 1057-7130 (print), 1558-125X (electronic) OR 10577130 (print), 1558125X (electronic)
ISSNL: 1057-7130 OR 10577130
bibdate: Sat Jul 16 08:40:52 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:52 MDT
fjournal: IEEE transactions on circuits and systems. 2, Analog and digital signal processing
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82
rawauthor: L. Montgomery Smith and B. W. Bomar and R. D. Joseph and G. C. J. Yang
rawtitle: Floating-Point Roundoff Noise Analysis of Second-Order State-Space Digital Filter Structures
entry:
@Article{Smith:1992:FPR,
  author =       "L. Montgomery Smith and B. W. Bomar and R. D. Joseph
                 and G. C. J. Yang",
  title =        "Floating-Point Roundoff Noise Analysis of Second-Order
                 State-Space Digital Filter Structures",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-2,
  volume =       "39",
  number =       "2",
  pages =        "90--98",
  month =        feb,
  year =         "1992",
  CODEN =        "ICSPE5",
  DOI =          "https://doi.org/10.1109/82.205812",
  ISSN =         "1057-7130 (print), 1558-125X (electronic)",
  ISSN-L =       "1057-7130",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE transactions on circuits and systems. 2, Analog
                 and digital signal processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
  summary =      "A parametric approach is used to determine the
                 roundoff noise in all real second-order floating-point
                 state-space realizations of a transfer function having
                 complex conjugate poles. The parametric roundoff noise
                 analysis is then verified by experiment \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Soudris:1992:SDAa
author: D. Soudris and V. Paliouras and T. Stouraitis
title: Systematic development of architectures for multidimensional DSP using the residue number system
volume: 3
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 397--400
year: 1992
DOI: https://doi.org/10.1109/ICASSP.1992.226192
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: D. Soudris and V. Paliouras and T. Stouraitis
rawtitle: Systematic development of architectures for multidimensional {DSP} using the residue number system
booktitle:
IEEE International Conference on Acoustics, Speech, and Signal Processing. ICASSP-92, 23--26 March 1992

rawbooktitle:
{IEEE} International Conference on Acoustics, Speech, and Signal Processing. {ICASSP-92, 23--26} March 1992

entry:
@InProceedings{Soudris:1992:SDAa,
  author =       "D. Soudris and V. Paliouras and T. Stouraitis",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing. {ICASSP-92, 23--26} March 1992",
  title =        "Systematic development of architectures for
                 multidimensional {DSP} using the residue number
                 system",
  volume =       "3",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "397--400",
  year =         "1992",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ICASSP.1992.226192",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A systematic methodology for mapping multidimensional
                 algorithms onto array processor architectures based on
                 the quadratic residue number system is presented. A
                 class of algorithms with separable functions, which can
                 be reduced to the computation of \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Soudris:1992:SDAb
author: D. Soudris and V. Paliouras and T. Stouraitis
title: Systematic development of architectures for multidimensional DSP using the residue number system
volume: 3
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 397--400
year: 1992
DOI: https://doi.org/10.1109/ICASSP.1992.226192
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: D. Soudris and V. Paliouras and T. Stouraitis
rawtitle: Systematic development of architectures for multidimensional {DSP} using the residue number system
booktitle:
IEEE International Conference on Acoustics, Speech, and Signal Processing. ICASSP-92, 23--26 March 1992

rawbooktitle:
{IEEE} International Conference on Acoustics, Speech, and Signal Processing. {ICASSP-92, 23--26} March 1992

entry:
@InProceedings{Soudris:1992:SDAb,
  author =       "D. Soudris and V. Paliouras and T. Stouraitis",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing. {ICASSP-92, 23--26} March 1992",
  title =        "Systematic development of architectures for
                 multidimensional {DSP} using the residue number
                 system",
  volume =       "3",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "397--400",
  year =         "1992",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ICASSP.1992.226192",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A systematic methodology for mapping multidimensional
                 algorithms onto array processor architectures based on
                 the quadratic residue number system is presented. A
                 class of algorithms with separable functions, which can
                 be reduced to the computation of \ldots{}",
}


bibtype: book
filename: fparith.bib
label: SPARC:1992:SAM
author: SPARC International, Inc.
title: The SPARC Architecture Manual --- Version 8
publisher: pub-PH
address: pub-PH:adr
pages: xxix + 316
year: 1992
ISBN: 0-13-825001-4 OR 0138250014
ISBN13: 978-0-13-825001-0 OR 9780138250010
LCCN: QA76.9.A73 S647 1992
bibdate: Thu Dec 16 09:12:32 1993
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1993.12.16 09:12:32 ???
acknowledgement: ack-nhfb
rawauthor: {SPARC International, Inc.}
rawtitle: The {SPARC} Architecture Manual\emdash{}Version 8
entry:
@Book{SPARC:1992:SAM,
  author =       "{SPARC International, Inc.}",
  title =        "The {SPARC} Architecture Manual\emdash{}Version 8",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xxix + 316",
  year =         "1992",
  ISBN =         "0-13-825001-4",
  ISBN-13 =      "978-0-13-825001-0",
  LCCN =         "QA76.9.A73 S647 1992",
  bibdate =      "Thu Dec 16 09:12:32 1993",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Sparmann:1992:DHQ
author: Uwe Sparmann
title: Derivation of high quality tests for large heterogeneous circuits: floating-point operations
journal: Informatik
volume: 1
pages: 425--439
year: 1992
MRclass: 94C12 (93C05)
MRnumber: 93j:94039
bibdate: Fri Dec 8 08:24:13 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 08:24:13 ???
series: Teubner-Texte Inform.
keywords: floating-point testing
acknowledgement: ack-nhfb
reviewer: Adrian Adascalitei
rawauthor: Uwe Sparmann
rawtitle: Derivation of high quality tests for large heterogeneous circuits: floating-point operations
entry:
@Article{Sparmann:1992:DHQ,
  author =       "Uwe Sparmann",
  title =        "Derivation of high quality tests for large
                 heterogeneous circuits: floating-point operations",
  journal =      "Informatik",
  volume =       "1",
  pages =        "425--439",
  year =         "1992",
  MRclass =      "94C12 (93C05)",
  MRnumber =     "93j:94039",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Teubner-Texte Inform.",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point testing",
  reviewer =     "Adrian Ad{\u{a}}sc{\u{a}}li{\c{t}}ei",
}


bibtype: article
filename: fparith.bib
label: Srinivas:1992:SFV
author: S. Srinivas and K. Dybvig
title: Superscalar Floating-Point Vector Computation in Scheme
journal: j-LECT-NOTES-COMP-SCI
number: 634
pages: 811--812
year: 1992
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: S. Srinivas and K. Dybvig
rawtitle: Superscalar Floating-Point Vector Computation in Scheme
entry:
@Article{Srinivas:1992:SFV,
  author =       "S. Srinivas and K. Dybvig",
  title =        "Superscalar Floating-Point Vector Computation in
                 Scheme",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "??",
  number =       "634",
  pages =        "811--812",
  year =         "1992",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Steidley:1992:FPA
author: C. W. Steidley
title: Floating point arithmetic basic exercises in mathematical reasoning for computer science majors
journal: j-COMP-EDU-J
volume: 2
number: 4
pages: 1--6
month: oct
monthnumber: 10
year: 1992
CODEN: CEJOE7
ISSN: 1069-3769 OR 10693769
bibdate: Tue Dec 12 09:27:13 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.12 09:27:13 MST
fjournal: Computers in education journal
acknowledgement: ack-nhfb
affiliation: Department of Computer Science, Southeastern Louisiana University, Hammond, LA, USA
rawauthor: C. W. Steidley
rawtitle: Floating point arithmetic basic exercises in mathematical reasoning for computer science majors
abstract:
Efficient mathematical (numerical) computing requires floating point computation since fixed point arithmetic limits the range of the numbers being manipulated. Fixed point arithmetic also adds to the complexity of operation by demanding a great deal of scaling among numbers with different `implicit' radix (base) points. Thus, floating point arithmetic has become a modern computing necessity. In 1988, Central Washington University introduced CPSC 321 Systems Programming into the curriculum. The course was intended to give students an opportunity to learn more about the hardware, architecture, and organization of computing machines by studying and writing systems software. Some topics considered for the initial offering of the course included: a simple assembler, a basic loader, or a simple compiler. However, many of these topics are covered in other courses and after discussions with many colleagues in the Department of Mathematics regarding the coverage of representation and use of decimal arithmetic on computers, it was decided that the fundamentals of some systems programs could be covered by introducing the basic aspects of doing mathematics on a computer from the systems point of view.

keywords:
Computer science majors; Computing machines; Computing necessity; CPSC 321 Systems Programming; Curriculum; decimal floating-point arithmetic; Floating point arithmetic; Floating point computation; Mathematical reasoning; Students; Systems software

thesaurus:
Computer science education; Digital arithmetic; Educational courses; Mathematics computing; Systems analysis; Teaching

rawabstract:
Efficient mathematical (numerical) computing requires floating point computation since fixed point arithmetic limits the range of the numbers being manipulated. Fixed point arithmetic also adds to the complexity of operation by demanding a great deal of scaling among numbers with different `implicit' radix (base) points. Thus, floating point arithmetic has become a modern computing necessity. In 1988, Central Washington University introduced CPSC 321 Systems Programming into the curriculum. The course was intended to give students an opportunity to learn more about the hardware, architecture, and organization of computing machines by studying and writing systems software. Some topics considered for the initial offering of the course included: a simple assembler, a basic loader, or a simple compiler. However, many of these topics are covered in other courses and after discussions with many colleagues in the Department of Mathematics regarding the coverage of representation and use of decimal arithmetic on computers, it was decided that the fundamentals of some systems programs could be covered by introducing the basic aspects of doing mathematics on a computer from the systems point of view.

entry:
@Article{Steidley:1992:FPA,
  author =       "C. W. Steidley",
  title =        "Floating point arithmetic basic exercises in
                 mathematical reasoning for computer science majors",
  journal =      j-COMP-EDU-J,
  volume =       "2",
  number =       "4",
  pages =        "1--6",
  month =        oct # "--" # dec,
  year =         "1992",
  CODEN =        "CEJOE7",
  ISSN =         "1069-3769",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Efficient mathematical (numerical) computing requires
                 floating point computation since fixed point arithmetic
                 limits the range of the numbers being manipulated.
                 Fixed point arithmetic also adds to the complexity of
                 operation by demanding a great deal of scaling among
                 numbers with different `implicit' radix (base) points.
                 Thus, floating point arithmetic has become a modern
                 computing necessity. In 1988, Central Washington
                 University introduced CPSC 321 Systems Programming into
                 the curriculum. The course was intended to give
                 students an opportunity to learn more about the
                 hardware, architecture, and organization of computing
                 machines by studying and writing systems software. Some
                 topics considered for the initial offering of the
                 course included: a simple assembler, a basic loader, or
                 a simple compiler. However, many of these topics are
                 covered in other courses and after discussions with
                 many colleagues in the Department of Mathematics
                 regarding the coverage of representation and use of
                 decimal arithmetic on computers, it was decided that
                 the fundamentals of some systems programs could be
                 covered by introducing the basic aspects of doing
                 mathematics on a computer from the systems point of
                 view.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Computer Science, Southeastern Louisiana
                 University, Hammond, LA, USA",
  classification = "C0220 (Education and training); C5230 (Digital
                 arithmetic methods); C6110 (Systems analysis and
                 programming); C7310 (Mathematics)",
  fjournal =     "Computers in education journal",
  keywords =     "Computer science majors; Computing machines; Computing
                 necessity; CPSC 321 Systems Programming; Curriculum;
                 decimal floating-point arithmetic; Floating point
                 arithmetic; Floating point computation; Mathematical
                 reasoning; Students; Systems software",
  thesaurus =    "Computer science education; Digital arithmetic;
                 Educational courses; Mathematics computing; Systems
                 analysis; Teaching",
}


bibtype: article
filename: fparith.bib
label: Stetter:1992:ICR
author: F. Stetter
title: Internal computer representation of integer numbers
journal: j-INFORMATIK-SPEKTRUM
volume: 15
number: 6
pages: 352--354
month: dec
monthnumber: 12
year: 1992
CODEN: INSKDW
ISSN: 0170-6012 (print), 1432-122X (electronic) OR 01706012 (print), 1432122X (electronic)
ISSNL: 0170-6012 OR 01706012
bibdate: Tue Dec 12 09:27:13 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.12 09:27:13 MST
fjournal: Informatik Spektrum
language: German
acknowledgement: ack-nhfb
affiliation: Mannheim University, Germany
journalURL: http://link.springer.com/journal/287
thesaurus: Digital arithmetic
rawauthor: F. Stetter
rawtitle: Internal computer representation of integer numbers
abstract:
Compares floating point and integer representations and presents a proposal for a unified integer representation which allows for sign. Definitions are given of two's complement and one's complement representations and rules are proposed for integer addition and subtraction, multiplication and division with various translation algorithms.

keywords:
Division; Floating point; Integer addition; Integer numbers; Integer representations; Multiplication; Subtraction; Unified integer representation

rawabstract:
Compares floating point and integer representations and presents a proposal for a unified integer representation which allows for sign. Definitions are given of two's complement and one's complement representations and rules are proposed for integer addition and subtraction, multiplication and division with various translation algorithms.

entry:
@Article{Stetter:1992:ICR,
  author =       "F. Stetter",
  title =        "Internal computer representation of integer numbers",
  journal =      j-INFORMATIK-SPEKTRUM,
  volume =       "15",
  number =       "6",
  pages =        "352--354",
  month =        dec,
  year =         "1992",
  CODEN =        "INSKDW",
  ISSN =         "0170-6012 (print), 1432-122X (electronic)",
  ISSN-L =       "0170-6012",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Compares floating point and integer representations
                 and presents a proposal for a unified integer
                 representation which allows for sign. Definitions are
                 given of two's complement and one's complement
                 representations and rules are proposed for integer
                 addition and subtraction, multiplication and division
                 with various translation algorithms.",
  acknowledgement = ack-nhfb,
  affiliation =  "Mannheim University, Germany",
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "Informatik Spektrum",
  journal-URL =  "http://link.springer.com/journal/287",
  keywords =     "Division; Floating point; Integer addition; Integer
                 numbers; Integer representations; Multiplication;
                 Subtraction; Unified integer representation",
  language =     "German",
  pubcountry =   "Germany",
  thesaurus =    "Digital arithmetic",
}


bibtype: article
filename: fparith.bib
label: Stouraitis:1992:ECR
author: T. Stouraitis
title: Efficient convertors for residue and quadratic-residue number systems
journal: Circuits, Devices and Systems, IEE Proceedings G
volume: 139
number: 6
pages: 626--634
month: dec
monthnumber: 12
year: 1992
DOI: https://doi.org/10.1109/78.157231
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
URL: https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4741
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: T. Stouraitis
rawtitle: Efficient convertors for residue and quadratic-residue number systems
entry:
@Article{Stouraitis:1992:ECR,
  author =       "T. Stouraitis",
  title =        "Efficient convertors for residue and quadratic-residue
                 number systems",
  journal =      "Circuits, Devices and Systems, IEE Proceedings G",
  volume =       "139",
  number =       "6",
  pages =        "626--634",
  month =        dec,
  year =         "1992",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/78.157231",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4741",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "The quadratic-residue number system (QRNS) is known to
                 be efficient for complex-number calculations, since it
                 eliminates the need for cross-product terms and offers
                 high speed with small hardware complexity. However, the
                 conversion overhead between \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Sun:1992:CTA
author: J.-D. Sun and H. Krishna
journal: j-IEEE-TRANS-CIRCUITS-SYST-2
volume: 39
number: 1
pages: 18--34
month: jan
monthnumber: 1
year: 1992
CODEN: ICSPE5
DOI: https://doi.org/10.1109/82.204107
ISSN: 1057-7130 (print), 1558-125X (electronic) OR 10577130 (print), 1558125X (electronic)
ISSNL: 1057-7130 OR 10577130
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
URL: https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=5240
fjournal: IEEE Transactions on Circuits and Systems. 2, Analog and Digital Signal Processing
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82
rawauthor: J.-D. Sun and H. Krishna
title:
A coding theory approach to error control in redundant residue number systems. II. Multiple error detection and correction

rawtitle:
A coding theory approach to error control in redundant residue number systems. {II}. Multiple error detection and correction

entry:
@Article{Sun:1992:CTA,
  author =       "J.-D. Sun and H. Krishna",
  title =        "A coding theory approach to error control in redundant
                 residue number systems. {II}. Multiple error detection
                 and correction",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-2,
  volume =       "39",
  number =       "1",
  pages =        "18--34",
  month =        jan,
  year =         "1992",
  CODEN =        "ICSPE5",
  DOI =          "https://doi.org/10.1109/82.204107",
  ISSN =         "1057-7130 (print), 1558-125X (electronic)",
  ISSN-L =       "1057-7130",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=5240",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems. 2, Analog
                 and Digital Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
  keywords =     "residue arithmetic; residue number system",
  summary =      "For pt.I see ibid., vol.39, no.1, p.8-17 (1992). The
                 coding theory approach to error control in redundant
                 residue number systems (RRNSs) is extended by deriving
                 computationally efficient algorithms for correcting
                 multiple errors, single-burst-error, \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Takagi:1992:MMH
author: N. Takagi and S. Yajima
journal: j-IEEE-TRANS-COMPUT
volume: 41
number: 7
pages: 887--891
month: jul
monthnumber: 7
year: 1992
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.256444
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 10:49:18 MDT 2011
bibtimestamp: 2011.07.07 10:49:18 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=256444
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: N. Takagi and S. Yajima
title:
Modular multiplication hardware algorithms with a redundant representation and their application to RSA cryptosystem

bibsource:
https://www.math.utah.edu/pub/tex/bib/cryptography1990.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib

rawtitle:
Modular multiplication hardware algorithms with a redundant representation and their application to {RSA} cryptosystem

entry:
@Article{Takagi:1992:MMH,
  author =       "N. Takagi and S. Yajima",
  title =        "Modular multiplication hardware algorithms with a
                 redundant representation and their application to {RSA}
                 cryptosystem",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "7",
  pages =        "887--891",
  month =        jul,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.256444",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 10:49:18 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=256444",
  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: Takagi:1992:RMM
author: N. Takagi
title: A radix-$4$ modular multiplication hardware algorithm for modular exponentiation
journal: j-IEEE-TRANS-COMPUT
volume: 41
number: 8
pages: 949--956
month: aug
monthnumber: 8
year: 1992
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.156537
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 10:49:19 MDT 2011
bibtimestamp: 2011.07.07 10:49:19 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156537
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: N. Takagi
rawtitle: A radix-$4$ modular multiplication hardware algorithm for modular exponentiation
entry:
@Article{Takagi:1992:RMM,
  author =       "N. Takagi",
  title =        "A radix-$4$ modular multiplication hardware algorithm
                 for modular exponentiation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "8",
  pages =        "949--956",
  month =        aug,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.156537",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 10:49:19 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156537",
  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: Tang:1992:TDI
author: Ping Tak Peter Tang
title: Table-Driven Implementation of the tt Expm1 Function in IEEE Floating-Point Arithmetic
journal: j-TOMS
volume: 18
number: 2
pages: 211--222
month: jun
monthnumber: 6
year: 1992
CODEN: ACMSCU
DOI: https://doi.org/10.1145/146847.146928
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 65D15
MRnumber: 1 167 891
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
note: See independent analysis and accuracy confirmation of this algorithm in cite Kramer:1998:PWC.
URL: http://www.acm.org/pubs/citations/journals/toms/1992-18-2/p211-tang/
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Ping Tak Peter Tang
rawnote: See independent analysis and accuracy confirmation of this algorithm in \cite{Kramer:1998:PWC}.
rawtitle: Table-Driven Implementation of the {{\tt Expm1}} Function in {IEEE} Floating-Point Arithmetic
abstract:
Algorithms and implementation details for the function $ e^x - 1 $ in both single and double precision of IEEE 754 arithmetic are presented here. With a table of moderate size, the implementations need only working-precision arithmetic and are provably accurate to within 0.58 ulp.

subject:
bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic. bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Error analysis. bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.

rawabstract:
Algorithms and implementation details for the function $ e^x - 1 $ in both single and double precision of IEEE 754 arithmetic are presented here. With a table of moderate size, the implementations need only working-precision arithmetic and are provably accurate to within 0.58 ulp.

entry:
@Article{Tang:1992:TDI,
  author =       "Ping Tak Peter Tang",
  title =        "Table-Driven Implementation of the {{\tt Expm1}}
                 Function in {IEEE} Floating-Point Arithmetic",
  journal =      j-TOMS,
  volume =       "18",
  number =       "2",
  pages =        "211--222",
  month =        jun,
  year =         "1992",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/146847.146928",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D15",
  MRnumber =     "1 167 891",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See independent analysis and accuracy confirmation of
                 this algorithm in \cite{Kramer:1998:PWC}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1992-18-2/p211-tang/",
  abstract =     "Algorithms and implementation details for the function
                 $ e^x - 1 $ in both single and double precision of IEEE
                 754 arithmetic are presented here. With a table of
                 moderate size, the implementations need only
                 working-precision arithmetic and are provably accurate
                 to within 0.58 ulp.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Computer arithmetic. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Error analysis. {\bf G.1.0}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Algorithm analysis.",
}


bibtype: inproceedings
filename: fparith.bib
label: Teufel:1992:IFP
author: Thomas Teufel
crossref: Atanassova:1992:CAE
pages: 147--156
year: 1992
bibdate: Sat Sep 17 19:12:26 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.17 19:12:26 ???
acknowledgement: ack-nhfb
rawauthor: Thomas Teufel
title:
Implementation of a floating-point arithmetic with an accurate scalar product for digital signal processing

rawtitle:
Implementation of a floating-point arithmetic with an accurate scalar product for digital signal processing

entry:
@InProceedings{Teufel:1992:IFP,
  author =       "Thomas Teufel",
  title =        "Implementation of a floating-point arithmetic with an
                 accurate scalar product for digital signal processing",
  crossref =     "Atanassova:1992:CAE",
  pages =        "147--156",
  year =         "1992",
  bibdate =      "Sat Sep 17 19:12:26 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: mastersthesis
filename: fparith.bib
label: Thirumalaiswamy:1992:DSB
author: Vijayashree Thirumalaiswamy
title: Design and simulation of bit-serial floating point arithmetic co-processor
type: Thesis (M.S.)
school: University of Texas at El Paso
address: El Paso, TX, USA
pages: xii + 113
year: 1992
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Array processors --- Design.; Floating-point arithmetic.
acknowledgement: ack-nhfb
rawauthor: Vijayashree Thirumalaiswamy
rawtitle: Design and simulation of bit-serial floating point arithmetic co-processor
entry:
@MastersThesis{Thirumalaiswamy:1992:DSB,
  author =       "Vijayashree Thirumalaiswamy",
  title =        "Design and simulation of bit-serial floating point
                 arithmetic co-processor",
  type =         "Thesis ({M.S.})",
  school =       "University of Texas at El Paso",
  address =      "El Paso, TX, USA",
  pages =        "xii + 113",
  year =         "1992",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Array processors --- Design.; Floating-point
                 arithmetic.",
}


bibtype: article
filename: fparith.bib
label: Timmermann:1992:LLT
author: D. Timmermann and H. Hahn and B. J. Hosticka
title: Low Latency Time CORDIC Algorithms
journal: j-IEEE-TRANS-COMPUT
volume: 41
number: 8
pages: 1010--1015
month: aug
monthnumber: 8
year: 1992
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.156543
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Sep 08 00:52:02 1994
bibtimestamp: 1994.09.08 00:52:02 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: D. Timmermann and H. Hahn and B. J. Hosticka
rawtitle: Low Latency Time {CORDIC} Algorithms
bibsource:
https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib

entry:
@Article{Timmermann:1992:LLT,
  author =       "D. Timmermann and H. Hahn and B. J. Hosticka",
  title =        "Low Latency Time {CORDIC} Algorithms",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "8",
  pages =        "1010--1015",
  month =        aug,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.156543",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 08 00:52:02 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  acknowledgement = ack-nj,
  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: Vowels:1992:D
author: R. A. Vowels
title: Division by 10
journal: j-AUSTRALIAN-COMP-J
volume: 24
number: 3
pages: 81--85
month: aug
monthnumber: 8
year: 1992
CODEN: ACMJB2
ISSN: 0004-8917 OR 00048917
bibdate: Tue Dec 12 09:27:13 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.12 09:27:13 MST
fjournal: Australian Computer Journal
acknowledgement: ack-nhfb
affiliation: Department of Computer Science, R. Melbourne Inst. of Technol. Ltd., Vic., Australia
thesaurus: Digital arithmetic; Mathematics computing
rawauthor: R. A. Vowels
rawtitle: Division by 10
abstract:
Division of a binary integer and a binary floating-point mantissa by 10 can be performed with shifts and adds, yielding a significant improvement in hardware execution time, and in software execution time if no hardware divide instruction is available. Several algorithms are given, appropriate to specific machine word sizes, hardware and hardware instructions available, and depending on whether a remainder is required. The integer division algorithms presented here contain a new strategy that produces the correct quotient directly, without the need for the supplementary correction required of previously-published algorithms. The algorithms are competitive in time with binary coded decimal (BCD) divide by 10. Both the integer and floating-point algorithms are an order of magnitude faster than conventional division.

keywords:
Binary integer; decimal floating-point arithmetic; Floating-point algorithms; Hardware execution time; Integer division algorithms; Software execution time

rawabstract:
Division of a binary integer and a binary floating-point mantissa by 10 can be performed with shifts and adds, yielding a significant improvement in hardware execution time, and in software execution time if no hardware divide instruction is available. Several algorithms are given, appropriate to specific machine word sizes, hardware and hardware instructions available, and depending on whether a remainder is required. The integer division algorithms presented here contain a new strategy that produces the correct quotient directly, without the need for the supplementary correction required of previously-published algorithms. The algorithms are competitive in time with binary coded decimal (BCD) divide by 10. Both the integer and floating-point algorithms are an order of magnitude faster than conventional division.

entry:
@Article{Vowels:1992:D,
  author =       "R. A. Vowels",
  title =        "Division by 10",
  journal =      j-AUSTRALIAN-COMP-J,
  volume =       "24",
  number =       "3",
  pages =        "81--85",
  month =        aug,
  year =         "1992",
  CODEN =        "ACMJB2",
  ISSN =         "0004-8917",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Division of a binary integer and a binary
                 floating-point mantissa by 10 can be performed with
                 shifts and adds, yielding a significant improvement in
                 hardware execution time, and in software execution time
                 if no hardware divide instruction is available. Several
                 algorithms are given, appropriate to specific machine
                 word sizes, hardware and hardware instructions
                 available, and depending on whether a remainder is
                 required. The integer division algorithms presented
                 here contain a new strategy that produces the correct
                 quotient directly, without the need for the
                 supplementary correction required of
                 previously-published algorithms. The algorithms are
                 competitive in time with binary coded decimal (BCD)
                 divide by 10. Both the integer and floating-point
                 algorithms are an order of magnitude faster than
                 conventional division.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Computer Science, R. Melbourne Inst. of
                 Technol. Ltd., Vic., Australia",
  classification = "C7310 (Mathematics)",
  fjournal =     "Australian Computer Journal",
  keywords =     "Binary integer; decimal floating-point arithmetic;
                 Floating-point algorithms; Hardware execution time;
                 Integer division algorithms; Software execution time",
  pubcountry =   "Australia",
  thesaurus =    "Digital arithmetic; Mathematics computing",
}


bibtype: mastersthesis
filename: fparith.bib
label: Wang:1992:RAF
author: Jie Wang
title: Response analysis for floating point implementations of linear discrete systems
type: Thesis (M.S.E.E.)
school: University of Notre Dame
address: Notre Dame, IN 46556, USA
pages: xi + 83
year: 1992
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
acknowledgement: ack-nhfb
rawauthor: Jie Wang
rawtitle: Response analysis for floating point implementations of linear discrete systems
entry:
@MastersThesis{Wang:1992:RAF,
  author =       "Jie Wang",
  title =        "Response analysis for floating point implementations
                 of linear discrete systems",
  type =         "Thesis ({M.S.E.E.})",
  school =       "University of Notre Dame",
  address =      "Notre Dame, IN 46556, USA",
  pages =        "xi + 83",
  year =         "1992",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Weber-Wulff:1992:REC
author: Debora Weber-Wulff
title: Rounding error changes Parliament makeup
journal: The Risks Digest
volume: 13
number: 37
pages: 8--8
year: 1992
bibdate: Sat Apr 28 19:12:42 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.04.28 19:12:42 ???
URL: http://catless.ncl.ac.uk/Risks/13.37.html#subj4
acknowledgement: ack-nhfb
rawauthor: Debora Weber-Wulff
rawtitle: Rounding error changes {Parliament} makeup
entry:
@Article{Weber-Wulff:1992:REC,
  author =       "Debora Weber-Wulff",
  title =        "Rounding error changes {Parliament} makeup",
  journal =      "The Risks Digest",
  volume =       "13",
  number =       "37",
  pages =        "8--8",
  year =         "1992",
  bibdate =      "Sat Apr 28 19:12:42 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://catless.ncl.ac.uk/Risks/13.37.html#subj4",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Werter:1992:SLC
author: M. J. Werter
journal: j-IEEE-TRANS-SIG-PROC
volume: 40
number: 6
pages: 1599--1601
month: jun
monthnumber: 6
year: 1992
CODEN: ITPRED
ISSN: 1053-587X (print), 1941-0476 (electronic) OR 1053587X (print), 19410476 (electronic)
ISSNL: 1053-587X OR 1053587X
bibdate: Sat Jul 16 11:25:03 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:03 MDT
fjournal: IEEE Transactions on Signal Processing
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78
rawauthor: M. J. Werter
title:
Suppression of limit cycles in the first-order two-dimensional direct form digital filter with a controlled rounding arithmetic

rawtitle:
Suppression of limit cycles in the first-order two-dimensional direct form digital filter with a controlled rounding arithmetic

entry:
@Article{Werter:1992:SLC,
  author =       "M. J. Werter",
  title =        "Suppression of limit cycles in the first-order
                 two-dimensional direct form digital filter with a
                 controlled rounding arithmetic",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "40",
  number =       "6",
  pages =        "1599--1601",
  month =        jun,
  year =         "1992",
  CODEN =        "ITPRED",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  bibdate =      "Sat Jul 16 11:25:03 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  summary =      "The first-order two-dimensional direct-form digital
                 filter with magnitude truncation is known to be free
                 from limit cycles for a limited range of allowed filter
                 coefficients. In this correspondence, the quantization
                 technique of controlled rounding \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Wesner:1992:TS
author: J. Wesner
title: Ein Tick schneller toenglish A Tick Faster endtoenglish
journal: j-MC
volume: 2
pages: 80--86
year: 1992
ISSN: 0720-4442, 0941-777x, 0943-5409 OR 07204442, 0941777x, 09435409
bibdate: Fri Sep 16 16:30:40 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.16 16:30:40 ???
fjournal: MC: Die Mikrocomputer-Zeitschrift
acknowledgement: ack-nj
rawauthor: J. Wesner
rawtitle: {Ein Tick schneller} \toenglish {A Tick Faster} \endtoenglish
entry:
@Article{Wesner:1992:TS,
  author =       "J. Wesner",
  title =        "{Ein Tick schneller} \toenglish {A Tick Faster}
                 \endtoenglish",
  journal =      j-MC,
  volume =       "2",
  pages =        "80--86",
  year =         "1992",
  ISSN =         "0720-4442, 0941-777x, 0943-5409",
  bibdate =      "Fri Sep 16 16:30:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "MC: Die Mikrocomputer-Zeitschrift",
}


bibtype: article
filename: fparith.bib
label: Wichmann:1992:NUF
author: Brian A. Wichmann
title: A Note on the Use of Floating Point in Critical Systems
journal: j-COMP-J
volume: 35
number: 1
pages: 41--44
month: feb
monthnumber: 2
year: 1992
CODEN: CMPJA6
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
bibdate: Sat Feb 24 15:01:45 MST 1996
bibtimestamp: 1996.02.24 15:01:45 MST
URL: http://www3.oup.co.uk/computer_journal/Volume_35/Issue_01/Vol35_01.body.html#AbstractWichmann
fjournal: The Computer Journal
keywords: critical systems; digital arithmetic; faults; floating point; Floating point; safety systems
acknowledgement: ack-nhfb
affiliation: NPL, Teddington, UK
classcodes: C5230 (Digital arithmetic methods)
corpsource: NPL, Teddington, UK
journalURL: http://comjnl.oxfordjournals.org/
thesaurus: Digital arithmetic; Safety systems
treatment: P Practical
rawauthor: Brian A. Wichmann
rawtitle: A Note on the Use of Floating Point in Critical Systems
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://www3.oup.co.uk/computer_journal/Volume_35/Issue_01/Vol35_01.index.html; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
Floating point is a well tried technology which, it might seem, can be used without reservation. Unfortunately, there are dangers which arise from faults in implementation and incorrect use. These are often hard to locate. The paper addresses these dangers.

rawabstract:
Floating point is a well tried technology which, it might seem, can be used without reservation. Unfortunately, there are dangers which arise from faults in implementation and incorrect use. These are often hard to locate. The paper addresses these dangers.

entry:
@Article{Wichmann:1992:NUF,
  author =       "Brian A. Wichmann",
  title =        "A Note on the Use of Floating Point in Critical
                 Systems",
  journal =      j-COMP-J,
  volume =       "35",
  number =       "1",
  pages =        "41--44",
  month =        feb,
  year =         "1992",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www3.oup.co.uk/computer_journal/Volume_35/Issue_01/Vol35_01.index.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/Volume_35/Issue_01/Vol35_01.body.html#AbstractWichmann",
  abstract =     "Floating point is a well tried technology which, it
                 might seem, can be used without reservation.
                 Unfortunately, there are dangers which arise from
                 faults in implementation and incorrect use. These are
                 often hard to locate. The paper addresses these
                 dangers.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "NPL, Teddington, UK",
  author-1-adr = "National Physical Laboratory, Teddington, Middlesex
                 TW11 OLW",
  classcodes =   "C5230 (Digital arithmetic methods)",
  classification = "C5230 (Digital arithmetic methods)",
  corpsource =   "NPL, Teddington, UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "critical systems; digital arithmetic; faults; floating
                 point; Floating point; safety systems",
  pubcountry =   "UK",
  thesaurus =    "Digital arithmetic; Safety systems",
  treatment =    "P Practical",
}


bibtype: article
filename: fparith.bib
label: Wichmann:1992:SFW
author: Brian A. Wichmann
title: Surveyor's Forum: ``What Every Computer Scientist Should Know About Floating-Point Arithmetic''
journal: j-COMP-SURV
volume: 24
number: 3
pages: 319--319
month: sep
monthnumber: 9
year: 1992
CODEN: CMSVAN
ISSN: 0360-0300 (print), 1557-7341 (electronic) OR 03600300 (print), 15577341 (electronic)
ISSNL: 0360-0300 OR 03600300
bibdate: Sun Sep 25 10:14:37 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.25 10:14:37 ???
note: See cite Goldberg:1991:WEC,Goldberg:1991:CWE,Dunham:1992:SFW.
fjournal: ACM Computing Surveys
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J204
rawauthor: Brian A. Wichmann
rawnote: See \cite{Goldberg:1991:WEC,Goldberg:1991:CWE,Dunham:1992:SFW}.
rawtitle: {Surveyor's Forum}: ``{What} Every Computer Scientist Should Know About Floating-Point Arithmetic''
entry:
@Article{Wichmann:1992:SFW,
  author =       "Brian A. Wichmann",
  title =        "{Surveyor's Forum}: ``{What} Every Computer Scientist
                 Should Know About Floating-Point Arithmetic''",
  journal =      j-COMP-SURV,
  volume =       "24",
  number =       "3",
  pages =        "319--319",
  month =        sep,
  year =         "1992",
  CODEN =        "CMSVAN",
  ISSN =         "0360-0300 (print), 1557-7341 (electronic)",
  ISSN-L =       "0360-0300",
  bibdate =      "Sun Sep 25 10:14:37 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See
                 \cite{Goldberg:1991:WEC,Goldberg:1991:CWE,Dunham:1992:SFW}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Computing Surveys",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J204",
}


bibtype: article
filename: fparith.bib
label: Wilkes:1992:E
author: Maurice V. Wilkes
title: EDSAC 2
journal: j-IEEE-ANN-HIST-COMPUT
volume: 14
number: 4
pages: 49--56
month: oct
monthnumber: 10
year: 1992
CODEN: IAHCEX
DOI: https://doi.org/10.1109/85.194055
ISSN: 1058-6180 (print), 1934-1547 (electronic) OR 10586180 (print), 19341547 (electronic)
ISSNL: 1058-6180 OR 10586180
bibdate: Thu Jul 12 06:22:54 MDT 2001
bibtimestamp: 2001.07.12 06:22:54 MDT
fjournal: IEEE Annals of the History of Computing
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=85
rawauthor: Maurice V. Wilkes
rawtitle: {EDSAC 2}
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeeannhistcomput.bib

URL:
http://dlib.computer.org/an/books/an1992/pdf/a4049.pdf; http://www.computer.org/annals/an1992/a4049abs.htm

remark:
From page 54: ``When the machine was initialized for a new program to be run, every bit in the memory was set to a 1, rather than to a 0. Since, according to the format used for floating numbers, no floating number could consist entirely of 1's, any attempt to read a floating-point number from part of the memory that had not been written into caused the machine to stop. Many a programmer must have been grateful to [David J.] Wheeler for his foresight in making this happen.''

