# bibtab

bibtype: article
filename: fparith.bib
label: IFIF:1992:CVD
author: IFIP Working Group 2.5 (Numerical Software)
title: Comments on version 3.1 of draft ISO / IEC 10967:1991 Language Compatible Arithmetic
journal: j-SIGNUM
volume: 27
number: 1
pages: 2--3
month: jan
monthnumber: 1
year: 1992
CODEN: SNEWD6
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Tue Apr 12 07:50:21 MDT 2005
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.04.12 07:50:21 MDT
fjournal: ACM SIGNUM Newsletter
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/signum
rawauthor: {IFIP Working Group 2.5 (Numerical Software)}
rawtitle: Comments on version 3.1 of draft {ISO\slash IEC 10967:1991 Language Compatible Arithmetic}
entry:
@Article{IFIF:1992:CVD,
  author =       "{IFIP Working Group 2.5 (Numerical Software)}",
  title =        "Comments on version 3.1 of draft {ISO\slash IEC
                 10967:1991 Language Compatible Arithmetic}",
  journal =      j-SIGNUM,
  volume =       "27",
  number =       "1",
  pages =        "2--3",
  month =        jan,
  year =         "1992",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:21 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: inproceedings
filename: fparith.bib
label: Jackson:1992:DTF
author: P. B. Jackson
title: Developing a toolkit for floating-point hardware in the Nuprl proof development system
crossref: Prinetto:1992:CHD
pages: 401--419
year: 1992
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
acknowledgement: ack-nhfb
affiliation: Department of Computer Science, Cornell University, Ithaca, NY, USA
thesaurus: Digital arithmetic; Formal specification; Software tools; Theorem proving
rawauthor: P. B. Jackson
rawtitle: Developing a toolkit for floating-point hardware in the {Nuprl} proof development system
abstract:
Describes current work in building a toolkit of theorems, definitions and tactics in the Nuprl proof development system for the verification of floating-point hardware designs. The approach emphasizes reasoning over a wide range of levels of abstraction within a single system. For example the specification of the IEEE's floating point standard makes free use of rational arithmetic, as well as talking explicitly about the input and output bit-vectors of floating-point circuits.

keywords:
Floating-point hardware; Nuprl proof development system; Rational arithmetic; Reasoning; Toolkit; Verification

rawabstract:
Describes current work in building a toolkit of theorems, definitions and tactics in the Nuprl proof development system for the verification of floating-point hardware designs. The approach emphasizes reasoning over a wide range of levels of abstraction within a single system. For example the specification of the IEEE's floating point standard makes free use of rational arithmetic, as well as talking explicitly about the input and output bit-vectors of floating-point circuits.

entry:
@InProceedings{Jackson:1992:DTF,
  author =       "P. B. Jackson",
  title =        "Developing a toolkit for floating-point hardware in
                 the {Nuprl} proof development system",
  crossref =     "Prinetto:1992:CHD",
  pages =        "401--419",
  year =         "1992",
  bibdate =      "Wed Dec 13 13:13:34 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Describes current work in building a toolkit of
                 theorems, definitions and tactics in the Nuprl proof
                 development system for the verification of
                 floating-point hardware designs. The approach
                 emphasizes reasoning over a wide range of levels of
                 abstraction within a single system. For example the
                 specification of the IEEE's floating point standard
                 makes free use of rational arithmetic, as well as
                 talking explicitly about the input and output
                 bit-vectors of floating-point circuits.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Computer Science, Cornell University,
                 Ithaca, NY, USA",
  classification = "C4210 (Formal logic); C5230 (Digital arithmetic
                 methods); C6110B (Software engineering techniques);
                 C6115 (Programming support)",
  keywords =     "Floating-point hardware; Nuprl proof development
                 system; Rational arithmetic; Reasoning; Toolkit;
                 Verification",
  thesaurus =    "Digital arithmetic; Formal specification; Software
                 tools; Theorem proving",
}


bibtype: article
filename: fparith.bib
label: Jacobson:1992:ETF
author: David Jacobson
title: Engineer's Toolbox: Floating Point in Mathematica
journal: j-MATHEMATICA-J
volume: 2
number: 3
pages: 42--46
month: Summer
year: 1992
ISSN: 1047-5974 (print), 1097-1610 (electronic) OR 10475974 (print), 10971610 (electronic)
ISSNL: 1047-5974 OR 10475974
bibdate: Sat Nov 6 13:33:40 MDT 2010
bibsource: http://www.mathematica-journal.com/issue/v2i3/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.11.06 13:33:40 MDT
URL: http://www.mathematica-journal.com/issue/v2i3/tutorials/toolbox/index.html
fjournal: Mathematica Journal
acknowledgement: ack-nhfb
journalURL: http://www.mathematica-journal.com/
rawauthor: David Jacobson
rawtitle: Engineer's Toolbox: Floating Point in {Mathematica}
abstract:
Mathematica provides both traditional machine-level floating point numbers and software-implemented variable-precision floating-point numbers. There are two different notions of precision: an estimate of the maximum possible relative error, which is propagated through arithmetic operations based on the precision of the operands; and the number of digits used to represent the significand (mantissa). Mathematica links the first notion to the second, throwing away digits that it cannot prove are significant. In iterative calculations the precision can ratchet down a little each iteration, until there is nothing left.

rawabstract:
Mathematica provides both traditional machine-level floating point numbers and software-implemented variable-precision floating-point numbers. There are two different notions of precision: an estimate of the maximum possible relative error, which is propagated through arithmetic operations based on the precision of the operands; and the number of digits used to represent the significand (mantissa). Mathematica links the first notion to the second, throwing away digits that it cannot prove are significant. In iterative calculations the precision can ratchet down a little each iteration, until there is nothing left.

entry:
@Article{Jacobson:1992:ETF,
  author =       "David Jacobson",
  title =        "Engineer's Toolbox: Floating Point in {Mathematica}",
  journal =      j-MATHEMATICA-J,
  volume =       "2",
  number =       "3",
  pages =        "42--46",
  month =        "Summer",
  year =         "1992",
  CODEN =        "????",
  ISSN =         "1047-5974 (print), 1097-1610 (electronic)",
  ISSN-L =       "1047-5974",
  bibdate =      "Sat Nov 6 13:33:40 MDT 2010",
  bibsource =    "http://www.mathematica-journal.com/issue/v2i3/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.mathematica-journal.com/issue/v2i3/tutorials/toolbox/index.html",
  abstract =     "Mathematica provides both traditional machine-level
                 floating point numbers and software-implemented
                 variable-precision floating-point numbers. There are
                 two different notions of precision: an estimate of the
                 maximum possible relative error, which is propagated
                 through arithmetic operations based on the precision of
                 the operands; and the number of digits used to
                 represent the significand (mantissa). Mathematica links
                 the first notion to the second, throwing away digits
                 that it cannot prove are significant. In iterative
                 calculations the precision can ratchet down a little
                 each iteration, until there is nothing left.",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematica Journal",
  journal-URL =  "http://www.mathematica-journal.com/",
}


bibtype: article
filename: fparith.bib
label: Jaffar:1992:AMC
author: Joxan Jaffar and Peter J. Stuckey and Spiro Michaylov and Roland H. C. Yap
title: An abstract machine for CLP$ (mathcal R) $
journal: j-SIGPLAN
volume: 27
number: 7
pages: 128--139
month: jul
monthnumber: 7
year: 1992
CODEN: SINODQ
ISBN: 0-89791-475-9 OR 0897914759
ISBN13: 978-0-89791-475-8 OR 9780897914758
ISSN: 0362-1340 (print), 1523-2867 (print), 1558-1160 OR 03621340 (print), 15232867 (print), 15581160
ISSNL: 0362-1340 OR 03621340
LCCN: QA76.7.S53 1992
bibdate: Sun Dec 14 09:16:22 MST 2003
bibtimestamp: 2003.12.14 09:16:22 MST
URL: http://www.acm.org:80/pubs/citations/proceedings/pldi/143095/p128-jaffar/
fjournal: ACM SIGPLAN Notices
acknowledgement: ack-nhfb
affiliation: IBM T. J. Watson Research Cent
affiliationaddress: Yorktown Heights, NY, USA
annote: Published as part of the Proceedings of PLDI'92.
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J706
journalabr: SIGPLAN Not
rawauthor: Joxan Jaffar and Peter J. Stuckey and Spiro Michaylov and Roland H. C. Yap
rawtitle: An abstract machine for {CLP$ (\mathcal {R}) $}
bibsource:
Compendex database; http://portal.acm.org/; http://www.acm.org/pubs/contents/proceedings/pldi/143095/index.html; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
An abstract machine is described for the CLP$ (mathcal R) $ programming language. It is intended as a first step toward enabling CLP$ (mathcal R) $ programs to be executed with efficiency approaching that of conventional languages. The core Constraint Logic Arithmetic Machine (CLAM) extends the Warren Abstract Machine (WAM) for compiling Prolog with facilities for handling real arithmetic constraints. The full CLAM includes facilities for taking advantage of information obtained from global program analysis.

keywords:
Abstract machine; algorithms; Computer programming; Computer programming languages; Constraint logic arithmetic machine; design; Global program analysis; languages; Program compilers; prolog (programming language)

subject:
bf D.3.2 Software, PROGRAMMING LANGUAGES, Language Classifications, Prolog. bf D.1.6 Software, PROGRAMMING TECHNIQUES, Logic Programming. bf D.3.3 Software, PROGRAMMING LANGUAGES, Language Constructs and Features, Data types and structures. bf D.3.4 Software, PROGRAMMING LANGUAGES, Processors, Optimization.

rawabstract:
An abstract machine is described for the CLP$ (\mathcal {R}) $ programming language. It is intended as a first step toward enabling CLP$ (\mathcal {R}) $ programs to be executed with efficiency approaching that of conventional languages. The core Constraint Logic Arithmetic Machine (CLAM) extends the Warren Abstract Machine (WAM) for compiling Prolog with facilities for handling real arithmetic constraints. The full CLAM includes facilities for taking advantage of information obtained from global program analysis.

entry:
@Article{Jaffar:1992:AMC,
  author =       "Joxan Jaffar and Peter J. Stuckey and Spiro Michaylov
                 and Roland H. C. Yap",
  title =        "An abstract machine for {CLP$ (\mathcal {R}) $}",
  journal =      j-SIGPLAN,
  volume =       "27",
  number =       "7",
  pages =        "128--139",
  month =        jul,
  year =         "1992",
  CODEN =        "SINODQ",
  ISBN =         "0-89791-475-9",
  ISBN-13 =      "978-0-89791-475-8",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  LCCN =         "QA76.7.S53 1992",
  bibdate =      "Sun Dec 14 09:16:22 MST 2003",
  bibsource =    "Compendex database; http://portal.acm.org/;
                 http://www.acm.org/pubs/contents/proceedings/pldi/143095/index.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/pldi/143095/p128-jaffar/",
  abstract =     "An abstract machine is described for the CLP$
                 (\mathcal {R}) $ programming language. It is intended
                 as a first step toward enabling CLP$ (\mathcal {R}) $
                 programs to be executed with efficiency approaching
                 that of conventional languages. The core Constraint
                 Logic Arithmetic Machine (CLAM) extends the Warren
                 Abstract Machine (WAM) for compiling Prolog with
                 facilities for handling real arithmetic constraints.
                 The full CLAM includes facilities for taking advantage
                 of information obtained from global program analysis.",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM T. J. Watson Research Cent",
  affiliationaddress = "Yorktown Heights, NY, USA",
  annote =       "Published as part of the Proceedings of PLDI'92.",
  classification = "723.1",
  conference =   "Proceedings of the ACM SIGPLAN '92 Conference on
                 Programming Language Design and Implementation",
  conferenceyear = "1992",
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  journalabr =   "SIGPLAN Not",
  keywords =     "Abstract machine; algorithms; Computer programming;
                 Computer programming languages; Constraint logic
                 arithmetic machine; design; Global program analysis;
                 languages; Program compilers; prolog (programming
                 language)",
  meetingaddress = "San Francisco, CA, USA",
  meetingdate =  "Jun 17--19 1992",
  meetingdate2 = "06/17--19/92",
  sponsor =      "ACM",
  subject =      "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language
                 Classifications, Prolog. {\bf D.1.6} Software,
                 PROGRAMMING TECHNIQUES, Logic Programming. {\bf D.3.3}
                 Software, PROGRAMMING LANGUAGES, Language Constructs
                 and Features, Data types and structures. {\bf D.3.4}
                 Software, PROGRAMMING LANGUAGES, Processors,
                 Optimization.",
}


bibtype: inproceedings
filename: fparith.bib
label: Jain:1992:AEA
author: V. K. Jain and G. E. Perez and E. E. Swartzlander
title: Arithmetic Error Analysis of a New Reciprocal Cell
crossref: IEEE:1992:IIC
pages: 106--109
year: 1992
bibdate: Thu Sep 08 00:34:18 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.08 00:34:18 ???
acknowledgement: ack-nj
rawauthor: V. K. Jain and G. E. Perez and E. E. Swartzlander
rawtitle: Arithmetic Error Analysis of a New Reciprocal Cell
entry:
@InProceedings{Jain:1992:AEA,
  author =       "V. K. Jain and G. E. Perez and E. E. Swartzlander",
  title =        "Arithmetic Error Analysis of a New Reciprocal Cell",
  crossref =     "IEEE:1992:IIC",
  pages =        "106--109",
  year =         "1992",
  bibdate =      "Thu Sep 08 00:34:18 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: mastersthesis
filename: fparith.bib
label: James:1992:DRC
author: Shelton L. James
title: A distributed remote computational server
type: Thesis (M.S.)
school: University of Missouri, Columbia
address: Columbia, MO, USA
pages: vi + 183
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: Shelton L. James
rawtitle: A distributed remote computational server
keywords:
Distributed operating systems (Computers); Electronic networks.; Floating-point systems.; OSI (Computer network standard)

entry:
@MastersThesis{James:1992:DRC,
  author =       "Shelton L. James",
  title =        "A distributed remote computational server",
  type =         "Thesis ({M.S.})",
  school =       "University of Missouri, Columbia",
  address =      "Columbia, MO, USA",
  pages =        "vi + 183",
  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 =     "Distributed operating systems (Computers); Electronic
                 networks.; Floating-point systems.; OSI (Computer
                 network standard)",
}


bibtype: inproceedings
filename: fparith.bib
label: Johnstone:1992:RNA
author: P. Johnstone and F. E. Petry
title: Rational number approximation in higher radix floating point systems
crossref: IEEE:1992:PIS
pages: 501--504 vol.2
year: 1992
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
acknowledgement: ack-nhfb
affiliation: Telerate Syst. Inc., New Orleans, LA, USA
thesaurus: Digital arithmetic
rawauthor: P. Johnstone and F. E. Petry
rawtitle: Rational number approximation in higher radix floating point systems
abstract:
Recent research has shown that hybrid non-binary floating point bases, particularly decimal-based systems, can match or exceed the error performance of more traditional binary systems. The authors address a more general question of whether such bases offer any further advantages in the domain of rational number approximation. They 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 terminating and representable results can be expected is considered for binary, decimal, and other potentially interesting bases (base 30 and base 210).

keywords:
Base 10; Base 2; Base 210; Base 30; Bits per datum; decimal floating-point arithmetic; Error performance; Floating point representations; Fractions; Higher radix floating point systems; Limited exponent range; Normalized encodings; Rational number approximation; Storage allocated

rawabstract:
Recent research has shown that hybrid non-binary floating point bases, particularly decimal-based systems, can match or exceed the error performance of more traditional binary systems. The authors address a more general question of whether such bases offer any further advantages in the domain of rational number approximation. They 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 terminating and representable results can be expected is considered for binary, decimal, and other potentially interesting bases (base 30 and base 210).

entry:
@InProceedings{Johnstone:1992:RNA,
  author =       "P. Johnstone and F. E. Petry",
  title =        "Rational number approximation in higher radix floating
                 point systems",
  crossref =     "IEEE:1992:PIS",
  pages =        "501--504 vol.2",
  year =         "1992",
  bibdate =      "Wed Dec 13 13:13:34 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Recent research has shown that hybrid non-binary
                 floating point bases, particularly decimal-based
                 systems, can match or exceed the error performance of
                 more traditional binary systems. The authors address a
                 more general question of whether such bases offer any
                 further advantages in the domain of rational number
                 approximation. They 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 terminating and representable results can be
                 expected is considered for binary, decimal, and other
                 potentially interesting bases (base 30 and base 210).",
  acknowledgement = ack-nhfb,
  affiliation =  "Telerate Syst. Inc., New Orleans, LA, USA",
  classification = "C5230 (Digital arithmetic methods)",
  keywords =     "Base 10; Base 2; Base 210; Base 30; Bits per datum;
                 decimal floating-point arithmetic; Error performance;
                 Floating point representations; Fractions; Higher radix
                 floating point systems; Limited exponent range;
                 Normalized encodings; Rational number approximation;
                 Storage allocated",
  thesaurus =    "Digital arithmetic",
}


bibtype: article
filename: fparith.bib
label: Kahan:1992:ARL
author: W. Kahan
title: Analysis and Refutation of the LCAS
journal: j-SIGPLAN
volume: 27
number: 1
pages: 61--74
month: jan
monthnumber: 1
year: 1992
CODEN: SINODQ
ISSN: 0362-1340 (print), 1523-2867 (print), 1558-1160 OR 03621340 (print), 15232867 (print), 15581160
ISSNL: 0362-1340 OR 03621340
bibdate: Thu Aug 18 02:37:25 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.08.18 02:37:25 ???
fjournal: ACM SIGPLAN Notices
keywords: LCAS (Language Compatible Arithmetic Standard)
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J706
rawauthor: W. Kahan
rawtitle: Analysis and Refutation of the {LCAS}
entry:
@Article{Kahan:1992:ARL,
  author =       "W. Kahan",
  title =        "Analysis and Refutation of the {LCAS}",
  journal =      j-SIGPLAN,
  volume =       "27",
  number =       "1",
  pages =        "61--74",
  month =        jan,
  year =         "1992",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Thu Aug 18 02:37:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "LCAS (Language Compatible Arithmetic Standard)",
}


bibtype: unpublished
filename: fparith.bib
label: Kahan:1992:FPE
author: W. Kahan
title: Floating-Point Exception-Handling
institution: inst-BERKELEY-CS
address: inst-BERKELEY-CS:adr
pages: 2
day: 31
month: jul
monthnumber: 7
year: 1992
bibdate: Mon Apr 25 18:24:02 2005
bibtimestamp: 2005.04.25 18:24:02 ???
note: Manuscript
acknowledgement: ack-nhfb
rawauthor: W. Kahan
rawnote: Manuscript
rawtitle: Floating-Point Exception-Handling
entry:
@Unpublished{Kahan:1992:FPE,
  author =       "W. Kahan",
  title =        "Floating-Point Exception-Handling",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  pages =        "2",
  day =          "31",
  month =        jul,
  year =         "1992",
  bibdate =      "Mon Apr 25 18:24:02 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Manuscript",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Kahaner:1992:SJC
author: D. K. Kahaner and U. Wattenberg
title: Supercomputing-Japan: a competitive assessment
journal: j-IEEE-SPECTRUM
volume: 29
number: 9
pages: 42--47
month: sep
monthnumber: 9
year: 1992
CODEN: IEESAM
DOI: https://doi.org/10.1109/6.155708
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: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6
rawauthor: D. K. Kahaner and U. Wattenberg
rawtitle: {Supercomputing-Japan}: a competitive assessment
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeespectrum1990.bib; https://www.math.utah.edu/pub/tex/bib/super.bib

keywords:
5 to 8 GFLOPS; Arithmetic; Central Processing Unit; Computer industry; Hardware; high-speed single processor systems; Home computing; Information technology; intuitive information processing; Japanese supercomputers; Manufacturing industries; Ministry of International Trade and Industry; National electric code; parallel machines; Real-World Computing Program; research initiatives; Supercomputers; Telephony; US machines; vector processing functions

entry:
@Article{Kahaner:1992:SJC,
  author =       "D. K. Kahaner and U. Wattenberg",
  title =        "{Supercomputing-Japan}: a competitive assessment",
  journal =      j-IEEE-SPECTRUM,
  volume =       "29",
  number =       "9",
  pages =        "42--47",
  month =        sep,
  year =         "1992",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/6.155708",
  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;
                 https://www.math.utah.edu/pub/tex/bib/super.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
  keywords =     "5 to 8 GFLOPS; Arithmetic; Central Processing Unit;
                 Computer industry; Hardware; high-speed single
                 processor systems; Home computing; Information
                 technology; intuitive information processing; Japanese
                 supercomputers; Manufacturing industries; Ministry of
                 International Trade and Industry; National electric
                 code; parallel machines; Real-World Computing Program;
                 research initiatives; Supercomputers; Telephony; US
                 machines; vector processing functions",
}


bibtype: inproceedings
filename: fparith.bib
label: Kalliojarvi:1992:DRN
author: K. Kalliojarvi and Y. Neuvo
title: Distribution of roundoff noise in binary floating-point addition
crossref: White:1992:IIS
volume: 4
pages: 1796--1799
year: 1992
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: Signal Process. Lab., Tampere University of Technol., Finland
bookpages: 3028
thesaurus: Digital arithmetic; Digital simulation; Roundoff errors; Signal processing
rawauthor: K. Kalliojarvi and Y. Neuvo
rawtitle: Distribution of roundoff noise in binary floating-point addition
abstract:
A method for deriving the distribution of relative round off error in addition of two binary floating-point numbers is introduced. The distribution is needed in the calculation of variance of the relative roundoff error in floating-point addition. The resulting distribution depends on the statistics of the addends and the rounding strategy chosen. As an example, the distribution is derived for the addition of two uncorrelated numbers from Gaussian distribution. The result was verified by simulation.

