# bibtab

bibtype: article
filename: fparith.bib
label: Chassaing:1991:DSP
author: Chassaing and Horning
title: Digital Signal Processing with Fixed- and Floating-Point Processors
journal: j-COED
volume: II
number: 1
pages: 1--4
month: jan
monthnumber: 1
year: 1991
CODEN: CWLJDP
ISSN: 0736-8607 OR 07368607
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: CoED
acknowledgement: ack-nhfb
rawauthor: Chassaing and Horning
rawtitle: Digital Signal Processing with Fixed- and Floating-Point Processors
entry:
@Article{Chassaing:1991:DSP,
  author =       "Chassaing and Horning",
  title =        "Digital Signal Processing with Fixed- and
                 Floating-Point Processors",
  journal =      j-COED,
  volume =       "II",
  number =       "1",
  pages =        "1--4",
  month =        jan,
  year =         "1991",
  CODEN =        "CWLJDP",
  ISSN =         "0736-8607",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "CoED",
}


bibtype: inproceedings
filename: fparith.bib
label: Chatelin:1991:AAA
author: F. Chatelin and V. Fraysse
title: Analysis of arithmetic algorithms: a statistical study
crossref: Kornerup:1991:PIS
pages: 10--16
year: 1991
bibdate: Sat Nov 27 12:40:58 MST 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.27 12:40:58 MST
URL: http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Chatelin.pdf
keywords: ARITH-10
acknowledgement: ack-nhfb
rawauthor: F. Chatelin and V. Frayss{\'e}
rawtitle: Analysis of arithmetic algorithms: a statistical study
entry:
@InProceedings{Chatelin:1991:AAA,
  author =       "F. Chatelin and V. Frayss{\'e}",
  title =        "Analysis of arithmetic algorithms: a statistical
                 study",
  crossref =     "Kornerup:1991:PIS",
  pages =        "10--16",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Chatelin.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}


bibtype: article
filename: fparith.bib
label: Chen:1991:BDR
author: F. Chen and C. S. Chen
title: A 20~b dynamic-range floating-point data acquisition system
journal: j-IEEE-TRANS-IND-ELECTRON
volume: 38
number: 1
pages: 10--14
month: feb
monthnumber: 2
year: 1991
CODEN: ITIED6
DOI: https://doi.org/10.1109/41.103477
ISSN: 0278-0046 (print), 1557-9948 (electronic) OR 02780046 (print), 15579948 (electronic)
ISSNL: 0278-0046 OR 02780046
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 Industrial Electronics
acknowledgement: ack-nhfb
rawauthor: F. Chen and C. S. Chen
rawtitle: A {20~b} dynamic-range floating-point data acquisition system
entry:
@Article{Chen:1991:BDR,
  author =       "F. Chen and C. S. Chen",
  title =        "A {20~b} dynamic-range floating-point data acquisition
                 system",
  journal =      j-IEEE-TRANS-IND-ELECTRON,
  volume =       "38",
  number =       "1",
  pages =        "10--14",
  month =        feb,
  year =         "1991",
  CODEN =        "ITIED6",
  DOI =          "https://doi.org/10.1109/41.103477",
  ISSN =         "0278-0046 (print), 1557-9948 (electronic)",
  ISSN-L =       "0278-0046",
  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 Industrial Electronics",
  summary =      "The design and engineering of a floating-point
                 data-acquisition system are described. The system has
                 both automatic gain and software-programmable gain
                 adjustment features. In automatic gain adjustment mode,
                 the gain is set automatically dependent on \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Chiang:1991:FNR
author: Jen-Shiun Chiang and Mi Lu
title: Floating-point numbers in residue number systems
journal: j-COMPUT-MATH-APPL
volume: 22
number: 10
pages: 127--140
year: 1991
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
MRclass: 65Y10
MRnumber: 92h:65212
bibdate: Wed Dec 13 18:13:40 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.13 18:13:40 ???
fjournal: Computers and Mathematics with Applications
keywords: Floating-point RNS; Residue number system; RNS
acknowledgement: ack-nhfb
affiliation: Department of Electr. Eng., Texas A&M University, College Station, TX, USA
journalURL: http://www.sciencedirect.com/science/journal/08981221
thesaurus: Digital arithmetic
rawauthor: Jen-Shiun Chiang and Mi Lu
rawtitle: Floating-point numbers in residue number systems
abstract:
Introduce a new type of the residue number system (RNS), floating-point RNS, which can significantly increase the range of the numbers represented by RNS. The concept of the RNS floating-point arithmetics are presented, and the approaches to perform these arithmetic operations are proposed. The introduced methods are simple, efficient and easy to implement. (6 Refs.)

rawabstract:
Introduce a new type of the residue number system (RNS), floating-point RNS, which can significantly increase the range of the numbers represented by RNS. The concept of the RNS floating-point arithmetics are presented, and the approaches to perform these arithmetic operations are proposed. The introduced methods are simple, efficient and easy to implement. (6 Refs.)

entry:
@Article{Chiang:1991:FNR,
  author =       "Jen-Shiun Chiang and Mi Lu",
  title =        "Floating-point numbers in residue number systems",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "22",
  number =       "10",
  pages =        "127--140",
  month =        "????",
  year =         "1991",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  MRclass =      "65Y10",
  MRnumber =     "92h:65212",
  bibdate =      "Wed Dec 13 18:13:40 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Introduce a new type of the residue number system
                 (RNS), floating-point RNS, which can significantly
                 increase the range of the numbers represented by RNS.
                 The concept of the RNS floating-point arithmetics are
                 presented, and the approaches to perform these
                 arithmetic operations are proposed. The introduced
                 methods are simple, efficient and easy to implement. (6
                 Refs.)",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Electr. Eng., Texas A\&M University,
                 College Station, TX, USA",
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  keywords =     "Floating-point RNS; Residue number system; RNS",
  pubcountry =   "UK",
  thesaurus =    "Digital arithmetic",
}


bibtype: article
filename: fparith.bib
label: Chiang:1991:FPNa
author: Jen-Shiun Chiang and Mi Lu
title: Floating-point numbers in residue number systems
journal: j-COMPUT-MATH-APPL
volume: 22
number: 10
pages: 127--140
year: 1991
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
MRclass: 65Y10
MRnumber: 92h:65212
bibdate: Wed Dec 13 18:13:40 1995
bibtimestamp: 1995.12.13 18:13:40 ???
fjournal: Computers and Mathematics with Applications
keywords: Floating-point RNS; Residue number system; RNS
acknowledgement: ack-nhfb
affiliation: Department of Electr. Eng., Texas A&M University, College Station, TX, USA
journalURL: http://www.sciencedirect.com/science/journal/08981221
thesaurus: Digital arithmetic
rawauthor: Jen-Shiun Chiang and Mi Lu
rawtitle: Floating-point numbers in residue number systems
bibsource:
https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
Introduce a new type of the residue number system (RNS), floating-point RNS, which can significantly increase the range of the numbers represented by RNS. The concept of the RNS floating-point arithmetics are presented, and the approaches to perform these arithmetic operations are proposed. The introduced methods are simple, efficient and easy to implement. (6 Refs.)

entry:
@Article{Chiang:1991:FPNa,
  author =       "Jen-Shiun Chiang and Mi Lu",
  title =        "Floating-point numbers in residue number systems",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "22",
  number =       "10",
  pages =        "127--140",
  month =        "????",
  year =         "1991",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  MRclass =      "65Y10",
  MRnumber =     "92h:65212",
  bibdate =      "Wed Dec 13 18:13:40 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Introduce a new type of the residue number system
                 (RNS), floating-point RNS, which can significantly
                 increase the range of the numbers represented by RNS.
                 The concept of the RNS floating-point arithmetics are
                 presented, and the approaches to perform these
                 arithmetic operations are proposed. The introduced
                 methods are simple, efficient and easy to implement. (6
                 Refs.)",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Electr. Eng., Texas A\&M University,
                 College Station, TX, USA",
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  keywords =     "Floating-point RNS; Residue number system; RNS",
  pubcountry =   "UK",
  thesaurus =    "Digital arithmetic",
}


bibtype: article
filename: fparith.bib
label: Chiang:1991:FPNb
author: Jen-Shiun Chiang and Mi Lu
title: Floating-point numbers in residue number systems
journal: j-COMPUT-MATH-APPL
volume: 22
number: 10
pages: 127--140
year: 1991
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 19:11:01 MST 2017
bibtimestamp: 2017.03.01 19:11:01 MST
URL: http://www.sciencedirect.com/science/article/pii/089812219190200N
fjournal: Computers and Mathematics with Applications
keywords: Floating-point RNS; Residue number system; RNS
acknowledgement: ack-nhfb
affiliation: Department of Electr. Eng., Texas A and M University, College Station, TX, USA
journalURL: http://www.sciencedirect.com/science/journal/08981221
thesaurus: Digital arithmetic
rawauthor: Jen-Shiun Chiang and Mi Lu
rawtitle: Floating-point numbers in residue number systems
bibsource:
https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
Introduce a new type of the residue number system (RNS), floating-point RNS, which can significantly increase the range of the numbers represented by RNS. The concept of the RNS floating-point arithmetics are presented, and the approaches to perform these arithmetic operations are proposed. The introduced methods are simple, efficient and easy to implement.

rawabstract:
Introduce a new type of the residue number system (RNS), floating-point RNS, which can significantly increase the range of the numbers represented by RNS. The concept of the RNS floating-point arithmetics are presented, and the approaches to perform these arithmetic operations are proposed. The introduced methods are simple, efficient and easy to implement.

entry:
@Article{Chiang:1991:FPNb,
  author =       "Jen-Shiun Chiang and Mi Lu",
  title =        "Floating-point numbers in residue number systems",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "22",
  number =       "10",
  pages =        "127--140",
  month =        "????",
  year =         "1991",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 19:11:01 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/089812219190200N",
  abstract =     "Introduce a new type of the residue number system
                 (RNS), floating-point RNS, which can significantly
                 increase the range of the numbers represented by RNS.
                 The concept of the RNS floating-point arithmetics are
                 presented, and the approaches to perform these
                 arithmetic operations are proposed. The introduced
                 methods are simple, efficient and easy to implement.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Electr. Eng., Texas A and M University,
                 College Station, TX, USA",
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  keywords =     "Floating-point RNS; Residue number system; RNS",
  pubcountry =   "UK",
  thesaurus =    "Digital arithmetic",
}


bibtype: inproceedings
filename: fparith.bib
label: Chiang:1991:GDA
author: J.-S. Chiang and M. Lu
title: A general division algorithm for residue number systems
crossref: Kornerup:1991:PIS
pages: 76--83
year: 1991
DOI: https://doi.org/10.1109/ARITH.1991.145537
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
URL: http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Chiang.pdf
keywords: ARITH-10; residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: J.-S. Chiang and M. Lu
rawtitle: A general division algorithm for residue number systems
entry:
@InProceedings{Chiang:1991:GDA,
  author =       "J.-S. Chiang and M. Lu",
  title =        "A general division algorithm for residue number
                 systems",
  crossref =     "Kornerup:1991:PIS",
  pages =        "76--83",
  year =         "1991",
  DOI =          "https://doi.org/10.1109/ARITH.1991.145537",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Chiang.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10; residue arithmetic; residue number system",
  summary =      "A general algorithm for signed number division in
                 residue number systems (RNSs) is presented. A parity
                 checking technique is used to accomplish the sign and
                 overflow detection in this algorithm. Compared with
                 conventional methods of sign and \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Cmelik:1991:AMS
author: Robert F. Cmelik and Shing I. Kong and David R. Ditzel and Edmund J. Kelly
title: An Analysis of MIPS and SPARC Instruction Set Utilization on the SPEC Benchmarks
journal: j-SIGPLAN
volume: 26
number: 4
pages: 290--301 (or 290--302??)
month: apr
monthnumber: 4
year: 1991
CODEN: SINODQ
ISSN: 0362-1340 (print), 1523-2867 (print), 1558-1160 OR 03621340 (print), 15232867 (print), 15581160
ISSNL: 0362-1340 OR 03621340
bibdate: Tue Dec 12 09:20:21 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.12 09:20:21 MST
fjournal: ACM SIGPLAN Notices
acknowledgement: ack-nhfb
affiliation: Sun Microsyst. Inc., Mountain View, CA, USA
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J706
thesaurus: Instruction sets; Performance evaluation; Reduced instruction set computing
rawauthor: Robert F. Cmelik and Shing I. Kong and David R. Ditzel and Edmund J. Kelly
rawtitle: An Analysis of {MIPS} and {SPARC} Instruction Set Utilization on the {SPEC} Benchmarks
abstract:
The dynamic instruction counts of MIPS and SPARC are compared using the SPEC benchmarks. MIPS typically executes more user-level instructions than SPARC. This difference can be accounted for by architectural differences, compiler differences, and library differences. The most significant differences are that SPARC's double-precision floating point load/store is an architectural advantage in the SPEC floating point benchmarks while MIPS's compare-and-branch instruction is an architectural advantage in the SPEC integer benchmarks. After the differences in the two architectures are isolated, it appears that although MIPS and SPARC each have strengths and weaknesses in their compilers and library routines, the combined effect of compilers and library routines does not give either MIPS or SPARC a clear advantage in these areas.

keywords:
Architectural differences; Compare-and-branch instruction; Compiler differences; Double-precision floating point load/store; Dynamic instruction counts; Instruction set utilization; Library differences; MIPS; SPARC; SPEC floating point benchmarks; SPEC integer benchmarks; User-level instructions

rawabstract:
The dynamic instruction counts of MIPS and SPARC are compared using the SPEC benchmarks. MIPS typically executes more user-level instructions than SPARC. This difference can be accounted for by architectural differences, compiler differences, and library differences. The most significant differences are that SPARC's double-precision floating point load/store is an architectural advantage in the SPEC floating point benchmarks while MIPS's compare-and-branch instruction is an architectural advantage in the SPEC integer benchmarks. After the differences in the two architectures are isolated, it appears that although MIPS and SPARC each have strengths and weaknesses in their compilers and library routines, the combined effect of compilers and library routines does not give either MIPS or SPARC a clear advantage in these areas.

entry:
@Article{Cmelik:1991:AMS,
  author =       "Robert F. Cmelik and Shing I. Kong and David R. Ditzel
                 and Edmund J. Kelly",
  title =        "An Analysis of {MIPS} and {SPARC} Instruction Set
                 Utilization on the {SPEC} Benchmarks",
  journal =      j-SIGPLAN,
  volume =       "26",
  number =       "4",
  pages =        "290--301 (or 290--302??)",
  month =        apr,
  year =         "1991",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Tue Dec 12 09:20:21 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The dynamic instruction counts of MIPS and SPARC are
                 compared using the SPEC benchmarks. MIPS typically
                 executes more user-level instructions than SPARC. This
                 difference can be accounted for by architectural
                 differences, compiler differences, and library
                 differences. The most significant differences are that
                 SPARC's double-precision floating point load/store is
                 an architectural advantage in the SPEC floating point
                 benchmarks while MIPS's compare-and-branch instruction
                 is an architectural advantage in the SPEC integer
                 benchmarks. After the differences in the two
                 architectures are isolated, it appears that although
                 MIPS and SPARC each have strengths and weaknesses in
                 their compilers and library routines, the combined
                 effect of compilers and library routines does not give
                 either MIPS or SPARC a clear advantage in these
                 areas.",
  acknowledgement = ack-nhfb,
  affiliation =  "Sun Microsyst. Inc., Mountain View, CA, USA",
  classification = "C5220 (Computer architecture); C5470 (Performance
                 evaluation and testing); C6140B (Machine-oriented
                 languages)",
  confdate =     "8-11 April 1991",
  conflocation = "Santa Clara, CA, USA",
  confsponsor =  "IEEE; ACM",
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "Architectural differences; Compare-and-branch
                 instruction; Compiler differences; Double-precision
                 floating point load/store; Dynamic instruction counts;
                 Instruction set utilization; Library differences; MIPS;
                 SPARC; SPEC floating point benchmarks; SPEC integer
                 benchmarks; User-level instructions",
  thesaurus =    "Instruction sets; Performance evaluation; Reduced
                 instruction set computing",
}


bibtype: inproceedings
filename: fparith.bib
label: Cody:1991:KAA
author: W. J. Cody
title: Keynote Address: Arithmetic Standards: The Long Road
crossref: Kornerup:1991:PIS
pages: ix--ix
year: 1991
bibdate: Sat Nov 17 08:46:25 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.17 08:46:25 ???
URL: http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_keynote.pdf
keywords: ARITH-10
acknowledgement: ack-nhfb
rawauthor: W. J. Cody
rawtitle: Keynote Address: Arithmetic Standards: The Long Road
entry:
@InProceedings{Cody:1991:KAA,
  author =       "W. J. Cody",
  title =        "Keynote Address: Arithmetic Standards: The Long Road",
  crossref =     "Kornerup:1991:PIS",
  pages =        "ix--ix",
  year =         "1991",
  bibdate =      "Sat Nov 17 08:46:25 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_keynote.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}


bibtype: article
filename: fparith.bib
label: Cody:1991:PEP
author: W. J. Cody
title: Performance Evaluation of Programs Related to the Real Gamma Function
journal: j-TOMS
volume: 17
number: 1
pages: 46--54
month: mar
monthnumber: 3
year: 1991
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 65D20 (65Y20)
MRnumber: 91m:65052
bibdate: Sun Sep 04 23:33:02 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.04 23:33:02 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: measurement; performance; reliability
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: W. J. Cody
rawtitle: Performance Evaluation of Programs Related to the Real Gamma Function
URL:
http://doi.acm.org/10.1145/103147.103153; http://www.acm.org/pubs/citations/journals/toms/1991-17-1/p46-cody/

abstract:
Methods are presented for evaluating the performance of programs for the functions $ Gamma (x) $, $ ln Gamma (x) $, and $ psi (x) $. Accuracy estimates are based on comparisons using the manipulation theorem. Ideas for checking robustness are also given, and details on specific implementations of test programs are included.

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

rawabstract:
Methods are presented for evaluating the performance of programs for the functions $ \Gamma (x) $, $ \ln \Gamma (x) $, and $ \psi (x) $. Accuracy estimates are based on comparisons using the manipulation theorem. Ideas for checking robustness are also given, and details on specific implementations of test programs are included.

entry:
@Article{Cody:1991:PEP,
  author =       "W. J. Cody",
  title =        "Performance Evaluation of Programs Related to the Real
                 Gamma Function",
  journal =      j-TOMS,
  volume =       "17",
  number =       "1",
  pages =        "46--54",
  month =        mar,
  year =         "1991",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D20 (65Y20)",
  MRnumber =     "91m:65052",
  bibdate =      "Sun Sep 04 23:33:02 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://doi.acm.org/10.1145/103147.103153;
                 http://www.acm.org/pubs/citations/journals/toms/1991-17-1/p46-cody/",
  abstract =     "Methods are presented for evaluating the performance
                 of programs for the functions $ \Gamma (x) $, $ \ln
                 \Gamma (x) $, and $ \psi (x) $. Accuracy estimates are
                 based on comparisons using the manipulation theorem.
                 Ideas for checking robustness are also given, and
                 details on specific implementations of test programs
                 are included.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "measurement; performance; reliability",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Numerical algorithms. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Certification and testing.",
}


bibtype: article
filename: fparith.bib
label: Cody:1991:UTS
author: W. J. Cody and L. Stoltz
title: The Use of Taylor Series to Test Accuracy of Function Programs
journal: j-TOMS
volume: 17
number: 1
pages: 55--63
month: mar
monthnumber: 3
year: 1991
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 65D20 (65Y20)
MRnumber: 91m:65053
bibdate: Sun Sep 04 23:36:36 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.04 23:36:36 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms; measurement; performance; verification
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: W. J. Cody and L. Stoltz
rawtitle: The Use of {Taylor} Series to Test Accuracy of Function Programs
URL:
http://doi.acm.org/10.1145/103147.103154; http://www.acm.org/pubs/citations/journals/toms/1991-17-1/p55-cody/

abstract:
This paper discusses the use of local Taylor series expansions for determining the accuracy of computer programs for special functions. The main example is testing of programs for exponential integrals. Additional applications include testing of programs for certain Bessel functions, Dawson's integral, and error 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 the use of local Taylor series expansions for determining the accuracy of computer programs for special functions. The main example is testing of programs for exponential integrals. Additional applications include testing of programs for certain Bessel functions, Dawson's integral, and error functions.

entry:
@Article{Cody:1991:UTS,
  author =       "W. J. Cody and L. Stoltz",
  title =        "The Use of {Taylor} Series to Test Accuracy of
                 Function Programs",
  journal =      j-TOMS,
  volume =       "17",
  number =       "1",
  pages =        "55--63",
  month =        mar,
  year =         "1991",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D20 (65Y20)",
  MRnumber =     "91m:65053",
  bibdate =      "Sun Sep 04 23:36:36 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://doi.acm.org/10.1145/103147.103154;
                 http://www.acm.org/pubs/citations/journals/toms/1991-17-1/p55-cody/",
  abstract =     "This paper discusses the use of local Taylor series
                 expansions for determining the accuracy of computer
                 programs for special functions. The main example is
                 testing of programs for exponential integrals.
                 Additional applications include testing of programs for
                 certain Bessel functions, Dawson's integral, and error
                 functions.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; measurement; performance; verification",
  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: Compan:1991:GPS
author: A. Compan and P. Debaud and V. Delorme and J. A. Francois and H. Mehrez and F. Pecheux
title: GAF: a portable standard-cell floating point adder generator using the CXgen function library
journal: j-MICROPROC-MICROPROG
volume: 32
number: 1
pages: 637--644
month: aug
monthnumber: 8
year: 1991
CODEN: MMICDT
ISSN: 0165-6074 (print), 1878-7061 (electronic) OR 01656074 (print), 18787061 (electronic)
ISSNL: 0165-6074 OR 01656074
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: Microprocessing and Microprogramming
acknowledgement: ack-nhfb
journalURL: https://www.sciencedirect.com/journal/microprocessing-and-microprogramming/issues
rawauthor: A. Compan and P. Debaud and V. Delorme and J. A. Fran{\c{c}}ois and H. Mehrez and F. Pecheux
rawtitle: {GAF}: a portable standard-cell floating point adder generator using the {CXgen} function library
entry:
@Article{Compan:1991:GPS,
  author =       "A. Compan and P. Debaud and V. Delorme and J. A.
                 Fran{\c{c}}ois and H. Mehrez and F. Pecheux",
  title =        "{GAF}: a portable standard-cell floating point adder
                 generator using the {CXgen} function library",
  journal =      j-MICROPROC-MICROPROG,
  volume =       "32",
  number =       "1",
  pages =        "637--644",
  month =        aug,
  year =         "1991",
  CODEN =        "MMICDT",
  ISSN =         "0165-6074 (print), 1878-7061 (electronic)",
  ISSN-L =       "0165-6074",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Microprocessing and Microprogramming",
  journal-URL =  "https://www.sciencedirect.com/journal/microprocessing-and-microprogramming/issues",
}


bibtype: book
filename: fparith.bib
label: Counihan:1991:F
author: Martin Counihan
title: Fortran 90
publisher: pub-PITMAN
address: pub-PITMAN:adr
pages: 309
year: 1991
ISBN: 0-273-03073-6 OR 0273030736
ISBN13: 978-0-273-03073-7 OR 9780273030737
LCCN: QA76.73.F25 C68 1991
bibdate: Sun May 02 07:48:16 1999
bibtimestamp: 1999.05.02 07:48:16 ???
note: See cite ANSI:ftn92.
acknowledgement: ack-nhfb
rawauthor: Martin Counihan
rawnote: See \cite{ANSI:ftn92}.
rawtitle: {Fortran 90}
bibsource:
https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/master.bib

keywords:
Fortran 90 (computer program language); Programming languages; Fortran 90 (Computer program language)