entry:
@Article{Wilkes:1992:E,
  author =       "Maurice V. Wilkes",
  title =        "{EDSAC 2}",
  journal =      j-IEEE-ANN-HIST-COMPUT,
  volume =       "14",
  number =       "4",
  pages =        "49--56",
  month =        oct # "--" # dec,
  year =         "1992",
  CODEN =        "IAHCEX",
  DOI =          "https://doi.org/10.1109/85.194055",
  ISSN =         "1058-6180 (print), 1934-1547 (electronic)",
  ISSN-L =       "1058-6180",
  bibdate =      "Thu Jul 12 06:22:54 MDT 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeeannhistcomput.bib",
  URL =          "http://dlib.computer.org/an/books/an1992/pdf/a4049.pdf;
                 http://www.computer.org/annals/an1992/a4049abs.htm",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Annals of the History of Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=85",
  remark =       "From page 54: ``When the machine was initialized for a
                 new program to be run, every bit in the memory was set
                 to a 1, rather than to a 0. Since, according to the
                 format used for floating numbers, no floating number
                 could consist entirely of 1's, any attempt to read a
                 floating-point number from part of the memory that had
                 not been written into caused the machine to stop. Many
                 a programmer must have been grateful to [David J.]
                 Wheeler for his foresight in making this happen.''",
}


bibtype: article
filename: fparith.bib
label: Wilt:1992:ALP
author: Nicholas Wilt
title: Assembly language programming for the 80*87
journal: j-DDJ
volume: 17
number: 3
pages: 36, 38, 40, 42, 88
month: mar
monthnumber: 3
year: 1992
CODEN: DDJOEB
ISSN: 1044-789X OR 1044789X
bibdate: Tue Sep 10 10:06:23 MDT 1996
bibsource: http://www.ddj.com/index/author/index.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.09.10 10:06:23 MDT
fjournal: Dr. Dobb's Journal of Software Tools
acknowledgement: ack-nhfb
rawauthor: Nicholas Wilt
rawtitle: Assembly language programming for the 80*87
keywords:
80*87 Coprocessor; Assembly language programming; Floating point arithmetic; Numeric coprocessors; Optimization

thesaurus:
Assembly language listings; Digital arithmetic; Microprocessor chips; Optimisation; Programming; Satellite computers

entry:
@Article{Wilt:1992:ALP,
  author =       "Nicholas Wilt",
  title =        "Assembly language programming for the 80*87",
  journal =      j-DDJ,
  volume =       "17",
  number =       "3",
  pages =        "36, 38, 40, 42, 88",
  month =        mar,
  year =         "1992",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Tue Sep 10 10:06:23 MDT 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C5130 (Microprocessor chips); C5230 (Digital
                 arithmetic methods); C6110 (Systems analysis and
                 programming)",
  fjournal =     "Dr. Dobb's Journal of Software Tools",
  keywords =     "80*87 Coprocessor; Assembly language programming;
                 Floating point arithmetic; Numeric coprocessors;
                 Optimization",
  thesaurus =    "Assembly language listings; Digital arithmetic;
                 Microprocessor chips; Optimisation; Programming;
                 Satellite computers",
}


bibtype: article
filename: fparith.bib
label: Wong:1992:DSR
author: W. F. Wong and E. Goto
title: Division and square-rooting using a split multiplier
journal: j-ELECT-LETTERS
volume: 28
number: 18
pages: 1758--1759
day: 27
month: aug
monthnumber: 8
year: 1992
CODEN: ELLEAK
ISSN: 0013-5194 (print), 1350-911X (electronic) OR 00135194 (print), 1350911X (electronic)
ISSNL: 0013-5194 OR 00135194
bibdate: Wed Dec 13 13:13:34 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.13 13:13:34 MST
fjournal: Electronics Letters
keywords: Division; Fast floating point multiplication circuit; Split multiplier; Square-rooting
acknowledgement: ack-nhfb
affiliation: Goto Lab., Inst. of Phys. and Chem. Res., Saitama, Japan
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220
thesaurus: Digital arithmetic; Dividing circuits; Logic circuits; Multiplying circuits
rawauthor: W. F. Wong and E. Goto
rawtitle: Division and square-rooting using a split multiplier
abstract:
A modification is proposed to the traditional design of a fast floating point multiplication circuit such that instead of just performing $ A * B $ where $A$ and $B$ are $m$ bits long, it is also capable of performing $ C * x_0$ and $ D * x_1$ where $C$ and $D$ are still m bits long but $ x_0$ and $ x_1$ are $ m / 2$ bits long using about the same amount of hardware resources but in two thirds of the time. Such a circuit is called a split multiplier. The authors show how such a split multiplier can be used to compute division and $ Y sqrt X$ accurately and quickly.

rawabstract:
A modification is proposed to the traditional design of a fast floating point multiplication circuit such that instead of just performing $ A * B $ where $A$ and $B$ are $m$ bits long, it is also capable of performing $ C * x_0$ and $ D * x_1$ where $C$ and $D$ are still m bits long but $ x_0$ and $ x_1$ are $ m / 2$ bits long using about the same amount of hardware resources but in two thirds of the time. Such a circuit is called a split multiplier. The authors show how such a split multiplier can be used to compute division and $ Y \sqrt {X}$ accurately and quickly.

entry:
@Article{Wong:1992:DSR,
  author =       "W. F. Wong and E. Goto",
  title =        "Division and square-rooting using a split multiplier",
  journal =      j-ELECT-LETTERS,
  volume =       "28",
  number =       "18",
  pages =        "1758--1759",
  day =          "27",
  month =        aug,
  year =         "1992",
  CODEN =        "ELLEAK",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Wed Dec 13 13:13:34 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A modification is proposed to the traditional design
                 of a fast floating point multiplication circuit such
                 that instead of just performing $ A * B $ where $A$ and
                 $B$ are $m$ bits long, it is also capable of performing
                 $ C * x_0$ and $ D * x_1$ where $C$ and $D$ are still m
                 bits long but $ x_0$ and $ x_1$ are $ m / 2$ bits long
                 using about the same amount of hardware resources but
                 in two thirds of the time. Such a circuit is called a
                 split multiplier. The authors show how such a split
                 multiplier can be used to compute division and $ Y
                 \sqrt {X}$ accurately and quickly.",
  acknowledgement = ack-nhfb,
  affiliation =  "Goto Lab., Inst. of Phys. and Chem. Res., Saitama,
                 Japan",
  classification = "B1265B (Logic circuits); C5120 (Logic and switching
                 circuits); C5230 (Digital arithmetic methods)",
  fjournal =     "Electronics Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  keywords =     "Division; Fast floating point multiplication circuit;
                 Split multiplier; Square-rooting",
  pubcountry =   "UK",
  thesaurus =    "Digital arithmetic; Dividing circuits; Logic circuits;
                 Multiplying circuits",
}


bibtype: article
filename: fparith.bib
label: Wong:1992:FDU
author: D. Wong and M. Flynn
title: Fast Division Using Accurate Quotient Approximations to Reduce the Number of Iterations
journal: j-IEEE-TRANS-COMPUT
volume: 41
number: 8
pages: 981--995
month: aug
monthnumber: 8
year: 1992
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.156541
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 10:49:19 MDT 2011
bibtimestamp: 2011.07.07 10:49:19 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156541
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: D. Wong and M. Flynn
rawtitle: Fast Division Using Accurate Quotient Approximations to Reduce the Number of Iterations
entry:
@Article{Wong:1992:FDU,
  author =       "D. Wong and M. Flynn",
  title =        "Fast Division Using Accurate Quotient Approximations
                 to Reduce the Number of Iterations",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "8",
  pages =        "981--995",
  month =        aug,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.156541",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 10:49:19 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156541",
  acknowledgement = ack-nj # "\slash " # 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: Woods:1992:HPD
author: R. F. Woods and S. E. McQuillan and J. Dowling and J. V. McCanny
booktitle: Proceedings of Fifth Annual IEEE International ASIC Conference and Exhibit, 1992
title: High performance DSP ASIC for multiply, divide and square root
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 209--213
year: 1992
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: R. F. Woods and S. E. McQuillan and J. Dowling and J. V. McCanny
rawbooktitle: Proceedings of Fifth Annual {IEEE} International {ASIC} Conference and Exhibit, 1992
rawtitle: High performance {DSP} {ASIC} for multiply, divide and square root
entry:
@InProceedings{Woods:1992:HPD,
  author =       "R. F. Woods and S. E. McQuillan and J. Dowling and J.
                 V. McCanny",
  booktitle =    "Proceedings of Fifth Annual {IEEE} International
                 {ASIC} Conference and Exhibit, 1992",
  title =        "High performance {DSP} {ASIC} for multiply, divide and
                 square root",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "209--213",
  year =         "1992",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "The design of a high-speed ASIC that combines the
                 operations of multiplication, division and square root
                 is described. The chip is based on a systolic array
                 architecture that uses a redundant number system and
                 allows multiplication, division, and \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Yeyios:1992:TSA
author: A. K. Yeyios
title: On two sequences of algorithms for approximating square roots
journal: j-J-COMPUT-APPL-MATH
volume: 40
number: 1
pages: 63--72
month: jun
monthnumber: 6
year: 1992
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Thu Sep 1 10:15:56 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:15:56 ???
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nj
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: A. K. Yeyios
rawtitle: On two sequences of algorithms for approximating square roots
entry:
@Article{Yeyios:1992:TSA,
  author =       "A. K. Yeyios",
  title =        "On two sequences of algorithms for approximating
                 square roots",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "40",
  number =       "1",
  pages =        "63--72",
  month =        jun,
  year =         "1992",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Thu Sep 1 10:15:56 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: fparith.bib
label: Yokoo:1992:OUF
author: H. Yokoo
journal: j-IEEE-TRANS-COMPUT
volume: 41
number: 8
pages: 1033--1039
month: aug
monthnumber: 8
year: 1992
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.156546
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 10:49:19 MDT 2011
bibtimestamp: 2011.07.07 10:49:19 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156546
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
affiliation: Department of Computer Science, Gunma University, Kiryu, Japan
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
thesaurus: Digital arithmetic; Number theory
rawauthor: H. Yokoo
title:
Overflow / Underflow-Free Floating-Point Number Representations with Self-Delimiting Variable-Length Exponent Field

abstract:
A class of new floating-point representations of real numbers, based on representations of the integers, is described. In the class, every representation uses a self-delimiting representation of the integers as a variable length field of the exponent, and neither overflow nor underflow appears in practice. The adopted representations of the integers are defined systematically, so that representation's of numbers greater than one have both exponent-significant and integer-fraction interpretations. Since representation errors are characterized by the length function of an underlying representation of the integers, superior systems in precision can be easily selected from the proposed class.

keywords:
Floating-point number representations; Integer representation; Real numbers; Self-delimiting variable-length exponent field

rawabstract:
A class of new floating-point representations of real numbers, based on representations of the integers, is described. In the class, every representation uses a self-delimiting representation of the integers as a variable length field of the exponent, and neither overflow nor underflow appears in practice. The adopted representations of the integers are defined systematically, so that representation's of numbers greater than one have both exponent-significant and integer-fraction interpretations. Since representation errors are characterized by the length function of an underlying representation of the integers, superior systems in precision can be easily selected from the proposed class.

rawtitle:
Overflow\slash Underflow-Free Floating-Point Number Representations with Self-Delimiting Variable-Length Exponent Field

entry:
@Article{Yokoo:1992:OUF,
  author =       "H. Yokoo",
  title =        "Overflow\slash Underflow-Free Floating-Point Number
                 Representations with Self-Delimiting Variable-Length
                 Exponent Field",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "8",
  pages =        "1033--1039",
  month =        aug,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.156546",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 10:49:19 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156546",
  abstract =     "A class of new floating-point representations of real
                 numbers, based on representations of the integers, is
                 described. In the class, every representation uses a
                 self-delimiting representation of the integers as a
                 variable length field of the exponent, and neither
                 overflow nor underflow appears in practice. The adopted
                 representations of the integers are defined
                 systematically, so that representation's of numbers
                 greater than one have both exponent-significant and
                 integer-fraction interpretations. Since representation
                 errors are characterized by the length function of an
                 underlying representation of the integers, superior
                 systems in precision can be easily selected from the
                 proposed class.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Computer Science, Gunma University,
                 Kiryu, Japan",
  ajournal =     "IEEE Trans. Comput.",
  classification = "B0250 (Combinatorial mathematics); B1265B (Logic
                 circuits); C1160 (Combinatorial mathematics); C5230
                 (Digital arithmetic methods)",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Floating-point number representations; Integer
                 representation; Real numbers; Self-delimiting
                 variable-length exponent field",
  summary =      "A class of new floating-point representations of real
                 numbers, based on representations of the integers, is
                 described. In the class, every representation uses a
                 self-delimiting representation of the integers as a
                 variable length field of the exponent \ldots{}",
  thesaurus =    "Digital arithmetic; Number theory",
}


bibtype: article
filename: fparith.bib
label: Zelniker:1992:RMC
author: G. S. Zelniker and F. J. Taylor
title: On the reduction in multiplicative complexity achieved by the polynomial residue number system
journal: j-IEEE-TRANS-SIG-PROC
volume: 40
number: 9
pages: 2318--2320
month: sep
monthnumber: 9
year: 1992
CODEN: ITPRED
DOI: https://doi.org/10.1109/78.157231
ISSN: 1053-587X (print), 1941-0476 (electronic) OR 1053587X (print), 19410476 (electronic)
ISSNL: 1053-587X OR 1053587X
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
URL: https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4075
fjournal: IEEE Transactions on Signal Processing
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78
rawauthor: G. S. Zelniker and F. J. Taylor
rawtitle: On the reduction in multiplicative complexity achieved by the polynomial residue number system
entry:
@Article{Zelniker:1992:RMC,
  author =       "G. S. Zelniker and F. J. Taylor",
  title =        "On the reduction in multiplicative complexity achieved
                 by the polynomial residue number system",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "40",
  number =       "9",
  pages =        "2318--2320",
  month =        sep,
  year =         "1992",
  CODEN =        "ITPRED",
  DOI =          "https://doi.org/10.1109/78.157231",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4075",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  keywords =     "residue arithmetic; residue number system",
  summary =      "The polynomial residue number system is known to
                 reduce the complexity of polynomial multiplication from
                 O(N 2) to O(N). A new interpretation of this complexity
                 reduction is given in the context of \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Alam:1993:RTO
author: M. S. Alam and M. A. Karim
title: Real-Time Optical Arithmetic / Logical Processing
journal: j-J-PAR-DIST-COMP
volume: 17
number: 3
pages: 251--258
month: mar
monthnumber: 3
year: 1993
CODEN: JPDCER
DOI: https://doi.org/10.1006/jpdc.1993.1024
ISSN: 0743-7315 (print), 1096-0848 (electronic) OR 07437315 (print), 10960848 (electronic)
ISSNL: 0743-7315 OR 07437315
bibdate: Thu Mar 9 09:18:51 MST 2000
bibtimestamp: 2000.03.09 09:18:51 MST
fjournal: Journal of Parallel and Distributed Computing
acknowledgement: ack-nhfb
corpsource: Department of Eng., Purdue University, Fort Wayne, IN, USA
journalURL: http://www.sciencedirect.com/science/journal/07437315
treatment: P Practical
rawauthor: M. S. Alam and M. A. Karim
rawtitle: Real-Time Optical Arithmetic\slash Logical Processing
bibsource:
http://www.idealibrary.com/servlet/useragent?func=showAllIssues&curIssueID=jpdc; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://www.idealibrary.com/links/doi/10.1006/jpdc.1993.1024/production; http://www.idealibrary.com/links/doi/10.1006/jpdc.1993.1024/production/pdf

keywords:
autocorrelation peaks; binary; coding scheme; digital arithmetic; full adder; input joint image; joint transform correlator; minterms; multiple outputs; optical logic; real time logical processing; real-time optical arithmetic; real-time systems

entry:
@Article{Alam:1993:RTO,
  author =       "M. S. Alam and M. A. Karim",
  title =        "Real-Time Optical Arithmetic\slash Logical
                 Processing",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "17",
  number =       "3",
  pages =        "251--258",
  month =        mar,
  year =         "1993",
  CODEN =        "JPDCER",
  DOI =          "https://doi.org/10.1006/jpdc.1993.1024",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Thu Mar 9 09:18:51 MST 2000",
  bibsource =    "http://www.idealibrary.com/servlet/useragent?func=showAllIssues&curIssueID=jpdc;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.idealibrary.com/links/doi/10.1006/jpdc.1993.1024/production;
                 http://www.idealibrary.com/links/doi/10.1006/jpdc.1993.1024/production/pdf",
  acknowledgement = ack-nhfb,
  classification = "B4180 (Optical logic devices and optical computing
                 techniques); C5110D (Optical logic elements)C5120
                 (Logic and switching circuits); C5230 (Digital
                 arithmetic methods); C5270 (Optical computing
                 techniques)",
  corpsource =   "Department of Eng., Purdue University, Fort Wayne, IN,
                 USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  keywords =     "autocorrelation peaks; binary; coding scheme; digital
                 arithmetic; full adder; input joint image; joint
                 transform correlator; minterms; multiple outputs;
                 optical logic; real time logical processing; real-time
                 optical arithmetic; real-time systems",
  treatment =    "P Practical",
}


bibtype: book
filename: fparith.bib
label: Albrecht:1993:VNT
editor: R. (Rudolf F.) Albrecht and G. (Gotz) Alefeld and H. (Hans) J. Stetter
title: Validation numerics: theory and applications
volume: 9
publisher: pub-SV
address: pub-SV:adr
pages: 291
year: 1993
ISBN: 3-211-82451-0 (Wien), 0-387-82451-0 (New York) OR 3211824510 (Wien), 0387824510 (New York)
LCCN: QA297 .V27 1993
bibdate: Thu Apr 02 09:18:32 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.04.02 09:18:32 ???
series: Computing (Springer-Verlag). Supplementum
acknowledgement: ack-nhfb
raweditor: R. (Rudolf F.) Albrecht and G. (G{\"o}tz) Alefeld and H. (Hans) J. Stetter
rawtitle: Validation numerics: theory and applications
ISBN13:
978-3-211-82451-1 (Wien), 978-0-387-82451-2 (New York) OR 9783211824511 (Wien), 9780387824512 (New York)

note:
This volume is dedicated to Professor Dr. Ulrich Kulisch, ldots on the occasion of his 60th birthday.

rawnote:
This volume is dedicated to Professor Dr. Ulrich Kulisch, \ldots{} on the occasion of his 60th birthday.

entry:
@Book{Albrecht:1993:VNT,
  editor =       "R. (Rudolf F.) Albrecht and G. (G{\"o}tz) Alefeld and
                 H. (Hans) J. Stetter",
  title =        "Validation numerics: theory and applications",
  volume =       "9",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "291",
  year =         "1993",
  ISBN =         "3-211-82451-0 (Wien), 0-387-82451-0 (New York)",
  ISBN-13 =      "978-3-211-82451-1 (Wien), 978-0-387-82451-2 (New
                 York)",
  LCCN =         "QA297 .V27 1993",
  bibdate =      "Thu Apr 02 09:18:32 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "This volume is dedicated to Professor Dr. Ulrich
                 Kulisch, \ldots{} on the occasion of his 60th
                 birthday.",
  series =       "Computing (Springer-Verlag). Supplementum",
  acknowledgement = ack-nhfb,
}


bibtype: mastersthesis
filename: fparith.bib
label: Alqeisi:1993:FPF
author: Yousuf Alqeisi
title: A 16-bit floating point fast Fourier transform processor using Xlinx's FPGA's
type: Thesis (M.S.)
school: Department of Electrical Engineering, Southern Illinois University at Carbondale
address: Carbondale, IL, USA
pages: v + 60
year: 1993
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
acknowledgement: ack-nhfb
rawauthor: Yousuf Alqeisi
rawtitle: A 16-bit floating point fast {Fourier} transform processor using {Xlinx}'s {FPGA's}
entry:
@MastersThesis{Alqeisi:1993:FPF,
  author =       "Yousuf Alqeisi",
  title =        "A 16-bit floating point fast {Fourier} transform
                 processor using {Xlinx}'s {FPGA's}",
  type =         "Thesis ({M.S.})",
  school =       "Department of Electrical Engineering, Southern
                 Illinois University at Carbondale",
  address =      "Carbondale, IL, USA",
  pages =        "v + 60",
  year =         "1993",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Anonymous:1993:FPa
author: Anonymous
title: Floating Point
journal: j-COMPUT-AIDED-ENG
volume: 12
number: 1
pages: 56--??
month: jan
monthnumber: 1
year: 1993
CODEN: CCAEDJ
ISSN: 0733-3536 (print), 2162-1365 (electronic) OR 07333536 (print), 21621365 (electronic)
ISSNL: 0733-3536 OR 07333536
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
abstract: Making a Case for Pencil Plotters.
fjournal: Computer-aided engineering: CAE
acknowledgement: ack-nhfb
rawabstract: Making a Case for Pencil Plotters.
rawauthor: Anonymous
rawtitle: Floating Point
entry:
@Article{Anonymous:1993:FPa,
  author =       "Anonymous",
  title =        "Floating Point",
  journal =      j-COMPUT-AIDED-ENG,
  volume =       "12",
  number =       "1",
  pages =        "56--??",
  month =        jan,
  year =         "1993",
  CODEN =        "CCAEDJ",
  ISSN =         "0733-3536 (print), 2162-1365 (electronic)",
  ISSN-L =       "0733-3536",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Making a Case for Pencil Plotters.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer-aided engineering: CAE",
}


bibtype: article
filename: fparith.bib
label: Anonymous:1993:FPb
author: Anonymous
title: Floating Point
journal: j-COMPUT-AIDED-ENG
volume: 12
number: 5
pages: 67--??
month: may
monthnumber: 5
year: 1993
CODEN: CCAEDJ
ISSN: 0733-3536 (print), 2162-1365 (electronic) OR 07333536 (print), 21621365 (electronic)
ISSNL: 0733-3536 OR 07333536
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
abstract: Component Technology.
fjournal: Computer-aided engineering: CAE
acknowledgement: ack-nhfb
rawabstract: Component Technology.
rawauthor: Anonymous
rawtitle: Floating Point
entry:
@Article{Anonymous:1993:FPb,
  author =       "Anonymous",
  title =        "Floating Point",
  journal =      j-COMPUT-AIDED-ENG,
  volume =       "12",
  number =       "5",
  pages =        "67--??",
  month =        may,
  year =         "1993",
  CODEN =        "CCAEDJ",
  ISSN =         "0733-3536 (print), 2162-1365 (electronic)",
  ISSN-L =       "0733-3536",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Component Technology.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer-aided engineering: CAE",
}


bibtype: article
filename: fparith.bib
label: Anonymous:1993:FPc
author: Anonymous
title: Floating Point
journal: j-COMPUT-AIDED-ENG
volume: 12
number: 9
pages: 48--??
month: sep
monthnumber: 9
year: 1993
CODEN: CCAEDJ
ISSN: 0733-3536 (print), 2162-1365 (electronic) OR 07333536 (print), 21621365 (electronic)
ISSNL: 0733-3536 OR 07333536
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
abstract: ProStep.
fjournal: Computer-aided engineering: CAE
acknowledgement: ack-nhfb
rawabstract: ProStep.
rawauthor: Anonymous
rawtitle: Floating Point
entry:
@Article{Anonymous:1993:FPc,
  author =       "Anonymous",
  title =        "Floating Point",
  journal =      j-COMPUT-AIDED-ENG,
  volume =       "12",
  number =       "9",
  pages =        "48--??",
  month =        sep,
  year =         "1993",
  CODEN =        "CCAEDJ",
  ISSN =         "0733-3536 (print), 2162-1365 (electronic)",
  ISSN-L =       "0733-3536",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "ProStep.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer-aided engineering: CAE",
}


bibtype: article
filename: fparith.bib
label: Anonymous:1993:FPd
author: Anonymous
title: Floating Point
journal: j-COMPUT-AIDED-ENG
volume: 12
number: 10
pages: 98--??
month: oct
monthnumber: 10
year: 1993
CODEN: CCAEDJ
ISSN: 0733-3536 (print), 2162-1365 (electronic) OR 07333536 (print), 21621365 (electronic)
ISSNL: 0733-3536 OR 07333536
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
abstract: Open Modeling Still Going Strong.
fjournal: Computer-aided engineering: CAE
acknowledgement: ack-nhfb
rawabstract: Open Modeling Still Going Strong.
rawauthor: Anonymous
rawtitle: Floating Point
entry:
@Article{Anonymous:1993:FPd,
  author =       "Anonymous",
  title =        "Floating Point",
  journal =      j-COMPUT-AIDED-ENG,
  volume =       "12",
  number =       "10",
  pages =        "98--??",
  month =        oct,
  year =         "1993",
  CODEN =        "CCAEDJ",
  ISSN =         "0733-3536 (print), 2162-1365 (electronic)",
  ISSN-L =       "0733-3536",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Open Modeling Still Going Strong.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer-aided engineering: CAE",
}


bibtype: article
filename: fparith.bib
label: Anonymous:1993:FPe
author: Anonymous
title: Floating Point
journal: j-COMPUT-AIDED-ENG
volume: 12
number: 11
pages: 42--??
month: nov
monthnumber: 11
year: 1993
CODEN: CCAEDJ
ISSN: 0733-3536 (print), 2162-1365 (electronic) OR 07333536 (print), 21621365 (electronic)
ISSNL: 0733-3536 OR 07333536
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
abstract: Cost Benefits CAD/CAM.
fjournal: Computer-aided engineering: CAE
acknowledgement: ack-nhfb
rawabstract: Cost Benefits CAD/CAM.
rawauthor: Anonymous
rawtitle: Floating Point
entry:
@Article{Anonymous:1993:FPe,
  author =       "Anonymous",
  title =        "Floating Point",
  journal =      j-COMPUT-AIDED-ENG,
  volume =       "12",
  number =       "11",
  pages =        "42--??",
  month =        nov,
  year =         "1993",
  CODEN =        "CCAEDJ",
  ISSN =         "0733-3536 (print), 2162-1365 (electronic)",
  ISSN-L =       "0733-3536",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Cost Benefits CAD/CAM.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer-aided engineering: CAE",
}


bibtype: article
filename: fparith.bib
label: Anonymous:1993:FSB
author: Anonymous
journal: j-PC-WEEK
volume: 10
number: 22
pages: 85--??
month: jun
monthnumber: 6
year: 1993
ISSN: 0740-1604 OR 07401604
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
fjournal: PC Week
acknowledgement: ack-nhfb
rawauthor: Anonymous
title:
The ``fastest system on the block'' label must be qualified with new multiplatform, floating-point benchmarks

rawtitle:
The ``fastest system on the block'' label must be qualified with new multiplatform, floating-point benchmarks

entry:
@Article{Anonymous:1993:FSB,
  author =       "Anonymous",
  title =        "The ``fastest system on the block'' label must be
                 qualified with new multiplatform, floating-point
                 benchmarks",
  journal =      j-PC-WEEK,
  volume =       "10",
  number =       "22",
  pages =        "85--??",
  month =        jun,
  year =         "1993",
  ISSN =         "0740-1604",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "PC Week",
}


bibtype: book
filename: fparith.bib
label: Anonymous:1993:SRT
author: Anonymous
title: The Square Root of Two to 100,000 digits
volume: 52
publisher: pub-PROJECT-GUTENBERG
address: pub-PROJECT-GUTENBERG:adr
pages: 85--??
year: 1993
bibdate: Sun Jan 24 10:00:27 MST 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1999.01.24 10:00:27 MST
series: ser-PROJECT-GUTENBERG
URL: ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext93/2sqrt10.zip
subject: Mathematical constants.
acknowledgement: ack-nhfb
rawauthor: Anonymous
rawtitle: The Square Root of Two to 100,000 digits
entry:
@Book{Anonymous:1993:SRT,
  author =       "Anonymous",
  title =        "The Square Root of Two to 100,000 digits",
  volume =       "52",
  publisher =    pub-PROJECT-GUTENBERG,
  address =      pub-PROJECT-GUTENBERG:adr,
  year =         "1993",
  bibdate =      "Sun Jan 24 10:00:27 MST 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       ser-PROJECT-GUTENBERG,
  URL =          "ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext93/2sqrt10.zip",
  acknowledgement = ack-nhfb # " and " # ack-st,
  subject =      "Mathematical constants.",
}


bibtype: article
filename: fparith.bib
label: Asprey:1993:PFP
author: T. Asprey and G. Averill and E. DeLano and R. Mason and B. Weiner and J. Yetter
title: Performance features of the PA7100 microprocessor
journal: j-IEEE-MICRO
volume: 13
number: 3
pages: 22--35
month: may
monthnumber: 5
year: 1993
CODEN: IEMIDZ
DOI: https://doi.org/10.1109/40.216746
ISSN: 0272-1732 (print), 1937-4143 (electronic) OR 02721732 (print), 19374143 (electronic)
ISSNL: 0272-1732 OR 02721732
bibdate: Thu Apr 2 08:38:35 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.04.02 08:38:35 ???
fjournal: IEEE Micro
acknowledgement: ack-sfo
journalURL: http://www.computer.org/csdl/mags/mi/index.html
rawauthor: T. Asprey and G. Averill and E. DeLano and R. Mason and B. Weiner and J. Yetter
rawtitle: Performance features of the {PA7100} microprocessor
entry:
@Article{Asprey:1993:PFP,
  author =       "T. Asprey and G. Averill and E. DeLano and R. Mason
                 and B. Weiner and J. Yetter",
  title =        "Performance features of the {PA7100} microprocessor",
  journal =      j-IEEE-MICRO,
  volume =       "13",
  number =       "3",
  pages =        "22--35",
  month =        may # "\slash " # jun,
  year =         "1993",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/40.216746",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
}


bibtype: book
filename: fparith.bib
label: ASTM:1993:AES
author: ASTM
publisher: ASTM International
address: West Conshohocken, PA, USA
pages: 22--35
year: 1993
bibdate: Mon May 21 17:19:21 2018
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2018.05.21 17:19:21 ???
note: Superseded by cite ASTM:2008:AES.
URL: https://www.astm.org/DATABASE.CART/HISTORICAL/E29-08.htm
remark: Cited in cite [ref. 32]Carter:2013:ESF.
acknowledgement: ack-nhfb
rawauthor: {ASTM}
rawnote: Superseded by \cite{ASTM:2008:AES}.
title:
ASTM E29-08: Standard Practice for Using Significant Digits in Test Data to Determine Conformance with Specifications

rawtitle:
{ASTM E29-08}: Standard Practice for Using Significant Digits in Test Data to Determine Conformance with Specifications

entry:
@Book{ASTM:1993:AES,
  author =       "{ASTM}",
  title =        "{ASTM E29-08}: Standard Practice for Using Significant
                 Digits in Test Data to Determine Conformance with
                 Specifications",
  publisher =    "ASTM International",
  address =      "West Conshohocken, PA, USA",
  year =         "1993",
  bibdate =      "Mon May 21 17:19:21 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Superseded by \cite{ASTM:2008:AES}.",
  URL =          "https://www.astm.org/DATABASE.CART/HISTORICAL/E29-08.htm",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite[ref. 32]{Carter:2013:ESF}.",
}


bibtype: article
filename: fparith.bib
label: Bailey:1993:AMT
author: David H. Bailey
title: Algorithm 719: Multiprecision Translation and Execution of FORTRAN Programs
journal: j-TOMS
volume: 19
number: 3
pages: 288--319
month: sep
monthnumber: 9
year: 1993
CODEN: ACMSCU
DOI: https://doi.org/10.1145/155743.155767
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Wed Dec 13 18:37:31 1995
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.13 18:37:31 ???
URL: http://www.acm.org/pubs/citations/journals/toms/1993-19-3/p288-bailey/
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
affiliation: NASA Ames Res. Center, Moffett Field, CA, USA
journalURL: https://dl.acm.org/loi/toms
rawauthor: David H. Bailey
rawtitle: {Algorithm 719}: Multiprecision Translation and Execution of {FORTRAN} Programs
abstract:
This paper describes two Fortran utilities for multiprecision computation. The first is a package of Fortran subroutines that perform a variety of arithmetic operations and transcendental functions on floating point numbers of arbitrarily high precision. This package is in some cases over 200 times faster than that of certain other packages that have been developed for this purpose.par The second utility is a translator program, which facilitates the conversion of ordinary Fortran programs to use this package. By means of source directives (special comments) in the original Fortran program, the user declares the precision level and specifies which variables in each subprogram are to be treated as multiprecision. The translator program reads this source program and outputs a program with the appropriate multiprecision subroutine calls.par This translator supports multiprecision integer, real, and complex datatypes. The required array space for multiprecision data types is automatically allocated. In the evaluation of computational expressions, all of the usual conventions for operator precedence and mixed mode operations are upheld. Furthermore, most of the Fortran-77 intrinsics, such as ABS, MOD, NINT, COS, EXP are supported and produce true multiprecision values.

keywords:
Algorithm 719; Arithmetic operations; Array space; Complex data types; Computational expressions; Floating point numbers; Fortran programs; Fortran subroutines; Fortran utilities; Fortran-77 intrinsics; Mixed mode operations; Multiprecision computation; Multiprecision data types; Multiprecision subroutine calls; Multiprecision translation; Operator precedence; Source directives; Transcendental functions; Translator program

subject:
F.2.1 [Analysis of Algorithms and Problem Complexity]: Numerical Algorithms and Problems; G.1.0 [Numerical Analysis]: General; G.1.2 [Numerical Analysis]; Approximation

thesaurus:
Data structures; Digital arithmetic; FORTRAN; Mathematics computing; Program interpreters; Subroutines

rawabstract:
This paper describes two Fortran utilities for multiprecision computation. The first is a package of Fortran subroutines that perform a variety of arithmetic operations and transcendental functions on floating point numbers of arbitrarily high precision. This package is in some cases over 200 times faster than that of certain other packages that have been developed for this purpose.\par The second utility is a translator program, which facilitates the conversion of ordinary Fortran programs to use this package. By means of source directives (special comments) in the original Fortran program, the user declares the precision level and specifies which variables in each subprogram are to be treated as multiprecision. The translator program reads this source program and outputs a program with the appropriate multiprecision subroutine calls.\par This translator supports multiprecision integer, real, and complex datatypes. The required array space for multiprecision data types is automatically allocated. In the evaluation of computational expressions, all of the usual conventions for operator precedence and mixed mode operations are upheld. Furthermore, most of the Fortran-77 intrinsics, such as ABS, MOD, NINT, COS, EXP are supported and produce true multiprecision values.

entry:
@Article{Bailey:1993:AMT,
  author =       "David H. Bailey",
  title =        "{Algorithm 719}: Multiprecision Translation and
                 Execution of {FORTRAN} Programs",
  journal =      j-TOMS,
  volume =       "19",
  number =       "3",
  pages =        "288--319",
  month =        sep,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/155743.155767",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Dec 13 18:37:31 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-3/p288-bailey/",
  abstract =     "This paper describes two Fortran utilities for
                 multiprecision computation. The first is a package of
                 Fortran subroutines that perform a variety of
                 arithmetic operations and transcendental functions on
                 floating point numbers of arbitrarily high precision.
                 This package is in some cases over 200 times faster
                 than that of certain other packages that have been
                 developed for this purpose.\par

                 The second utility is a translator program, which
                 facilitates the conversion of ordinary Fortran programs
                 to use this package. By means of source directives
                 (special comments) in the original Fortran program, the
                 user declares the precision level and specifies which
                 variables in each subprogram are to be treated as
                 multiprecision. The translator program reads this
                 source program and outputs a program with the
                 appropriate multiprecision subroutine calls.\par

                 This translator supports multiprecision integer, real,
                 and complex datatypes. The required array space for
                 multiprecision data types is automatically allocated.
                 In the evaluation of computational expressions, all of
                 the usual conventions for operator precedence and mixed
                 mode operations are upheld. Furthermore, most of the
                 Fortran-77 intrinsics, such as ABS, MOD, NINT, COS, EXP
                 are supported and produce true multiprecision values.",
  abstract-2 =   "The author describes two Fortran utilities for
                 multiprecision computation. The first is a package of
                 Fortran subroutines that perform a variety of
                 arithmetic operations and transcendental functions on
                 floating point numbers of arbitrarily high precision.
                 This package is in some cases over 200 times faster
                 than that of certain other packages that have been
                 developed for this purpose. The second utility is a
                 translator program, which facilitates the conversion of
                 ordinary Fortran programs to use this package. By means
                 of source directives (special comments) in the original
                 Fortran program, the user declares the precision level
                 and specifies which variables in each subprogram are to
                 be treated as multiprecision. The translator program
                 reads this source program and outputs a program with
                 the appropriate multiprecision subroutine calls. This
                 translator supports multiprecision integer, real, and
                 complex datatypes. The required array space for
                 multiprecision data types is automatically allocated.
                 In the evaluation of computational expressions, all of
                 the usual conventions for operator precedence and mixed
                 mode operations are upheld. Furthermore, most of the
                 Fortran-77 intrinsics, such as ABS, MOD, NINT, COS, EXP
                 are supported and produce true multiprecision values.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "NASA Ames Res. Center, Moffett Field, CA, USA",
  classification = "C5230 (Digital arithmetic methods); C6120 (File
                 organisation); C6140D (High level languages); C6150C
                 (Compilers, interpreters and other processors); C7310
                 (Mathematics)",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Algorithm 719; Arithmetic operations; Array space;
                 Complex data types; Computational expressions; Floating
                 point numbers; Fortran programs; Fortran subroutines;
                 Fortran utilities; Fortran-77 intrinsics; Mixed mode
                 operations; Multiprecision computation; Multiprecision
                 data types; Multiprecision subroutine calls;
                 Multiprecision translation; Operator precedence; Source
                 directives; Transcendental functions; Translator
                 program",
  subject =      "F.2.1 [Analysis of Algorithms and Problem Complexity]:
                 Numerical Algorithms and Problems; G.1.0 [Numerical
                 Analysis]: General; G.1.2 [Numerical Analysis];
                 Approximation",
  thesaurus =    "Data structures; Digital arithmetic; FORTRAN;
                 Mathematics computing; Program interpreters;
                 Subroutines",
}


bibtype: inproceedings
filename: fparith.bib
label: Bailey:1993:MPM
author: David H. Bailey and Robert Krasny and Richard Pelz
title: Multiple precision, multiple processor vortex sheet roll-up computation
crossref: Sincovec:1993:PSS
pages: 52--56
year: 1993
bibdate: Thu Nov 25 10:04:31 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.25 10:04:31 ???
acknowledgement: ack-nhfb
rawauthor: David H. Bailey and Robert Krasny and Richard Pelz
rawtitle: Multiple precision, multiple processor vortex sheet roll-up computation
entry:
@InProceedings{Bailey:1993:MPM,
  author =       "David H. Bailey and Robert Krasny and Richard Pelz",
  title =        "Multiple precision, multiple processor vortex sheet
                 roll-up computation",
  crossref =     "Sincovec:1993:PSS",
  pages =        "52--56",
  year =         "1993",
  bibdate =      "Thu Nov 25 10:04:31 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Bajard:1993:BNH
author: J. C. Bajard and S. Kla and Jean-Michel Muller
title: BKM: a New Hardware Algorithm for Complex Elementary Functions
crossref: Swartzlander:1993:SCA
pages: 146--153
year: 1993
bibdate: Sat Nov 17 09:46:07 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.17 09:46:07 ???
URL: http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Bajard.pdf
keywords: ARITH-11
acknowledgement: ack-nhfb
rawauthor: J. C. Bajard and S. Kla and Jean-Michel Muller
rawtitle: {BKM}: a New Hardware Algorithm for Complex Elementary Functions
entry:
@InProceedings{Bajard:1993:BNH,
  author =       "J. C. Bajard and S. Kla and Jean-Michel Muller",
  title =        "{BKM}: a New Hardware Algorithm for Complex Elementary
                 Functions",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "146--153",
  year =         "1993",
  bibdate =      "Sat Nov 17 09:46:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Bajard.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
}


bibtype: article
filename: fparith.bib
label: Baker:1993:SLR
author: Henry G. Baker, Jr.
title: Safe and leakproof resource management using Ada83 limited types
journal: j-SIGADA-LETTERS
volume: 13
number: 5
pages: 32--42
month: sep
monthnumber: 9
year: 1993
CODEN: AALEE5
ISSN: 1094-3641 (print), 1557-9476 (electronic) OR 10943641 (print), 15579476 (electronic)
ISSNL: 1094-3641 OR 10943641
bibdate: Sat Aug 9 09:05:49 MDT 2003
bibtimestamp: 2003.08.09 09:05:49 MDT
fjournal: ACM SIGAda Ada Letters
acknowledgement: ack-nhfb
affiliation: Nimble Computer Corp
affiliationaddress: Encino, CA, USA
corpsource: Nimble Comput. Corp., Encino, CA, USA
journalURL: http://portal.acm.org/citation.cfm?id=J32
journalabr: Ada Lett
treatment: P Practical; T Theoretical or Mathematical
rawauthor: Henry G. {Baker, Jr.}
rawtitle: Safe and leakproof resource management using {Ada83} limited types
bibsource:
Compendex database; http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/sigada.bib

abstract:
Safe, leakproof and automatic resource managers are essential to the implementation of every embedded system, yet the standard examples of Ada83 resource managers are either unsafe: they risk allocating the same resource for two different purposes, leaky: they risk permanently losing track of some resources, or non-automatic: they require explicit deallocation, which allows for a host of opportunities for single-point system failures. Nevertheless, it is possible to construct a safe, leakproof and automatic resource manager --- at least for systems with only a single task --- by a careful combination of certain features of Ada83, and a careful avoidance of other features. We illustrate our scheme with a safe, leakproof and fully automatic dynamic-string package. The same techniques also work for an arbitrary precision arithmetic package [Fisher83] and for managing the `roots' of a real-time garbage-collected heap [Baker78] [Baker91SP] [Baker92Tread]. Suggestions are offered to improve the use of limited private types in Ada9X for automatic, safe and leakproof resource management.