keywords:
Addends; Binary floating-point addition; Calculation of variance; Distribution of relative round off error; Gaussian distribution; Relative roundoff error; Rounding strategy; Roundoff noise; Simulation; Two uncorrelated numbers

rawabstract:
A method for deriving the distribution of relative round off error in addition of two binary floating-point numbers is introduced. The distribution is needed in the calculation of variance of the relative roundoff error in floating-point addition. The resulting distribution depends on the statistics of the addends and the rounding strategy chosen. As an example, the distribution is derived for the addition of two uncorrelated numbers from Gaussian distribution. The result was verified by simulation.

entry:
@InProceedings{Kalliojarvi:1992:DRN,
  author =       "K. Kalliojarvi and Y. Neuvo",
  title =        "Distribution of roundoff noise in binary
                 floating-point addition",
  crossref =     "White:1992:IIS",
  volume =       "4",
  bookpages =    "3028",
  pages =        "1796--1799",
  year =         "1992",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A method for deriving the distribution of relative
                 round off error in addition of two binary
                 floating-point numbers is introduced. The distribution
                 is needed in the calculation of variance of the
                 relative roundoff error in floating-point addition. The
                 resulting distribution depends on the statistics of the
                 addends and the rounding strategy chosen. As an
                 example, the distribution is derived for the addition
                 of two uncorrelated numbers from Gaussian distribution.
                 The result was verified by simulation.",
  acknowledgement = ack-nhfb,
  affiliation =  "Signal Process. Lab., Tampere University of Technol.,
                 Finland",
  classification = "C1260 (Information theory); C5230 (Digital
                 arithmetic methods); C5260 (Digital signal
                 processing)",
  keywords =     "Addends; Binary floating-point addition; Calculation
                 of variance; Distribution of relative round off error;
                 Gaussian distribution; Relative roundoff error;
                 Rounding strategy; Roundoff noise; Simulation; Two
                 uncorrelated numbers",
  thesaurus =    "Digital arithmetic; Digital simulation; Roundoff
                 errors; Signal processing",
}


bibtype: book
filename: fparith.bib
label: Kane:1992:MRA
author: Gerry Kane and Joe Heinrich
title: MIPS RISC Architecture
publisher: pub-PH
address: pub-PH:adr
pages: 1796--1799
year: 1992
ISBN: 0-13-590472-2 OR 0135904722
ISBN13: 978-0-13-590472-5 OR 9780135904725
LCCN: QA76.8.M52 K37 1992
bibdate: Wed Dec 15 10:35:45 1993
bibtimestamp: 1993.12.15 10:35:45 ???
keywords: computer architecture; MIPS R2000 series microprocessors; reduced instruction set computers
acknowledgement: ack-nhfb
rawauthor: Gerry Kane and Joe Heinrich
rawtitle: {MIPS RISC} Architecture
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/master.bib; https://www.math.utah.edu/pub/tex/bib/microchip.bib

TOC:
RISC Architecture: An Overview MIPS Processor Architecture Overview CPU Instruction Set Summary Memory Management System Caches Exception Processing FPU Overview FPU Instruction Set Summary and Instruction Pipeline Floating Point Exceptions Appendixes Index

rawTOC:
RISC Architecture: An Overview \\ MIPS Processor Architecture Overview \\ CPU Instruction Set Summary \\ Memory Management System \\ Caches \\ Exception Processing \\ FPU Overview \\ FPU Instruction Set Summary and Instruction Pipeline \\ Floating Point Exceptions \\ Appendixes \\ Index

entry:
@Book{Kane:1992:MRA,
  author =       "Gerry Kane and Joe Heinrich",
  title =        "{MIPS RISC} Architecture",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  year =         "1992",
  ISBN =         "0-13-590472-2",
  ISBN-13 =      "978-0-13-590472-5",
  LCCN =         "QA76.8.M52 K37 1992",
  bibdate =      "Wed Dec 15 10:35:45 1993",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/microchip.bib",
  acknowledgement = ack-nhfb,
  keywords =     "computer architecture; MIPS R2000 series
                 microprocessors; reduced instruction set computers",
  tableofcontents = "RISC Architecture: An Overview \\
                 MIPS Processor Architecture Overview \\
                 CPU Instruction Set Summary \\
                 Memory Management System \\
                 Caches \\
                 Exception Processing \\
                 FPU Overview \\
                 FPU Instruction Set Summary and Instruction Pipeline
                 \\
                 Floating Point Exceptions \\
                 Appendixes \\
                 Index",
}


bibtype: book
filename: fparith.bib
label: Klatte:1992:PXP
author: Rudi Klatte and Ulrich Kulisch and Michael Neaga and Dietmar Ratz and Christian Ullrich
title: PASCAL-XSC: language reference with examples
publisher: pub-SV
address: pub-SV:adr
pages: x + 344
year: 1992
DOI: https://doi.org/10.1007/978-3-642-77277-1
ISBN: 3-540-55137-9 (Berlin), 0-387-55137-9 (New York) OR 3540551379 (Berlin), 0387551379 (New York)
LCCN: QA76.73.P2 P4213 1992
bibdate: Thu Jan 21 17:16:51 MST 2016
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2016.01.21 17:16:51 MST
note: Translated by G. F. Corliss and others.
language: English.
remark: Translation of: PASCAL-XSC.
subject: Pascal (Computer program language)
acknowledgement: ack-nhfb
rawauthor: Rudi Klatte and Ulrich Kulisch and Michael Neaga and Dietmar Ratz and Christian Ullrich
rawnote: Translated by G. F. Corliss and others.
rawtitle: {PASCAL-XSC}: language reference with examples
ISBN13:
978-3-540-55137-9 (Berlin), 978-0-387-55137-1 (New York) OR 9783540551379 (Berlin), 9780387551371 (New York)

abstract:
The programming language PASCAL-XSC (PASCAL eXtension for Scientific Computation) significantly simplifies programming in the area of scientific and technical computing. PASCAL-XSC provides a large number of predefined data types with arithmetic operators and predefined functions of highest accuracy for real and complex numbers, for real and complex intervals, and for the corresponding vectors and matrices. Thus PASCAL-XSC makes the computer more powerful concerning the arithmetic. Through an implementation in C, compilers for PASCAL-XSC are available for a large variety of computers such as personal computers, workstations, mainframes, and supercomputers. PASCAL-XSC provides a module concept, an operator concept, functions and operators with general result type, overloading of functions, procedures, and operators, dynamic arrays, access to subarrays, rounding control by the user, and accurate evaluation of expressions. The language is particularly suited for the development of numerical algorithms that deliver highly accurate and automatically verified results. A number of problem-solving routines with automatic result verification have already been implemented. PASCAL-XSC contains Standard PASCAL. It is immediately usable by PASCAL programmers. PASCAL-XSC is easy to learn and ideal for programming education. The book can be used as a textbook for lectures on computer programming. It contains a major chapter with sample programs, exercises, and solutions. A complete set of syntax diagrams, detailed tables, and indices complete the book.

TOC:
1 Introduction 1.1 Typography 1.2 Historical Remarks and Motivation 1.3 Advanced Computer Arithmetic 1.4 Connection with Programming Languages 1.5 Survey of PASCAL-XSC 2 Language Reference 2.1 Basic Symbols 2.2 Identifiers 2.3 Constants, Types, and Variables 2.4 Expressions 2.5 Statements 2.6 Program Structure 2.7 Subroutines 2.8 Modules 2.9 String Handling and Text Processing 2.10 How to Use Dynamic Arrays 3 The Arithmetic Modules 3.1 The Module C_ARI 3.2 The Module I_ARI 3.3 The Module CI_ARI 3.4 The Module MV_ARI 3.5 The Module MVC_ARI 3.6 The Module MVI_ARI 3.7 The Module MVCI_ARI 3.8 The Hierarchy of the Arithmetic Modules 3.9 A Complete Sample Program 4 Problem-Solving Routines 5 Exercises with Solutions 5.1 Test of Representability 5.2 Summation of Exponential Series 5.3 Influence of Rounding Errors 5.4 Scalar Product 5.5 Boothroyd/Dekker Matrices 5.6 Complex Functions 5.7 Surface Area of a Parallelepiped 5.8 Parallelism and Intersection of Lines 5.9 Transposed Matrix, Symmetry 5.10 Rail Route Map 5.11 Inventory Lists 5.12 Complex Numbers and Polar Representation 5.13 Complex Division 5.14 Electric Circuit 5.15 Alternating Current Measuring Bridge 5.16 Optical Lens 5.17 Interval Evaluation of a Polynomial 5.18 Calculations for Interval Matrices 5.19 Differentiation Arithmetic 5.20 Newton's Method with Automatic Differentiation 5.21 Measurement of Time 5.22 Iterative Method 5.23 Trace of a Product Matrix 5.24 Calculator for Polynomials 5.25 Interval Newton Method 5.26 Runge-Kutta Method 5.27 Rational Arithmetic 5.28 Evaluation of Polynomials A Syntax Diagrams B Indices and Lists B.1 Syntax Diagrams B.2 Reserved Words B.3 Predefined Identifiers B.4 Operators B.4.1 Basic Operators B.4.2 Arithmetic Operators B.4.3 Relational Operators for the Arithmetic Types B.4.4 Assignment Operators B.5 Predefined Functions B.6 Transfer Functions B.7 Predefined Procedures B.8 #-Expressions B.8.1 Real and Complex #-Expressions B.8.2 Real and Complex Interval #-Expressions Bibliography Index

rawabstract:
The programming language PASCAL-XSC (PASCAL eXtension for Scientific Computation) significantly simplifies programming in the area of scientific and technical computing. PASCAL-XSC provides a large number of predefined data types with arithmetic operators and predefined functions of highest accuracy for real and complex numbers, for real and complex intervals, and for the corresponding vectors and matrices. Thus PASCAL-XSC makes the computer more powerful concerning the arithmetic. Through an implementation in C, compilers for PASCAL-XSC are available for a large variety of computers such as personal computers, workstations, mainframes, and supercomputers. PASCAL-XSC provides a module concept, an operator concept, functions and operators with general result type, overloading of functions, procedures, and operators, dynamic arrays, access to subarrays, rounding control by the user, and accurate evaluation of expressions. The language is particularly suited for the development of numerical algorithms that deliver highly accurate and automatically verified results. A number of problem-solving routines with automatic result verification have already been implemented. PASCAL-XSC contains Standard PASCAL. It is immediately usable by PASCAL programmers. PASCAL-XSC is easy to learn and ideal for programming education. The book can be used as a textbook for lectures on computer programming. It contains a major chapter with sample programs, exercises, and solutions. A complete set of syntax diagrams, detailed tables, and indices complete the book.

rawTOC:
1 Introduction \\ 1.1 Typography \\ 1.2 Historical Remarks and Motivation \\ 1.3 Advanced Computer Arithmetic \\ 1.4 Connection with Programming Languages \\ 1.5 Survey of PASCAL-XSC \\ 2 Language Reference \\ 2.1 Basic Symbols \\ 2.2 Identifiers \\ 2.3 Constants, Types, and Variables \\ 2.4 Expressions \\ 2.5 Statements \\ 2.6 Program Structure \\ 2.7 Subroutines \\ 2.8 Modules \\ 2.9 String Handling and Text Processing \\ 2.10 How to Use Dynamic Arrays \\ 3 The Arithmetic Modules \\ 3.1 The Module C\_ARI \\ 3.2 The Module I\_ARI \\ 3.3 The Module CI\_ARI \\ 3.4 The Module MV\_ARI \\ 3.5 The Module MVC\_ARI \\ 3.6 The Module MVI\_ARI \\ 3.7 The Module MVCI\_ARI \\ 3.8 The Hierarchy of the Arithmetic Modules \\ 3.9 A Complete Sample Program \\ 4 Problem-Solving Routines \\ 5 Exercises with Solutions \\ 5.1 Test of Representability \\ 5.2 Summation of Exponential Series \\ 5.3 Influence of Rounding Errors \\ 5.4 Scalar Product \\ 5.5 Boothroyd/Dekker Matrices \\ 5.6 Complex Functions \\ 5.7 Surface Area of a Parallelepiped \\ 5.8 Parallelism and Intersection of Lines \\ 5.9 Transposed Matrix, Symmetry \\ 5.10 Rail Route Map \\ 5.11 Inventory Lists \\ 5.12 Complex Numbers and Polar Representation \\ 5.13 Complex Division \\ 5.14 Electric Circuit \\ 5.15 Alternating Current Measuring Bridge \\ 5.16 Optical Lens \\ 5.17 Interval Evaluation of a Polynomial \\ 5.18 Calculations for Interval Matrices \\ 5.19 Differentiation Arithmetic \\ 5.20 Newton's Method with Automatic Differentiation \\ 5.21 Measurement of Time \\ 5.22 Iterative Method \\ 5.23 Trace of a Product Matrix \\ 5.24 Calculator for Polynomials \\ 5.25 Interval Newton Method \\ 5.26 Runge-Kutta Method \\ 5.27 Rational Arithmetic \\ 5.28 Evaluation of Polynomials \\ A Syntax Diagrams \\ B Indices and Lists \\ B.1 Syntax Diagrams \\ B.2 Reserved Words \\ B.3 Predefined Identifiers \\ B.4 Operators \\ B.4.1 Basic Operators \\ B.4.2 Arithmetic Operators \\ B.4.3 Relational Operators for the Arithmetic Types \\ B.4.4 Assignment Operators \\ B.5 Predefined Functions \\ B.6 Transfer Functions \\ B.7 Predefined Procedures \\ B.8 \#-Expressions \\ B.8.1 Real and Complex \#-Expressions \\ B.8.2 Real and Complex Interval \#-Expressions \\ Bibliography \\ Index

entry:
@Book{Klatte:1992:PXP,
  author =       "Rudi Klatte and Ulrich Kulisch and Michael Neaga and
                 Dietmar Ratz and Christian Ullrich",
  title =        "{PASCAL-XSC}: language reference with examples",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "x + 344",
  year =         "1992",
  DOI =          "https://doi.org/10.1007/978-3-642-77277-1",
  ISBN =         "3-540-55137-9 (Berlin), 0-387-55137-9 (New York)",
  ISBN-13 =      "978-3-540-55137-9 (Berlin), 978-0-387-55137-1 (New
                 York)",
  LCCN =         "QA76.73.P2 P4213 1992",
  bibdate =      "Thu Jan 21 17:16:51 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "Translated by G. F. Corliss and others.",
  price =        "DM 64.00",
  abstract =     "The programming language PASCAL-XSC (PASCAL eXtension
                 for Scientific Computation) significantly simplifies
                 programming in the area of scientific and technical
                 computing. PASCAL-XSC provides a large number of
                 predefined data types with arithmetic operators and
                 predefined functions of highest accuracy for real and
                 complex numbers, for real and complex intervals, and
                 for the corresponding vectors and matrices. Thus
                 PASCAL-XSC makes the computer more powerful concerning
                 the arithmetic. Through an implementation in C,
                 compilers for PASCAL-XSC are available for a large
                 variety of computers such as personal computers,
                 workstations, mainframes, and supercomputers.
                 PASCAL-XSC provides a module concept, an operator
                 concept, functions and operators with general result
                 type, overloading of functions, procedures, and
                 operators, dynamic arrays, access to subarrays,
                 rounding control by the user, and accurate evaluation
                 of expressions. The language is particularly suited for
                 the development of numerical algorithms that deliver
                 highly accurate and automatically verified results. A
                 number of problem-solving routines with automatic
                 result verification have already been implemented.
                 PASCAL-XSC contains Standard PASCAL. It is immediately
                 usable by PASCAL programmers. PASCAL-XSC is easy to
                 learn and ideal for programming education. The book can
                 be used as a textbook for lectures on computer
                 programming. It contains a major chapter with sample
                 programs, exercises, and solutions. A complete set of
                 syntax diagrams, detailed tables, and indices complete
                 the book.",
  acknowledgement = ack-nhfb,
  language =     "English.",
  remark =       "Translation of: PASCAL-XSC.",
  subject =      "Pascal (Computer program language)",
  tableofcontents = "1 Introduction \\
                 1.1 Typography \\
                 1.2 Historical Remarks and Motivation \\
                 1.3 Advanced Computer Arithmetic \\
                 1.4 Connection with Programming Languages \\
                 1.5 Survey of PASCAL-XSC \\
                 2 Language Reference \\
                 2.1 Basic Symbols \\
                 2.2 Identifiers \\
                 2.3 Constants, Types, and Variables \\
                 2.4 Expressions \\
                 2.5 Statements \\
                 2.6 Program Structure \\
                 2.7 Subroutines \\
                 2.8 Modules \\
                 2.9 String Handling and Text Processing \\
                 2.10 How to Use Dynamic Arrays \\
                 3 The Arithmetic Modules \\
                 3.1 The Module C\_ARI \\
                 3.2 The Module I\_ARI \\
                 3.3 The Module CI\_ARI \\
                 3.4 The Module MV\_ARI \\
                 3.5 The Module MVC\_ARI \\
                 3.6 The Module MVI\_ARI \\
                 3.7 The Module MVCI\_ARI \\
                 3.8 The Hierarchy of the Arithmetic Modules \\
                 3.9 A Complete Sample Program \\
                 4 Problem-Solving Routines \\
                 5 Exercises with Solutions \\
                 5.1 Test of Representability \\
                 5.2 Summation of Exponential Series \\
                 5.3 Influence of Rounding Errors \\
                 5.4 Scalar Product \\
                 5.5 Boothroyd/Dekker Matrices \\
                 5.6 Complex Functions \\
                 5.7 Surface Area of a Parallelepiped \\
                 5.8 Parallelism and Intersection of Lines \\
                 5.9 Transposed Matrix, Symmetry \\
                 5.10 Rail Route Map \\
                 5.11 Inventory Lists \\
                 5.12 Complex Numbers and Polar Representation \\
                 5.13 Complex Division \\
                 5.14 Electric Circuit \\
                 5.15 Alternating Current Measuring Bridge \\
                 5.16 Optical Lens \\
                 5.17 Interval Evaluation of a Polynomial \\
                 5.18 Calculations for Interval Matrices \\
                 5.19 Differentiation Arithmetic \\
                 5.20 Newton's Method with Automatic Differentiation \\
                 5.21 Measurement of Time \\
                 5.22 Iterative Method \\
                 5.23 Trace of a Product Matrix \\
                 5.24 Calculator for Polynomials \\
                 5.25 Interval Newton Method \\
                 5.26 Runge-Kutta Method \\
                 5.27 Rational Arithmetic \\
                 5.28 Evaluation of Polynomials \\
                 A Syntax Diagrams \\
                 B Indices and Lists \\
                 B.1 Syntax Diagrams \\
                 B.2 Reserved Words \\
                 B.3 Predefined Identifiers \\
                 B.4 Operators \\
                 B.4.1 Basic Operators \\
                 B.4.2 Arithmetic Operators \\
                 B.4.3 Relational Operators for the Arithmetic Types \\
                 B.4.4 Assignment Operators \\
                 B.5 Predefined Functions \\
                 B.6 Transfer Functions \\
                 B.7 Predefined Procedures \\
                 B.8 \#-Expressions \\
                 B.8.1 Real and Complex \#-Expressions \\
                 B.8.2 Real and Complex Interval \#-Expressions \\
                 Bibliography \\
                 Index",
}