TOC:
1: Introduction 1.1: Fortran 90 / 1 1.2: Programs and Programming / 2 2: What is Fortran 90? 2.1: Program Structure / 5 2.2: Intrinsic Procedures / 6 2.3: Statement Types / 7 2.4: What Fortran 90 Isn't / 7 2.5: New Features in Fortran 90 / 8 Notes / 10 3: Getting Started 3.1: The Character Set / 11 3.2: A Simple Program / 14 3.3: Arithmetic Operators / 18 Exercises 3A / 19 3.4: Names and Other Lexical Tokens / 20 3.5: Fortran Source Form / 21 Exercises 3B / 24 Notes / 25 4: Intrinsic Data Types 4.1: Integers / 26 4.2: Real Numbers / 29 Exercises A / 31 4.3: Simple Form of the Type Declaration Statement / 32 4.4: Kinds Real Numbers / 32 4.5: Complex Numbers / 33 4.6: Logical Data; Logical and Relational Operators / 35 4.7: Characters and Strings / 38 Exercises 4B / 40 Notes / 42 5: Some Intrinsic Procedures 5.1: An Intrinsic Subroutine / 43 5.2: Mathematical Functions / 44 5.3: Numeric Functions / 46 Exercises 5A / 50 Notes / 52 6: More About Characters 6.1: Declaring Character Data / 53 6.2: Character Constants / 54 6.3: Character Operators / 55 6.4: Intrinsic Character Functions / 56 6.5: Substrings / 59 Exercises / 61 Notes / 62 7: Arrays 7.1: Declaring Arrays / 63 7.2: Using Arrays / 65 7.3: Array Constructors / 67 7.4: Array Sections / 68 7.5: Array Sections, Character Strings and Substrings / 70 7.6: Where / 72 7.7: Arrays and Intrinsic Functions / 73 Exercises 7B / 74 8: Execution Control 8.1: The ``CASE'' Construct / 76 8.2: The ``IF'' Construct / 80 Exercises / 81 8.3: The ``DO'' Construct / 82 8.4: Stop / 88 Exercises 8B / 88 Notes / 89 9: Functions and Subroutines (1) 9.1: Functions / 90 Exercises 9A / 93 9.2: Subroutines / 93 9.3: Procedures and Arrays / 96 Exercises 9B / 99 Notes / 100 10: More Intrinsic Procedures; Statement Labels 10.1: Intrinsic Subroutines / 102 10.2: Functions for Use with Arrays / 104 Exercises 10A / 110 10.3: Numeric Inquiry Functions and Floating-Point Manipulation Functions / 110 10.4: Statement Labels and ``GO TO'' / 111 Notes / 114 11: Modules 11.1: Data Modules / 116 Module Procedures / 120 11.3: More About ``USE'' Statements / 124 Exercises / 126 Notes / 127 12: Functions and Subroutines (2) 12.1: Recursive Procedures / 128 Exercises 12A / 130 12.2: Interface Blocks / 131 12.3: Argument Keywords / 132 12.4: More About Arguments: ``PRESENT'' / 133 12.5: Functions / 134 12.6: Operators / 135 12.7: Generic Names / 138 12.8: Parallel Processing / 141 Exercises 12B / 142 Notes / 143 13: The Type Declaration Statement 13.1: General Form of the TDS / 144 13.2: Character Length Selectors / 147 13.3: Attribute Specifications / 149 13.4: Array Specifications / 152 13.5: The Entity Declaration List / 157 13.6: Summary / 158 Exercises 13A / 159 Notes / 161 14: Derived Types 14.1: Derived-Type Definition / 164 14.2: Structure Constructors / 166 14.3: Structure Components / 168 Exercises 14A / 169 14.4: Structures of Structures / 170 Exercises 14B / 171 14.5: Functions and Operators with Derived Types / 172 14.6: Defined Assignment / 174 Exercises 14C / 178 Notes / 180 15: Arrays and Pointers 15.1: Array Element Order, Array Constructors; RESHAPE / 181 15.2: Vector Subscripts / 184 15.3: Allocatable Arrays / 187 Exercises 15A / 190 15.4: LBOUND, SHAPE and SIZE / 190 Exercises 15B / 191 15.5: Simple Pointers / 192 15.6: Pointers as Structures and as Structure Components / 197 15.7: Pointers and Procedures / 204 15.8: Array Pointers / 205 Exercises 15C / 207 Notes / 208 16: Input and Output; Data Format Specifications 16.1: Data Transfer Statements / 209 16.2: The Item List / 210 16.3: List-Directed Input / 212 16.4: List-Directed Output / 216 16.5: Explicit Formats / 217 Exercises 16A / 219 16.6: Data Edit Descriptors and Character Edit Descriptors / 219 16.7: Control Edit Descriptors / 223 Exercises 16B / 225 16.8: Namelists / 226 16.9: Unformatted / 228 16.10: The TRANSFER Function / 229 16.11: Summary / 231 Notes / 232 17: File Handling 17.1: Units, Files and Records / 233 17.2: Opening and Closing Files / 235 17.3: BACKSPACE, ENDFTLE and REWIND / 240 17.4: Control Specifications for / 240 17.5: The ``INQUIRE'' Statement / 242 17.6: Internal Files / 246 Exercises 17A / 248 Notes / 249 18: Bits 18.1: Inside Integers / 250 18.2: Bit Logic / 251 18.3: A Warning / 252 Exercises 18A / 253 19: Programming Conventions and Program Architecture: Putting It All Together 19.1: Coding Conventions / 254 19.2: Towards Fortran 90 / 255 Fortran 90 Recommended Statements / 256 Intrinsic Functions / 257 19.3: Program Unit Structure / 258 19.4: Program Structure / 261 19.5: Final Remarks / 262 Answers to Selected Exercises / 263 Appendices A: Fortran 90 Statements B: Intrinsic Procedures / 286 C: Intrinsic Procedures: Names / 292 D: Argument Keywords in Intrinsic Procedures / 294 E: Edit Descriptors / 297 F: The ASCII Character Set / 301 Index / 304

rawTOC:
1: Introduction \\ 1.1: Fortran 90 / 1 \\ 1.2: Programs and Programming / 2 \\ 2: What is Fortran 90? \\ 2.1: Program Structure / 5 \\ 2.2: Intrinsic Procedures / 6 \\ 2.3: Statement Types / 7 \\ 2.4: What Fortran 90 Isn't / 7 \\ 2.5: New Features in Fortran 90 / 8 \\ Notes / 10 \\ 3: Getting Started \\ 3.1: The Character Set / 11 \\ 3.2: A Simple Program / 14 \\ 3.3: Arithmetic Operators / 18 \\ Exercises 3A / 19 \\ 3.4: Names and Other Lexical Tokens / 20 \\ 3.5: Fortran Source Form / 21 \\ Exercises 3B / 24 \\ Notes / 25 \\ 4: Intrinsic Data Types \\ 4.1: Integers / 26 \\ 4.2: Real Numbers / 29 \\ Exercises A / 31 \\ 4.3: Simple Form of the Type Declaration Statement / 32 \\ 4.4: Kinds Real Numbers / 32 \\ 4.5: Complex Numbers / 33 \\ 4.6: Logical Data; Logical and Relational Operators / 35 \\ 4.7: Characters and Strings / 38 \\ Exercises 4B / 40 \\ Notes / 42 \\ 5: Some Intrinsic Procedures \\ 5.1: An Intrinsic Subroutine / 43 \\ 5.2: Mathematical Functions / 44 \\ 5.3: Numeric Functions / 46 \\ Exercises 5A / 50 \\ Notes / 52 \\ 6: More About Characters \\ 6.1: Declaring Character Data / 53 \\ 6.2: Character Constants / 54 \\ 6.3: Character Operators / 55 \\ 6.4: Intrinsic Character Functions / 56 \\ 6.5: Substrings / 59 \\ Exercises / 61 \\ Notes / 62 \\ 7: Arrays \\ 7.1: Declaring Arrays / 63 \\ 7.2: Using Arrays / 65 \\ 7.3: Array Constructors / 67 \\ 7.4: Array Sections / 68 \\ 7.5: Array Sections, Character Strings and Substrings / 70 \\ 7.6: Where / 72 \\ 7.7: Arrays and Intrinsic Functions / 73 \\ Exercises 7B / 74 \\ 8: Execution Control \\ 8.1: The ``CASE'' Construct / 76 \\ 8.2: The ``IF'' Construct / 80 \\ Exercises / 81 \\ 8.3: The ``DO'' Construct / 82 \\ 8.4: Stop / 88 \\ Exercises 8B / 88 \\ Notes / 89 \\ 9: Functions and Subroutines (1) \\ 9.1: Functions / 90 \\ Exercises 9A / 93 \\ 9.2: Subroutines / 93 \\ 9.3: Procedures and Arrays / 96 \\ Exercises 9B / 99 \\ Notes / 100 \\ 10: More Intrinsic Procedures; Statement Labels \\ 10.1: Intrinsic Subroutines / 102 \\ 10.2: Functions for Use with Arrays / 104 \\ Exercises 10A / 110 \\ 10.3: Numeric Inquiry Functions and Floating-Point Manipulation Functions / 110 \\ 10.4: Statement Labels and ``GO TO'' / 111 \\ Notes / 114 \\ 11: Modules \\ 11.1: Data Modules / 116 \\ Module Procedures / 120 \\ 11.3: More About ``USE'' Statements / 124 \\ Exercises / 126 \\ Notes / 127 \\ 12: Functions and Subroutines (2) \\ 12.1: Recursive Procedures / 128 \\ Exercises 12A / 130 \\ 12.2: Interface Blocks / 131 \\ 12.3: Argument Keywords / 132 \\ 12.4: More About Arguments: ``PRESENT'' / 133 \\ 12.5: Functions / 134 \\ 12.6: Operators / 135 \\ 12.7: Generic Names / 138 \\ 12.8: Parallel Processing / 141 \\ Exercises 12B / 142 \\ Notes / 143 \\ 13: The Type Declaration Statement \\ 13.1: General Form of the TDS / 144 \\ 13.2: Character Length Selectors / 147 \\ 13.3: Attribute Specifications / 149 \\ 13.4: Array Specifications / 152 \\ 13.5: The Entity Declaration List / 157 \\ 13.6: Summary / 158 \\ Exercises 13A / 159 \\ Notes / 161 \\ 14: Derived Types \\ 14.1: Derived-Type Definition / 164 \\ 14.2: Structure Constructors / 166 \\ 14.3: Structure Components / 168 \\ Exercises 14A / 169 \\ 14.4: Structures of Structures / 170 \\ Exercises 14B / 171 \\ 14.5: Functions and Operators with Derived Types / 172 \\ 14.6: Defined Assignment / 174 \\ Exercises 14C / 178 \\ Notes / 180 \\ 15: Arrays and Pointers \\ 15.1: Array Element Order, Array Constructors; RESHAPE / 181 \\ 15.2: Vector Subscripts / 184 \\ 15.3: Allocatable Arrays / 187 \\ Exercises 15A / 190 \\ 15.4: LBOUND, SHAPE and SIZE / 190 \\ Exercises 15B / 191 \\ 15.5: Simple Pointers / 192 \\ 15.6: Pointers as Structures and as Structure Components / 197 \\ 15.7: Pointers and Procedures / 204 \\ 15.8: Array Pointers / 205 \\ Exercises 15C / 207 \\ Notes / 208 \\ 16: Input and Output; Data Format Specifications \\ 16.1: Data Transfer Statements / 209 \\ 16.2: The Item List / 210 \\ 16.3: List-Directed Input / 212 \\ 16.4: List-Directed Output / 216 \\ 16.5: Explicit Formats / 217 \\ Exercises 16A / 219 \\ 16.6: Data Edit Descriptors and Character Edit Descriptors / 219 \\ 16.7: Control Edit Descriptors / 223 \\ Exercises 16B / 225 \\ 16.8: Namelists / 226 \\ 16.9: Unformatted / 228 \\ 16.10: The TRANSFER Function / 229 \\ 16.11: Summary / 231 \\ Notes / 232 \\ 17: File Handling \\ 17.1: Units, Files and Records / 233 \\ 17.2: Opening and Closing Files / 235 \\ 17.3: BACKSPACE, ENDFTLE and REWIND / 240 \\ 17.4: Control Specifications for / 240 \\ 17.5: The ``INQUIRE'' Statement / 242 \\ 17.6: Internal Files / 246 \\ Exercises 17A / 248 \\ Notes / 249 \\ 18: Bits \\ 18.1: Inside Integers / 250 \\ 18.2: Bit Logic / 251 \\ 18.3: A Warning / 252 \\ Exercises 18A / 253 \\ 19: Programming Conventions and Program Architecture: Putting It All Together \\ 19.1: Coding Conventions / 254 \\ 19.2: Towards Fortran 90 / 255 \\ Fortran 90 Recommended Statements / 256 \\ Intrinsic Functions / 257 \\ 19.3: Program Unit Structure / 258 \\ 19.4: Program Structure / 261 \\ 19.5: Final Remarks / 262 \\ Answers to Selected Exercises / 263 \\ Appendices \\ A: Fortran 90 Statements \\ B: Intrinsic Procedures / 286 \\ C: Intrinsic Procedures: Names / 292 \\ D: Argument Keywords in Intrinsic Procedures / 294 \\ E: Edit Descriptors / 297 \\ F: The ASCII Character Set / 301 \\ Index / 304

entry:
@Book{Counihan:1991:F,
  author =       "Martin Counihan",
  title =        "{Fortran 90}",
  publisher =    pub-PITMAN,
  address =      pub-PITMAN:adr,
  pages =        "309",
  year =         "1991",
  ISBN =         "0-273-03073-6",
  ISBN-13 =      "978-0-273-03073-7",
  LCCN =         "QA76.73.F25 C68 1991",
  bibdate =      "Sun May 02 07:48:16 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  note =         "See \cite{ANSI:ftn92}.",
  acknowledgement = ack-nhfb,
  keywords =     "Fortran 90 (computer program language); Programming
                 languages; {Fortran 90} (Computer program language)",
  libnote =      "Not yet in my library.",
  tableofcontents = "1: Introduction \\
                 1.1: Fortran 90 / 1 \\
                 1.2: Programs and Programming / 2 \\
                 2: What is Fortran 90? \\
                 2.1: Program Structure / 5 \\
                 2.2: Intrinsic Procedures / 6 \\
                 2.3: Statement Types / 7 \\
                 2.4: What Fortran 90 Isn't / 7 \\
                 2.5: New Features in Fortran 90 / 8 \\
                 Notes / 10 \\
                 3: Getting Started \\
                 3.1: The Character Set / 11 \\
                 3.2: A Simple Program / 14 \\
                 3.3: Arithmetic Operators / 18 \\
                 Exercises 3A / 19 \\
                 3.4: Names and Other Lexical Tokens / 20 \\
                 3.5: Fortran Source Form / 21 \\
                 Exercises 3B / 24 \\
                 Notes / 25 \\
                 4: Intrinsic Data Types \\
                 4.1: Integers / 26 \\
                 4.2: Real Numbers / 29 \\
                 Exercises A / 31 \\
                 4.3: Simple Form of the Type Declaration Statement / 32
                 \\
                 4.4: Kinds Real Numbers / 32 \\
                 4.5: Complex Numbers / 33 \\
                 4.6: Logical Data; Logical and Relational Operators /
                 35 \\
                 4.7: Characters and Strings / 38 \\
                 Exercises 4B / 40 \\
                 Notes / 42 \\
                 5: Some Intrinsic Procedures \\
                 5.1: An Intrinsic Subroutine / 43 \\
                 5.2: Mathematical Functions / 44 \\
                 5.3: Numeric Functions / 46 \\
                 Exercises 5A / 50 \\
                 Notes / 52 \\
                 6: More About Characters \\
                 6.1: Declaring Character Data / 53 \\
                 6.2: Character Constants / 54 \\
                 6.3: Character Operators / 55 \\
                 6.4: Intrinsic Character Functions / 56 \\
                 6.5: Substrings / 59 \\
                 Exercises / 61 \\
                 Notes / 62 \\
                 7: Arrays \\
                 7.1: Declaring Arrays / 63 \\
                 7.2: Using Arrays / 65 \\
                 7.3: Array Constructors / 67 \\
                 7.4: Array Sections / 68 \\
                 7.5: Array Sections, Character Strings and Substrings /
                 70 \\
                 7.6: Where / 72 \\
                 7.7: Arrays and Intrinsic Functions / 73 \\
                 Exercises 7B / 74 \\
                 8: Execution Control \\
                 8.1: The ``CASE'' Construct / 76 \\
                 8.2: The ``IF'' Construct / 80 \\
                 Exercises / 81 \\
                 8.3: The ``DO'' Construct / 82 \\
                 8.4: Stop / 88 \\
                 Exercises 8B / 88 \\
                 Notes / 89 \\
                 9: Functions and Subroutines (1) \\
                 9.1: Functions / 90 \\
                 Exercises 9A / 93 \\
                 9.2: Subroutines / 93 \\
                 9.3: Procedures and Arrays / 96 \\
                 Exercises 9B / 99 \\
                 Notes / 100 \\
                 10: More Intrinsic Procedures; Statement Labels \\
                 10.1: Intrinsic Subroutines / 102 \\
                 10.2: Functions for Use with Arrays / 104 \\
                 Exercises 10A / 110 \\
                 10.3: Numeric Inquiry Functions and Floating-Point
                 Manipulation Functions / 110 \\
                 10.4: Statement Labels and ``GO TO'' / 111 \\
                 Notes / 114 \\
                 11: Modules \\
                 11.1: Data Modules / 116 \\
                 Module Procedures / 120 \\
                 11.3: More About ``USE'' Statements / 124 \\
                 Exercises / 126 \\
                 Notes / 127 \\
                 12: Functions and Subroutines (2) \\
                 12.1: Recursive Procedures / 128 \\
                 Exercises 12A / 130 \\
                 12.2: Interface Blocks / 131 \\
                 12.3: Argument Keywords / 132 \\
                 12.4: More About Arguments: ``PRESENT'' / 133 \\
                 12.5: Functions / 134 \\
                 12.6: Operators / 135 \\
                 12.7: Generic Names / 138 \\
                 12.8: Parallel Processing / 141 \\
                 Exercises 12B / 142 \\
                 Notes / 143 \\
                 13: The Type Declaration Statement \\
                 13.1: General Form of the TDS / 144 \\
                 13.2: Character Length Selectors / 147 \\
                 13.3: Attribute Specifications / 149 \\
                 13.4: Array Specifications / 152 \\
                 13.5: The Entity Declaration List / 157 \\
                 13.6: Summary / 158 \\
                 Exercises 13A / 159 \\
                 Notes / 161 \\
                 14: Derived Types \\
                 14.1: Derived-Type Definition / 164 \\
                 14.2: Structure Constructors / 166 \\
                 14.3: Structure Components / 168 \\
                 Exercises 14A / 169 \\
                 14.4: Structures of Structures / 170 \\
                 Exercises 14B / 171 \\
                 14.5: Functions and Operators with Derived Types / 172
                 \\
                 14.6: Defined Assignment / 174 \\
                 Exercises 14C / 178 \\
                 Notes / 180 \\
                 15: Arrays and Pointers \\
                 15.1: Array Element Order, Array Constructors; RESHAPE
                 / 181 \\
                 15.2: Vector Subscripts / 184 \\
                 15.3: Allocatable Arrays / 187 \\
                 Exercises 15A / 190 \\
                 15.4: LBOUND, SHAPE and SIZE / 190 \\
                 Exercises 15B / 191 \\
                 15.5: Simple Pointers / 192 \\
                 15.6: Pointers as Structures and as Structure
                 Components / 197 \\
                 15.7: Pointers and Procedures / 204 \\
                 15.8: Array Pointers / 205 \\
                 Exercises 15C / 207 \\
                 Notes / 208 \\
                 16: Input and Output; Data Format Specifications \\
                 16.1: Data Transfer Statements / 209 \\
                 16.2: The Item List / 210 \\
                 16.3: List-Directed Input / 212 \\
                 16.4: List-Directed Output / 216 \\
                 16.5: Explicit Formats / 217 \\
                 Exercises 16A / 219 \\
                 16.6: Data Edit Descriptors and Character Edit
                 Descriptors / 219 \\
                 16.7: Control Edit Descriptors / 223 \\
                 Exercises 16B / 225 \\
                 16.8: Namelists / 226 \\
                 16.9: Unformatted / 228 \\
                 16.10: The TRANSFER Function / 229 \\
                 16.11: Summary / 231 \\
                 Notes / 232 \\
                 17: File Handling \\
                 17.1: Units, Files and Records / 233 \\
                 17.2: Opening and Closing Files / 235 \\
                 17.3: BACKSPACE, ENDFTLE and REWIND / 240 \\
                 17.4: Control Specifications for / 240 \\
                 17.5: The ``INQUIRE'' Statement / 242 \\
                 17.6: Internal Files / 246 \\
                 Exercises 17A / 248 \\
                 Notes / 249 \\
                 18: Bits \\
                 18.1: Inside Integers / 250 \\
                 18.2: Bit Logic / 251 \\
                 18.3: A Warning / 252 \\
                 Exercises 18A / 253 \\
                 19: Programming Conventions and Program Architecture:
                 Putting It All Together \\
                 19.1: Coding Conventions / 254 \\
                 19.2: Towards Fortran 90 / 255 \\
                 Fortran 90 Recommended Statements / 256 \\
                 Intrinsic Functions / 257 \\
                 19.3: Program Unit Structure / 258 \\
                 19.4: Program Structure / 261 \\
                 19.5: Final Remarks / 262 \\
                 Answers to Selected Exercises / 263 \\
                 Appendices \\
                 A: Fortran 90 Statements \\
                 B: Intrinsic Procedures / 286 \\
                 C: Intrinsic Procedures: Names / 292 \\
                 D: Argument Keywords in Intrinsic Procedures / 294 \\
                 E: Edit Descriptors / 297 \\
                 F: The ASCII Character Set / 301 \\
                 Index / 304",
}


bibtype: article
filename: fparith.bib
label: Cox:1991:TSS
author: Christopher L. Cox and James A. Knisely
title: A tridiagonal system solver for distributed memory parallel processors with vector nodes
journal: j-J-PAR-DIST-COMP
volume: 13
number: 3
pages: 325--331
month: nov
monthnumber: 11
year: 1991
CODEN: JPDCER
ISSN: 0743-7315 (print), 1096-0848 (electronic) OR 07437315 (print), 10960848 (electronic)
ISSNL: 0743-7315 OR 07437315
bibdate: Sat Apr 12 19:06:31 MDT 1997
bibsource: Compendex database; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.04.12 19:06:31 MDT
fjournal: Journal of Parallel and Distributed Computing
acknowledgement: ack-nhfb
affiliation: Clemson Univ
affiliationaddress: Clemson, SC, USA
corpsource: Department of Math. Sci., Clemson University, SC, USA
journalURL: http://www.sciencedirect.com/science/journal/07437315
journalabr: J Parallel Distrib Comput
treatment: A Application; P Practical
rawauthor: Christopher L. Cox and James A. Knisely
rawtitle: A tridiagonal system solver for distributed memory parallel processors with vector nodes
keywords:
algebraic routine; algorithm; computer; Computer Programming languages--fortran; Computer Programming--Algorithms; Computer Systems, Digital; Cyclic reduction algorithms; Data Storage, Digital; digital arithmetic; Distributed memories; distributed memory parallel; divide and conquer strategy; Floating Point Systems FPS T-20; FORTRAN; Intel iPSC/2-VX; linear algebra; Mathematical Techniques--Matrix Algebra; mathematics computing; odd-even cyclic reduction; parallel architectures; Parallel Processing; partitioning; performance evaluation; processors; programs; redundancy; scaled speedup; tridiagonal system solver; Tridiagonal systems; Vector nodes; vector nodes; vector processors

entry:
@Article{Cox:1991:TSS,
  author =       "Christopher L. Cox and James A. Knisely",
  title =        "A tridiagonal system solver for distributed memory
                 parallel processors with vector nodes",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "13",
  number =       "3",
  pages =        "325--331",
  month =        nov,
  year =         "1991",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Sat Apr 12 19:06:31 MDT 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Clemson Univ",
  affiliationaddress = "Clemson, SC, USA",
  classification = "721; 722; 723; 921; C4140 (Linear algebra); C5220P
                 (Parallel architecture); C5230 (Digital arithmetic
                 methods); C5470 (Performance evaluation and testing);
                 C7310 (Mathematics)",
  corpsource =   "Department of Math. Sci., Clemson University, SC,
                 USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "algebraic routine; algorithm; computer; Computer
                 Programming languages--fortran; Computer
                 Programming--Algorithms; Computer Systems, Digital;
                 Cyclic reduction algorithms; Data Storage, Digital;
                 digital arithmetic; Distributed memories; distributed
                 memory parallel; divide and conquer strategy; Floating
                 Point Systems FPS T-20; FORTRAN; Intel iPSC/2-VX;
                 linear algebra; Mathematical Techniques--Matrix
                 Algebra; mathematics computing; odd-even cyclic
                 reduction; parallel architectures; Parallel Processing;
                 partitioning; performance evaluation; processors;
                 programs; redundancy; scaled speedup; tridiagonal
                 system solver; Tridiagonal systems; Vector nodes;
                 vector nodes; vector processors",
  treatment =    "A Application; P Practical",
}


bibtype: article
filename: fparith.bib
label: Crenshaw:1991:SRS
author: J. W. Crenshaw
title: Square roots are simple?
journal: j-EMBED-SYS-PROG
volume: 4
number: 11
pages: 30--52
month: nov
monthnumber: 11
year: 1991
CODEN: EYPRE4
ISSN: 1040-3272 OR 10403272
bibdate: Wed Sep 14 19:14:52 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 19:14:52 ???
fjournal: Embedded Systems Programming
acknowledgement: ack-nj
rawauthor: J. W. Crenshaw
rawtitle: Square roots are simple?
entry:
@Article{Crenshaw:1991:SRS,
  author =       "J. W. Crenshaw",
  title =        "Square roots are simple?",
  journal =      j-EMBED-SYS-PROG,
  volume =       "4",
  number =       "11",
  pages =        "30--52",
  month =        nov,
  year =         "1991",
  CODEN =        "EYPRE4",
  ISSN =         "1040-3272",
  bibdate =      "Wed Sep 14 19:14:52 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 =     "Embedded Systems Programming",
}


bibtype: article
filename: fparith.bib
label: Davida:1991:FPA
author: George I. Davida and Bruce Litow
title: Fast Parallel Arithmetic via Modular Representation
journal: j-SIAM-J-COMPUT
volume: 20
number: 4
pages: 756--765
month: aug
monthnumber: 8
year: 1991
CODEN: SMJCAT
ISSN: 0097-5397 (print), 1095-7111 (electronic) OR 00975397 (print), 10957111 (electronic)
ISSNL: 0097-5397 OR 00975397
MRclass: 68Q10
MRnumber: 92c:68046
bibdate: Mon Nov 29 11:01:48 MST 2010
bibtimestamp: 2010.11.29 11:01:48 MST
fjournal: SIAM Journal on Computing
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sicomp
rawauthor: George I. Davida and Bruce Litow
rawtitle: Fast Parallel Arithmetic via Modular Representation
bibsource:
http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/20/4; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Davida:1991:FPA,
  author =       "George I. Davida and Bruce Litow",
  title =        "Fast Parallel Arithmetic via Modular Representation",
  journal =      j-SIAM-J-COMPUT,
  volume =       "20",
  number =       "4",
  pages =        "756--765",
  month =        aug,
  year =         "1991",
  CODEN =        "SMJCAT",
  ISSN =         "0097-5397 (print), 1095-7111 (electronic)",
  ISSN-L =       "0097-5397",
  MRclass =      "68Q10",
  MRnumber =     "92c:68046",
  bibdate =      "Mon Nov 29 11:01:48 MST 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/20/4;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Computing",
  journal-URL =  "http://epubs.siam.org/sicomp",
}


bibtype: mastersthesis
filename: fparith.bib
label: Davies:1991:FPS
author: Davies, T. C. (Tudor Craddock)
title: A floating point systolic array processing element using serial communication
type: Thesis (M.Eng.)
school: Royal Military College of Canada
address: Kingston, ON, Canada
pages: 756--765
year: 1991
ISBN: 0-315-60644-4 OR 0315606444
ISBN13: 978-0-315-60644-9 OR 9780315606449
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: 2 microfiches. University Microfilms order no. UMI00285885
series: National Library of Canada = Bibliotheque nationale du Canada; Canadian theses = Theses canadiennes
acknowledgement: ack-nhfb
rawauthor: Davies, T. C. (Tudor Craddock)
rawnote: 2 microfiches. University Microfilms order no. UMI00285885
rawtitle: A floating point systolic array processing element using serial communication
entry:
@MastersThesis{Davies:1991:FPS,
  author =       "Davies, T. C. (Tudor Craddock)",
  title =        "A floating point systolic array processing element
                 using serial communication",
  type =         "Thesis ({M.Eng.})",
  school =       "Royal Military College of Canada",
  address =      "Kingston, ON, Canada",
  year =         "1991",
  ISBN =         "0-315-60644-4",
  ISBN-13 =      "978-0-315-60644-9",
  LCCN =         "????",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "2 microfiches. University Microfilms order no.
                 UMI00285885",
  series =       "National Library of Canada = Bibliotheque nationale du
                 Canada; Canadian theses = Theses canadiennes",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Davis:1991:CC
author: Warren Davis and Kan Yabumoto
title: A coprocessor for a coprocessor?
journal: j-DDJ
volume: 16
number: 5
pages: 16--28, 84--88
month: may
monthnumber: 5
year: 1991
CODEN: DDJOEB
ISSN: 1044-789X OR 1044789X
bibdate: Tue Sep 10 09:11:02 MDT 1996
bibtimestamp: 1996.09.10 09:11:02 MDT
fjournal: Dr. Dobb's Journal of Software Tools
acknowledgement: ack-nhfb
affiliation: Pixelab Inc., Lisle, IL, USA
rawauthor: Warren Davis and Kan Yabumoto
rawtitle: A coprocessor for a coprocessor?
bibsource:
http://www.ddj.com/index/author/index.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib; UnCover database

abstract:
When fast graphics aren't fast enough, the TI 34020 graphics coprocessor employs its own coprocessor -- the 34082 FPU -- for even higher system performance.

keywords:
Built-in graphics-related instructions; Floating point coprocessor; General-purpose microprocessor; Graphics System Processor; Programmable graphics coprocessor; Texas Instruments; TMS34020; TMS34082; Video control circuitry

thesaurus:
Assembly language listings; C listings; Computer graphic equipment; Microprocessor chips; Satellite computers; Texas Instruments computers

rawabstract:
When fast graphics aren't fast enough, the TI 34020 graphics coprocessor employs its own coprocessor -- the 34082 FPU -- for even higher system performance.