keywords:
Ada; Ada (programming language); Ada listings; Ada83 limited types; Ada83 resource; Ada9X; arbitrary precision; Arbitrary precision arithmetic package; arithmetic package; Automatic resource manager; automatic resource managers; Computer operating systems; Computer system recovery; Computer systems programming; Data collection; data structures; Deallocation; dynamic-string package; Embedded system; embedded system; explicit deallocation; failures; Information management; Interfaces (computer); Large scale systems; leakproof resource management; limited private types; management; managers; Program debugging; Real time garbage collected heap; Real time systems; real-time garbage-collected heap; real-time systems; Resource allocation; resource allocation; Resource management; Single point system failures; single-point system; software reliability; storage; Storage allocation (computer); Supervisory and executive programs; System failure

classcodes:
C6150J (Operating systems); C6110B (Software engineering techniques); C6120 (File organisation); C6140D (High level languages)

rawabstract:
Safe, leakproof and automatic resource managers are essential to the implementation of every embedded system, yet the standard examples of Ada83 resource managers are either unsafe: they risk allocating the same resource for two different purposes, leaky: they risk permanently losing track of some resources, or non-automatic: they require explicit deallocation, which allows for a host of opportunities for single-point system failures. Nevertheless, it is possible to construct a safe, leakproof and automatic resource manager --- at least for systems with only a single task --- by a careful combination of certain features of Ada83, and a careful avoidance of other features. We illustrate our scheme with a safe, leakproof and fully automatic dynamic-string package. The same techniques also work for an arbitrary precision arithmetic package [Fisher83] and for managing the `roots' of a real-time garbage-collected heap [Baker78] [Baker91SP] [Baker92Tread]. Suggestions are offered to improve the use of limited private types in Ada9X for automatic, safe and leakproof resource management.

entry:
@Article{Baker:1993:SLR,
  author =       "Henry G. {Baker, Jr.}",
  title =        "Safe and leakproof resource management using {Ada83}
                 limited types",
  journal =      j-SIGADA-LETTERS,
  volume =       "13",
  number =       "5",
  pages =        "32--42",
  month =        sep # "\slash " # oct,
  year =         "1993",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Sat Aug 9 09:05:49 MDT 2003",
  bibsource =    "Compendex database; http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigada.bib",
  abstract =     "Safe, leakproof and automatic resource managers are
                 essential to the implementation of every embedded
                 system, yet the standard examples of Ada83 resource
                 managers are either unsafe: they risk allocating the
                 same resource for two different purposes, leaky: they
                 risk permanently losing track of some resources, or
                 non-automatic: they require explicit deallocation,
                 which allows for a host of opportunities for
                 single-point system failures. Nevertheless, it is
                 possible to construct a safe, leakproof and automatic
                 resource manager --- at least for systems with only a
                 single task --- by a careful combination of certain
                 features of Ada83, and a careful avoidance of other
                 features. We illustrate our scheme with a safe,
                 leakproof and fully automatic dynamic-string package.
                 The same techniques also work for an arbitrary
                 precision arithmetic package [Fisher83] and for
                 managing the `roots' of a real-time garbage-collected
                 heap [Baker78] [Baker91SP] [Baker92Tread]. Suggestions
                 are offered to improve the use of limited private types
                 in Ada9X for automatic, safe and leakproof resource
                 management.",
  acknowledgement = ack-nhfb,
  affiliation =  "Nimble Computer Corp",
  affiliationaddress = "Encino, CA, USA",
  classcodes =   "C6150J (Operating systems); C6110B (Software
                 engineering techniques); C6120 (File organisation);
                 C6140D (High level languages)",
  classification = "722.1; 722.4; 723.1; 723.1.1; 723.2",
  conferenceyear = "1993",
  corpsource =   "Nimble Comput. Corp., Encino, CA, USA",
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  journalabr =   "Ada Lett",
  keywords =     "Ada; Ada (programming language); Ada listings; Ada83
                 limited types; Ada83 resource; Ada9X; arbitrary
                 precision; Arbitrary precision arithmetic package;
                 arithmetic package; Automatic resource manager;
                 automatic resource managers; Computer operating
                 systems; Computer system recovery; Computer systems
                 programming; Data collection; data structures;
                 Deallocation; dynamic-string package; Embedded system;
                 embedded system; explicit deallocation; failures;
                 Information management; Interfaces (computer); Large
                 scale systems; leakproof resource management; limited
                 private types; management; managers; Program debugging;
                 Real time garbage collected heap; Real time systems;
                 real-time garbage-collected heap; real-time systems;
                 Resource allocation; resource allocation; Resource
                 management; Single point system failures; single-point
                 system; software reliability; storage; Storage
                 allocation (computer); Supervisory and executive
                 programs; System failure",
  treatment =    "P Practical; T Theoretical or Mathematical",
}


bibtype: article
filename: fparith.bib
label: Bakhrakh:1993:NIF
title: Numerical investigation of floating-point arithmetic operations
journal: j-PROG-COMP-SOFT
volume: 18
number: 6
pages: 255--258
year: 1993
CODEN: PCSODA
ISSN: 0361-7688 (print), 1608-3261 (electronic) OR 03617688 (print), 16083261 (electronic)
ISSNL: 0361-7688 OR 03617688
bibdate: Wed Dec 13 18:18:07 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.13 18:18:07 ???
note: Original Russian language paper in cite Bakhrakh:1992:NIF.
fjournal: Programming and Computer Software; translation of Programmirovaniye (Moscow, USSR) Plenum
remark: English translation of: Programmirovanie
acknowledgement: ack-nhfb
affiliation: Inst. for Control Sci., Acad. of Sci., Russia
journalURL: http://link.springer.com/journal/11086
thesaurus: Digital arithmetic
rawnote: Original Russian language paper in \cite{Bakhrakh:1992:NIF}.
rawtitle: Numerical investigation of floating-point arithmetic operations
author:
S. M. Bakhrakh and S. V. Velichko and N. E. Pilipchatin and V. F. Spiridonov and E. G. Sukhov and Yu. G. Fedorova and V. I. Kheifets

abstract:
This article analyzes the sources of accumulated computational error in certain computers (of ES and PS types) in floating-point mode. Results of numerical experiments are given. These experiments demonstrate the influence of rounding on accumulated error. (5 Refs.)

keywords:
Accumulated error rounding; Computational error; Digital arithmetic; ES computers; Floating-point arithmetic; Numerical investigation; PS computers

rawabstract:
This article analyzes the sources of accumulated computational error in certain computers (of ES and PS types) in floating-point mode. Results of numerical experiments are given. These experiments demonstrate the influence of rounding on accumulated error. (5 Refs.)

entry:
@Article{Bakhrakh:1993:NIF,
  author =       "S. M. Bakhrakh and S. V. Velichko and N. E.
                 Pilipchatin and V. F. Spiridonov and E. G. Sukhov and
                 Yu. G. Fedorova and V. I. Kheifets",
  title =        "Numerical investigation of floating-point arithmetic
                 operations",
  journal =      j-PROG-COMP-SOFT,
  volume =       "18",
  number =       "6",
  pages =        "255--258",
  year =         "1993",
  CODEN =        "PCSODA",
  ISSN =         "0361-7688 (print), 1608-3261 (electronic)",
  ISSN-L =       "0361-7688",
  bibdate =      "Wed Dec 13 18:18:07 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Original Russian language paper in
                 \cite{Bakhrakh:1992:NIF}.",
  abstract =     "This article analyzes the sources of accumulated
                 computational error in certain computers (of ES and PS
                 types) in floating-point mode. Results of numerical
                 experiments are given. These experiments demonstrate
                 the influence of rounding on accumulated error. (5
                 Refs.)",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. for Control Sci., Acad. of Sci., Russia",
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "Programming and Computer Software; translation of
                 Programmirovaniye (Moscow, USSR) Plenum",
  journal-URL =  "http://link.springer.com/journal/11086",
  keywords =     "Accumulated error rounding; Computational error;
                 Digital arithmetic; ES computers; Floating-point
                 arithmetic; Numerical investigation; PS computers",
  pubcountry =   "Russia",
  remark =       "English translation of: Programmirovanie",
  thesaurus =    "Digital arithmetic",
}


bibtype: article
filename: fparith.bib
label: Barrera:1993:IBS
author: Tony Barrera and Pelle Olsson
title: An Integer Based Square Root Algorithm
journal: j-BIT
volume: 33
number: 2
pages: 253--261
month: jun
monthnumber: 6
year: 1993
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01989748
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
MRclass: 68M07
MRnumber: 1 326 017
bibdate: Wed Dec 13 18:20:52 1995
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.13 18:20:52 ???
fjournal: BIT (Nordisk tidskrift for informationsbehandling)
acknowledgement: ack-nhfb
affiliation: AB Consonant, Uppsala, Sweden
journalURL: http://link.springer.com/journal/10543
thesaurus: Digital arithmetic
rawauthor: Tony Barrera and Pelle Olsson
rawtitle: An Integer Based Square Root Algorithm
URL:
http://www.mai.liu.se/BIT/contents/bit33.html; http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=33&issue=2&spage=253

abstract:
The authors propose a fast integer based method for computing square roots of floating point numbers. This implies high accuracy and robustness, since no precision will be lost during the computation. Only integer addition and shifts are necessary to obtain the square root. Comparisons made with the modified Newton method indicate that the suggested method is twice as fast for computing floating point square roots. (5 Refs.)

keywords:
Floating point numbers; floating-point arithmetic; Integer based square root algorithm; Modified Newton method; Robustness

rawabstract:
The authors propose a fast integer based method for computing square roots of floating point numbers. This implies high accuracy and robustness, since no precision will be lost during the computation. Only integer addition and shifts are necessary to obtain the square root. Comparisons made with the modified Newton method indicate that the suggested method is twice as fast for computing floating point square roots. (5 Refs.)

entry:
@Article{Barrera:1993:IBS,
  author =       "Tony Barrera and Pelle Olsson",
  title =        "An Integer Based Square Root Algorithm",
  journal =      j-BIT,
  volume =       "33",
  number =       "2",
  pages =        "253--261",
  month =        jun,
  year =         "1993",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01989748",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "68M07",
  MRnumber =     "1 326 017",
  bibdate =      "Wed Dec 13 18:20:52 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.mai.liu.se/BIT/contents/bit33.html;
                 http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=33&issue=2&spage=253",
  abstract =     "The authors propose a fast integer based method for
                 computing square roots of floating point numbers. This
                 implies high accuracy and robustness, since no
                 precision will be lost during the computation. Only
                 integer addition and shifts are necessary to obtain the
                 square root. Comparisons made with the modified Newton
                 method indicate that the suggested method is twice as
                 fast for computing floating point square roots. (5
                 Refs.)",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "AB Consonant, Uppsala, Sweden",
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "Floating point numbers; floating-point arithmetic;
                 Integer based square root algorithm; Modified Newton
                 method; Robustness",
  pubcountry =   "Denmark",
  thesaurus =    "Digital arithmetic",
  xxpages =      "254--261",
}


bibtype: article
filename: fparith.bib
label: Bauer:1993:LCB
author: P. H. Bauer and J. Wang
title: Limit cycle bounds for floating point implementations of second-order recursive digital filters
journal: j-IEEE-TRANS-CIRCUITS-SYST-2
volume: 40
number: 8
pages: 493--501
month: aug
monthnumber: 8
year: 1993
CODEN: ICSPE5
DOI: https://doi.org/10.1109/82.242338
ISSN: 1057-7130 (print), 1558-125X (electronic) OR 10577130 (print), 1558125X (electronic)
ISSNL: 1057-7130 OR 10577130
bibdate: Sat Jul 16 08:40:52 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:52 MDT
fjournal: IEEE Transactions on Circuits and Systems. 2, Analog and Digital Signal Processing
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82
rawauthor: P. H. Bauer and J. Wang
rawtitle: Limit cycle bounds for floating point implementations of second-order recursive digital filters
entry:
@Article{Bauer:1993:LCB,
  author =       "P. H. Bauer and J. Wang",
  title =        "Limit cycle bounds for floating point implementations
                 of second-order recursive digital filters",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-2,
  volume =       "40",
  number =       "8",
  pages =        "493--501",
  month =        aug,
  year =         "1993",
  CODEN =        "ICSPE5",
  DOI =          "https://doi.org/10.1109/82.242338",
  ISSN =         "1057-7130 (print), 1558-125X (electronic)",
  ISSN-L =       "1057-7130",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems. 2, Analog
                 and Digital Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
  summary =      "It is shown that floating point realizations of
                 linearly stable systems can exhibit four fundamental
                 types of free responses. Sufficient conditions for the
                 existence or nonexistence of some of these periodic
                 response types in a given system are presented
                 \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Beckmann:1993:FFTa
author: P. E. Beckmann and B. R. Musicus
title: Fast fault-tolerant digital convolution using a polynomial residue number system
journal: j-IEEE-TRANS-SIG-PROC
volume: 41
number: 7
pages: 2300--2313
month: jul
monthnumber: 7
year: 1993
CODEN: ITPRED
DOI: https://doi.org/10.1109/78.224241
ISSN: 1053-587X (print), 1941-0476 (electronic) OR 1053587X (print), 19410476 (electronic)
ISSNL: 1053-587X OR 1053587X
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
URL: https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=5864
fjournal: IEEE Transactions on Signal Processing
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78
rawauthor: P. E. Beckmann and B. R. Musicus
rawtitle: Fast fault-tolerant digital convolution using a polynomial residue number system
entry:
@Article{Beckmann:1993:FFTa,
  author =       "P. E. Beckmann and B. R. Musicus",
  title =        "Fast fault-tolerant digital convolution using a
                 polynomial residue number system",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "41",
  number =       "7",
  pages =        "2300--2313",
  month =        jul,
  year =         "1993",
  CODEN =        "ITPRED",
  DOI =          "https://doi.org/10.1109/78.224241",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=5864",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A fault-tolerant convolution algorithm that is an
                 extension of residue-number-system fault-tolerance
                 schemes applied to polynomial rings is described. The
                 algorithm is suitable for implementation on
                 multiprocessor systems and is able to concurrently
                 \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Beckmann:1993:FFTb
author: P. E. Beckmann and B. R. Musicus
title: Fast fault-tolerant digital convolution using a polynomial residue number system
journal: j-IEEE-TRANS-SIG-PROC
volume: 41
number: 7
pages: 2300--2313
month: jul
monthnumber: 7
year: 1993
CODEN: ITPRED
DOI: https://doi.org/10.1109/78.224241
ISSN: 1053-587X (print), 1941-0476 (electronic) OR 1053587X (print), 19410476 (electronic)
ISSNL: 1053-587X OR 1053587X
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
URL: https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=5864
fjournal: IEEE Transactions on Signal Processing
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78
rawauthor: P. E. Beckmann and B. R. Musicus
rawtitle: Fast fault-tolerant digital convolution using a polynomial residue number system
entry:
@Article{Beckmann:1993:FFTb,
  author =       "P. E. Beckmann and B. R. Musicus",
  title =        "Fast fault-tolerant digital convolution using a
                 polynomial residue number system",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "41",
  number =       "7",
  pages =        "2300--2313",
  month =        jul,
  year =         "1993",
  CODEN =        "ITPRED",
  DOI =          "https://doi.org/10.1109/78.224241",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=5864",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A fault-tolerant convolution algorithm that is an
                 extension of residue-number-system fault-tolerance
                 schemes applied to polynomial rings is described. The
                 algorithm is suitable for implementation on
                 multiprocessor systems and is able to concurrently
                 \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Benouamer:1993:LEA
author: M. O. Benouamer and P. Jaillon and D. Michelucci and J.-M. Moreau
title: A Lazy Exact Arithmetic
crossref: Swartzlander:1993:SCA
pages: 242--249
year: 1993
bibdate: Sat Nov 17 09:46:07 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.17 09:46:07 ???
URL: http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Benouamer.pdf
keywords: ARITH-11
acknowledgement: ack-nhfb
rawauthor: M. O. Benouamer and P. Jaillon and D. Michelucci and J.-M. Moreau
rawtitle: A Lazy Exact Arithmetic
entry:
@InProceedings{Benouamer:1993:LEA,
  author =       "M. O. Benouamer and P. Jaillon and D. Michelucci and
                 J.-M. Moreau",
  title =        "A Lazy Exact Arithmetic",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "242--249",
  year =         "1993",
  bibdate =      "Sat Nov 17 09:46:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Benouamer.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
}


bibtype: inproceedings
filename: fparith.bib
label: Bickerstaff:1993:RAM
author: K'Andrea C. Bickerstaff and Michael J. Schulte and Earl E. Swartzlander, Jr.
title: Reduced Area Multipliers
crossref: Wah:1993:ICA
pages: 478--489
year: 1993
bibdate: Sun Mar 04 10:43:38 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.03.04 10:43:38 ???
URL: http://mesa.ece.wisc.edu/publications/cp_1993-03.pdf
acknowledgement: ack-nhfb
rawauthor: K'Andrea C. Bickerstaff and Michael J. Schulte and Earl E. {Swartzlander, Jr.}
rawtitle: Reduced Area Multipliers
entry:
@InProceedings{Bickerstaff:1993:RAM,
  author =       "K'Andrea C. Bickerstaff and Michael J. Schulte and
                 Earl E. {Swartzlander, Jr.}",
  title =        "Reduced Area Multipliers",
  crossref =     "Wah:1993:ICA",
  pages =        "478--489",
  year =         "1993",
  bibdate =      "Sun Mar 04 10:43:38 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1993-03.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Bizzan:1993:IMA
author: S. S. Bizzan and G. A. Jullien and N. M. Wigley and W. C. Miller
title: Integer Mapping Architectures for the Polynomial Ring Engine
crossref: Swartzlander:1993:SCA
pages: 44--51
year: 1993
bibdate: Sat Nov 17 09:46:07 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.17 09:46:07 ???
URL: http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Bizzan.pdf
keywords: ARITH-11
acknowledgement: ack-nhfb
rawauthor: S. S. Bizzan and G. A. Jullien and N. M. Wigley and W. C. Miller
rawtitle: Integer Mapping Architectures for the Polynomial Ring Engine
entry:
@InProceedings{Bizzan:1993:IMA,
  author =       "S. S. Bizzan and G. A. Jullien and N. M. Wigley and W.
                 C. Miller",
  title =        "Integer Mapping Architectures for the Polynomial Ring
                 Engine",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "44--51",
  year =         "1993",
  bibdate =      "Sat Nov 17 09:46:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Bizzan.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
}


bibtype: incollection
filename: fparith.bib
label: Bohlender:1993:PAF
author: G. Bohlender and D. Cordes and A. Knofel and U. Kulisch and R. Lohner and W. V. Walter
title: Proposal for accurate floating-point vector arithmetic
crossref: Adams:1993:SCA
pages: 87--102
year: 1993
bibdate: Tue Dec 12 09:27:13 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.12 09:27:13 MST
acknowledgement: ack-nhfb
affiliation: Inst. fur Angewandte Math., Karlsruhe University, Germany
thesaurus: Digital arithmetic; Mathematics computing; Roundoff errors; Standards
rawauthor: G. Bohlender and D. Cordes and A. Kn{\"o}fel and U. Kulisch and R. Lohner and W. V. Walter
rawtitle: Proposal for accurate floating-point vector arithmetic
abstract:
Many computers provide accurate and reliable scalar arithmetic for floating point numbers. An accurate definition of the four elementary floating-point operations +, -, *, / is given in the IEEE standards for floating-point arithmetic and was well established long before. An increasing number of computers (especially PC's and workstations) feature IEEE arithmetic. In many numerical algorithms, however, compound operations such as the summation of a sequence of numbers or the dot product of two vectors are highly common. A simulation of these compound operations by means of elementary floating-point operations leads to accumulation of rounding errors and may suffer from catastrophic cancellation of leading digits. Existing standards for floating-point arithmetic do not improve this situation. The goal of the proposal is to define vector operations in a manner consistent with the elementary scalar arithmetic operations. The rounding modes and accuracy requirements as well as the data formats of the operands and results of the vector operations described in the proposal are chosen to be fully consistent with the existing scalar floating-point arithmetic.

keywords:
Accuracy requirements; Catastrophic cancellation; Compound operations; Data formats; Dot product; Elementary floating-point operations; Elementary scalar arithmetic operations; Floating point numbers; IEEE arithmetic; IEEE standards; Leading digits; Numerical algorithms; Operands; Rounding errors; Rounding modes; Scalar floating-point arithmetic; Sequence; Standards; Summation; Vector operations

rawabstract:
Many computers provide accurate and reliable scalar arithmetic for floating point numbers. An accurate definition of the four elementary floating-point operations +, -, *, / is given in the IEEE standards for floating-point arithmetic and was well established long before. An increasing number of computers (especially PC's and workstations) feature IEEE arithmetic. In many numerical algorithms, however, compound operations such as the summation of a sequence of numbers or the dot product of two vectors are highly common. A simulation of these compound operations by means of elementary floating-point operations leads to accumulation of rounding errors and may suffer from catastrophic cancellation of leading digits. Existing standards for floating-point arithmetic do not improve this situation. The goal of the proposal is to define vector operations in a manner consistent with the elementary scalar arithmetic operations. The rounding modes and accuracy requirements as well as the data formats of the operands and results of the vector operations described in the proposal are chosen to be fully consistent with the existing scalar floating-point arithmetic.

entry:
@InCollection{Bohlender:1993:PAF,
  author =       "G. Bohlender and D. Cordes and A. Kn{\"o}fel and U.
                 Kulisch and R. Lohner and W. V. Walter",
  title =        "Proposal for accurate floating-point vector
                 arithmetic",
  crossref =     "Adams:1993:SCA",
  pages =        "87--102",
  year =         "1993",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Many computers provide accurate and reliable scalar
                 arithmetic for floating point numbers. An accurate
                 definition of the four elementary floating-point
                 operations +, -, *, / is given in the IEEE standards
                 for floating-point arithmetic and was well established
                 long before. An increasing number of computers
                 (especially PC's and workstations) feature IEEE
                 arithmetic. In many numerical algorithms, however,
                 compound operations such as the summation of a sequence
                 of numbers or the dot product of two vectors are highly
                 common. A simulation of these compound operations by
                 means of elementary floating-point operations leads to
                 accumulation of rounding errors and may suffer from
                 catastrophic cancellation of leading digits. Existing
                 standards for floating-point arithmetic do not improve
                 this situation. The goal of the proposal is to define
                 vector operations in a manner consistent with the
                 elementary scalar arithmetic operations. The rounding
                 modes and accuracy requirements as well as the data
                 formats of the operands and results of the vector
                 operations described in the proposal are chosen to be
                 fully consistent with the existing scalar
                 floating-point arithmetic.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. fur Angewandte Math., Karlsruhe University,
                 Germany",
  classification = "C5230 (Digital arithmetic methods); C6130 (Data
                 handling techniques); C7310 (Mathematics)",
  keywords =     "Accuracy requirements; Catastrophic cancellation;
                 Compound operations; Data formats; Dot product;
                 Elementary floating-point operations; Elementary scalar
                 arithmetic operations; Floating point numbers; IEEE
                 arithmetic; IEEE standards; Leading digits; Numerical
                 algorithms; Operands; Rounding errors; Rounding modes;
                 Scalar floating-point arithmetic; Sequence; Standards;
                 Summation; Vector operations",
  thesaurus =    "Digital arithmetic; Mathematics computing; Roundoff
                 errors; Standards",
}


bibtype: inproceedings
filename: fparith.bib
label: Booth:1993:ECA
author: Andrew D. Booth
title: Early Computer Arithmetic
crossref: Swartzlander:1993:SCA
pages: ix--ix
year: 1993
bibdate: Sat Nov 17 09:46:07 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.17 09:46:07 ???
URL: http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_keynote.pdf
keywords: ARITH-11
acknowledgement: ack-nhfb
rawauthor: Andrew D. Booth
rawtitle: Early Computer Arithmetic
remark:
The author developed ``Booth's Algorithm'' for two's complement multiplication, the APEXC computer at the University of London (one of the world's first three electronic digital computers), and the M3 series of computers at the University of Saskatchewan (the first all Canadian electronic computer).

entry:
@InProceedings{Booth:1993:ECA,
  author =       "Andrew D. Booth",
  title =        "Early Computer Arithmetic",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "ix--ix",
  year =         "1993",
  bibdate =      "Sat Nov 17 09:46:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_keynote.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
  remark =       "The author developed ``Booth's Algorithm'' for two's
                 complement multiplication, the APEXC computer at the
                 University of London (one of the world's first three
                 electronic digital computers), and the M3 series of
                 computers at the University of Saskatchewan (the first
                 all Canadian electronic computer).",
}


bibtype: inproceedings
filename: fparith.bib
label: Briggs:1993:XBM
author: W. S. Briggs and D. W. Matula
title: A $ 17 times 69 $ Bit Multiply and Add Unit with Redundant Binary Feedback and Single Cycle Latency
crossref: Swartzlander:1993:SCA
pages: 163--170
year: 1993
bibdate: Thu Jun 20 10:16:11 2002
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.06.20 10:16:11 ???
URL: http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Briggs.pdf
keywords: ARITH-11
acknowledgement: ack-nj
rawauthor: W. S. Briggs and D. W. Matula
rawtitle:
A $ 17 \times 69 $ Bit Multiply and Add Unit with Redundant Binary Feedback and Single Cycle Latency

entry:
@InProceedings{Briggs:1993:XBM,
  author =       "W. S. Briggs and D. W. Matula",
  title =        "A $ 17 \times 69 $ Bit Multiply and Add Unit with
                 Redundant Binary Feedback and Single Cycle Latency",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "163--170",
  year =         "1993",
  bibdate =      "Thu Jun 20 10:16:11 2002",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Briggs.pdf",
  acknowledgement = ack-nj,
  keywords =     "ARITH-11",
}


bibtype: inproceedings
filename: fparith.bib
label: Callaway:1993:EPC
author: Thomas K. Callaway and Earl E. Swartzlander, Jr.
title: Estimating the Power Consumption of CMOS Adders
crossref: Swartzlander:1993:SCA
pages: 210--216
year: 1993
bibdate: Sat Nov 17 09:46:07 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.17 09:46:07 ???
URL: http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Callaway.pdf
keywords: ARITH-11
acknowledgement: ack-nhfb
rawauthor: Thomas K. Callaway and Earl E. {Swartzlander, Jr.}
rawtitle: Estimating the Power Consumption of {CMOS} Adders
entry:
@InProceedings{Callaway:1993:EPC,
  author =       "Thomas K. Callaway and Earl E. {Swartzlander, Jr.}",
  title =        "Estimating the Power Consumption of {CMOS} Adders",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "210--216",
  year =         "1993",
  bibdate =      "Sat Nov 17 09:46:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Callaway.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
}


bibtype: article
filename: fparith.bib
label: Chang:1993:REP
author: Long-Wen Chang
title: Roundoff Error Problem of the Systolic Array for DFT
journal: j-IEEE-TRANS-SIG-PROC
volume: 41
number: 1
pages: 395
month: jan
monthnumber: 1
year: 1993
CODEN: ITPRED
ISSN: 1053-587X (print), 1941-0476 (electronic) OR 1053587X (print), 19410476 (electronic)
ISSNL: 1053-587X OR 1053587X
bibdate: Sat Jul 16 11:25:06 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:06 MDT
fjournal: IEEE Transactions on Signal Processing
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78
rawauthor: Long-Wen Chang
rawtitle: Roundoff Error Problem of the Systolic Array for {DFT}
entry:
@Article{Chang:1993:REP,
  author =       "Long-Wen Chang",
  title =        "Roundoff Error Problem of the Systolic Array for
                 {DFT}",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "41",
  number =       "1",
  pages =        "395",
  month =        jan,
  year =         "1993",
  CODEN =        "ITPRED",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  bibdate =      "Sat Jul 16 11:25:06 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  summary =      "Not \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Choi:1993:FPR
author: H. Choi and W. P. Burleson and D. S. Phatak
booktitle: Proceedings of 1993 International Joint Conference on Neural Networks. IJCNN '93-Nagoya
title: Fixed-point roundoff error analysis of large feedforward neural networks
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1947--1950
year: 1993
bibdate: Sat Jul 16 11:25:07 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:07 MDT
acknowledgement: ack-nhfb
rawauthor: H. Choi and W. P. Burleson and D. S. Phatak
rawbooktitle: Proceedings of 1993 International Joint Conference on Neural Networks. {IJCNN '93-Nagoya}
rawtitle: Fixed-point roundoff error analysis of large feedforward neural networks
entry:
@InProceedings{Choi:1993:FPR,
  author =       "H. Choi and W. P. Burleson and D. S. Phatak",
  booktitle =    "Proceedings of 1993 International Joint Conference on
                 Neural Networks. {IJCNN '93-Nagoya}",
  title =        "Fixed-point roundoff error analysis of large
                 feedforward neural networks",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1947--1950",
  year =         "1993",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:07 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Digital implementations of neural nets must consider
                 finite wordlength effects. For large sized nets, it is
                 particularly important to investigate the roundoff
                 errors in order to realize low-cost hardware
                 implementations while satisfying precision \ldots{}",
}


bibtype: misc
filename: fparith.bib
label: Chu:1993:FPA
author: Tan V. Chu and Faraydon O. Karim and Christopher H. Olson
title: Floating point arithmetic unit with size efficient pipelined multiply-add architecture
pages: 1947--1950
day: 31
month: aug
monthnumber: 8
year: 1993
bibdate: Thu Oct 17 10:40:01 2019
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2019.10.17 10:40:01 ???
URL: https://patents.google.com/patent/US5241493A
remark: Patent filed 16 December 1991, granted to IBM on 31 August 1993, possibly expired 16 December 2011.
acknowledgement: ack-nhfb
howpublished: US Patent 5,241,493
rawauthor: Tan V. Chu and Faraydon O. Karim and Christopher H. Olson
rawtitle: Floating point arithmetic unit with size efficient pipelined multiply-add architecture
abstract:
An architecture and method relating to a floating point operation which performs the mathematical computation of A * B + C. The multiplication is accomplished in two or more stages, each stage involving corresponding sets of partial products and concurrently accomplished incremental summations. A pipelined architecture provides for the summation of the least significant bits of an intermediate product with operand C at a stage preceding entry into a full adder. Thereby, a significant portion of the full adder can be replaced by a simpler and smaller incrementer circuit. Partitioning of the multiplication operation into two or more partial product operations proportionally reduces the size of the multiplier required. Pipelining and concurrence execution of multiplication and addition operation in the multiplier provides in two cycles the results of the mathematical operation A * B + C while using a full adder of three-quarters normal size.

rawabstract:
An architecture and method relating to a floating point operation which performs the mathematical computation of A * B + C. The multiplication is accomplished in two or more stages, each stage involving corresponding sets of partial products and concurrently accomplished incremental summations. A pipelined architecture provides for the summation of the least significant bits of an intermediate product with operand C at a stage preceding entry into a full adder. Thereby, a significant portion of the full adder can be replaced by a simpler and smaller incrementer circuit. Partitioning of the multiplication operation into two or more partial product operations proportionally reduces the size of the multiplier required. Pipelining and concurrence execution of multiplication and addition operation in the multiplier provides in two cycles the results of the mathematical operation A * B + C while using a full adder of three-quarters normal size.

entry:
@Misc{Chu:1993:FPA,
  author =       "Tan V. Chu and Faraydon O. Karim and Christopher H.
                 Olson",
  title =        "Floating point arithmetic unit with size efficient
                 pipelined multiply-add architecture",
  howpublished = "US Patent 5,241,493",
  day =          "31",
  month =        aug,
  year =         "1993",
  bibdate =      "Thu Oct 17 10:40:01 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://patents.google.com/patent/US5241493A",
  abstract =     "An architecture and method relating to a floating
                 point operation which performs the mathematical
                 computation of A * B + C. The multiplication is
                 accomplished in two or more stages, each stage
                 involving corresponding sets of partial products and
                 concurrently accomplished incremental summations. A
                 pipelined architecture provides for the summation of
                 the least significant bits of an intermediate product
                 with operand C at a stage preceding entry into a full
                 adder. Thereby, a significant portion of the full adder
                 can be replaced by a simpler and smaller incrementer
                 circuit. Partitioning of the multiplication operation
                 into two or more partial product operations
                 proportionally reduces the size of the multiplier
                 required. Pipelining and concurrence execution of
                 multiplication and addition operation in the multiplier
                 provides in two cycles the results of the mathematical
                 operation A * B + C while using a full adder of
                 three-quarters normal size.",
  acknowledgement = ack-nhfb,
  remark =       "Patent filed 16 December 1991, granted to IBM on 31
                 August 1993, possibly expired 16 December 2011.",
}


bibtype: article
filename: fparith.bib
label: Cody:1993:ACP
author: W. J. Cody
title: Algorithm 714: CELEFUNT: a Portable Test Package for Complex Elementary Functions
journal: j-TOMS
volume: 19
number: 1
pages: 1--21
month: mar
monthnumber: 3
year: 1993
CODEN: ACMSCU
DOI: https://doi.org/10.1145/151271.151272
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Mon Sep 05 09:15:25 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.05 09:15:25 ???
URL: http://www.acm.org/pubs/citations/journals/toms/1993-19-1/p1-cody/
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms; measurement; performance
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: W. J. Cody
rawtitle: {Algorithm 714}: {CELEFUNT}: a Portable Test Package for Complex Elementary Functions
abstract:
This paper discusses CELEFUNT, a package of Fortran programs for testing complex elementary functions.

subject:
bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms.

rawabstract:
This paper discusses CELEFUNT, a package of Fortran programs for testing complex elementary functions.

entry:
@Article{Cody:1993:ACP,
  author =       "W. J. Cody",
  title =        "{Algorithm 714}: {CELEFUNT}: a Portable Test Package
                 for Complex Elementary Functions",
  journal =      j-TOMS,
  volume =       "19",
  number =       "1",
  pages =        "1--21",
  month =        mar,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/151271.151272",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 05 09:15:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-1/p1-cody/",
  abstract =     "This paper discusses CELEFUNT, a package of Fortran
                 programs for testing complex elementary functions.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; measurement; performance",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Certification and testing. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Numerical algorithms.",
}


bibtype: article
filename: fparith.bib
label: Cody:1993:AFS
author: W. J. Cody and Jerome T. Coonen
title: Algorithm 722: Functions to Support the IEEE Standard for Binary Floating-Point Arithmetic
journal: j-TOMS
volume: 19
number: 4
pages: 443--451
month: dec
monthnumber: 12
year: 1993
CODEN: ACMSCU
DOI: https://doi.org/10.1145/168173.168185
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
URL: http://www.acm.org/pubs/citations/journals/toms/1993-19-4/p443-cody/
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
affiliation: Argonne Nat. Lab., IL, USA
journalURL: https://dl.acm.org/loi/toms
thesaurus: Data handling; Digital arithmetic; Mathematics computing; Standards
rawauthor: W. J. Cody and Jerome T. Coonen
rawtitle: {Algorithm 722}: Functions to Support the {IEEE} Standard for Binary Floating-Point Arithmetic
abstract:
This paper describes C programs for the support functions em copysign(x,y), logb(x), scalb(x,n), nextafter(x,y), finite(x), and em isnan(x) recommended in the Appendix to the em IEEE Standard for Binary Floating-Point Arithmetic. In the case of em logb, the modified definition given in the later em IEEE Standard for Radix-Independent Floating-Point Arithmetic is followed. These programs should run without modification on most systems conforming to the binary standard.

keywords:
C programs; Copysign(x,y); Finite(x); IEEE Standard for Binary Floating-point arithmetic; Isnan(x); Logb(x); Nextafter(x,y); Numerical software; Scalb(x,n)

subject:
G.1.0 [Numerical Analysis]: General -- numerical algorithms; G.4 [Numerical Analysis]: Mathematical Software -- certification and testing

rawabstract:
This paper describes C programs for the support functions {\em copysign(x,y), logb(x), scalb(x,n), nextafter(x,y), finite(x)}, and {\em isnan(x)} recommended in the Appendix to the {\em IEEE Standard for Binary Floating-Point Arithmetic.} In the case of {\em logb}, the modified definition given in the later {\em IEEE Standard for Radix-Independent Floating-Point Arithmetic} is followed. These programs should run without modification on most systems conforming to the binary standard.

entry:
@Article{Cody:1993:AFS,
  author =       "W. J. Cody and Jerome T. Coonen",
  title =        "{Algorithm 722}: Functions to Support the {IEEE}
                 Standard for Binary Floating-Point Arithmetic",
  journal =      j-TOMS,
  volume =       "19",
  number =       "4",
  pages =        "443--451",
  month =        dec,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/168173.168185",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-4/p443-cody/",
  abstract =     "This paper describes C programs for the support
                 functions {\em copysign(x,y), logb(x), scalb(x,n),
                 nextafter(x,y), finite(x)}, and {\em isnan(x)}
                 recommended in the Appendix to the {\em IEEE Standard
                 for Binary Floating-Point Arithmetic.} In the case of
                 {\em logb}, the modified definition given in the later
                 {\em IEEE Standard for Radix-Independent Floating-Point
                 Arithmetic} is followed. These programs should run
                 without modification on most systems conforming to the
                 binary standard.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "Argonne Nat. Lab., IL, USA",
  classification = "C5230 (Digital arithmetic methods); C6130 (Data
                 handling techniques); C7310 (Mathematics)",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "C programs; Copysign(x,y); Finite(x); IEEE Standard
                 for Binary Floating-point arithmetic; Isnan(x);
                 Logb(x); Nextafter(x,y); Numerical software;
                 Scalb(x,n)",
  subject =      "G.1.0 [Numerical Analysis]: General -- numerical
                 algorithms; G.4 [Numerical Analysis]: Mathematical
                 Software -- certification and testing",
  thesaurus =    "Data handling; Digital arithmetic; Mathematics
                 computing; Standards",
}


bibtype: article
filename: fparith.bib
label: Cody:1993:ASE
author: W. J. Cody
title: Algorithm 715: SPECFUN --- A Portable FORTRAN Package of Special Function Routines and Test Drivers
journal: j-TOMS
volume: 19
number: 1
pages: 22--32
month: mar
monthnumber: 3
year: 1993
CODEN: ACMSCU
DOI: https://doi.org/10.1145/151271.151273
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Mar 09 10:23:18 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1999.03.09 10:23:18 ???
note: See remark cite Price:1996:RA.
URL: http://www.acm.org/pubs/citations/journals/toms/1993-19-1/p22-cody/
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: W. J. Cody
rawnote: See remark \cite{Price:1996:RA}.
abstract:
SPECFUN is a package containing transportable FORTRAN special function programs for real arguments and accompanying test drivers. Components include Bessel functions, exponential integrals, error functions and related functions, and gamma functions and related functions.