bibtype: article
filename: fparith.bib
label: Koc:1992:AAS
author: Cetin K. Koc and Ching-Yu Hung
journal: j-COMPUT-MATH-APPL
volume: 24
number: 3
pages: 3--12
month: aug
monthnumber: 8
year: 1992
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 19:11:08 MST 2017
bibtimestamp: 2017.03.01 19:11:08 MST
URL: http://www.sciencedirect.com/science/article/pii/089812219290209Z
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: {\c{C}}etin K. Ko{\c{c}} and Ching-Yu Hung
title:
Adaptive $m$-ary segmentation and canonical recoding algorithms for multiplication of large binary numbers

rawtitle:
Adaptive $m$-ary segmentation and canonical recoding algorithms for multiplication of large binary numbers

entry:
@Article{Koc:1992:AAS,
  author =       "{\c{C}}etin K. Ko{\c{c}} and Ching-Yu Hung",
  title =        "Adaptive $m$-ary segmentation and canonical recoding
                 algorithms for multiplication of large binary numbers",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "24",
  number =       "3",
  pages =        "3--12",
  month =        aug,
  year =         "1992",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 19:11:08 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/089812219290209Z",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: article
filename: fparith.bib
label: Kola:1992:MQP
author: M. Kolar and T. Sasaki
title: Multivariate quotient by power-series division
journal: j-SIGSAM
volume: 26
number: 3
pages: 17--20
month: aug
monthnumber: 8
year: 1992
CODEN: SIGSBZ
ISSN: 0163-5824 (print), 1557-9492 (electronic) OR 01635824 (print), 15579492 (electronic)
ISSNL: 0163-5824 OR 01635824
bibdate: Fri Feb 8 18:27:02 MST 2002
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.02.08 18:27:02 MST
fjournal: SIGSAM Bulletin
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J1000
rawauthor: M. Kol{\'a}r and T. Sasaki
rawtitle: Multivariate quotient by power-series division
entry:
@Article{Kola:1992:MQP,
  author =       "M. Kol{\'a}r and T. Sasaki",
  title =        "Multivariate quotient by power-series division",
  journal =      j-SIGSAM,
  volume =       "26",
  number =       "3",
  pages =        "17--20",
  month =        aug,
  year =         "1992",
  CODEN =        "SIGSBZ",
  ISSN =         "0163-5824 (print), 1557-9492 (electronic)",
  ISSN-L =       "0163-5824",
  bibdate =      "Fri Feb 8 18:27:02 MST 2002",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIGSAM Bulletin",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}


bibtype: inproceedings
filename: fparith.bib
label: Kontro:1992:FAS
author: J. Kontro and K. Kalliojarvi and Y. Neuvo
title: Floating-point arithmetic in signal processing
crossref: White:1992:IIS
pages: 1784--1791 vol.4
year: 1992
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: Signal Process. Lab., Tampere University of Technol., Finland
rawauthor: J. Kontro and K. Kalliojarvi and Y. Neuvo
rawtitle: Floating-point arithmetic in signal processing
abstract:
The use of floating-point arithmetic in digital signal processing is considered. An introduction to floating-point arithmetic based on the IEEE floating-point standards is given. Finite wordlength effects of these arithmetic systems are presented. Floating-point hardware is discussed. The emphasis is on audio applications. As an example, amplitude distributions and signal-to-noise ratios of quantized music are considered, and audio standards using floating-point arithmetic are presented.

keywords:
Amplitude distributions; Audio applications; Audio standards; Digital signal processing; Finite wordlength effects; Floating-point arithmetic; Hardware; IEEE floating-point standards; Quantized music; Signal-to-noise ratios

thesaurus:
Audio equipment; Audio signals; Digital arithmetic; Digital signal processing chips; Roundoff errors; Signal processing

rawabstract:
The use of floating-point arithmetic in digital signal processing is considered. An introduction to floating-point arithmetic based on the IEEE floating-point standards is given. Finite wordlength effects of these arithmetic systems are presented. Floating-point hardware is discussed. The emphasis is on audio applications. As an example, amplitude distributions and signal-to-noise ratios of quantized music are considered, and audio standards using floating-point arithmetic are presented.

entry:
@InProceedings{Kontro:1992:FAS,
  author =       "J. Kontro and K. Kalliojarvi and Y. Neuvo",
  title =        "Floating-point arithmetic in signal processing",
  crossref =     "White:1992:IIS",
  pages =        "1784--1791 vol.4",
  year =         "1992",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The use of floating-point arithmetic in digital signal
                 processing is considered. An introduction to
                 floating-point arithmetic based on the IEEE
                 floating-point standards is given. Finite wordlength
                 effects of these arithmetic systems are presented.
                 Floating-point hardware is discussed. The emphasis is
                 on audio applications. As an example, amplitude
                 distributions and signal-to-noise ratios of quantized
                 music are considered, and audio standards using
                 floating-point arithmetic are presented.",
  acknowledgement = ack-nhfb,
  affiliation =  "Signal Process. Lab., Tampere University of Technol.,
                 Finland",
  classification = "B1265F (Microprocessors and microcomputers); B6140
                 (Signal processing and detection); B6450 (Audio
                 equipment and systems); C1260 (Information theory);
                 C5130 (Microprocessor chips); C5230 (Digital arithmetic
                 methods); C5260 (Digital signal processing)",
  keywords =     "Amplitude distributions; Audio applications; Audio
                 standards; Digital signal processing; Finite wordlength
                 effects; Floating-point arithmetic; Hardware; IEEE
                 floating-point standards; Quantized music;
                 Signal-to-noise ratios",
  thesaurus =    "Audio equipment; Audio signals; Digital arithmetic;
                 Digital signal processing chips; Roundoff errors;
                 Signal processing",
}


bibtype: article
filename: fparith.bib
label: Kontro:1992:USF
author: J. Kontro and K. Kalliojarvi and Y. Neuvo
title: Use of Short Floating-Point Formats in Audio Applications
journal: j-IEEE-TRANS-CONSUMER-ELECTRONICS
volume: 38
number: 3
pages: 200--207
month: aug
monthnumber: 8
year: 1992
CODEN: ITCEDA
ISSN: 0098-3063 (print), 1558-4127 (electronic) OR 00983063 (print), 15584127 (electronic)
ISSNL: 0098-3063 OR 00983063
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 Consumer Electronics
acknowledgement: ack-nhfb
rawauthor: J. Kontro and K. Kalliojarvi and Y. Neuvo
rawtitle: Use of Short Floating-Point Formats in Audio Applications
entry:
@Article{Kontro:1992:USF,
  author =       "J. Kontro and K. Kalliojarvi and Y. Neuvo",
  title =        "Use of Short Floating-Point Formats in Audio
                 Applications",
  journal =      j-IEEE-TRANS-CONSUMER-ELECTRONICS,
  volume =       "38",
  number =       "3",
  pages =        "200--207",
  month =        aug,
  year =         "1992",
  CODEN =        "ITCEDA",
  ISSN =         "0098-3063 (print), 1558-4127 (electronic)",
  ISSN-L =       "0098-3063",
  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 Consumer Electronics",
  summary =      "Use of short floating-point formats that are shorter
                 than the IEEE floating-point standard (ANSI/IEEE S+A
                 754-1985), 24+8-b, in digital audio applications is
                 studied. The performance of these formats is analyzed
                 in different parts of the digital audio \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Krishna:1992:CTA
author: H. Krishna and K.-Y. Lin and J.-D. Sun
journal: j-IEEE-TRANS-CIRCUITS-SYST-2
volume: 39
number: 1
pages: 8--17
month: jan
monthnumber: 1
year: 1992
CODEN: ICSPE5
DOI: https://doi.org/10.1109/82.204106
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: http://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: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82
rawauthor: H. Krishna and K.-Y. Lin and J.-D. Sun
title:
A coding theory approach to error control in redundant residue number systems. I. Theory and single error correction

rawtitle:
A coding theory approach to error control in redundant residue number systems. {I}. Theory and single error correction

entry:
@Article{Krishna:1992:CTA,
  author =       "H. Krishna and K.-Y. Lin and J.-D. Sun",
  title =        "A coding theory approach to error control in redundant
                 residue number systems. {I}. Theory and single error
                 correction",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-2,
  volume =       "39",
  number =       "1",
  pages =        "8--17",
  month =        jan,
  year =         "1992",
  CODEN =        "ICSPE5",
  DOI =          "https://doi.org/10.1109/82.204106",
  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 =          "http://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 =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A coding theory approach to error control in redundant
                 residue number systems (RRNSs) is presented. The
                 concepts of Hamming weight, minimum distance, weight
                 distribution, and error detection and correction
                 capabilities in redundant residue number \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Krishnan:1992:CGF
author: R. Krishnan and G. A. Jullien and W. C. Miller
title: Computation of generalized FIR filter structure using the modified quadratic residue number system
journal: j-IEEE-TRANS-CIRCUITS-SYST-2
volume: 39
number: 1
pages: 58--62
month: jan
monthnumber: 1
year: 1992
CODEN: ICSPE5
DOI: https://doi.org/10.1109/82.204110
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: http://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: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82
rawauthor: R. Krishnan and G. A. Jullien and W. C. Miller
rawtitle:
Computation of generalized {FIR} filter structure using the modified quadratic residue number system

entry:
@Article{Krishnan:1992:CGF,
  author =       "R. Krishnan and G. A. Jullien and W. C. Miller",
  title =        "Computation of generalized {FIR} filter structure
                 using the modified quadratic residue number system",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-2,
  volume =       "39",
  number =       "1",
  pages =        "58--62",
  month =        jan,
  year =         "1992",
  CODEN =        "ICSPE5",
  DOI =          "https://doi.org/10.1109/82.204110",
  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 =          "http://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 =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
  keywords =     "residue arithmetic; residue number system",
  summary =      "The systematic approach for generating the generalized
                 number theoretic FIR filter structure based on the
                 complex number theoretic z-transform is presented. A
                 step-by-step computational method that can be used in
                 the implementation and \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Kubosawa:1992:BFP
author: H. Kubosawa and A. Katsuno and H. Takahashi and T. Sato and A. Suga and G. Goto
title: A 64-bit floating point processing unit for a RISC microprocessor
crossref: Anonymous:1992:EAP
pages: 270--273
year: 1992
DOI: https://doi.org/10.1109/EUASIC.1992.228042
bibdate: Thu Mar 02 09:45:28 2006
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2006.03.02 09:45:28 ???
URL: http://ieeexplore.ieee.org/iel2/416/5911/00228042.pdf
keywords: 25MHz SPARC S-25 microprocessor; CMOS; PGA; RISC
acknowledgement: ack-nhfb
rawauthor: H. Kubosawa and A. Katsuno and H. Takahashi and T. Sato and A. Suga and G. Goto
rawtitle: A 64-bit floating point processing unit for a {RISC} microprocessor
entry:
@InProceedings{Kubosawa:1992:BFP,
  author =       "H. Kubosawa and A. Katsuno and H. Takahashi and T.
                 Sato and A. Suga and G. Goto",
  title =        "A 64-bit floating point processing unit for a {RISC}
                 microprocessor",
  crossref =     "Anonymous:1992:EAP",
  pages =        "270--273",
  year =         "1992",
  DOI =          "https://doi.org/10.1109/EUASIC.1992.228042",
  bibdate =      "Thu Mar 02 09:45:28 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ieeexplore.ieee.org/iel2/416/5911/00228042.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "25MHz SPARC S-25 microprocessor; CMOS; PGA; RISC",
}


bibtype: inproceedings
filename: fparith.bib
label: Kutuso:1992:EMO
author: K. N. Kutuso and H. M. Yassine
booktitle: Proceedings of the 35th Midwest Symposium on Circuits and Systems, 1992
title: Effect of moduli ordering of mixed radix conversion methods in residue number systems
volume: 1
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 678--680
year: 1992
DOI: https://doi.org/10.1109/MWSCAS.1992.271232
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: K. N. Kutuso and H. M. Yassine
rawbooktitle: Proceedings of the 35th Midwest Symposium on Circuits and Systems, 1992
rawtitle: Effect of moduli ordering of mixed radix conversion methods in residue number systems
entry:
@InProceedings{Kutuso:1992:EMO,
  author =       "K. N. Kutuso and H. M. Yassine",
  booktitle =    "Proceedings of the 35th Midwest Symposium on Circuits
                 and Systems, 1992",
  title =        "Effect of moduli ordering of mixed radix conversion
                 methods in residue number systems",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "678--680",
  year =         "1992",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/MWSCAS.1992.271232",
  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 effect of moduli ordering in different methods for
                 converting residue numbers to decimal numbers using the
                 mixed radix approach is investigated. The number of
                 operations involved in the conversion process of
                 residue numbers to their decimal \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Lacroix:1992:DDM
author: A. Lacroix and F. Hartwig
title: Distribution densities of the mantissa and exponent of floating point numbers
crossref: White:1992:IIS
pages: 1792--1795 vol.4
year: 1992
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
note: 6 vol.
acknowledgement: ack-nhfb
affiliation: Inst. fuer Angewandte Phys., J. W. Goethe-University, Frankfurt am Main, Germany
thesaurus: Digital arithmetic; Digital filters; Roundoff errors; Signal processing
rawauthor: A. Lacroix and F. Hartwig
rawnote: 6 vol.
rawtitle: Distribution densities of the mantissa and exponent of floating point numbers
abstract:
The relations between the probability densities of real numbers and the corresponding mantissa and exponent densities in the floating point number format are investigated. Assumptions about continuity of the probability density of real numbers lead to certain restrictions in terms of the density of the mantissa. A few real number densities of practical importance were treated analytically and experimentally. During arithmetic operations like addition and multiplication which are essential for signal processing the operand density is altered. The effect concerning the densities of mantissa and exponent of the result is discussed. The reciprocal density of the mantissas plays a central role. Applications in roundoff-noise-analysis of signal processing with finite wordlength are considered. (5 Refs.)

keywords:
Addition; Arithmetic operations; Exponent densities; Finite wordlength; Floating point number format; Floating point numbers; Mantissa densities; Multiplication; Operand density; Probability densities; Real numbers; Reciprocal density; Roundoff-noise-analysis; Signal processing

rawabstract:
The relations between the probability densities of real numbers and the corresponding mantissa and exponent densities in the floating point number format are investigated. Assumptions about continuity of the probability density of real numbers lead to certain restrictions in terms of the density of the mantissa. A few real number densities of practical importance were treated analytically and experimentally. During arithmetic operations like addition and multiplication which are essential for signal processing the operand density is altered. The effect concerning the densities of mantissa and exponent of the result is discussed. The reciprocal density of the mantissas plays a central role. Applications in roundoff-noise-analysis of signal processing with finite wordlength are considered. (5 Refs.)

entry:
@InProceedings{Lacroix:1992:DDM,
  author =       "A. Lacroix and F. Hartwig",
  title =        "Distribution densities of the mantissa and exponent of
                 floating point numbers",
  crossref =     "White:1992:IIS",
  pages =        "1792--1795 vol.4",
  year =         "1992",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "6 vol.",
  abstract =     "The relations between the probability densities of
                 real numbers and the corresponding mantissa and
                 exponent densities in the floating point number format
                 are investigated. Assumptions about continuity of the
                 probability density of real numbers lead to certain
                 restrictions in terms of the density of the mantissa. A
                 few real number densities of practical importance were
                 treated analytically and experimentally. During
                 arithmetic operations like addition and multiplication
                 which are essential for signal processing the operand
                 density is altered. The effect concerning the densities
                 of mantissa and exponent of the result is discussed.
                 The reciprocal density of the mantissas plays a central
                 role. Applications in roundoff-noise-analysis of signal
                 processing with finite wordlength are considered. (5
                 Refs.)",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. fuer Angewandte Phys., J. W. Goethe-University,
                 Frankfurt am Main, Germany",
  classification = "B1270F (Digital filters); B6140 (Signal processing
                 and detection); C1260 (Information theory); C5230
                 (Digital arithmetic methods); C5240 (Digital filters);
                 C5260 (Digital signal processing)",
  keywords =     "Addition; Arithmetic operations; Exponent densities;
                 Finite wordlength; Floating point number format;
                 Floating point numbers; Mantissa densities;
                 Multiplication; Operand density; Probability densities;
                 Real numbers; Reciprocal density;
                 Roundoff-noise-analysis; Signal processing",
  thesaurus =    "Digital arithmetic; Digital filters; Roundoff errors;
                 Signal processing",
}


bibtype: article
filename: fparith.bib
label: Lang:1992:HRS
author: T. Lang and P. Montuschi
title: Higher radix square root with prescaling
journal: j-IEEE-TRANS-COMPUT
volume: 41
number: 8
pages: 996--1009
month: aug
monthnumber: 8
year: 1992
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.156542
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: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156542
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: T. Lang and P. Montuschi
rawtitle: Higher radix square root with prescaling
entry:
@Article{Lang:1992:HRS,
  author =       "T. Lang and P. Montuschi",
  title =        "Higher radix square root with prescaling",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "8",
  pages =        "996--1009",
  month =        aug,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.156542",
  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 =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156542",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "A scheme for performing higher radix square root based
                 on prescaling of the radicand is presented to reduce
                 the complexity of the result-digit selection. The
                 scheme requires several steps, namely multiplication
                 for prescaling the radicand, square \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Lee:1992:ACR
author: J. H. M. Lee and M. H. van Emden
title: Adapting $ rm CLP(sc R) $ to floating-point arithmetic
journal: Fifth generation computer systems, vol 1
volume: 2
publisher: Ohm
address: Tokyo, Japan
pages: 996--1003
year: 1992
MRclass: 68N15 (68N17 68Q40)
MRnumber: 93m:68027
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 ???
acknowledgement: ack-nhfb
rawauthor: J. H. M. Lee and M. H. {van Emden}
rawtitle: Adapting {$ {\rm CLP}(\sc {R}) $} to floating-point arithmetic
entry:
@Article{Lee:1992:ACR,
  author =       "J. H. M. Lee and M. H. {van Emden}",
  title =        "Adapting {$ {\rm CLP}(\sc {R}) $} to floating-point
                 arithmetic",
  journal =      "Fifth generation computer systems, vol 1",
  volume =       "2",
  publisher =    "Ohm",
  address =      "Tokyo, Japan",
  pages =        "996--1003",
  year =         "1992",
  MRclass =      "68N15 (68N17 68Q40)",
  MRnumber =     "93m:68027",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Lee:1992:FPP
author: K. Lee
title: On the Floating Point Performance of the i860 Microprocessor
journal: j-INT-J-HIGH-SPEED-COMPUTING
volume: 4
number: 4
pages: 251--268
month: dec
monthnumber: 12
year: 1992
CODEN: IHSCEZ
ISSN: 0129-0533 OR 01290533
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: International Journal of High Speed Computing
acknowledgement: ack-nhfb
journalURL: http://www.worldscientific.com/worldscinet/ijhsc
rawauthor: K. Lee
rawtitle: On the Floating Point Performance of the i860 Microprocessor
entry:
@Article{Lee:1992:FPP,
  author =       "K. Lee",
  title =        "On the Floating Point Performance of the i860
                 Microprocessor",
  journal =      j-INT-J-HIGH-SPEED-COMPUTING,
  volume =       "4",
  number =       "4",
  pages =        "251--268",
  month =        dec,
  year =         "1992",
  CODEN =        "IHSCEZ",
  ISSN =         "0129-0533",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of High Speed Computing",
  journal-URL =  "http://www.worldscientific.com/worldscinet/ijhsc",
}