entry:
@Article{Davis:1991:CC,
  author =       "Warren Davis and Kan Yabumoto",
  title =        "A coprocessor for a coprocessor?",
  journal =      j-DDJ,
  volume =       "16",
  number =       "5",
  pages =        "16--28, 84--88",
  month =        may,
  year =         "1991",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Tue Sep 10 09:11:02 MDT 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 UnCover database",
  abstract =     "When fast graphics aren't fast enough, the TI 34020
                 graphics coprocessor employs its own coprocessor -- the
                 34082 FPU -- for even higher system performance.",
  acknowledgement = ack-nhfb,
  affiliation =  "Pixelab Inc., Lisle, IL, USA",
  classification = "C5130 (Microprocessor chips); C5540 (Terminals and
                 graphic displays)",
  fjournal =     "Dr. Dobb's Journal of Software Tools",
  keywords =     "Built-in graphics-related instructions; Floating point
                 coprocessor; General-purpose microprocessor; Graphics
                 System Processor; Programmable graphics coprocessor;
                 Texas Instruments; TMS34020; TMS34082; Video control
                 circuitry",
  thesaurus =    "Assembly language listings; C listings; Computer
                 graphic equipment; Microprocessor chips; Satellite
                 computers; Texas Instruments computers",
}


bibtype: phdthesis
filename: fparith.bib
label: Deb:1991:BFF
author: Kalyanmoy Deb
title: Binary and floating-point function optimization using messy genetic algorithms
type: Thesis (Ph.D.)
school: Department of Engineering Mechanics, University of Alabama
address: Tuscaloosa, AL, USA
pages: xvii + 166
year: 1991
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: Algorithms.; Combinatorial optimization.
acknowledgement: ack-nhfb
rawauthor: Kalyanmoy Deb
rawtitle: Binary and floating-point function optimization using messy genetic algorithms
entry:
@PhdThesis{Deb:1991:BFF,
  author =       "Kalyanmoy Deb",
  title =        "Binary and floating-point function optimization using
                 messy genetic algorithms",
  type =         "Thesis ({Ph.D.})",
  school =       "Department of Engineering Mechanics, University of
                 Alabama",
  address =      "Tuscaloosa, AL, USA",
  pages =        "xvii + 166",
  year =         "1991",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Algorithms.; Combinatorial optimization.",
}


bibtype: inproceedings
filename: fparith.bib
label: deLange:1991:DIF
author: Alfons A. J. de Lange and Ed F. Deprettere
crossref: Kornerup:1991:PIS
pages: 272--281
year: 1991
bibdate: Sat Nov 27 12:40:58 MST 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.27 12:40:58 MST
URL: http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Lange.pdf
keywords: ARITH-10
acknowledgement: ack-nhfb
rawauthor: Alfons A. J. de Lange and Ed F. Deprettere
title:
Design and implementation of a floating-point quasi-systolic general purpose CORDIC rotator for high-rate parallel data and signal processing

rawtitle:
Design and implementation of a floating-point quasi-systolic general purpose {CORDIC} rotator for high-rate parallel data and signal processing

entry:
@InProceedings{deLange:1991:DIF,
  author =       "Alfons A. J. de Lange and Ed F. Deprettere",
  title =        "Design and implementation of a floating-point
                 quasi-systolic general purpose {CORDIC} rotator for
                 high-rate parallel data and signal processing",
  crossref =     "Kornerup:1991:PIS",
  pages =        "272--281",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Lange.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}


bibtype: article
filename: fparith.bib
label: Demmel:1991:OIA
author: James W. Demmel
title: On the odor of IEEE arithmetic
journal: j-NA-DIGEST
volume: 91
number: 39
pages: 272--281
day: 29
month: sep
monthnumber: 9
year: 1991
bibdate: Thu Aug 23 06:19:41 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.08.23 06:19:41 ???
note: Rebuttal to cite Grcar:1991:IAS.
URL: http://www.netlib.org/na-digest/91/v91n39
fjournal: NA Digest
acknowledgement: ack-nhfb
rawauthor: James W. Demmel
rawnote: Rebuttal to \cite{Grcar:1991:IAS}.
rawtitle: On the odor of {IEEE} arithmetic
entry:
@Article{Demmel:1991:OIA,
  author =       "James W. Demmel",
  title =        "On the odor of {IEEE} arithmetic",
  journal =      j-NA-DIGEST,
  volume =       "91",
  number =       "39",
  day =          "29",
  month =        sep,
  year =         "1991",
  bibdate =      "Thu Aug 23 06:19:41 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Rebuttal to \cite{Grcar:1991:IAS}.",
  URL =          "http://www.netlib.org/na-digest/91/v91n39",
  acknowledgement = ack-nhfb,
  fjournal =     "NA Digest",
}


bibtype: inproceedings
filename: fparith.bib
label: Dongarra:1991:GBP
author: J. J. Dongarra and A. Karp and K. Miura and H. D. Simon
title: Gordon Bell Prize lectures (supercomputer applications)
crossref: IEEE:1991:PSA
pages: 328--337
year: 1991
bibdate: Wed Apr 15 16:28:01 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.04.15 16:28:01 MDT
acknowledgement: ack-nhfb
corpsource: Department of Computer Science, Tennessee University, Knoxville, TN, USA
treatment: G General Review; P Practical
rawauthor: J. J. Dongarra and A. Karp and K. Miura and H. D. Simon
rawtitle: {Gordon Bell Prize} lectures (supercomputer applications)
keywords:
128-node Intel iPSC/860; compiler speedup; Connections Machine; electronic structure; floating point processors; Fortran 77; Fortran 90; grid generation program; parallel processing; partial differential equation; price/performance award; scientific and engineering problems; supercomputers

entry:
@InProceedings{Dongarra:1991:GBP,
  author =       "J. J. Dongarra and A. Karp and K. Miura and H. D.
                 Simon",
  title =        "{Gordon Bell Prize} lectures (supercomputer
                 applications)",
  crossref =     "IEEE:1991:PSA",
  pages =        "328--337",
  year =         "1991",
  bibdate =      "Wed Apr 15 16:28:01 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C5440 (Multiprocessor systems and techniques)",
  corpsource =   "Department of Computer Science, Tennessee University,
                 Knoxville, TN, USA",
  keywords =     "128-node Intel iPSC/860; compiler speedup; Connections
                 Machine; electronic structure; floating point
                 processors; Fortran 77; Fortran 90; grid generation
                 program; parallel processing; partial differential
                 equation; price/performance award; scientific and
                 engineering problems; supercomputers",
  sponsororg =   "IEEE; ACM",
  treatment =    "G General Review; P Practical",
}


bibtype: article
filename: fparith.bib
label: Dunham:1991:ABA
author: C. Dunham
title: Applications of Best Approximation
journal: j-SIGNUM
volume: 26
number: 2
pages: 2--10
month: apr
monthnumber: 4
year: 1991
CODEN: SNEWD6
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Thu Sep 1 10:15:40 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:15:40 ???
fjournal: ACM SIGNUM Newsletter
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/signum
rawauthor: C. Dunham
rawtitle: Applications of Best Approximation
entry:
@Article{Dunham:1991:ABA,
  author =       "C. Dunham",
  title =        "Applications of Best Approximation",
  journal =      j-SIGNUM,
  volume =       "26",
  number =       "2",
  pages =        "2--10",
  month =        apr,
  year =         "1991",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Thu Sep 1 10:15:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
}


bibtype: inproceedings
filename: fparith.bib
label: Duprat:1991:NRR
author: Jean Duprat and Yvan Herreros and Sylvanus Kla
title: New redundant representations of complex numbers and vectors
crossref: Kornerup:1991:PIS
pages: 2--9
year: 1991
bibdate: Sat Nov 27 12:40:58 MST 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.27 12:40:58 MST
URL: http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Duprat.pdf
keywords: ARITH-10
acknowledgement: ack-nhfb
rawauthor: Jean Duprat and Yvan Herreros and Sylvanus Kla
rawtitle: New redundant representations of complex numbers and vectors
entry:
@InProceedings{Duprat:1991:NRR,
  author =       "Jean Duprat and Yvan Herreros and Sylvanus Kla",
  title =        "New redundant representations of complex numbers and
                 vectors",
  crossref =     "Kornerup:1991:PIS",
  pages =        "2--9",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Duprat.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}


bibtype: article
filename: fparith.bib
label: Duprat:1991:WND
author: J. Duprat and Jean-Michel Muller
title: Writing numbers differently for faster calculation
journal: j-TECHNIQUE-SCI-INFORMATIQUES
volume: 10
number: 3
pages: 211--224
year: 1991
CODEN: TTSIDJ
ISSN: 0752-4072, 0264-7419 OR 07524072, 02647419
ISSNL: 0752-4072 OR 07524072
bibdate: Tue Dec 12 09:20:21 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.12 09:20:21 MST
fjournal: Technique et science informatiques : TSI
language: French
acknowledgement: ack-nhfb
affiliation: Ecole Normale Superieure de Lyon, France
thesaurus: Digital arithmetic
rawauthor: J. Duprat and Jean-Michel Muller
rawtitle: Writing numbers differently for faster calculation
abstract:
Instead of Avizienis' or the carry save methods a borrow save (BS) notation is proposed. Examples are given of BS addition, subtraction, shifting and multiplication with the necessary elementary cells being proposed and circuits for testing zero and sign being described. Floating point arithmetic is explained, involving pseudo normalisation and applications are covered including the Cordic algorithm.

keywords:
Addition; Borrow save; Carry save methods; Cordic algorithm; Floating point arithmetic; Multiplication; Pseudo normalisation; Shifting; Subtraction; Zero

rawabstract:
Instead of Avizienis' or the carry save methods a borrow save (BS) notation is proposed. Examples are given of BS addition, subtraction, shifting and multiplication with the necessary elementary cells being proposed and circuits for testing zero and sign being described. Floating point arithmetic is explained, involving pseudo normalisation and applications are covered including the Cordic algorithm.

entry:
@Article{Duprat:1991:WND,
  author =       "J. Duprat and Jean-Michel Muller",
  title =        "Writing numbers differently for faster calculation",
  journal =      j-TECHNIQUE-SCI-INFORMATIQUES,
  volume =       "10",
  number =       "3",
  pages =        "211--224",
  month =        "????",
  year =         "1991",
  CODEN =        "TTSIDJ",
  ISSN =         "0752-4072, 0264-7419",
  ISSN-L =       "0752-4072",
  bibdate =      "Tue Dec 12 09:20:21 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Instead of Avizienis' or the carry save methods a
                 borrow save (BS) notation is proposed. Examples are
                 given of BS addition, subtraction, shifting and
                 multiplication with the necessary elementary cells
                 being proposed and circuits for testing zero and sign
                 being described. Floating point arithmetic is
                 explained, involving pseudo normalisation and
                 applications are covered including the Cordic
                 algorithm.",
  acknowledgement = ack-nhfb,
  affiliation =  "Ecole Normale Superieure de Lyon, France",
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "Technique et science informatiques : TSI",
  keywords =     "Addition; Borrow save; Carry save methods; Cordic
                 algorithm; Floating point arithmetic; Multiplication;
                 Pseudo normalisation; Shifting; Subtraction; Zero",
  language =     "French",
  pubcountry =   "France",
  thesaurus =    "Digital arithmetic",
}


bibtype: article
filename: fparith.bib
label: Ercegovac:1991:MPM
author: Milos D. Ercegovac and Tomas Lang
journal: j-J-PAR-DIST-COMP
volume: 11
number: 3
pages: 212--221
month: mar
monthnumber: 3
year: 1991
CODEN: JPDCER
ISSN: 0743-7315 (print), 1096-0848 (electronic) OR 07437315 (print), 10960848 (electronic)
ISSNL: 0743-7315 OR 07437315
bibdate: Sat Apr 12 19:06:31 MDT 1997
bibsource: Compendex database; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.04.12 19:06:31 MDT
fjournal: Journal of Parallel and Distributed Computing
acknowledgement: ack-nhfb
affiliation: Univ of California Los Angeles
affiliationaddress: Los Angeles, CA, USA
corpsource: Department of Computer Science, California University, Los Angeles, CA, USA
journalURL: http://www.sciencedirect.com/science/journal/07437315
journalabr: J Parallel Distrib Comput
treatment: P Practical
rawauthor: Milo{\v{s}} D. Ercegovac and Tomas Lang
title:
Module to perform multiplication, division, and square root in systolic arrays for matrix computations

keywords:
Applications; carry-save; complexity; Computer Programming --- Algorithms; Computers; digital arithmetic; division; matrix algebra; Matrix Computations; matrix computations; module; multiplication; Multiplication/Division/Square Root Module; Normalization; On-The-Fly Conversion; radix-2 divider; result-digit selection; Rounding; signed-digit; square root; Systolic Arrays; systolic arrays

rawtitle:
Module to perform multiplication, division, and square root in systolic arrays for matrix computations

entry:
@Article{Ercegovac:1991:MPM,
  author =       "Milo{\v{s}} D. Ercegovac and Tomas Lang",
  title =        "Module to perform multiplication, division, and square
                 root in systolic arrays for matrix computations",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "11",
  number =       "3",
  pages =        "212--221",
  month =        mar,
  year =         "1991",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Sat Apr 12 19:06:31 MDT 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ of California Los Angeles",
  affiliationaddress = "Los Angeles, CA, USA",
  classification = "722; 723; 921; C4140 (Linear algebra); C5220
                 (Computer architecture); C5230 (Digital arithmetic
                 methods)",
  corpsource =   "Department of Computer Science, California University,
                 Los Angeles, CA, USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "Applications; carry-save; complexity; Computer
                 Programming --- Algorithms; Computers; digital
                 arithmetic; division; matrix algebra; Matrix
                 Computations; matrix computations; module;
                 multiplication; Multiplication/Division/Square Root
                 Module; Normalization; On-The-Fly Conversion; radix-2
                 divider; result-digit selection; Rounding;
                 signed-digit; square root; Systolic Arrays; systolic
                 arrays",
  treatment =    "P Practical",
}


bibtype: article
filename: fparith.bib
label: Even:1991:SMM
author: Shimon Even
title: Systolic Modular Multiplication
journal: j-LECT-NOTES-COMP-SCI
volume: 537
pages: 619--??
year: 1991
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Tue Feb 5 11:48:02 MST 2002
bibtimestamp: 2002.02.05 11:48:02 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Shimon Even
rawtitle: Systolic Modular Multiplication
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t0537.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/0537/05370619.htm; http://link.springer-ny.com/link/service/series/0558/papers/0537/05370619.pdf

entry:
@Article{Even:1991:SMM,
  author =       "Shimon Even",
  title =        "Systolic Modular Multiplication",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "537",
  pages =        "619--??",
  year =         "1991",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Feb 5 11:48:02 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t0537.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/0537/05370619.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/0537/05370619.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: inproceedings
filename: fparith.bib
label: Ferguson:1991:AMA
author: Warren E. Ferguson, Jr. and Tom Brightman
title: Accurate and Monotone Approximations of Some Transcendental Functions
crossref: Kornerup:1991:PIS
pages: 237--244
year: 1991
bibdate: Sat Nov 27 12:40:58 MST 2004
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.27 12:40:58 MST
URL: http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Ferguson.pdf
keywords: ARITH-10
acknowledgement: ack-nj
rawauthor: Warren E. {Ferguson, Jr.} and Tom Brightman
rawtitle: Accurate and Monotone Approximations of Some Transcendental Functions
entry:
@InProceedings{Ferguson:1991:AMA,
  author =       "Warren E. {Ferguson, Jr.} and Tom Brightman",
  title =        "Accurate and Monotone Approximations of Some
                 Transcendental Functions",
  crossref =     "Kornerup:1991:PIS",
  pages =        "237--244",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  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/arith10/papers/ARITH10_Ferguson.pdf",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  keywords =     "ARITH-10",
}


bibtype: article
filename: fparith.bib
label: Ferguson:1991:SMC
author: Warren E. Ferguson, Jr.
title: Selecting math coprocessors
journal: j-IEEE-SPECTRUM
volume: 28
number: 7
pages: 38--41
month: jul
monthnumber: 7
year: 1991
CODEN: IEESAM
DOI: https://doi.org/10.1109/6.83469
ISSN: 0018-9235 (print), 1939-9340 (electronic) OR 00189235 (print), 19399340 (electronic)
ISSNL: 0018-9235 OR 00189235
bibdate: Thu Sep 01 16:17:34 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2011.09.01 16:17:34 ???
fjournal: IEEE Spectrum
keywords: floating-point arithmetic
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6
rawauthor: Warren E. {Ferguson, Jr.}
rawtitle: Selecting math coprocessors
remark:
Contains performance-comparison tables for Cyrix, Intel, Motorola, and Weitek floating-point coprocessor chips.

entry:
@Article{Ferguson:1991:SMC,
  author =       "Warren E. {Ferguson, Jr.}",
  title =        "Selecting math coprocessors",
  journal =      j-IEEE-SPECTRUM,
  volume =       "28",
  number =       "7",
  pages =        "38--41",
  month =        jul,
  year =         "1991",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/6.83469",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Thu Sep 01 16:17:34 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
  keywords =     "floating-point arithmetic",
  remark =       "Contains performance-comparison tables for Cyrix,
                 Intel, Motorola, and Weitek floating-point coprocessor
                 chips.",
}


bibtype: inproceedings
filename: fparith.bib
label: Fleurkens:1991:HLD
author: H. Fleurkens and R. Tangelder
title: The high level design of the long accumulator chip
crossref: IEEE:1991:PFC
pages: 299--301
year: 1991
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: Eindhoven University of Technol., Netherlands
thesaurus: Circuit CAD; Digital arithmetic; Integrated logic circuits; Logic CAD; Parallel architectures
rawauthor: H. Fleurkens and R. Tangelder
rawtitle: The high level design of the long accumulator chip
abstract:
The authors discuss an architecture and its high level description of a long accumulator chip suited for the exact calculation of the inner products of floating point numbers. A highly parallel implementation is developed using eight independent adder stations, which add products to two circular long accumulators. A dispatcher schedules each product to the best available station. To validate this architecture and to calculate its performance, a high level description is created. This description is made with ESCHER+, an interactive schematic entry tool with a built-in simulator. The resulting description showed to be the basis for the further implementation of the chip.

keywords:
Built-in simulator; ESCHER+; Floating point numbers; High level description; High level design; Highly parallel implementation; Inner products calculation; Interactive schematic entry tool; Long accumulator chip

rawabstract:
The authors discuss an architecture and its high level description of a long accumulator chip suited for the exact calculation of the inner products of floating point numbers. A highly parallel implementation is developed using eight independent adder stations, which add products to two circular long accumulators. A dispatcher schedules each product to the best available station. To validate this architecture and to calculate its performance, a high level description is created. This description is made with ESCHER+, an interactive schematic entry tool with a built-in simulator. The resulting description showed to be the basis for the further implementation of the chip.

entry:
@InProceedings{Fleurkens:1991:HLD,
  author =       "H. Fleurkens and R. Tangelder",
  title =        "The high level design of the long accumulator chip",
  crossref =     "IEEE:1991:PFC",
  pages =        "299--301",
  year =         "1991",
  bibdate =      "Wed Dec 13 13:13:34 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The authors discuss an architecture and its high level
                 description of a long accumulator chip suited for the
                 exact calculation of the inner products of floating
                 point numbers. A highly parallel implementation is
                 developed using eight independent adder stations, which
                 add products to two circular long accumulators. A
                 dispatcher schedules each product to the best available
                 station. To validate this architecture and to calculate
                 its performance, a high level description is created.
                 This description is made with ESCHER+, an interactive
                 schematic entry tool with a built-in simulator. The
                 resulting description showed to be the basis for the
                 further implementation of the chip.",
  acknowledgement = ack-nhfb,
  affiliation =  "Eindhoven University of Technol., Netherlands",
  classification = "B1130B (Computer-aided circuit analysis and design);
                 B1265B (Logic circuits); C5120 (Logic and switching
                 circuits); C5210B (Computer-aided logic design); C5220P
                 (Parallel architecture); C5230 (Digital arithmetic
                 methods); C7410D (Electronic engineering)",
  keywords =     "Built-in simulator; ESCHER+; Floating point numbers;
                 High level description; High level design; Highly
                 parallel implementation; Inner products calculation;
                 Interactive schematic entry tool; Long accumulator
                 chip",
  thesaurus =    "Circuit CAD; Digital arithmetic; Integrated logic
                 circuits; Logic CAD; Parallel architectures",
}


bibtype: article
filename: fparith.bib
label: Fossmeier:1991:ALH
author: R. Foss meier
journal: j-COMPUTING
volume: 46
number: 2
pages: 175--182
month: jun
monthnumber: 6
year: 1991
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
MRclass: 65G99
MRnumber: 92e:65064
bibdate: Tue Oct 12 16:33:42 MDT 1999
bibtimestamp: 1999.10.12 16:33:42 MDT
fjournal: Computing
language: German
acknowledgement: ack-nhfb
affiliation: Inst. fur Inf., Tech. University of Munchen, Germany
journalURL: http://link.springer.com/journal/607
journalabr: Comput Vienna New York
thesaurus: Number theory; Numerical analysis
rawauthor: R. F{\"o}{\ss}meier
title:
Zur Axiomatisierung logarithmischer und halblogarithmischer Zahlensysteme. (German) [On the axiomatization of logarithmic and semi-logarithmic number systems]

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

abstract:
In the history of numerical analysis there have been various approaches to gain stricter control of numerical computation by axiomatization of approximative arithmetic systems. In the case of floating-point-like systems, the limitations to this approach originate essentially in the fact that addition is not associative. By suitably weakening the axiomatic system of the real numbers the author arrives at a system which can be fulfilled by approximative arithmetic structures. Comparisons show that structures fulfilling this system cannot be arbitrarily distant from reasonable approximative structures. This shows that it is possible to describe approximative structures by approximations of the laws of the original structure.

keywords:
Approximative arithmetic structures; Axiomatization; computers, digital --- Computational Methods; Floating-Point Arithmetic; Logarithmic; mathematical techniques; Number systems; Number Systems; Numerical analysis; Semi-logarithmic number systems

rawabstract:
In the history of numerical analysis there have been various approaches to gain stricter control of numerical computation by axiomatization of approximative arithmetic systems. In the case of floating-point-like systems, the limitations to this approach originate essentially in the fact that addition is not associative. By suitably weakening the axiomatic system of the real numbers the author arrives at a system which can be fulfilled by approximative arithmetic structures. Comparisons show that structures fulfilling this system cannot be arbitrarily distant from reasonable approximative structures. This shows that it is possible to describe approximative structures by approximations of the laws of the original structure.

rawtitle:
{Zur Axiomatisierung logarithmischer und halblogarithmischer Zahlensysteme}. ({German}) [{On} the axiomatization of logarithmic and semi-logarithmic number systems]

entry:
@Article{Fossmeier:1991:ALH,
  author =       "R. F{\"o}{\ss}meier",
  title =        "{Zur Axiomatisierung logarithmischer und
                 halblogarithmischer Zahlensysteme}. ({German}) [{On}
                 the axiomatization of logarithmic and semi-logarithmic
                 number systems]",
  journal =      j-COMPUTING,
  volume =       "46",
  number =       "2",
  pages =        "175--182",
  month =        jun,
  year =         "1991",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65G99",
  MRnumber =     "92e:65064",
  bibdate =      "Tue Oct 12 16:33:42 MDT 1999",
  bibsource =    "Compendex database;
                 http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
                 https://www.math.utah.edu/pub/tex/bib/computing.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 MathSciNet database; OCLC Contents1st database",
  abstract =     "In the history of numerical analysis there have been
                 various approaches to gain stricter control of
                 numerical computation by axiomatization of
                 approximative arithmetic systems. In the case of
                 floating-point-like systems, the limitations to this
                 approach originate essentially in the fact that
                 addition is not associative. By suitably weakening the
                 axiomatic system of the real numbers the author arrives
                 at a system which can be fulfilled by approximative
                 arithmetic structures. Comparisons show that structures
                 fulfilling this system cannot be arbitrarily distant
                 from reasonable approximative structures. This shows
                 that it is possible to describe approximative
                 structures by approximations of the laws of the
                 original structure.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. f{\"u}r Inf., Tech. University of Munchen,
                 Germany",
  classification = "723; 921; C4100 (Numerical analysis)",
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  journalabr =   "Comput Vienna New York",
  keywords =     "Approximative arithmetic structures; Axiomatization;
                 computers, digital --- Computational Methods;
                 Floating-Point Arithmetic; Logarithmic; mathematical
                 techniques; Number systems; Number Systems; Numerical
                 analysis; Semi-logarithmic number systems",
  language =     "German",
  pubcountry =   "Austria",
  thesaurus =    "Number theory; Numerical analysis",
}


bibtype: article
filename: fparith.bib
label: Fossmeier:1991:ALS
author: R. Fossmeier
title: On the axiomatization of logarithmic and semi-logarithmic number systems
journal: j-COMPUTING
volume: 46
number: 2
pages: 175--182
year: 1991
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
bibdate: Tue Dec 12 09:20:21 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.12 09:20:21 MST
fjournal: Computing: Archiv fur informatik und numerik
language: German
acknowledgement: ack-nhfb
affiliation: Inst. fur Inf., Tech. University of Munchen, Germany
journalURL: http://link.springer.com/journal/607
thesaurus: Number theory; Numerical analysis
rawauthor: R. Fossmeier
rawtitle: On the axiomatization of logarithmic and semi-logarithmic number systems
abstract:
In the history of numerical analysis there have been various approaches to gain stricter control of numerical computation by axiomatization of approximative arithmetic systems. In the case of floating-point-like systems, the limitations to this approach originate essentially in the fact that addition is not associative. By suitably weakening the axiomatic system of the real numbers the author arrives at a system which can be fulfilled by approximative arithmetic structures. Comparisons show that structures fulfilling this system cannot be arbitrarily distant from reasonable approximative structures. This shows that it is possible to describe approximative structures by approximations of the laws of the original structure.