subject:
bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms.

rawabstract:
SPECFUN is a package containing transportable FORTRAN special function programs for real arguments and accompanying test drivers. Components include Bessel functions, exponential integrals, error functions and related functions, and gamma functions and related functions.

rawtitle:
{Algorithm 715}: {SPECFUN}\emdash {A} Portable {FORTRAN} Package of Special Function Routines and Test Drivers

entry:
@Article{Cody:1993:ASE,
  author =       "W. J. Cody",
  title =        "{Algorithm 715}: {SPECFUN}\emdash {A} Portable
                 {FORTRAN} Package of Special Function Routines and Test
                 Drivers",
  journal =      j-TOMS,
  volume =       "19",
  number =       "1",
  pages =        "22--32",
  month =        mar,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/151271.151273",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 09 10:23:18 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See remark \cite{Price:1996:RA}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-1/p22-cody/",
  abstract =     "SPECFUN is a package containing transportable FORTRAN
                 special function programs for real arguments and
                 accompanying test drivers. Components include Bessel
                 functions, exponential integrals, error functions and
                 related functions, and gamma functions and related
                 functions.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Certification and testing. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Numerical algorithms.",
}


bibtype: article
filename: fparith.bib
label: Cole:1993:SAA
author: T. J. Cole
title: Statistical Algorithms: Algorithm AS 281: Scaling and Rounding Regression Coefficients to Integers
journal: j-APPL-STAT
volume: 42
number: 1
pages: 261--268
year: 1993
CODEN: APSTAG
ISSN: 0035-9254 (print), 1467-9876 (electronic) OR 00359254 (print), 14679876 (electronic)
ISSNL: 0035-9254 OR 00359254
bibdate: Sat Apr 21 10:26:43 MDT 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database
bibtimestamp: 2001.04.21 10:26:43 MDT
URL: http://lib.stat.cmu.edu/apstat/281
fjournal: Applied Statistics
acknowledgement: ack-nhfb
journalURL: http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues
rawauthor: T. J. Cole
rawtitle:
Statistical Algorithms: {Algorithm AS 281}: Scaling and Rounding Regression Coefficients to Integers

entry:
@Article{Cole:1993:SAA,
  author =       "T. J. Cole",
  title =        "Statistical Algorithms: {Algorithm AS 281}: Scaling
                 and Rounding Regression Coefficients to Integers",
  journal =      j-APPL-STAT,
  volume =       "42",
  number =       "1",
  pages =        "261--268",
  year =         "1993",
  CODEN =        "APSTAG",
  ISSN =         "0035-9254 (print), 1467-9876 (electronic)",
  ISSN-L =       "0035-9254",
  bibdate =      "Sat Apr 21 10:26:43 MDT 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  URL =          "http://lib.stat.cmu.edu/apstat/281",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Statistics",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues",
}


bibtype: inproceedings
filename: fparith.bib
label: Cortadella:1993:DSQ
author: Jordi Cortadella and Tomas Lang
title: Division with Speculation of Quotient Digits
crossref: Swartzlander:1993:SCA
pages: 87--94
year: 1993
bibdate: Sat Nov 17 09:46:07 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.17 09:46:07 ???
URL: http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Cortadella.pdf
keywords: ARITH-11
acknowledgement: ack-nhfb
rawauthor: Jordi Cortadella and Tom{\'a}s Lang
rawtitle: Division with Speculation of Quotient Digits
entry:
@InProceedings{Cortadella:1993:DSQ,
  author =       "Jordi Cortadella and Tom{\'a}s Lang",
  title =        "Division with Speculation of Quotient Digits",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "87--94",
  year =         "1993",
  bibdate =      "Sat Nov 17 09:46:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Cortadella.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
}


bibtype: inproceedings
filename: fparith.bib
label: Dadda:1993:MPC
author: Luigi Dadda and Vincenzo Piuri and Renato Stefanelli
title: Multi-Parallel Convolvers
crossref: Swartzlander:1993:SCA
pages: 70--77
year: 1993
bibdate: Sat Nov 17 09:46:07 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.17 09:46:07 ???
URL: http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Dadda.pdf
keywords: ARITH-11
acknowledgement: ack-nhfb
authordates: 29 April 1923--26 October 2012
rawauthor: Luigi Dadda and Vincenzo Piuri and Renato Stefanelli
rawtitle: Multi-Parallel Convolvers
entry:
@InProceedings{Dadda:1993:MPC,
  author =       "Luigi Dadda and Vincenzo Piuri and Renato Stefanelli",
  title =        "Multi-Parallel Convolvers",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "70--77",
  year =         "1993",
  bibdate =      "Sat Nov 17 09:46:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Dadda.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "29 April 1923--26 October 2012",
  keywords =     "ARITH-11",
}


bibtype: inproceedings
filename: fparith.bib
label: Daumas:1993:DFV
author: Marc Daumas and D. W. Matula
title: Design of a Fast Validated Dot Product Operation
crossref: Swartzlander:1993:SCA
pages: 62--69
year: 1993
bibdate: Sat Nov 17 09:46:07 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.17 09:46:07 ???
URL: http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Daumas.pdf
keywords: ARITH-11
acknowledgement: ack-nhfb
rawauthor: Marc Daumas and D. W. Matula
rawtitle: Design of a Fast Validated Dot Product Operation
entry:
@InProceedings{Daumas:1993:DFV,
  author =       "Marc Daumas and D. W. Matula",
  title =        "Design of a Fast Validated Dot Product Operation",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "62--69",
  year =         "1993",
  bibdate =      "Sat Nov 17 09:46:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Daumas.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
}


bibtype: mastersthesis
filename: fparith.bib
label: Delgado:1993:DSP
author: Maria Luisa Delgado
title: Design and simulation of a pipeline floating-point adder
type: Thesis (M.S.)
school: University of Texas at El Paso
address: El Paso, TX, USA
pages: x + 90
year: 1993
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Floating-point arithmetic.; Parallel processing (Electronic computers)
acknowledgement: ack-nhfb
rawauthor: Maria Luisa Delgado
rawtitle: Design and simulation of a pipeline floating-point adder
entry:
@MastersThesis{Delgado:1993:DSP,
  author =       "Maria Luisa Delgado",
  title =        "Design and simulation of a pipeline floating-point
                 adder",
  type =         "Thesis ({M.S.})",
  school =       "University of Texas at El Paso",
  address =      "El Paso, TX, USA",
  pages =        "x + 90",
  year =         "1993",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.; Parallel processing
                 (Electronic computers)",
}


bibtype: inproceedings
filename: fparith.bib
label: Demmel:1993:FNA
author: James W. Demmel and Xiaoye Li
title: Faster numerical algorithms via exception handling
crossref: Swartzlander:1993:SCA
pages: 234--241
year: 1993
bibdate: Thu Jun 20 10:16:21 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.06.20 10:16:21 ???
URL: http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Demmel.pdf
keywords: ARITH-11
acknowledgement: ack-nhfb
rawauthor: James W. Demmel and Xiaoye Li
rawtitle: Faster numerical algorithms via exception handling
entry:
@InProceedings{Demmel:1993:FNA,
  author =       "James W. Demmel and Xiaoye Li",
  title =        "Faster numerical algorithms via exception handling",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "234--241",
  year =         "1993",
  bibdate =      "Thu Jun 20 10:16:21 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Demmel.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
}


bibtype: techreport
filename: fparith.bib
label: Desaulniers:1993:BEA
author: H. Desaulniers and Stewart, N. F. (Neil Frederick)
title: Backward error analysis for floating-point operations on rectilinear $r$-sets
type: Publication
number: 816
institution: Universite de Montreal, Departement d'informatique et de recherche operationnelle
address: Montreal, Quebec, Canada
pages: 64
year: 1993
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Computer-aided design.
acknowledgement: ack-nhfb
rawauthor: H. Desaulniers and Stewart, N. F. (Neil Frederick)
rawtitle: Backward error analysis for floating-point operations on rectilinear $r$-sets
remark:
``January 5, 1993.'' Supported in part by the Natural Sciences and Engineering Research Council of Canada

entry:
@TechReport{Desaulniers:1993:BEA,
  author =       "H. Desaulniers and Stewart, N. F. (Neil Frederick)",
  title =        "Backward error analysis for floating-point operations
                 on rectilinear $r$-sets",
  type =         "Publication",
  number =       "816",
  institution =  "Universit{\'{e}} de Montr{\'{e}}al, Departement
                 d'informatique et de recherche operationnelle",
  address =      "Montr{\'{e}}al, Qu{\'{e}}bec, Canada",
  pages =        "64",
  year =         "1993",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer-aided design.",
  remark =       "``January 5, 1993.'' Supported in part by the Natural
                 Sciences and Engineering Research Council of Canada",
}


bibtype: article
filename: fparith.bib
label: DiClaudio:1993:SRR
author: E. D. Di Claudio and G. Orlandi and F. Piazza
title: A systolic redundant residue arithmetic error correction circuit
journal: j-IEEE-TRANS-COMPUT
volume: 42
number: 4
pages: 427--432
month: apr
monthnumber: 4
year: 1993
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.214689
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 07:58:48 MDT 2011
bibtimestamp: 2011.07.07 07:58:48 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=214689
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: E. D. {Di Claudio} and G. Orlandi and F. Piazza
rawtitle: A systolic redundant residue arithmetic error correction circuit
entry:
@Article{DiClaudio:1993:SRR,
  author =       "E. D. {Di Claudio} and G. Orlandi and F. Piazza",
  title =        "A systolic redundant residue arithmetic error
                 correction circuit",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "42",
  number =       "4",
  pages =        "427--432",
  month =        apr,
  year =         "1993",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.214689",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:58:48 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=214689",
  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: DiLecce:1993:CES
author: V. Di Lecce and E. Di Sciascio
title: A comparative evaluation of solutions for inner product
journal: j-INT-J-MINI-MICROCOMPUTERS
volume: 15
number: 2
pages: 71--77
year: 1993
CODEN: IJMMDE
ISSN: 0702-0481 OR 07020481
bibdate: Tue Dec 12 09:27:13 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.12 09:27:13 MST
fjournal: International Journal of Mini and Microcomputers
acknowledgement: ack-nhfb
affiliation: Department of Electron. Eng., Politecnico di Bari, Italy
thesaurus: Digital arithmetic; Digital signal processing chips; Performance evaluation
rawauthor: V. Di Lecce and E. Di Sciascio
rawtitle: A comparative evaluation of solutions for inner product
abstract:
This paper proposes the design and performance evaluation of a bit-serial processing element for inner product computation in fine-grain architectures. Some solutions proposed in the scientific literature for inner product are presented and evaluated. The processing element architecture and its operating mode are described; a single floating-point inner product computation can be accomplished in e*(n+1) clock cycles (2*(n+1) in pipelined mode), supposing that mantissas and exponents have the same length n. The VLSI implementation of the processing element is discussed with reference to both standard cell and full custom design styles. A comparative evaluation with the previously described solutions is proposed, relative to some particularly significant parameters.

keywords:
Bit-serial processing element; Comparative evaluation; DSP chips; Exponents; Fine-grain architectures; Full custom design styles; Inner product; Mantissas; Operating mode; Performance evaluation; VLSI implementation

rawabstract:
This paper proposes the design and performance evaluation of a bit-serial processing element for inner product computation in fine-grain architectures. Some solutions proposed in the scientific literature for inner product are presented and evaluated. The processing element architecture and its operating mode are described; a single floating-point inner product computation can be accomplished in e*(n+1) clock cycles (2*(n+1) in pipelined mode), supposing that mantissas and exponents have the same length n. The VLSI implementation of the processing element is discussed with reference to both standard cell and full custom design styles. A comparative evaluation with the previously described solutions is proposed, relative to some particularly significant parameters.

entry:
@Article{DiLecce:1993:CES,
  author =       "V. Di Lecce and E. Di Sciascio",
  title =        "A comparative evaluation of solutions for inner
                 product",
  journal =      j-INT-J-MINI-MICROCOMPUTERS,
  volume =       "15",
  number =       "2",
  pages =        "71--77",
  month =        "????",
  year =         "1993",
  CODEN =        "IJMMDE",
  ISSN =         "0702-0481",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper proposes the design and performance
                 evaluation of a bit-serial processing element for inner
                 product computation in fine-grain architectures. Some
                 solutions proposed in the scientific literature for
                 inner product are presented and evaluated. The
                 processing element architecture and its operating mode
                 are described; a single floating-point inner product
                 computation can be accomplished in e*(n+1) clock cycles
                 (2*(n+1) in pipelined mode), supposing that mantissas
                 and exponents have the same length n. The VLSI
                 implementation of the processing element is discussed
                 with reference to both standard cell and full custom
                 design styles. A comparative evaluation with the
                 previously described solutions is proposed, relative to
                 some particularly significant parameters.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Electron. Eng., Politecnico di Bari,
                 Italy",
  classification = "B1265F (Microprocessors and microcomputers); C5135
                 (Digital signal processing chips); C5220 (Computer
                 architecture); C5230 (Digital arithmetic methods);
                 C5260 (Digital signal processing)",
  fjournal =     "International Journal of Mini and Microcomputers",
  keywords =     "Bit-serial processing element; Comparative evaluation;
                 DSP chips; Exponents; Fine-grain architectures; Full
                 custom design styles; Inner product; Mantissas;
                 Operating mode; Performance evaluation; VLSI
                 implementation",
  thesaurus =    "Digital arithmetic; Digital signal processing chips;
                 Performance evaluation",
}


bibtype: article
filename: fparith.bib
label: Dimauro:1993:NTF
author: G. Dimauro and S. Impedovo and G. Pirlo
title: A new technique for fast number comparison in the residue number system
journal: j-IEEE-TRANS-COMPUT
volume: 42
number: 5
pages: 608--612
month: may
monthnumber: 5
year: 1993
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.223680
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 07:58:49 MDT 2011
bibtimestamp: 2011.07.07 07:58:49 MDT
fjournal: IEEE Transactions on Computers
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: G. Dimauro and S. Impedovo and G. Pirlo
rawtitle: A new technique for fast number comparison in the residue number system
URL:
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=5840; https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=223680

entry:
@Article{Dimauro:1993:NTF,
  author =       "G. Dimauro and S. Impedovo and G. Pirlo",
  title =        "A new technique for fast number comparison in the
                 residue number system",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "42",
  number =       "5",
  pages =        "608--612",
  month =        may,
  year =         "1993",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.223680",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:58:49 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=5840;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=223680",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A technique for number comparison in the residue
                 number system is presented, and its theoretical
                 validity is proved. The proposed solution is based on
                 using a diagonal function to obtain a magnitude order
                 of the numbers. In a first approach the \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Dittmer:1993:EUC
author: Ingo Dittmer
title: Error in Unix commands tt dc and tt bc for multiple-precision-arithmetic
journal: j-SIGNUM
volume: 28
number: 2
pages: 8--11
month: apr
monthnumber: 4
year: 1993
CODEN: SNEWD6
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Tue Apr 12 07:50:23 MDT 2005
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.04.12 07:50:23 MDT
fjournal: ACM SIGNUM Newsletter
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/signum
rawauthor: Ingo Dittmer
rawtitle: Error in {Unix} commands {\tt dc} and {\tt bc} for multiple-precision-arithmetic
entry:
@Article{Dittmer:1993:EUC,
  author =       "Ingo Dittmer",
  title =        "Error in {Unix} commands {\tt dc} and {\tt bc} for
                 multiple-precision-arithmetic",
  journal =      j-SIGNUM,
  volume =       "28",
  number =       "2",
  pages =        "8--11",
  month =        apr,
  year =         "1993",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:23 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
}


bibtype: book
filename: fparith.bib
label: Dowd:1993:HPC
author: Kevin Dowd
title: High Performance Computing
publisher: pub-ORA
address: pub-ORA:adr
pages: xxv + 371
year: 1993
ISBN: 1-56592-032-5 OR 1565920325
ISBN13: 978-1-56592-032-3 OR 9781565920323
LCCN: QA76.88 .D6 1993; QA76.9.A73 D68 1993
bibdate: Mon Jan 3 18:34:37 1994
bibtimestamp: 1994.01.03 18:34:37 ???
series: RISC architectures, optimization and benchmarks; A Nutshell handbook
URL: http://www.oreilly.com/catalog/9781565920323
acknowledgement: ack-nhfb
rawauthor: Kevin Dowd
rawtitle: High Performance Computing
bibsource:
https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/hpfortran.bib; https://www.math.utah.edu/pub/tex/bib/master.bib; https://www.math.utah.edu/pub/tex/bib/ora.bib; z3950.loc.gov:7090/Voyager

subject:
Computer architecture; Electronic digital computers; Parallel processing (Electronic computers); Supercomputers

TOC:
Preface / xxi Who Should Buy This Book? / xxii What's in This Book / xxii Conventions / xxiv Acknowledgments / xxv 1 Modern Computer Architectures / 1 1: What is High Performance Computing? / 3 Why Worry About Performance? / 3 Measuring Performance / 5 The Next Step / 6 2: RISC Computers / 9 Why CISC? / 10 Space and Time / 10 Beliefs About Complex Instruction Sets / 11 Memory Addressing Modes / 12 Microcode / 14 Making the Most of a Clock Tick / 17 Pipelines / 18 Instruction Pipelining / 19 Why RISC? / 21 Characterizing RISC / 22 A Few More Words About Pipelining / 27 Memory References / 27 Floating Point Pipelines / 28 Classes of Processors / 29 Superscalar Processors / 30 Superpipelined Processors / 32 Long Instruction Word (LIW) / 34 Other Advanced Features / 35 Register Bypass / 36 Register Renaming / 36 Reducing Branch Penalties / 37 Closing Notes / 40 3: Memory / 43 Memory Technology / 44 Random Access Memory / 45 Access Time / 47 Caches / 48 Direct Mapped Cache / 50 Fully Associative Cache / 52 Set Associative Cache / 52 Uses of Cache / 54 Virtual Memory / 54 Page Tables / 55 Translation Lookaside Buffer / 56 Page Faults / 57 Improving Bandwidth / 59 Large Caches / 60 Interleaved Memory Systems / 60 Software Managed Caches / 64 Memory Reference Reordering / 64 Multiple References / 66 Closing Notes / 67 IL Porting and Tuning Software / 91 4: What an Optimizing Compiler Does / 69 Optimizing Compiler Tour / 70 Intermediate Language Representation / 70 Basic Blocks / 72 Forming a DAG / 74 Uses and Definitions / 76 Loops / 78 Object Code Generation / 80 Classical Optimizations / 81 Copy Propagation / 81 Constant Folding / 82 Dead Code Removal / 83 Strength Reduction / 84 Variable Renaming / 84 Common Subexpression Elimination / 85 Loop Invariant Code Motion / 86 Induction Variable Simplification / 87 Register Variable Detection / 88 Closing Notes / 88 5: Clarity / 93 Under Construction / 94 Comments / 94 Clues in the Landscape / 95 Variable Names / 96 Variable Types / 98 Named Constants / 99 INCLUDE Statements / 100 Use of COMMON / 101 The Shape of Data / 102 Closing Notes / 104 6: Finding Porting Problems / 105 Problems in Argument Lists / 106 Aliasing / 106 Argument Type Mismatch / 108 Storage Issues / 110 Equivalenced Storage / 111 Memory Reference Alignment Restrictions / 112 Closing Notes / 115 7: Timing and Profiling / 119 Timing / 120 Timing a Whole Program / 120 Timing a Portion of the Program / 124 Using Timing Information / 126 Subroutine Profiling / 127 prof / 130 gprof / 133 gprofs Flat Profile / 138 Accumulating the Results of Several gprof Runs / 139 A Few Words About Accuracy / 140 Basic Block Profilers / 140 tcov / 141 !prof / 142 pixie / 143 Closing Notes / 144 8: Understanding Parallelism / 147 A Few Important Concepts / 148 Constants / 148 Scalars / 150 Vectors and Vector Processing / 150 Dependencies / 153 Data Dependencies / 154 Control Dependencies / 159 Ambiguous References / 161 Closing Notes / 162 9: Eliminating Clutter / 165 Subroutine Calls / 166 Macros / 168 Procedure Inlining / 170 Branches / 171 Wordy Conditionals / 171 Redundant Tests / 172 Branches Within Loops / 173 Loop Invariant Conditionals / 174 Loop Index Dependent Conditionals / 175 Independent Loop Conditionals / 176 Dependent Loop Conditionals / 177 Reductions / 178 Conditionals That Transfer Control / 179 A Few Words About Branch Probability / 180 Other Clutter / 181 Data Type Conversions / 181 Doing Your Own Common Subexpression Elimination / 182 Doing Your Own Code Motion / 183 Handling Array Elements in Loops / 184 Closing Notes / 185 10: Loop Optimizations / 187 Basic Loop Unrolling / 188 Qualifying Candidates for Loop Unrolling / 189 Loops with Low Trip Counts / 190 Fat Loops / 191 Loops Containing Procedure Calls / 191 Loops with Branches in Them / 193 Recursive Loops / 194 Negatives of Loop Unrolling / 195 Unrolling by the Wrong Factor / 196 Register Thrashing / 196 Instruction Cache Miss / 197 Other Hardware Delays / 197 Outer Loop Unrolling / 197 Outer Loop Unrolling to Expose Computations / 199 Associative Transformations / 200 Reductions / 202 Dot Products and daxpys / 204 Matrix Multiplication / 206 Loop Interchange / 208 Loop Interchange to Move Computations to the Center / 208 Operation Counting / 209 Closing Notes / 211 11: Memory Reference Optimizations / 213 Memory Access Patterns / 214 Loop Interchange to Ease Memory Access Patterns / 215 Blocking to Ease Memory Access Patterns / 216 Ambiguity in Memory References / 223 Ambiguity in Vector Operations / 224 Pointer Ambiguity in Numerical C Applications / 225 Programs That Require More Memory Than You Have / 227 Software-Managed, Out-of-Core Solutions / 227 Virtual Memory / 228 Instruction Cache Ordering / 231 Closing Notes / 232 12: Language Support for Performance / 235 Subroutine Libraries / 235 Vectorizing Preprocessors / 237 Explicitly Parallel Languages / 243 Fortran 90 / 244 High Performance Fortran (HPF) / 250 Explicitly Parallel Programming Environments / 251 Closing Notes / 253 1/L Evaluating Performance / 255 13: Industry Benchmarks / 257 What is a MIP? / 258 VAX MIPS / 259 Dhrystones / 259 Floating Point Benchmarks / 261 Linpack / 262 Whetstone / 264 The SPEC Benchmarks / 265 Individual SPEC Benchmarks / 266 030.matrix300 Was Deleted / 272 Transaction Processing Benchmarks / 272 TPC-A / 273 TPC-B / 273 TPC-C / 273 Closing Notes / 273 14: Running Your Own Benchmarks / 275 Choosing What to Benchmark / 275 Benchmark Run Time / 276 Benchmark Memory Size / 277 Kernels and Sanitized Benchmarks / 277 Benchmarking Third Party Codes / 278 Types of Benchmarks / 279 Single Stream Benchmarks / 280 Throughput Benchmarks / 282 Interactive Benchmarks / 283 Preparing the Code / 285 Portability / 285 Making a Benchmark Kit / 286 Benchmarking Checklist / 287 Closing Notes / 288 IV. Parallel Computing / 291 15: Large Scale Parallel Computing / 293 Problem Decomposition / 294 Data Decomposition / 295 Control Decomposition / 299 Distributing Work Fairly / 300 Classes of Parallel Architectures / 302 Single Instruction, Multiple Data / 303 SIMD Architecture / 305 Mechanics of Programming a SIMD Machine / 309 Multiple Instruction, Multiple Data / 312 Distributed Memory MIMD Architecture / 314 Programming a Distributed Memory MIMD Machine / 315 A Few Words About Data Layout Directives / 319 Virtual Shared Memory / 320 Closing Notes / 323 16: Shared-Memory Multiprocessors / 325 Symmetric Multiprocessing / 326 Operating System Support for Multiprocessing / 327 Multiprocessor Architecture / 329 Shared Memory / 330 Conservation of Bandwidth / 330 Coherency / 332 Data Placement / 334 Multiprocessor Software Concepts / 334 Fork and Join / 335 Synchronization with Locks / 337 Synchronization with Barriers / 340 Automatic Parallelization / 341 Loop Splitting / 341 Subroutine Calls in Loops / 342 Nested Loops / 342 Manual Parallelism / 344 Closing Notes / 345 A: Processor Overview / 347 B: How to Tell When Loops Can Be Interchanged / 351 C: Obtaining Sample Programs and Problem Set Answers / 357 FTP / 357 FTPMAIL / 358 BITFTP / 359 UUCP / 359 Figures 2: RISC Computers / 9 2-1 Registers, a single common data path, and an adder / 15 2-2 A pipeline / 18 2-3 Three instructions in flight through one pipeline / 20 2-4 Variable length instructions make pipelining difficult / 23 2-5 Variable length CISC versus fixed length RISC instructions / 23 2-6 Processor encounters a branch / 26 2-7 The Branch Delay Slot --- ZERO R3 executes either way / 27 2-8 Memory references scheduled early to account for pipeline depth / 28 2-9 Decomposing a serial stream / 30 2-10 RS/ 6000 functional blocks / 31 2-11 MIPS R4000 Instruction Pipeline / 33 2-12 Intel i860 transition between modes / 35 3: Memory / 43 3-1 Row--Column memory address / 46 3-2 Direct mapping of memory address to RAM / 46 3-3 Cache lines can come from different parts of memory / 49 3-4 Many memory addresses map to same cache line / 51 3-5 Two -way set associative cache / 53 3-6 Virtual to physical address mapping / 55 3-7 Simple memory system / 59 3-8 Page mode cache refill / 60 3-9 Multi-banked memory system / 62 3-10 Cache refill from interleaved memory / 63 4: What an Optimizing Compiler Does / 69 4-1 Example 4-1 divided into basic blocks / 73 4-2 Tuple mapped into a DAG / 74 4-3 Basic Block B / 75 4-4 DAG for Block B / 75 4-5 Revised Basic Block B / 76 4-6 Flow graph for data flow analysis / 77 4-7 Flow graph with a loop in it / 79 5: Clarity / 93 5-1 Array C in two -dimensional memory / 103 6: Finding Porting Problems / 105 6-1 IEEE 754 floating point formats / 109 6-2 IBM 370 floating point formats / 110 6-3 Equivalence storage relationship on most computers / 111 6-4 Misaligned variables / 113 7: Timing and Pro.filing / 119 7-1 The built-in csh time function / 123 7-2 Sharp profile --- dominated by routine 1 / 128 7-3 Flat profile --- no routine predominates / 129 7-4 Simple call graph / 134 7-5 FORTRAN example / 135 7-6 Quantization Errors in Profiling / 140 8: Understanding Parallelism / 147 8-1 Vector Computer / 152 8-2 A little section of your program / 159 8-3 Expensive operation moved so that it's rarely executed / 160 11: Memory Reference Optimizations / 213 11-1 Arrays A and B / 217 11-2 How array elements are stored / 218 11-3 2x2 squares / 219 11-4 Picture of unblocked versus blocked references / 220 11-5 Optimization performance for various sized loops / 222 11-6 Vector machine memory access / 223 12: Language Support for Performance / 235 12-1 Linda's Tuple Space Bulletin Board / 252 14: Running Your Own Benchmarks / 275 14-1 Kernel benchmark / 278 14-2 Single stream benchmarks / 280 14-3 Computing an overall benchmark score / 281 14-4 Wrong way to run a throughput benchmark / 282 14-5 Benchmark stone wall / 283 14-6 Interactive use benchmark / 284 _15:Large Scale Parallel Computing / 293 15-1 Domain decomposition / 295 15-2 Cells with X's have life / 296 15-3 One iteration later / 297 15-4 Two examples of division of cells between four CPUs / 298 15-5 Each processor with a piece of the domain / 300 15-6 Duplicated data domain / 301 15-7 Iterations mapped onto SIMD nodes / 304 15-8 Mapping a route through a strictly Cartesian mesh / 306 15-9 Four nodes / 307 15-10 A 3-cube and a 4-cube / 307 15-11 Front-end and SIMD machine / 309 15-12 KSR-1 ring of rings architecture / 322 16: Shared-Memory Multiprocessors / 325 16-1 A typical bus architecture / 329 16-2 A $4 times 4$ crossbar / 330 16-3 High cache hit rate reduces main memory traffic / 331 16-4 Multiple copies of variable A / 332 16-5 Fork and join / 335 16-6 Integration / 337 16-7 Implementation of a spinlock / 339 B: How to Tell When Loops Can Be Interchanged / 351 B-1 $4 times 4$ matrix / 352 B-2 One iteration complete / 353 B-3 All iterations completed / 354 B-4 Movement of data in array A / 355 Examples 4: What an Optimizing Compiler Does / 69 4-1 Intermediate Language for a Single Loop / 72 5: Clarity / 93 5-1 Comments, asterisks, and pretty printing / 95 5-2 Variable names count / 97 5-3 Parameter statements 5-4 Declarations / 100 5-5 Routine using both INCLUDE files / 100 5-6 Changing the Shape of an Array / 100 / 102 6: Finding Porting Problems / 105 6-1 Program for creating misaligned references 6-2 Misaligned reference in C / 114 / 115 7: Timing and Profiling / 119 7-1 FORTRAN program using etime / 125 7-2 etime implemented in C / 126 7-3 loops.c --- a program for testing profilers / 131 7-4 Profile of loops.c / 132 7-5 A portion of gprof output / 135 7-6 gprof flat profile / 138 8: Understanding Parallelism / 147 8-1 Vector Addition / 150 9: Eliminating Clutter / 165 9-1 Macro definition and use / 168 10: Loop Optimizations / 187 10-1 Loop containing a procedure call / 192 10-2 Matrix multiply with daxpy inner loop / 206 10-3 Matrix multiply with dot product inner loop / 206 11: Memory Reference Optimizations / 213 11-1 Two-dimensional vector sum / 216 11-2 Outer and inner loop unrolled / 217 B: How to Tell When Loops Can Be Interchanged / 351 B-1 Each iteration is independent / 351 B-2 Can we interchange these loops? / 352 B-3 Legal alternate loop nests / 354 B-4 More complicated references / 355 B-5 More complicated references / 356 Tables 6: Finding Porting Problems / 105 6-1 Preferred Alignment Boundaries on Most Computers / 113 15: Large Scale Parallel Computing / 293 15-1 Worst Case Communication / 308 A: Processor Overview / 347 A-1 CPU Characteristics / 347 A-2 Cache and Branch Architecture / 348 A-2 Cache and Branch Architecture (continued) / 349