bibtype: book
filename: fparith.bib
label: Leighton:1992:IPA
author: Frank Thomson Leighton
title: Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes
publisher: pub-MORGAN-KAUFMANN
address: pub-MORGAN-KAUFMANN:adr
pages: xviii + 831
year: 1992
ISBN: 1-55860-117-1 OR 1558601171
ISBN13: 978-1-55860-117-8 OR 9781558601178
LCCN: QA76.5 .L45 1992
bibdate: Mon Sep 16 16:21:01 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.09.16 16:21:01 ???
acknowledgement: ack-nhfb
rawauthor: Frank Thomson Leighton
rawtitle: Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes
entry:
@Book{Leighton:1992:IPA,
  author =       "Frank Thomson Leighton",
  title =        "Introduction to Parallel Algorithms and Architectures:
                 Arrays, Trees, Hypercubes",
  publisher =    pub-MORGAN-KAUFMANN,
  address =      pub-MORGAN-KAUFMANN:adr,
  pages =        "xviii + 831",
  year =         "1992",
  ISBN =         "1-55860-117-1",
  ISBN-13 =      "978-1-55860-117-8",
  LCCN =         "QA76.5 .L45 1992",
  bibdate =      "Mon Sep 16 16:21:01 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$54.95",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Li:1992:CSC
author: Zhenyu Li and Victor Milenkovic
title: Constructing Strongly Convex Hulls Using Exact or Rounded Arithmetic
journal: j-ALGORITHMICA
volume: 8
number: 5--6
pages: 345--364
year: 1992
CODEN: ALGOEJ
ISSN: 0178-4617 (print), 1432-0541 (electronic) OR 01784617 (print), 14320541 (electronic)
ISSNL: 0178-4617 OR 01784617
MRclass: 68U05 (52B55)
MRnumber: MR1195157 (93k:68104)
MRreviewer: Nikolaj M. Korneenko
bibdate: Mon Jan 22 05:31:33 MST 2001
bibtimestamp: 2001.01.22 05:31:33 MST
note: 1990 Computational Geometry Symposium (Berkeley, CA, 1990)
fjournal: Algorithmica. An International Journal in Computer Science
keywords: exact arithmetic; floating-point arithmetic; rounding errors
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/453
rawauthor: Zhenyu Li and Victor Milenkovic
rawnote: 1990 Computational Geometry Symposium (Berkeley, CA, 1990)
rawtitle: Constructing Strongly Convex Hulls Using Exact or Rounded Arithmetic
bibsource:
dblp-journals-algorithmica.bib; http://dblp.uni-trier.de/db/journals/algorithmica/algorithmica8.html#LiM92; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/index-table-a.html#algorithmica; MathSciNet database

entry:
@Article{Li:1992:CSC,
  author =       "Zhenyu Li and Victor Milenkovic",
  title =        "Constructing Strongly Convex Hulls Using Exact or
                 Rounded Arithmetic",
  journal =      j-ALGORITHMICA,
  volume =       "8",
  number =       "5--6",
  pages =        "345--364",
  year =         "1992",
  CODEN =        "ALGOEJ",
  ISSN =         "0178-4617 (print), 1432-0541 (electronic)",
  ISSN-L =       "0178-4617",
  MRclass =      "68U05 (52B55)",
  MRnumber =     "MR1195157 (93k:68104)",
  MRreviewer =   "Nikolaj M. Korneenko",
  bibdate =      "Mon Jan 22 05:31:33 MST 2001",
  bibsource =    "dblp-journals-algorithmica.bib;
                 http://dblp.uni-trier.de/db/journals/algorithmica/algorithmica8.html#LiM92;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/index-table-a.html#algorithmica;
                 MathSciNet database",
  note =         "1990 Computational Geometry Symposium (Berkeley, CA,
                 1990)",
  acknowledgement = ack-nhfb,
  fjournal =     "Algorithmica. An International Journal in Computer
                 Science",
  journal-URL =  "http://link.springer.com/journal/453",
  keywords =     "exact arithmetic; floating-point arithmetic; rounding
                 errors",
  oldlabel =     "LiM92",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/algorithmica/LiM92",
}


bibtype: article
filename: fparith.bib
label: Lim:1992:SPM
author: Y. C. Lim
title: Single-precision multiplier with reduced circuit complexity for signal processing applications
journal: j-IEEE-TRANS-COMPUT
volume: 41
number: 10
pages: 1333--1336
month: oct
monthnumber: 10
year: 1992
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.166611
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 10:49:20 MDT 2011
bibtimestamp: 2011.07.07 10:49:20 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=166611
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Y. C. Lim
rawtitle: Single-precision multiplier with reduced circuit complexity for signal processing applications
entry:
@Article{Lim:1992:SPM,
  author =       "Y. C. Lim",
  title =        "Single-precision multiplier with reduced circuit
                 complexity for signal processing applications",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "10",
  pages =        "1333--1336",
  month =        oct,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.166611",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 10:49:20 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=166611",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Liu:1992:QBS
author: K. J. R. Liu and E. Frantzeskakis
booktitle: Workshop on VLSI Signal Processing, V, 1992
title: Qrd-based Square Root Free and Division Free Algorithms and Architectures
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 459--468
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: K. J. R. Liu and E. Frantzeskakis
rawbooktitle: Workshop on {VLSI} Signal Processing, V, 1992
rawtitle: Qrd-based Square Root Free and Division Free Algorithms and Architectures
entry:
@InProceedings{Liu:1992:QBS,
  author =       "K. J. R. Liu and E. Frantzeskakis",
  booktitle =    "Workshop on {VLSI} Signal Processing, V, 1992",
  title =        "Qrd-based Square Root Free and Division Free
                 Algorithms and Architectures",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "459--468",
  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 =      "Not \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Lozier:1992:RPC
author: D. W. Lozier and P. R. Turner
journal: j-COMPUTING
volume: 48
number: 3-4
pages: 239--258 (or 239--257??)
year: 1992
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
MRclass: 65Y05 (65-04 65G05)
MRnumber: 93e:65161
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
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/607
rawauthor: D. W. Lozier and P. R. Turner
title:
Robust Parallel Computation in Floating-Point and SLI Arithmetic. Robuste Parallel-Verarbeitung in Gleitkomma-und SLI-Arithmetik

rawtitle:
Robust Parallel Computation in Floating-Point and {SLI} Arithmetic. {Robuste Parallel-Verarbeitung in Gleitkomma-und SLI-Arithmetik}

entry:
@Article{Lozier:1992:RPC,
  author =       "D. W. Lozier and P. R. Turner",
  title =        "Robust Parallel Computation in Floating-Point and
                 {SLI} Arithmetic. {Robuste Parallel-Verarbeitung in
                 Gleitkomma-und SLI-Arithmetik}",
  journal =      j-COMPUTING,
  volume =       "48",
  number =       "3-4",
  pages =        "239--258 (or 239--257??)",
  year =         "1992",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65Y05 (65-04 65G05)",
  MRnumber =     "93e:65161",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
}


bibtype: article
filename: fparith.bib
label: Lozier:1992:RPV
author: D. W. Lozier and P. R. Turner
journal: j-COMPUTING
volume: 48
number: 3--4
pages: 239--257
month: sep
monthnumber: 9
year: 1992
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
MRclass: 65Y05 (65-04 65G05)
MRnumber: 93e:65161
bibdate: Mon Oct 11 20:38:38 MDT 1999
bibtimestamp: 1999.10.11 20:38:38 MDT
fjournal: Computing
language: German
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/607
rawauthor: D. W. Lozier and P. R. Turner
title:
Robuste Parallel-Verarbeitung in Gleitkomma- und SLI-Arithmetik. (German) [Robust Parallel Computation in Floating-Point and SLI Arithmetic]

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

rawtitle:
{Robuste Parallel-Verarbeitung in Gleitkomma- und SLI-Arithmetik}. ({German}) [{Robust} Parallel Computation in Floating-Point and {SLI} Arithmetic]

entry:
@Article{Lozier:1992:RPV,
  author =       "D. W. Lozier and P. R. Turner",
  title =        "{Robuste Parallel-Verarbeitung in Gleitkomma- und
                 SLI-Arithmetik}. ({German}) [{Robust} Parallel
                 Computation in Floating-Point and {SLI} Arithmetic]",
  journal =      j-COMPUTING,
  volume =       "48",
  number =       "3--4",
  pages =        "239--257",
  month =        sep,
  year =         "1992",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65Y05 (65-04 65G05)",
  MRnumber =     "93e:65161",
  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",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  language =     "German",
}


bibtype: article
filename: fparith.bib
label: Lozier:1992:SLI
author: Daniel W. Lozier and P. R. Turner
title: Symmetric Level-Index Arithmetic in Simulation and Modeling
journal: j-J-RES-NATL-BUR-STAND
volume: 97
number: 4
pages: 471--485
month: jul
monthnumber: 7
year: 1992
CODEN: JRNBAG
DOI: https://doi.org/10.6028/jres.097.020
ISSN: 0091-0635 (print), 2376-5305 (electronic) OR 00910635 (print), 23765305 (electronic)
ISSNL: 0091-0635 OR 00910635
bibdate: Fri Jul 09 07:24:16 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.07.09 07:24:16 ???
URL: https://nvlpubs.nist.gov/nistpubs/jres/097/jresv97n4p471_A1b.pdf
acknowledgement: ack-nhfb
journalURL: https://www.nist.gov/nist-research-library/journal-research-nist/past-papers
rawauthor: Daniel W. Lozier and P. R. Turner
rawtitle: Symmetric Level-Index Arithmetic in Simulation and Modeling
abstract:
This paper begins with a general introduction to the symmetric level-index, SLI, system of number representation and arithmetic. This system provides a robust framework in which experimental computation can be performed without the risk of failure due to overflow/underflow or to poor scaling of the original problem. There follows a brief summary of some existing computational experience with this system to illustrate its strengths in numerical, graphical and parallel computational settings. An example of the use of SLI arithmetic to overcome graphics failure in the modeling of a turbulent combustion problem is presented. The main thrust of this paper is to introduce the idea of SLI-linear least squares data fitting. The use of generalized logarithm and exponential functions is seen to offer significant improvement over the more conventional linear regression tools for fitting data from a compound exponential decay such as the decay of radioactive materials.

keywords:
computer graphics; generalized logarithms and exponentials; least-squares data-fitting; overflow, underflow, and scaling; parallel computing; symmetric level-index arithmetic.

rawabstract:
This paper begins with a general introduction to the symmetric level-index, SLI, system of number representation and arithmetic. This system provides a robust framework in which experimental computation can be performed without the risk of failure due to overflow/underflow or to poor scaling of the original problem. There follows a brief summary of some existing computational experience with this system to illustrate its strengths in numerical, graphical and parallel computational settings. An example of the use of SLI arithmetic to overcome graphics failure in the modeling of a turbulent combustion problem is presented. The main thrust of this paper is to introduce the idea of SLI-linear least squares data fitting. The use of generalized logarithm and exponential functions is seen to offer significant improvement over the more conventional linear regression tools for fitting data from a compound exponential decay such as the decay of radioactive materials.

entry:
@Article{Lozier:1992:SLI,
  author =       "Daniel W. Lozier and P. R. Turner",
  title =        "Symmetric Level-Index Arithmetic in Simulation and
                 Modeling",
  journal =      j-J-RES-NATL-BUR-STAND,
  volume =       "97",
  number =       "4",
  pages =        "471--485",
  month =        jul,
  year =         "1992",
  CODEN =        "JRNBAG",
  DOI =          "https://doi.org/10.6028/jres.097.020",
  ISSN =         "0091-0635 (print), 2376-5305 (electronic)",
  ISSN-L =       "0091-0635",
  bibdate =      "Fri Jul 09 07:24:16 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://nvlpubs.nist.gov/nistpubs/jres/097/jresv97n4p471_A1b.pdf",
  abstract =     "This paper begins with a general introduction to the
                 symmetric level-index, SLI, system of number
                 representation and arithmetic. This system provides a
                 robust framework in which experimental computation can
                 be performed without the risk of failure due to
                 overflow/underflow or to poor scaling of the original
                 problem. There follows a brief summary of some existing
                 computational experience with this system to illustrate
                 its strengths in numerical, graphical and parallel
                 computational settings. An example of the use of SLI
                 arithmetic to overcome graphics failure in the modeling
                 of a turbulent combustion problem is presented. The
                 main thrust of this paper is to introduce the idea of
                 SLI-linear least squares data fitting. The use of
                 generalized logarithm and exponential functions is seen
                 to offer significant improvement over the more
                 conventional linear regression tools for fitting data
                 from a compound exponential decay such as the decay of
                 radioactive materials.",
  acknowledgement = ack-nhfb,
  journal-URL =  "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
  keywords =     "computer graphics; generalized logarithms and
                 exponentials; least-squares data-fitting; overflow,
                 underflow, and scaling; parallel computing; symmetric
                 level-index arithmetic.",
}


bibtype: article
filename: fparith.bib
label: Lu:1992:NDA
author: M. Lu and J.-S. Chiang
title: A novel division algorithm for the residue number system
journal: j-IEEE-TRANS-COMPUT
volume: 41
number: 8
pages: 1026--1032
month: aug
monthnumber: 8
year: 1992
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.156545
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
fjournal: IEEE Transactions on Computers
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: M. Lu and J.-S. Chiang
rawtitle: A novel division algorithm for the residue number system
URL:
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156545; http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4052

entry:
@Article{Lu:1992:NDA,
  author =       "M. Lu and J.-S. Chiang",
  title =        "A novel division algorithm for the residue number
                 system",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "8",
  pages =        "1026--1032",
  month =        aug,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.156545",
  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 =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156545;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4052",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A novel general algorithm for signed number division
                 in the residue number system (RNS) is presented. The
                 parity checking technique used for sign and overflow
                 detection in this algorithm is more efficient and
                 practical than conventional methods. \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Lynch:1992:FCA
author: Thomas W. Lynch and Earl E. Swartzlander, Jr.
title: A Formalization for Computer Arithmetic
crossref: Atanassova:1992:CAE
pages: 137--145
year: 1992
bibdate: Sat Sep 17 19:09:42 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.17 19:09:42 ???
acknowledgement: ack-nhfb
rawauthor: Thomas W. Lynch and Earl E. {Swartzlander, Jr.}
rawtitle: A Formalization for Computer Arithmetic
note:
From the abstract: ``The formalism, when applied to IEEE Std 754 shows that the non-trapping mode can produce incorrect numeric and non-numeric results.''

rawnote:
From the abstract: ``The formalism, when applied to IEEE Std 754 shows that the non-trapping mode can produce incorrect numeric and non-numeric results.''

entry:
@InProceedings{Lynch:1992:FCA,
  author =       "Thomas W. Lynch and Earl E. {Swartzlander, Jr.}",
  title =        "A Formalization for Computer Arithmetic",
  crossref =     "Atanassova:1992:CAE",
  pages =        "137--145",
  year =         "1992",
  bibdate =      "Sat Sep 17 19:09:42 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "From the abstract: ``The formalism, when applied to
                 IEEE Std 754 shows that the non-trapping mode can
                 produce incorrect numeric and non-numeric results.''",
  acknowledgement = ack-nhfb,
}


bibtype: misc
filename: fparith.bib
label: Lynch:1992:HSD
author: T. Lynch and S. McIntyre and K. Tseng and S. Shaw and T. Hurson
title: High speed divider with square root capability
pages: 137--145
year: 1992
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 ???
note: U.S. Patent No. 5,128,891.
acknowledgement: ack-sfo
rawauthor: T. Lynch and S. McIntyre and K. Tseng and S. Shaw and T. Hurson
rawnote: U.S. Patent No. 5,128,891.
rawtitle: High speed divider with square root capability
entry:
@Misc{Lynch:1992:HSD,
  author =       "T. Lynch and S. McIntyre and K. Tseng and S. Shaw and
                 T. Hurson",
  title =        "High speed divider with square root capability",
  year =         "1992",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "U.S. Patent No. 5,128,891.",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Maguire:1992:MD
author: J. Maguire
title: MC8810: Datapath
crossref: Juj:1992:NCR
pages: 193--197
year: 1992
bibdate: Wed Sep 7 22:32:42 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.07 22:32:42 ???
acknowledgement: ack-nj
rawauthor: J. Maguire
rawtitle: {MC8810}: Datapath
entry:
@InProceedings{Maguire:1992:MD,
  author =       "J. Maguire",
  title =        "{MC8810}: Datapath",
  crossref =     "Juj:1992:NCR",
  pages =        "193--197",
  year =         "1992",
  bibdate =      "Wed Sep 7 22:32:42 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: mastersthesis
filename: fparith.bib
label: Makhdumi:1992:CCS
author: Shazia Makhdumi
title: Comparison of current switch bipolar circuits for high performance floating point arithmetic
type: Thesis (M.S.)
school: Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science
address: Cambridge, MA, USA
pages: 107
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: Shazia Makhdumi
rawtitle: Comparison of current switch bipolar circuits for high performance floating point arithmetic
entry:
@MastersThesis{Makhdumi:1992:CCS,
  author =       "Shazia Makhdumi",
  title =        "Comparison of current switch bipolar circuits for high
                 performance floating point arithmetic",
  type =         "Thesis ({M.S.})",
  school =       "Massachusetts Institute of Technology, Dept. of
                 Electrical Engineering and Computer Science",
  address =      "Cambridge, MA, USA",
  pages =        "107",
  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: book
filename: fparith.bib
label: Mar:1992:DSP
editor: Amy Mar
title: Digital signal processing applications using the ADSP-2100 family
publisher: pub-PH
address: pub-PH:adr
year: 1992
ISBN: 0-13-219726-X (vol. 1), 0-13-178567-2 (vol. 2) OR 013219726X (vol. 1), 0131785672 (vol. 2)
LCCN: TK5102.9 .D53 1992
bibdate: Sat Jan 15 05:58:58 MST 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2005.01.15 05:58:58 MST
subject: Signal processing; Digital techniques; Microprocessors
acknowledgement: ack-nhfb
raweditor: Amy Mar
rawtitle: Digital signal processing applications using the {ADSP}-2100 family
ISBN13:
978-0-13-219726-7 (vol. 1), 978-0-13-178567-0 (vol. 2) OR 9780132197267 (vol. 1), 9780131785670 (vol. 2)

remark:
Vol. 2: edited by Jere Babst. System requirements for computer disks: IBM-compatible PC; DOS 3.0 or higher; high-density disk drive.

entry:
@Book{Mar:1992:DSP,
  editor =       "Amy Mar",
  title =        "Digital signal processing applications using the
                 {ADSP}-2100 family",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "????",
  year =         "1992",
  ISBN =         "0-13-219726-X (vol. 1), 0-13-178567-2 (vol. 2)",
  ISBN-13 =      "978-0-13-219726-7 (vol. 1), 978-0-13-178567-0 (vol.
                 2)",
  LCCN =         "TK5102.9 .D53 1992",
  bibdate =      "Sat Jan 15 05:58:58 MST 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  remark =       "Vol. 2: edited by Jere Babst. System requirements for
                 computer disks: IBM-compatible PC; DOS 3.0 or higher;
                 high-density disk drive.",
  subject =      "Signal processing; Digital techniques;
                 Microprocessors",
}


bibtype: article
filename: fparith.bib
label: McQuillan:1992:VMH
author: S. E. McQuillan and J. V. McCanny
title: VLSI module for high-performance multiply, square root and divide
journal: j-IEE-PROC-COMPUT-DIGIT-TECH
volume: 139
number: 6
pages: 505--510
month: nov
monthnumber: 11
year: 1992
CODEN: ICDTEA
ISSN: 1350-2387 (print), 1359-7027 (electronic) OR 13502387 (print), 13597027 (electronic)
ISSNL: 1350-2387 OR 13502387
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
fjournal: IEE Proceedings. Computers and Digital Techniques
acknowledgement: ack-nhfb
rawauthor: S. E. McQuillan and J. V. McCanny
rawtitle: {VLSI} module for high-performance multiply, square root and divide
entry:
@Article{McQuillan:1992:VMH,
  author =       "S. E. McQuillan and J. V. McCanny",
  title =        "{VLSI} module for high-performance multiply, square
                 root and divide",
  journal =      j-IEE-PROC-COMPUT-DIGIT-TECH,
  volume =       "139",
  number =       "6",
  pages =        "505--510",
  month =        nov,
  year =         "1992",
  CODEN =        "ICDTEA",
  ISSN =         "1350-2387 (print), 1359-7027 (electronic)",
  ISSN-L =       "1350-2387",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEE Proceedings. Computers and Digital Techniques",
  summary =      "A high-performance VLSI architecture to perform
                 multiply-accumulate, division and square root
                 operations is proposed. The circuit is highly regular,
                 requires only minimal control and ean be pipelined
                 right down to the bit level. The system can also
                 \ldots{}",
}


bibtype: techreport
filename: fparith.bib
label: MenissierMorain:1992:CNR
author: V. Menissier-Morain
title: CAML numbers reference manual
number: 141
institution: Inst. Nat. Recherche Inf. Autom.
address: Le Chesnay, France
pages: 157
month: jul
monthnumber: 7
year: 1992
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
thesaurus: Digital arithmetic; Functional programming; High level languages; Mathematics computing
rawauthor: V. M{\'e}nissier-Morain
rawtitle: {CAML} numbers reference manual
abstract:
An overview is given of the arithmetic of the functional language CAML V3.1. This arithmetic includes floating point numbers, arbitrary large integers and rationals and a complete set of primitives. Its implementation relies on the efficient BigNum package (J.-C. Herve et al., 1989).