keywords:
Approximative arithmetic structures; Axiomatization; Logarithmic; Number systems; Numerical analysis; Semi-logarithmic number systems

entry:
@Article{Fossmeier:1991:ALS,
  author =       "R. Fossmeier",
  title =        "On the axiomatization of logarithmic and
                 semi-logarithmic number systems",
  journal =      j-COMPUTING,
  volume =       "46",
  number =       "2",
  pages =        "175--182",
  month =        "????",
  year =         "1991",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Tue Dec 12 09:20:21 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In the history of numerical analysis there have been
                 various approaches to gain stricter control of
                 numerical computation by axiomatization of
                 approximative arithmetic systems. In the case of
                 floating-point-like systems, the limitations to this
                 approach originate essentially in the fact that
                 addition is not associative. By suitably weakening the
                 axiomatic system of the real numbers the author arrives
                 at a system which can be fulfilled by approximative
                 arithmetic structures. Comparisons show that structures
                 fulfilling this system cannot be arbitrarily distant
                 from reasonable approximative structures. This shows
                 that it is possible to describe approximative
                 structures by approximations of the laws of the
                 original structure.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. fur Inf., Tech. University of Munchen, Germany",
  classification = "C4100 (Numerical analysis)",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
  keywords =     "Approximative arithmetic structures; Axiomatization;
                 Logarithmic; Number systems; Numerical analysis;
                 Semi-logarithmic number systems",
  language =     "German",
  pubcountry =   "Austria",
  thesaurus =    "Number theory; Numerical analysis",
}


bibtype: article
filename: fparith.bib
label: Foster:1991:PM
author: Kenneth R. Foster
title: Prepackaged math
journal: j-IEEE-SPECTRUM
volume: 28
number: 11
pages: 44--50
month: nov
monthnumber: 11
year: 1991
CODEN: IEESAM
DOI: https://doi.org/10.1109/6.99016
ISSN: 0018-9235 (print), 1939-9340 (electronic) OR 00189235 (print), 19399340 (electronic)
ISSNL: 0018-9235 OR 00189235
bibdate: Wed Jan 15 16:15:28 2020
bibtimestamp: 2020.01.15 16:15:28 ???
fjournal: IEEE Spectrum
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6
rawauthor: Kenneth R. Foster
rawtitle: Prepackaged math
bibsource:
https://www.math.utah.edu/pub/tex/bib/axiom.bib; 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/macsyma.bib; https://www.math.utah.edu/pub/tex/bib/maple-extract.bib; https://www.math.utah.edu/pub/tex/bib/mathematica.bib; https://www.math.utah.edu/pub/tex/bib/matlab.bib

keywords:
Chemical analysis; Data engineering; Data visualization; Differential equations; Graphics; Hard disks; manipulation; mathematical problems; mathematics computing; matrices; matrix algebra; Packaging; Personal communication networks; software packages; Software packages; Workstations

entry:
@Article{Foster:1991:PM,
  author =       "Kenneth R. Foster",
  title =        "Prepackaged math",
  journal =      j-IEEE-SPECTRUM,
  volume =       "28",
  number =       "11",
  pages =        "44--50",
  month =        nov,
  year =         "1991",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/6.99016",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Wed Jan 15 16:15:28 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/axiom.bib;
                 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/macsyma.bib;
                 https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathematica.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
  keywords =     "Chemical analysis; Data engineering; Data
                 visualization; Differential equations; Graphics; Hard
                 disks; manipulation; mathematical problems; mathematics
                 computing; matrices; matrix algebra; Packaging;
                 Personal communication networks; software packages;
                 Software packages; Workstations",
}


bibtype: inproceedings
filename: fparith.bib
label: Frougny:1991:RNN
author: Christiane Frougny
title: Representation of numbers in nonclassical numeration systems
crossref: Kornerup:1991:PIS
pages: 17--21
year: 1991
bibdate: Sat Nov 27 12:40:58 MST 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.27 12:40:58 MST
URL: http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Frougny.pdf
keywords: ARITH-10
acknowledgement: ack-nhfb
rawauthor: Christiane Frougny
rawtitle: Representation of numbers in nonclassical numeration systems
entry:
@InProceedings{Frougny:1991:RNN,
  author =       "Christiane Frougny",
  title =        "Representation of numbers in nonclassical numeration
                 systems",
  crossref =     "Kornerup:1991:PIS",
  pages =        "17--21",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Frougny.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}


bibtype: article
filename: fparith.bib
label: Gal:1991:AEM
author: Shmuel Gal and Boris Bachelis
title: An Accurate Elementary Mathematical Library for the IEEE Floating Point Standard
journal: j-TOMS
volume: 17
number: 1
pages: 26--45
month: mar
monthnumber: 3
year: 1991
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 65D20 (65-04 65D15)
MRnumber: 92a:65069
bibdate: Sun Sep 04 23:33:02 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.04 23:33:02 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms; correct rounding; floating-point arithmetic; theory
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Shmuel Gal and Boris Bachelis
rawtitle: An Accurate Elementary Mathematical Library for the {IEEE} Floating Point Standard
URL:
http://doi.acm.org/10.1145/103147.103151; http://www.acm.org/pubs/citations/journals/toms/1991-17-1/p26-gal/

abstract:
The algorithms used by the IBM Israel Scientific Center for the elementary mathematical library using the IEEE standard for binary floating point arithmetic are described. The algorithms are based on the ``accurate tables method.'' This methodology achieves high performance and produces very accurate results. It overcomes one of the main problems encountered in elementary mathematical functions computations: achieving last bit accuracy. The results obtained are correctly rounded for almost all argument values.par Our main idea in the accurate tables method is to use ``nonstandard tables,'' which are different from the natural tables of equally spaced points in which the rounding error prevents obtaining last bit accuracy. In order to achieve a small error we use the following idea: Perturb the original, equally spaced, points in such a way that the table value (or tables values in case we need several tables) will be very close to numbers which can be exactly represented by the computer (much closer than the usual double precision representation). Thus we were able to control the error introduced by the computer representation of real numbers and extended the accuracy without actually using extended precision arithmetic.

subject:
bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic. bf G.1.2: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation.

rawabstract:
The algorithms used by the IBM Israel Scientific Center for the elementary mathematical library using the IEEE standard for binary floating point arithmetic are described. The algorithms are based on the ``accurate tables method.'' This methodology achieves high performance and produces very accurate results. It overcomes one of the main problems encountered in elementary mathematical functions computations: achieving last bit accuracy. The results obtained are correctly rounded for almost all argument values.\par Our main idea in the accurate tables method is to use ``nonstandard tables,'' which are different from the natural tables of equally spaced points in which the rounding error prevents obtaining last bit accuracy. In order to achieve a small error we use the following idea: Perturb the original, equally spaced, points in such a way that the table value (or tables values in case we need several tables) will be very close to numbers which can be exactly represented by the computer (much closer than the usual double precision representation). Thus we were able to control the error introduced by the computer representation of real numbers and extended the accuracy without actually using extended precision arithmetic.

entry:
@Article{Gal:1991:AEM,
  author =       "Shmuel Gal and Boris Bachelis",
  title =        "An Accurate Elementary Mathematical Library for the
                 {IEEE} Floating Point Standard",
  journal =      j-TOMS,
  volume =       "17",
  number =       "1",
  pages =        "26--45",
  month =        mar,
  year =         "1991",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D20 (65-04 65D15)",
  MRnumber =     "92a:65069",
  bibdate =      "Sun Sep 04 23:33:02 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://doi.acm.org/10.1145/103147.103151;
                 http://www.acm.org/pubs/citations/journals/toms/1991-17-1/p26-gal/",
  abstract =     "The algorithms used by the IBM Israel Scientific
                 Center for the elementary mathematical library using
                 the IEEE standard for binary floating point arithmetic
                 are described. The algorithms are based on the
                 ``accurate tables method.'' This methodology achieves
                 high performance and produces very accurate results. It
                 overcomes one of the main problems encountered in
                 elementary mathematical functions computations:
                 achieving last bit accuracy. The results obtained are
                 correctly rounded for almost all argument
                 values.\par

                 Our main idea in the accurate tables method is to use
                 ``nonstandard tables,'' which are different from the
                 natural tables of equally spaced points in which the
                 rounding error prevents obtaining last bit accuracy. In
                 order to achieve a small error we use the following
                 idea: Perturb the original, equally spaced, points in
                 such a way that the table value (or tables values in
                 case we need several tables) will be very close to
                 numbers which can be exactly represented by the
                 computer (much closer than the usual double precision
                 representation). Thus we were able to control the error
                 introduced by the computer representation of real
                 numbers and extended the accuracy without actually
                 using extended precision arithmetic.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; correct rounding; floating-point
                 arithmetic; theory",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Computer arithmetic. {\bf G.1.2}:
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation.",
}


bibtype: inproceedings
filename: fparith.bib
label: Gamberger:1991:NAI
author: Dragan Gamberger
title: New approach to integer division in residue number systems
crossref: Kornerup:1991:PIS
pages: 84--91
year: 1991
DOI: https://doi.org/10.1109/ARITH.1991.145538
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
URL: http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Gamberger.pdf
keywords: ARITH-10; residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: Dragan Gamberger
rawtitle: New approach to integer division in residue number systems
entry:
@InProceedings{Gamberger:1991:NAI,
  author =       "Dragan Gamberger",
  title =        "New approach to integer division in residue number
                 systems",
  crossref =     "Kornerup:1991:PIS",
  pages =        "84--91",
  year =         "1991",
  DOI =          "https://doi.org/10.1109/ARITH.1991.145538",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Gamberger.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10; residue arithmetic; residue number system",
  summary =      "A novel division algorithm that is especially
                 appropriate for residue number systems (RNSs) is
                 presented. It makes use of the fact that the
                 multiplicative inverse element of a divisor which is
                 relatively prime to system moduli can be easily
                 \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Gladshtein:1991:MDD
author: M. A. Gladshtein
title: A method of designing a decimal arithmetic processor
journal: j-AUTO-CTL-COMP-SCI
volume: 25
number: 6
pages: 51--56
year: 1991
CODEN: ACCSCE
ISSN: 0132-4160 OR 01324160
ISSNL: 0146-4116 OR 01464116
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: Automatic Control and Computer Sciences
remark: English translation of: Avtomatika i Vychislitel'naya Tekhnika
acknowledgement: ack-nhfb
thesaurus: Digital arithmetic; Microprocessor chips
rawauthor: M. A. Gladshtein
rawtitle: A method of designing a decimal arithmetic processor
abstract:
The advantages and drawbacks of binary numeric coding in digital computers are considered. This type of coding has is shown to be ineffective in processing large data arrays especially when represented in the floating-point form. Also, the low efficiency of conventionally employed decimal computational procedures using the so-called corrections is noted. It is proposed, in designing digital computers, to renounce the principle of binary computations in favor of decimal operations on the basis of stored addition and multiplication tables using binary-decimal numeric coding. A version of circuit design for a decimal processor, algorithms and microprograms for addition and multiplication operations are described. Advantages inherent in the method proposed are analyzed. (10 Refs.)

keywords:
Addition tables; BCD code; Binary numeric coding; Binary-decimal numeric coding; Circuit design; Decimal arithmetic processor; decimal floating-point arithmetic; Decimal operations; Digital computers; Microprograms; Multiplication tables

rawabstract:
The advantages and drawbacks of binary numeric coding in digital computers are considered. This type of coding has is shown to be ineffective in processing large data arrays especially when represented in the floating-point form. Also, the low efficiency of conventionally employed decimal computational procedures using the so-called corrections is noted. It is proposed, in designing digital computers, to renounce the principle of binary computations in favor of decimal operations on the basis of stored addition and multiplication tables using binary-decimal numeric coding. A version of circuit design for a decimal processor, algorithms and microprograms for addition and multiplication operations are described. Advantages inherent in the method proposed are analyzed. (10 Refs.)

entry:
@Article{Gladshtein:1991:MDD,
  author =       "M. A. Gladshtein",
  title =        "A method of designing a decimal arithmetic processor",
  journal =      j-AUTO-CTL-COMP-SCI,
  volume =       "25",
  number =       "6",
  pages =        "51--56",
  month =        "????",
  year =         "1991",
  CODEN =        "ACCSCE",
  ISSN =         "0132-4160",
  ISSN-L =       "0146-4116",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The advantages and drawbacks of binary numeric coding
                 in digital computers are considered. This type of
                 coding has is shown to be ineffective in processing
                 large data arrays especially when represented in the
                 floating-point form. Also, the low efficiency of
                 conventionally employed decimal computational
                 procedures using the so-called corrections is noted. It
                 is proposed, in designing digital computers, to
                 renounce the principle of binary computations in favor
                 of decimal operations on the basis of stored addition
                 and multiplication tables using binary-decimal numeric
                 coding. A version of circuit design for a decimal
                 processor, algorithms and microprograms for addition
                 and multiplication operations are described. Advantages
                 inherent in the method proposed are analyzed. (10
                 Refs.)",
  acknowledgement = ack-nhfb,
  classification = "B1265F (Microprocessors and microcomputers); C5130
                 (Microprocessor chips); C5230 (Digital arithmetic
                 methods)",
  fjournal =     "Automatic Control and Computer Sciences",
  keywords =     "Addition tables; BCD code; Binary numeric coding;
                 Binary-decimal numeric coding; Circuit design; Decimal
                 arithmetic processor; decimal floating-point
                 arithmetic; Decimal operations; Digital computers;
                 Microprograms; Multiplication tables",
  pubcountry =   "Latvia",
  remark =       "English translation of: Avtomatika i Vychislitel'naya
                 Tekhnika",
  thesaurus =    "Digital arithmetic; Microprocessor chips",
}


bibtype: article
filename: fparith.bib
label: Goldberg:1991:CWE
author: David Goldberg
title: Corrigendum: ``What Every Computer Scientist Should Know About Floating-Point Arithmetic''
journal: j-COMP-SURV
volume: 23
number: 3
pages: 413--413
month: sep
monthnumber: 9
year: 1991
CODEN: CMSVAN
ISSN: 0360-0300 (print), 1557-7341 (electronic) OR 03600300 (print), 15577341 (electronic)
ISSNL: 0360-0300 OR 03600300
bibdate: Sun Sep 25 09:58:43 1994
bibtimestamp: 1994.09.25 09:58:43 ???
note: See cite Goldberg:1991:WEC,Dunham:1992:SFW,Wichmann:1992:SFW.
fjournal: ACM Computing Surveys
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J204
rawauthor: David Goldberg
rawnote: See \cite{Goldberg:1991:WEC,Dunham:1992:SFW,Wichmann:1992:SFW}.
rawtitle: Corrigendum: {``What Every Computer Scientist Should Know About Floating-Point Arithmetic''}
bibsource:
https://www.math.utah.edu/pub/tex/bib/compsurv.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Goldberg:1991:CWE,
  author =       "David Goldberg",
  title =        "Corrigendum: {``What Every Computer Scientist Should
                 Know About Floating-Point Arithmetic''}",
  journal =      j-COMP-SURV,
  volume =       "23",
  number =       "3",
  pages =        "413--413",
  month =        sep,
  year =         "1991",
  CODEN =        "CMSVAN",
  ISSN =         "0360-0300 (print), 1557-7341 (electronic)",
  ISSN-L =       "0360-0300",
  bibdate =      "Sun Sep 25 09:58:43 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compsurv.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See
                 \cite{Goldberg:1991:WEC,Dunham:1992:SFW,Wichmann: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: Goldberg:1991:WEC
author: David Goldberg
title: What Every Computer Scientist Should Know About Floating-Point Arithmetic
journal: j-COMP-SURV
volume: 23
number: 1
pages: 5--48
month: mar
monthnumber: 3
year: 1991
CODEN: CMSVAN
DOI: https://doi.org/10.1145/103162.103163
ISSN: 0360-0300 (print), 1557-7341 (electronic) OR 03600300 (print), 15577341 (electronic)
ISSNL: 0360-0300 OR 03600300
bibdate: Thu Jun 19 09:40:16 MDT 2008
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2008.06.19 09:40:16 MDT
note: See also cite Goldberg:1991:CWE,Dunham:1992:SFW,Wichmann:1992:SFW.
URL: http://www.acm.org/pubs/toc/Abstracts/0360-0300/103163.html
fjournal: ACM Computing Surveys
acknowledgement: ack-nhfb
affiliation: Xerox Palo Alto Res. Center, CA, USA
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J204
thesaurus: digital arithmetic; roundoff errors
rawauthor: David Goldberg
rawnote: See also \cite{Goldberg:1991:CWE,Dunham:1992:SFW,Wichmann:1992:SFW}.
rawtitle: What Every Computer Scientist Should Know About Floating-Point Arithmetic
abstract:
Floating-point arithmetic is considered an esoteric subject by many people. This is rather surprising, because floating-point is ubiquitous in computer systems: almost every language has a floating-point datatype; computers from PCs to supercomputers have floating-point accelerators; most compilers will be called upon to compile floating-point algorithms from time to time; and virtually every operating system must respond to floating-point exceptions such as overflow. This paper presents a tutorial on the aspects of floating-point that have a direct impact on designers of computer systems. It begins with background on floating-point representation and rounding error, continues with a discussion of the IEEE floating-point standard, and concludes with examples of how computer system builders can better support floating point.

keywords:
algorithms; compilers; computer scientist; computer systems; denormalized number; design; exception; floating-point; floating-point accelerators; floating-point algorithms; floating-point datatype; floating-point exceptions; floating-point representation; floating-point standard; gradual underflow; guard digit; IEEE floating-point standard; languages; NaN; operating system; overflow; PCs; relative error; rounding error; rounding mode; standardization; supercomputers; ulp; underflow

subject:
bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic. bf K.1: Computing Milieux, THE COMPUTER INDUSTRY, Standards. bf C.0: Computer Systems Organization, GENERAL, Instruction set design. bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms.

rawabstract:
Floating-point arithmetic is considered an esoteric subject by many people. This is rather surprising, because floating-point is ubiquitous in computer systems: almost every language has a floating-point datatype; computers from PCs to supercomputers have floating-point accelerators; most compilers will be called upon to compile floating-point algorithms from time to time; and virtually every operating system must respond to floating-point exceptions such as overflow. This paper presents a tutorial on the aspects of floating-point that have a direct impact on designers of computer systems. It begins with background on floating-point representation and rounding error, continues with a discussion of the IEEE floating-point standard, and concludes with examples of how computer system builders can better support floating point.

entry:
@Article{Goldberg:1991:WEC,
  author =       "David Goldberg",
  title =        "What Every Computer Scientist Should Know About
                 Floating-Point Arithmetic",
  journal =      j-COMP-SURV,
  volume =       "23",
  number =       "1",
  pages =        "5--48",
  month =        mar,
  year =         "1991",
  CODEN =        "CMSVAN",
  DOI =          "https://doi.org/10.1145/103162.103163",
  ISSN =         "0360-0300 (print), 1557-7341 (electronic)",
  ISSN-L =       "0360-0300",
  bibdate =      "Thu Jun 19 09:40:16 MDT 2008",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See also
                 \cite{Goldberg:1991:CWE,Dunham:1992:SFW,Wichmann:1992:SFW}.",
  URL =          "http://www.acm.org/pubs/toc/Abstracts/0360-0300/103163.html",
  abstract =     "Floating-point arithmetic is considered an esoteric
                 subject by many people. This is rather surprising,
                 because floating-point is ubiquitous in computer
                 systems: almost every language has a floating-point
                 datatype; computers from PCs to supercomputers have
                 floating-point accelerators; most compilers will be
                 called upon to compile floating-point algorithms from
                 time to time; and virtually every operating system must
                 respond to floating-point exceptions such as overflow.
                 This paper presents a tutorial on the aspects of
                 floating-point that have a direct impact on designers
                 of computer systems. It begins with background on
                 floating-point representation and rounding error,
                 continues with a discussion of the IEEE floating-point
                 standard, and concludes with examples of how computer
                 system builders can better support floating point.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "Xerox Palo Alto Res. Center, CA, USA",
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "ACM Computing Surveys",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J204",
  keywords =     "algorithms; compilers; computer scientist; computer
                 systems; denormalized number; design; exception;
                 floating-point; floating-point accelerators;
                 floating-point algorithms; floating-point datatype;
                 floating-point exceptions; floating-point
                 representation; floating-point standard; gradual
                 underflow; guard digit; IEEE floating-point standard;
                 languages; NaN; operating system; overflow; PCs;
                 relative error; rounding error; rounding mode;
                 standardization; supercomputers; ulp; underflow",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Computer arithmetic. {\bf K.1}:
                 Computing Milieux, THE COMPUTER INDUSTRY, Standards.
                 {\bf C.0}: Computer Systems Organization, GENERAL,
                 Instruction set design. {\bf G.1.0}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Numerical
                 algorithms.",
  thesaurus =    "digital arithmetic; roundoff errors",
}


bibtype: techreport
filename: fparith.bib
label: Golubev:1991:FPM
author: Yu. F. Golubev and I. A. Seregin and R. Z. Khaui rullin
type: Inst. Prikl. Mat. Preprint
number: 50
institution: Akad. Nauk SSSR
pages: 28
year: 1991
MRclass: 65K10 (49N55 70-08 70Q05)
MRnumber: 166 839
bibdate: Fri Dec 8 08:24:14 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 08:24:14 ???
language: Russian
acknowledgement: ack-nhfb
rawauthor: Yu. F. Golubev and I. A. Seregin and R. Z. Kha{\u\i}rullin
title:
The floating point method in problems of the optimization of motion during the descent of a spacecraft into the atmosphere. (Russian)

rawtitle:
The floating point method in problems of the optimization of motion during the descent of a spacecraft into the atmosphere. ({Russian})

entry:
@TechReport{Golubev:1991:FPM,
  author =       "Yu. F. Golubev and I. A. Seregin and R. Z.
                 Kha{\u\i}rullin",
  title =        "The floating point method in problems of the
                 optimization of motion during the descent of a
                 spacecraft into the atmosphere. ({Russian})",
  type =         "{Inst. Prikl. Mat.} Preprint",
  number =       "50",
  institution =  "Akad. Nauk SSSR",
  pages =        "28",
  year =         "1991",
  MRclass =      "65K10 (49N55 70-08 70Q05)",
  MRnumber =     "166 839",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}


bibtype: article
filename: fparith.bib
label: Gonnella:1991:ACF
author: J. Gonnella
title: The application of core functions to residue number systems
journal: j-IEEE-TRANS-SIG-PROC
volume: 39
number: 1
pages: 69--75
month: jan
monthnumber: 1
year: 1991
CODEN: ITPRED
DOI: https://doi.org/10.1109/78.80766
ISSN: 1053-587X (print), 1941-0476 (electronic) OR 1053587X (print), 19410476 (electronic)
ISSNL: 1053-587X OR 1053587X
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
URL: https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=2655
fjournal: IEEE Transactions on Signal Processing
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78
rawauthor: J. Gonnella
rawtitle: The application of core functions to residue number systems
entry:
@Article{Gonnella:1991:ACF,
  author =       "J. Gonnella",
  title =        "The application of core functions to residue number
                 systems",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "39",
  number =       "1",
  pages =        "69--75",
  month =        jan,
  year =         "1991",
  CODEN =        "ITPRED",
  DOI =          "https://doi.org/10.1109/78.80766",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=2655",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A theory of core functions is presented, and the
                 application of this theory to the difficult residue
                 number system (RNS) operations is described. Potential
                 applications for special-purpose core-based RNS
                 processors include adaptive array processing,
                 \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Gotze:1991:SRD
author: J. Gotze and U. Schwiegelshohn
journal: j-SIAM-J-SCI-STAT-COMP
volume: 12
number: 4
pages: 800--807
month: jul
monthnumber: 7
year: 1991
CODEN: SIJCD4
ISSN: 0196-5204 OR 01965204
MRclass: 65F20 (65F25)
MRnumber: 92a:65125
bibdate: Sat Oct 24 13:20:45 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.10.24 13:20:45 MDT
fjournal: SIAM Journal on Scientific and Statistical Computing
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/loi/sijcd4
rawauthor: J. G{\"o}tze and U. Schwiegelshohn
title:
A Square Root and Division Free Givens Rotation for Solving Least Squares Problems on Systolic Arrays

rawtitle:
A Square Root and Division Free {Givens} Rotation for Solving Least Squares Problems on Systolic Arrays

entry:
@Article{Gotze:1991:SRD,
  author =       "J. G{\"o}tze and U. Schwiegelshohn",
  title =        "A Square Root and Division Free {Givens} Rotation for
                 Solving Least Squares Problems on Systolic Arrays",
  journal =      j-SIAM-J-SCI-STAT-COMP,
  volume =       "12",
  number =       "4",
  pages =        "800--807",
  month =        jul,
  year =         "1991",
  CODEN =        "SIJCD4",
  ISSN =         "0196-5204",
  MRclass =      "65F20 (65F25)",
  MRnumber =     "92a:65125",
  bibdate =      "Sat Oct 24 13:20:45 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific and Statistical Computing",
  journal-URL =  "http://epubs.siam.org/loi/sijcd4",
}


bibtype: article
filename: fparith.bib
label: Grcar:1991:IAS
author: Joe Grcar
title: IEEE Arithmetic Stinks
journal: j-NA-DIGEST
volume: 91
number: 33
pages: 800--807
day: 18
month: aug
monthnumber: 8
year: 1991
bibdate: Thu Aug 23 06:22:13 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.08.23 06:22:13 ???
note: See rebuttal cite Demmel:1991:OIA.
URL: http://www.netlib.org/na-digest/91/v91n33
fjournal: NA Digest
acknowledgement: ack-nhfb
rawauthor: Joe Grcar
rawnote: See rebuttal \cite{Demmel:1991:OIA}.
rawtitle: {IEEE} Arithmetic Stinks
entry:
@Article{Grcar:1991:IAS,
  author =       "Joe Grcar",
  title =        "{IEEE} Arithmetic Stinks",
  journal =      j-NA-DIGEST,
  volume =       "91",
  number =       "33",
  day =          "18",
  month =        aug,
  year =         "1991",
  bibdate =      "Thu Aug 23 06:22:13 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See rebuttal \cite{Demmel:1991:OIA}.",
  URL =          "http://www.netlib.org/na-digest/91/v91n33",
  acknowledgement = ack-nhfb,
  fjournal =     "NA Digest",
}


bibtype: article
filename: fparith.bib
label: Griffin:1991:REA
author: C. Griffin and P. Rao and F. Taylor
title: Roundoff error analysis of the discrete Wigner distribution using fixed-point arithmetic
journal: j-IEEE-TRANS-SIG-PROC
volume: 39
number: 9
pages: 2096--2098
month: sep
monthnumber: 9
year: 1991
CODEN: ITPRED
ISSN: 1053-587X (print), 1941-0476 (electronic) OR 1053587X (print), 19410476 (electronic)
ISSNL: 1053-587X OR 1053587X
bibdate: Sat Jul 16 11:25:06 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:06 MDT
fjournal: IEEE Transactions on Signal Processing
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78
rawauthor: C. Griffin and P. Rao and F. Taylor
rawtitle: Roundoff error analysis of the discrete {Wigner} distribution using fixed-point arithmetic
entry:
@Article{Griffin:1991:REA,
  author =       "C. Griffin and P. Rao and F. Taylor",
  title =        "Roundoff error analysis of the discrete {Wigner}
                 distribution using fixed-point arithmetic",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "39",
  number =       "9",
  pages =        "2096--2098",
  month =        sep,
  year =         "1991",
  CODEN =        "ITPRED",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  bibdate =      "Sat Jul 16 11:25:06 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  summary =      "The issue of roundoff noise effects in the
                 implementation of the discrete Wigner distribution
                 using fixed-point arithmetic is addressed. The
                 sign-magnitude number representation is assumed
                 throughout the analysis. The measure of roundoff noise
                 \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Gusev:1991:NCS
author: A. V. Gusev and I. V. Melezhnikov
title: Noise in a Constant-Current SQUID with a Floating Operating Point
journal: j-TELECOMM-RADIO-ENG
volume: 46
number: 8
pages: 125--127
year: 1991
CODEN: TCREAG
ISSN: 0040-2508 (print), 1943-6009 (electronic) OR 00402508 (print), 19436009 (electronic)
ISSNL: 0040-2508 OR 00402508
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: Telecommunications and Radio Engineering
acknowledgement: ack-nhfb
rawauthor: A. V. Gusev and I. V. Melezhnikov
rawtitle: Noise in a Constant-Current {SQUID} with a Floating Operating Point
entry:
@Article{Gusev:1991:NCS,
  author =       "A. V. Gusev and I. V. Melezhnikov",
  title =        "Noise in a Constant-Current {SQUID} with a Floating
                 Operating Point",
  journal =      j-TELECOMM-RADIO-ENG,
  volume =       "46",
  number =       "8",
  pages =        "125--127",
  year =         "1991",
  CODEN =        "TCREAG",
  ISSN =         "0040-2508 (print), 1943-6009 (electronic)",
  ISSN-L =       "0040-2508",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Telecommunications and Radio Engineering",
}


bibtype: inproceedings
filename: fparith.bib
label: Guyot:1991:OAV
author: Alain Guyot
title: OCAPI: Architecture of a VLSI Coprocessor for the GCD and the Extended GCD of Large Numbers
crossref: Kornerup:1991:PIS
pages: 226--231
year: 1991
bibdate: Sat Nov 17 08:46:25 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.17 08:46:25 ???
URL: http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Guyot.pdf
keywords: ARITH-10
acknowledgement: ack-nhfb
rawauthor: Alain Guyot
rawtitle: {OCAPI}: Architecture of a {VLSI} Coprocessor for the {GCD} and the Extended {GCD} of Large Numbers
entry:
@InProceedings{Guyot:1991:OAV,
  author =       "Alain Guyot",
  title =        "{OCAPI}: Architecture of a {VLSI} Coprocessor for the
                 {GCD} and the Extended {GCD} of Large Numbers",
  crossref =     "Kornerup:1991:PIS",
  pages =        "226--231",
  year =         "1991",
  bibdate =      "Sat Nov 17 08:46:25 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Guyot.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}