rawTOC:
Preface / xxi \\ Who Should Buy This Book? / xxii \\ What's in This Book / xxii \\ Conventions / xxiv \\ Acknowledgments / xxv \\ 1 Modern Computer Architectures / 1 \\ 1: What is High Performance Computing? / 3 \\ Why Worry About Performance? / 3 \\ Measuring Performance / 5 \\ The Next Step / 6 \\ 2: RISC Computers / 9 \\ Why CISC? / 10 \\ Space and Time / 10 \\ Beliefs About Complex Instruction Sets / 11 \\ Memory Addressing Modes / 12 \\ Microcode / 14 \\ Making the Most of a Clock Tick / 17 \\ Pipelines / 18 \\ Instruction Pipelining / 19 \\ Why RISC? / 21 \\ Characterizing RISC / 22 \\ A Few More Words About Pipelining / 27 \\ Memory References / 27 \\ Floating Point Pipelines / 28 \\ Classes of Processors / 29 \\ Superscalar Processors / 30 \\ Superpipelined Processors / 32 \\ Long Instruction Word (LIW) / 34 \\ Other Advanced Features / 35 \\ Register Bypass / 36 \\ Register Renaming / 36 \\ Reducing Branch Penalties / 37 \\ Closing Notes / 40 \\ 3: Memory / 43 \\ Memory Technology / 44 \\ Random Access Memory / 45 \\ Access Time / 47 \\ Caches / 48 \\ Direct Mapped Cache / 50 \\ Fully Associative Cache / 52 \\ Set Associative Cache / 52 \\ Uses of Cache / 54 \\ Virtual Memory / 54 \\ Page Tables / 55 \\ Translation Lookaside Buffer / 56 \\ Page Faults / 57 \\ Improving Bandwidth / 59 \\ Large Caches / 60 \\ Interleaved Memory Systems / 60 \\ Software Managed Caches / 64 \\ Memory Reference Reordering / 64 \\ Multiple References / 66 \\ Closing Notes / 67 \\ IL Porting and Tuning Software / 91 \\ 4: What an Optimizing Compiler Does / 69 \\ Optimizing Compiler Tour / 70 \\ Intermediate Language Representation / 70 \\ Basic Blocks / 72 \\ Forming a DAG / 74 \\ Uses and Definitions / 76 \\ Loops / 78 \\ Object Code Generation / 80 \\ Classical Optimizations / 81 \\ Copy Propagation / 81 \\ Constant Folding / 82 \\ Dead Code Removal / 83 \\ Strength Reduction / 84 \\ Variable Renaming / 84 \\ Common Subexpression Elimination / 85 \\ Loop Invariant Code Motion / 86 \\ Induction Variable Simplification / 87 \\ Register Variable Detection / 88 \\ Closing Notes / 88 \\ 5: Clarity / 93 \\ Under Construction / 94 \\ Comments / 94 \\ Clues in the Landscape / 95 \\ Variable Names / 96 \\ Variable Types / 98 \\ Named Constants / 99 \\ INCLUDE Statements / 100 \\ Use of COMMON / 101 \\ The Shape of Data / 102 \\ Closing Notes / 104 \\ 6: Finding Porting Problems / 105 \\ Problems in Argument Lists / 106 \\ Aliasing / 106 \\ Argument Type Mismatch / 108 \\ Storage Issues / 110 \\ Equivalenced Storage / 111 \\ Memory Reference Alignment Restrictions / 112 \\ Closing Notes / 115 \\ 7: Timing and Profiling / 119 \\ Timing / 120 \\ Timing a Whole Program / 120 \\ Timing a Portion of the Program / 124 \\ Using Timing Information / 126 \\ Subroutine Profiling / 127 \\ prof / 130 \\ gprof / 133 \\ gprofs Flat Profile / 138 \\ Accumulating the Results of Several gprof Runs / 139 \\ A Few Words About Accuracy / 140 \\ Basic Block Profilers / 140 \\ tcov / 141 \\ !prof / 142 \\ pixie / 143 \\ Closing Notes / 144 \\ 8: Understanding Parallelism / 147 \\ A Few Important Concepts / 148 \\ Constants / 148 \\ Scalars / 150 \\ Vectors and Vector Processing / 150 \\ Dependencies / 153 \\ Data Dependencies / 154 \\ Control Dependencies / 159 \\ Ambiguous References / 161 \\ Closing Notes / 162 \\ 9: Eliminating Clutter / 165 \\ Subroutine Calls / 166 \\ Macros / 168 \\ Procedure Inlining / 170 \\ Branches / 171 \\ Wordy Conditionals / 171 \\ Redundant Tests / 172 \\ Branches Within Loops / 173 \\ Loop Invariant Conditionals / 174 \\ Loop Index Dependent Conditionals / 175 \\ Independent Loop Conditionals / 176 \\ Dependent Loop Conditionals / 177 \\ Reductions / 178 \\ Conditionals That Transfer Control / 179 \\ A Few Words About Branch Probability / 180 \\ Other Clutter / 181 \\ Data Type Conversions / 181 \\ Doing Your Own Common Subexpression Elimination / 182 \\ Doing Your Own Code Motion / 183 \\ Handling Array Elements in Loops / 184 \\ Closing Notes / 185 \\ 10: Loop Optimizations / 187 \\ Basic Loop Unrolling / 188 \\ Qualifying Candidates for Loop Unrolling / 189 \\ Loops with Low Trip Counts / 190 \\ Fat Loops / 191 \\ Loops Containing Procedure Calls / 191 \\ Loops with Branches in Them / 193 \\ Recursive Loops / 194 \\ Negatives of Loop Unrolling / 195 \\ Unrolling by the Wrong Factor / 196 \\ Register Thrashing / 196 \\ Instruction Cache Miss / 197 \\ Other Hardware Delays / 197 \\ Outer Loop Unrolling / 197 \\ Outer Loop Unrolling to Expose Computations / 199 \\ Associative Transformations / 200 \\ Reductions / 202 \\ Dot Products and daxpys / 204 \\ Matrix Multiplication / 206 \\ Loop Interchange / 208 \\ Loop Interchange to Move Computations to the Center / 208 \\ Operation Counting / 209 \\ Closing Notes / 211 \\ 11: Memory Reference Optimizations / 213 \\ Memory Access Patterns / 214 \\ Loop Interchange to Ease Memory Access Patterns / 215 \\ Blocking to Ease Memory Access Patterns / 216 \\ Ambiguity in Memory References / 223 \\ Ambiguity in Vector Operations / 224 \\ Pointer Ambiguity in Numerical C Applications / 225 \\ Programs That Require More Memory Than You Have / 227 \\ Software-Managed, Out-of-Core Solutions / 227 \\ Virtual Memory / 228 \\ Instruction Cache Ordering / 231 \\ Closing Notes / 232 \\ 12: Language Support for Performance / 235 \\ Subroutine Libraries / 235 \\ Vectorizing Preprocessors / 237 \\ Explicitly Parallel Languages / 243 \\ Fortran 90 / 244 \\ High Performance Fortran (HPF) / 250 \\ Explicitly Parallel Programming Environments / 251 \\ Closing Notes / 253 \\ 1/L Evaluating Performance / 255 \\ 13: Industry Benchmarks / 257 \\ What is a MIP? / 258 \\ VAX MIPS / 259 \\ Dhrystones / 259 \\ Floating Point Benchmarks / 261 \\ Linpack / 262 \\ Whetstone / 264 \\ The SPEC Benchmarks / 265 \\ Individual SPEC Benchmarks / 266 \\ 030.matrix300 Was Deleted / 272 \\ Transaction Processing Benchmarks / 272 \\ TPC-A / 273 \\ TPC-B / 273 \\ TPC-C / 273 \\ Closing Notes / 273 \\ 14: Running Your Own Benchmarks / 275 \\ Choosing What to Benchmark / 275 \\ Benchmark Run Time / 276 \\ Benchmark Memory Size / 277 \\ Kernels and Sanitized Benchmarks / 277 \\ Benchmarking Third Party Codes / 278 \\ Types of Benchmarks / 279 \\ Single Stream Benchmarks / 280 \\ Throughput Benchmarks / 282 \\ Interactive Benchmarks / 283 \\ Preparing the Code / 285 \\ Portability / 285 \\ Making a Benchmark Kit / 286 \\ Benchmarking Checklist / 287 \\ Closing Notes / 288 \\ IV. Parallel Computing / 291 \\ 15: Large Scale Parallel Computing / 293 \\ Problem Decomposition / 294 \\ Data Decomposition / 295 \\ Control Decomposition / 299 \\ Distributing Work Fairly / 300 \\ Classes of Parallel Architectures / 302 \\ Single Instruction, Multiple Data / 303 \\ SIMD Architecture / 305 \\ Mechanics of Programming a SIMD Machine / 309 \\ Multiple Instruction, Multiple Data / 312 \\ Distributed Memory MIMD Architecture / 314 \\ Programming a Distributed Memory MIMD Machine / 315 \\ A Few Words About Data Layout Directives / 319 \\ Virtual Shared Memory / 320 \\ Closing Notes / 323 \\ 16: Shared-Memory Multiprocessors / 325 \\ Symmetric Multiprocessing / 326 \\ Operating System Support for Multiprocessing / 327 \\ Multiprocessor Architecture / 329 \\ Shared Memory / 330 \\ Conservation of Bandwidth / 330 \\ Coherency / 332 \\ Data Placement / 334 \\ Multiprocessor Software Concepts / 334 \\ Fork and Join / 335 \\ Synchronization with Locks / 337 \\ Synchronization with Barriers / 340 \\ Automatic Parallelization / 341 \\ Loop Splitting / 341 \\ Subroutine Calls in Loops / 342 \\ Nested Loops / 342 \\ Manual Parallelism / 344 \\ Closing Notes / 345 \\ A: Processor Overview / 347 \\ B: How to Tell When Loops Can Be Interchanged / 351 \\ C: Obtaining Sample Programs and Problem Set Answers / 357 \\ FTP / 357 \\ FTPMAIL / 358 \\ BITFTP / 359 \\ UUCP / 359 \\ Figures \\ 2: RISC Computers / 9 \\ 2-1 Registers, a single common data path, and an adder / 15 \\ 2-2 A pipeline / 18 \\ 2-3 Three instructions in flight through one pipeline / 20 \\ 2-4 Variable length instructions make pipelining difficult / 23 \\ 2-5 Variable length CISC versus fixed length RISC instructions / 23 \\ 2-6 Processor encounters a branch / 26 \\ 2-7 The Branch Delay Slot --- ZERO R3 executes either way / 27 \\ 2-8 Memory references scheduled early to account for pipeline depth / 28 \\ 2-9 Decomposing a serial stream / 30 \\ 2-10 RS/ 6000 functional blocks / 31 \\ 2-11 MIPS R4000 Instruction Pipeline / 33 \\ 2-12 Intel i860 transition between modes / 35 \\ 3: Memory / 43 \\ 3-1 Row--Column memory address / 46 \\ 3-2 Direct mapping of memory address to RAM / 46 \\ 3-3 Cache lines can come from different parts of memory / 49 \\ 3-4 Many memory addresses map to same cache line / 51 \\ 3-5 Two -way set associative cache / 53 \\ 3-6 Virtual to physical address mapping / 55 \\ 3-7 Simple memory system / 59 \\ 3-8 Page mode cache refill / 60 \\ 3-9 Multi-banked memory system / 62 \\ 3-10 Cache refill from interleaved memory / 63 \\ 4: What an Optimizing Compiler Does / 69 \\ 4-1 Example 4-1 divided into basic blocks / 73 \\ 4-2 Tuple mapped into a DAG / 74 \\ 4-3 Basic Block B / 75 \\ 4-4 DAG for Block B / 75 \\ 4-5 Revised Basic Block B / 76 \\ 4-6 Flow graph for data flow analysis / 77 \\ 4-7 Flow graph with a loop in it / 79 \\ 5: Clarity / 93 \\ 5-1 Array C in two -dimensional memory / 103 \\ 6: Finding Porting Problems / 105 \\ 6-1 IEEE 754 floating point formats / 109 \\ 6-2 IBM 370 floating point formats / 110 \\ 6-3 Equivalence storage relationship on most computers / 111 \\ 6-4 Misaligned variables / 113 \\ 7: Timing and Pro.filing / 119 \\ 7-1 The built-in csh time function / 123 \\ 7-2 Sharp profile --- dominated by routine 1 / 128 \\ 7-3 Flat profile --- no routine predominates / 129 \\ 7-4 Simple call graph / 134 \\ 7-5 FORTRAN example / 135 \\ 7-6 Quantization Errors in Profiling / 140 \\ 8: Understanding Parallelism / 147 \\ 8-1 Vector Computer / 152 \\ 8-2 A little section of your program / 159 \\ 8-3 Expensive operation moved so that it's rarely executed / 160 \\ 11: Memory Reference Optimizations / 213 \\ 11-1 Arrays A and B / 217 \\ 11-2 How array elements are stored / 218 \\ 11-3 2x2 squares / 219 \\ 11-4 Picture of unblocked versus blocked references / 220 \\ 11-5 Optimization performance for various sized loops / 222 \\ 11-6 Vector machine memory access / 223 \\ 12: Language Support for Performance / 235 \\ 12-1 Linda's Tuple Space Bulletin Board / 252 \\ 14: Running Your Own Benchmarks / 275 \\ 14-1 Kernel benchmark / 278 \\ 14-2 Single stream benchmarks / 280 \\ 14-3 Computing an overall benchmark score / 281 \\ 14-4 Wrong way to run a throughput benchmark / 282 \\ 14-5 Benchmark stone wall / 283 \\ 14-6 Interactive use benchmark / 284 \\ _15:Large Scale Parallel Computing / 293 \\ 15-1 Domain decomposition / 295 \\ 15-2 Cells with X's have life / 296 \\ 15-3 One iteration later / 297 \\ 15-4 Two examples of division of cells between four CPUs / 298 \\ 15-5 Each processor with a piece of the domain / 300 \\ 15-6 Duplicated data domain / 301 \\ 15-7 Iterations mapped onto SIMD nodes / 304 \\ 15-8 Mapping a route through a strictly Cartesian mesh / 306 \\ 15-9 Four nodes / 307 \\ 15-10 A 3-cube and a 4-cube / 307 \\ 15-11 Front-end and SIMD machine / 309 \\ 15-12 KSR-1 ring of rings architecture / 322 \\ 16: Shared-Memory Multiprocessors / 325 \\ 16-1 A typical bus architecture / 329 \\ 16-2 A $4 \times 4$ crossbar / 330 \\ 16-3 High cache hit rate reduces main memory traffic / 331 \\ 16-4 Multiple copies of variable A / 332 \\ 16-5 Fork and join / 335 \\ 16-6 Integration / 337 \\ 16-7 Implementation of a spinlock / 339 \\ B: How to Tell When Loops Can Be Interchanged / 351 \\ B-1 $4 \times 4$ matrix / 352 \\ B-2 One iteration complete / 353 \\ B-3 All iterations completed / 354 \\ B-4 Movement of data in array A / 355 \\ Examples \\ 4: What an Optimizing Compiler Does / 69 \\ 4-1 Intermediate Language for a Single Loop / 72 \\ 5: Clarity / 93 \\ 5-1 Comments, asterisks, and pretty printing / 95 \\ 5-2 Variable names count / 97 \\ 5-3 Parameter statements \\ 5-4 Declarations / 100 \\ 5-5 Routine using both INCLUDE files / 100 \\ 5-6 Changing the Shape of an Array / 100 \\ / 102 \\ 6: Finding Porting Problems / 105 \\ 6-1 Program for creating misaligned references \\ 6-2 Misaligned reference in C / 114 \\ / 115 \\ 7: Timing and Profiling / 119 \\ 7-1 FORTRAN program using etime / 125 \\ 7-2 etime implemented in C / 126 \\ 7-3 loops.c --- a program for testing profilers / 131 \\ 7-4 Profile of loops.c / 132 \\ 7-5 A portion of gprof output / 135 \\ 7-6 gprof flat profile / 138 \\ 8: Understanding Parallelism / 147 \\ 8-1 Vector Addition / 150 \\ 9: Eliminating Clutter / 165 \\ 9-1 Macro definition and use / 168 \\ 10: Loop Optimizations / 187 \\ 10-1 Loop containing a procedure call / 192 \\ 10-2 Matrix multiply with daxpy inner loop / 206 \\ 10-3 Matrix multiply with dot product inner loop / 206 \\ 11: Memory Reference Optimizations / 213 \\ 11-1 Two-dimensional vector sum / 216 \\ 11-2 Outer and inner loop unrolled / 217 \\ B: How to Tell When Loops Can Be Interchanged / 351 \\ B-1 Each iteration is independent / 351 \\ B-2 Can we interchange these loops? / 352 \\ B-3 Legal alternate loop nests / 354 \\ B-4 More complicated references / 355 \\ B-5 More complicated references / 356 \\ Tables \\ 6: Finding Porting Problems / 105 \\ 6-1 Preferred Alignment Boundaries on Most Computers / 113 \\ 15: Large Scale Parallel Computing / 293 \\ 15-1 Worst Case Communication / 308 \\ A: Processor Overview / 347 \\ A-1 CPU Characteristics / 347 \\ A-2 Cache and Branch Architecture / 348 \\ A-2 Cache and Branch Architecture (continued) / 349

entry:
@Book{Dowd:1993:HPC,
  author =       "Kevin Dowd",
  title =        "High Performance Computing",
  publisher =    pub-ORA,
  address =      pub-ORA:adr,
  pages =        "xxv + 371",
  year =         "1993",
  ISBN =         "1-56592-032-5",
  ISBN-13 =      "978-1-56592-032-3",
  LCCN =         "QA76.88 .D6 1993; QA76.9.A73 D68 1993",
  bibdate =      "Mon Jan 3 18:34:37 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/hpfortran.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/ora.bib;
                 z3950.loc.gov:7090/Voyager",
  price =        "US\$25.95",
  series =       "RISC architectures, optimization and benchmarks; A
                 Nutshell handbook",
  URL =          "http://www.oreilly.com/catalog/9781565920323",
  acknowledgement = ack-nhfb,
  subject =      "Computer architecture; Electronic digital computers;
                 Parallel processing (Electronic computers);
                 Supercomputers",
  tableofcontents = "Preface / xxi \\
                 Who Should Buy This Book? / xxii \\
                 What's in This Book / xxii \\
                 Conventions / xxiv \\
                 Acknowledgments / xxv \\
                 1 Modern Computer Architectures / 1 \\
                 1: What is High Performance Computing? / 3 \\
                 Why Worry About Performance? / 3 \\
                 Measuring Performance / 5 \\
                 The Next Step / 6 \\
                 2: RISC Computers / 9 \\
                 Why CISC? / 10 \\
                 Space and Time / 10 \\
                 Beliefs About Complex Instruction Sets / 11 \\
                 Memory Addressing Modes / 12 \\
                 Microcode / 14 \\
                 Making the Most of a Clock Tick / 17 \\
                 Pipelines / 18 \\
                 Instruction Pipelining / 19 \\
                 Why RISC? / 21 \\
                 Characterizing RISC / 22 \\
                 A Few More Words About Pipelining / 27 \\
                 Memory References / 27 \\
                 Floating Point Pipelines / 28 \\
                 Classes of Processors / 29 \\
                 Superscalar Processors / 30 \\
                 Superpipelined Processors / 32 \\
                 Long Instruction Word (LIW) / 34 \\
                 Other Advanced Features / 35 \\
                 Register Bypass / 36 \\
                 Register Renaming / 36 \\
                 Reducing Branch Penalties / 37 \\
                 Closing Notes / 40 \\
                 3: Memory / 43 \\
                 Memory Technology / 44 \\
                 Random Access Memory / 45 \\
                 Access Time / 47 \\
                 Caches / 48 \\
                 Direct Mapped Cache / 50 \\
                 Fully Associative Cache / 52 \\
                 Set Associative Cache / 52 \\
                 Uses of Cache / 54 \\
                 Virtual Memory / 54 \\
                 Page Tables / 55 \\
                 Translation Lookaside Buffer / 56 \\
                 Page Faults / 57 \\
                 Improving Bandwidth / 59 \\
                 Large Caches / 60 \\
                 Interleaved Memory Systems / 60 \\
                 Software Managed Caches / 64 \\
                 Memory Reference Reordering / 64 \\
                 Multiple References / 66 \\
                 Closing Notes / 67 \\
                 IL Porting and Tuning Software / 91 \\
                 4: What an Optimizing Compiler Does / 69 \\
                 Optimizing Compiler Tour / 70 \\
                 Intermediate Language Representation / 70 \\
                 Basic Blocks / 72 \\
                 Forming a DAG / 74 \\
                 Uses and Definitions / 76 \\
                 Loops / 78 \\
                 Object Code Generation / 80 \\
                 Classical Optimizations / 81 \\
                 Copy Propagation / 81 \\
                 Constant Folding / 82 \\
                 Dead Code Removal / 83 \\
                 Strength Reduction / 84 \\
                 Variable Renaming / 84 \\
                 Common Subexpression Elimination / 85 \\
                 Loop Invariant Code Motion / 86 \\
                 Induction Variable Simplification / 87 \\
                 Register Variable Detection / 88 \\
                 Closing Notes / 88 \\
                 5: Clarity / 93 \\
                 Under Construction / 94 \\
                 Comments / 94 \\
                 Clues in the Landscape / 95 \\
                 Variable Names / 96 \\
                 Variable Types / 98 \\
                 Named Constants / 99 \\
                 INCLUDE Statements / 100 \\
                 Use of COMMON / 101 \\
                 The Shape of Data / 102 \\
                 Closing Notes / 104 \\
                 6: Finding Porting Problems / 105 \\
                 Problems in Argument Lists / 106 \\
                 Aliasing / 106 \\
                 Argument Type Mismatch / 108 \\
                 Storage Issues / 110 \\
                 Equivalenced Storage / 111 \\
                 Memory Reference Alignment Restrictions / 112 \\
                 Closing Notes / 115 \\
                 7: Timing and Profiling / 119 \\
                 Timing / 120 \\
                 Timing a Whole Program / 120 \\
                 Timing a Portion of the Program / 124 \\
                 Using Timing Information / 126 \\
                 Subroutine Profiling / 127 \\
                 prof / 130 \\
                 gprof / 133 \\
                 gprofs Flat Profile / 138 \\
                 Accumulating the Results of Several gprof Runs / 139
                 \\
                 A Few Words About Accuracy / 140 \\
                 Basic Block Profilers / 140 \\
                 tcov / 141 \\
                 !prof / 142 \\
                 pixie / 143 \\
                 Closing Notes / 144 \\
                 8: Understanding Parallelism / 147 \\
                 A Few Important Concepts / 148 \\
                 Constants / 148 \\
                 Scalars / 150 \\
                 Vectors and Vector Processing / 150 \\
                 Dependencies / 153 \\
                 Data Dependencies / 154 \\
                 Control Dependencies / 159 \\
                 Ambiguous References / 161 \\
                 Closing Notes / 162 \\
                 9: Eliminating Clutter / 165 \\
                 Subroutine Calls / 166 \\
                 Macros / 168 \\
                 Procedure Inlining / 170 \\
                 Branches / 171 \\
                 Wordy Conditionals / 171 \\
                 Redundant Tests / 172 \\
                 Branches Within Loops / 173 \\
                 Loop Invariant Conditionals / 174 \\
                 Loop Index Dependent Conditionals / 175 \\
                 Independent Loop Conditionals / 176 \\
                 Dependent Loop Conditionals / 177 \\
                 Reductions / 178 \\
                 Conditionals That Transfer Control / 179 \\
                 A Few Words About Branch Probability / 180 \\
                 Other Clutter / 181 \\
                 Data Type Conversions / 181 \\
                 Doing Your Own Common Subexpression Elimination / 182
                 \\
                 Doing Your Own Code Motion / 183 \\
                 Handling Array Elements in Loops / 184 \\
                 Closing Notes / 185 \\
                 10: Loop Optimizations / 187 \\
                 Basic Loop Unrolling / 188 \\
                 Qualifying Candidates for Loop Unrolling / 189 \\
                 Loops with Low Trip Counts / 190 \\
                 Fat Loops / 191 \\
                 Loops Containing Procedure Calls / 191 \\
                 Loops with Branches in Them / 193 \\
                 Recursive Loops / 194 \\
                 Negatives of Loop Unrolling / 195 \\
                 Unrolling by the Wrong Factor / 196 \\
                 Register Thrashing / 196 \\
                 Instruction Cache Miss / 197 \\
                 Other Hardware Delays / 197 \\
                 Outer Loop Unrolling / 197 \\
                 Outer Loop Unrolling to Expose Computations / 199 \\
                 Associative Transformations / 200 \\
                 Reductions / 202 \\
                 Dot Products and daxpys / 204 \\
                 Matrix Multiplication / 206 \\
                 Loop Interchange / 208 \\
                 Loop Interchange to Move Computations to the Center /
                 208 \\
                 Operation Counting / 209 \\
                 Closing Notes / 211 \\
                 11: Memory Reference Optimizations / 213 \\
                 Memory Access Patterns / 214 \\
                 Loop Interchange to Ease Memory Access Patterns / 215
                 \\
                 Blocking to Ease Memory Access Patterns / 216 \\
                 Ambiguity in Memory References / 223 \\
                 Ambiguity in Vector Operations / 224 \\
                 Pointer Ambiguity in Numerical C Applications / 225 \\
                 Programs That Require More Memory Than You Have / 227
                 \\
                 Software-Managed, Out-of-Core Solutions / 227 \\
                 Virtual Memory / 228 \\
                 Instruction Cache Ordering / 231 \\
                 Closing Notes / 232 \\
                 12: Language Support for Performance / 235 \\
                 Subroutine Libraries / 235 \\
                 Vectorizing Preprocessors / 237 \\
                 Explicitly Parallel Languages / 243 \\
                 Fortran 90 / 244 \\
                 High Performance Fortran (HPF) / 250 \\
                 Explicitly Parallel Programming Environments / 251 \\
                 Closing Notes / 253 \\
                 1/L Evaluating Performance / 255 \\
                 13: Industry Benchmarks / 257 \\
                 What is a MIP? / 258 \\
                 VAX MIPS / 259 \\
                 Dhrystones / 259 \\
                 Floating Point Benchmarks / 261 \\
                 Linpack / 262 \\
                 Whetstone / 264 \\
                 The SPEC Benchmarks / 265 \\
                 Individual SPEC Benchmarks / 266 \\
                 030.matrix300 Was Deleted / 272 \\
                 Transaction Processing Benchmarks / 272 \\
                 TPC-A / 273 \\
                 TPC-B / 273 \\
                 TPC-C / 273 \\
                 Closing Notes / 273 \\
                 14: Running Your Own Benchmarks / 275 \\
                 Choosing What to Benchmark / 275 \\
                 Benchmark Run Time / 276 \\
                 Benchmark Memory Size / 277 \\
                 Kernels and Sanitized Benchmarks / 277 \\
                 Benchmarking Third Party Codes / 278 \\
                 Types of Benchmarks / 279 \\
                 Single Stream Benchmarks / 280 \\
                 Throughput Benchmarks / 282 \\
                 Interactive Benchmarks / 283 \\
                 Preparing the Code / 285 \\
                 Portability / 285 \\
                 Making a Benchmark Kit / 286 \\
                 Benchmarking Checklist / 287 \\
                 Closing Notes / 288 \\
                 IV. Parallel Computing / 291 \\
                 15: Large Scale Parallel Computing / 293 \\
                 Problem Decomposition / 294 \\
                 Data Decomposition / 295 \\
                 Control Decomposition / 299 \\
                 Distributing Work Fairly / 300 \\
                 Classes of Parallel Architectures / 302 \\
                 Single Instruction, Multiple Data / 303 \\
                 SIMD Architecture / 305 \\
                 Mechanics of Programming a SIMD Machine / 309 \\
                 Multiple Instruction, Multiple Data / 312 \\
                 Distributed Memory MIMD Architecture / 314 \\
                 Programming a Distributed Memory MIMD Machine / 315 \\
                 A Few Words About Data Layout Directives / 319 \\
                 Virtual Shared Memory / 320 \\
                 Closing Notes / 323 \\
                 16: Shared-Memory Multiprocessors / 325 \\
                 Symmetric Multiprocessing / 326 \\
                 Operating System Support for Multiprocessing / 327 \\
                 Multiprocessor Architecture / 329 \\
                 Shared Memory / 330 \\
                 Conservation of Bandwidth / 330 \\
                 Coherency / 332 \\
                 Data Placement / 334 \\
                 Multiprocessor Software Concepts / 334 \\
                 Fork and Join / 335 \\
                 Synchronization with Locks / 337 \\
                 Synchronization with Barriers / 340 \\
                 Automatic Parallelization / 341 \\
                 Loop Splitting / 341 \\
                 Subroutine Calls in Loops / 342 \\
                 Nested Loops / 342 \\
                 Manual Parallelism / 344 \\
                 Closing Notes / 345 \\
                 A: Processor Overview / 347 \\
                 B: How to Tell When Loops Can Be Interchanged / 351 \\
                 C: Obtaining Sample Programs and Problem Set Answers /
                 357 \\
                 FTP / 357 \\
                 FTPMAIL / 358 \\
                 BITFTP / 359 \\
                 UUCP / 359 \\
                 Figures \\
                 2: RISC Computers / 9 \\
                 2-1 Registers, a single common data path, and an adder
                 / 15 \\
                 2-2 A pipeline / 18 \\
                 2-3 Three instructions in flight through one pipeline /
                 20 \\
                 2-4 Variable length instructions make pipelining
                 difficult / 23 \\
                 2-5 Variable length CISC versus fixed length RISC
                 instructions / 23 \\
                 2-6 Processor encounters a branch / 26 \\
                 2-7 The Branch Delay Slot --- ZERO R3 executes either
                 way / 27 \\
                 2-8 Memory references scheduled early to account for
                 pipeline depth / 28 \\
                 2-9 Decomposing a serial stream / 30 \\
                 2-10 RS/ 6000 functional blocks / 31 \\
                 2-11 MIPS R4000 Instruction Pipeline / 33 \\
                 2-12 Intel i860 transition between modes / 35 \\
                 3: Memory / 43 \\
                 3-1 Row--Column memory address / 46 \\
                 3-2 Direct mapping of memory address to RAM / 46 \\
                 3-3 Cache lines can come from different parts of memory
                 / 49 \\
                 3-4 Many memory addresses map to same cache line / 51
                 \\
                 3-5 Two -way set associative cache / 53 \\
                 3-6 Virtual to physical address mapping / 55 \\
                 3-7 Simple memory system / 59 \\
                 3-8 Page mode cache refill / 60 \\
                 3-9 Multi-banked memory system / 62 \\
                 3-10 Cache refill from interleaved memory / 63 \\
                 4: What an Optimizing Compiler Does / 69 \\
                 4-1 Example 4-1 divided into basic blocks / 73 \\
                 4-2 Tuple mapped into a DAG / 74 \\
                 4-3 Basic Block B / 75 \\
                 4-4 DAG for Block B / 75 \\
                 4-5 Revised Basic Block B / 76 \\
                 4-6 Flow graph for data flow analysis / 77 \\
                 4-7 Flow graph with a loop in it / 79 \\
                 5: Clarity / 93 \\
                 5-1 Array C in two -dimensional memory / 103 \\
                 6: Finding Porting Problems / 105 \\
                 6-1 IEEE 754 floating point formats / 109 \\
                 6-2 IBM 370 floating point formats / 110 \\
                 6-3 Equivalence storage relationship on most computers
                 / 111 \\
                 6-4 Misaligned variables / 113 \\
                 7: Timing and Pro.filing / 119 \\
                 7-1 The built-in csh time function / 123 \\
                 7-2 Sharp profile --- dominated by routine 1 / 128 \\
                 7-3 Flat profile --- no routine predominates / 129 \\
                 7-4 Simple call graph / 134 \\
                 7-5 FORTRAN example / 135 \\
                 7-6 Quantization Errors in Profiling / 140 \\
                 8: Understanding Parallelism / 147 \\
                 8-1 Vector Computer / 152 \\
                 8-2 A little section of your program / 159 \\
                 8-3 Expensive operation moved so that it's rarely
                 executed / 160 \\
                 11: Memory Reference Optimizations / 213 \\
                 11-1 Arrays A and B / 217 \\
                 11-2 How array elements are stored / 218 \\
                 11-3 2x2 squares / 219 \\
                 11-4 Picture of unblocked versus blocked references /
                 220 \\
                 11-5 Optimization performance for various sized loops /
                 222 \\
                 11-6 Vector machine memory access / 223 \\
                 12: Language Support for Performance / 235 \\
                 12-1 Linda's Tuple Space Bulletin Board / 252 \\
                 14: Running Your Own Benchmarks / 275 \\
                 14-1 Kernel benchmark / 278 \\
                 14-2 Single stream benchmarks / 280 \\
                 14-3 Computing an overall benchmark score / 281 \\
                 14-4 Wrong way to run a throughput benchmark / 282 \\
                 14-5 Benchmark stone wall / 283 \\
                 14-6 Interactive use benchmark / 284 \\
                 _15:Large Scale Parallel Computing / 293 \\
                 15-1 Domain decomposition / 295 \\
                 15-2 Cells with X's have life / 296 \\
                 15-3 One iteration later / 297 \\
                 15-4 Two examples of division of cells between four
                 CPUs / 298 \\
                 15-5 Each processor with a piece of the domain / 300
                 \\
                 15-6 Duplicated data domain / 301 \\
                 15-7 Iterations mapped onto SIMD nodes / 304 \\
                 15-8 Mapping a route through a strictly Cartesian mesh
                 / 306 \\
                 15-9 Four nodes / 307 \\
                 15-10 A 3-cube and a 4-cube / 307 \\
                 15-11 Front-end and SIMD machine / 309 \\
                 15-12 KSR-1 ring of rings architecture / 322 \\
                 16: Shared-Memory Multiprocessors / 325 \\
                 16-1 A typical bus architecture / 329 \\
                 16-2 A $4 \times 4$ crossbar / 330 \\
                 16-3 High cache hit rate reduces main memory traffic /
                 331 \\
                 16-4 Multiple copies of variable A / 332 \\
                 16-5 Fork and join / 335 \\
                 16-6 Integration / 337 \\
                 16-7 Implementation of a spinlock / 339 \\
                 B: How to Tell When Loops Can Be Interchanged / 351 \\
                 B-1 $4 \times 4$ matrix / 352 \\
                 B-2 One iteration complete / 353 \\
                 B-3 All iterations completed / 354 \\
                 B-4 Movement of data in array A / 355 \\
                 Examples \\
                 4: What an Optimizing Compiler Does / 69 \\
                 4-1 Intermediate Language for a Single Loop / 72 \\
                 5: Clarity / 93 \\
                 5-1 Comments, asterisks, and pretty printing / 95 \\
                 5-2 Variable names count / 97 \\
                 5-3 Parameter statements \\
                 5-4 Declarations / 100 \\
                 5-5 Routine using both INCLUDE files / 100 \\
                 5-6 Changing the Shape of an Array / 100 \\
                 / 102 \\
                 6: Finding Porting Problems / 105 \\
                 6-1 Program for creating misaligned references \\
                 6-2 Misaligned reference in C / 114 \\
                 / 115 \\
                 7: Timing and Profiling / 119 \\
                 7-1 FORTRAN program using etime / 125 \\
                 7-2 etime implemented in C / 126 \\
                 7-3 loops.c --- a program for testing profilers / 131
                 \\
                 7-4 Profile of loops.c / 132 \\
                 7-5 A portion of gprof output / 135 \\
                 7-6 gprof flat profile / 138 \\
                 8: Understanding Parallelism / 147 \\
                 8-1 Vector Addition / 150 \\
                 9: Eliminating Clutter / 165 \\
                 9-1 Macro definition and use / 168 \\
                 10: Loop Optimizations / 187 \\
                 10-1 Loop containing a procedure call / 192 \\
                 10-2 Matrix multiply with daxpy inner loop / 206 \\
                 10-3 Matrix multiply with dot product inner loop / 206
                 \\
                 11: Memory Reference Optimizations / 213 \\
                 11-1 Two-dimensional vector sum / 216 \\
                 11-2 Outer and inner loop unrolled / 217 \\
                 B: How to Tell When Loops Can Be Interchanged / 351 \\
                 B-1 Each iteration is independent / 351 \\
                 B-2 Can we interchange these loops? / 352 \\
                 B-3 Legal alternate loop nests / 354 \\
                 B-4 More complicated references / 355 \\
                 B-5 More complicated references / 356 \\
                 Tables \\
                 6: Finding Porting Problems / 105 \\
                 6-1 Preferred Alignment Boundaries on Most Computers /
                 113 \\
                 15: Large Scale Parallel Computing / 293 \\
                 15-1 Worst Case Communication / 308 \\
                 A: Processor Overview / 347 \\
                 A-1 CPU Characteristics / 347 \\
                 A-2 Cache and Branch Architecture / 348 \\
                 A-2 Cache and Branch Architecture (continued) / 349",
}


bibtype: article
filename: fparith.bib
label: Duncan:1993:CES
author: Roy Duncan and John Tunstall and Brian T. Smith and Richard Brankin
title: Correspondence: Expert Systems for Re-ordering Arithmetic Expressions?
journal: j-FORTRAN-FORUM
volume: 12
number: 3
pages: 12--14
month: sep
monthnumber: 9
year: 1993
ISSN: 1061-7264 (print), 1931-1311 (electronic) OR 10617264 (print), 19311311 (electronic)
ISSNL: 1061-7264 OR 10617264
bibdate: Tue Apr 23 14:50:51 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.04.23 14:50:51 ???
fjournal: ACM Fortran Forum
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/toc.cfm?id=J286
issue: 35
rawauthor: Roy Duncan and John Tunstall and Brian T. Smith and Richard Brankin
rawtitle: Correspondence: Expert Systems for Re-ordering Arithmetic Expressions?
entry:
@Article{Duncan:1993:CES,
  author =       "Roy Duncan and John Tunstall and Brian T. Smith and
                 Richard Brankin",
  title =        "Correspondence: Expert Systems for Re-ordering
                 Arithmetic Expressions?",
  journal =      j-FORTRAN-FORUM,
  volume =       "12",
  number =       "3",
  pages =        "12--14",
  month =        sep,
  year =         "1993",
  CODEN =        "????",
  ISSN =         "1061-7264 (print), 1931-1311 (electronic)",
  ISSN-L =       "1061-7264",
  bibdate =      "Tue Apr 23 14:50:51 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Fortran Forum",
  issue =        "35",
  journal-URL =  "http://portal.acm.org/toc.cfm?id=J286",
}


bibtype: article
filename: fparith.bib
label: Duprat:1993:CAN
author: J. Duprat and J. Muller
title: The CORDIC Algorithm: New Results for Fast VLSI Implementation
journal: j-IEEE-TRANS-COMPUT
volume: 42
number: 2
pages: 168--178
month: feb
monthnumber: 2
year: 1993
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.204786
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Sep 1 10:15:40 1994
bibtimestamp: 1994.09.01 10:15:40 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: J. Duprat and J. Muller
rawtitle: The {CORDIC} Algorithm: New Results for Fast {VLSI} Implementation
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib

entry:
@Article{Duprat:1993:CAN,
  author =       "J. Duprat and J. Muller",
  title =        "The {CORDIC} Algorithm: New Results for Fast {VLSI}
                 Implementation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "42",
  number =       "2",
  pages =        "168--178",
  month =        feb,
  year =         "1993",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.204786",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 1 10:15:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  acknowledgement = ack-nj,
  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: Eisig:1993:DBI
author: David Eisig and Josh Rotstain and Israel Koren
title: The Design of a 64-bit Integer Multiplier / Divider Unit
crossref: Swartzlander:1993:SCA
pages: 171--178
year: 1993
bibdate: Sat Nov 17 09:46:07 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.17 09:46:07 ???
URL: http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Eisig.pdf
keywords: ARITH-11
acknowledgement: ack-nhfb
rawauthor: David Eisig and Josh Rotstain and Israel Koren
rawtitle: The Design of a 64-bit Integer Multiplier\slash Divider Unit
entry:
@InProceedings{Eisig:1993:DBI,
  author =       "David Eisig and Josh Rotstain and Israel Koren",
  title =        "The Design of a 64-bit Integer Multiplier\slash
                 Divider Unit",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "171--178",
  year =         "1993",
  bibdate =      "Sat Nov 17 09:46:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Eisig.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
}


bibtype: article
filename: fparith.bib
label: Eldridge:1993:HIM
author: S. E. Eldridge and C. D. Walter
title: Hardware implementation of Montgomery's modular multiplication algorithm
journal: j-IEEE-TRANS-COMPUT
volume: 42
number: 6
pages: 693--699
month: jun
monthnumber: 6
year: 1993
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.277287
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 07:58:49 MDT 2011
bibtimestamp: 2011.07.07 07:58:49 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=277287
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: S. E. Eldridge and C. D. Walter
rawtitle: Hardware implementation of {Montgomery}'s modular multiplication algorithm
entry:
@Article{Eldridge:1993:HIM,
  author =       "S. E. Eldridge and C. D. Walter",
  title =        "Hardware implementation of {Montgomery}'s modular
                 multiplication algorithm",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "42",
  number =       "6",
  pages =        "693--699",
  month =        jun,
  year =         "1993",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.277287",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:58:49 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=277287",
  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: Ercegovac:1993:VHR
author: Milos D. Ercegovac and Tomas Lang and Paolo Montuschi
title: Very high radix division with selection by rounding and prescaling
crossref: Swartzlander:1993:SCA
pages: 112--119
year: 1993
bibdate: Sat Jul 16 11:25:04 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:04 MDT
URL: http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Ercegovac.pdf
keywords: ARITH-11
acknowledgement: ack-nhfb
rawauthor: Milo{\v{s}} D. Ercegovac and Tom{\'a}s Lang and Paolo Montuschi
rawtitle: Very high radix division with selection by rounding and prescaling
entry:
@InProceedings{Ercegovac:1993:VHR,
  author =       "Milo{\v{s}} D. Ercegovac and Tom{\'a}s Lang and Paolo
                 Montuschi",
  title =        "Very high radix division with selection by rounding
                 and prescaling",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "112--119",
  year =         "1993",
  bibdate =      "Sat Jul 16 11:25:04 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Ercegovac.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
  summary =      "A division algorithm in which the quotient-digit
                 selection is performed by rounding the shifted residual
                 in carry-save form is presented. To allow the use of
                 this simple function, the divisor (and dividend) is
                 prescaled to a range close to one. The \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Etiemble:1993:AMV
author: D. Etiemble and K. Navi
crossref: Swartzlander:1993:SCA
pages: 194--201
year: 1993
bibdate: Sat Nov 17 09:46:07 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.17 09:46:07 ???
URL: http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Etiemble.pdf
keywords: ARITH-11
acknowledgement: ack-nhfb
rawauthor: D. Etiemble and K. Navi
title:
Algorithms and Multi-Valued Circuits for the Multioperand Addition in the Binary Stored-Carry Number System

rawtitle:
Algorithms and Multi-Valued Circuits for the Multioperand Addition in the Binary Stored-Carry Number System

entry:
@InProceedings{Etiemble:1993:AMV,
  author =       "D. Etiemble and K. Navi",
  title =        "Algorithms and Multi-Valued Circuits for the
                 Multioperand Addition in the Binary Stored-Carry Number
                 System",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "194--201",
  year =         "1993",
  bibdate =      "Sat Nov 17 09:46:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Etiemble.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
}


bibtype: inproceedings
filename: fparith.bib
label: Fortune:1993:EEA
author: Steven Fortune and Christopher J. Van Wyk
editor: ACM
title: Efficient Exact Arithmetic for Computational Geometry
publisher: pub-ACM
address: pub-ACM:adr
pages: 163--172
year: 1993
DOI: https://doi.org/10.1145/160985.161015
ISBN: 0-89791-582-8 OR 0897915828
ISBN13: 978-0-89791-582-3 OR 9780897915823
LCCN: QA448.D38 S96 1993
bibdate: Tue Nov 13 21:44:58 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.13 21:44:58 ???
acknowledgement: ack-nhfb
bookpages: vii + 406
rawauthor: Steven Fortune and Christopher J. {Van Wyk}
raweditor: {ACM}
rawtitle: Efficient Exact Arithmetic for Computational Geometry
booktitle:
Proceedings of the 9th ACM Symposium on Computational Geometry, May 19--21, 1993, San Diego, CA, USA

rawbooktitle:
{Proceedings of the 9th ACM Symposium on Computational Geometry, May 19--21, 1993, San Diego, CA, USA}

entry:
@InProceedings{Fortune:1993:EEA,
  author =       "Steven Fortune and Christopher J. {Van Wyk}",
  editor =       "{ACM}",
  booktitle =    "{Proceedings of the 9th ACM Symposium on Computational
                 Geometry, May 19--21, 1993, San Diego, CA, USA}",
  title =        "Efficient Exact Arithmetic for Computational
                 Geometry",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  bookpages =    "vii + 406",
  pages =        "163--172",
  year =         "1993",
  DOI =          "https://doi.org/10.1145/160985.161015",
  ISBN =         "0-89791-582-8",
  ISBN-13 =      "978-0-89791-582-3",
  LCCN =         "QA448.D38 S96 1993",
  bibdate =      "Tue Nov 13 21:44:58 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Fowkes:1993:HEA
author: R. E. Fowkes
title: Hardware Efficient Algorithms for Trigonometric Functions
journal: j-IEEE-TRANS-COMPUT
volume: 42
number: 3
pages: 235--239
month: feb
monthnumber: 2
year: 1993
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.204796
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Sep 1 10:16:09 1994
bibtimestamp: 1994.09.01 10:16:09 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: R. E. Fowkes
rawtitle: Hardware Efficient Algorithms for Trigonometric Functions
entry:
@Article{Fowkes:1993:HEA,
  author =       "R. E. Fowkes",
  title =        "Hardware Efficient Algorithms for Trigonometric
                 Functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "42",
  number =       "3",
  pages =        "235--239",
  month =        feb,
  year =         "1993",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.204796",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 1 10:16:09 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  acknowledgement = ack-nj,
  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: Fox:1993:HLS
author: J. R. Fox
title: A higher level of synthesis (CAD)
journal: j-IEEE-SPECTRUM
volume: 30
number: 3
pages: 43--47
month: mar
monthnumber: 3
year: 1993
CODEN: IEESAM
DOI: https://doi.org/10.1109/6.211955
ISSN: 0018-9235 (print), 1939-9340 (electronic) OR 00189235 (print), 19399340 (electronic)
ISSNL: 0018-9235 OR 00189235
bibdate: Thu Jan 16 07:37:23 2020
bibtimestamp: 2020.01.16 07:37:23 ???
fjournal: IEEE Spectrum
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6
rawauthor: J. R. Fox
rawtitle: A higher level of synthesis ({CAD})
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeespectrum1990.bib

keywords:
abstraction; Arithmetic; CAD; Circuit synthesis; Clocks; design automation; Design automation; Design engineering; design synthesis systems; Fabrication; Hardware; hardware description languages; Logic circuits; Logic design; Microarchitecture; software tools; specification languages; testability; top-down design

entry:
@Article{Fox:1993:HLS,
  author =       "J. R. Fox",
  title =        "A higher level of synthesis ({CAD})",
  journal =      j-IEEE-SPECTRUM,
  volume =       "30",
  number =       "3",
  pages =        "43--47",
  month =        mar,
  year =         "1993",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/6.211955",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Thu Jan 16 07:37:23 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeespectrum1990.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
  keywords =     "abstraction; Arithmetic; CAD; Circuit synthesis;
                 Clocks; design automation; Design automation; Design
                 engineering; design synthesis systems; Fabrication;
                 Hardware; hardware description languages; Logic
                 circuits; Logic design; Microarchitecture; software
                 tools; specification languages; testability; top-down
                 design",
}


bibtype: mastersthesis
filename: fparith.bib
label: Geraminejad:1993:DIC
author: Mohsen Geraminejad
title: Design and implementation of a 16-bit CMOS floating point multiplier
type: Research paper (M.S.)
school: Department of Electrical Engineering, Southern Illinois University at Carbondale
address: Carbondale, IL, USA
pages: vii + 54
year: 1993
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
acknowledgement: ack-nhfb
rawauthor: Mohsen Geraminejad
rawtitle: Design and implementation of a 16-bit {CMOS} floating point multiplier
entry:
@MastersThesis{Geraminejad:1993:DIC,
  author =       "Mohsen Geraminejad",
  title =        "Design and implementation of a 16-bit {CMOS} floating
                 point multiplier",
  type =         "Research paper ({M.S.})",
  school =       "Department of Electrical Engineering, Southern
                 Illinois University at Carbondale",
  address =      "Carbondale, IL, USA",
  pages =        "vii + 54",
  year =         "1993",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Gibbons:1993:FMW
author: Jeremy Gibbons
editor: John Hosking
title: Formal Methods: Why Should I Care? The development of the T800 transputer floating-point unit
publisher: New Zealand Computer Society
address: Wellington, NZ
pages: 207--217
year: 1993
ISBN: 0-9597657-6-X; 0-9597657-5-1 OR 095976576X; 0959765751
ISBN13: 978-0-9597657-6-2; 978-0-9597657-5-5 OR 9780959765762; 9780959765755
bibdate: Tue Nov 13 21:37:21 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.13 21:37:21 ???
keywords: Inmos T800 transputer
acknowledgement: ack-nhfb
rawauthor: Jeremy Gibbons
raweditor: John Hosking
booktitle:
Proceedings of the 13th New Zealand Computer Society Conference: Applying the future today, Aotea Centre, Auckland, 18--20 August 1993

abstract:
The term `formal methods' is a general term for precise mathematically-based techniques used in the development of computer systems, both hardware and software. This paper discusses formal methods in general, and in particular describes their successful role in specifying, constructing and proving correct the floating-point unit of the Inmos T800 transputer chip.