keywords:
Arbitrary large integers; Arithmetic; BigNum package; Floating point numbers; Functional language CAML; Primitives; Rationals

rawabstract:
An overview is given of the arithmetic of the functional language CAML V3.1. This arithmetic includes floating point numbers, arbitrary large integers and rationals and a complete set of primitives. Its implementation relies on the efficient BigNum package (J.-C. Herve et al., 1989).

entry:
@TechReport{MenissierMorain:1992:CNR,
  author =       "V. M{\'e}nissier-Morain",
  title =        "{CAML} numbers reference manual",
  number =       "141",
  institution =  "Inst. Nat. Recherche Inf. Autom.",
  address =      "Le Chesnay, France",
  pages =        "157",
  month =        jul,
  year =         "1992",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "An overview is given of the arithmetic of the
                 functional language CAML V3.1. This arithmetic includes
                 floating point numbers, arbitrary large integers and
                 rationals and a complete set of primitives. Its
                 implementation relies on the efficient BigNum package
                 (J.-C. Herve et al., 1989).",
  acknowledgement = ack-nhfb,
  classification = "C5230 (Digital arithmetic methods); C6110 (Systems
                 analysis and programming); C6140D (High level
                 languages); C7310 (Mathematics)",
  keywords =     "Arbitrary large integers; Arithmetic; BigNum package;
                 Floating point numbers; Functional language CAML;
                 Primitives; Rationals",
  pubcountry =   "France",
  thesaurus =    "Digital arithmetic; Functional programming; High level
                 languages; Mathematics computing",
}


bibtype: book
filename: fparith.bib
label: Menninger:1992:NWN
author: Karl Menninger
title: Number Words and Number Symbols: a Cultural History of Numbers
publisher: pub-DOVER
address: pub-DOVER:adr
pages: xiii + 480
year: 1992
ISBN: 0-486-27096-3 OR 0486270963
ISBN13: 978-0-486-27096-8 OR 9780486270968
LCCN: QA141.2 .M4513 1992
bibdate: Fri Nov 28 18:29:23 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 18:29:23 ???
acknowledgement: ack-mfc
rawauthor: Karl Menninger
rawtitle: Number Words and Number Symbols: a Cultural History of Numbers
entry:
@Book{Menninger:1992:NWN,
  author =       "Karl Menninger",
  title =        "Number Words and Number Symbols: a Cultural History of
                 Numbers",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "xiii + 480",
  year =         "1992",
  ISBN =         "0-486-27096-3",
  ISBN-13 =      "978-0-486-27096-8",
  LCCN =         "QA141.2 .M4513 1992",
  bibdate =      "Fri Nov 28 18:29:23 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Meredith:1992:NPF
author: Roger W. Meredith
title: Numeric precision in FORTRAN computing
journal: j-COMPUT-PHYS
volume: 6
number: 5
pages: 506--512
month: sep
monthnumber: 9
year: 1992
CODEN: CPHYE2
DOI: https://doi.org/10.1063/1.168438
ISSN: 0894-1866 (print), 1558-4208 (electronic) OR 08941866 (print), 15584208 (electronic)
ISSNL: 0894-1866 OR 08941866
bibdate: Wed Apr 10 08:45:36 MDT 2019
bibtimestamp: 2019.04.10 08:45:36 MDT
URL: https://aip.scitation.org/doi/10.1063/1.168438
fjournal: Computers in Physics
acknowledgement: ack-nhfb
ajournal: Comput. Phys
journalURL: https://aip.scitation.org/journal/cip
rawauthor: Roger W. Meredith
rawtitle: Numeric precision in {FORTRAN} computing
bibsource:
https://www.math.utah.edu/pub/tex/bib/computphys.bib; https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Meredith:1992:NPF,
  author =       "Roger W. Meredith",
  title =        "Numeric precision in {FORTRAN} computing",
  journal =      j-COMPUT-PHYS,
  volume =       "6",
  number =       "5",
  pages =        "506--512",
  month =        sep # "\slash " # oct,
  year =         "1992",
  CODEN =        "CPHYE2",
  DOI =          "https://doi.org/10.1063/1.168438",
  ISSN =         "0894-1866 (print), 1558-4208 (electronic)",
  ISSN-L =       "0894-1866",
  bibdate =      "Wed Apr 10 08:45:36 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computphys.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://aip.scitation.org/doi/10.1063/1.168438",
  acknowledgement = ack-nhfb,
  ajournal =     "Comput. Phys",
  fjournal =     "Computers in Physics",
  journal-URL =  "https://aip.scitation.org/journal/cip",
}


bibtype: article
filename: fparith.bib
label: Mikami:1992:NDO
author: N. Mikami and M. Kobayashi and Y. Yokoyama
title: A New DSP-Oriented Algorithm for Calculation of the Square Root Using a Nonlinear Digital Filter
journal: j-IEEE-TRANS-SIG-PROC
volume: 40
number: 7
pages: 1663--1669
month: jul
monthnumber: 7
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 15:28:13 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 15:28:13 MDT
fjournal: IEEE Transactions on Signal Processing
acknowledgement: ack-nj
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78
rawauthor: N. Mikami and M. Kobayashi and Y. Yokoyama
rawtitle: A New {DSP}-Oriented Algorithm for Calculation of the Square Root Using a Nonlinear Digital Filter
entry:
@Article{Mikami:1992:NDO,
  author =       "N. Mikami and M. Kobayashi and Y. Yokoyama",
  title =        "A New {DSP}-Oriented Algorithm for Calculation of the
                 Square Root Using a Nonlinear Digital Filter",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "40",
  number =       "7",
  pages =        "1663--1669",
  month =        jul,
  year =         "1992",
  CODEN =        "ITPRED",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  bibdate =      "Sat Jul 16 15:28:13 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 Transactions on Signal Processing",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  summary =      "A high-speed algorithm for calculating the square root
                 is proposed. This algorithm, which can be regarded as
                 calculation of the step response of a kind of nonlinear
                 IIR filter, requires no divisions. Therefore, it is
                 suitable for a VLSI digital \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Mitchell:1992:VFA
author: H. B. Mitchell
title: Very fast accurate square-root algorithm for use with gradient edge operators
journal: j-ELECT-LETTERS
volume: 28
number: 10
pages: 922--923
day: 7
month: may
monthnumber: 5
year: 1992
CODEN: ELLEAK
ISSN: 0013-5194 (print), 1350-911X (electronic) OR 00135194 (print), 1350911X (electronic)
ISSNL: 0013-5194 OR 00135194
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
fjournal: Electronics Letters
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220
rawauthor: H. B. Mitchell
rawtitle: Very fast accurate square-root algorithm for use with gradient edge operators
entry:
@Article{Mitchell:1992:VFA,
  author =       "H. B. Mitchell",
  title =        "Very fast accurate square-root algorithm for use with
                 gradient edge operators",
  journal =      j-ELECT-LETTERS,
  volume =       "28",
  number =       "10",
  pages =        "922--923",
  day =          "7",
  month =        may,
  year =         "1992",
  CODEN =        "ELLEAK",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  summary =      "Commonly used gradient edge operators such as the
                 Sobel, Prewitt and Roberts operators all required a
                 square root operation; this is, however,
                 computationally intensive and, consequently, simple but
                 very inaccurate approximations are often used
                 \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Montuschi:1992:DAC
author: P. Montuschi and L. Ciminiera and A. Giustina
title: A Division Architecture Combining Newton--Raphson Approximations and Direct Methods Iterations
crossref: Singh:1992:CRT
pages: 376--380
year: 1992
bibdate: Wed Dec 13 18:19:38 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.13 18:19:38 ???
acknowledgement: ack-nj
affiliation: Dipartimento di Autom. e Inf., Politecnico di Torino, Italy
thesaurus: Convergence of numerical methods; Digital arithmetic; Dividing circuits; Iterative methods
rawauthor: P. Montuschi and L. Ciminiera and A. Giustina
rawtitle: A Division Architecture Combining {Newton--Raphson} Approximations and Direct Methods Iterations
abstract:
The authors consider the possibility of designing architectures which combine in the best possible way the convergence with the square advantages of the Newton--Raphson method with the precision characteristics of the digit-by-digit algorithms so as to obtain units which satisfy the IEEE 754 floating point standard requirements. This is a general method which can be extended with simple and minor changes also to square root. Attention is focused on a possible implementation of this design methodology for division. The evaluation shows that the proposed unit offers an alternative architecture for division which provides interesting performances.

keywords:
Convergence; Digit-by-digit algorithms; Direct methods iterations; Division architecture; IEEE 754 floating point standard; Newton--Raphson method; Square advantages; Square root

rawabstract:
The authors consider the possibility of designing architectures which combine in the best possible way the convergence with the square advantages of the Newton--Raphson method with the precision characteristics of the digit-by-digit algorithms so as to obtain units which satisfy the IEEE 754 floating point standard requirements. This is a general method which can be extended with simple and minor changes also to square root. Attention is focused on a possible implementation of this design methodology for division. The evaluation shows that the proposed unit offers an alternative architecture for division which provides interesting performances.

entry:
@InProceedings{Montuschi:1992:DAC,
  author =       "P. Montuschi and L. Ciminiera and A. Giustina",
  title =        "A Division Architecture Combining {Newton--Raphson}
                 Approximations and Direct Methods Iterations",
  crossref =     "Singh:1992:CRT",
  pages =        "376--380",
  year =         "1992",
  bibdate =      "Wed Dec 13 18:19:38 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The authors consider the possibility of designing
                 architectures which combine in the best possible way
                 the convergence with the square advantages of the
                 Newton--Raphson method with the precision
                 characteristics of the digit-by-digit algorithms so as
                 to obtain units which satisfy the IEEE 754 floating
                 point standard requirements. This is a general method
                 which can be extended with simple and minor changes
                 also to square root. Attention is focused on a possible
                 implementation of this design methodology for division.
                 The evaluation shows that the proposed unit offers an
                 alternative architecture for division which provides
                 interesting performances.",
  acknowledgement = ack-nj,
  affiliation =  "Dipartimento di Autom. e Inf., Politecnico di Torino,
                 Italy",
  classification = "B0290F (Interpolation and function approximation);
                 B1265B (Logic circuits); C4130 (Interpolation and
                 function approximation); C5230 (Digital arithmetic
                 methods)",
  keywords =     "Convergence; Digit-by-digit algorithms; Direct methods
                 iterations; Division architecture; IEEE 754 floating
                 point standard; Newton--Raphson method; Square
                 advantages; Square root",
  thesaurus =    "Convergence of numerical methods; Digital arithmetic;
                 Dividing circuits; Iterative methods",
}


bibtype: article
filename: fparith.bib
label: Montuschi:1992:DRD
author: P. Montuschi and L. Ciminiera
title: Design of a radix $4$ division unit with simple selection table
journal: j-IEEE-TRANS-COMPUT
volume: 41
number: 12
pages: 1606--1611
month: dec
monthnumber: 12
year: 1992
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.214670
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 10:49:22 MDT 2011
bibtimestamp: 2011.07.07 10:49:22 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=214670
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: P. Montuschi and L. Ciminiera
rawtitle: Design of a radix $4$ division unit with simple selection table
entry:
@Article{Montuschi:1992:DRD,
  author =       "P. Montuschi and L. Ciminiera",
  title =        "Design of a radix $4$ division unit with simple
                 selection table",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "12",
  pages =        "1606--1611",
  month =        dec,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.214670",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 10:49:22 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=214670",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Moore:1992:PRP
author: David L. Moore
title: Programming the 29050 (RISC programming)
journal: j-DDJ
volume: 17
number: 1
pages: 34, 36, 38, 40, 42
month: jan
monthnumber: 1
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
thesaurus: Assembly language; Microprogramming; Reduced instruction set computing
rawauthor: David L. Moore
rawtitle: Programming the 29050 ({RISC} programming)
keywords:
29000 Family; AM29050; Assembly language programming; Flat address space; Floating-point operations; Registers; RISC processors

entry:
@Article{Moore:1992:PRP,
  author =       "David L. Moore",
  title =        "Programming the 29050 ({RISC} programming)",
  journal =      j-DDJ,
  volume =       "17",
  number =       "1",
  pages =        "34, 36, 38, 40, 42",
  month =        jan,
  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 = "C5220 (Computer architecture); C6110 (Systems
                 analysis and programming); C6140B (Machine-oriented
                 languages)",
  fjournal =     "Dr. Dobb's Journal of Software Tools",
  keywords =     "29000 Family; AM29050; Assembly language programming;
                 Flat address space; Floating-point operations;
                 Registers; RISC processors",
  thesaurus =    "Assembly language; Microprogramming; Reduced
                 instruction set computing",
}


bibtype: book
filename: fparith.bib
label: Morgan:1992:NM
author: Don Morgan
title: Numerical Methods: Real-time and Embedded Systems Programming
publisher: pub-MT
address: pub-MT:adr
pages: 496
year: 1992
LCCN: QA76.6 .M669 1992
bibdate: Wed Sep 14 19:16:35 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.14 19:16:35 ???
acknowledgement: ack-nj
rawauthor: Don Morgan
rawtitle: Numerical Methods: Real-time and Embedded Systems Programming
ISBN:
1-55851-232-2 (book only), 1-55851-233-0 (disk only), 1-55851-234-9 (book and disk set) OR 1558512322 (book only), 1558512330 (disk only), 1558512349 (book and disk set)

ISBN13:
978-1-55851-232-0 (book only), 978-1-55851-233-7 (disk only), 978-1-55851-234-4 (book and disk set) OR 9781558512320 (book only), 9781558512337 (disk only), 9781558512344 (book and disk set)

entry:
@Book{Morgan:1992:NM,
  author =       "Don Morgan",
  title =        "Numerical Methods: Real-time and Embedded Systems
                 Programming",
  publisher =    pub-MT,
  address =      pub-MT:adr,
  pages =        "496",
  year =         "1992",
  ISBN =         "1-55851-232-2 (book only), 1-55851-233-0 (disk only),
                 1-55851-234-9 (book and disk set)",
  ISBN-13 =      "978-1-55851-232-0 (book only), 978-1-55851-233-7 (disk
                 only), 978-1-55851-234-4 (book and disk set)",
  LCCN =         "QA76.6 .M669 1992",
  bibdate =      "Wed Sep 14 19:16:35 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$34.95",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: Mou:1992:OSA
author: Z.-J. Mou and F. Jutand
title: `Overturned-stairs' adder trees and multiplier design
journal: j-IEEE-TRANS-COMPUT
volume: 41
number: 8
pages: 940--948
month: aug
monthnumber: 8
year: 1992
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.156536
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: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156536
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Z.-J. Mou and F. Jutand
rawtitle: {`Overturned-stairs'} adder trees and multiplier design
entry:
@Article{Mou:1992:OSA,
  author =       "Z.-J. Mou and F. Jutand",
  title =        "{`Overturned-stairs'} adder trees and multiplier
                 design",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "8",
  pages =        "940--948",
  month =        aug,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.156536",
  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 =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156536",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Mutrie:1992:AFE
author: Mark P. W. Mutrie and Richard H. Bartels and Bruce W. Char
title: An approach for floating-point error analysis using computer algebra
crossref: Wang:1992:PII
pages: 284--293
year: 1992
bibdate: Thu Mar 12 08:39:32 MST 1998
bibtimestamp: 1998.03.12 08:39:32 MST
URL: http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p284-mutrie/
keywords: algorithms
acknowledgement: ack-nhfb
rawauthor: Mark P. W. Mutrie and Richard H. Bartels and Bruce W. Char
rawtitle: An approach for floating-point error analysis using computer algebra
bibsource:
http://www.acm.org/pubs/toc/; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/issac.bib

subject:
bf I.1.0 Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. bf I.1.2 Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. bf G.1.0 Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic. bf I.1.3 Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, Maple. bf G.2.2 Mathematics of Computing, DISCRETE MATHEMATICS, Graph Theory, Graph algorithms.

entry:
@InProceedings{Mutrie:1992:AFE,
  author =       "Mark P. W. Mutrie and Richard H. Bartels and Bruce W.
                 Char",
  title =        "An approach for floating-point error analysis using
                 computer algebra",
  crossref =     "Wang:1992:PII",
  pages =        "284--293",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p284-mutrie/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf I.1.2} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Algorithms, Algebraic algorithms. {\bf G.1.0}
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Computer arithmetic. {\bf I.1.3} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Languages and Systems, Maple. {\bf G.2.2} Mathematics
                 of Computing, DISCRETE MATHEMATICS, Graph Theory, Graph
                 algorithms.",
}


bibtype: phdthesis
filename: fparith.bib
label: Mutrie:1992:TSS
author: Mark P. W. Mutrie
title: Towards a symbolic system for floating-point error analysis
type: Thesis (Ph.D.)
publisher: National Library of Canada = Bibliotheque nationale du Canada
school: University of Waterloo
address: Waterloo, ON, Canada
pages: 284--293
year: 1992
ISBN: 0-315-72486-2 OR 0315724862
ISBN13: 978-0-315-72486-0 OR 9780315724860
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
note: 8 microfiches. University Microfilms order no. UMI00359027
series: Canadian theses = Theses canadiennes
acknowledgement: ack-nhfb
rawauthor: Mark P. W. Mutrie
rawnote: 8 microfiches. University Microfilms order no. UMI00359027
rawtitle: Towards a symbolic system for floating-point error analysis
entry:
@PhdThesis{Mutrie:1992:TSS,
  author =       "Mark P. W. Mutrie",
  title =        "Towards a symbolic system for floating-point error
                 analysis",
  type =         "Thesis ({Ph.D.})",
  publisher =    "National Library of Canada = Bibliotheque nationale du
                 Canada",
  school =       "University of Waterloo",
  address =      "Waterloo, ON, Canada",
  year =         "1992",
  ISBN =         "0-315-72486-2",
  ISBN-13 =      "978-0-315-72486-0",
  LCCN =         "????",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "8 microfiches. University Microfilms order no.
                 UMI00359027",
  series =       "Canadian theses = Theses canadiennes",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Nakano:1992:AHS
title: An accurate, high speed implementation of division by the quasi-unity divisor method
journal: j-IFIP-TRANS-A
volume: A-12
pages: 261--267
year: 1992
CODEN: ITATEC
ISSN: 0926-5473 OR 09265473
bibdate: Thu Dec 14 15:33:50 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.14 15:33:50 ???
note: Algorithms, Software, Architecture. Information Processing 92. IFIP 12th World Computer Congress.
fjournal: IFIP Transactions. A. Computer Science and Technology
acknowledgement: ack-nhfb
affiliation: Corporate R and D, Matsushita Electric Industrial Co. Ltd., Osaka, Japan
thesaurus: Digital arithmetic; Table lookup
rawnote: Algorithms, Software, Architecture. Information Processing 92. IFIP 12th World Computer Congress.
rawtitle: An accurate, high speed implementation of division by the quasi-unity divisor method
author:
H. Nakano and M. Nakajima and Y. Nakakura and T. Yoshida and Y. Goi and Y. Nakai and R. Segawa and T. Kishida

abstract:
A first-order convergent division algorithm is generally thought to be accurate but slow. Using a large look-up table and a multiplier improves speed. Since a partial quotient is not negative and iterations use only one formula, an iteration is carried out in the form of a partial carry and a partial sum. This paper describes a new developed division algorithm with the above-mentioned characteristics. This algorithm is compared to other similar algorithms. In a hardware implementation, this algorithm is applied to the 53-bit significand part of a floating-point double precision divider. The execution time is division of 8 or 9 cycles.