bibtype: article
filename: fparith.bib
label: Hamza:1991:MBD
author: K. M. Hamza and M. A. H. Abdul-Karim
title: Microprocessor Based Direct Square Root Extractor
journal: Modelling
volume: 34
number: 1
pages: 45--48
year: 1991
bibdate: Thu Sep 1 10:15:42 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:15:42 ???
acknowledgement: ack-nj
rawauthor: K. M. Hamza and M. A. H. Abdul-Karim
rawtitle: Microprocessor Based Direct Square Root Extractor
entry:
@Article{Hamza:1991:MBD,
  author =       "K. M. Hamza and M. A. H. Abdul-Karim",
  title =        "Microprocessor Based Direct Square Root Extractor",
  journal =      "Modelling",
  volume =       "34",
  number =       "1",
  pages =        "45--48",
  month =        "????",
  year =         "1991",
  bibdate =      "Thu Sep 1 10:15:42 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: article
filename: fparith.bib
label: Heidtmann:1991:ASA
author: K. D. Heidtmann
title: Arithmetic spectrum applied to fault detection for combinational networks
journal: j-IEEE-TRANS-COMPUT
volume: 40
number: 3
pages: 320--324
month: mar
monthnumber: 3
year: 1991
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.76409
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 12:52:19 MDT 2011
bibtimestamp: 2011.07.07 12:52:19 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=76409
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: K. D. Heidtmann
rawtitle: Arithmetic spectrum applied to fault detection for combinational networks
entry:
@Article{Heidtmann:1991:ASA,
  author =       "K. D. Heidtmann",
  title =        "Arithmetic spectrum applied to fault detection for
                 combinational networks",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "40",
  number =       "3",
  pages =        "320--324",
  month =        mar,
  year =         "1991",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.76409",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 12:52:19 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=76409",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: mastersthesis
filename: fparith.bib
label: Holmes:1991:FSD
author: Ian Holmes
title: A feasibility study into the design of a 64-bit floating point processor
type: Thesis (M.Sc. in Electronics)
school: University of Southampton, Department of Electronics and Computer Science
address: Southampton, UK
pages: 320--324
year: 1991
bibdate: Thu May 09 08:35:32 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.09 08:35:32 ???
acknowledgement: ack-nhfb
rawauthor: Ian Holmes
rawtitle: A feasibility study into the design of a 64-bit floating point processor
entry:
@MastersThesis{Holmes:1991:FSD,
  author =       "Ian Holmes",
  title =        "A feasibility study into the design of a 64-bit
                 floating point processor",
  type =         "Thesis ({M.Sc. in Electronics})",
  school =       "University of Southampton, Department of Electronics
                 and Computer Science",
  address =      "Southampton, UK",
  year =         "1991",
  bibdate =      "Thu May 09 08:35:32 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Horiguchi:1991:HFN
author: Hiroshi Horiguchi and Tsutomu Tayama and Kazuaki Kajitori
title: Hamada Floating-Point Numbers and Real Numbers
journal: j-ADV-SOFT-SCI-TECH
volume: 2
pages: 123--??
year: 1991
ISSN: 1044-7997 OR 10447997
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: Advances in software science and technology
acknowledgement: ack-nhfb
rawauthor: Hiroshi Horiguchi and Tsutomu Tayama and Kazuaki Kajitori
rawtitle: {Hamada} Floating-Point Numbers and Real Numbers
entry:
@Article{Horiguchi:1991:HFN,
  author =       "Hiroshi Horiguchi and Tsutomu Tayama and Kazuaki
                 Kajitori",
  title =        "{Hamada} Floating-Point Numbers and Real Numbers",
  journal =      j-ADV-SOFT-SCI-TECH,
  volume =       "2",
  number =       "??",
  pages =        "123--??",
  year =         "1991",
  ISSN =         "1044-7997",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Advances in software science and technology",
}


bibtype: article
filename: fparith.bib
label: Horiguchi:1991:PEP
author: Susumu Horiguchi and Takeo Nakada
title: Performance Evaluation of Parallel Fast Fourier Transform on a Multiprocessor Workstation
journal: j-J-PAR-DIST-COMP
volume: 12
number: 2
pages: 158--163
month: jun
monthnumber: 6
year: 1991
CODEN: JPDCER
ISSN: 0743-7315 (print), 1096-0848 (electronic) OR 07437315 (print), 10960848 (electronic)
ISSNL: 0743-7315 OR 07437315
bibdate: Sat Apr 12 17:13:17 MDT 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.04.12 17:13:17 MDT
fjournal: Journal of Parallel and Distributed Computing
acknowledgement: ack-nhfb
corpsource: Department of Inf. Sci., Tohoku University, Sendai, Japan
journalURL: http://www.sciencedirect.com/science/journal/07437315
treatment: P Practical
rawauthor: Susumu Horiguchi and Takeo Nakada
rawtitle: Performance Evaluation of Parallel Fast {Fourier} Transform on a Multiprocessor Workstation
keywords:
algorithms; cache protocols; fast Fourier transform; fast Fourier transforms; FFT; floating-; multiprocess operating system; multiprocessing systems; multiprocessor workstation; multithread operating system; operating systems; parallel; parallel FFT; performance; performance evaluation; point coprocessors

entry:
@Article{Horiguchi:1991:PEP,
  author =       "Susumu Horiguchi and Takeo Nakada",
  title =        "Performance Evaluation of Parallel Fast {Fourier}
                 Transform on a Multiprocessor Workstation",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "12",
  number =       "2",
  pages =        "158--163",
  month =        jun,
  year =         "1991",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Sat Apr 12 17:13:17 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C4190 (Other numerical methods); C4240 (Programming
                 and algorithm theory); C5440 (Multiprocessor systems
                 and techniques)",
  corpsource =   "Department of Inf. Sci., Tohoku University, Sendai,
                 Japan",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  keywords =     "algorithms; cache protocols; fast Fourier transform;
                 fast Fourier transforms; FFT; floating-; multiprocess
                 operating system; multiprocessing systems;
                 multiprocessor workstation; multithread operating
                 system; operating systems; parallel; parallel FFT;
                 performance; performance evaluation; point
                 coprocessors",
  treatment =    "P Practical",
}


bibtype: misc
filename: fparith.bib
label: Hough:1991:TBC
author: David G. Hough and Vern Paxson
title: Testbase: base conversion test program
pages: 158--163
day: 20
month: jul
monthnumber: 7
year: 1991
bibdate: Wed May 26 07:22:52 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.05.26 07:22:52 ???
note: See cite Paxson:1991:PTI.
URL: http://www.netlib.org/fp/testbase
keywords: floating-point testing
acknowledgement: ack-nhfb
howpublished: World-Wide Web document
rawauthor: David G. Hough and Vern Paxson
rawnote: See \cite{Paxson:1991:PTI}.
rawtitle: Testbase: base conversion test program
entry:
@Misc{Hough:1991:TBC,
  author =       "David G. Hough and Vern Paxson",
  title =        "Testbase: base conversion test program",
  howpublished = "World-Wide Web document",
  day =          "20",
  month =        jul,
  year =         "1991",
  bibdate =      "Wed May 26 07:22:52 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Paxson:1991:PTI}.",
  URL =          "http://www.netlib.org/fp/testbase",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point testing",
}


bibtype: inproceedings
filename: fparith.bib
label: Hsiao:1991:CHA
author: Shen-Fu Hsiao and Jean-Marc Delosme
title: The CORDIC Householder algorithm
crossref: Kornerup:1991:PIS
pages: 256--263
year: 1991
bibdate: Sat Nov 27 12:40:58 MST 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.27 12:40:58 MST
URL: http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Hsiao.pdf
keywords: ARITH-10
acknowledgement: ack-nhfb
rawauthor: Shen-Fu Hsiao and Jean-Marc Delosme
rawtitle: The {CORDIC Householder} algorithm
entry:
@InProceedings{Hsiao:1991:CHA,
  author =       "Shen-Fu Hsiao and Jean-Marc Delosme",
  title =        "The {CORDIC Householder} algorithm",
  crossref =     "Kornerup:1991:PIS",
  pages =        "256--263",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Hsiao.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}


bibtype: article
filename: fparith.bib
label: Hu:1991:ERC
author: X. Hu and R. G. Harber and S. C. Bass
title: Expanding the Range of Convergence of the CORDIC Algorithm
journal: j-IEEE-TRANS-COMPUT
volume: 40
number: 1
pages: 13--21
month: jan
monthnumber: 1
year: 1991
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.67316
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Sep 08 00:50:12 1994
bibtimestamp: 1994.09.08 00:50:12 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: X. Hu and R. G. Harber and S. C. Bass
rawtitle: Expanding the Range of Convergence of the {CORDIC} Algorithm
bibsource:
https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib

entry:
@Article{Hu:1991:ERC,
  author =       "X. Hu and R. G. Harber and S. C. Bass",
  title =        "Expanding the Range of Convergence of the {CORDIC}
                 Algorithm",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "40",
  number =       "1",
  pages =        "13--21",
  month =        jan,
  year =         "1991",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.67316",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 08 00:50:12 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  acknowledgement = ack-nj,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Hui:1991:DFD
author: S. Hui and D. P. Brown
booktitle: IEEE Pacific Rim Conference on Communications, Computers and Signal Processing, 9--10 May 1991
title: Digital filter design with a combination of fixed point and residue number systems
volume: 1
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 331--334
year: 1991
DOI: https://doi.org/10.1109/PACRIM.1991.160746
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: S. Hui and D. P. Brown
rawbooktitle: {IEEE} Pacific Rim Conference on Communications, Computers and Signal Processing, 9--10 May 1991
rawtitle: Digital filter design with a combination of fixed point and residue number systems
entry:
@InProceedings{Hui:1991:DFD,
  author =       "S. Hui and D. P. Brown",
  booktitle =    "{IEEE} Pacific Rim Conference on Communications,
                 Computers and Signal Processing, 9--10 May 1991",
  title =        "Digital filter design with a combination of fixed
                 point and residue number systems",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "331--334",
  year =         "1991",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/PACRIM.1991.160746",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A new design method using a combination of fixed-point
                 and RNS (residue number system) arithmetics is
                 presented. It is proven that an IIR digital filter can
                 be efficiently implemented in a system that combines
                 both fixed-point and RNS arithmetics. \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Hull:1991:SVP
author: T. E. Hull and M. S. Cohen and C. B. Hall
title: Specifications for a variable-precision arithmetic coprocessor
crossref: Kornerup:1991:PIS
pages: 127--131
year: 1991
bibdate: Sat Nov 27 12:40:58 MST 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.27 12:40:58 MST
URL: http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Hull.pdf
acknowledgement: ack-nhfb
affiliation: Department of Computer Science, Toronto University, Ont., Canada
thesaurus: Digital arithmetic; Logic circuits; Microprocessor chips; Satellite computers
rawauthor: T. E. Hull and M. S. Cohen and C. B. Hall
rawtitle: Specifications for a variable-precision arithmetic coprocessor
abstract:
The authors have been developing a programming system intended to be especially convenient for scientific computing. Its main features are variable precision (decimal) floating-point arithmetic and convenient exception handling. The software implementation of the system has evolved over a number of years, and a partial hardware implementation of the arithmetic itself was constructed and used during the early stages of the project. Based on this experience, the authors have developed a set of specifications for an arithmetic coprocessor to support such a system. These specifications are described. An outline of the language features and how they can be used is also provided, to help justify the particular choice of coprocessor specifications. The authors also indicate what other hardware features would be most helpful to the systems programmer, especially for implementation of the exception handling.

keywords:
ARITH-10; decimal floating-point arithmetic; Exception handling; Floating-point arithmetic; Programming system; Scientific computing; Variable-precision arithmetic coprocessor

rawabstract:
The authors have been developing a programming system intended to be especially convenient for scientific computing. Its main features are variable precision (decimal) floating-point arithmetic and convenient exception handling. The software implementation of the system has evolved over a number of years, and a partial hardware implementation of the arithmetic itself was constructed and used during the early stages of the project. Based on this experience, the authors have developed a set of specifications for an arithmetic coprocessor to support such a system. These specifications are described. An outline of the language features and how they can be used is also provided, to help justify the particular choice of coprocessor specifications. The authors also indicate what other hardware features would be most helpful to the systems programmer, especially for implementation of the exception handling.

entry:
@InProceedings{Hull:1991:SVP,
  author =       "T. E. Hull and M. S. Cohen and C. B. Hall",
  title =        "Specifications for a variable-precision arithmetic
                 coprocessor",
  crossref =     "Kornerup:1991:PIS",
  pages =        "127--131",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Hull.pdf",
  abstract =     "The authors have been developing a programming system
                 intended to be especially convenient for scientific
                 computing. Its main features are variable precision
                 (decimal) floating-point arithmetic and convenient
                 exception handling. The software implementation of the
                 system has evolved over a number of years, and a
                 partial hardware implementation of the arithmetic
                 itself was constructed and used during the early stages
                 of the project. Based on this experience, the authors
                 have developed a set of specifications for an
                 arithmetic coprocessor to support such a system. These
                 specifications are described. An outline of the
                 language features and how they can be used is also
                 provided, to help justify the particular choice of
                 coprocessor specifications. The authors also indicate
                 what other hardware features would be most helpful to
                 the systems programmer, especially for implementation
                 of the exception handling.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Computer Science, Toronto University,
                 Ont., Canada",
  classification = "B1265B (Logic circuits); B1265F (Microprocessors and
                 microcomputers); B2570 (Semiconductor integrated
                 circuits); C5120 (Logic and switching circuits); C5130
                 (Microprocessor chips); C5230 (Digital arithmetic
                 methods)",
  keywords =     "ARITH-10; decimal floating-point arithmetic; Exception
                 handling; Floating-point arithmetic; Programming
                 system; Scientific computing; Variable-precision
                 arithmetic coprocessor",
  thesaurus =    "Digital arithmetic; Logic circuits; Microprocessor
                 chips; Satellite computers",
}


bibtype: book
filename: fparith.bib
label: Ince:1991:SQR
author: D. (Darrel) Ince
title: Software quality and reliability tools and methods
publisher: Chapman and Hall
address: London, UK
pages: 178
year: 1991
ISBN: 0-442-31314-4, 0-412-37810-8 OR 0442313144, 0412378108
ISBN13: 978-0-442-31314-2, 978-0-412-37810-2 OR 9780442313142, 9780412378102
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
series: Unicom applied information technology reports; [6]
acknowledgement: ack-nhfb
rawauthor: D. (Darrel) Ince
rawtitle: Software quality and reliability tools and methods
keywords:
Computer software --- Quality control.; Computer software --- Reliability.; Software --- Quality control

remark:
Aspects of path testing and mutation testing / M. R. Woodward --- Quality-- an integrated approach / A. Smith --- Quality management and software engineering / R. Hailstone --- The role of verification and validation tools in the production of critical software / J.T. Webb --- The real importance of software quality and the role of quality systems / A. Voss --- Software testing tools / E. Fergus ldots [et al.] --- FPV-- a floating point validation package / J. Du Croz --- Building in quality through the use of software tools / P.A.V. Hall --- Software requirements analysis, formal methods and software prototyping / D. Ince --- Increasing software quality by objectives and residual fault prognosis / K. Moller --- Towards a software quality control environment / M. Adam ldots [et al.] --- Expert system software quality problems / S. Ronchi and M. Martignano --- Quality assurance management for real-time software systems: the experience of the Spanish Civil Aviation Administration / J.P. Buendia, C. Bravo --- The PRX/A software reliability investigation / A.E.J. van Delft.

entry:
@Book{Ince:1991:SQR,
  author =       "D. (Darrel) Ince",
  title =        "Software quality and reliability tools and methods",
  publisher =    "Chapman and Hall",
  address =      "London, UK",
  pages =        "178",
  year =         "1991",
  ISBN =         "0-442-31314-4, 0-412-37810-8",
  ISBN-13 =      "978-0-442-31314-2, 978-0-412-37810-2",
  LCCN =         "????",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Unicom applied information technology reports; [6]",
  acknowledgement = ack-nhfb,
  keywords =     "Computer software --- Quality control.; Computer
                 software --- Reliability.; Software --- Quality
                 control",
  remark =       "Aspects of path testing and mutation testing / M. R.
                 Woodward --- Quality-- an integrated approach / A.
                 Smith --- Quality management and software engineering /
                 R. Hailstone --- The role of verification and
                 validation tools in the production of critical software
                 / J.T. Webb --- The real importance of software quality
                 and the role of quality systems / A. Voss --- Software
                 testing tools / E. Fergus \ldots{} [et al.] --- FPV-- a
                 floating point validation package / J. Du Croz ---
                 Building in quality through the use of software tools /
                 P.A.V. Hall --- Software requirements analysis, formal
                 methods and software prototyping / D. Ince ---
                 Increasing software quality by objectives and residual
                 fault prognosis / K. Moller --- Towards a software
                 quality control environment / M. Adam \ldots{} [et al.]
                 --- Expert system software quality problems / S. Ronchi
                 and M. Martignano --- Quality assurance management for
                 real-time software systems: the experience of the
                 Spanish Civil Aviation Administration / J.P. Buendia,
                 C. Bravo --- The PRX/A software reliability
                 investigation / A.E.J. van Delft.",
}


bibtype: incollection
filename: fparith.bib
label: Iri:1991:HAD
author: M. Iri
editor: A. Griewank and G. F. Corliss
booktitle: Automatic Differentiation of Algorithms: Theory, Implementation, and Application
title: History of automatic differentiation and rounding error estimation
crossref: Griewank:1991:ADA
pages: 3--16
year: 1991
bibdate: Thu May 27 07:45:02 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.05.27 07:45:02 ???
acknowledgement: ack-nhfb
rawauthor: M. Iri
rawbooktitle: Automatic Differentiation of Algorithms: Theory, Implementation, and Application
raweditor: A. Griewank and G. F. Corliss
rawtitle: History of automatic differentiation and rounding error estimation
entry:
@InCollection{Iri:1991:HAD,
  author =       "M. Iri",
  editor =       "A. Griewank and G. F. Corliss",
  booktitle =    "Automatic Differentiation of Algorithms: Theory,
                 Implementation, and Application",
  title =        "History of automatic differentiation and rounding
                 error estimation",
  crossref =     "Griewank:1991:ADA",
  pages =        "3--16",
  year =         "1991",
  bibdate =      "Thu May 27 07:45:02 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Jain:1991:CSN
author: Suneel Jain
title: Circular scheduling: a new technique to perform software pipelining
journal: j-SIGPLAN
volume: 26
number: 6
pages: 219--228
month: jun
monthnumber: 6
year: 1991
CODEN: SINODQ
ISSN: 0362-1340 (print), 1523-2867 (print), 1558-1160 OR 03621340 (print), 15232867 (print), 15581160
ISSNL: 0362-1340 OR 03621340
bibdate: Sun Dec 14 09:16:07 MST 2003
bibtimestamp: 2003.12.14 09:16:07 MST
URL: http://www.acm.org:80/pubs/citations/proceedings/pldi/113445/p219-jain/
fjournal: ACM SIGPLAN Notices
acknowledgement: ack-nhfb
affiliation: MIPS Comput. Syst. Inc., Sunnyvale, CA, USA
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J706
rawauthor: Suneel Jain
rawtitle: Circular scheduling: a new technique to perform software pipelining
bibsource:
http://portal.acm.org/; http://www.acm.org/pubs/contents/proceedings/pldi/113445/index.html; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
With the advent of deeply pipelined RISC processors, static instruction scheduling by the compiler has become extremely important to obtain high processor performance. This is especially true for floating point code. The author suggests using a new algorithm called circular scheduling to perform software pipelining. Software pipelining has previously been investigated mostly for VLIW architectures. The algorithm described is shown to be quite effective for a scalar architecture. Register renaming, an idea that originates from dynamic instruction scheduling, is used in conjunction with this algorithm to augment its performance. The techniques described here have been implemented as part of a commercial, production quality optimizing compiler for a RISC architecture. The resulting performance improvement has verified the feasibility and practicality of the techniques.

keywords:
algorithms; Circular scheduling; Deeply pipelined RISC processors; Dynamic instruction scheduling; experimentation; performance; Production quality optimizing compiler; RISC architecture; Scalar architecture; Software pipelining; Static instruction scheduling; VLIW architectures

subject:
bf D.3.4 Software, PROGRAMMING LANGUAGES, Processors, Compilers. bf D.3.4 Software, PROGRAMMING LANGUAGES, Processors, Optimization.

thesaurus:
Parallel programming; Pipeline processing; Program compilers; Reduced instruction set computing; Scheduling

rawabstract:
With the advent of deeply pipelined RISC processors, static instruction scheduling by the compiler has become extremely important to obtain high processor performance. This is especially true for floating point code. The author suggests using a new algorithm called circular scheduling to perform software pipelining. Software pipelining has previously been investigated mostly for VLIW architectures. The algorithm described is shown to be quite effective for a scalar architecture. Register renaming, an idea that originates from dynamic instruction scheduling, is used in conjunction with this algorithm to augment its performance. The techniques described here have been implemented as part of a commercial, production quality optimizing compiler for a RISC architecture. The resulting performance improvement has verified the feasibility and practicality of the techniques.

entry:
@Article{Jain:1991:CSN,
  author =       "Suneel Jain",
  title =        "Circular scheduling: a new technique to perform
                 software pipelining",
  journal =      j-SIGPLAN,
  volume =       "26",
  number =       "6",
  pages =        "219--228",
  month =        jun,
  year =         "1991",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sun Dec 14 09:16:07 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.acm.org/pubs/contents/proceedings/pldi/113445/index.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/pldi/113445/p219-jain/",
  abstract =     "With the advent of deeply pipelined RISC processors,
                 static instruction scheduling by the compiler has
                 become extremely important to obtain high processor
                 performance. This is especially true for floating point
                 code. The author suggests using a new algorithm called
                 circular scheduling to perform software pipelining.
                 Software pipelining has previously been investigated
                 mostly for VLIW architectures. The algorithm described
                 is shown to be quite effective for a scalar
                 architecture. Register renaming, an idea that
                 originates from dynamic instruction scheduling, is used
                 in conjunction with this algorithm to augment its
                 performance. The techniques described here have been
                 implemented as part of a commercial, production quality
                 optimizing compiler for a RISC architecture. The
                 resulting performance improvement has verified the
                 feasibility and practicality of the techniques.",
  acknowledgement = ack-nhfb,
  affiliation =  "MIPS Comput. Syst. Inc., Sunnyvale, CA, USA",
  classification = "C5220 (Computer architecture); C6110 (Systems
                 analysis and programming); C6150C (Compilers,
                 interpreters and other processors); C6150J (Operating
                 systems)",
  confdate =     "26-28 June 1991",
  conflocation = "Toronto, Ont., Canada",
  confsponsor =  "ACM",
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "algorithms; Circular scheduling; Deeply pipelined RISC
                 processors; Dynamic instruction scheduling;
                 experimentation; performance; Production quality
                 optimizing compiler; RISC architecture; Scalar
                 architecture; Software pipelining; Static instruction
                 scheduling; VLIW architectures",
  subject =      "{\bf D.3.4} Software, PROGRAMMING LANGUAGES,
                 Processors, Compilers. {\bf D.3.4} Software,
                 PROGRAMMING LANGUAGES, Processors, Optimization.",
  thesaurus =    "Parallel programming; Pipeline processing; Program
                 compilers; Reduced instruction set computing;
                 Scheduling",
}


bibtype: inproceedings
filename: fparith.bib
label: Jain:1991:NRS
author: V. K. Jain and G. E. Perez and J. M. Wills
title: Novel reciprocal and square-root VLSI cell: architecture and application to signal processing
crossref: IEEE:1991:VCA
volume: 2
pages: 1201--1204
year: 1991
bibdate: Sat Jul 16 15:28:14 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 15:28:14 MDT
acknowledgement: ack-nj
rawauthor: V. K. Jain and G. E. Perez and J. M. Wills
rawtitle: Novel reciprocal and square-root {VLSI} cell: architecture and application to signal processing
entry:
@InProceedings{Jain:1991:NRS,
  author =       "V. K. Jain and G. E. Perez and J. M. Wills",
  title =        "Novel reciprocal and square-root {VLSI} cell:
                 architecture and application to signal processing",
  crossref =     "IEEE:1991:VCA",
  volume =       "2",
  pages =        "1201--1204",
  year =         "1991",
  bibdate =      "Sat Jul 16 15:28:14 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,
  summary =      "A novel high-speed cell, capable of performing a
                 square-root or a reciprocal function in two clock
                 cycles, is presented. Its performance signifies an
                 estimated three-fold increase in speed over existing
                 approaches. Furthermore, since both functions
                 \ldots{}",
}


bibtype: techreport
filename: fparith.bib
label: Kahan:1991:APL
author: William Kahan and J. W. Thomas
title: Augmenting a Programming Language with Complex Arithmetic
number: NCEG/91-039, UCB/CSD 91/667
institution: inst-BERKELEY-CS
address: inst-BERKELEY-CS:adr
pages: 8
day: 15
month: nov
monthnumber: 11
year: 1991
bibdate: Mon Dec 26 21:13:51 GMT 1994
bibtimestamp: 1994.12.26 21:13:51 GMT
note: Manuscript
acknowledgement: ack-nhfb
rawauthor: William Kahan and J. W. Thomas
rawnote: Manuscript
rawtitle: Augmenting a Programming Language with Complex Arithmetic
entry:
@TechReport{Kahan:1991:APL,
  author =       "William Kahan and J. W. Thomas",
  title =        "Augmenting a Programming Language with Complex
                 Arithmetic",
  number =       "NCEG/91-039, UCB/CSD 91/667",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  pages =        "8",
  day =          "15",
  month =        nov,
  year =         "1991",
  bibdate =      "Mon Dec 26 21:13:51 GMT 1994",
  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: Kahan:1991:ARL
author: W. Kahan
title: Analysis and Refutation of the LCAS
journal: j-SIGNUM
volume: 26
number: 3
pages: 2--15
month: jul
monthnumber: 7
year: 1991
CODEN: SNEWD6
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Fri Jan 5 07:58:42 MST 1996
bibtimestamp: 1996.01.05 07:58:42 MST
fjournal: ACM SIGNUM Newsletter
keywords: LCAS (Language Compatible Arithmetic Standard)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/signum
rawauthor: W. Kahan
rawtitle: Analysis and Refutation of the {LCAS}
bibsource:
http://portal.acm.org/; 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-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/signum.bib

entry:
@Article{Kahan:1991:ARL,
  author =       "W. Kahan",
  title =        "Analysis and Refutation of the {LCAS}",
  journal =      j-SIGNUM,
  volume =       "26",
  number =       "3",
  pages =        "2--15",
  month =        jul,
  year =         "1991",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Fri Jan 5 07:58:42 MST 1996",
  bibsource =    "http://portal.acm.org/;
                 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-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/signum.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "LCAS (Language Compatible Arithmetic Standard)",
}


bibtype: inproceedings
filename: fparith.bib
label: Kantabutra:1991:DOC
author: Vitit Kantabutra
title: Designing optimum carry-skip adders
crossref: Kornerup:1991:PIS
pages: 146--153
year: 1991
bibdate: Sat Nov 27 12:40:58 MST 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.27 12:40:58 MST
URL: http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Kantabutra.pdf
keywords: ARITH-10
acknowledgement: ack-nhfb
rawauthor: Vitit Kantabutra
rawtitle: Designing optimum carry-skip adders
entry:
@InProceedings{Kantabutra:1991:DOC,
  author =       "Vitit Kantabutra",
  title =        "Designing optimum carry-skip adders",
  crossref =     "Kornerup:1991:PIS",
  pages =        "146--153",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Kantabutra.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}