rawabstract:
The term `formal methods' is a general term for precise mathematically-based techniques used in the development of computer systems, both hardware and software. This paper discusses formal methods in general, and in particular describes their successful role in specifying, constructing and proving correct the floating-point unit of the Inmos T800 transputer chip.

rawbooktitle:
{Proceedings of the 13th New Zealand Computer Society Conference: Applying the future today, Aotea Centre, Auckland, 18--20 August 1993}

rawtitle:
Formal Methods: {Why} Should {I} Care? {The} development of the {T800} transputer floating-point unit

entry:
@InProceedings{Gibbons:1993:FMW,
  author =       "Jeremy Gibbons",
  editor =       "John Hosking",
  booktitle =    "{Proceedings of the 13th New Zealand Computer Society
                 Conference: Applying the future today, Aotea Centre,
                 Auckland, 18--20 August 1993}",
  title =        "Formal Methods: {Why} Should {I} Care? {The}
                 development of the {T800} transputer floating-point
                 unit",
  publisher =    "New Zealand Computer Society",
  address =      "Wellington, NZ",
  pages =        "207--217",
  year =         "1993",
  ISBN =         "0-9597657-6-X; 0-9597657-5-1",
  ISBN-13 =      "978-0-9597657-6-2; 978-0-9597657-5-5",
  LCCN =         "????",
  bibdate =      "Tue Nov 13 21:37:21 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The term `formal methods' is a general term for
                 precise mathematically-based techniques used in the
                 development of computer systems, both hardware and
                 software. This paper discusses formal methods in
                 general, and in particular describes their successful
                 role in specifying, constructing and proving correct
                 the floating-point unit of the Inmos T800 transputer
                 chip.",
  acknowledgement = ack-nhfb,
  keywords =     "Inmos T800 transputer",
}


bibtype: techreport
filename: fparith.bib
label: Goldberg:1993:DFP
author: David Goldberg
title: The design of floating-point data types
type: Technical report
number: CSL-93-3
institution: Xerox Corp., Palo Alto Research Center
address: Palo Alto, CA, USA
pages: 19
year: 1993
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Abstract data types (Computer science)
acknowledgement: ack-nhfb
rawauthor: David Goldberg
rawtitle: The design of floating-point data types
remark:
``A version of this paper will appear in Letters on Programming Languages and Systems.'' ``February 1993.'' Abstract: ``We discuss the issues involved in designing the floating-point part of a programming language. Looking at the language specifications for most existing languages might suggest that this design involves only trivial issues such as whether to have one or two types of REALs or how to name the functions that convert from INTEGER to REAL. We show that there are more significant semantic issues involved. After discussing the tradeoffs for the major design decisions, we illustrate them by presenting the design of the floating-point part of the Modula-3 language.''

entry:
@TechReport{Goldberg:1993:DFP,
  author =       "David Goldberg",
  title =        "The design of floating-point data types",
  type =         "Technical report",
  number =       "CSL-93-3",
  institution =  "Xerox Corp., Palo Alto Research Center",
  address =      "Palo Alto, CA, USA",
  pages =        "19",
  year =         "1993",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Abstract data types (Computer science)",
  remark =       "``A version of this paper will appear in Letters on
                 Programming Languages and Systems.'' ``February 1993.''
                 Abstract: ``We discuss the issues involved in designing
                 the floating-point part of a programming language.
                 Looking at the language specifications for most
                 existing languages might suggest that this design
                 involves only trivial issues such as whether to have
                 one or two types of REALs or how to name the functions
                 that convert from INTEGER to REAL. We show that there
                 are more significant semantic issues involved. After
                 discussing the tradeoffs for the major design
                 decisions, we illustrate them by presenting the design
                 of the floating-point part of the Modula-3
                 language.''",
}


bibtype: techreport
filename: fparith.bib
label: Gudeman:1993:RTI
author: David Gudeman
title: Representing Type Information in Dynamically Typed Languages
type: Technical report
number: TR 93-27
institution: Department of Computer Science, The University of Arizona
address: Tucson, AZ 85721, USA
pages: 40
month: oct
monthnumber: 10
year: 1993
bibdate: Wed Oct 13 08:12:36 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.13 08:12:36 ???
keywords: floating-point arithmetic; integer arithmetic; Lisp; Prolog; typed objects
remark: Discusses implementation of fast arithmetic for typed integer and floating-point data.
acknowledgement: ack-nhfb
rawauthor: David Gudeman
rawtitle: Representing Type Information in Dynamically Typed Languages
URL:
ftp://ftp.cs.arizona.edu/reports/1993/TR93-27.ps; http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.39.4394

abstract:
This report is a discussion of various techniques for representing type information in dynamically typed languages, as implemented on general-purpose machines (and costs are discussed in terms of modern RISC machines). It is intended to make readily available a large body of knowledge that currently has to be absorbed piecemeal from the literature or re-invented by each language implementer. This discussion covers not only tagging schemes but other forms of representation as well, although the discussion is strictly limited to the representation of type information. It should also be noted that this report does not purport to contain a survey of the relevant literature. Instead, this report gathers together a body of folklore, organizes it into a logical structure, makes some generalizations, and then discusses the results in terms of modern hardware.

rawabstract:
This report is a discussion of various techniques for representing type information in dynamically typed languages, as implemented on general-purpose machines (and costs are discussed in terms of modern RISC machines). It is intended to make readily available a large body of knowledge that currently has to be absorbed piecemeal from the literature or re-invented by each language implementer. This discussion covers not only tagging schemes but other forms of representation as well, although the discussion is strictly limited to the representation of type information. It should also be noted that this report does not purport to contain a survey of the relevant literature. Instead, this report gathers together a body of folklore, organizes it into a logical structure, makes some generalizations, and then discusses the results in terms of modern hardware.

entry:
@TechReport{Gudeman:1993:RTI,
  author =       "David Gudeman",
  title =        "Representing Type Information in Dynamically Typed
                 Languages",
  type =         "Technical report",
  number =       "TR 93-27",
  institution =  "Department of Computer Science, The University of
                 Arizona",
  address =      "Tucson, AZ 85721, USA",
  pages =        "40",
  month =        oct,
  year =         "1993",
  bibdate =      "Wed Oct 13 08:12:36 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://ftp.cs.arizona.edu/reports/1993/TR93-27.ps;
                 http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.39.4394",
  abstract =     "This report is a discussion of various techniques for
                 representing type information in dynamically typed
                 languages, as implemented on general-purpose machines
                 (and costs are discussed in terms of modern RISC
                 machines). It is intended to make readily available a
                 large body of knowledge that currently has to be
                 absorbed piecemeal from the literature or re-invented
                 by each language implementer. This discussion covers
                 not only tagging schemes but other forms of
                 representation as well, although the discussion is
                 strictly limited to the representation of type
                 information. It should also be noted that this report
                 does not purport to contain a survey of the relevant
                 literature. Instead, this report gathers together a
                 body of folklore, organizes it into a logical
                 structure, makes some generalizations, and then
                 discusses the results in terms of modern hardware.",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point arithmetic; integer arithmetic; Lisp;
                 Prolog; typed objects",
  remark =       "Discusses implementation of fast arithmetic for typed
                 integer and floating-point data.",
}


bibtype: misc
filename: fparith.bib
label: Gupta:1993:NPF
author: S. Gupta and R. Periman and T. Lynch and B. McMinn
title: Normalizing pipelined floating point processing units
pages: 40
day: 30
month: nov
monthnumber: 11
year: 1993
bibdate: Fri Nov 28 15:27:34 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 15:27:34 ???
note: U.S. Patent No. 5,267,186.
acknowledgement: ack-nhfb
rawauthor: S. Gupta and R. Periman and T. Lynch and B. McMinn
rawnote: U.S. Patent No. 5,267,186.
rawtitle: Normalizing pipelined floating point processing units
entry:
@Misc{Gupta:1993:NPF,
  author =       "S. Gupta and R. Periman and T. Lynch and B. McMinn",
  title =        "Normalizing pipelined floating point processing
                 units",
  day =          "30",
  month =        nov,
  year =         "1993",
  bibdate =      "Fri Nov 28 15:27:34 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "U.S. Patent No. 5,267,186.",
  acknowledgement = ack-nhfb,
}


bibtype: incollection
filename: fparith.bib
label: Hammer:1993:PXN
author: R. Hammer and M. Neaga and D. Ratz
title: PASCAL-XSC: New Concepts for Scientific Computation and Numerical Data Processing
crossref: Adams:1993:SCA
pages: 15--44
year: 1993
bibdate: Wed Oct 13 22:38:56 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.13 22:38:56 ???
acknowledgement: ack-nhfb
rawauthor: R. Hammer and M. Neaga and D. Ratz
rawtitle: {PASCAL-XSC}: New Concepts for Scientific Computation and Numerical Data Processing
entry:
@InCollection{Hammer:1993:PXN,
  author =       "R. Hammer and M. Neaga and D. Ratz",
  title =        "{PASCAL-XSC}: New Concepts for Scientific Computation
                 and Numerical Data Processing",
  crossref =     "Adams:1993:SCA",
  pages =        "15--44",
  year =         "1993",
  bibdate =      "Wed Oct 13 22:38:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Hasan:1993:MMO
author: M. A. Hasan and M. Z. Wang and V. K. Bhargava
title: A modified Massey--Omura parallel multiplier for a class of finite fields
journal: j-IEEE-TRANS-COMPUT
volume: 42
number: 10
pages: 1278--1280
month: oct
monthnumber: 10
year: 1993
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.257715
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 07:58:51 MDT 2011
bibtimestamp: 2011.07.07 07:58:51 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=257715
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: M. A. Hasan and M. Z. Wang and V. K. Bhargava
rawtitle: A modified {Massey--Omura} parallel multiplier for a class of finite fields
entry:
@Article{Hasan:1993:MMO,
  author =       "M. A. Hasan and M. Z. Wang and V. K. Bhargava",
  title =        "A modified {Massey--Omura} parallel multiplier for a
                 class of finite fields",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "42",
  number =       "10",
  pages =        "1278--1280",
  month =        oct,
  year =         "1993",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.257715",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:58:51 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=257715",
  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: Hatzinakos:1993:AFP
author: D. Hatzinakos
title: Analysis of floating point roundoff errors in the estimation of higher-order statistics
journal: IEE proceedings. F, Radar and signal processing
volume: 140
number: 6
pages: 371--379
month: dec
monthnumber: 12
year: 1993
ISSN: 0956-375X OR 0956375X
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
acknowledgement: ack-nhfb
rawauthor: D. Hatzinakos
rawtitle: Analysis of floating point roundoff errors in the estimation of higher-order statistics
entry:
@Article{Hatzinakos:1993:AFP,
  author =       "D. Hatzinakos",
  title =        "Analysis of floating point roundoff errors in the
                 estimation of higher-order statistics",
  journal =      "IEE proceedings. F, Radar and signal processing",
  volume =       "140",
  number =       "6",
  pages =        "371--379",
  month =        dec,
  year =         "1993",
  ISSN =         "0956-375X",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "A floating point roundoff error analysis in the
                 estimation of higher-order statistics, moments or
                 cumulants of real stationary processes from single data
                 records is provided. Closed form expressions or upper
                 bounds are derived for the mean and \ldots{}",
}


bibtype: book
filename: fparith.bib
label: Heinrich:1993:MRM
author: Joe Heinrich
title: MIPS R4000 Microprocessor User's Manual
publisher: pub-PHPTR
address: pub-PHPTR:adr
pages: xxvi + 438 + A182 + B62 + C6 + D4 + E4
year: 1993
ISBN: 0-13-105925-4 OR 0131059254
ISBN13: 978-0-13-105925-2 OR 9780131059252
LCCN: QA76.8.M523H45 1993
bibdate: Wed Aug 10 11:02:27 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/master.bib
bibtimestamp: 1994.08.10 11:02:27 ???
acknowledgement: ack-nhfb
rawauthor: Joe Heinrich
rawtitle: {MIPS R4000} Microprocessor User's Manual
TOC:
Introduction CPU Instruction Set Summary The CPU Pipeline Memory Management CPU Exception Processing Floating-Point Unit Floating-Point Exceptions R4000 Processor Signal Descriptions Initialization Interface Clock Interface Cache Organization, Operation, and Coherency System Interface Secondary Cache Interface JTAG Interface R4000 Processor Interrupts Error Checking and Correcting CPU Instruction Set Details FPU Instruction Set Details Subblock Ordering Output Buffer ldots Di ldots Dt Control Mechanism PLL Passive Components R4000 Coprocessor 0 Hazards

rawTOC:
Introduction \\ CPU Instruction Set Summary \\ The CPU Pipeline \\ Memory Management \\ CPU Exception Processing \\ Floating-Point Unit \\ Floating-Point Exceptions \\ R4000 Processor Signal Descriptions \\ Initialization Interface \\ Clock Interface \\ Cache Organization, Operation, and Coherency \\ System Interface \\ Secondary Cache Interface \\ JTAG Interface \\ R4000 Processor Interrupts \\ Error Checking and Correcting \\ CPU Instruction Set Details \\ FPU Instruction Set Details \\ Subblock Ordering \\ Output Buffer \ldots{} Di \ldots{} Dt Control Mechanism \\ PLL Passive Components \\ R4000 Coprocessor 0 Hazards

entry:
@Book{Heinrich:1993:MRM,
  author =       "Joe Heinrich",
  title =        "{MIPS R4000} Microprocessor User's Manual",
  publisher =    pub-PHPTR,
  address =      pub-PHPTR:adr,
  pages =        "xxvi + 438 + A182 + B62 + C6 + D4 + E4",
  year =         "1993",
  ISBN =         "0-13-105925-4",
  ISBN-13 =      "978-0-13-105925-2",
  LCCN =         "QA76.8.M523H45 1993",
  bibdate =      "Wed Aug 10 11:02:27 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  price =        "US\$34.00",
  acknowledgement = ack-nhfb,
  libnote =      "Not yet in my library.",
  tableofcontents = "Introduction \\
                 CPU Instruction Set Summary \\
                 The CPU Pipeline \\
                 Memory Management \\
                 CPU Exception Processing \\
                 Floating-Point Unit \\
                 Floating-Point Exceptions \\
                 R4000 Processor Signal Descriptions \\
                 Initialization Interface \\
                 Clock Interface \\
                 Cache Organization, Operation, and Coherency \\
                 System Interface \\
                 Secondary Cache Interface \\
                 JTAG Interface \\
                 R4000 Processor Interrupts \\
                 Error Checking and Correcting \\
                 CPU Instruction Set Details \\
                 FPU Instruction Set Details \\
                 Subblock Ordering \\
                 Output Buffer \ldots{} Di \ldots{} Dt Control Mechanism
                 \\
                 PLL Passive Components \\
                 R4000 Coprocessor 0 Hazards",
}


bibtype: inproceedings
filename: fparith.bib
label: Hekstra:1993:FPC
author: Gerben J. Hekstra and Ed F. A. Deprettere
title: Floating Point Cordic
crossref: Swartzlander:1993:SCA
pages: 130--137
year: 1993
bibdate: Sat Nov 17 09:46:07 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.17 09:46:07 ???
URL: http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Hekstra.pdf
keywords: ARITH-11
acknowledgement: ack-nhfb
rawauthor: Gerben J. Hekstra and Ed F. A. Deprettere
rawtitle: Floating Point {Cordic}
entry:
@InProceedings{Hekstra:1993:FPC,
  author =       "Gerben J. Hekstra and Ed F. A. Deprettere",
  title =        "Floating Point {Cordic}",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "130--137",
  year =         "1993",
  bibdate =      "Sat Nov 17 09:46:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Hekstra.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
}


bibtype: inproceedings
filename: fparith.bib
label: Hemkumar:1993:ECM
author: Nariankadu D. Hemkumar and Joseph R. Cavallaro
title: Efficient Complex Matrix Transformations with CORDIC
crossref: Swartzlander:1993:SCA
pages: 122--129
year: 1993
bibdate: Sat Nov 17 09:46:07 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.17 09:46:07 ???
URL: http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Hemkumar.pdf
keywords: ARITH-11
acknowledgement: ack-nhfb
rawauthor: Nariankadu D. Hemkumar and Joseph R. Cavallaro
rawtitle: Efficient Complex Matrix Transformations with {CORDIC}
entry:
@InProceedings{Hemkumar:1993:ECM,
  author =       "Nariankadu D. Hemkumar and Joseph R. Cavallaro",
  title =        "Efficient Complex Matrix Transformations with
                 {CORDIC}",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "122--129",
  year =         "1993",
  bibdate =      "Sat Nov 17 09:46:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Hemkumar.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
}


bibtype: article
filename: fparith.bib
label: Hendtlass:1993:MNIa
author: T. Hendtlass
title: Math-who needs it?
journal: j-FORTH-DIMENSIONS
volume: 14
number: 6
pages: 27--38
month: mar
monthnumber: 3
year: 1993
CODEN: FODMD5
ISSN: 0884-0822 OR 08840822
bibdate: Tue Dec 12 09:27:13 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.12 09:27:13 MST
fjournal: Forth Dimensions
acknowledgement: ack-nhfb
thesaurus: FORTH; FORTH listings; Mathematics computing
rawauthor: T. Hendtlass
rawtitle: Math-who needs it?
abstract:
A thorough treatment of integer, double-precision, fixed-point, and floating-point mathematics. A mathematician's toolbox of code is presented, and tables compare the benefits bestowed and the penalties extracted by the routines.

keywords:
Code toolbox; Double precision arithmetic; Fixed-point arithmetic; Floating-point mathematics; Integer

rawabstract:
A thorough treatment of integer, double-precision, fixed-point, and floating-point mathematics. A mathematician's toolbox of code is presented, and tables compare the benefits bestowed and the penalties extracted by the routines.

entry:
@Article{Hendtlass:1993:MNIa,
  author =       "T. Hendtlass",
  title =        "Math-who needs it?",
  journal =      j-FORTH-DIMENSIONS,
  volume =       "14",
  number =       "6",
  pages =        "27--38",
  month =        mar # "--" # apr,
  year =         "1993",
  CODEN =        "FODMD5",
  ISSN =         "0884-0822",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A thorough treatment of integer, double-precision,
                 fixed-point, and floating-point mathematics. A
                 mathematician's toolbox of code is presented, and
                 tables compare the benefits bestowed and the penalties
                 extracted by the routines.",
  acknowledgement = ack-nhfb,
  classification = "C6140D (High level languages); C7310 (Mathematics)",
  fjournal =     "Forth Dimensions",
  keywords =     "Code toolbox; Double precision arithmetic; Fixed-point
                 arithmetic; Floating-point mathematics; Integer",
  thesaurus =    "FORTH; FORTH listings; Mathematics computing",
}


bibtype: article
filename: fparith.bib
label: Hendtlass:1993:MNIb
author: T. Hendtlass
title: Math---who needs it?
journal: j-FORTH-DIMENSIONS
volume: 15
number: 1
pages: 38--39
month: may
monthnumber: 5
year: 1993
CODEN: FODMD5
ISSN: 0884-0822 OR 08840822
bibdate: Tue Dec 12 09:27:13 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.12 09:27:13 MST
fjournal: Forth Dimensions
keywords: Double-precision; Fixed-point; Floating-point routines; Forth program; Math; Source code; Toolbox
acknowledgement: ack-nhfb
thesaurus: Digital arithmetic; FORTH listings; Mathematics computing; Programming
rawauthor: T. Hendtlass
rawtitle: Math---who needs it?
abstract:
The continuation of the source code for a Forth program is presented (see ibid., vol.14, no.6, 1993). The software is a math professor's toolbox of integer, double-precision, fixed-point and floating-point routines.

rawabstract:
The continuation of the source code for a Forth program is presented (see ibid., vol.14, no.6, 1993). The software is a math professor's toolbox of integer, double-precision, fixed-point and floating-point routines.

entry:
@Article{Hendtlass:1993:MNIb,
  author =       "T. Hendtlass",
  title =        "Math---who needs it?",
  journal =      j-FORTH-DIMENSIONS,
  volume =       "15",
  number =       "1",
  pages =        "38--39",
  month =        may # "--" # jun,
  year =         "1993",
  CODEN =        "FODMD5",
  ISSN =         "0884-0822",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The continuation of the source code for a Forth
                 program is presented (see ibid., vol.14, no.6, 1993).
                 The software is a math professor's toolbox of integer,
                 double-precision, fixed-point and floating-point
                 routines.",
  acknowledgement = ack-nhfb,
  classification = "C6110 (Systems analysis and programming); C7310
                 (Mathematics)",
  fjournal =     "Forth Dimensions",
  keywords =     "Double-precision; Fixed-point; Floating-point
                 routines; Forth program; Math; Source code; Toolbox",
  thesaurus =    "Digital arithmetic; FORTH listings; Mathematics
                 computing; Programming",
}


bibtype: article
filename: fparith.bib
label: Higginbotham:1993:ISR
author: T. F. Higginbotham
title: The integer square root of N via a binary search
journal: j-SIGCSE
volume: 25
number: 4
pages: 41--45
month: dec
monthnumber: 12
year: 1993
CODEN: SIGSD3
DOI: https://doi.org/10.1145/164205.164229
ISSN: 0097-8418 (print), 2331-3927 (electronic) OR 00978418 (print), 23313927 (electronic)
ISSNL: 0097-8418 OR 00978418
bibdate: Sat Nov 17 18:57:24 MST 2012
bibtimestamp: 2012.11.17 18:57:24 MST
fjournal: SIGCSE Bulletin (ACM Special Interest Group on Computer Science Education)
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J688
rawauthor: T. F. Higginbotham
rawtitle: The integer square root of {N} via a binary search
bibsource:
http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/sigcse1990.bib

abstract:
An algorithm is presented which may be used to find the integer square root of N. The method is intended for use on a binary computer, where only addition, subtraction, multiplication, or division by 2 is required. The problem arose when the author was working on factoring large numbers, where the machine, the Honeywell DPS 8, had double precision integer addition and subtraction, and the simulation of multiplication was easy. The actual factoring of the large number was to be Fermat's Method, requiring only addition and subtraction, but the integer square root is required in order to test for termination. The algorithm is implemented in FORTRAN for ease of reading. Students enjoy the unconventional approach to solving this problem. It isn't long before some of them think of other unusual solutions.

rawabstract:
An algorithm is presented which may be used to find the integer square root of N. The method is intended for use on a binary computer, where only addition, subtraction, multiplication, or division by 2 is required. The problem arose when the author was working on factoring large numbers, where the machine, the Honeywell DPS 8, had double precision integer addition and subtraction, and the simulation of multiplication was easy. The actual factoring of the large number was to be Fermat's Method, requiring only addition and subtraction, but the integer square root is required in order to test for termination. The algorithm is implemented in FORTRAN for ease of reading. Students enjoy the unconventional approach to solving this problem. It isn't long before some of them think of other unusual solutions.

entry:
@Article{Higginbotham:1993:ISR,
  author =       "T. F. Higginbotham",
  title =        "The integer square root of {N} via a binary search",
  journal =      j-SIGCSE,
  volume =       "25",
  number =       "4",
  pages =        "41--45",
  month =        dec,
  year =         "1993",
  CODEN =        "SIGSD3",
  DOI =          "https://doi.org/10.1145/164205.164229",
  ISSN =         "0097-8418 (print), 2331-3927 (electronic)",
  ISSN-L =       "0097-8418",
  bibdate =      "Sat Nov 17 18:57:24 MST 2012",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigcse1990.bib",
  abstract =     "An algorithm is presented which may be used to find
                 the integer square root of N. The method is intended
                 for use on a binary computer, where only addition,
                 subtraction, multiplication, or division by 2 is
                 required. The problem arose when the author was working
                 on factoring large numbers, where the machine, the
                 Honeywell DPS 8, had double precision integer addition
                 and subtraction, and the simulation of multiplication
                 was easy. The actual factoring of the large number was
                 to be Fermat's Method, requiring only addition and
                 subtraction, but the integer square root is required in
                 order to test for termination. The algorithm is
                 implemented in FORTRAN for ease of reading. Students
                 enjoy the unconventional approach to solving this
                 problem. It isn't long before some of them think of
                 other unusual solutions.",
  acknowledgement = ack-nhfb,
  fjournal =     "SIGCSE Bulletin (ACM Special Interest Group on
                 Computer Science Education)",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J688",
}


bibtype: article
filename: fparith.bib
label: Higham:1993:AFP
author: Nicholas J. Higham
title: The accuracy of floating point summation
journal: j-SIAM-J-SCI-COMP
volume: 14
number: 4
pages: 783--799
month: jul
monthnumber: 7
year: 1993
CODEN: SJOCE3
DOI: https://doi.org/10.1137/0914050
ISSN: 1064-8275 (print), 1095-7197 (electronic) OR 10648275 (print), 10957197 (electronic)
ISSNL: 1064-8275 OR 10648275
MRclass: 65G05 (65B10)
MRnumber: 94a:65025
bibdate: Thu Aug 23 06:36:53 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.08.23 06:36:53 ???
fjournal: SIAM Journal on Scientific Computing
acknowledgement: ack-nhfb
affiliation: Department of Math., Manchester University, UK
journalURL: http://epubs.siam.org/sisc
thesaurus: Digital arithmetic; Error analysis
rawauthor: Nicholas J. Higham
rawtitle: The accuracy of floating point summation
URL:
http://citeseer.nj.nec.com/higham93accuracy.html; http://www.maths.man.ac.uk/~nareports/narep198.pdf; http://www.maths.man.ac.uk/~nareports/narep198.ps.gz

abstract:
The usual recursive summation technique is just one of several ways of computing the sum of $n$ floating point numbers. Five summation methods and their variations are analyzed. The accuracy of the methods is compared using rounding error analysis and numerical experiments. Four of the methods are shown to be special cases of a general class of methods, and an error analysis is given for this class. No one method is uniformly more accurate than the others, but some guidelines are given on the choice of method in particular cases.

keywords:
accurate floating-point summation; floating point numbers; numerical experiments; recursive summation technique; rounding error analysis

rawabstract:
The usual recursive summation technique is just one of several ways of computing the sum of $n$ floating point numbers. Five summation methods and their variations are analyzed. The accuracy of the methods is compared using rounding error analysis and numerical experiments. Four of the methods are shown to be special cases of a general class of methods, and an error analysis is given for this class. No one method is uniformly more accurate than the others, but some guidelines are given on the choice of method in particular cases.

entry:
@Article{Higham:1993:AFP,
  author =       "Nicholas J. Higham",
  title =        "The accuracy of floating point summation",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "14",
  number =       "4",
  pages =        "783--799",
  month =        jul,
  year =         "1993",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/0914050",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  MRclass =      "65G05 (65B10)",
  MRnumber =     "94a:65025",
  bibdate =      "Thu Aug 23 06:36:53 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://citeseer.nj.nec.com/higham93accuracy.html;
                 http://www.maths.man.ac.uk/~nareports/narep198.pdf;
                 http://www.maths.man.ac.uk/~nareports/narep198.ps.gz",
  abstract =     "The usual recursive summation technique is just one of
                 several ways of computing the sum of $n$ floating point
                 numbers. Five summation methods and their variations
                 are analyzed. The accuracy of the methods is compared
                 using rounding error analysis and numerical
                 experiments. Four of the methods are shown to be
                 special cases of a general class of methods, and an
                 error analysis is given for this class. No one method
                 is uniformly more accurate than the others, but some
                 guidelines are given on the choice of method in
                 particular cases.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Math., Manchester University, UK",
  classification = "C4110 (Error analysis in numerical methods); C5230
                 (Digital arithmetic methods)",
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  keywords =     "accurate floating-point summation; floating point
                 numbers; numerical experiments; recursive summation
                 technique; rounding error analysis",
  thesaurus =    "Digital arithmetic; Error analysis",
}


bibtype: mastersthesis
filename: fparith.bib
label: Holler:1993:IFP
author: Paul T. Holler
title: Integrating a floating point unit into the AT&T Hobbit microprocessor
type: Thesis (M.S.)
school: Lehigh University
address: Bethlehem, PA, USA
pages: viii + 85
year: 1993
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Floating-point arithmetic.; Microprocessors.
acknowledgement: ack-nhfb
rawauthor: Paul T. Holler
rawtitle: Integrating a floating point unit into the {AT\&T Hobbit} microprocessor
entry:
@MastersThesis{Holler:1993:IFP,
  author =       "Paul T. Holler",
  title =        "Integrating a floating point unit into the {AT\&T
                 Hobbit} microprocessor",
  type =         "Thesis ({M.S.})",
  school =       "Lehigh University",
  address =      "Bethlehem, PA, USA",
  pages =        "viii + 85",
  year =         "1993",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.; Microprocessors.",
}


bibtype: article
filename: fparith.bib
label: Hopkins:1993:CEM
author: Tim Hopkins and John Slater
title: A Comment on the Eispack Machine Epsilon Routine
journal: j-SIGNUM
volume: 28
number: 4
pages: 2--6
month: oct
monthnumber: 10
year: 1993
CODEN: SNEWD6
DOI: https://doi.org/10.1145/165639.165641
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Tue Apr 12 07:50:24 MDT 2005
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.04.12 07:50:24 MDT
fjournal: ACM SIGNUM Newsletter
keywords: Binary floating-point system; Eispack machine epsilon routine
acknowledgement: ack-nhfb
affiliation: Comput. Lab., Kent University, Canterbury, UK
journalURL: https://dl.acm.org/loi/signum
thesaurus: Digital arithmetic
rawauthor: Tim Hopkins and John Slater
rawtitle: A Comment on the {Eispack} Machine Epsilon Routine
abstract:
The authors analyze the algorithm used to generate the value for the machine epsilon in the Eispack suite of routines and show that it can fail on a binary floating-point system. The comments in the code describing the conditions under which this method will work are not restrictive enough and the authors provide a replacement set of assumptions. They conclude by suggesting how the algorithm may be modified to overcome most of the shortcomings.

rawabstract:
The authors analyze the algorithm used to generate the value for the machine epsilon in the Eispack suite of routines and show that it can fail on a binary floating-point system. The comments in the code describing the conditions under which this method will work are not restrictive enough and the authors provide a replacement set of assumptions. They conclude by suggesting how the algorithm may be modified to overcome most of the shortcomings.