keywords:
53-Bit significand part; First-order convergent division algorithm; Floating-point double precision divider; Look-up table; Multiplier; Partial carry; Partial sum; Quasi-unity divisor method

rawabstract:
A first-order convergent division algorithm is generally thought to be accurate but slow. Using a large look-up table and a multiplier improves speed. Since a partial quotient is not negative and iterations use only one formula, an iteration is carried out in the form of a partial carry and a partial sum. This paper describes a new developed division algorithm with the above-mentioned characteristics. This algorithm is compared to other similar algorithms. In a hardware implementation, this algorithm is applied to the 53-bit significand part of a floating-point double precision divider. The execution time is division of 8 or 9 cycles.

rawauthor:
H. Nakano and M. Nakajima and Y. Nakakura and T. Yoshida and Y. Goi and Y. Nakai and R. Segawa and T. Kishida

entry:
@Article{Nakano:1992:AHS,
  author =       "H. Nakano and M. Nakajima and Y. Nakakura and T.
                 Yoshida and Y. Goi and Y. Nakai and R. Segawa and T.
                 Kishida",
  title =        "An accurate, high speed implementation of division by
                 the quasi-unity divisor method",
  journal =      j-IFIP-TRANS-A,
  volume =       "A-12",
  pages =        "261--267",
  month =        "????",
  year =         "1992",
  CODEN =        "ITATEC",
  ISSN =         "0926-5473",
  bibdate =      "Thu Dec 14 15:33:50 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Algorithms, Software, Architecture. Information
                 Processing 92. IFIP 12th World Computer Congress.",
  abstract =     "A first-order convergent division algorithm is
                 generally thought to be accurate but slow. Using a
                 large look-up table and a multiplier improves speed.
                 Since a partial quotient is not negative and iterations
                 use only one formula, an iteration is carried out in
                 the form of a partial carry and a partial sum. This
                 paper describes a new developed division algorithm with
                 the above-mentioned characteristics. This algorithm is
                 compared to other similar algorithms. In a hardware
                 implementation, this algorithm is applied to the 53-bit
                 significand part of a floating-point double precision
                 divider. The execution time is division of 8 or 9
                 cycles.",
  acknowledgement = ack-nhfb,
  affiliation =  "Corporate R and D, Matsushita Electric Industrial Co.
                 Ltd., Osaka, Japan",
  classification = "C5230 (Digital arithmetic methods)",
  confdate =     "7-11 Sept. 1992",
  conflocation = "Madrid, Spain",
  confsponsor =  "IFIP",
  fjournal =     "IFIP Transactions. A. Computer Science and
                 Technology",
  keywords =     "53-Bit significand part; First-order convergent
                 division algorithm; Floating-point double precision
                 divider; Look-up table; Multiplier; Partial carry;
                 Partial sum; Quasi-unity divisor method",
  pubcountry =   "Netherlands",
  thesaurus =    "Digital arithmetic; Table lookup",
}


bibtype: article
filename: fparith.bib
label: Nakano:1992:FPB
title: An 80-FLOPS (Peak) 64-b Microprocessor for Parallel Computer
journal: j-IEEE-J-SOLID-STATE-CIRCUITS
volume: 27
number: 3
pages: 365--372
month: mar
monthnumber: 3
year: 1992
CODEN: IJSCBC
ISSN: 0018-9200 (print), 1558-173X (electronic) OR 00189200 (print), 1558173X (electronic)
ISSNL: 0018-9200 OR 00189200
bibdate: Wed Sep 7 22:32:42 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.07 22:32:42 ???
fjournal: IEEE Journal of Solid-State Circuits
acknowledgement: ack-nj
rawtitle: An 80-{FLOPS} (Peak) 64-b Microprocessor for Parallel Computer
author:
H. Nakano and M. Nakajima and Y. Nakakura and T. Yoshida and Y. Goi and Y. Nakai and R. Segawa and T. Kishida and H. Kadota

rawauthor:
H. Nakano and M. Nakajima and Y. Nakakura and T. Yoshida and Y. Goi and Y. Nakai and R. Segawa and T. Kishida and H. Kadota

entry:
@Article{Nakano:1992:FPB,
  author =       "H. Nakano and M. Nakajima and Y. Nakakura and T.
                 Yoshida and Y. Goi and Y. Nakai and R. Segawa and T.
                 Kishida and H. Kadota",
  title =        "An 80-{FLOPS} (Peak) 64-b Microprocessor for Parallel
                 Computer",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "27",
  number =       "3",
  pages =        "365--372",
  month =        mar,
  year =         "1992",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Wed Sep 7 22:32:42 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 =     "IEEE Journal of Solid-State Circuits",
}


bibtype: article
filename: fparith.bib
label: Ng:1992:ARH
author: K. C. Ng
title: Argument Reduction for Huge Arguments: Good to the Last Bit
journal: SunPro
pages: 365--372
day: 13
month: jul
monthnumber: 7
year: 1992
bibdate: Thu Sep 1 10:16:08 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 10:16:08 ???
note: Work in progress.
URL: http://www.validlab.com/arg.pdf
keywords: range reduction
acknowledgement: ack-nj
rawauthor: K. C. Ng
rawnote: Work in progress.
rawtitle: Argument Reduction for Huge Arguments: Good to the Last Bit
entry:
@Article{Ng:1992:ARH,
  author =       "K. C. Ng",
  title =        "Argument Reduction for Huge Arguments: Good to the
                 Last Bit",
  journal =      "SunPro",
  volume =       "??",
  number =       "??",
  day =          "13",
  month =        jul,
  year =         "1992",
  bibdate =      "Thu Sep 1 10:16:08 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Work in progress.",
  URL =          "http://www.validlab.com/arg.pdf",
  acknowledgement = ack-nj,
  keywords =     "range reduction",
}


bibtype: inproceedings
filename: fparith.bib
label: Nishimura:1992:FPR
author: S. Nishimura
booktitle: Proceedings of the 35th Midwest Symposium on Circuits and Systems, 1992
title: A fixed-point roundoff error analysis of adaptive notch filters
volume: 1
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 373--376
year: 1992
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: S. Nishimura
rawbooktitle: Proceedings of the 35th Midwest Symposium on Circuits and Systems, 1992
rawtitle: A fixed-point roundoff error analysis of adaptive notch filters
entry:
@InProceedings{Nishimura:1992:FPR,
  author =       "S. Nishimura",
  booktitle =    "Proceedings of the 35th Midwest Symposium on Circuits
                 and Systems, 1992",
  title =        "A fixed-point roundoff error analysis of adaptive
                 notch filters",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "373--376",
  year =         "1992",
  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 =      "Methods to analyze the convergence and steady-state
                 characteristics of an adaptive notch filter when the
                 effects of fixed-point arithmetic are taken into
                 account are presented. The adaptive detection of a
                 sinusoid with white Gaussian noise is \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Obaidat:1992:DMA
author: Mohammad S. Obaidat and Saleh A. Bleha
title: A Decimal Multiplication Algorithm for Microcomputers
journal: j-COMPUT-ELECTR-ENG
volume: 18
number: 5
pages: 357--363
month: sep
monthnumber: 9
year: 1992
CODEN: CPEEBQ
ISSN: 0045-7906 (print), 1879-0755 (electronic) OR 00457906 (print), 18790755 (electronic)
ISSNL: 0045-7906 OR 00457906
bibdate: Thu Sep 1 10:16:11 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 10:16:11 ???
fjournal: Computers and Electrical Engineering
keywords: decimal floating-point arithmetic
acknowledgement: ack-nj
rawauthor: Mohammad S. Obaidat and Saleh A. Bleha
rawtitle: A Decimal Multiplication Algorithm for Microcomputers
entry:
@Article{Obaidat:1992:DMA,
  author =       "Mohammad S. Obaidat and Saleh A. Bleha",
  title =        "A Decimal Multiplication Algorithm for
                 Microcomputers",
  journal =      j-COMPUT-ELECTR-ENG,
  volume =       "18",
  number =       "5",
  pages =        "357--363",
  month =        sep,
  year =         "1992",
  CODEN =        "CPEEBQ",
  ISSN =         "0045-7906 (print), 1879-0755 (electronic)",
  ISSN-L =       "0045-7906",
  bibdate =      "Thu Sep 1 10:16:11 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 =     "Computers and Electrical Engineering",
  keywords =     "decimal floating-point arithmetic",
}


bibtype: article
filename: fparith.bib
label: Ochs:1992:SIR
author: T. Ochs
title: This sine is also right!
journal: j-COMP-LANG-MAG
volume: 9
number: 1
pages: 89--93
month: jan
monthnumber: 1
year: 1992
CODEN: COMLEF
ISSN: 0749-2839 OR 07492839
bibdate: Thu Sep 01 10:44:04 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 10:44:04 ???
fjournal: Computer Language Magazine
acknowledgement: ack-nj
rawauthor: T. Ochs
rawtitle: This sine is also right!
entry:
@Article{Ochs:1992:SIR,
  author =       "T. Ochs",
  title =        "This sine is also right!",
  journal =      j-COMP-LANG-MAG,
  volume =       "9",
  number =       "1",
  pages =        "89--93",
  month =        jan,
  year =         "1992",
  CODEN =        "COMLEF",
  ISSN =         "0749-2839",
  bibdate =      "Thu Sep 01 10:44:04 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 =     "Computer Language Magazine",
}


bibtype: article
filename: fparith.bib
label: Okada:1992:AQE
author: Kazuho Okada and Yasuaki Kuroe
journal: j-ELECT-COMM-JAPAN-3-FUND-ELECT-SCI
volume: 75
number: 6
pages: 1--??
month: jun
monthnumber: 6
year: 1992
CODEN: ECJSER
ISSN: 1042-0967 (print), 1520-6440 (electronic) OR 10420967 (print), 15206440 (electronic)
ISSNL: 1042-0967 OR 10420967
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: Electronics and communications in Japan. Part 3, Fundamental electronic science
acknowledgement: ack-nhfb
rawauthor: Kazuho Okada and Yasuaki Kuroe
title:
Analysis of Quantization Errors in Digital Control Systems Using Floating-Point Arithmetic--Considering Computational Order in Controller

rawtitle:
Analysis of Quantization Errors in Digital Control Systems Using Floating-Point Arithmetic--Considering Computational Order in Controller

entry:
@Article{Okada:1992:AQE,
  author =       "Kazuho Okada and Yasuaki Kuroe",
  title =        "Analysis of Quantization Errors in Digital Control
                 Systems Using Floating-Point Arithmetic--Considering
                 Computational Order in Controller",
  journal =      j-ELECT-COMM-JAPAN-3-FUND-ELECT-SCI,
  volume =       "75",
  number =       "6",
  pages =        "1--??",
  month =        jun,
  year =         "1992",
  CODEN =        "ECJSER",
  ISSN =         "1042-0967 (print), 1520-6440 (electronic)",
  ISSN-L =       "1042-0967",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics and communications in Japan. Part 3,
                 Fundamental electronic science",
}


bibtype: article
filename: fparith.bib
label: Orton:1992:NFT
author: G. A. Orton and L. E. Peppard and S. E. Tavares
title: New fault tolerant techniques for residue number systems
journal: j-IEEE-TRANS-COMPUT
volume: 41
number: 11
pages: 1453--1464
month: nov
monthnumber: 11
year: 1992
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.177315
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 10:49:21 MDT 2011
bibtimestamp: 2011.07.07 10:49:21 MDT
fjournal: IEEE Transactions on Computers
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: G. A. Orton and L. E. Peppard and S. E. Tavares
rawtitle: New fault tolerant techniques for residue number systems
URL:
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=177315; http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4475

entry:
@Article{Orton:1992:NFT,
  author =       "G. A. Orton and L. E. Peppard and S. E. Tavares",
  title =        "New fault tolerant techniques for residue number
                 systems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "11",
  pages =        "1453--1464",
  month =        nov,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.177315",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 10:49:21 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=177315;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4475",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "Previously proposed error detection algorithms for the
                 residue number system require a complete recombination.
                 A weighted approximation via the Chinese remainder
                 theorem is shown to be sufficient to detect 100\% of
                 single errors. This makes real-time \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Paliouras:1992:SDP
author: V. Paliouras and D. Soudris and T. Stouraitis
booktitle: IEEE International Symposium on Circuits and Systems. ISCAS '92. Proceedings, 3--6 May 1992
title: Systematic derivation of the processing element of a systolic array based on residue number system
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 815--818
year: 1992
DOI: https://doi.org/10.1109/ISCAS.1992.230097
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: V. Paliouras and D. Soudris and T. Stouraitis
rawbooktitle: {IEEE} International Symposium on Circuits and Systems. {ISCAS '92}. Proceedings, 3--6 May 1992
rawtitle: Systematic derivation of the processing element of a systolic array based on residue number system
entry:
@InProceedings{Paliouras:1992:SDP,
  author =       "V. Paliouras and D. Soudris and T. Stouraitis",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems. {ISCAS '92}. Proceedings, 3--6 May 1992",
  title =        "Systematic derivation of the processing element of a
                 systolic array based on residue number system",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "815--818",
  year =         "1992",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.1992.230097",
  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 synthesizing optimal VLSI
                 residue number system architectures using full adders
                 (FAs) as the basic building block is introduced. The
                 design methodology derives array architectures starting
                 from the algorithmic level. \ldots{}",
}


bibtype: techreport
filename: fparith.bib
label: Pan:1992:CWU
author: V. Y. Pan
title: Can we utilize the cancellation of the most significant digits?
type: Report
number: TR 92 061
institution: The International Computer Science Institute
address: Berkeley, CA, USA
pages: 815--818
year: 1992
bibdate: Mon Mar 06 17:00:31 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2017.03.06 17:00:31 ???
acknowledgement: ack-nhfb
rawauthor: V. Y. Pan
rawtitle: Can we utilize the cancellation of the most significant digits?
entry:
@TechReport{Pan:1992:CWU,
  author =       "V. Y. Pan",
  title =        "Can we utilize the cancellation of the most
                 significant digits?",
  type =         "Report",
  number =       "TR 92 061",
  institution =  "The International Computer Science Institute",
  address =      "Berkeley, CA, USA",
  year =         "1992",
  bibdate =      "Mon Mar 06 17:00:31 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Park:1992:MED
author: Haesun Park
title: On Multiple Error Detection in Matrix Triangularizations Using Checksum Methods
journal: j-J-PAR-DIST-COMP
volume: 14
number: 1
pages: 90--97
month: jan
monthnumber: 1
year: 1992
CODEN: JPDCER
ISSN: 0743-7315 (print), 1096-0848 (electronic) OR 07437315 (print), 10960848 (electronic)
ISSNL: 0743-7315 OR 07437315
MRclass: 65F05 (65F25)
MRnumber: 92i:65060
bibdate: Mon Apr 14 08:15:42 1997
bibsource: Compendex database; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.04.14 08:15:42 ???
fjournal: Journal of Parallel and Distributed Computing
acknowledgement: ack-nhfb
affiliation: Univ of Minnesota
affiliationaddress: Minneapolis, MN, USA
corpsource: Department of Computer Science, Minnesota University, Minneapolis, MN, USA
journalURL: http://www.sciencedirect.com/science/journal/07437315
journalabr: J Parallel Distrib Comput
treatment: P Practical
rawauthor: Haesun Park
rawtitle: On Multiple Error Detection in Matrix Triangularizations Using Checksum Methods
keywords:
Checksum methods; checksum methods; Codes, Symbolic--Error Detection; Computer Systems, Digital--Fault Tolerant Capability; correct rounding; detection; digital arithmetic; error; error analysis; error correction; errors; floating-point arithmetic; floating-point error analysis; Gaussian elimination; LU decomposition; Mathematical Techniques; matrix; Matrix Algebra; Matrix triangularizations; multiple error correction; multiple error detection; pairwise pivoting; parallel architectures; performance evaluation; QR decomposition; rounding; transient errors; triangularizations

entry:
@Article{Park:1992:MED,
  author =       "Haesun Park",
  title =        "On Multiple Error Detection in Matrix
                 Triangularizations Using Checksum Methods",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "14",
  number =       "1",
  pages =        "90--97",
  month =        jan,
  year =         "1992",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  MRclass =      "65F05 (65F25)",
  MRnumber =     "92i:65060",
  bibdate =      "Mon Apr 14 08:15:42 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ of Minnesota",
  affiliationaddress = "Minneapolis, MN, USA",
  classification = "722; 723; 921; 922; C4110 (Error analysis in
                 numerical methods); C5220P (Parallel architecture);
                 C5230 (Digital arithmetic methods); C5470 (Performance
                 evaluation and testing)",
  corpsource =   "Department of Computer Science, Minnesota University,
                 Minneapolis, MN, USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "Checksum methods; checksum methods; Codes,
                 Symbolic--Error Detection; Computer Systems,
                 Digital--Fault Tolerant Capability; correct rounding;
                 detection; digital arithmetic; error; error analysis;
                 error correction; errors; floating-point arithmetic;
                 floating-point error analysis; Gaussian elimination; LU
                 decomposition; Mathematical Techniques; matrix; Matrix
                 Algebra; Matrix triangularizations; multiple error
                 correction; multiple error detection; pairwise
                 pivoting; parallel architectures; performance
                 evaluation; QR decomposition; rounding; transient
                 errors; triangularizations",
  treatment =    "P Practical",
}


bibtype: article
filename: fparith.bib
label: Parker:1992:OVN
author: A. Parker and J. O. Hamblen
title: Optimal value for the Newton--Raphson division algorithm
journal: j-INFO-PROC-LETT
volume: 42
number: 3
pages: 141--144
day: 25
month: may
monthnumber: 5
year: 1992
CODEN: IFPLAT
ISSN: 0020-0190 (print), 1872-6119 (electronic) OR 00200190 (print), 18726119 (electronic)
ISSNL: 0020-0190 OR 00200190
bibdate: Wed Nov 11 07:31:13 1998
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.11.11 07:31:13 ???
fjournal: Information Processing Letters
keywords: fast division; floating-point arithmetic
acknowledgement: ack-nj
journalURL: http://www.sciencedirect.com/science/journal/00200190
rawauthor: A. Parker and J. O. Hamblen
rawtitle: Optimal value for the {Newton--Raphson} division algorithm
entry:
@Article{Parker:1992:OVN,
  author =       "A. Parker and J. O. Hamblen",
  title =        "Optimal value for the {Newton--Raphson} division
                 algorithm",
  journal =      j-INFO-PROC-LETT,
  volume =       "42",
  number =       "3",
  pages =        "141--144",
  day =          "25",
  month =        may,
  year =         "1992",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  bibdate =      "Wed Nov 11 07:31:13 1998",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
  keywords =     "fast division; floating-point arithmetic",
}


bibtype: article
filename: fparith.bib
label: Pichat:1992:SFR
author: Michele Pichat
title: Sets of floating-point results associated with an algebraic algorithm
journal: Computational and applied mathematics, I (Dublin, 1991)
publisher: pub-NORTH-HOLLAND
address: pub-NORTH-HOLLAND:adr
pages: 409--418
year: 1992
MRclass: 68M07 (65G05)
MRnumber: 93m:68010
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 ???
acknowledgement: ack-nhfb
rawauthor: Mich{\`e}le Pichat
rawtitle: Sets of floating-point results associated with an algebraic algorithm
entry:
@Article{Pichat:1992:SFR,
  author =       "Mich{\`e}le Pichat",
  title =        "Sets of floating-point results associated with an
                 algebraic algorithm",
  journal =      "Computational and applied mathematics, I (Dublin,
                 1991)",
  publisher =    pub-NORTH-HOLLAND,
  address =      pub-NORTH-HOLLAND:adr,
  pages =        "409--418",
  year =         "1992",
  MRclass =      "68M07 (65G05)",
  MRnumber =     "93m:68010",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: fparith.bib
label: Plauger:1992:SCL
author: P. J. Plauger
title: The Standard C Library
publisher: pub-PH
address: pub-PH:adr
pages: xiv + 498
year: 1992
ISBN: 0-13-838012-0 OR 0138380120
ISBN13: 978-0-13-838012-0 OR 9780138380120
LCCN: QA76.73.C15 P563 1991
bibdate: Wed Dec 15 10:40:47 1993
bibtimestamp: 1993.12.15 10:40:47 ???
acknowledgement: ack-nhfb
rawauthor: P. J. Plauger
rawtitle: The {Standard C} Library
bibsource:
https://www.math.utah.edu/pub/tex/bib/ansistd.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/litprog.bib; https://www.math.utah.edu/pub/tex/bib/master.bib; https://www.math.utah.edu/pub/tex/bib/unix.bib

abstract:
booktitle The Standard C Library shows you how to use all of the library functions mandated by the ANSI and ISO Standards for the programming language C. To help you understand how to use the library, this book also shows you how to implement it. You see approximately 9,000 lines of tested, working code that is highly portable across diverse computer architectures. booktitle The Standard C Library explains how the library was meant to be used and how it can be used. It places particular emphasis on features added to C as part of the C Standard. These features include support for multiple locales (cultural conventions) and very large character sets (such as Kanji). The code presented in this book has been tested with C compilers from Borland, Saber, Project Gnu, Sun, UNIX, and VAX, ULTRIX. It has passed the widely used Plum Hall Validation Suite tests for library functions. It has also survived an assortment of public-domain programs designed to stress C implementations and illuminate their darker corners. The mathematical functions are particularly well-engineered and tested. Finally, booktitle The Standard C Library shows you many principles of library design in general. You learn how to design and implement libraries that are highly cohesive and reusable.