bibtype: article
filename: fparith.bib
label: Kim:1991:ERB
author: Jin Yul Kim and Kyu Ho Park and Hwang Soo Lee
title: Efficient residue-to-binary conversion technique with rounding error compensation
journal: j-IEEE-TRANS-CIRCUITS-SYST
volume: 38
number: 3
pages: 315--317
month: mar
monthnumber: 3
year: 1991
CODEN: ICSYBT
ISSN: 0098-4094 (print), 1558-1276 (electronic) OR 00984094 (print), 15581276 (electronic)
ISSNL: 0098-4094 OR 00984094
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 Circuits and Systems
acknowledgement: ack-nhfb
rawauthor: Jin Yul Kim and Kyu Ho Park and Hwang Soo Lee
rawtitle: Efficient residue-to-binary conversion technique with rounding error compensation
entry:
@Article{Kim:1991:ERB,
  author =       "Jin Yul Kim and Kyu Ho Park and Hwang Soo Lee",
  title =        "Efficient residue-to-binary conversion technique with
                 rounding error compensation",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "38",
  number =       "3",
  pages =        "315--317",
  month =        mar,
  year =         "1991",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  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 Circuits and Systems",
  summary =      "An improved scaled-decoding technique (defined as
                 residue-to-binary conversion of which outputs are
                 scaled by a constant) for hardware implementations in
                 the residue number system (RNS) is presented. The
                 technique is based on the Chinese remainder \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Kim:1991:NIC
author: S. W. Kim and T. Stouraitis
booktitle: IEEE International Symposium on Circuits and Systems, 11--14 June 1991
title: New implementations of converters for the residue and quadratic residue number system
volume: 5
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 2959--2962
year: 1991
DOI: https://doi.org/10.1109/ISCAS.1991.176166
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: S. W. Kim and T. Stouraitis
rawbooktitle: {IEEE} International Symposium on Circuits and Systems, 11--14 June 1991
rawtitle: New implementations of converters for the residue and quadratic residue number system
entry:
@InProceedings{Kim:1991:NIC,
  author =       "S. W. Kim and T. Stouraitis",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems, 11--14 June 1991",
  title =        "New implementations of converters for the residue and
                 quadratic residue number system",
  volume =       "5",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "2959--2962",
  year =         "1991",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.1991.176166",
  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 =      "Full adder (FA)-based converters are proposed for
                 efficiently performing complex number calculations. The
                 basic idea is to use FA arrays to decompose 2 i terms
                 into 2 j terms, where j{$<$}i, by modulo arithmetic.
                 \ldots{}",
}


bibtype: book
filename: fparith.bib
label: Klatte:1991:PSB
author: R. Klatte and U. Kulisch and M. Neaga and D. Ratz and Ch. Ullrich
title: PASCAL-XSC: Sprachbeschreibung mit Beispielen
publisher: pub-SV
address: pub-SV:adr
pages: x + 345
year: 1991
ISBN: 0-387-53714-7 OR 0387537147
ISBN13: 978-0-387-53714-6 OR 9780387537146
LCCN: QA76.73.P2 P42 1991
bibdate: Mon Dec 18 09:37:18 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.18 09:37:18 ???
note: English translation is available as cite Klatte:1991:PXP.
acknowledgement: ack-nhfb
rawauthor: R. Klatte and U. Kulisch and M. Neaga and D. Ratz and Ch. Ullrich
rawnote: English translation is available as \cite{Klatte:1991:PXP}.
rawtitle: {PASCAL-XSC: Sprachbeschreibung mit Beispielen}
entry:
@Book{Klatte:1991:PSB,
  author =       "R. Klatte and U. Kulisch and M. Neaga and D. Ratz and
                 Ch. Ullrich",
  title =        "{PASCAL-XSC: Sprachbeschreibung mit Beispielen}",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "x + 345",
  year =         "1991",
  ISBN =         "0-387-53714-7",
  ISBN-13 =      "978-0-387-53714-6",
  LCCN =         "QA76.73.P2 P42 1991",
  bibdate =      "Mon Dec 18 09:37:18 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "English translation is available as
                 \cite{Klatte:1991:PXP}.",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: fparith.bib
label: Klatte:1991:PXP
author: R. Klatte and U. Kulisch and M. Neaga and D. Ratz and Ch. Ullrich
title: PASCAL-XSC: A PASCAL Extension for Scientific Computation
publisher: pub-SV
address: pub-SV:adr
pages: x + 344
year: 1991
ISBN: 0-387-55137-9 (New York), 3-540-55137-9 (Berlin) OR 0387551379 (New York), 3540551379 (Berlin)
LCCN: QA76.73.P2 P4213 1992
bibdate: Thu Nov 8 14:50:35 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.08 14:50:35 ???
note: English translation of cite Klatte:1991:PSB.
acknowledgement: ack-nhfb
rawauthor: R. Klatte and U. Kulisch and M. Neaga and D. Ratz and Ch. Ullrich
rawnote: English translation of \cite{Klatte:1991:PSB}.
rawtitle: {PASCAL-XSC}: {A PASCAL} Extension for Scientific Computation
ISBN13:
978-0-387-55137-1 (New York), 978-3-540-55137-9 (Berlin) OR 9780387551371 (New York), 9783540551379 (Berlin)

entry:
@Book{Klatte:1991:PXP,
  author =       "R. Klatte and U. Kulisch and M. Neaga and D. Ratz and
                 Ch. Ullrich",
  title =        "{PASCAL-XSC}: {A PASCAL} Extension for Scientific
                 Computation",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "x + 344",
  year =         "1991",
  ISBN =         "0-387-55137-9 (New York), 3-540-55137-9 (Berlin)",
  ISBN-13 =      "978-0-387-55137-1 (New York), 978-3-540-55137-9
                 (Berlin)",
  LCCN =         "QA76.73.P2 P4213 1992",
  bibdate =      "Thu Nov 8 14:50:35 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "English translation of \cite{Klatte:1991:PSB}.",
  price =        "DM64.00",
  acknowledgement = ack-nhfb,
  referred =     "[Corl91a].",
}


bibtype: inproceedings
filename: fparith.bib
label: Knofel:1991:FHU
author: Andreas Knofel
title: Fast hardware units for the computation of accurate dot products
crossref: Kornerup:1991:PIS
pages: 70--74
year: 1991
bibdate: Sat Nov 27 12:40:58 MST 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.27 12:40:58 MST
URL: http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Knofel.pdf
keywords: ARITH-10
acknowledgement: ack-nhfb
rawauthor: Andreas Kn{\"o}fel
rawtitle: Fast hardware units for the computation of accurate dot products
entry:
@InProceedings{Knofel:1991:FHU,
  author =       "Andreas Kn{\"o}fel",
  title =        "Fast hardware units for the computation of accurate
                 dot products",
  crossref =     "Kornerup:1991:PIS",
  pages =        "70--74",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Knofel.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}


bibtype: inproceedings
filename: fparith.bib
label: Knowles:1991:APD
author: S. Knowles
title: Arithmetic Processor Design for the T9000 Transputer
crossref: SPIE:1991:PSI
pages: 230--243
year: 1991
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: S. Knowles
rawtitle: Arithmetic Processor Design for the {T9000} Transputer
entry:
@InProceedings{Knowles:1991:APD,
  author =       "S. Knowles",
  title =        "Arithmetic Processor Design for the {T9000}
                 Transputer",
  crossref =     "SPIE:1991:PSI",
  pages =        "230--243",
  year =         "1991",
  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: article
filename: fparith.bib
label: Koc:1991:FAG
author: Cetin K. Koc and Sarath N. Arachchige
title: A fast algorithm for Gaussian elimination over GF(2) and its implementation on the GAPP
journal: j-J-PAR-DIST-COMP
volume: 13
number: 1
pages: 118--122
day: 1
month: sep
monthnumber: 9
year: 1991
CODEN: JPDCER
ISSN: 0743-7315 (print), 1096-0848 (electronic) OR 07437315 (print), 10960848 (electronic)
ISSNL: 0743-7315 OR 07437315
bibdate: Sat Apr 12 19:06:31 MDT 1997
bibsource: Compendex database; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.04.12 19:06:31 MDT
fjournal: Journal of Parallel and Distributed Computing
acknowledgement: ack-nhfb
affiliation: Univ of Houston
affiliationaddress: Houston, TX, USA
corpsource: Department of Electr. Eng., Houston University, TX, USA
journalURL: http://www.sciencedirect.com/science/journal/07437315
journalabr: J Parallel Distrib Comput
treatment: T Theoretical or Mathematical
rawauthor: Cetin K. Koc and Sarath N. Arachchige
rawtitle: A fast algorithm for {Gaussian} elimination over {GF(2)} and its implementation on the {GAPP}
keywords:
1s location; Algorithms; algorithms; arithmetic parallel processor; binary matrix; binary search; Binary search technique; bit operations; bit-array; columns; computational complexity; Computer Programming; Computer Systems, Digital--Parallel Processing; Galois fields; GAPP; Gaussian elimination; geometric; Geometric arithmetic parallel processors; GF(2); Large binary matrices; Mathematical Techniques--Matrix Algebra; matrix algebra; ones location; parallel; Triangularization; triangularize; vertical memory

entry:
@Article{Koc:1991:FAG,
  author =       "Cetin K. Koc and Sarath N. Arachchige",
  title =        "A fast algorithm for {Gaussian} elimination over
                 {GF(2)} and its implementation on the {GAPP}",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "13",
  number =       "1",
  pages =        "118--122",
  day =          "1",
  month =        sep,
  year =         "1991",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Sat Apr 12 19:06:31 MDT 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ of Houston",
  affiliationaddress = "Houston, TX, USA",
  classification = "722; 723; 921; C4140 (Linear algebra); C4240
                 (Programming and algorithm theory)",
  corpsource =   "Department of Electr. Eng., Houston University, TX,
                 USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "1s location; Algorithms; algorithms; arithmetic
                 parallel processor; binary matrix; binary search;
                 Binary search technique; bit operations; bit-array;
                 columns; computational complexity; Computer
                 Programming; Computer Systems, Digital--Parallel
                 Processing; Galois fields; GAPP; Gaussian elimination;
                 geometric; Geometric arithmetic parallel processors;
                 GF(2); Large binary matrices; Mathematical
                 Techniques--Matrix Algebra; matrix algebra; ones
                 location; parallel; Triangularization; triangularize;
                 vertical memory",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: fparith.bib
label: Koc:1991:IAM
author: Cetin K. Koc
title: An improved algorithm for mixed-radix conversion of residue numbers
journal: j-COMPUT-MATH-APPL
volume: 22
number: 8
pages: 63--71
year: 1991
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 19:11:04 MST 2017
bibtimestamp: 2017.03.01 19:11:04 MST
URL: http://www.sciencedirect.com/science/article/pii/089812219190014U
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}}
rawtitle: An improved algorithm for mixed-radix conversion of residue numbers
entry:
@Article{Koc:1991:IAM,
  author =       "{\c{C}}etin K. Ko{\c{c}}",
  title =        "An improved algorithm for mixed-radix conversion of
                 residue numbers",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "22",
  number =       "8",
  pages =        "63--71",
  month =        "????",
  year =         "1991",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 19:11:04 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/089812219190014U",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: mastersthesis
filename: fparith.bib
label: Kohprasert:1991:FAC
author: Teera Kohprasert
title: 32-bit floating-point arithmetic coprocessor design using VHDL
type: Thesis (M.S.)
school: Florida Institute of Technology
address: Melbourne, FL, USA
pages: xiv + 456
year: 1991
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: Teera Kohprasert
rawtitle: 32-bit floating-point arithmetic coprocessor design using {VHDL}
keywords:
Computer arithmetic and logic units --- Design and construction.; VHDL (Computer hardware description language).

entry:
@MastersThesis{Kohprasert:1991:FAC,
  author =       "Teera Kohprasert",
  title =        "32-bit floating-point arithmetic coprocessor design
                 using {VHDL}",
  type =         "Thesis ({M.S.})",
  school =       "Florida Institute of Technology",
  address =      "Melbourne, FL, USA",
  pages =        "xiv + 456",
  year =         "1991",
  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 arithmetic and logic units --- Design and
                 construction.; VHDL (Computer hardware description
                 language).",
}


bibtype: article
filename: fparith.bib
label: Kostopoulos:1991:ACB
author: D. K. Kostopoulos
title: An Algorithm for the Computation of Binary Logarithms
journal: j-IEEE-TRANS-COMPUT
volume: 40
number: 11
pages: 1267--1270
month: nov
monthnumber: 11
year: 1991
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.102831
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Sep 1 10:16:09 1994
bibtimestamp: 1994.09.01 10:16:09 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: D. K. Kostopoulos
rawtitle: An Algorithm for the Computation of Binary Logarithms
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib

entry:
@Article{Kostopoulos:1991:ACB,
  author =       "D. K. Kostopoulos",
  title =        "An Algorithm for the Computation of Binary
                 Logarithms",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "40",
  number =       "11",
  pages =        "1267--1270",
  month =        nov,
  year =         "1991",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.102831",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 1 10:16:09 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  acknowledgement = ack-nj,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: techreport
filename: fparith.bib
label: Kramer:1991:EFA
author: David Kramer and Isaac D. Scherson
type: Technical report
number: 91-73
institution: Information and Computer Science, University of California, Irvine
address: Irvine, CA, USA
pages: 18
year: 1991
LCCN: Z699 .C3 no. 91-73
bibdate: Fri Jan 5 11:51:46 MST 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.01.05 11:51:46 MST
acknowledgement: ack-nhfb
rawauthor: David Kramer and Isaac D. Scherson
title:
The effect of FPU architecture on a dynamic precision algorithm for the solution of differential equations

rawtitle:
The effect of {FPU} architecture on a dynamic precision algorithm for the solution of differential equations

entry:
@TechReport{Kramer:1991:EFA,
  author =       "David Kramer and Isaac D. Scherson",
  title =        "The effect of {FPU} architecture on a dynamic
                 precision algorithm for the solution of differential
                 equations",
  type =         "Technical report",
  number =       "91-73",
  institution =  "Information and Computer Science, University of
                 California, Irvine",
  address =      "Irvine, CA, USA",
  pages =        "18",
  year =         "1991",
  LCCN =         "Z699 .C3 no. 91-73",
  bibdate =      "Fri Jan 5 11:51:46 MST 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Kuhnel:1991:OPS
author: Lars Kuhnel
title: Optimal purely systolic addition
crossref: Kornerup:1991:PIS
pages: 172--179
year: 1991
bibdate: Sat Nov 27 12:40:58 MST 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.27 12:40:58 MST
URL: http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Kuhnel.pdf
keywords: ARITH-10
acknowledgement: ack-nhfb
rawauthor: Lars K{\"u}hnel
rawtitle: Optimal purely systolic addition
entry:
@InProceedings{Kuhnel:1991:OPS,
  author =       "Lars K{\"u}hnel",
  title =        "Optimal purely systolic addition",
  crossref =     "Kornerup:1991:PIS",
  pages =        "172--179",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Kuhnel.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}


bibtype: article
filename: fparith.bib
label: Kurokawa:1991:CGU
author: T. Kurokawa and T. Mizukoshi
title: Computer graphics using logarithmic number systems
journal: IEICE Transactions
volume: E74
number: 2
pages: 447--451
month: feb
monthnumber: 2
year: 1991
ISSN: 0917-1673 OR 09171673
bibdate: Tue Dec 12 09:20:21 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.12 09:20:21 MST
acknowledgement: ack-nhfb
affiliation: Department of Ind. Eng., Aichi Inst. of Technol., Toyota, Japan
thesaurus: Computer graphics; Digital arithmetic
rawauthor: T. Kurokawa and T. Mizukoshi
rawtitle: Computer graphics using logarithmic number systems
abstract:
Logarithmic arithmetic (LA) is a very fast computational method for real numbers. Its precision is better than a floating point arithmetic of equivalent word length and range. This paper shows a method to use LA in computer graphics-picture generation of almost any kind. Various experiments are done-from curve drawing to 3D image generation. The results are all excellent for quality and speed.

keywords:
3D image generation; Computer graphics; Curve drawing; Fast computational method for real numbers; Logarithmic arithmetic; Logarithmic number systems; Picture generation; Precision; Word length

rawabstract:
Logarithmic arithmetic (LA) is a very fast computational method for real numbers. Its precision is better than a floating point arithmetic of equivalent word length and range. This paper shows a method to use LA in computer graphics-picture generation of almost any kind. Various experiments are done-from curve drawing to 3D image generation. The results are all excellent for quality and speed.

entry:
@Article{Kurokawa:1991:CGU,
  author =       "T. Kurokawa and T. Mizukoshi",
  title =        "Computer graphics using logarithmic number systems",
  journal =      "IEICE Transactions",
  volume =       "E74",
  number =       "2",
  pages =        "447--451",
  month =        feb,
  year =         "1991",
  ISSN =         "0917-1673",
  bibdate =      "Tue Dec 12 09:20:21 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Logarithmic arithmetic (LA) is a very fast
                 computational method for real numbers. Its precision is
                 better than a floating point arithmetic of equivalent
                 word length and range. This paper shows a method to use
                 LA in computer graphics-picture generation of almost
                 any kind. Various experiments are done-from curve
                 drawing to 3D image generation. The results are all
                 excellent for quality and speed.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Ind. Eng., Aichi Inst. of Technol.,
                 Toyota, Japan",
  classification = "C5230 (Digital arithmetic methods); C6130B (Graphics
                 techniques)",
  keywords =     "3D image generation; Computer graphics; Curve drawing;
                 Fast computational method for real numbers; Logarithmic
                 arithmetic; Logarithmic number systems; Picture
                 generation; Precision; Word length",
  pubcountry =   "Japan",
  thesaurus =    "Computer graphics; Digital arithmetic",
}


bibtype: article
filename: fparith.bib
label: Lai:1991:HNS
author: F.-S. Lai and C.-F. E. Wu
title: A hybrid number system processor with geometric and complex arithmetic capabilities
journal: j-IEEE-TRANS-COMPUT
volume: 40
number: 8
pages: 952--962
month: aug
monthnumber: 8
year: 1991
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.83639
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 12:52:23 MDT 2011
bibtimestamp: 2011.07.07 12:52:23 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=83639
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
affiliation: IBM Thomas J. Watson Res. Center, Yorktown Heights, NY, USA
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
thesaurus: Digital arithmetic
rawauthor: F.-S. Lai and C.-F. E. Wu
rawtitle: A hybrid number system processor with geometric and complex arithmetic capabilities
abstract:
The architecture, design, and performance of a hybrid number system processor are described. The processor performs multiplication, division, square root, and square in the logarithmic number system (LNS) domain. However, the input, output, addition, and subtraction are all executed in the 32-b IEEE standard floating-point number system. With the LNS multiplier and pipelined architecture, the processor is able to perform the geometric and complex arithmetic very effectively. The processor is also shown to compare well to an existing 32-b floating-point DSP (digital signal processor) chip. For the same level of CMOS technology, the performance ratios between the hybrid number system and the floating-point processor are shown to be 6.4:1 and 8:1 for division and square root, respectively; for the complex FFT (fast Fourier transform) algorithm, the ratio is around 2:1. (27 Refs.)

keywords:
Complex arithmetic; Division; Floating-point number system; Geometric; Hybrid number system processor; Logarithmic number system; Multiplication; Square; Square root

rawabstract:
The architecture, design, and performance of a hybrid number system processor are described. The processor performs multiplication, division, square root, and square in the logarithmic number system (LNS) domain. However, the input, output, addition, and subtraction are all executed in the 32-b IEEE standard floating-point number system. With the LNS multiplier and pipelined architecture, the processor is able to perform the geometric and complex arithmetic very effectively. The processor is also shown to compare well to an existing 32-b floating-point DSP (digital signal processor) chip. For the same level of CMOS technology, the performance ratios between the hybrid number system and the floating-point processor are shown to be 6.4:1 and 8:1 for division and square root, respectively; for the complex FFT (fast Fourier transform) algorithm, the ratio is around 2:1. (27 Refs.)

entry:
@Article{Lai:1991:HNS,
  author =       "F.-S. Lai and C.-F. E. Wu",
  title =        "A hybrid number system processor with geometric and
                 complex arithmetic capabilities",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "40",
  number =       "8",
  pages =        "952--962",
  month =        aug,
  year =         "1991",
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  DOI =          "https://doi.org/10.1109/12.83639",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 12:52:23 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=83639",
  abstract =     "The architecture, design, and performance of a hybrid
                 number system processor are described. The processor
                 performs multiplication, division, square root, and
                 square in the logarithmic number system (LNS) domain.
                 However, the input, output, addition, and subtraction
                 are all executed in the 32-b IEEE standard
                 floating-point number system. With the LNS multiplier
                 and pipelined architecture, the processor is able to
                 perform the geometric and complex arithmetic very
                 effectively. The processor is also shown to compare
                 well to an existing 32-b floating-point DSP (digital
                 signal processor) chip. For the same level of CMOS
                 technology, the performance ratios between the hybrid
                 number system and the floating-point processor are
                 shown to be 6.4:1 and 8:1 for division and square root,
                 respectively; for the complex FFT (fast Fourier
                 transform) algorithm, the ratio is around 2:1. (27
                 Refs.)",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM Thomas J. Watson Res. Center, Yorktown Heights,
                 NY, USA",
  ajournal =     "IEEE Trans. Comput.",
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
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                 Logarithmic number system; Multiplication; Square;
                 Square root",
  thesaurus =    "Digital arithmetic",
}


bibtype: article
filename: fparith.bib
label: Lee:1991:FPPa
author: Roland L. Lee and Alex Y. Kwok and Faye A. Briggs
title: The Floating Point Performance of a superscalar SPARC Processor
journal: j-COMP-ARCH-NEWS
volume: 19
number: 2
pages: 28--37
month: apr
monthnumber: 4
year: 1991
CODEN: CANED2
ISSN: 0163-5964 (print), 1943-5851 (electronic) OR 01635964 (print), 19435851 (electronic)
ISSNL: 0163-5964 OR 01635964
bibdate: Fri May 12 09:40:40 MDT 2006
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2006.05.12 09:40:40 MDT
note: Co-published in em Operating Systems Review, bf 28(3S).
fjournal: ACM SIGARCH Computer Architecture News
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/sigarch
rawauthor: Roland L. Lee and Alex Y. Kwok and Fay{\'e} A. Briggs
rawnote: Co-published in {\em Operating Systems Review}, {\bf 28}(3S).
rawtitle: The Floating Point Performance of a superscalar {SPARC} Processor
entry:
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  title =        "The Floating Point Performance of a superscalar
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  number =       "2",
  pages =        "28--37",
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  ISSN-L =       "0163-5964",
  bibdate =      "Fri May 12 09:40:40 MDT 2006",
  bibsource =    "http://portal.acm.org/;
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  note =         "Co-published in {\em Operating Systems Review}, {\bf
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  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "https://dl.acm.org/loi/sigarch",
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bibtype: article
filename: fparith.bib
label: Lee:1991:FPPb
author: Roland L. Lee and Alex Y. Kwok and Faye A. Briggs
title: The floating-point performance of a superscalar SPARC processor
journal: j-OPER-SYS-REV
volume: 25
number: 3S
pages: 28--37
month: apr
monthnumber: 4
year: 1991
CODEN: OSRED8
ISSN: 0163-5980 (print), 1943-586X (electronic) OR 01635980 (print), 1943586X (electronic)
ISSNL: 0163-5980 OR 01635980
bibdate: Sat Aug 26 15:24:15 MDT 2006
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2006.08.26 15:24:15 MDT
fjournal: Operating Systems Review
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J597
rawauthor: Roland L. Lee and Alex Y. Kwok and Fay{\'e} A. Briggs
rawtitle: The floating-point performance of a superscalar {SPARC} processor
entry:
@Article{Lee:1991:FPPb,
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  title =        "The floating-point performance of a superscalar
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  volume =       "25",
  number =       "3S",
  pages =        "28--37",
  month =        apr,
  year =         "1991",
  CODEN =        "OSRED8",
  ISSN =         "0163-5980 (print), 1943-586X (electronic)",
  ISSN-L =       "0163-5980",
  bibdate =      "Sat Aug 26 15:24:15 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Operating Systems Review",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J597",
}


bibtype: article
filename: fparith.bib
label: Lee:1991:FPPc
author: Roland L. Lee and Alex Y. Kwok and Faye A. Briggs
title: The Floating-Point Performance of a Superscalar SPARC Processor
journal: j-SIGPLAN
volume: 26
number: 4
pages: 28--37
month: apr
monthnumber: 4
year: 1991
CODEN: SINODQ
ISSN: 0362-1340 (print), 1523-2867 (print), 1558-1160 OR 03621340 (print), 15232867 (print), 15581160
ISSNL: 0362-1340 OR 03621340
bibdate: Tue Dec 12 09:20:21 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.12 09:20:21 MST
fjournal: ACM SIGPLAN Notices
acknowledgement: ack-nhfb
affiliation: Sun Microsyst. Inc., Mountain View, CA, USA
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J706
thesaurus: Optimisation; Parallel architectures; Performance evaluation; Pipeline processing; Scheduling
rawauthor: Roland L. Lee and Alex Y. Kwok and Fay{\'e} A. Briggs
rawtitle: The Floating-Point Performance of a Superscalar {SPARC} Processor
abstract:
The floating point performance of superscalar SPARC processors is evaluated based on empirical data from 12 benchmarks. This evaluation is done in the context of two software instruction scheduling optimizations: loop unrolling and software pipelining, and for three machine models: 1-scalar, 2-scalar and 4-scalar. The authors also consider the effect of the memory system on the performance improvements. Superscalar hardware alone exhibit little performance improvement without software optimization. Of the two scheduling methods, software pipelining more effectively takes advantage of increased hardware parallelism, and achieves near optimal speedup on the 4-scalar machine model. The performance of loop unrolling is restricted by the limited number of floating point registers in the SPARC architecture. The best performance level is obtained by applying both optimization techniques. A superscalar SPARC processor can provide improved floating point performance but with significant software and hardware development costs.

keywords:
Benchmarks; Development costs; Floating point performance; Floating point registers; Hardware parallelism; Loop unrolling; Memory system; N-scalar machine models; Optimal speedup; Software instruction scheduling optimizations; Software pipelining; SPARC architecture; Superscalar SPARC processor

rawabstract:
The floating point performance of superscalar SPARC processors is evaluated based on empirical data from 12 benchmarks. This evaluation is done in the context of two software instruction scheduling optimizations: loop unrolling and software pipelining, and for three machine models: 1-scalar, 2-scalar and 4-scalar. The authors also consider the effect of the memory system on the performance improvements. Superscalar hardware alone exhibit little performance improvement without software optimization. Of the two scheduling methods, software pipelining more effectively takes advantage of increased hardware parallelism, and achieves near optimal speedup on the 4-scalar machine model. The performance of loop unrolling is restricted by the limited number of floating point registers in the SPARC architecture. The best performance level is obtained by applying both optimization techniques. A superscalar SPARC processor can provide improved floating point performance but with significant software and hardware development costs.