entry:
@Article{Hopkins:1993:CEM,
  author =       "Tim Hopkins and John Slater",
  title =        "A Comment on the {Eispack} Machine Epsilon Routine",
  journal =      j-SIGNUM,
  volume =       "28",
  number =       "4",
  pages =        "2--6",
  month =        oct,
  year =         "1993",
  CODEN =        "SNEWD6",
  DOI =          "https://doi.org/10.1145/165639.165641",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:24 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The authors analyze the algorithm used to generate the
                 value for the machine epsilon in the Eispack suite of
                 routines and show that it can fail on a binary
                 floating-point system. The comments in the code
                 describing the conditions under which this method will
                 work are not restrictive enough and the authors provide
                 a replacement set of assumptions. They conclude by
                 suggesting how the algorithm may be modified to
                 overcome most of the shortcomings.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "Comput. Lab., Kent University, Canterbury, UK",
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "Binary floating-point system; Eispack machine epsilon
                 routine",
  thesaurus =    "Digital arithmetic",
}


bibtype: techreport
filename: fparith.bib
label: Horning:1993:SUM
author: Jim Horning and Bill Kalsow and Paul McJones and Greg Nelson
title: Some Useful Modula-3 Interfaces
type: Memo
number: 113
institution: Digital Equipment Corporation, Systems Research Center
address: Palo Alto, CA, USA
pages: 2--6
month: dec
monthnumber: 12
year: 1993
bibdate: Wed Jan 29 16:39:06 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.01.29 16:39:06 ???
remark: From cite Steele:2004:RHP: ``The floating-point reader has been implemented in ldots to Modula-3''.
acknowledgement: ack-nhfb
rawauthor: Jim Horning and Bill Kalsow and Paul McJones and Greg Nelson
rawtitle: Some Useful {Modula-3} Interfaces
entry:
@TechReport{Horning:1993:SUM,
  author =       "Jim Horning and Bill Kalsow and Paul McJones and Greg
                 Nelson",
  title =        "Some Useful {Modula-3} Interfaces",
  type =         "Memo",
  number =       "113",
  institution =  "Digital Equipment Corporation, Systems Research
                 Center",
  address =      "Palo Alto, CA, USA",
  month =        dec,
  year =         "1993",
  bibdate =      "Wed Jan 29 16:39:06 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "From \cite{Steele:2004:RHP}: ``The floating-point
                 reader has been implemented in \ldots{} to
                 Modula-3''.",
}


bibtype: article
filename: fparith.bib
label: Hu:1993:EIS
author: X. Hu and S. C. Bass and R. G. Harber
journal: j-J-PAR-DIST-COMP
volume: 17
number: 4
pages: 360--362
month: apr
monthnumber: 4
year: 1993
CODEN: JPDCER
DOI: https://doi.org/10.1006/jpdc.1993.1034
ISSN: 0743-7315 (print), 1096-0848 (electronic) OR 07437315 (print), 10960848 (electronic)
ISSNL: 0743-7315 OR 07437315
bibdate: Thu Mar 9 09:18:52 MST 2000
bibtimestamp: 2000.03.09 09:18:52 MST
fjournal: Journal of Parallel and Distributed Computing
acknowledgement: ack-nhfb
corpsource: General Motors Res. Labs., Warren, MI, USA
journalURL: http://www.sciencedirect.com/science/journal/07437315
treatment: A Application; P Practical
rawauthor: X. Hu and S. C. Bass and R. G. Harber
title:
An Efficient Implementation of Singular Value Decomposition Rotation Transformations with CORDIC Processors

bibsource:
http://www.idealibrary.com/servlet/useragent?func=showAllIssues&curIssueID=jpdc; https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://www.idealibrary.com/links/doi/10.1006/jpdc.1993.1034/production; http://www.idealibrary.com/links/doi/10.1006/jpdc.1993.1034/production/pdf

keywords:
2*2 matrices; CORDIC processors; digital arithmetic; mathematics computing; matrix algebra; singular value decomposition rotation transformations

rawtitle:
An Efficient Implementation of Singular Value Decomposition Rotation Transformations with {CORDIC} Processors

entry:
@Article{Hu:1993:EIS,
  author =       "X. Hu and S. C. Bass and R. G. Harber",
  title =        "An Efficient Implementation of Singular Value
                 Decomposition Rotation Transformations with {CORDIC}
                 Processors",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "17",
  number =       "4",
  pages =        "360--362",
  month =        apr,
  year =         "1993",
  CODEN =        "JPDCER",
  DOI =          "https://doi.org/10.1006/jpdc.1993.1034",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Thu Mar 9 09:18:52 MST 2000",
  bibsource =    "http://www.idealibrary.com/servlet/useragent?func=showAllIssues&curIssueID=jpdc;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.idealibrary.com/links/doi/10.1006/jpdc.1993.1034/production;
                 http://www.idealibrary.com/links/doi/10.1006/jpdc.1993.1034/production/pdf",
  acknowledgement = ack-nhfb,
  classification = "C4140 (Linear algebra); C5230 (Digital arithmetic
                 methods); C7310 (Mathematics)",
  corpsource =   "General Motors Res. Labs., Warren, MI, USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  keywords =     "2*2 matrices; CORDIC processors; digital arithmetic;
                 mathematics computing; matrix algebra; singular value
                 decomposition rotation transformations",
  treatment =    "A Application; P Practical",
}


bibtype: inproceedings
filename: fparith.bib
label: Hu:1993:NES
author: Xiaobo Hu and Steven C. Bass
title: Neglected Error Source in the CORDIC Algorithm
crossref: Swartzlander:1993:SCA
pages: 766--769
year: 1993
bibdate: Wed Nov 12 10:45:34 2025
bibtimestamp: 2025.11.12 10:45:34 ???
acknowledgement: ack-nhfb
rawauthor: Xiaobo Hu and Steven C. Bass
rawtitle: Neglected Error Source in the {CORDIC} Algorithm
entry:
@InProceedings{Hu:1993:NES,
  author =       "Xiaobo Hu and Steven C. Bass",
  title =        "Neglected Error Source in the {CORDIC} Algorithm",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "766--769",
  year =         "1993",
  bibdate =      "Wed Nov 12 10:45:34 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: fparith.bib
label: IBM:1993:IPA
author: IBM Corporation
title: The IBM PowerPC Architecture: a New Family of RISC Processors
publisher: pub-MORGAN-KAUFMANN
address: pub-MORGAN-KAUFMANN:adr
pages: 766--769
year: 1993
ISBN: 1-55860-316-6 OR 1558603166
ISBN13: 978-1-55860-316-5 OR 9781558603165
LCCN: QA76.8.P67P68 1994
bibdate: Sat Oct 15 12:26:00 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.10.15 12:26:00 ???
acknowledgement: ack-nhfb
rawauthor: {IBM Corporation}
rawtitle: The {IBM PowerPC} Architecture: a New Family of {RISC} Processors
entry:
@Book{IBM:1993:IPA,
  author =       "{IBM Corporation}",
  title =        "The {IBM PowerPC} Architecture: a New Family of {RISC}
                 Processors",
  publisher =    pub-MORGAN-KAUFMANN,
  address =      pub-MORGAN-KAUFMANN:adr,
  year =         "1993",
  ISBN =         "1-55860-316-6",
  ISBN-13 =      "978-1-55860-316-5",
  LCCN =         "QA76.8.P67P68 1994",
  bibdate =      "Sat Oct 15 12:26:00 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$49.95",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Ide:1993:CFP
title: A 320-MFLOPS CMOS Floating-Point Processing Unit for Superscalar Processors
journal: j-IEEE-J-SOLID-STATE-CIRCUITS
volume: 28
number: 3
pages: 352--361
month: mar
monthnumber: 3
year: 1993
CODEN: IJSCBC
ISSN: 0018-9200 (print), 1558-173X (electronic) OR 00189200 (print), 1558173X (electronic)
ISSNL: 0018-9200 OR 00189200
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
fjournal: IEEE Journal of Solid-State Circuits
acknowledgement: ack-nhfb
rawtitle: A {320-MFLOPS} {CMOS} Floating-Point Processing Unit for Superscalar Processors
author:
N. Ide and H. Fukuhisa and Y. Kondo and T. Yoshida and M. Nagamatsu and J. Mori and I. Yamazaki and K. Ueno

rawauthor:
N. Ide and H. Fukuhisa and Y. Kondo and T. Yoshida and M. Nagamatsu and J. Mori and I. Yamazaki and K. Ueno

entry:
@Article{Ide:1993:CFP,
  author =       "N. Ide and H. Fukuhisa and Y. Kondo and T. Yoshida and
                 M. Nagamatsu and J. Mori and I. Yamazaki and K. Ueno",
  title =        "A {320-MFLOPS} {CMOS} Floating-Point Processing Unit
                 for Superscalar Processors",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "28",
  number =       "3",
  pages =        "352--361",
  month =        mar,
  year =         "1993",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
}


bibtype: article
filename: fparith.bib
label: Ide:1993:MCF
title: A 320-MFLOPS CMOS Floating-Point Processing Unit for Superscalar Processors
journal: j-IEEE-J-SOLID-STATE-CIRCUITS
volume: 28
number: 3
pages: 352--361
month: mar
monthnumber: 3
year: 1993
CODEN: IJSCBC
ISSN: 0018-9200 (print), 1558-173X (electronic) OR 00189200 (print), 1558173X (electronic)
ISSNL: 0018-9200 OR 00189200
bibdate: Sat Jul 16 08:40:52 MDT 2005
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:52 MDT
fjournal: IEEE Journal of Solid-State Circuits
acknowledgement: ack-nj
rawtitle: A 320-{MFLOPS CMOS} Floating-Point Processing Unit for Superscalar Processors
author:
Nobuhiro Ide and Hiroto Fukuhisa and Yoshihisa Kondo and Takeshi Yoshida and Masato Nagamatsu and Junji Mori and Itaru Yamazaki and Kiyoji Ueno

rawauthor:
Nobuhiro Ide and Hiroto Fukuhisa and Yoshihisa Kondo and Takeshi Yoshida and Masato Nagamatsu and Junji Mori and Itaru Yamazaki and Kiyoji Ueno

entry:
@Article{Ide:1993:MCF,
  author =       "Nobuhiro Ide and Hiroto Fukuhisa and Yoshihisa Kondo
                 and Takeshi Yoshida and Masato Nagamatsu and Junji Mori
                 and Itaru Yamazaki and Kiyoji Ueno",
  title =        "A 320-{MFLOPS CMOS} Floating-Point Processing Unit for
                 Superscalar Processors",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "28",
  number =       "3",
  pages =        "352--361",
  month =        mar,
  year =         "1993",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  summary =      "A CMOS pipelined floating-point processing unit (FPU)
                 for superscalar processors is described. It is
                 fabricated using a 0.5 $\mu$m CMOS triple-metal-layer
                 technology on a 61 mm 2 die. The FPU has two execution
                 modes to meet precise scientific computations and
                 real-time applications. It can start two FPU operations
                 in each cycle, and this achieves a peak performance of
                 160 MFLOPS double or single precision with an 80 MHz
                 clock. Furthermore, the original computation mode, twin
                 single-precision computation, double the peak
                 performance and delivers 320 MFLOPS single precision.
                 Its full bypass reduces the latency of operations,
                 including load and store, and achieves an effective
                 throughput even in nonvectorizable computations. An
                 out-of-order completion is provided by using a new
                 exception prediction method and a pipeline stall
                 technique.",
}


bibtype: article
filename: fparith.bib
label: Jahn:1993:LIF
author: K.-U. Jahn
title: Loop Invariants in Floating Point Algorithms. Schleifen-Invarianten in Gleitpunktalgorithmen
journal: j-COMPUTING
volume: 50
number: 3
pages: 255--264
year: 1993
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
MRclass: 65G05 (65G10)
MRnumber: 94f:65052
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
fjournal: Computing: Archiv fur informatik und numerik
keywords: Directed roundings; Enclosure sets; Floating point algorithms; Loop conditions; Loop invariants
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/607
thesaurus: Program verification
rawauthor: K.-U. Jahn
rawtitle: Loop Invariants in Floating Point Algorithms. {Schleifen-Invarianten in Gleitpunktalgorithmen}
abstract:
It is shown that by using directed roundings with respect to enclosure sets for the exact values, the loop conditions and loop invariants of numerical algorithms can be generalized for computing in a discrete screen. It is possible to verify the received results. Thereby only inherent properties of the algorithms are used, which moreover guarantee that the loops terminate.

rawabstract:
It is shown that by using directed roundings with respect to enclosure sets for the exact values, the loop conditions and loop invariants of numerical algorithms can be generalized for computing in a discrete screen. It is possible to verify the received results. Thereby only inherent properties of the algorithms are used, which moreover guarantee that the loops terminate.

entry:
@Article{Jahn:1993:LIF,
  author =       "K.-U. Jahn",
  title =        "Loop Invariants in Floating Point Algorithms.
                 {Schleifen-Invarianten in Gleitpunktalgorithmen}",
  journal =      j-COMPUTING,
  volume =       "50",
  number =       "3",
  pages =        "255--264",
  year =         "1993",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65G05 (65G10)",
  MRnumber =     "94f:65052",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "It is shown that by using directed roundings with
                 respect to enclosure sets for the exact values, the
                 loop conditions and loop invariants of numerical
                 algorithms can be generalized for computing in a
                 discrete screen. It is possible to verify the received
                 results. Thereby only inherent properties of the
                 algorithms are used, which moreover guarantee that the
                 loops terminate.",
  acknowledgement = ack-nhfb,
  classification = "C4240P (Parallel programming and algorithm theory);
                 C6150G (Diagnostic, testing, debugging and evaluating
                 systems)",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
  keywords =     "Directed roundings; Enclosure sets; Floating point
                 algorithms; Loop conditions; Loop invariants",
  pubcountry =   "Austria",
  thesaurus =    "Program verification",
}


bibtype: article
filename: fparith.bib
label: Jahn:1993:SIG
author: K.-U. Jahn
journal: j-COMPUTING
volume: 50
number: 3
pages: 255--264
month: sep
monthnumber: 9
year: 1993
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
MRclass: 65G05 (65G10)
MRnumber: 94f:65052
bibdate: Mon Oct 11 20:38:38 MDT 1999
bibtimestamp: 1999.10.11 20:38:38 MDT
fjournal: Computing
keywords: Directed roundings; Enclosure sets; Floating point algorithms; Loop conditions; Loop invariants
language: German
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/607
thesaurus: Program verification
rawauthor: K.-U. Jahn
title:
Schleifen-Invarianten in Gleitpunktalgorithmen. (German) [Loop Invariants in Floating Point Algorithms]

bibsource:
http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X; https://www.math.utah.edu/pub/tex/bib/computing.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; MathSciNet database; OCLC Contents1st database

abstract:
It is shown that by using directed roundings with respect to enclosure sets for the exact values, the loop conditions and loop invariants of numerical algorithms can be generalized for computing in a discrete screen. It is possible to verify the received results. Thereby only inherent properties of the algorithms are used, which moreover guarantee that the loops terminate.

rawtitle:
{Schleifen-Invarianten in Gleitpunktalgorithmen}. ({German}) [{Loop} Invariants in Floating Point Algorithms]

entry:
@Article{Jahn:1993:SIG,
  author =       "K.-U. Jahn",
  title =        "{Schleifen-Invarianten in Gleitpunktalgorithmen}.
                 ({German}) [{Loop} Invariants in Floating Point
                 Algorithms]",
  journal =      j-COMPUTING,
  volume =       "50",
  number =       "3",
  pages =        "255--264",
  month =        sep,
  year =         "1993",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65G05 (65G10)",
  MRnumber =     "94f:65052",
  bibdate =      "Mon Oct 11 20:38:38 MDT 1999",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
                 https://www.math.utah.edu/pub/tex/bib/computing.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 MathSciNet database; OCLC Contents1st database",
  abstract =     "It is shown that by using directed roundings with
                 respect to enclosure sets for the exact values, the
                 loop conditions and loop invariants of numerical
                 algorithms can be generalized for computing in a
                 discrete screen. It is possible to verify the received
                 results. Thereby only inherent properties of the
                 algorithms are used, which moreover guarantee that the
                 loops terminate.",
  acknowledgement = ack-nhfb,
  classification = "C4240P (Parallel programming and algorithm theory);
                 C6150G (Diagnostic, testing, debugging and evaluating
                 systems)",
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  keywords =     "Directed roundings; Enclosure sets; Floating point
                 algorithms; Loop conditions; Loop invariants",
  language =     "German",
  pubcountry =   "Austria",
  thesaurus =    "Program verification",
}


bibtype: inproceedings
filename: fparith.bib
label: Jebelean:1993:CSG
author: T. Jebelean
title: Comparing Several GCD Algorithms
crossref: Swartzlander:1993:SCA
pages: 180--185
month: jun
monthnumber: 6
year: 1993
bibdate: Wed Nov 14 18:46:15 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 18:46:15 ???
URL: http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Jebelean.pdf
keywords: ARITH-11
acknowledgement: ack-nhfb
rawauthor: T. Jebelean
rawtitle: Comparing Several {GCD} Algorithms
entry:
@InProceedings{Jebelean:1993:CSG,
  author =       "T. Jebelean",
  title =        "Comparing Several {GCD} Algorithms",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "180--185",
  month =        jun,
  year =         "1993",
  bibdate =      "Wed Nov 14 18:46:15 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Jebelean.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
}


bibtype: inproceedings
filename: fparith.bib
label: Jenkins:1993:CSL
author: W. K. Jenkins and B. A. Schnaufer and A. J. Mansen
crossref: Swartzlander:1993:SCA
pages: 28--35
year: 1993
bibdate: Sat Nov 17 09:46:07 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.17 09:46:07 ???
URL: http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Jenkins.pdf
keywords: ARITH-11
acknowledgement: ack-nhfb
rawauthor: W. K. Jenkins and B. A. Schnaufer and A. J. Mansen
title:
Combined System-Level Redundancy and Modular Arithmetic for Fault Tolerant Digital Signal Processing

rawtitle:
Combined System-Level Redundancy and Modular Arithmetic for Fault Tolerant Digital Signal Processing

entry:
@InProceedings{Jenkins:1993:CSL,
  author =       "W. K. Jenkins and B. A. Schnaufer and A. J. Mansen",
  title =        "Combined System-Level Redundancy and Modular
                 Arithmetic for Fault Tolerant Digital Signal
                 Processing",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "28--35",
  year =         "1993",
  bibdate =      "Sat Nov 17 09:46:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Jenkins.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
}


bibtype: article
filename: fparith.bib
label: Johnstone:1993:RNA
author: P. Johnstone and F. E. Petry
title: Rational number approximation in higher radix floating point systems
journal: j-COMPUT-MATH-APPL
volume: 25
number: 6
pages: 103--108
month: mar
monthnumber: 3
year: 1993
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Tue Dec 12 09:27:13 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.12 09:27:13 MST
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
affiliation: New Orleans Tech. Dev. Group, Telerate Systems Inc., LA, USA
journalURL: http://www.sciencedirect.com/science/journal/08981221
thesaurus: Digital arithmetic
rawauthor: P. Johnstone and F. E. Petry
rawtitle: Rational number approximation in higher radix floating point systems
abstract:
Mathematical researchers have long recognized that some bases offer some representational advantages in that they generate fewer nonterminate values when representing arbitrary rational numbers. While such results are true for abstract number systems, little attention has been paid to machine based computation and its finite resources. In the paper, such results are considered in an environment more typical of computer based models of number systems. Specifically, the authors consider the effect of the choice of floating point base on rational number approximation in systems which exhibit the typical characteristics of floating point representations-normalized encodings, limited exponent range and storage allocated in a fixed number of `bits' per datum. The frequency with which terminate and representable results can be expected is considered for binary, decimal, and other potentially interesting bases.

keywords:
Computer based models; decimal floating-point arithmetic; Floating point base; Floating point systems; Number systems; Rational number approximation

rawabstract:
Mathematical researchers have long recognized that some bases offer some representational advantages in that they generate fewer nonterminate values when representing arbitrary rational numbers. While such results are true for abstract number systems, little attention has been paid to machine based computation and its finite resources. In the paper, such results are considered in an environment more typical of computer based models of number systems. Specifically, the authors consider the effect of the choice of floating point base on rational number approximation in systems which exhibit the typical characteristics of floating point representations-normalized encodings, limited exponent range and storage allocated in a fixed number of `bits' per datum. The frequency with which terminate and representable results can be expected is considered for binary, decimal, and other potentially interesting bases.

entry:
@Article{Johnstone:1993:RNA,
  author =       "P. Johnstone and F. E. Petry",
  title =        "Rational number approximation in higher radix floating
                 point systems",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "25",
  number =       "6",
  pages =        "103--108",
  month =        mar,
  year =         "1993",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Mathematical researchers have long recognized that
                 some bases offer some representational advantages in
                 that they generate fewer nonterminate values when
                 representing arbitrary rational numbers. While such
                 results are true for abstract number systems, little
                 attention has been paid to machine based computation
                 and its finite resources. In the paper, such results
                 are considered in an environment more typical of
                 computer based models of number systems. Specifically,
                 the authors consider the effect of the choice of
                 floating point base on rational number approximation in
                 systems which exhibit the typical characteristics of
                 floating point representations-normalized encodings,
                 limited exponent range and storage allocated in a fixed
                 number of `bits' per datum. The frequency with which
                 terminate and representable results can be expected is
                 considered for binary, decimal, and other potentially
                 interesting bases.",
  acknowledgement = ack-nhfb,
  affiliation =  "New Orleans Tech. Dev. Group, Telerate Systems Inc.,
                 LA, USA",
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  keywords =     "Computer based models; decimal floating-point
                 arithmetic; Floating point base; Floating point
                 systems; Number systems; Rational number
                 approximation",
  pubcountry =   "UK",
  thesaurus =    "Digital arithmetic",
}


bibtype: inproceedings
filename: fparith.bib
label: Ju:1993:WCB
author: Chwen-Jye Ju
title: What can block floating-point arithmetic do for DSP applications
crossref: Anonymous:1993:IPF
pages: 641--650 vol.1
year: 1993
bibdate: Tue Dec 12 09:29:07 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.12 09:29:07 MST
acknowledgement: ack-nhfb
affiliation: Sharp Microelectron. Technol. Inc., Camas, WA, USA
bookpages: 1675
rawauthor: Chwen-Jye Ju
rawtitle: What can block floating-point arithmetic do for {DSP} applications
abstract:
Block floating-point arithmetic for filtering was proposed by Oppenheim two decades ago. Although it has the advantages of both integer and floating-point arithmetic, it is scarcely used in DSP applications because the required signal reference level adjustment (scaling) usually offsets its advantages. To conquer the scaling problem, the unified indexing concept has been proposed by the author for the M-D FFT implementation. This paper will extend the concept to derive the general block-oriented block floating-point DSP algorithms. Therefore, the block floating-point processors such as the LH9124/LH9320 can provide self-contained solutions for some classes of DSP applications.

keywords:
Block floating-point arithmetic; Block floating-point processors; DSP applications; General block-oriented block floating-point DSP algorithms; LH9124/LH9320; M-D FFT implementation; Oppenheim; Scaling problem; Signal reference level adjustment; Unified indexing concept

thesaurus:
Array signal processing; Digital arithmetic; Digital filters; Digital signal processing chips; Fast Fourier transforms

rawabstract:
Block floating-point arithmetic for filtering was proposed by Oppenheim two decades ago. Although it has the advantages of both integer and floating-point arithmetic, it is scarcely used in DSP applications because the required signal reference level adjustment (scaling) usually offsets its advantages. To conquer the scaling problem, the unified indexing concept has been proposed by the author for the M-D FFT implementation. This paper will extend the concept to derive the general block-oriented block floating-point DSP algorithms. Therefore, the block floating-point processors such as the LH9124/LH9320 can provide self-contained solutions for some classes of DSP applications.

entry:
@InProceedings{Ju:1993:WCB,
  author =       "Chwen-Jye Ju",
  title =        "What can block floating-point arithmetic do for {DSP}
                 applications",
  crossref =     "Anonymous:1993:IPF",
  bookpages =    "1675",
  pages =        "641--650 vol.1",
  year =         "1993",
  bibdate =      "Tue Dec 12 09:29:07 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Block floating-point arithmetic for filtering was
                 proposed by Oppenheim two decades ago. Although it has
                 the advantages of both integer and floating-point
                 arithmetic, it is scarcely used in DSP applications
                 because the required signal reference level adjustment
                 (scaling) usually offsets its advantages. To conquer
                 the scaling problem, the unified indexing concept has
                 been proposed by the author for the M-D FFT
                 implementation. This paper will extend the concept to
                 derive the general block-oriented block floating-point
                 DSP algorithms. Therefore, the block floating-point
                 processors such as the LH9124/LH9320 can provide
                 self-contained solutions for some classes of DSP
                 applications.",
  acknowledgement = ack-nhfb,
  affiliation =  "Sharp Microelectron. Technol. Inc., Camas, WA, USA",
  classification = "B1265F (Microprocessors and microcomputers); B6140
                 (Signal processing and detection); C5135 (Digital
                 signal processing chips); C5230 (Digital arithmetic
                 methods); C5260 (Digital signal processing)",
  keywords =     "Block floating-point arithmetic; Block floating-point
                 processors; DSP applications; General block-oriented
                 block floating-point DSP algorithms; LH9124/LH9320; M-D
                 FFT implementation; Oppenheim; Scaling problem; Signal
                 reference level adjustment; Unified indexing concept",
  thesaurus =    "Array signal processing; Digital arithmetic; Digital
                 filters; Digital signal processing chips; Fast Fourier
                 transforms",
}


bibtype: techreport
filename: fparith.bib
label: Juffa:1993:EYA
author: Norbert Juffa
title: Everything You Always Wanted to Know about Math Coprocessors
type: Report
pages: 641--650 vol.1
month: jan
monthnumber: 1
year: 1993
bibdate: Thu Nov 13 06:08:13 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2025.11.13 06:08:13 ???
URL: https://dougx.net/gaming/coproc.html
acknowledgement: ack-nhfb
rawauthor: Norbert Juffa
rawtitle: Everything You Always Wanted to Know about Math Coprocessors
entry:
@TechReport{Juffa:1993:EYA,
  author =       "Norbert Juffa",
  title =        "Everything You Always Wanted to Know about Math
                 Coprocessors",
  type =         "Report",
  institution =  "????",
  address =      "????",
  month =        jan,
  year =         "1993",
  bibdate =      "Thu Nov 13 06:08:13 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://dougx.net/gaming/coproc.html",
  acknowledgement = ack-nhfb,
  remark-1 =     "From the report: ``Unlike Intel's coprocessors, which
                 use the CORDIC algorithm to compute the transcendental
                 functions, Cyrix uses polynomial and rational
                 approximations to the functions.''",
  remark-2 =     "From the report: ``The Cyrix 83D87 uses a fast array
                 multiplier, making its transcendental functions faster
                 than those of any other 387 compatible coprocessor. It
                 also uses 75 bit for the mantissa in intermediate
                 calculations (as opposed to 68 bits on other
                 coprocessors), making its transcendental functions more
                 accurate than those of any other coprocessor or FPU.''",
  remark-3 =     "From the report: ``The Weitek Abacus 3167 and 4167
                 coprocessors are 'mostly compatible' with IEEE-754.
                 \ldots{} One of the most notable omissions is the
                 missing support for denormal numbers; denormals are
                 always flushed to zero on Weitek chips.''",
  remark-4 =     "This is an interesting comparison, made a dozen years
                 after the Intel 8087 floating-point coprocessor
                 appeared on the market, of pin-compatible chips from
                 Intel and others. The 8087 uses CORDIC algorithms for
                 all of its elementary functions, and does the job in
                 about 64K transistors, with 67-bit significands. That
                 gives three additional bits over the 64 needed for the
                 IEEE 754 binary80 format, and they serve as the Guard,
                 Round, and Sticky bits needed to implement the four
                 required rounding modes. Measured worst-case errors in
                 the functions are below 3 units in the last place
                 (ulps).\par

                 The transcendental functions offered in hardware on the
                 8087 have restricted argument ranges, and thus require
                 a software interface to carry out range reduction of
                 general arguments before the chip instructions can be
                 used.\par

                 Juffa reports that the Cyrix FasMath CX-83D87
                 coprocessor instead uses rational polynomial
                 representations of the elementary functions, with
                 75-bit significands. Its accuracy is superior to all of
                 its competitors: Cyrix claimed that results are almost
                 always within 0.5 ulp of the infinitely precise exact
                 value, and thus, are almost always correctly
                 rounded.\par

                 Thanks to semiconductor density improvements, the Intel
                 486DX, introduced in 1989, put the coprocessor on the
                 same chip as the CPU, more than tripling floating-point
                 performance over the previous generation Intel 387DX.
                 By the mid 1990s, floating-point support was available
                 in all major commercial CPUs, but in some, such as the
                 DEC Alpha, it takes a major part of the chip
                 area.\par

                 Although not mentioned in this article, Motorola's
                 68881 and 68882 coprocessors offered similar
                 floating-point hardware instructions as the Intel 8087,
                 but later CPUs from ARM, DEC (Alpha), HP (HPPA), IBM
                 (POWER, PowerPC, s390x, and z-Series), Loongson, MIPS,
                 RISC-V, and Sun/Fujitsu SPARC. and also the Intel i860,
                 omit the elementary functions, requiring their
                 implementation in software.",
}


bibtype: techreport
filename: fparith.bib
label: Karp:1993:HPD
author: A. H. Karp and P. Markstein
title: High precision division and square root
number: HPL-93-42
institution: Hewlett--Packard Lab.
address: Palo Alto, CA, USA
pages: 20
month: jun
monthnumber: 6
year: 1993
bibdate: Tue Dec 12 09:27:13 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.12 09:27:13 MST
keywords: Division; Floating point hardware; Square root algorithms
acknowledgement: ack-nhfb
thesaurus: Digital arithmetic
rawauthor: A. H. Karp and P. Markstein
rawtitle: High precision division and square root
abstract:
The authors present division and square root algorithms for calculations with more bits than are handled by the floating point hardware. These algorithms avoid the need to multiply two high precision numbers, speeding up the last iteration by as much as a factor of ten.

rawabstract:
The authors present division and square root algorithms for calculations with more bits than are handled by the floating point hardware. These algorithms avoid the need to multiply two high precision numbers, speeding up the last iteration by as much as a factor of ten.

entry:
@TechReport{Karp:1993:HPD,
  author =       "A. H. Karp and P. Markstein",
  title =        "High precision division and square root",
  number =       "HPL-93-42",
  institution =  "Hewlett--Packard Lab.",
  address =      "Palo Alto, CA, USA",
  pages =        "20",
  month =        jun,
  year =         "1993",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The authors present division and square root
                 algorithms for calculations with more bits than are
                 handled by the floating point hardware. These
                 algorithms avoid the need to multiply two high
                 precision numbers, speeding up the last iteration by as
                 much as a factor of ten.",
  acknowledgement = ack-nhfb,
  classification = "C5230 (Digital arithmetic methods)",
  keywords =     "Division; Floating point hardware; Square root
                 algorithms",
  thesaurus =    "Digital arithmetic",
}


bibtype: inproceedings
filename: fparith.bib
label: Kim:1993:FABa
author: S. W. Kim and T. Stouraitis and A. Skavantzos
booktitle: IEEE International Symposium on Circuits and Systems, ISCAS '93, 3--6 May 1993
title: Full adder-based inner product step processors for residue and quadratic residue number systems
volume: 3
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1821--1824
year: 1993
DOI: https://doi.org/10.1109/ISCAS.1993.394100
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: S. W. Kim and T. Stouraitis and A. Skavantzos
rawbooktitle: {IEEE} International Symposium on Circuits and Systems, {ISCAS '93}, 3--6 May 1993
rawtitle: Full adder-based inner product step processors for residue and quadratic residue number systems
entry:
@InProceedings{Kim:1993:FABa,
  author =       "S. W. Kim and T. Stouraitis and A. Skavantzos",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems, {ISCAS '93}, 3--6 May 1993",
  title =        "Full adder-based inner product step processors for
                 residue and quadratic residue number systems",
  volume =       "3",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1821--1824",
  year =         "1993",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.1993.394100",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A full adder-based arithmetic unit of a modulus $m$,
                 called an FA-based AU$_m$, is proposed. It performs
                 both addition and multiplication at the same time.
                 Since the proposed AU$_m$'s use full adders as their
                 basic units, they lead to modular and regular designs
                 which result in lower cost and easier implementation in
                 VLSI.",
}


bibtype: inproceedings
filename: fparith.bib
label: Kim:1993:FABb
author: Seon Wook Kim and T. Stouraitis and A. Skavantzos
booktitle: IEEE International Symposium on Circuits and Systems, ISCAS '93, 3--6 May 1993
title: Full adder-based inner product step processors for residue and quadratic residue number systems
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1821--1824
year: 1993
DOI: https://doi.org/10.1109/EDAC.1993.386412
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: Seon Wook Kim and T. Stouraitis and A. Skavantzos
rawbooktitle: {IEEE} International Symposium on Circuits and Systems, {ISCAS '93}, 3--6 May 1993
rawtitle: Full adder-based inner product step processors for residue and quadratic residue number systems
entry:
@InProceedings{Kim:1993:FABb,
  author =       "Seon Wook Kim and T. Stouraitis and A. Skavantzos",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems, {ISCAS '93}, 3--6 May 1993",
  title =        "Full adder-based inner product step processors for
                 residue and quadratic residue number systems",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1821--1824",
  year =         "1993",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/EDAC.1993.386412",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
}


bibtype: inproceedings
filename: fparith.bib
label: Kim:1993:FABc
author: S. W. Kim and T. Stouraitis and A. Skavantzos
booktitle: IEEE International Symposium on Circuits and Systems, ISCAS '93, 3--6 May 1993
title: Full adder-based inner product step processors for residue and quadratic residue number systems
volume: 3
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1821--1824
year: 1993
DOI: https://doi.org/10.1109/ISCAS.1993.394100
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: S. W. Kim and T. Stouraitis and A. Skavantzos
rawbooktitle: {IEEE} International Symposium on Circuits and Systems, {ISCAS '93}, 3--6 May 1993
rawtitle: Full adder-based inner product step processors for residue and quadratic residue number systems
entry:
@InProceedings{Kim:1993:FABc,
  author =       "S. W. Kim and T. Stouraitis and A. Skavantzos",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems, {ISCAS '93}, 3--6 May 1993",
  title =        "Full adder-based inner product step processors for
                 residue and quadratic residue number systems",
  volume =       "3",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1821--1824",
  year =         "1993",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.1993.394100",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A full adder-based arithmetic unit of a modulus m,
                 called an FA-based AU m, is proposed. It performs both
                 addition and multiplication at the same time. Since the
                 proposed AU m's use full adders as their basic units,
                 they \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Kim:1993:FABd
author: Seon Wook Kim and T. Stouraitis and A. Skavantzos
booktitle: IEEE International Symposium on Circuits and Systems, ISCAS '93, 3--6 May 1993
title: Full adder-based inner product step processors for residue and quadratic residue number systems
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1821--1824
year: 1993
DOI: https://doi.org/10.1109/EDAC.1993.386412
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: Seon Wook Kim and T. Stouraitis and A. Skavantzos
rawbooktitle: {IEEE} International Symposium on Circuits and Systems, {ISCAS '93}, 3--6 May 1993
rawtitle: Full adder-based inner product step processors for residue and quadratic residue number systems
entry:
@InProceedings{Kim:1993:FABd,
  author =       "Seon Wook Kim and T. Stouraitis and A. Skavantzos",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems, {ISCAS '93}, 3--6 May 1993",
  title =        "Full adder-based inner product step processors for
                 residue and quadratic residue number systems",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1821--1824",
  year =         "1993",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/EDAC.1993.386412",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
}


bibtype: inproceedings
filename: fparith.bib
label: Kirsch:1993:ABU
author: Bary J. Kirsch and Peter R. Turner
title: Adaptive Beamforming Using RNS Arithmetic
crossref: Swartzlander:1993:SCA
pages: 36--43
year: 1993
bibdate: Sat Nov 17 09:46:07 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.17 09:46:07 ???
URL: http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Kirsch.pdf
keywords: ARITH-11; residue number system
acknowledgement: ack-nhfb
rawauthor: Bary J. Kirsch and Peter R. Turner
rawtitle: Adaptive Beamforming Using {RNS} Arithmetic
entry:
@InProceedings{Kirsch:1993:ABU,
  author =       "Bary J. Kirsch and Peter R. Turner",
  title =        "Adaptive Beamforming Using {RNS} Arithmetic",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "36--43",
  year =         "1993",
  bibdate =      "Sat Nov 17 09:46:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Kirsch.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11; residue number system",
}


bibtype: book
filename: fparith.bib
label: Klatte:1993:CXC
editor: Rudi Klatte and Ulrich Kulisch and Christian Lawo and Michael Rauch and Andreas Wiethoff
title: C-XSC: a C++ class library for extended scientific computing
publisher: pub-SV
address: pub-SV:adr
pages: xii + 269
year: 1993
ISBN: 3-540-56328-8 (Berlin), 0-387-56328-8 (New York) OR 3540563288 (Berlin), 0387563288 (New York)
LCCN: QA76.73.C153 C9 1993
bibdate: Fri Jun 24 20:05:29 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2005.06.24 20:05:29 MDT
remark: This book is a translation of an unpublished German manuscript.
acknowledgement: ack-nhfb
raweditor: Rudi Klatte and Ulrich Kulisch and Christian Lawo and Michael Rauch and Andreas Wiethoff
rawtitle: {C-XSC}: a {C++} class library for extended scientific computing
ISBN13:
978-3-540-56328-0 (Berlin), 978-0-387-56328-2 (New York) OR 9783540563280 (Berlin), 9780387563282 (New York)

abstract:
C-XSC is a tool for the development of numerical algorithms delivering highly accurate and automatically verified results. It provides a large number of predefined numerical data types and operators. These types are implemented as C++ classes. Thus, C-XSC allows high-level programming of numerical applications in C and C++. The most important features of C-XSC are: real, complex, interval, and complex interval arithmetic; dynamic vectors and matrices; subarrays of vectors and matrices; dotprecision data types, predefined arithmetic operators with maximum accuracy; standard functions of high accuracy; multiple precision arithmetic and standard functions; rounding control for I/O data; error handling, and library of problem solving routines with automatic result verification. Thus, C-XSC makes the computer more powerful concerning the arithmetic. C-XSC is immediately usable by C programmers, easy to learn, user-extendable, and may also be combined with other tools. The book can be used as a textbook and as a reference manual. It consists of an introduction to advanced computer arithmetic, a chapter describing the programming languages C and C++, the major chapter ``C-XSC Reference'', sample programs, and indices.

subject:
C++ (Computer program language); C-XSC; Mathematics; Numerical analysis; Mathematics.; Numerical analysis.