TOC:
Preface / ix Introduction / 1 <assert.h> / 17 <ctype.h> / 25 <errno.h> / 47 <float.h> / 57 <limits.h> / 73 <locale.h> / 81 <math.h> / 127 <setjmp.h> / 181 <signal.h> / 193 <stdarg.h> / 205 <stddef.h> / 215 <stdio.h> / 225 <stdlib.h> / 333 <string.h> / 387 <time.h> / 415 Interfaces / 445 Names / 453 Terms / 463 Index / 475

rawabstract:
\booktitle{The Standard C Library} shows you how to use all of the library functions mandated by the ANSI and ISO Standards for the programming language C. To help you understand how to use the library, this book also shows you how to implement it. You see approximately 9,000 lines of tested, working code that is highly portable across diverse computer architectures. \booktitle{The Standard C Library} explains how the library was meant to be used and how it can be used. It places particular emphasis on features added to C as part of the C Standard. These features include support for multiple locales (cultural conventions) and very large character sets (such as Kanji). The code presented in this book has been tested with C compilers from Borland, Saber, Project Gnu, Sun, UNIX, and VAX, ULTRIX. It has passed the widely used Plum Hall Validation Suite tests for library functions. It has also survived an assortment of public-domain programs designed to stress C implementations and illuminate their darker corners. The mathematical functions are particularly well-engineered and tested. Finally, \booktitle{The Standard C Library} shows you many principles of library design in general. You learn how to design and implement libraries that are highly cohesive and reusable.

rawTOC:
Preface / ix \\ Introduction / 1 \\ <assert.h> / 17 \\ <ctype.h> / 25 \\ <errno.h> / 47 \\ <float.h> / 57 \\ <limits.h> / 73 \\ <locale.h> / 81 \\ <math.h> / 127 \\ <setjmp.h> / 181 \\ <signal.h> / 193 \\ <stdarg.h> / 205 \\ <stddef.h> / 215 \\ <stdio.h> / 225 \\ <stdlib.h> / 333 \\ <string.h> / 387 \\ <time.h> / 415 \\ Interfaces / 445 \\ Names / 453 \\ Terms / 463 \\ Index / 475

entry:
@Book{Plauger:1992:SCL,
  author =       "P. J. Plauger",
  title =        "The {Standard C} Library",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xiv + 498",
  year =         "1992",
  ISBN =         "0-13-838012-0",
  ISBN-13 =      "978-0-13-838012-0",
  LCCN =         "QA76.73.C15 P563 1991",
  bibdate =      "Wed Dec 15 10:40:47 1993",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/ansistd.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/litprog.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/unix.bib",
  abstract =     "\booktitle{The Standard C Library} shows you how to
                 use all of the library functions mandated by the ANSI
                 and ISO Standards for the programming language C. To
                 help you understand how to use the library, this book
                 also shows you how to implement it. You see
                 approximately 9,000 lines of tested, working code that
                 is highly portable across diverse computer
                 architectures. \booktitle{The Standard C Library}
                 explains how the library was meant to be used and how
                 it can be used. It places particular emphasis on
                 features added to C as part of the C Standard. These
                 features include support for multiple locales (cultural
                 conventions) and very large character sets (such as
                 Kanji). The code presented in this book has been tested
                 with C compilers from Borland, Saber, Project Gnu, Sun,
                 UNIX, and VAX, ULTRIX. It has passed the widely used
                 Plum Hall Validation Suite tests for library functions.
                 It has also survived an assortment of public-domain
                 programs designed to stress C implementations and
                 illuminate their darker corners. The mathematical
                 functions are particularly well-engineered and tested.
                 Finally, \booktitle{The Standard C Library} shows you
                 many principles of library design in general. You learn
                 how to design and implement libraries that are highly
                 cohesive and reusable.",
  acknowledgement = ack-nhfb,
  tableofcontents = "Preface / ix \\
                 Introduction / 1 \\
                 <assert.h> / 17 \\
                 <ctype.h> / 25 \\
                 <errno.h> / 47 \\
                 <float.h> / 57 \\
                 <limits.h> / 73 \\
                 <locale.h> / 81 \\
                 <math.h> / 127 \\
                 <setjmp.h> / 181 \\
                 <signal.h> / 193 \\
                 <stdarg.h> / 205 \\
                 <stddef.h> / 215 \\
                 <stdio.h> / 225 \\
                 <stdlib.h> / 333 \\
                 <string.h> / 387 \\
                 <time.h> / 415 \\
                 Interfaces / 445 \\
                 Names / 453 \\
                 Terms / 463 \\
                 Index / 475",
}


bibtype: techreport
filename: fparith.bib
label: Posch:1992:MRR
author: K. C. Posch and R. Posch
title: Modulo reduction in residue number systems
institution: Inst., TU, Ges.
pages: 16
year: 1992
bibdate: Thu Nov 18 09:44:56 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.11.18 09:44:56 ???
series: IIG-report-series
URL: http://books.google.com/books?id=YPLKHAAACAAJ
acknowledgement: ack-nhfb
rawauthor: K. C. Posch and R. Posch
rawtitle: Modulo reduction in residue number systems
abstract:
Residue number systems provide a good means for extremely long integer arithmetic. Their carry-free operations make parallel implementations feasible. Some applications involving very long integers, such as public key encryption, rely heavily on fast modulo reductions. This paper shows a new combination of residue number systems with efficient modulo reduction methods. Two methods are compared, and the faster one is scrutinized in detail. Both methods have the same order of complexity, $ O(log n) $, with $n$ denoting the amount of registers involved.

rawabstract:
Residue number systems provide a good means for extremely long integer arithmetic. Their carry-free operations make parallel implementations feasible. Some applications involving very long integers, such as public key encryption, rely heavily on fast modulo reductions. This paper shows a new combination of residue number systems with efficient modulo reduction methods. Two methods are compared, and the faster one is scrutinized in detail. Both methods have the same order of complexity, $ O(\log n) $, with $n$ denoting the amount of registers involved.

entry:
@TechReport{Posch:1992:MRR,
  author =       "K. C. Posch and R. Posch",
  title =        "Modulo reduction in residue number systems",
  institution =  "Inst., TU, Ges.",
  address =      "????",
  pages =        "16",
  year =         "1992",
  bibdate =      "Thu Nov 18 09:44:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "IIG-report-series",
  URL =          "http://books.google.com/books?id=YPLKHAAACAAJ",
  abstract =     "Residue number systems provide a good means for
                 extremely long integer arithmetic. Their carry-free
                 operations make parallel implementations feasible. Some
                 applications involving very long integers, such as
                 public key encryption, rely heavily on fast modulo
                 reductions. This paper shows a new combination of
                 residue number systems with efficient modulo reduction
                 methods. Two methods are compared, and the faster one
                 is scrutinized in detail. Both methods have the same
                 order of complexity, $ O(\log n) $, with $n$ denoting
                 the amount of registers involved.",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Posch:1992:RNS
author: K. C. Posch and R. Posch
booktitle: Proceedings of the Fourth IEEE Symposium on Parallel and Distributed Processing 1992
title: Residue number systems: a key to parallelism in public key cryptography
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 432--435
year: 1992
DOI: https://doi.org/10.1109/SPDP.1992.242713
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: K. C. Posch and R. Posch
rawbooktitle: Proceedings of the Fourth {IEEE} Symposium on Parallel and Distributed Processing 1992
rawtitle: Residue number systems: a key to parallelism in public key cryptography
entry:
@InProceedings{Posch:1992:RNS,
  author =       "K. C. Posch and R. Posch",
  booktitle =    "Proceedings of the Fourth {IEEE} Symposium on Parallel
                 and Distributed Processing 1992",
  title =        "Residue number systems: a key to parallelism in public
                 key cryptography",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "432--435",
  year =         "1992",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/SPDP.1992.242713",
  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 =      "Public key cryptography and parallel algorithms are
                 considered. Special attention is paid to algorithms
                 using long integer modulo arithmetic. A modification of
                 the commonly known RSA algorithm is taken as a
                 candidate. So far all implementations have \ldots{}",
}


bibtype: book
filename: fparith.bib
label: Press:1992:NRC
author: W. H. Press and B. P. Flannery and S. A. Teukolsky and W. T. Vetterling
title: Numerical Recipes in C: The Art of Scientific Computing
publisher: pub-CAMBRIDGE
address: pub-CAMBRIDGE:adr
edition: Second
pages: xxvi + 994
year: 1992
ISBN: 0-521-43108-5, 0-521-43720-2 OR 0521431085, 0521437202
ISBN13: 978-0-521-43108-8, 978-0-521-43720-2 OR 9780521431088, 9780521437202
LCCN: QA297 .N864 1992
bibdate: Thu Sep 01 22:12:07 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 22:12:07 ???
acknowledgement: ack-nhfb
rawauthor: W. H. Press and B. P. Flannery and S. A. Teukolsky and W. T. Vetterling
rawtitle: Numerical Recipes in {C}: The Art of Scientific Computing
entry:
@Book{Press:1992:NRC,
  author =       "W. H. Press and B. P. Flannery and S. A. Teukolsky and
                 W. T. Vetterling",
  title =        "Numerical Recipes in {C}: The Art of Scientific
                 Computing",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  edition =      "Second",
  pages =        "xxvi + 994",
  year =         "1992",
  ISBN =         "0-521-43108-5, 0-521-43720-2",
  ISBN-13 =      "978-0-521-43108-8, 978-0-521-43720-2",
  LCCN =         "QA297 .N864 1992",
  bibdate =      "Thu Sep 01 22:12:07 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: phdthesis
filename: fparith.bib
label: Priest:1992:PFP
author: Douglas M. Priest
type: Thesis (Ph.D. in Mathematics)
school: Department of Computer Science, University of California, Berkeley
address: Berkeley, CA, USA
pages: iv + 136
month: dec
monthnumber: 12
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
note: UMI order number GAX93-30692.
URL: ftp://ftp.icsi.berkeley.edu/pub/theory/priest-thesis.ps.Z
acknowledgement: ack-nhfb
rawauthor: Douglas M. Priest
rawnote: UMI order number GAX93-30692.
title:
On Properties of Floating Point Arithmetics: Numerical Stability and the Cost of Accurate Computations

abstract:
Floating point arithmetics generally possess many regularity properties in addition to those that are typically used in roundoff error analyses; these properties can be exploited to produce computations that are more accurate and cost effective than many programmers might think possible. Furthermore, many of these properties are quite simple to state and to comprehend, but few programmers seem to be aware of them (or at least willing to rely on them).par This dissertation presents some of these properties and explores their consequences for computability, accuracy, cost, and portability. For example, we consider several algorithms for summing a sequence of numbers and show that under very general hypotheses, we can compute a sum to full working precision at only somewhat greater cost than a simple accumulation, which can often produce a sum with no significant figures at all. This example, as well as others we present, can be generalized further by substituting still more complex algorithms; consequently, examples such as these oblige us to consider more carefully the tradeoffs between cost and accuracy.par At one end of the accuracy spectrum we find one of the least obvious consequences of the properties of floating point arithmetic: the accuracy of a computation consisting of rational arithmetic operations and comparisons need not be limited by the precision of the floating point arithmetic in which it is carried out. Of course, the more accuracy desired, the greater the cost of the computation, and the cost of computing a very accurate result may be quite high; we illustrate this possibility in the case of polynomial evaluation. At the other end of the spectrum, however, we give an example of a problem for which simply computing a result to a modest guaranteed accuracy costs far less than the contortions required to accommodate inaccurate results. As a consequence of examples such as these, we conclude that programmers and theorists alike must be willing to adopt a more sophisticated view of floating point arithmetic, even if only to consider that more accurate and reliable computations than those presently in common use might be possible based on stronger hypotheses than are customarily assumed.

keywords:
accurate floating-point summation; Dept. of Mathematics; Dissertations; floating-point arithmetic; University of California, Berkeley

rawabstract:
Floating point arithmetics generally possess many regularity properties in addition to those that are typically used in roundoff error analyses; these properties can be exploited to produce computations that are more accurate and cost effective than many programmers might think possible. Furthermore, many of these properties are quite simple to state and to comprehend, but few programmers seem to be aware of them (or at least willing to rely on them).\par This dissertation presents some of these properties and explores their consequences for computability, accuracy, cost, and portability. For example, we consider several algorithms for summing a sequence of numbers and show that under very general hypotheses, we can compute a sum to full working precision at only somewhat greater cost than a simple accumulation, which can often produce a sum with no significant figures at all. This example, as well as others we present, can be generalized further by substituting still more complex algorithms; consequently, examples such as these oblige us to consider more carefully the tradeoffs between cost and accuracy.\par At one end of the accuracy spectrum we find one of the least obvious consequences of the properties of floating point arithmetic: the accuracy of a computation consisting of rational arithmetic operations and comparisons need not be limited by the precision of the floating point arithmetic in which it is carried out. Of course, the more accuracy desired, the greater the cost of the computation, and the cost of computing a very accurate result may be quite high; we illustrate this possibility in the case of polynomial evaluation. At the other end of the spectrum, however, we give an example of a problem for which simply computing a result to a modest guaranteed accuracy costs far less than the contortions required to accommodate inaccurate results. As a consequence of examples such as these, we conclude that programmers and theorists alike must be willing to adopt a more sophisticated view of floating point arithmetic, even if only to consider that more accurate and reliable computations than those presently in common use might be possible based on stronger hypotheses than are customarily assumed.

rawtitle:
On Properties of Floating Point Arithmetics: Numerical Stability and the Cost of Accurate Computations

entry:
@PhdThesis{Priest:1992:PFP,
  author =       "Douglas M. Priest",
  title =        "On Properties of Floating Point Arithmetics: Numerical
                 Stability and the Cost of Accurate Computations",
  type =         "Thesis ({Ph.D.} in Mathematics)",
  school =       "Department of Computer Science, University of
                 California, Berkeley",
  address =      "Berkeley, CA, USA",
  pages =        "iv + 136",
  month =        dec,
  year =         "1992",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "UMI order number GAX93-30692.",
  URL =          "ftp://ftp.icsi.berkeley.edu/pub/theory/priest-thesis.ps.Z",
  abstract =     "Floating point arithmetics generally possess many
                 regularity properties in addition to those that are
                 typically used in roundoff error analyses; these
                 properties can be exploited to produce computations
                 that are more accurate and cost effective than many
                 programmers might think possible. Furthermore, many of
                 these properties are quite simple to state and to
                 comprehend, but few programmers seem to be aware of
                 them (or at least willing to rely on them).\par

                 This dissertation presents some of these properties and
                 explores their consequences for computability,
                 accuracy, cost, and portability. For example, we
                 consider several algorithms for summing a sequence of
                 numbers and show that under very general hypotheses, we
                 can compute a sum to full working precision at only
                 somewhat greater cost than a simple accumulation, which
                 can often produce a sum with no significant figures at
                 all. This example, as well as others we present, can be
                 generalized further by substituting still more complex
                 algorithms; consequently, examples such as these oblige
                 us to consider more carefully the tradeoffs between
                 cost and accuracy.\par

                 At one end of the accuracy spectrum we find one of the
                 least obvious consequences of the properties of
                 floating point arithmetic: the accuracy of a
                 computation consisting of rational arithmetic
                 operations and comparisons need not be limited by the
                 precision of the floating point arithmetic in which it
                 is carried out. Of course, the more accuracy desired,
                 the greater the cost of the computation, and the cost
                 of computing a very accurate result may be quite high;
                 we illustrate this possibility in the case of
                 polynomial evaluation. At the other end of the
                 spectrum, however, we give an example of a problem for
                 which simply computing a result to a modest guaranteed
                 accuracy costs far less than the contortions required
                 to accommodate inaccurate results. As a consequence of
                 examples such as these, we conclude that programmers
                 and theorists alike must be willing to adopt a more
                 sophisticated view of floating point arithmetic, even
                 if only to consider that more accurate and reliable
                 computations than those presently in common use might
                 be possible based on stronger hypotheses than are
                 customarily assumed.",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation; Dept. of
                 Mathematics; Dissertations; floating-point arithmetic;
                 University of California, Berkeley",
}


bibtype: article
filename: fparith.bib
label: Quach:1992:HSA
author: N. T. Quach and M. J. Flynn
title: High-speed addition in CMOS
journal: j-IEEE-TRANS-COMPUT
volume: 41
number: 12
pages: 1612--1615
month: dec
monthnumber: 12
year: 1992
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.214671
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
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 Transactions on Computers
acknowledgement: ack-sfo
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: N. T. Quach and M. J. Flynn
rawtitle: High-speed addition in {CMOS}
entry:
@Article{Quach:1992:HSA,
  author =       "N. T. Quach and M. J. Flynn",
  title =        "High-speed addition in {CMOS}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "12",
  pages =        "1612--1615",
  month =        dec,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.214671",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  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,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: techreport
filename: fparith.bib
label: Quach:1992:RFP
author: N. Quach and M. Flynn
title: A radix-64 floating-point divider
type: Technical Report
number: CSL-TR-92-529
institution: Computer Systems Laboratory, Stanford University
address: Stanford, CA, USA
pages: 1612--1615
month: jun
monthnumber: 6
year: 1992
bibdate: Thu Apr 2 08:38:35 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.04.02 08:38:35 ???
acknowledgement: ack-sfo
rawauthor: N. Quach and M. Flynn
rawtitle: A radix-64 floating-point divider
entry:
@TechReport{Quach:1992:RFP,
  author =       "N. Quach and M. Flynn",
  title =        "A radix-64 floating-point divider",
  type =         "Technical Report",
  number =       "CSL-TR-92-529",
  institution =  "Computer Systems Laboratory, Stanford University",
  address =      "Stanford, CA, USA",
  month =        jun,
  year =         "1992",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Rao:1992:FPA
author: B. D. Rao
title: Floating point arithmetic and digital filters
journal: j-IEEE-TRANS-SIG-PROC
volume: 40
number: 1
pages: 85--95
month: jan
monthnumber: 1
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 08:40:52 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:52 MDT
fjournal: IEEE Transactions on Signal Processing
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78
rawauthor: B. D. Rao
rawtitle: Floating point arithmetic and digital filters
entry:
@Article{Rao:1992:FPA,
  author =       "B. D. Rao",
  title =        "Floating point arithmetic and digital filters",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "40",
  number =       "1",
  pages =        "85--95",
  month =        jan,
  year =         "1992",
  CODEN =        "ITPRED",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  summary =      "The roundoff noise properties of floating point
                 digital filters are examined. To make the analysis
                 tractable, a high level model to deal with the errors
                 in the inner product operation is developed. This model
                 establishes a broad connection between \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Rix:1992:CFA
author: B. Rix and D. Timmermann and H. Hahn and B. J. Hosticka
title: A CORDIC-based floating-point arithmetic unit
crossref: IEEE:1992:PIC
pages: 30.3/1--4
year: 1992
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: Department of Electr. Eng., Duisburg University, Germany
bookpages: 766
thesaurus: CMOS integrated circuits; Digital arithmetic; Digital signal processing chips
rawauthor: B. Rix and D. Timmermann and H. Hahn and B. J. Hosticka
rawtitle: A {CORDIC}-based floating-point arithmetic unit
abstract:
A floating-point arithmetic unit based on the CORDIC algorithm is described. It computes a wide range of arithmetic, trigonometric, and hyperbolic functions and achieves a normalized peak performance of 220 MFLOPS. The unit is implemented in 1.6- mu m double-metal CMOS technology and packaged in a 280-pin PGA.