entry:
@Article{Lee:1991:FPPc,
  author =       "Roland L. Lee and Alex Y. Kwok and Fay{\'e} A.
                 Briggs",
  title =        "The Floating-Point Performance of a Superscalar
                 {SPARC} Processor",
  journal =      j-SIGPLAN,
  volume =       "26",
  number =       "4",
  pages =        "28--37",
  month =        apr,
  year =         "1991",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Tue Dec 12 09:20:21 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The floating point performance of superscalar SPARC
                 processors is evaluated based on empirical data from 12
                 benchmarks. This evaluation is done in the context of
                 two software instruction scheduling optimizations: loop
                 unrolling and software pipelining, and for three
                 machine models: 1-scalar, 2-scalar and 4-scalar. The
                 authors also consider the effect of the memory system
                 on the performance improvements. Superscalar hardware
                 alone exhibit little performance improvement without
                 software optimization. Of the two scheduling methods,
                 software pipelining more effectively takes advantage of
                 increased hardware parallelism, and achieves near
                 optimal speedup on the 4-scalar machine model. The
                 performance of loop unrolling is restricted by the
                 limited number of floating point registers in the SPARC
                 architecture. The best performance level is obtained by
                 applying both optimization techniques. A superscalar
                 SPARC processor can provide improved floating point
                 performance but with significant software and hardware
                 development costs.",
  acknowledgement = ack-nhfb,
  affiliation =  "Sun Microsyst. Inc., Mountain View, CA, USA",
  classification = "C5220 (Computer architecture); C5470 (Performance
                 evaluation and testing)",
  confdate =     "8-11 April 1991",
  conflocation = "Santa Clara, CA, USA",
  confsponsor =  "IEEE; ACM",
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "Benchmarks; Development costs; Floating point
                 performance; Floating point registers; Hardware
                 parallelism; Loop unrolling; Memory system; N-scalar
                 machine models; Optimal speedup; Software instruction
                 scheduling optimizations; Software pipelining; SPARC
                 architecture; Superscalar SPARC processor",
  thesaurus =    "Optimisation; Parallel architectures; Performance
                 evaluation; Pipeline processing; Scheduling",
}


bibtype: inproceedings
filename: fparith.bib
label: Lee:1991:SCF
author: Jeong-A. Lee and Tomas Lang
title: SVD by constant-factor-redundant-CORDIC
crossref: Kornerup:1991:PIS
pages: 264--271
year: 1991
bibdate: Sat Nov 27 12:40:58 MST 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.27 12:40:58 MST
URL: http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Lee.pdf
keywords: ARITH-10
acknowledgement: ack-nhfb
rawauthor: Jeong-A. Lee and Tom{\'a}s Lang
rawtitle: {SVD} by constant-factor-redundant-{CORDIC}
entry:
@InProceedings{Lee:1991:SCF,
  author =       "Jeong-A. Lee and Tom{\'a}s Lang",
  title =        "{SVD} by constant-factor-redundant-{CORDIC}",
  crossref =     "Kornerup:1991:PIS",
  pages =        "264--271",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Lee.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}


bibtype: article
filename: fparith.bib
label: Letcher:1991:GNC
author: John H. Letcher
title: Getting numeric coprocessors up to speed
journal: j-DDJ
volume: 16
number: 5
pages: 36, 38, 40, 42
month: may
monthnumber: 5
year: 1991
CODEN: DDJOEB
ISSN: 1044-789X OR 1044789X
bibdate: Tue Sep 10 09:11:02 MDT 1996
bibtimestamp: 1996.09.10 09:11:02 MDT
abstract: Memory-mapped math coprocessors can boost performance without sacrificing compatibility.
fjournal: Dr. Dobb's Journal of Software Tools
keywords: 80*86 Integer CPU; Floating point coprocessors; Numeric coprocessors; Processing speeds
acknowledgement: ack-nhfb
affiliation: Tulsa University, OK, USA
thesaurus: Digital arithmetic; Microprocessor chips; Satellite computers
rawabstract: Memory-mapped math coprocessors can boost performance without sacrificing compatibility.
rawauthor: John H. Letcher
rawtitle: Getting numeric coprocessors up to speed
bibsource:
http://www.ddj.com/index/author/index.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib; UnCover database

entry:
@Article{Letcher:1991:GNC,
  author =       "John H. Letcher",
  title =        "Getting numeric coprocessors up to speed",
  journal =      j-DDJ,
  volume =       "16",
  number =       "5",
  pages =        "36, 38, 40, 42",
  month =        may,
  year =         "1991",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Tue Sep 10 09:11:02 MDT 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 UnCover database",
  abstract =     "Memory-mapped math coprocessors can boost performance
                 without sacrificing compatibility.",
  acknowledgement = ack-nhfb,
  affiliation =  "Tulsa University, OK, USA",
  classification = "C5130 (Microprocessor chips); C5230 (Digital
                 arithmetic methods)",
  fjournal =     "Dr. Dobb's Journal of Software Tools",
  keywords =     "80*86 Integer CPU; Floating point coprocessors;
                 Numeric coprocessors; Processing speeds",
  thesaurus =    "Digital arithmetic; Microprocessor chips; Satellite
                 computers",
}


bibtype: article
filename: fparith.bib
label: Lo:1991:BHS
author: H.-Y. Lo and T. C. Yang
title: Balanced high-speed residue number VLSI multiplier with error detection
journal: Circuits, Devices and Systems, IEE Proceedings G
volume: 138
number: 3
pages: 421--423
month: jun
monthnumber: 6
year: 1991
DOI: https://doi.org/10.1109/78.80821
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
URL: https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=6544
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: H.-Y. Lo and T. C. Yang
rawtitle: Balanced high-speed residue number {VLSI} multiplier with error detection
entry:
@Article{Lo:1991:BHS,
  author =       "H.-Y. Lo and T. C. Yang",
  title =        "Balanced high-speed residue number {VLSI} multiplier
                 with error detection",
  journal =      "Circuits, Devices and Systems, IEE Proceedings G",
  volume =       "138",
  number =       "3",
  pages =        "421--423",
  month =        jun,
  year =         "1991",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/78.80821",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=6544",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A balanced residue number VLSI multiplier is proposed
                 which eliminates the extra delay for an unbalanced
                 residue multiplier. The number of adding stages used in
                 the VLSI multiplier is reduced from three to two. The
                 authors also describe how \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Lyashenko:1991:PAR
author: N. N. Lyashenko and M. S. Nikulin
title: Probability Analysis of Round-Off Errors in Floating-Point Arithmetic
journal: j-THEORY-PROBAB-APPL
volume: 35
number: 1
pages: 66--74
year: 1991
CODEN: TPRBAU
DOI: https://doi.org/10.1137/1135006
ISSN: 0040-585X (print), 1095-7219 (electronic) OR 0040585X (print), 10957219 (electronic)
ISSNL: 0040-585X OR 0040585X
bibdate: Tue Apr 1 10:40:31 MDT 2014
bibtimestamp: 2014.04.01 10:40:31 MDT
fjournal: Theory of Probability and its Applications
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/tvp
onlinedate: January 1991
rawauthor: N. N. Lyashenko and M. S. Nikulin
rawtitle: Probability Analysis of Round-Off Errors in Floating-Point Arithmetic
bibsource:
http://epubs.siam.org/sam-bin/dbq/toc/TVP/35/1; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/theoryprobabappl.bib

entry:
@Article{Lyashenko:1991:PAR,
  author =       "N. N. Lyashenko and M. S. Nikulin",
  title =        "Probability Analysis of Round-Off Errors in
                 Floating-Point Arithmetic",
  journal =      j-THEORY-PROBAB-APPL,
  volume =       "35",
  number =       "1",
  pages =        "66--74",
  month =        "????",
  year =         "1991",
  CODEN =        "TPRBAU",
  DOI =          "https://doi.org/10.1137/1135006",
  ISSN =         "0040-585X (print), 1095-7219 (electronic)",
  ISSN-L =       "0040-585X",
  bibdate =      "Tue Apr 1 10:40:31 MDT 2014",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/TVP/35/1;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/theoryprobabappl.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Theory of Probability and its Applications",
  journal-URL =  "http://epubs.siam.org/tvp",
  onlinedate =   "January 1991",
}


bibtype: inproceedings
filename: fparith.bib
label: Lynch:1991:RCA
author: Tom Lynch and Earl Swartzlander, Jr.
title: The redundant cell adder
crossref: Kornerup:1991:PIS
pages: 165--170
year: 1991
bibdate: Sat Nov 27 12:40:58 MST 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.27 12:40:58 MST
URL: http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Lynch.pdf
keywords: ARITH-10
acknowledgement: ack-nhfb
rawauthor: Tom Lynch and Earl {Swartzlander, Jr.}
rawtitle: The redundant cell adder
entry:
@InProceedings{Lynch:1991:RCA,
  author =       "Tom Lynch and Earl {Swartzlander, Jr.}",
  title =        "The redundant cell adder",
  crossref =     "Kornerup:1991:PIS",
  pages =        "165--170",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Lynch.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}


bibtype: inproceedings
filename: fparith.bib
label: Lyons:1991:FMF
author: Ken Lyons
title: A fast method for finding an integer square root
crossref: Koopman:1991:PST
pages: 27--30
year: 1991
bibdate: Tue May 4 05:57:50 MDT 1999
bibsource: http://www.acm.org/pubs/toc/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1999.05.04 05:57:50 MDT
URL: http://www.acm.org:80/pubs/citations/proceedings/plan/259965/p27-lyons/
acknowledgement: ack-nhfb
rawauthor: Ken Lyons
rawtitle: A fast method for finding an integer square root
entry:
@InProceedings{Lyons:1991:FMF,
  author =       "Ken Lyons",
  title =        "A fast method for finding an integer square root",
  crossref =     "Koopman:1991:PST",
  pages =        "27--30",
  year =         "1991",
  bibdate =      "Tue May 4 05:57:50 MDT 1999",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/plan/259965/p27-lyons/",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: MacKenzie:1991:FMS
author: Donald MacKenzie
title: Formal methods and the sociology of proof
crossref: Morris:1991:RWP
pages: 115--124
year: 1991
DOI: https://doi.org/10.1007/978-1-4471-3756-6_6
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 Sociol., Edinburgh University, UK
rawauthor: Donald MacKenzie
rawtitle: Formal methods and the sociology of proof
abstract:
The paper begins by asking whether a sociology of mathematical knowledge is possible. Having answered in the affirmative (drawing examples from the history of mathematics), it goes on to discuss the development of a similar analysis of the mathematical aspects of computer science. A brief vignette is presented: the processes of negotiation of the IEEE floating-point arithmetic specifications. Then the discussion moves on to the verification of software and hardware. If the sociology of mathematics is correct, then formal proofs can be seen as social, not just in the processes of their acceptance, but also in their internal structure. Placed in the context of pressure for formal verification of safety-critical and security-critical systems, this argument led the author and colleagues to the prediction that litigation involving the nature of mathematical proof was bound to occur. That prediction has now been borne out.

keywords:
Computer science; Formal proofs; Formal verification; IEEE floating-point arithmetic specifications; Litigation; Mathematical aspects; Mathematical knowledge; Negotiation; Safety-critical systems; Security-critical systems; Sociology of proof; Verification

thesaurus:
Economic and sociologic effects; Formal verification; Safety; Security of data; Software reliability; Theorem proving

rawabstract:
The paper begins by asking whether a sociology of mathematical knowledge is possible. Having answered in the affirmative (drawing examples from the history of mathematics), it goes on to discuss the development of a similar analysis of the mathematical aspects of computer science. A brief vignette is presented: the processes of negotiation of the IEEE floating-point arithmetic specifications. Then the discussion moves on to the verification of software and hardware. If the sociology of mathematics is correct, then formal proofs can be seen as social, not just in the processes of their acceptance, but also in their internal structure. Placed in the context of pressure for formal verification of safety-critical and security-critical systems, this argument led the author and colleagues to the prediction that litigation involving the nature of mathematical proof was bound to occur. That prediction has now been borne out.

entry:
@InProceedings{MacKenzie:1991:FMS,
  author =       "Donald MacKenzie",
  title =        "Formal methods and the sociology of proof",
  crossref =     "Morris:1991:RWP",
  pages =        "115--124",
  year =         "1991",
  DOI =          "https://doi.org/10.1007/978-1-4471-3756-6_6",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The paper begins by asking whether a sociology of
                 mathematical knowledge is possible. Having answered in
                 the affirmative (drawing examples from the history of
                 mathematics), it goes on to discuss the development of
                 a similar analysis of the mathematical aspects of
                 computer science. A brief vignette is presented: the
                 processes of negotiation of the IEEE floating-point
                 arithmetic specifications. Then the discussion moves on
                 to the verification of software and hardware. If the
                 sociology of mathematics is correct, then formal proofs
                 can be seen as social, not just in the processes of
                 their acceptance, but also in their internal structure.
                 Placed in the context of pressure for formal
                 verification of safety-critical and security-critical
                 systems, this argument led the author and colleagues to
                 the prediction that litigation involving the nature of
                 mathematical proof was bound to occur. That prediction
                 has now been borne out.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Sociol., Edinburgh University, UK",
  classification = "C0230 (Economic, social and political aspects);
                 C4240 (Programming and algorithm theory); C6110B
                 (Software engineering techniques)",
  keywords =     "Computer science; Formal proofs; Formal verification;
                 IEEE floating-point arithmetic specifications;
                 Litigation; Mathematical aspects; Mathematical
                 knowledge; Negotiation; Safety-critical systems;
                 Security-critical systems; Sociology of proof;
                 Verification",
  thesaurus =    "Economic and sociologic effects; Formal verification;
                 Safety; Security of data; Software reliability; Theorem
                 proving",
}


bibtype: article
filename: fparith.bib
label: MacKenzie:1991:IAL
author: Donald MacKenzie
journal: j-ANN-HIST-COMPUT
volume: 13
number: 2
pages: 179--201
month: apr
monthnumber: 4
year: 1991
CODEN: AHCOE5
ISSN: 0164-1239 OR 01641239
bibdate: Fri Nov 1 15:29:15 MST 2002
bibtimestamp: 2002.11.01 15:29:15 MST
fjournal: Annals of the History of Computing
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650
rawauthor: Donald MacKenzie
title:
The Influence of the Los Alamos and Livermore National Laboratories on the Development of Supercomputing

bibsource:
Compendex database; ftp://ftp.ira.uka.de/pub/bibliography/Parallel/super.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Contents1st database

URL:
http://dlib.computer.org/an/books/an1991/pdf/a2179.pdf; http://www.computer.org/annals/an1991/a2179abs.htm

remark:
The author has this remark about Metropolis on page 194: ``What are the architectural consequences of this kind of influence? [of Los Alamos on computer design] One apparent in Stretch is that machine's noisy mode facility (Los Alamos interviews). The inspiration of these was Los Alamos Nicholas Metropolis, who in the 1950s developed what he called significance arithmetic: the attempt to determine the consequences, for the reliability of results, of errors caused by the need to represent numbers by words of finite length. In noisy mode the effects of truncation were handled differently from in normal operation so as to allow errors caused by truncation to be detected. By definition of ordinary normalized [floating-point] operations, numbers are frequently extended on the right by attaching zeros. During addition the $n$-digit operand that is not preshifted is extended with n zeros, so as to provide the extra positions to which the preshifted operand can be added. Any operand or result that is shifted left to be normalized requires a corresponding number of zeros to be shifted in at the right. Both sets of zeros tend to produce numbers smaller in absolute value than they would have been if more digits had been carried. In the noisy mode these numbers are simply extended with 1s instead of zeros (1s in a binary machine, 9s in a decimal machine). Now all numbers tend to be too large in absolute value. The true value, if there had been no significance loss, should lie between these two extremes. Hence, two runs, one made without and one made with the noisy mode, should show differences in result that indicate which digits may have been affected by significance loss (Buchholz 1962, p. 102).'' See cite Buchholz:1962:PCS for more information about the Stretch noisy mode.

rawtitle:
The Influence of the {Los Alamos} and {Livermore National Laboratories} on the Development of Supercomputing

entry:
@Article{MacKenzie:1991:IAL,
  author =       "Donald MacKenzie",
  title =        "The Influence of the {Los Alamos} and {Livermore
                 National Laboratories} on the Development of
                 Supercomputing",
  journal =      j-ANN-HIST-COMPUT,
  volume =       "13",
  number =       "2",
  pages =        "179--201",
  month =        apr # "\slash " # jun,
  year =         "1991",
  CODEN =        "AHCOE5",
  ISSN =         "0164-1239",
  bibdate =      "Fri Nov 1 15:29:15 MST 2002",
  bibsource =    "Compendex database;
                 ftp://ftp.ira.uka.de/pub/bibliography/Parallel/super.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC
                 Contents1st database",
  URL =          "http://dlib.computer.org/an/books/an1991/pdf/a2179.pdf;
                 http://www.computer.org/annals/an1991/a2179abs.htm",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of the History of Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650",
  remark =       "The author has this remark about Metropolis on page
                 194: ``What are the architectural consequences of this
                 kind of influence? [of Los Alamos on computer design]
                 One apparent in Stretch is that machine's noisy mode
                 facility (Los Alamos interviews). The inspiration of
                 these was Los Alamos Nicholas Metropolis, who in the
                 1950s developed what he called significance arithmetic:
                 the attempt to determine the consequences, for the
                 reliability of results, of errors caused by the need to
                 represent numbers by words of finite length. In noisy
                 mode the effects of truncation were handled differently
                 from in normal operation so as to allow errors caused
                 by truncation to be detected.

                 By definition of ordinary normalized [floating-point]
                 operations, numbers are frequently extended on the
                 right by attaching zeros. During addition the $n$-digit
                 operand that is not preshifted is extended with n
                 zeros, so as to provide the extra positions to which
                 the preshifted operand can be added. Any operand or
                 result that is shifted left to be normalized requires a
                 corresponding number of zeros to be shifted in at the
                 right. Both sets of zeros tend to produce numbers
                 smaller in absolute value than they would have been if
                 more digits had been carried. In the noisy mode these
                 numbers are simply extended with 1s instead of zeros
                 (1s in a binary machine, 9s in a decimal machine). Now
                 all numbers tend to be too large in absolute value. The
                 true value, if there had been no significance loss,
                 should lie between these two extremes. Hence, two runs,
                 one made without and one made with the noisy mode,
                 should show differences in result that indicate which
                 digits may have been affected by significance loss
                 (Buchholz 1962, p. 102).''

                 See \cite{Buchholz:1962:PCS} for more information about
                 the Stretch noisy mode.",
}


bibtype: book
filename: fparith.bib
label: MacKenzie:1991:NAC
author: Donald MacKenzie and Edinburgh Pict
title: Negotiating arithmetic, construction proof: the sociology of mathematics and information technology
volume: 38
publisher: Research Centre for Social Sciences, University of Edinburgh
address: Edinburgh
pages: 27
year: 1991
ISBN: 1-872287-42-5 OR 1872287425
ISBN13: 978-1-872287-42-3 OR 9781872287423
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
series: Edinburgh PICT working paper
keywords: Computer arithmetic; Computer security; Floating-point arithmetic
acknowledgement: ack-nhfb
rawauthor: Donald MacKenzie and Edinburgh Pict
rawtitle: Negotiating arithmetic, construction proof: the sociology of mathematics and information technology
entry:
@Book{MacKenzie:1991:NAC,
  author =       "Donald MacKenzie and Edinburgh Pict",
  title =        "Negotiating arithmetic, construction proof: the
                 sociology of mathematics and information technology",
  volume =       "38",
  publisher =    "Research Centre for Social Sciences, University of
                 Edinburgh",
  address =      "Edinburgh",
  pages =        "27",
  year =         "1991",
  ISBN =         "1-872287-42-5",
  ISBN-13 =      "978-1-872287-42-3",
  LCCN =         "????",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Edinburgh PICT working paper",
  acknowledgement = ack-nhfb,
  keywords =     "Computer arithmetic; Computer security; Floating-point
                 arithmetic",
}


bibtype: article
filename: fparith.bib
label: Marcus:1991:HSR
author: Marvin Marcus and Markus Sandy
title: Hadamard Square Roots
journal: j-SIAM-J-MAT-ANA-APPL
volume: 12
number: 1
pages: 49--69
month: jan
monthnumber: 1
year: 1991
CODEN: SJMAEL
ISSN: 0895-4798 (print), 1095-7162 (electronic) OR 08954798 (print), 10957162 (electronic)
ISSNL: 0895-4798 OR 08954798
MRclass: 15A57 (15A18 15A48 15A52 47B15 60H25)
MRnumber: 92a:15027
MRreviewer: Zdzis{\l}aw W. Trzaska
bibdate: Tue Jan 21 08:54:30 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.01.21 08:54:30 MST
fjournal: SIAM Journal on Matrix Analysis and Applications
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/simax
rawauthor: Marvin Marcus and Markus Sandy
rawtitle: {Hadamard} Square Roots
entry:
@Article{Marcus:1991:HSR,
  author =       "Marvin Marcus and Markus Sandy",
  title =        "{Hadamard} Square Roots",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "12",
  number =       "1",
  pages =        "49--69",
  month =        jan,
  year =         "1991",
  CODEN =        "SJMAEL",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "15A57 (15A18 15A48 15A52 47B15 60H25)",
  MRnumber =     "92a:15027",
  MRreviewer =   "Zdzis{\l}aw W. Trzaska",
  bibdate =      "Tue Jan 21 08:54:30 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}


bibtype: inproceedings
filename: fparith.bib
label: Markstein:1991:WFF
author: V. Markstein and P. Markstein and T. Nguyen and S. Poole
title: Wide Format Floating-Point Math Libraries
crossref: IEEE:1991:PSA
pages: 130--138
year: 1991
DOI: https://doi.org/10.1145/125826.125903
bibdate: Wed Dec 13 18:34:51 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 18:34:51 ???
acknowledgement: ack-nhfb
affiliation: ISQUARE, Inc., Austin, TX, USA
thesaurus: Digital arithmetic; Mathematics computing; Parallel processing; Performance evaluation
rawauthor: V. Markstein and P. Markstein and T. Nguyen and S. Poole
rawtitle: Wide Format Floating-Point Math Libraries
abstract:
The authors present the performance and accuracy evaluations of eleven transcendental functions found in 64- and 128-bit floating-point formats in math libraries on the Cray Y-MP, the IBM 3090E/VF, the Convex C-240, the Hewlett--Packard 9000/720, and the IBM System/6000. Both architecture and algorithms are shown to impact the results.

keywords:
128 Bit; 64 Bit; Accuracy evaluations; Convex C-240; Cray Y-MP; Floating-point formats; Hewlett--Packard 9000/720; IBM 3090E/VF; IBM System/6000; Math libraries; Performance; Transcendental functions; Wide format floating point math libraries

rawabstract:
The authors present the performance and accuracy evaluations of eleven transcendental functions found in 64- and 128-bit floating-point formats in math libraries on the Cray Y-MP, the IBM 3090E/VF, the Convex C-240, the Hewlett--Packard 9000/720, and the IBM System/6000. Both architecture and algorithms are shown to impact the results.

entry:
@InProceedings{Markstein:1991:WFF,
  author =       "V. Markstein and P. Markstein and T. Nguyen and S.
                 Poole",
  title =        "Wide Format Floating-Point Math Libraries",
  crossref =     "IEEE:1991:PSA",
  pages =        "130--138",
  year =         "1991",
  DOI =          "https://doi.org/10.1145/125826.125903",
  bibdate =      "Wed Dec 13 18:34:51 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The authors present the performance and accuracy
                 evaluations of eleven transcendental functions found in
                 64- and 128-bit floating-point formats in math
                 libraries on the Cray Y-MP, the IBM 3090E/VF, the
                 Convex C-240, the Hewlett--Packard 9000/720, and the
                 IBM System/6000. Both architecture and algorithms are
                 shown to impact the results.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "ISQUARE, Inc., Austin, TX, USA",
  classification = "C5230 (Digital arithmetic methods); C5470
                 (Performance evaluation and testing); C7310
                 (Mathematics)",
  confdate =     "18-22 Nov. 1991",
  conflocation = "Albuquerque, NM, USA",
  confsponsor =  "IEEE; ACM",
  keywords =     "128 Bit; 64 Bit; Accuracy evaluations; Convex C-240;
                 Cray Y-MP; Floating-point formats; Hewlett--Packard
                 9000/720; IBM 3090E/VF; IBM System/6000; Math
                 libraries; Performance; Transcendental functions; Wide
                 format floating point math libraries",
  numericalindex = "Word length 6.4E+01 bit; Word length 1.28E+02 bit",
  thesaurus =    "Digital arithmetic; Mathematics computing; Parallel
                 processing; Performance evaluation",
}


bibtype: article
filename: fparith.bib
label: McQuillan:1991:HPV
author: S. E. McQuillan and J. V. McCanny and R. F. Woods
title: High performance VLSI architecture for division and square root
journal: j-ELECT-LETTERS
volume: 27
number: 1
pages: 19--21
day: 3
month: jan
monthnumber: 1
year: 1991
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: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220
rawauthor: S. E. McQuillan and J. V. McCanny and R. F. Woods
rawtitle: High performance {VLSI} architecture for division and square root
entry:
@Article{McQuillan:1991:HPV,
  author =       "S. E. McQuillan and J. V. McCanny and R. F. Woods",
  title =        "High performance {VLSI} architecture for division and
                 square root",
  journal =      j-ELECT-LETTERS,
  volume =       "27",
  number =       "1",
  pages =        "19--21",
  day =          "3",
  month =        jan,
  year =         "1991",
  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 =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  summary =      "A novel high performance bit parallel architecture to
                 perform square root and division is proposed. Relevant
                 VLSI design issues have been addressed. By employing
                 redundant arithmetic and a semisystolic schedule, the
                 throughput has been made \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: McQuillan:1991:VAM
author: S. E. McQuillan and J. V. McCanny
title: A VLSI architecture for multiplication, division and square root
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1205--1208
year: 1991
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: S. E. McQuillan and J. V. McCanny
rawtitle: A {VLSI} architecture for multiplication, division and square root
booktitle:
1991 International Conference on Acoustics, Speech, and Signal Processing: ICASSP-91, 14--17 April 1991

rawbooktitle:
1991 International Conference on Acoustics, Speech, and Signal Processing: {ICASSP-91, 14--17} April 1991

entry:
@InProceedings{McQuillan:1991:VAM,
  author =       "S. E. McQuillan and J. V. McCanny",
  booktitle =    "1991 International Conference on Acoustics, Speech,
                 and Signal Processing: {ICASSP-91, 14--17} April 1991",
  title =        "A {VLSI} architecture for multiplication, division and
                 square root",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1205--1208",
  year =         "1991",
  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 =      "A high-performance VLSI architecture to perform
                 combined multiply-accumulate, divide, and square root
                 operations is proposed. The circuit is highly regular,
                 requires only minimal control, and can be reconfigured
                 for every cycle. The execution time \ldots{}",
}


bibtype: phdthesis
filename: fparith.bib
label: Mehrez:1991:AVP
author: Habib Mehrez
type: These Doctoral
school: Sciences Appliquees, Universite Paris 6
address: Paris, France
pages: 1205--1208
year: 1991
bibdate: Thu May 09 10:10:32 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.09 10:10:32 ???
note: Sous la direction de Alain Greiner.
language: French
acknowledgement: ack-nhfb
rawauthor: Habib Mehrez
rawnote: Sous la direction de Alain Greiner.
title:
Des architectures VLSI pipelines pour les algorithmes numeriques a flots de donnees en representations arithmetiques virgule fixe et virgule flottante. (French) [Pipelined VLSI architectures for numerical algorithms for numerical data in fixed- and floating-point arithmetic]

abstract:
Dans cette these, on se propose d'exposer certaines reflexions et contributions dans le developpement et la recherche en architectures VLSI pour l'implantation des algorithmes de traitement numerique a flots des donnees. On exposera en particulier une methodologie generale d'implantation concretisee par des etudes et des realisations des architectures specifiques a la transformee de Fourier rapide (TFR ou FFT). Ces architectures concernent aussi bien des traitements arithmetiques en virgule fixe qu'en virgule flottante et seront de type pipelines serie systolique. Des propositions d'implantation des operateurs arithmetiques de base et des chemins des donnees seront developpees ainsi que les evaluations des performances et de leur complexite correspondantes. Il sera discute des facteurs de classification et d'interactions entre les aspects fonctionnels et algorithmiques, les aspects structurels et architecturaux et finalement les aspects lies aux implantations VLSI. Ces derniers aspects concernent notamment les compromis et les choix logiques, electriques et topologiques. La methode de conception est basee sur l'utilisation d'une bibliotheque de cellules standards qui inclut la technique LSSD, de test et testabilite, au moment de la conception des circuits VLSI.