TOC:
1 Introduction 1.1 Typography 1.2 C-XSC: A Class Library in the Programming Language C++ 1.3 C-XSC: A Programming Environment for Scientific Computing with Result Verification 1.4 Survey of C-XSC 2 The Programming Languages C and C++ 2.1 A Short Introduction to C 2.2 Additional Features in C++ 3 C-XSC Reference 3.1 Constants, Data Types, and Variables 3.2 Expressions 3.3 Statements 3.4 Error Handling 3.5 Pitfalls for Programming with C XSC A Syntax Diagrams A.1 Data Types A.2 Management of Vectors and Matrices A.3 Definition of Variables A.4 Expressions A.5 Logical Expressions A.6 Type Castings A.7 Assignments A.8 Arithmetic Standard Functions A.9 Other Functions A.10 Input and Output A.11 Extension of a Syntax Diagram of C++ B The Structure of the C-XSC Package B.1 Header Files B.2 Module Libraries C Error List D Sample Programs D.1 Rounding Control of Arithmetic Operations D.2 Rounding Control of Input and Output D.3 Scalar Product D.4 Transpose of a Matrix D.5 Trace of a Product Matrix D.6 Inverse of a Matrix D.7 Multiple-Precision Arithmetic D.8 Interval Newton Method D.9 Runge-Kutta Method D.10 Complex Polynomial Arithmetic D.11 Automatic Differentiation E Scientific Computation with Verified Results E.1 Evaluation of Polynomials E.2 Matrix Inversion E.3 Linear Systems of Equations E.4 Eigenvalues of Symmetric Matrices E.5 Fast Fourier Transform E.6 Zeros of a Nonlinear Equation E.7 System of Nonlinear Equations E.8 Ordinary Differential Equations

rawabstract:
C-XSC is a tool for the development of numerical algorithms delivering highly accurate and automatically verified results. It provides a large number of predefined numerical data types and operators. These types are implemented as C++ classes. Thus, C-XSC allows high-level programming of numerical applications in C and C++. The most important features of C-XSC are: real, complex, interval, and complex interval arithmetic; dynamic vectors and matrices; subarrays of vectors and matrices; dotprecision data types, predefined arithmetic operators with maximum accuracy; standard functions of high accuracy; multiple precision arithmetic and standard functions; rounding control for I/O data; error handling, and library of problem solving routines with automatic result verification. Thus, C-XSC makes the computer more powerful concerning the arithmetic. C-XSC is immediately usable by C programmers, easy to learn, user-extendable, and may also be combined with other tools. The book can be used as a textbook and as a reference manual. It consists of an introduction to advanced computer arithmetic, a chapter describing the programming languages C and C++, the major chapter ``C-XSC Reference'', sample programs, and indices.

rawTOC:
1 Introduction \\ 1.1 Typography \\ 1.2 C-XSC: A Class Library in the Programming Language C++ \\ 1.3 C-XSC: A Programming Environment for Scientific Computing with Result Verification \\ 1.4 Survey of C-XSC \\ 2 The Programming Languages C and C++ \\ 2.1 A Short Introduction to C \\ 2.2 Additional Features in C++ \\ 3 C-XSC Reference \\ 3.1 Constants, Data Types, and Variables \\ 3.2 Expressions \\ 3.3 Statements \\ 3.4 Error Handling \\ 3.5 Pitfalls for Programming with C XSC \\ A Syntax Diagrams \\ A.1 Data Types \\ A.2 Management of Vectors and Matrices \\ A.3 Definition of Variables \\ A.4 Expressions \\ A.5 Logical Expressions \\ A.6 Type Castings \\ A.7 Assignments \\ A.8 Arithmetic Standard Functions \\ A.9 Other Functions \\ A.10 Input and Output \\ A.11 Extension of a Syntax Diagram of C++ \\ B The Structure of the C-XSC Package \\ B.1 Header Files \\ B.2 Module Libraries \\ C Error List \\ D Sample Programs \\ D.1 Rounding Control of Arithmetic Operations \\ D.2 Rounding Control of Input and Output \\ D.3 Scalar Product \\ D.4 Transpose of a Matrix \\ D.5 Trace of a Product Matrix \\ D.6 Inverse of a Matrix \\ D.7 Multiple-Precision Arithmetic \\ D.8 Interval Newton Method \\ D.9 Runge-Kutta Method \\ D.10 Complex Polynomial Arithmetic \\ D.11 Automatic Differentiation \\ E Scientific Computation with Verified Results \\ E.1 Evaluation of Polynomials \\ E.2 Matrix Inversion \\ E.3 Linear Systems of Equations \\ E.4 Eigenvalues of Symmetric Matrices \\ E.5 Fast Fourier Transform \\ E.6 Zeros of a Nonlinear Equation \\ E.7 System of Nonlinear Equations \\ E.8 Ordinary Differential Equations

entry:
@Book{Klatte:1993:CXC,
  editor =       "Rudi Klatte and Ulrich Kulisch and Christian Lawo and
                 Michael Rauch and Andreas Wiethoff",
  title =        "{C-XSC}: a {C++} class library for extended scientific
                 computing",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xii + 269",
  year =         "1993",
  ISBN =         "3-540-56328-8 (Berlin), 0-387-56328-8 (New York)",
  ISBN-13 =      "978-3-540-56328-0 (Berlin), 978-0-387-56328-2 (New
                 York)",
  LCCN =         "QA76.73.C153 C9 1993",
  bibdate =      "Fri Jun 24 20:05:29 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  price =        "DM74.00",
  abstract =     "C-XSC is a tool for the development of numerical
                 algorithms delivering highly accurate and automatically
                 verified results. It provides a large number of
                 predefined numerical data types and operators. These
                 types are implemented as C++ classes. Thus, C-XSC
                 allows high-level programming of numerical applications
                 in C and C++. The most important features of C-XSC are:
                 real, complex, interval, and complex interval
                 arithmetic; dynamic vectors and matrices; subarrays of
                 vectors and matrices; dotprecision data types,
                 predefined arithmetic operators with maximum accuracy;
                 standard functions of high accuracy; multiple precision
                 arithmetic and standard functions; rounding control for
                 I/O data; error handling, and library of problem
                 solving routines with automatic result verification.
                 Thus, C-XSC makes the computer more powerful concerning
                 the arithmetic. C-XSC is immediately usable by C
                 programmers, easy to learn, user-extendable, and may
                 also be combined with other tools. The book can be used
                 as a textbook and as a reference manual. It consists of
                 an introduction to advanced computer arithmetic, a
                 chapter describing the programming languages C and C++,
                 the major chapter ``C-XSC Reference'', sample programs,
                 and indices.",
  acknowledgement = ack-nhfb,
  remark =       "This book is a translation of an unpublished German
                 manuscript.",
  subject =      "C++ (Computer program language); C-XSC; Mathematics;
                 Numerical analysis; Mathematics.; Numerical analysis.",
  tableofcontents = "1 Introduction \\
                 1.1 Typography \\
                 1.2 C-XSC: A Class Library in the Programming Language
                 C++ \\
                 1.3 C-XSC: A Programming Environment for Scientific
                 Computing with Result Verification \\
                 1.4 Survey of C-XSC \\
                 2 The Programming Languages C and C++ \\
                 2.1 A Short Introduction to C \\
                 2.2 Additional Features in C++ \\
                 3 C-XSC Reference \\
                 3.1 Constants, Data Types, and Variables \\
                 3.2 Expressions \\
                 3.3 Statements \\
                 3.4 Error Handling \\
                 3.5 Pitfalls for Programming with C XSC \\
                 A Syntax Diagrams \\
                 A.1 Data Types \\
                 A.2 Management of Vectors and Matrices \\
                 A.3 Definition of Variables \\
                 A.4 Expressions \\
                 A.5 Logical Expressions \\
                 A.6 Type Castings \\
                 A.7 Assignments \\
                 A.8 Arithmetic Standard Functions \\
                 A.9 Other Functions \\
                 A.10 Input and Output \\
                 A.11 Extension of a Syntax Diagram of C++ \\
                 B The Structure of the C-XSC Package \\
                 B.1 Header Files \\
                 B.2 Module Libraries \\
                 C Error List \\
                 D Sample Programs \\
                 D.1 Rounding Control of Arithmetic Operations \\
                 D.2 Rounding Control of Input and Output \\
                 D.3 Scalar Product \\
                 D.4 Transpose of a Matrix \\
                 D.5 Trace of a Product Matrix \\
                 D.6 Inverse of a Matrix \\
                 D.7 Multiple-Precision Arithmetic \\
                 D.8 Interval Newton Method \\
                 D.9 Runge-Kutta Method \\
                 D.10 Complex Polynomial Arithmetic \\
                 D.11 Automatic Differentiation \\
                 E Scientific Computation with Verified Results \\
                 E.1 Evaluation of Polynomials \\
                 E.2 Matrix Inversion \\
                 E.3 Linear Systems of Equations \\
                 E.4 Eigenvalues of Symmetric Matrices \\
                 E.5 Fast Fourier Transform \\
                 E.6 Zeros of a Nonlinear Equation \\
                 E.7 System of Nonlinear Equations \\
                 E.8 Ordinary Differential Equations",
}


bibtype: book
filename: fparith.bib
label: Koren:1993:CAA
author: Israel Koren
title: Computer Arithmetic Algorithms
publisher: pub-PH
address: pub-PH:adr
pages: xiii + 210
year: 1993
ISBN: 0-13-151952-2 OR 0131519522
ISBN13: 978-0-13-151952-7 OR 9780131519527
LCCN: 76.9.C62 K67 1993
bibdate: Thu Sep 1 10:12:51 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:12:51 ???
acknowledgement: ack-nj
rawauthor: Israel Koren
rawtitle: Computer Arithmetic Algorithms
entry:
@Book{Koren:1993:CAA,
  author =       "Israel Koren",
  title =        "Computer Arithmetic Algorithms",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xiii + 210",
  year =         "1993",
  ISBN =         "0-13-151952-2",
  ISBN-13 =      "978-0-13-151952-7",
  LCCN =         "76.9.C62 K67 1993",
  bibdate =      "Thu Sep 1 10:12:51 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: inproceedings
filename: fparith.bib
label: Kornerup:1993:HRM
author: Peter Kornerup
title: High-Radix Modular Multiplication for Cryptosystems
crossref: Swartzlander:1993:SCA
pages: 277--283
year: 1993
bibdate: Wed Nov 14 18:46:45 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 18:46:45 ???
URL: http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Kornerup.pdf
keywords: ARITH-11
acknowledgement: ack-nhfb
rawauthor: Peter Kornerup
rawtitle: High-Radix Modular Multiplication for Cryptosystems
entry:
@InProceedings{Kornerup:1993:HRM,
  author =       "Peter Kornerup",
  title =        "High-Radix Modular Multiplication for Cryptosystems",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "277--283",
  year =         "1993",
  bibdate =      "Wed Nov 14 18:46:45 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Kornerup.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
}


bibtype: book
filename: fparith.bib
label: Kortemeyer:1993:CPT
author: Gerd Kortemeyer and others
publisher: pub-IWT
address: pub-IWT:adr
pages: 391
year: 1993
ISBN: 3-88322-439-1 OR 3883224391
ISBN13: 978-3-88322-439-8 OR 9783883224398
bibdate: Mon Sep 16 17:08:22 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.09.16 17:08:22 ???
acknowledgement: ack-nj
rawauthor: Gerd Kortemeyer and others
title:
Coprozessoren Programmierung mit Turbo Pascal und C++: eine grundlegende Einfuhrung in die mathematischen Coprozessoren ab 80387 und deren Programmierung toenglish Coprocessor Programming with Turbo Pascal and C++relax endtoenglish 

rawtitle:
{Coprozessoren Programmierung mit Turbo Pascal und C++: eine grundlegende Einf{\"u}hrung in die mathematischen Coprozessoren ab 80387 und deren Programmierung} \toenglish Coprocessor Programming with {Turbo Pascal} and {C++}\relax \endtoenglish

entry:
@Book{Kortemeyer:1993:CPT,
  author =       "Gerd Kortemeyer and others",
  title =        "{Coprozessoren Programmierung mit Turbo Pascal und
                 C++: eine grundlegende Einf{\"u}hrung in die
                 mathematischen Coprozessoren ab 80387 und deren
                 Programmierung} \toenglish Coprocessor Programming with
                 {Turbo Pascal} and {C++}\relax \endtoenglish",
  publisher =    pub-IWT,
  address =      pub-IWT:adr,
  pages =        "391",
  year =         "1993",
  ISBN =         "3-88322-439-1",
  ISBN-13 =      "978-3-88322-439-8",
  LCCN =         "????",
  bibdate =      "Mon Sep 16 17:08:22 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: Kota:1993:NAH
author: K. Kota and J. R. Cavallaro
title: Numerical Accuracy and Hardware Tradeoffs for CORDIC Arithmetic for Special-Purpose Processors
journal: j-IEEE-TRANS-COMPUT
volume: 42
number: 7
pages: 769--779
month: jul
monthnumber: 7
year: 1993
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.237718
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 07:58:50 MDT 2011
bibtimestamp: 2011.07.07 07:58:50 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=237718
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: K. Kota and J. R. Cavallaro
rawtitle: Numerical Accuracy and Hardware Tradeoffs for {CORDIC} Arithmetic for Special-Purpose Processors
bibsource:
https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib

entry:
@Article{Kota:1993:NAH,
  author =       "K. Kota and J. R. Cavallaro",
  title =        "Numerical Accuracy and Hardware Tradeoffs for {CORDIC}
                 Arithmetic for Special-Purpose Processors",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "42",
  number =       "7",
  pages =        "769--779",
  month =        jul,
  year =         "1993",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.237718",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:58:50 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=237718",
  acknowledgement = ack-nj # "\slash " # 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: Krandick:1993:EMF
author: Werner Krandick and Jeremy R. Johnson
title: Efficient multiprecision floating point multiplication with optimal directional rounding
crossref: Swartzlander:1993:SCA
pages: 228--233
year: 1993
bibdate: Thu Dec 14 11:25:18 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.14 11:25:18 MST
URL: http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Krandick.pdf
acknowledgement: ack-nhfb
affiliation: Res. Inst. for Symbolic Comput., Johannes Kepler University, Linz, Austria
thesaurus: Floating point arithmetic
rawauthor: Werner Krandick and Jeremy R. Johnson
rawtitle: Efficient multiprecision floating point multiplication with optimal directional rounding
abstract:
An algorithm is described for multiplying multiprecision floating-point numbers. The algorithm can produce either the smallest floating-point number greater than or equal to the true product, or the greatest floating-point number smaller than or equal to the true product. Software implementations of multiprecision floating-point multiplication can reduce the computation time by a factor of two if they do not compute the low-order digits of the product of the two mantissas. However, these algorithms do not necessarily provide optimally rounded results. The algorithms described here is guaranteed to produce optimally rounded results and typically obtains the same savings.

keywords:
ARITH-11; Floating-point numbers; Multiprecision floating point multiplication; Optimal directional rounding; Optimally rounded results

rawabstract:
An algorithm is described for multiplying multiprecision floating-point numbers. The algorithm can produce either the smallest floating-point number greater than or equal to the true product, or the greatest floating-point number smaller than or equal to the true product. Software implementations of multiprecision floating-point multiplication can reduce the computation time by a factor of two if they do not compute the low-order digits of the product of the two mantissas. However, these algorithms do not necessarily provide optimally rounded results. The algorithms described here is guaranteed to produce optimally rounded results and typically obtains the same savings.

entry:
@InProceedings{Krandick:1993:EMF,
  author =       "Werner Krandick and Jeremy R. Johnson",
  title =        "Efficient multiprecision floating point multiplication
                 with optimal directional rounding",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "228--233",
  year =         "1993",
  bibdate =      "Thu Dec 14 11:25:18 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Krandick.pdf",
  abstract =     "An algorithm is described for multiplying
                 multiprecision floating-point numbers. The algorithm
                 can produce either the smallest floating-point number
                 greater than or equal to the true product, or the
                 greatest floating-point number smaller than or equal to
                 the true product. Software implementations of
                 multiprecision floating-point multiplication can reduce
                 the computation time by a factor of two if they do not
                 compute the low-order digits of the product of the two
                 mantissas. However, these algorithms do not necessarily
                 provide optimally rounded results. The algorithms
                 described here is guaranteed to produce optimally
                 rounded results and typically obtains the same
                 savings.",
  acknowledgement = ack-nhfb,
  affiliation =  "Res. Inst. for Symbolic Comput., Johannes Kepler
                 University, Linz, Austria",
  classification = "C5230 (Digital arithmetic methods)",
  confdate =     "29 June-2 July 1993",
  conflocation = "Windsor, Ont., Canada",
  confsponsor =  "IEEE Comput. Soc.; IEEE Tech. Committee on VLSI;
                 Natural Sci. and Eng. Res.; Council of Canada",
  keywords =     "ARITH-11; Floating-point numbers; Multiprecision
                 floating point multiplication; Optimal directional
                 rounding; Optimally rounded results",
  thesaurus =    "Floating point arithmetic",
}


bibtype: article
filename: fparith.bib
label: Krishna:1993:TFA
author: H. Krishna and J.-D. Sun
title: On theory and fast algorithms for error correction in residue number system product codes
journal: j-IEEE-TRANS-COMPUT
volume: 42
number: 7
pages: 840--853
month: jul
monthnumber: 7
year: 1993
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.237724
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 07:58:50 MDT 2011
bibtimestamp: 2011.07.07 07:58:50 MDT
fjournal: IEEE Transactions on Computers
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: H. Krishna and J.-D. Sun
rawtitle: On theory and fast algorithms for error correction in residue number system product codes
URL:
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=6095; https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=237724

entry:
@Article{Krishna:1993:TFA,
  author =       "H. Krishna and J.-D. Sun",
  title =        "On theory and fast algorithms for error correction in
                 residue number system product codes",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "42",
  number =       "7",
  pages =        "840--853",
  month =        jul,
  year =         "1993",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.237724",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:58:50 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=6095;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=237724",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "The authors develop a coding theory approach to error
                 control in residue number system product codes. Based
                 on this coding theory framework, computationally
                 efficient algorithms are derived for correcting single
                 errors, double errors, and multiple \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Lee:1993:DAE
author: Joong-Eon Lee and Oh-Young Kwon and Tack-Don Han
title: Design of an area efficient unit for floating-point division and square root
journal: j-J-KOREA-INFO-SCI-SOCIETY
volume: 20
number: 7
pages: 1060--1071
month: jul
monthnumber: 7
year: 1993
CODEN: HJKHDC
ISSN: 0258-9125 OR 02589125
bibdate: Tue Dec 12 09:27:13 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.12 09:27:13 MST
fjournal: Journal of the Korea Information Science Society = Chongbo Kwahakhoe nonmunji
language: Korean
acknowledgement: ack-nhfb
thesaurus: Adders; Digital arithmetic; Parallel algorithms
rawauthor: Joong-Eon Lee and Oh-Young Kwon and Tack-Don Han
rawtitle: Design of an area efficient unit for floating-point division and square root
abstract:
The authors propose an algorithm for a high performance floating point division and square root unit that uses a parallel multiplier. The basic algorithm used in the design is the continued-product normalization method. In this method, an arbitrary number is constantly multiplied to the divisor and dividend and dividend/divisor ends up with quotient/1 and the desired result attained. However this method requires computation of x*(2-x) and x*(3-x)/2 and this is quite an overhead. Therefore they propose a new algorithm to compute (2-x) and (3-x)/2 by using the modified Booth algorithm. When applied to the continued-product normalization method, this algorithm can maximize the inherent parallelism of the continued-product normalization method, and reduce computation time by effectively applying pipelining, and also achieve area efficient design by eliminating one register and one carry propagate adder needed for computing (2-x) and (3-x)/2. When the designed unit is used with the seed generator which has the accuracy of 2/sup -7/, division can be executed in eight cycles and the square root operation in 13 cycles.

keywords:
Area efficient unit; Continued-product normalization method; Floating-point division; Modified Booth algorithm; Parallel multiplier; Pipelining; Seed generator; Square root

rawabstract:
The authors propose an algorithm for a high performance floating point division and square root unit that uses a parallel multiplier. The basic algorithm used in the design is the continued-product normalization method. In this method, an arbitrary number is constantly multiplied to the divisor and dividend and dividend/divisor ends up with quotient/1 and the desired result attained. However this method requires computation of x*(2-x) and x*(3-x)/2 and this is quite an overhead. Therefore they propose a new algorithm to compute (2-x) and (3-x)/2 by using the modified Booth algorithm. When applied to the continued-product normalization method, this algorithm can maximize the inherent parallelism of the continued-product normalization method, and reduce computation time by effectively applying pipelining, and also achieve area efficient design by eliminating one register and one carry propagate adder needed for computing (2-x) and (3-x)/2. When the designed unit is used with the seed generator which has the accuracy of 2/sup -7/, division can be executed in eight cycles and the square root operation in 13 cycles.

entry:
@Article{Lee:1993:DAE,
  author =       "Joong-Eon Lee and Oh-Young Kwon and Tack-Don Han",
  title =        "Design of an area efficient unit for floating-point
                 division and square root",
  journal =      j-J-KOREA-INFO-SCI-SOCIETY,
  volume =       "20",
  number =       "7",
  pages =        "1060--1071",
  month =        jul,
  year =         "1993",
  CODEN =        "HJKHDC",
  ISSN =         "0258-9125",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The authors propose an algorithm for a high
                 performance floating point division and square root
                 unit that uses a parallel multiplier. The basic
                 algorithm used in the design is the continued-product
                 normalization method. In this method, an arbitrary
                 number is constantly multiplied to the divisor and
                 dividend and dividend/divisor ends up with quotient/1
                 and the desired result attained. However this method
                 requires computation of x*(2-x) and x*(3-x)/2 and this
                 is quite an overhead. Therefore they propose a new
                 algorithm to compute (2-x) and (3-x)/2 by using the
                 modified Booth algorithm. When applied to the
                 continued-product normalization method, this algorithm
                 can maximize the inherent parallelism of the
                 continued-product normalization method, and reduce
                 computation time by effectively applying pipelining,
                 and also achieve area efficient design by eliminating
                 one register and one carry propagate adder needed for
                 computing (2-x) and (3-x)/2. When the designed unit is
                 used with the seed generator which has the accuracy of
                 2/sup -7/, division can be executed in eight cycles and
                 the square root operation in 13 cycles.",
  acknowledgement = ack-nhfb,
  classification = "B1265B (Logic circuits); C4240P (Parallel
                 programming and algorithm theory); C5120 (Logic and
                 switching circuits); C5230 (Digital arithmetic
                 methods)",
  fjournal =     "Journal of the Korea Information Science Society =
                 Chongbo Kwahakhoe nonmunji",
  keywords =     "Area efficient unit; Continued-product normalization
                 method; Floating-point division; Modified Booth
                 algorithm; Parallel multiplier; Pipelining; Seed
                 generator; Square root",
  language =     "Korean",
  pubcountry =   "South Korea",
  thesaurus =    "Adders; Digital arithmetic; Parallel algorithms",
}


bibtype: inproceedings
filename: fparith.bib
label: Lewis:1993:ALA
author: D. M. Lewis
title: An accurate LNS arithmetic unit using interleaved memory function interpolator
crossref: Swartzlander:1993:SCA
pages: 2--9
year: 1993
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
URL: http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Lewis.pdf
keywords: ARITH-11
acknowledgement: ack-nhfb
rawauthor: D. M. Lewis
rawtitle: An accurate {LNS} arithmetic unit using interleaved memory function interpolator
entry:
@InProceedings{Lewis:1993:ALA,
  author =       "D. M. Lewis",
  title =        "An accurate {LNS} arithmetic unit using interleaved
                 memory function interpolator",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "2--9",
  year =         "1993",
  bibdate =      "Sat Jul 16 16:14:38 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Lewis.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
  summary =      "A logarithmic number system (LNS) arithmetic unit
                 using a new method for polynomial interpolation in
                 hardware is described. The use of an interleaved memory
                 reduces storage requirements by allowing each stored
                 function value to be used in \ldots{}",
}


bibtype: misc
filename: fparith.bib
label: Lindsley:1993:DME
author: Brett L. Lindsley
title: Device and method for evaluating exponentials
pages: 2--9
day: 5
month: jan
monthnumber: 1
year: 1993
bibdate: Tue Jan 08 22:31:05 2008
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2008.01.08 22:31:05 ???
URL: http://www.freepatentsonline.com/5177702.html
acknowledgement: ack-nhfb
howpublished: United States Patent 5,177,702
rawauthor: Brett L. Lindsley
rawtitle: Device and method for evaluating exponentials
abstract:
A method and apparatus are described for processing an input value to provide an output exponential value of a desired base raised to the power of the input value. The method includes, and the apparatus included hardware for implementing, the steps of adjusting the input value relative to the input value, a predetermined base of a first exponential value, and the desired base of the output exponential value to obtain a first scaled value, modifying the scaled value to obtain an approximation value, determining the first exponential value of the approximation value, generating an adjusted error value relative to the first scaled value, the approximation value, and a logarithm of the predetermined base of the first exponential value, determining a correction value for the first exponential value and combining the first exponential value with the correction value to obtain, substantially, the output exponential value having the desired base raised to the power of the input value.

rawabstract:
A method and apparatus are described for processing an input value to provide an output exponential value of a desired base raised to the power of the input value. The method includes, and the apparatus included hardware for implementing, the steps of adjusting the input value relative to the input value, a predetermined base of a first exponential value, and the desired base of the output exponential value to obtain a first scaled value, modifying the scaled value to obtain an approximation value, determining the first exponential value of the approximation value, generating an adjusted error value relative to the first scaled value, the approximation value, and a logarithm of the predetermined base of the first exponential value, determining a correction value for the first exponential value and combining the first exponential value with the correction value to obtain, substantially, the output exponential value having the desired base raised to the power of the input value.

entry:
@Misc{Lindsley:1993:DME,
  author =       "Brett L. Lindsley",
  title =        "Device and method for evaluating exponentials",
  howpublished = "United States Patent 5,177,702",
  day =          "5",
  month =        jan,
  year =         "1993",
  bibdate =      "Tue Jan 08 22:31:05 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.freepatentsonline.com/5177702.html",
  abstract =     "A method and apparatus are described for processing an
                 input value to provide an output exponential value of a
                 desired base raised to the power of the input value.
                 The method includes, and the apparatus included
                 hardware for implementing, the steps of adjusting the
                 input value relative to the input value, a
                 predetermined base of a first exponential value, and
                 the desired base of the output exponential value to
                 obtain a first scaled value, modifying the scaled value
                 to obtain an approximation value, determining the first
                 exponential value of the approximation value,
                 generating an adjusted error value relative to the
                 first scaled value, the approximation value, and a
                 logarithm of the predetermined base of the first
                 exponential value, determining a correction value for
                 the first exponential value and combining the first
                 exponential value with the correction value to obtain,
                 substantially, the output exponential value having the
                 desired base raised to the power of the input value.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Linzer:1993:IEF
author: E. N. Linzer and E. Feig
title: Implementation of Efficient FFT Algorithms on Fused Multiply-Add Architectures
journal: j-IEEE-TRANS-SIG-PROC
volume: 41
number: 1
pages: 2--9
year: 1993
CODEN: ITPRED
DOI: https://doi.org/10.1109/TSP.1993.193130
ISSN: 1053-587X (print), 1941-0476 (electronic) OR 1053587X (print), 19410476 (electronic)
ISSNL: 1053-587X OR 1053587X
bibdate: Sun Feb 20 10:11:17 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2011.02.20 10:11:17 ???
fjournal: IEEE Transactions on Signal Processing
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78
rawauthor: E. N. Linzer and E. Feig
rawtitle: Implementation of Efficient {FFT} Algorithms on Fused Multiply-Add Architectures
entry:
@Article{Linzer:1993:IEF,
  author =       "E. N. Linzer and E. Feig",
  title =        "Implementation of Efficient {FFT} Algorithms on Fused
                 Multiply-Add Architectures",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "41",
  number =       "1",
  year =         "1993",
  CODEN =        "ITPRED",
  DOI =          "https://doi.org/10.1109/TSP.1993.193130",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  bibdate =      "Sun Feb 20 10:11:17 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
}


bibtype: article
filename: fparith.bib
label: Lo:1993:BCP
author: J.-C. Lo and S. Thanawastien and T. R. N. Rao
title: Berger check prediction for array multipliers and array dividers
journal: j-IEEE-TRANS-COMPUT
volume: 42
number: 7
pages: 892--896
month: jul
monthnumber: 7
year: 1993
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.237731
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 07:58:50 MDT 2011
bibtimestamp: 2011.07.07 07:58:50 MDT
note: See correction cite Lo:1996:CBC.
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=237731
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: J.-C. Lo and S. Thanawastien and T. R. N. Rao
rawnote: See correction \cite{Lo:1996:CBC}.
rawtitle: {Berger} check prediction for array multipliers and array dividers
entry:
@Article{Lo:1993:BCP,
  author =       "J.-C. Lo and S. Thanawastien and T. R. N. Rao",
  title =        "{Berger} check prediction for array multipliers and
                 array dividers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "42",
  number =       "7",
  pages =        "892--896",
  month =        jul,
  year =         "1993",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.237731",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:58:50 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  note =         "See correction \cite{Lo:1996:CBC}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=237731",
  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: Louie:1993:DRD
author: M. E. Louie and M. D. Ercegovac
title: On Digit-Recurrence Division Implementations for Field Programmable Gate Arrays
crossref: Swartzlander:1993:SCA
pages: 202--209
year: 1993
bibdate: Sat Nov 17 09:46:07 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.17 09:46:07 ???
URL: http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Louie.pdf
keywords: ARITH-11
acknowledgement: ack-nhfb
rawauthor: M. E. Louie and M. D. Ercegovac
rawtitle: On Digit-Recurrence Division Implementations for Field Programmable Gate Arrays
entry:
@InProceedings{Louie:1993:DRD,
  author =       "M. E. Louie and M. D. Ercegovac",
  title =        "On Digit-Recurrence Division Implementations for Field
                 Programmable Gate Arrays",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "202--209",
  year =         "1993",
  bibdate =      "Sat Nov 17 09:46:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Louie.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
}


bibtype: inproceedings
filename: fparith.bib
label: Louie:1993:DRS
author: M. E. Louie and M. D. Ercegovac
booktitle: Proceedings of the IEEE Workshop on FPGAs for Custom Computing Machines, 5--7 April 1993
title: A digit-recurrence square root implementation for field programmable gate arrays
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 178--183
year: 1993
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. E. Louie and M. D. Ercegovac
rawbooktitle: Proceedings of the {IEEE} Workshop on {FPGAs} for Custom Computing Machines, 5--7 April 1993
rawtitle: A digit-recurrence square root implementation for field programmable gate arrays
entry:
@InProceedings{Louie:1993:DRS,
  author =       "M. E. Louie and M. D. Ercegovac",
  booktitle =    "Proceedings of the {IEEE} Workshop on {FPGAs} for
                 Custom Computing Machines, 5--7 April 1993",
  title =        "A digit-recurrence square root implementation for
                 field programmable gate arrays",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "178--183",
  year =         "1993",
  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 =      "Creating efficient arithmetic processors requires a
                 pairing of high speed arithmetic algorithms with
                 optimal mapping strategies for a given technology. The
                 authors propose bit reduction as key to an efficient
                 pairing process for lookup table based \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Lozier:1993:UGF
author: D. W. Lozier
title: An underflow-induced graphics failure solved by SLI arithmetic
crossref: Swartzlander:1993:SCA
pages: 10--17
year: 1993
bibdate: Thu Dec 14 11:25:18 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.14 11:25:18 MST
URL: http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Lozier.pdf
acknowledgement: ack-nhfb
affiliation: Nat. Inst. of Stand. and Technol., Gaithersburg, MD, USA
thesaurus: Computer graphics; Floating point arithmetic
rawauthor: D. W. Lozier
rawtitle: An underflow-induced graphics failure solved by {SLI} arithmetic
abstract:
Floating-point underflow is often regarded as either harmless or as an indication that the computational algorithm is in need of scaling. A counterexample to this view is given of a function for which contour plotting is difficult due to floating-point underflow. The function arose as an asymptotic solution to a model problem in turbulent combustion in which two chemical species (fuel and oxidizer) mix and react in a vortex field. Scaling is not a viable option because of extreme sensitivity to a small physical parameter. Standard graphics software packages produce erroneous contours without any indication of difficulty. This example provides support for considering symmetric level-index arithmetic, a new form of computer arithmetic which is immune to underflow and overflow.

keywords:
ARITH-11; Asymptotic solution; Computer arithmetic; Contour plotting; Floating point underflow; Graphics failure; Graphics software packages; Turbulent combustion

rawabstract:
Floating-point underflow is often regarded as either harmless or as an indication that the computational algorithm is in need of scaling. A counterexample to this view is given of a function for which contour plotting is difficult due to floating-point underflow. The function arose as an asymptotic solution to a model problem in turbulent combustion in which two chemical species (fuel and oxidizer) mix and react in a vortex field. Scaling is not a viable option because of extreme sensitivity to a small physical parameter. Standard graphics software packages produce erroneous contours without any indication of difficulty. This example provides support for considering symmetric level-index arithmetic, a new form of computer arithmetic which is immune to underflow and overflow.

entry:
@InProceedings{Lozier:1993:UGF,
  author =       "D. W. Lozier",
  title =        "An underflow-induced graphics failure solved by {SLI}
                 arithmetic",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "10--17",
  year =         "1993",
  bibdate =      "Thu Dec 14 11:25:18 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Lozier.pdf",
  abstract =     "Floating-point underflow is often regarded as either
                 harmless or as an indication that the computational
                 algorithm is in need of scaling. A counterexample to
                 this view is given of a function for which contour
                 plotting is difficult due to floating-point underflow.
                 The function arose as an asymptotic solution to a model
                 problem in turbulent combustion in which two chemical
                 species (fuel and oxidizer) mix and react in a vortex
                 field. Scaling is not a viable option because of
                 extreme sensitivity to a small physical parameter.
                 Standard graphics software packages produce erroneous
                 contours without any indication of difficulty. This
                 example provides support for considering symmetric
                 level-index arithmetic, a new form of computer
                 arithmetic which is immune to underflow and overflow.",
  acknowledgement = ack-nhfb,
  affiliation =  "Nat. Inst. of Stand. and Technol., Gaithersburg, MD,
                 USA",
  classification = "C5230 (Digital arithmetic methods); C6130B (Graphics
                 techniques)",
  confdate =     "29 June-2 July 1993",
  conflocation = "Windsor, Ont., Canada",
  confsponsor =  "IEEE Comput. Soc.; IEEE Tech. Committee on VLSI;
                 Natural Sci. and Eng. Res.; Council of Canada",
  keywords =     "ARITH-11; Asymptotic solution; Computer arithmetic;
                 Contour plotting; Floating point underflow; Graphics
                 failure; Graphics software packages; Turbulent
                 combustion",
  thesaurus =    "Computer graphics; Floating point arithmetic",
}


bibtype: article
filename: fparith.bib
label: MacKenzie:1993:NAC
author: Donald MacKenzie
title: Negotiating Arithmetic, Constructing Proof: The Sociology of Mathematics and Information Technology
journal: j-SOC-STUD-SCI
volume: 23
number: 1
pages: 37--65
day: 1
month: feb
monthnumber: 2
year: 1993
CODEN: SSSCDH
DOI: https://doi.org/10.1177/030631293023001002
ISSN: 0306-3127 (print), 1460-3659 (electronic) OR 03063127 (print), 14603659 (electronic)
ISSNL: 0306-3127 OR 03063127
bibdate: Mon Dec 3 09:12:55 MST 2018
bibtimestamp: 2018.12.03 09:12:55 MST
note: Summary of the process of IEEE 754, several years after its initial adoption.
fjournal: Social Studies of Science
acknowledgement: ack-nhfb
journalURL: http://sss.sagepub.com/content/by/year
rawauthor: Donald MacKenzie
rawnote: Summary of the process of IEEE 754, several years after its initial adoption.
rawtitle: Negotiating Arithmetic, Constructing Proof: The Sociology of Mathematics and Information Technology
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/socstudsci.bib

URL:
https://ieeemilestones.ethw.org/w/images/1/10/Negotiating_Arithmetic_MacKenzie.pdf; https://journals.sagepub.com/doi/pdf/10.1177/030631293023001002

entry:
@Article{MacKenzie:1993:NAC,
  author =       "Donald MacKenzie",
  title =        "Negotiating Arithmetic, Constructing Proof: The
                 Sociology of Mathematics and Information Technology",
  journal =      j-SOC-STUD-SCI,
  volume =       "23",
  number =       "1",
  pages =        "37--65",
  day =          "1",
  month =        feb,
  year =         "1993",
  CODEN =        "SSSCDH",
  DOI =          "https://doi.org/10.1177/030631293023001002",
  ISSN =         "0306-3127 (print), 1460-3659 (electronic)",
  ISSN-L =       "0306-3127",
  bibdate =      "Mon Dec 3 09:12:55 MST 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/socstudsci.bib",
  note =         "Summary of the process of IEEE 754, several years
                 after its initial adoption.",
  URL =          "https://ieeemilestones.ethw.org/w/images/1/10/Negotiating_Arithmetic_MacKenzie.pdf;
                 https://journals.sagepub.com/doi/pdf/10.1177/030631293023001002",
  acknowledgement = ack-nhfb,
  fjournal =     "Social Studies of Science",
  journal-URL =  "http://sss.sagepub.com/content/by/year",
}


bibtype: article
filename: fparith.bib
label: Mandelbaum:1993:SRS
author: D. M. Mandelbaum
title: Some results on a SRT type division scheme
journal: j-IEEE-TRANS-COMPUT
volume: 42
number: 1
pages: 102--106
month: jan
monthnumber: 1
year: 1993
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.192218
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 07:58:46 MDT 2011
bibtimestamp: 2011.07.07 07:58:46 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=192218
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: D. M. Mandelbaum
rawtitle: Some results on a {SRT} type division scheme
entry:
@Article{Mandelbaum:1993:SRS,
  author =       "D. M. Mandelbaum",
  title =        "Some results on a {SRT} type division scheme",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "42",
  number =       "1",
  pages =        "102--106",
  month =        jan,
  year =         "1993",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.192218",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:58:46 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=192218",
  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: Maryoung:1993:DBP
author: James Maryoung
title: Development of a binary phase shift keying modem receiver with a floating point processor TMS320C30
type: Thesis (M.S.)
school: California State University, Long Beach
address: Long Beach, CA, USA
pages: xi + 265
year: 1993
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Signal processing --- Algorithms.; Signal processing --- Digital techniques.
acknowledgement: ack-nhfb
rawauthor: James Maryoung
rawtitle:
Development of a binary phase shift keying modem receiver with a floating point processor {TMS320C30}

entry:
@MastersThesis{Maryoung:1993:DBP,
  author =       "James Maryoung",
  title =        "Development of a binary phase shift keying modem
                 receiver with a floating point processor {TMS320C30}",
  type =         "Thesis ({M.S.})",
  school =       "California State University, Long Beach",
  address =      "Long Beach, CA, USA",
  pages =        "xi + 265",
  year =         "1993",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Signal processing --- Algorithms.; Signal processing
                 --- Digital techniques.",
}


bibtype: article
filename: fparith.bib
label: Masotti:1993:FNE
author: G. Masotti
title: Floating-point numbers with error estimates
journal: j-CAD
volume: 25
number: 9
pages: 524--538
month: sep
monthnumber: 9
year: 1993
CODEN: CAIDA5
ISSN: 0010-4485 (print), 1879-2685 (electronic) OR 00104485 (print), 18792685 (electronic)
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
acknowledgement: ack-nhfb
affiliation: Dept. di Elettr. Inf. e Sistem., Universita degli Studi di Bologna, Bologna, Italy
thesaurus: Digital arithmetic; Error statistics; Roundoff errors
rawauthor: G. Masotti
rawtitle: Floating-point numbers with error estimates
abstract:
Addresses the problem of precision in floating-point computations. A method for estimating the errors which affect intermediate and final results is presented, and a synthesis of many software simulations is discussed. The basic idea is to represent floating-point numbers by means of a data-structure collecting value and estimated error information. It has been found that, under certain circumstances, the estimate of the absolute error is accurate and has a compact statistical distribution. It is also shown that, by monitoring the estimated relative error during a computation (an ad hoc definition of relative error is used), the validity of results can be ensured. The error estimates enable robust algorithms to be implemented and ill-conditioned problems to be detected. A hardware implementation of the method by means of a special floating-point processor is outlined. A dynamic extension of number precision, under the control of error estimates, is also advocated, in order to compute results within given error bounds.

keywords:
Compact statistical distribution; Computer arithmetic; Data-structure collecting value; Dynamic extension; Dynamic precision extension; Error bounds; Error estimates; Final results; Floating-point numbers; Floating-point processor; Hardware implementation; Ill-conditioned problems; Intermediate results; Numerical accuracy; Relative error; Robust algorithms; Software simulations; Validity

rawabstract:
Addresses the problem of precision in floating-point computations. A method for estimating the errors which affect intermediate and final results is presented, and a synthesis of many software simulations is discussed. The basic idea is to represent floating-point numbers by means of a data-structure collecting value and estimated error information. It has been found that, under certain circumstances, the estimate of the absolute error is accurate and has a compact statistical distribution. It is also shown that, by monitoring the estimated relative error during a computation (an ad hoc definition of relative error is used), the validity of results can be ensured. The error estimates enable robust algorithms to be implemented and ill-conditioned problems to be detected. A hardware implementation of the method by means of a special floating-point processor is outlined. A dynamic extension of number precision, under the control of error estimates, is also advocated, in order to compute results within given error bounds.

entry:
@Article{Masotti:1993:FNE,
  author =       "G. Masotti",
  title =        "Floating-point numbers with error estimates",
  journal =      j-CAD,
  volume =       "25",
  number =       "9",
  pages =        "524--538",
  month =        sep,
  year =         "1993",
  CODEN =        "CAIDA5",
  ISSN =         "0010-4485 (print), 1879-2685 (electronic)",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Addresses the problem of precision in floating-point
                 computations. A method for estimating the errors which
                 affect intermediate and final results is presented, and
                 a synthesis of many software simulations is discussed.
                 The basic idea is to represent floating-point numbers
                 by means of a data-structure collecting value and
                 estimated error information. It has been found that,
                 under certain circumstances, the estimate of the
                 absolute error is accurate and has a compact
                 statistical distribution. It is also shown that, by
                 monitoring the estimated relative error during a
                 computation (an ad hoc definition of relative error is
                 used), the validity of results can be ensured. The
                 error estimates enable robust algorithms to be
                 implemented and ill-conditioned problems to be
                 detected. A hardware implementation of the method by
                 means of a special floating-point processor is
                 outlined. A dynamic extension of number precision,
                 under the control of error estimates, is also
                 advocated, in order to compute results within given
                 error bounds.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. di Elettr. Inf. e Sistem., Universita degli
                 Studi di Bologna, Bologna, Italy",
  classification = "C5230 (Digital arithmetic methods)",
  keywords =     "Compact statistical distribution; Computer arithmetic;
                 Data-structure collecting value; Dynamic extension;
                 Dynamic precision extension; Error bounds; Error
                 estimates; Final results; Floating-point numbers;
                 Floating-point processor; Hardware implementation;
                 Ill-conditioned problems; Intermediate results;
                 Numerical accuracy; Relative error; Robust algorithms;
                 Software simulations; Validity",
  pubcountry =   "UK",
  thesaurus =    "Digital arithmetic; Error statistics; Roundoff
                 errors",
}


bibtype: article
filename: fparith.bib
label: Mazenc:1993:CFU
author: Christophe Mazenc and Xavier Merrheim and Jean-Michel Muller
title: Computing functions $ cos ^-1 $ and $ sin ^-1 $ using Cordic
journal: j-IEEE-TRANS-COMPUT
volume: 42
number: 1
pages: 118--122
month: jan
monthnumber: 1
year: 1993
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.192222
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 07:58:47 MDT 2011
bibtimestamp: 2011.07.07 07:58:47 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=192222
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Christophe Mazenc and Xavier Merrheim and Jean-Michel Muller
rawtitle: Computing functions $ \cos^{-1} $ and $ \sin^{-1} $ using {Cordic}
entry:
@Article{Mazenc:1993:CFU,
  author =       "Christophe Mazenc and Xavier Merrheim and Jean-Michel
                 Muller",
  title =        "Computing functions $ \cos^{-1} $ and $ \sin^{-1} $
                 using {Cordic}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "42",
  number =       "1",
  pages =        "118--122",
  month =        jan,
  year =         "1993",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.192222",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:58:47 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=192222",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