keywords:
1.6 Micron; 220 MFLOPS; 280-Pin PGA; CORDIC algorithm; Double-metal CMOS technology; DSP; Floating-point arithmetic unit; Hyperbolic functions; Trigonometric functions

rawabstract:
A floating-point arithmetic unit based on the CORDIC algorithm is described. It computes a wide range of arithmetic, trigonometric, and hyperbolic functions and achieves a normalized peak performance of 220 MFLOPS. The unit is implemented in 1.6- mu m double-metal CMOS technology and packaged in a 280-pin PGA.

entry:
@InProceedings{Rix:1992:CFA,
  author =       "B. Rix and D. Timmermann and H. Hahn and B. J.
                 Hosticka",
  title =        "A {CORDIC}-based floating-point arithmetic unit",
  crossref =     "IEEE:1992:PIC",
  bookpages =    "766",
  pages =        "30.3/1--4",
  year =         "1992",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A floating-point arithmetic unit based on the CORDIC
                 algorithm is described. It computes a wide range of
                 arithmetic, trigonometric, and hyperbolic functions and
                 achieves a normalized peak performance of 220 MFLOPS.
                 The unit is implemented in 1.6- mu m double-metal CMOS
                 technology and packaged in a 280-pin PGA.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Electr. Eng., Duisburg University,
                 Germany",
  classification = "B1265F (Microprocessors and microcomputers); B2570D
                 (CMOS integrated circuits); C5135 (Digital signal
                 processing chips); C5230 (Digital arithmetic methods);
                 C5260 (Digital signal processing)",
  keywords =     "1.6 Micron; 220 MFLOPS; 280-Pin PGA; CORDIC algorithm;
                 Double-metal CMOS technology; DSP; Floating-point
                 arithmetic unit; Hyperbolic functions; Trigonometric
                 functions",
  numericalindex = "Computer speed 2.2E+08 FLOPS; Size 1.6E-06 m",
  thesaurus =    "CMOS integrated circuits; Digital arithmetic; Digital
                 signal processing chips",
}


bibtype: inproceedings
filename: fparith.bib
label: Sanz-Gonzalez:1992:OFP
author: J. L. Sanz-Gonzalez and F. Lopez-Ferreras
booktitle: Proceedings of the 3rd AFRICON Conference: AFRICON '92
title: Optimal floating-point structures for low roundoff noise digital filters
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 194--197
year: 1992
bibdate: Sat Jul 16 11:25:07 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:07 MDT
acknowledgement: ack-nhfb
rawauthor: J. L. Sanz-Gonzalez and F. Lopez-Ferreras
rawbooktitle: Proceedings of the 3rd {AFRICON} Conference: {AFRICON '92}
rawtitle: Optimal floating-point structures for low roundoff noise digital filters
entry:
@InProceedings{Sanz-Gonzalez:1992:OFP,
  author =       "J. L. Sanz-Gonzalez and F. Lopez-Ferreras",
  booktitle =    "Proceedings of the 3rd {AFRICON} Conference: {AFRICON
                 '92}",
  title =        "Optimal floating-point structures for low roundoff
                 noise digital filters",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "194--197",
  year =         "1992",
  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 =      "A theoretical analysis of roundoff noise power in
                 floating-point realizations of digital filters is
                 presented. Formulas are given for single-length and
                 double-length accumulators. The minimal-noise
                 floating-point structure is found to be identical
                 \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Scherson:1992:BPA
author: I. D. Scherson and D. A. Kramer and B. D. Alleyne
title: Bit-parallel arithmetic in a massively-parallel associative processor
journal: j-IEEE-TRANS-COMPUT
volume: 41
number: 10
pages: 1201--1210
month: oct
monthnumber: 10
year: 1992
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.166599
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 10:49:20 MDT 2011
bibtimestamp: 2011.07.07 10:49:20 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=166599
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: I. D. Scherson and D. A. Kramer and B. D. Alleyne
rawtitle: Bit-parallel arithmetic in a massively-parallel associative processor
entry:
@Article{Scherson:1992:BPA,
  author =       "I. D. Scherson and D. A. Kramer and B. D. Alleyne",
  title =        "Bit-parallel arithmetic in a massively-parallel
                 associative processor",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "10",
  pages =        "1201--1210",
  month =        oct,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.166599",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 10:49:20 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=166599",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Schwarz:1992:ASF
author: E. M. Schwarz and M. J. Flynn
title: Approximating the Sine Function With Combinational Logic
crossref: Singh:1992:CRT
pages: 386--390
year: 1992
bibdate: Thu Sep 08 08:02:20 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.08 08:02:20 ???
acknowledgement: ack-nj
rawauthor: E. M. Schwarz and M. J. Flynn
rawtitle: Approximating the Sine Function With Combinational Logic
entry:
@InProceedings{Schwarz:1992:ASF,
  author =       "E. M. Schwarz and M. J. Flynn",
  title =        "Approximating the Sine Function With Combinational
                 Logic",
  crossref =     "Singh:1992:CRT",
  pages =        "386--390",
  year =         "1992",
  bibdate =      "Thu Sep 08 08:02:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: Seznec:1992:CSH
author: Andre Seznec and Karl Courtel
title: Controlling and sequencing a heavily pipelined floating-point operator
journal: j-SIGMICRO
volume: 23
number: 1--2
pages: 111--114
month: dec
monthnumber: 12
year: 1992
CODEN: SIGMDJ
DOI: https://doi.org/10.1145/144965.145008
ISSN: 0163-5751, 1050-916X OR 01635751, 1050916X
ISSNL: 0163-5751 OR 01635751
bibdate: Fri Apr 16 10:27:43 MDT 2021
bibtimestamp: 2021.04.16 10:27:43 MDT
URL: https://dl.acm.org/doi/10.1145/144965.145008
fjournal: ACM SIGMICRO Newsletter
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/sigmicro
rawauthor: Andr{\'e} Seznec and Karl Courtel
rawtitle: Controlling and sequencing a heavily pipelined floating-point operator
entry:
@Article{Seznec:1992:CSH,
  author =       "Andr{\'e} Seznec and Karl Courtel",
  title =        "Controlling and sequencing a heavily pipelined
                 floating-point operator",
  journal =      j-SIGMICRO,
  volume =       "23",
  number =       "1--2",
  pages =        "111--114",
  month =        dec,
  year =         "1992",
  CODEN =        "SIGMDJ",
  DOI =          "https://doi.org/10.1145/144965.145008",
  ISSN =         "0163-5751, 1050-916X",
  ISSN-L =       "0163-5751",
  bibdate =      "Fri Apr 16 10:27:43 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigmicro.bib",
  URL =          "https://dl.acm.org/doi/10.1145/144965.145008",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGMICRO Newsletter",
  journal-URL =  "https://dl.acm.org/loi/sigmicro",
}


bibtype: article
filename: fparith.bib
label: Seznec:1992:OAF
author: Andre Seznec and Karl Courtel
title: OPAC (abstract): a floating-point coprocessor dedicated to compute-bound kernels
journal: j-COMP-ARCH-NEWS
volume: 20
number: 2
pages: 427--427
month: may
monthnumber: 5
year: 1992
CODEN: CANED2
ISSN: 0163-5964 (print), 1943-5851 (electronic) OR 01635964 (print), 19435851 (electronic)
ISSNL: 0163-5964 OR 01635964
bibdate: Fri May 12 09:40:43 MDT 2006
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2006.05.12 09:40:43 MDT
fjournal: ACM SIGARCH Computer Architecture News
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J89
rawauthor: Andr{\'e} Seznec and Karl Courtel
rawtitle: {OPAC} (abstract): a floating-point coprocessor dedicated to compute-bound kernels
entry:
@Article{Seznec:1992:OAF,
  author =       "Andr{\'e} Seznec and Karl Courtel",
  title =        "{OPAC} (abstract): a floating-point coprocessor
                 dedicated to compute-bound kernels",
  journal =      j-COMP-ARCH-NEWS,
  volume =       "20",
  number =       "2",
  pages =        "427--427",
  month =        may,
  year =         "1992",
  CODEN =        "CANED2",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Fri May 12 09:40:43 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J89",
}


bibtype: article
filename: fparith.bib
label: Seznec:1992:OFC
author: A. Seznec and K. Courtel
title: OPAC: a Floating-Point Coprocessor Dedicated to Compute-Bound Kernels
journal: j-COMP-ARCH-NEWS
volume: 20
number: 2
pages: 427--427
month: may
monthnumber: 5
year: 1992
CODEN: CANED2
ISSN: 0163-5964 (print), 1943-5851 (electronic) OR 01635964 (print), 19435851 (electronic)
ISSNL: 0163-5964 OR 01635964
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: ACM SIGARCH Computer Architecture News
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J89
rawauthor: A. Seznec and K. Courtel
rawtitle: {OPAC}: a Floating-Point Coprocessor Dedicated to Compute-Bound Kernels
entry:
@Article{Seznec:1992:OFC,
  author =       "A. Seznec and K. Courtel",
  title =        "{OPAC}: a Floating-Point Coprocessor Dedicated to
                 Compute-Bound Kernels",
  journal =      j-COMP-ARCH-NEWS,
  volume =       "20",
  number =       "2",
  pages =        "427--427",
  month =        may,
  year =         "1992",
  CODEN =        "CANED2",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J89",
}


bibtype: article
filename: fparith.bib
label: Simar:1992:FPP
title: Floating-Point Processors Join Forces in Parallel Processing Architectures
journal: j-IEEE-MICRO
volume: 12
number: 4
pages: 60--69
month: jul
monthnumber: 7
year: 1992
CODEN: IEMIDZ
DOI: https://doi.org/10.1109/40.149737
ISSN: 0272-1732 (print), 1937-4143 (electronic) OR 02721732 (print), 19374143 (electronic)
ISSNL: 0272-1732 OR 02721732
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 Micro
acknowledgement: ack-nhfb
journalURL: http://www.computer.org/csdl/mags/mi/index.html
rawtitle: Floating-Point Processors Join Forces in Parallel Processing Architectures
author:
Ray Simar, Jr. and Peter Koeppen and Jerald Leach and Steve Marshall and Dave Francis and Greg Mekras and Jeffrey Rosenstrauch and Scott Anderson

abstract:
Achieving cost-effective design performance goals with parallel DSP building blocks supported by extensive software

rawabstract:
Achieving cost-effective design performance goals with parallel DSP building blocks supported by extensive software

rawauthor:
Ray {Simar, Jr.} and Peter Koeppen and Jerald Leach and Steve Marshall and Dave Francis and Greg Mekras and Jeffrey Rosenstrauch and Scott Anderson

entry:
@Article{Simar:1992:FPP,
  author =       "Ray {Simar, Jr.} and Peter Koeppen and Jerald Leach
                 and Steve Marshall and Dave Francis and Greg Mekras and
                 Jeffrey Rosenstrauch and Scott Anderson",
  title =        "Floating-Point Processors Join Forces in Parallel
                 Processing Architectures",
  journal =      j-IEEE-MICRO,
  volume =       "12",
  number =       "4",
  pages =        "60--69",
  month =        jul # "\slash " # aug,
  year =         "1992",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/40.149737",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Achieving cost-effective design performance goals with
                 parallel DSP building blocks supported by extensive
                 software",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
  summary =      "The hardware architecture and software capabilities of
                 the TMS320C40 floating-point digital signal processor
                 are described. The C40 operates at 275 million
                 operations per second (MOPS) and transfers data at a
                 rate of 320 Mbytes/s with a 40-ns cycle time \ldots{}",
}


bibtype: book
filename: fparith.bib
label: Sites:1992:AAR
author: Richard L. Sites and Richard Witek and others
title: Alpha Architecture Reference Manual
publisher: pub-DP
address: pub-DP:adr
pages: 60--69
year: 1992
ISBN: 0-13-033663-7 (PH), 1-55558-098-X (DP: print) OR 0130336637 (PH), 155558098X (DP: print)
LCCN: QA76.9.A73 A46 1992
bibdate: Wed Jan 23 08:49:36 MST 2019
bibtimestamp: 2019.01.23 08:49:36 MST
acknowledgement: ack-nhfb
rawauthor: Richard L. Sites and Richard Witek and others
rawtitle: Alpha Architecture Reference Manual
ISBN13:
978-0-13-033663-7 (PH), 978-1-55558-098-8 (DP: print) OR 9780130336637 (PH), 9781555580988 (DP: print)

bibsource:
fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/microchip.bib

TOC:
Foreword Preface Common Architecture Introduction Basic Architecture Instruction Formats Instruction Descriptions System Architecture and Programming Implications Common PALcode Architecture Console Subsystem Overview Input/Output OpenVMS Alpha Software Introduction to OpenVMS Alpha OpenVMS PALcode Instruction Descriptions OpenVMS Memory Management OpenVMS Process Structure OpenVMS Internal Processor Registers OpenVMS Exceptions, Interrupts, and Machine Checks DEC OSF/1 Alpha Software Introduction to DEC OSF/1 Alpha OSF/1 PALcode Instruction Descriptions OSF/1 Memory Management OSF/I Process Structure OSF/1 Exceptions and Interrupts Appendix A: Software Considerations Appendix B: IEEE Floating-Point Conformance Appendix C: Instruction Encodings Index

rawTOC:
Foreword \\ Preface \\ Common Architecture \\ Introduction \\ Basic Architecture \\ Instruction Formats \\ Instruction Descriptions \\ System Architecture and Programming Implications \\ Common PALcode Architecture \\ Console Subsystem Overview \\ Input/Output \\ OpenVMS Alpha Software \\ Introduction to OpenVMS Alpha \\ OpenVMS PALcode Instruction Descriptions \\ OpenVMS Memory Management \\ OpenVMS Process Structure \\ OpenVMS Internal Processor Registers \\ OpenVMS Exceptions, Interrupts, and Machine Checks \\ DEC OSF/1 Alpha Software \\ Introduction to DEC OSF/1 Alpha \\ OSF/1 PALcode Instruction Descriptions \\ OSF/1 Memory Management \\ OSF/I Process Structure \\ OSF/1 Exceptions and Interrupts \\ Appendix A: Software Considerations \\ Appendix B: IEEE Floating-Point Conformance \\ Appendix C: Instruction Encodings \\ Index

entry:
@Book{Sites:1992:AAR,
  author =       "Richard L. Sites and Richard Witek and others",
  title =        "Alpha Architecture Reference Manual",
  publisher =    pub-DP # " and " # pub-PH,
  address =      pub-DP:adr # " and " # pub-PH:adr,
  year =         "1992",
  ISBN =         "0-13-033663-7 (PH), 1-55558-098-X (DP: print)",
  ISBN-13 =      "978-0-13-033663-7 (PH), 978-1-55558-098-8 (DP:
                 print)",
  LCCN =         "QA76.9.A73 A46 1992",
  bibdate =      "Wed Jan 23 08:49:36 MST 2019",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/microchip.bib",
  acknowledgement = ack-nhfb,
  tableofcontents = "Foreword \\
                 Preface \\
                 Common Architecture \\
                 Introduction \\
                 Basic Architecture \\
                 Instruction Formats \\
                 Instruction Descriptions \\
                 System Architecture and Programming Implications \\
                 Common PALcode Architecture \\
                 Console Subsystem Overview \\
                 Input/Output \\
                 OpenVMS Alpha Software \\
                 Introduction to OpenVMS Alpha \\
                 OpenVMS PALcode Instruction Descriptions \\
                 OpenVMS Memory Management \\
                 OpenVMS Process Structure \\
                 OpenVMS Internal Processor Registers \\
                 OpenVMS Exceptions, Interrupts, and Machine Checks \\
                 DEC OSF/1 Alpha Software \\
                 Introduction to DEC OSF/1 Alpha \\
                 OSF/1 PALcode Instruction Descriptions \\
                 OSF/1 Memory Management \\
                 OSF/I Process Structure \\
                 OSF/1 Exceptions and Interrupts \\
                 Appendix A: Software Considerations \\
                 Appendix B: IEEE Floating-Point Conformance \\
                 Appendix C: Instruction Encodings \\
                 Index",
  xxauthor =     "{Alpha Architecture Committee}",
}


bibtype: article
filename: fparith.bib
label: Skavantzos:1992:DCM
author: A. Skavantzos and T. Stouraitis
title: Decomposition of complex multipliers using polynomial encoding
journal: j-IEEE-TRANS-COMPUT
volume: 41
number: 10
pages: 1331--1333
month: oct
monthnumber: 10
year: 1992
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.166610
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 10:49:20 MDT 2011
bibtimestamp: 2011.07.07 10:49:20 MDT
note: See comments cite Katti:1994:CDC.
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=166610
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: A. Skavantzos and T. Stouraitis
rawnote: See comments \cite{Katti:1994:CDC}.
rawtitle: Decomposition of complex multipliers using polynomial encoding
entry:
@Article{Skavantzos:1992:DCM,
  author =       "A. Skavantzos and T. Stouraitis",
  title =        "Decomposition of complex multipliers using polynomial
                 encoding",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "10",
  pages =        "1331--1333",
  month =        oct,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.166610",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 10:49:20 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 comments \cite{Katti:1994:CDC}.",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=166610",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Skavantzos:1992:NMM
author: A. Skavantzos and P. B. Rao
title: New multipliers modulo $ 2^N - 1 $
journal: j-IEEE-TRANS-COMPUT
volume: 41
number: 8
pages: 957--961
month: aug
monthnumber: 8
year: 1992
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.156538
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: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156538
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: A. Skavantzos and P. B. Rao
rawtitle: New multipliers modulo {$ 2^N - 1 $}
entry:
@Article{Skavantzos:1992:NMM,
  author =       "A. Skavantzos and P. B. Rao",
  title =        "New multipliers modulo {$ 2^N - 1 $}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "8",
  pages =        "957--961",
  month =        aug,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.156538",
  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 =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156538",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: 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: http://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 =  "http://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
publisher: pub-TEUBNER
address: pub-TEUBNER:adr
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",
  publisher =    pub-TEUBNER,
  address =      pub-TEUBNER:adr,
  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: http://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 =          "http://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: http://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: http://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 =          "http://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 =  "http://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: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=256444
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://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 =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=256444",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: 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: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156537
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://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 =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156537",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: 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
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.08 00:52:02 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: D. Timmermann and H. Hahn and B. J. Hosticka
rawtitle: Low Latency Time {CORDIC} Algorithms
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/fparith.bib",
  acknowledgement = ack-nj,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: 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: http://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 =  "http://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: http://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 =  "http://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: http://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 =  "http://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: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156541
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: http://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 =          "http://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 =  "http://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: http://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: http://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 =          "http://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)",
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4075
fjournal: IEEE Transactions on Signal Processing
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78
rawauthor: 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 =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4075",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  keywords =     "residue arithmetic; residue number system",
  summary =      "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: http://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 =  "http://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: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=5864
fjournal: IEEE Transactions on Signal Processing
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78
rawauthor: 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 =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=5864",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  keywords =     "residue arithmetic; residue number system",
  summary =      "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: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=5864
fjournal: IEEE Transactions on Signal Processing
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78
rawauthor: 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 =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=5864",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  keywords =     "residue arithmetic; residue number system",
  summary =      "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: http://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 =  "http://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: M. 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: M. Daumas and D. W. Matula
rawtitle: Design of a Fast Validated Dot Product Operation
entry:
@InProceedings{Daumas:1993:DFV,
  author =       "M. 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: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=214689
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://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",
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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.

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  author =       "V. Di Lecce and E. Di Sciascio",
  title =        "A comparative evaluation of solutions for inner
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  abstract =     "This paper proposes the design and performance
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                 solutions proposed in the scientific literature for
                 inner product are presented and evaluated. The
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  acknowledgement = ack-nhfb,
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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: http://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/stamp/stamp.jsp?tp=&arnumber=223680; http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=5840

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",
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  volume =       "42",
  number =       "5",
  pages =        "608--612",
  month =        may,
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  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
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  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",
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  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",
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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",
}