rawabstract:
Dans cette th{\`e}se, on se propose d'exposer certaines reflexions et contributions dans le d{\'e}veloppement et la recherche en architectures VLSI pour l'implantation des algorithmes de traitement num{\'e}rique {\`a} flots des donn{\'e}es. On exposera en particulier une m{\'e}thodologie g{\'e}n{\'e}rale d'implantation concr{\'e}tis{\'e}e par des {\'e}tudes et des r{\'e}alisations des architectures sp{\'e}cifiques {\`a} la transform{\'e}e de Fourier rapide (TFR ou FFT). Ces architectures concernent aussi bien des traitements arithm{\'e}tiques en virgule fixe qu'en virgule flottante et seront de type pipelin{\'e}s serie systolique. Des propositions d'implantation des op{\'e}rateurs arithm{\'e}tiques de base et des chemins des donn{\'e}es seront developp{\'e}es ainsi que les {\'e}valuations des performances et de leur complexit{\'e} correspondantes. Il sera discut{\'e} des facteurs de classification et d'interactions entre les aspects fonctionnels et algorithmiques, les aspects structurels et architecturaux et finalement les aspects li{\'e}s aux implantations VLSI. Ces derniers aspects concernent notamment les compromis et les choix logiques, {\'e}lectriques et topologiques. La m{\'e}thode de conception est bas{\'e}e sur l'utilisation d'une biblioth{\`e}que de cellules standards qui inclut la technique LSSD, de test et testabilit{\'e}, au moment de la conception des circuits VLSI.

rawtitle:
Des architectures {VLSI} pipelin{\'e}s pour les algorithmes num{\'e}riques {\`a} flots de donn{\'e}es en repr{\'e}sentations arithm{\'e}tiques virgule fixe et virgule flottante. ({French}) [{Pipelined VLSI} architectures for numerical algorithms for numerical data in fixed- and floating-point arithmetic]

entry:
@PhdThesis{Mehrez:1991:AVP,
  author =       "Habib Mehrez",
  title =        "Des architectures {VLSI} pipelin{\'e}s pour les
                 algorithmes num{\'e}riques {\`a} flots de donn{\'e}es
                 en repr{\'e}sentations arithm{\'e}tiques virgule fixe
                 et virgule flottante. ({French}) [{Pipelined VLSI}
                 architectures for numerical algorithms for numerical
                 data in fixed- and floating-point arithmetic]",
  type =         "Th{\`e}se Doctoral",
  school =       "Sciences Appliqu{\'e}es, Universit{\'e} Paris 6",
  address =      "Paris, France",
  year =         "1991",
  bibdate =      "Thu May 09 10:10:32 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Sous la direction de Alain Greiner.",
  abstract =     "Dans cette th{\`e}se, on se propose d'exposer
                 certaines reflexions et contributions dans le
                 d{\'e}veloppement et la recherche en architectures VLSI
                 pour l'implantation des algorithmes de traitement
                 num{\'e}rique {\`a} flots des donn{\'e}es. On exposera
                 en particulier une m{\'e}thodologie g{\'e}n{\'e}rale
                 d'implantation concr{\'e}tis{\'e}e par des {\'e}tudes
                 et des r{\'e}alisations des architectures
                 sp{\'e}cifiques {\`a} la transform{\'e}e de Fourier
                 rapide (TFR ou FFT). Ces architectures concernent aussi
                 bien des traitements arithm{\'e}tiques en virgule fixe
                 qu'en virgule flottante et seront de type pipelin{\'e}s
                 serie systolique. Des propositions d'implantation des
                 op{\'e}rateurs arithm{\'e}tiques de base et des chemins
                 des donn{\'e}es seront developp{\'e}es ainsi que les
                 {\'e}valuations des performances et de leur
                 complexit{\'e} correspondantes. Il sera discut{\'e} des
                 facteurs de classification et d'interactions entre les
                 aspects fonctionnels et algorithmiques, les aspects
                 structurels et architecturaux et finalement les aspects
                 li{\'e}s aux implantations VLSI. Ces derniers aspects
                 concernent notamment les compromis et les choix
                 logiques, {\'e}lectriques et topologiques. La
                 m{\'e}thode de conception est bas{\'e}e sur
                 l'utilisation d'une biblioth{\`e}que de cellules
                 standards qui inclut la technique LSSD, de test et
                 testabilit{\'e}, au moment de la conception des
                 circuits VLSI.",
  acknowledgement = ack-nhfb,
  language =     "French",
}


bibtype: inproceedings
filename: fparith.bib
label: Mehta:1991:HSM
author: Mayur Mehta and Vijay Parmar and Earl Swartzlander, Jr.
title: High-speed multiplier design using multi-input counter and compressor circuits
crossref: Kornerup:1991:PIS
pages: 43--50
year: 1991
bibdate: Sat Nov 27 12:40:58 MST 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.27 12:40:58 MST
URL: http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Mehta.pdf
keywords: ARITH-10
acknowledgement: ack-nhfb
rawauthor: Mayur Mehta and Vijay Parmar and Earl {Swartzlander, Jr.}
rawtitle: High-speed multiplier design using multi-input counter and compressor circuits
entry:
@InProceedings{Mehta:1991:HSM,
  author =       "Mayur Mehta and Vijay Parmar and Earl {Swartzlander,
                 Jr.}",
  title =        "High-speed multiplier design using multi-input counter
                 and compressor circuits",
  crossref =     "Kornerup:1991:PIS",
  pages =        "43--50",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Mehta.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}


bibtype: inproceedings
filename: fparith.bib
label: Metafas:1991:FPP
author: D. E. Metafas and C. E. Goutis
booktitle: 1991 IEEE International Symposium on Circuits and Systems (ISCAS)
title: A floating point pipeline CORDIC processor with extended operation set
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 3066--3069 (vol. 5)
year: 1991
DOI: https://doi.org/10.1109/ISCAS.1991.176195
bibdate: Mon Oct 27 10:32:44 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2025.10.27 10:32:44 ???
acknowledgement: ack-nhfb
rawauthor: D. E. Metafas and C. E. Goutis
rawbooktitle: {1991 IEEE International Symposium on Circuits and Systems (ISCAS)}
rawtitle: A floating point pipeline {CORDIC} processor with extended operation set
keywords:
Arithmetic; Computer architecture; Convergence; Digital signal processing; Equations; Hardware; Iterative algorithms; Iterative methods; Pipelines; Signal processing algorithms

entry:
@InProceedings{Metafas:1991:FPP,
  author =       "D. E. Metafas and C. E. Goutis",
  booktitle =    "{1991 IEEE International Symposium on Circuits and
                 Systems (ISCAS)}",
  title =        "A floating point pipeline {CORDIC} processor with
                 extended operation set",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "3066--3069 (vol. 5)",
  year =         "1991",
  DOI =          "https://doi.org/10.1109/ISCAS.1991.176195",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Arithmetic; Computer architecture; Convergence;
                 Digital signal processing; Equations; Hardware;
                 Iterative algorithms; Iterative methods; Pipelines;
                 Signal processing algorithms",
}


bibtype: manual
filename: fparith.bib
label: Microsoft:1991:MCC
author: Microsoft Corporation
title: Microsoft C, C++: version 7.0: programming techniques for MS-DOS and Windows operating systems
organization: Microsoft Corp.
address: Redmond, WA, USA
pages: xix + 323
year: 1991
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: Microsoft C++.; Microsoft C.; MS - DOS (Computer file); Windows (Computer programs)
acknowledgement: ack-nhfb
rawauthor: {Microsoft Corporation}
remark:
Improving program performance: optimizing your programs; using precompiled header files; reducing program size with p-code; managing memory in C; managing memory in C++; using the inline assembler; controlling floating-point math operations --- Special environments: compiling with the QuickWin windows library; communicating with graphics; creating charts and graphs; programming with mixed languages; writing portable C programs --- P-code instruction tables. [The book] describes how to take advantage of the special features of Microsoft C/C++. The topics covered by this manual include language extensions, special-purpose library functions, and the interaction between programming strategies and compiler options. This manual is not a reference for the tools included with Microsoft C/C++. -Introd.

rawtitle:
{Microsoft C, C++}: version 7.0: programming techniques for {MS-DOS} and {Windows} operating systems

entry:
@Manual{Microsoft:1991:MCC,
  author =       "{Microsoft Corporation}",
  title =        "{Microsoft C, C++}: version 7.0: programming
                 techniques for {MS-DOS} and {Windows} operating
                 systems",
  organization = "Microsoft Corp.",
  address =      "Redmond, WA, USA",
  pages =        "xix + 323",
  year =         "1991",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Microsoft C++.; Microsoft C.; MS - DOS (Computer
                 file); Windows (Computer programs)",
  remark =       "Improving program performance: optimizing your
                 programs; using precompiled header files; reducing
                 program size with p-code; managing memory in C;
                 managing memory in C++; using the inline assembler;
                 controlling floating-point math operations --- Special
                 environments: compiling with the QuickWin windows
                 library; communicating with graphics; creating charts
                 and graphs; programming with mixed languages; writing
                 portable C programs --- P-code instruction tables. [The
                 book] describes how to take advantage of the special
                 features of Microsoft C/C++. The topics covered by this
                 manual include language extensions, special-purpose
                 library functions, and the interaction between
                 programming strategies and compiler options. This
                 manual is not a reference for the tools included with
                 Microsoft C/C++. -Introd.",
}


bibtype: article
filename: fparith.bib
label: Montuschi:1991:OAE
author: P. Montuschi and M. Mezzalama
title: Optimal Absolute Error Starting Values for Newton--Raphson Calculation of Square Root
journal: j-COMPUTING
volume: 46
number: 1
pages: 67--86
year: 1991
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
MRclass: 65H05 (65G99)
MRnumber: 92a:65161
bibdate: Tue Oct 12 16:33:42 MDT 1999
bibtimestamp: 1999.10.12 16:33:42 MDT
fjournal: Computing: Archiv fur informatik und numerik
acknowledgement: ack-nhfb
affiliation: Politecnico di Torino
affiliationaddress: Torino, Italy
journalURL: http://link.springer.com/journal/607
journalabr: Comput Vienna New York
rawauthor: P. Montuschi and M. Mezzalama
rawtitle: Optimal Absolute Error Starting Values for {Newton--Raphson} Calculation of Square Root
bibsource:
Compendex database; http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X; https://www.math.utah.edu/pub/tex/bib/fparith.bib; MathSciNet database; OCLC Contents1st database

keywords:
Absolute Error; Computer Programming --- Algorithms; Mathematical Techniques; Newton--Raphson Method; Optimization; Square Roots

entry:
@Article{Montuschi:1991:OAE,
  author =       "P. Montuschi and M. Mezzalama",
  title =        "Optimal Absolute Error Starting Values for
                 {Newton--Raphson} Calculation of Square Root",
  journal =      j-COMPUTING,
  volume =       "46",
  number =       "1",
  pages =        "67--86",
  year =         "1991",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65H05 (65G99)",
  MRnumber =     "92a:65161",
  bibdate =      "Tue Oct 12 16:33:42 MDT 1999",
  bibsource =    "Compendex database;
                 http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 MathSciNet database; OCLC Contents1st database",
  acknowledgement = ack-nhfb,
  affiliation =  "Politecnico di Torino",
  affiliationaddress = "Torino, Italy",
  classification = "723; 921",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
  journalabr =   "Comput Vienna New York",
  keywords =     "Absolute Error; Computer Programming --- Algorithms;
                 Mathematical Techniques; Newton--Raphson Method;
                 Optimization; Square Roots",
}


bibtype: inproceedings
filename: fparith.bib
label: Montuschi:1991:SRD
author: Paolo Montuschi and Luigi Ciminiera
title: Simple radix 2 division and square root with skipping of some addition steps
crossref: Kornerup:1991:PIS
pages: 202--209
year: 1991
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
URL: http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Montuschi.pdf
keywords: ARITH-10
acknowledgement: ack-nhfb
rawauthor: Paolo Montuschi and Luigi Ciminiera
rawtitle: Simple radix 2 division and square root with skipping of some addition steps
entry:
@InProceedings{Montuschi:1991:SRD,
  author =       "Paolo Montuschi and Luigi Ciminiera",
  title =        "Simple radix 2 division and square root with skipping
                 of some addition steps",
  crossref =     "Kornerup:1991:PIS",
  pages =        "202--209",
  year =         "1991",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Montuschi.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
  summary =      "The authors present a novel algorithm for shared radix
                 2 division and square root whose main characteristic is
                 the ability to avoid any addition when the digit 0 has
                 been selected. The solution presented uses a redundant
                 representation of the \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Mulder:1991:AMC
author: J. M. Mulder and N. T. Quach and M. J. Flynn
title: An area model for on-chip memories and its application
journal: j-IEEE-J-SOLID-STATE-CIRCUITS
volume: 26
number: 2
pages: 98--105
month: feb
monthnumber: 2
year: 1991
CODEN: IJSCBC
ISSN: 0018-9200 (print), 1558-173X (electronic) OR 00189200 (print), 1558173X (electronic)
ISSNL: 0018-9200 OR 00189200
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 Journal of Solid-State Circuits
acknowledgement: ack-sfo
rawauthor: J. M. Mulder and N. T. Quach and M. J. Flynn
rawtitle: An area model for on-chip memories and its application
entry:
@Article{Mulder:1991:AMC,
  author =       "J. M. Mulder and N. T. Quach and M. J. Flynn",
  title =        "An area model for on-chip memories and its
                 application",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "26",
  number =       "2",
  pages =        "98--105",
  month =        feb,
  year =         "1991",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  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 Journal of Solid-State Circuits",
}


bibtype: inproceedings
filename: fparith.bib
label: Muller:1991:EAF
author: Michael Muller and Christine Rub and Wolfgang Rulling
title: Exact accumulation of floating-point numbers
crossref: Kornerup:1991:PIS
pages: 64--69
year: 1991
bibdate: Sat Nov 27 12:40:58 MST 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.27 12:40:58 MST
URL: http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Muller.pdf
acknowledgement: ack-nhfb
affiliation: Max-Planck-Inst., Saarbrucken, Germany
thesaurus: Adders; Digital arithmetic
rawauthor: Michael M{\"u}ller and Christine R{\"u}b and Wolfgang R{\"u}lling
rawtitle: Exact accumulation of floating-point numbers
abstract:
The authors present a new idea for designing a chip which computes the exact sum of arbitrarily many floating-point numbers, i.e., it can accumulate the floating-point numbers without cancellation. Such a chip is needed to provide a fast implementation of Kulisch arithmetic. This is a new theory of floating-point arithmetic which makes it possible to compute least significant bit accurate solutions to even ill-conditioned numerical problems. The proposed approach avoids the disadvantages of previously suggested designs which are too large, too slow, or consume too much power. The crucial point is a technique for a fast carry resolution in a long accumulator. It can also be implemented in software.

keywords:
Accumulator; ARITH-10; Chip; Exact accumulation; Exact sum; Fast carry resolution; Floating-point arithmetic; Floating-point numbers; Ill-conditioned numerical problems; Kulisch arithmetic; Least significant bit accurate solutions

rawabstract:
The authors present a new idea for designing a chip which computes the exact sum of arbitrarily many floating-point numbers, i.e., it can accumulate the floating-point numbers without cancellation. Such a chip is needed to provide a fast implementation of Kulisch arithmetic. This is a new theory of floating-point arithmetic which makes it possible to compute least significant bit accurate solutions to even ill-conditioned numerical problems. The proposed approach avoids the disadvantages of previously suggested designs which are too large, too slow, or consume too much power. The crucial point is a technique for a fast carry resolution in a long accumulator. It can also be implemented in software.

entry:
@InProceedings{Muller:1991:EAF,
  author =       "Michael M{\"u}ller and Christine R{\"u}b and Wolfgang
                 R{\"u}lling",
  title =        "Exact accumulation of floating-point numbers",
  crossref =     "Kornerup:1991:PIS",
  pages =        "64--69",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Muller.pdf",
  abstract =     "The authors present a new idea for designing a chip
                 which computes the exact sum of arbitrarily many
                 floating-point numbers, i.e., it can accumulate the
                 floating-point numbers without cancellation. Such a
                 chip is needed to provide a fast implementation of
                 Kulisch arithmetic. This is a new theory of
                 floating-point arithmetic which makes it possible to
                 compute least significant bit accurate solutions to
                 even ill-conditioned numerical problems. The proposed
                 approach avoids the disadvantages of previously
                 suggested designs which are too large, too slow, or
                 consume too much power. The crucial point is a
                 technique for a fast carry resolution in a long
                 accumulator. It can also be implemented in software.",
  acknowledgement = ack-nhfb,
  affiliation =  "Max-Planck-Inst., Saarbrucken, Germany",
  classification = "B1265B (Logic circuits); C5120 (Logic and switching
                 circuits); C5230 (Digital arithmetic methods)",
  keywords =     "Accumulator; ARITH-10; Chip; Exact accumulation; Exact
                 sum; Fast carry resolution; Floating-point arithmetic;
                 Floating-point numbers; Ill-conditioned numerical
                 problems; Kulisch arithmetic; Least significant bit
                 accurate solutions",
  thesaurus =    "Adders; Digital arithmetic",
}


bibtype: inproceedings
filename: fparith.bib
label: Muller:1991:FSC
author: Jean-Michel Muller and Peter Kornerup and David W. Matula
title: Foreword: 10th Symposium on Computer Arithmetic, Grenoble, France, June 26--28, 1991
crossref: Kornerup:1991:PIS
pages: v--v
year: 1991
bibdate: Sat Nov 17 08:46:25 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.17 08:46:25 ???
keywords: ARITH-10
acknowledgement: ack-nhfb
rawauthor: Jean-Michel Muller and Peter Kornerup and David W. Matula
rawtitle: Foreword: {10th Symposium on Computer Arithmetic, Grenoble, France, June 26--28, 1991}
URL:
http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_contents.pdf; http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_foreword.pdf; http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_preface.pdf

entry:
@InProceedings{Muller:1991:FSC,
  author =       "Jean-Michel Muller and Peter Kornerup and David W.
                 Matula",
  title =        "Foreword: {10th Symposium on Computer Arithmetic,
                 Grenoble, France, June 26--28, 1991}",
  crossref =     "Kornerup:1991:PIS",
  pages =        "v--v",
  year =         "1991",
  bibdate =      "Sat Nov 17 08:46:25 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_contents.pdf;
                 http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_foreword.pdf;
                 http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_preface.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}


bibtype: article
filename: fparith.bib
label: Mundie:1991:OOR
author: David A. Mundie and David A. Fisher
title: Optimized Overload Resolution and Type Matching for Ada
journal: j-SIGADA-LETTERS
volume: 11
number: 3
pages: 83--90
month: Spring
year: 1991
CODEN: AALEE5
ISSN: 1094-3641 (print), 1557-9476 (electronic) OR 10943641 (print), 15579476 (electronic)
ISSNL: 1094-3641 OR 10943641
bibdate: Sat Aug 9 09:05:41 MDT 2003
bibtimestamp: 2003.08.09 09:05:41 MDT
fjournal: ACM SIGAda Ada Letters
acknowledgement: ack-nhfb
classcodes: C6140D (High level languages); C5230 (Digital arithmetic methods)
journalURL: http://portal.acm.org/citation.cfm?id=J32
treatment: P Practical; A Application
rawauthor: David A. Mundie and David A. Fisher
rawtitle: Optimized Overload Resolution and Type Matching for {Ada}
bibsource:
http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/sigada.bib

keywords:
Ada; computational methods; digital arithmetic; incremental environment; microprogramming interval arithmetic; nodes; overload resolution; pruning heuristics; recursive strategy; tree; type matching

corpsource:
Incremental Syst. Corp., Pittsburgh, PA, USA; Computer Sci. Dept., University of Wisconsin, Madison, WI, USA

entry:
@Article{Mundie:1991:OOR,
  author =       "David A. Mundie and David A. Fisher",
  title =        "Optimized Overload Resolution and Type Matching for
                 {Ada}",
  journal =      j-SIGADA-LETTERS,
  volume =       "11",
  number =       "3",
  pages =        "83--90",
  month =        "Spring",
  year =         "1991",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Sat Aug 9 09:05:41 MDT 2003",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigada.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C6140D (High level languages); C5230 (Digital
                 arithmetic methods)",
  conflocation = "Redondo Beach, CA, USA; 30 April-2 May 1990",
  conftitle =    "1st International Symposium on Environments and Tools
                 for Ada",
  corpsource =   "Incremental Syst. Corp., Pittsburgh, PA, USA; Computer
                 Sci. Dept., University of Wisconsin, Madison, WI, USA",
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "Ada; computational methods; digital arithmetic;
                 incremental environment; microprogramming interval
                 arithmetic; nodes; overload resolution; pruning
                 heuristics; recursive strategy; tree; type matching",
  sponsororg =   "IEEE",
  treatment =    "P Practical; A Application",
}


bibtype: phdthesis
filename: fparith.bib
label: Mutrie:1991:TSS
author: Mark P. W. Mutrie
title: Towards a Symbolic System for Floating-Point Error Analysis
school: University of Waterloo
pages: 83--90
year: 1991
bibdate: Thu Nov 8 14:50:35 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.08 14:50:35 ???
acknowledgement: ack-nj
rawauthor: Mark P. W. Mutrie
rawtitle: Towards a Symbolic System for Floating-Point Error Analysis
entry:
@PhdThesis{Mutrie:1991:TSS,
  author =       "Mark P. W. Mutrie",
  title =        "Towards a Symbolic System for Floating-Point Error
                 Analysis",
  school =       "University of Waterloo",
  year =         "1991",
  bibdate =      "Thu Nov 8 14:50:35 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: inproceedings
filename: fparith.bib
label: Myczkowski:1991:SMA
author: J. Myczkowski and G. Steele
title: Seismic modeling at 15 Gigaflops on the Connection Machine
crossref: IEEE:1991:PSA
pages: 316--326
year: 1991
bibdate: Wed Apr 15 16:28:01 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.04.15 16:28:01 MDT
acknowledgement: ack-nhfb
corpsource: Thinking Machines Corp., Cambridge, MA, USA
treatment: A Application; P Practical
rawauthor: J. Myczkowski and G. Steele
rawtitle: Seismic modeling at {15 Gigaflops} on the {Connection Machine}
keywords:
14 GFLOPS; acoustic wave equation; CM-2 supercomputer; Connection Machine; difference equations; finite difference algorithm; floating point unit; geophysics computing; instruction sequence; interprocessor grid communication; massively parallel machine; memory interface; parallel processing; seismic modelling code; seismology; sponge boundary conditions; stencil compiler

entry:
@InProceedings{Myczkowski:1991:SMA,
  author =       "J. Myczkowski and G. Steele",
  title =        "Seismic modeling at {15 Gigaflops} on the {Connection
                 Machine}",
  crossref =     "IEEE:1991:PSA",
  pages =        "316--326",
  year =         "1991",
  bibdate =      "Wed Apr 15 16:28:01 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "A9130 (Seismology); C4170 (Differential equations);
                 C5440 (Multiprocessor systems and techniques); C7340
                 (Geophysics)",
  corpsource =   "Thinking Machines Corp., Cambridge, MA, USA",
  keywords =     "14 GFLOPS; acoustic wave equation; CM-2 supercomputer;
                 Connection Machine; difference equations; finite
                 difference algorithm; floating point unit; geophysics
                 computing; instruction sequence; interprocessor grid
                 communication; massively parallel machine; memory
                 interface; parallel processing; seismic modelling code;
                 seismology; sponge boundary conditions; stencil
                 compiler",
  sponsororg =   "IEEE; ACM",
  treatment =    "A Application; P Practical",
}


bibtype: article
filename: fparith.bib
label: Nagal:1991:PEM
author: T. Nagal
title: Performance evaluation of mathematical functions
journal: j-SUPERCOMPUTER
volume: 8
number: 8
pages: 46--56
month: nov
monthnumber: 11
year: 1991
CODEN: SPCOEL
ISSN: 0168-7875 OR 01687875
bibdate: Thu Sep 1 10:15:07 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 10:15:07 ???
fjournal: Supercomputer
acknowledgement: ack-nj
rawauthor: T. Nagal
rawtitle: Performance evaluation of mathematical functions
entry:
@Article{Nagal:1991:PEM,
  author =       "T. Nagal",
  title =        "Performance evaluation of mathematical functions",
  journal =      j-SUPERCOMPUTER,
  volume =       "8",
  number =       "8",
  pages =        "46--56",
  month =        nov,
  year =         "1991",
  CODEN =        "SPCOEL",
  ISSN =         "0168-7875",
  bibdate =      "Thu Sep 1 10:15:07 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 =     "Supercomputer",
}


bibtype: inproceedings
filename: fparith.bib
label: Nakano:1991:MBM
title: A 80 MFLOPS 64-bit Microprocessor for Parallel Computer
crossref: IEEE:1991:PIC
pages: 15.2/1--4
year: 1991
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
rawtitle: A 80 {MFLOPS} 64-bit Microprocessor for Parallel Computer
author:
H. Nakano and M. Nakajima and Y. Nakahura and T. Yoshida and Y. Goi and Y. Nakai and R. Segawa and T. Kishida and H. Kadora

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

entry:
@InProceedings{Nakano:1991:MBM,
  author =       "H. Nakano and M. Nakajima and Y. Nakahura and T.
                 Yoshida and Y. Goi and Y. Nakai and R. Segawa and T.
                 Kishida and H. Kadora",
  title =        "A 80 {MFLOPS} 64-bit Microprocessor for Parallel
                 Computer",
  crossref =     "IEEE:1991:PIC",
  pages =        "15.2/1--4",
  year =         "1991",
  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: book
filename: fparith.bib
label: Nelson:1991:SPM
editor: Greg Nelson
title: Systems Programming with Modula-3
publisher: pub-PH
address: pub-PH:adr
pages: ix + 267
year: 1991
ISBN: 0-13-590464-1 OR 0135904641
ISBN13: 978-0-13-590464-0 OR 9780135904640
LCCN: QA76.66 .S87 1991
bibdate: Mon Sep 12 08:08:01 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.12 08:08:01 ???
acknowledgement: ack-nj
raweditor: Greg Nelson
rawtitle: Systems Programming with {Modula-3}
note:
A description of the Modula 3 programming language by the committee that designed it, with an entertaining appendix on how various design decisions were made. Section 3.4 describes three floating-point interfaces that provide parameters of the underlying floating-point system, access primitives, and exception handling.

rawnote:
A description of the Modula 3 programming language by the committee that designed it, with an entertaining appendix on how various design decisions were made. Section 3.4 describes three floating-point interfaces that provide parameters of the underlying floating-point system, access primitives, and exception handling.

entry:
@Book{Nelson:1991:SPM,
  editor =       "Greg Nelson",
  title =        "Systems Programming with {Modula-3}",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "ix + 267",
  year =         "1991",
  ISBN =         "0-13-590464-1",
  ISBN-13 =      "978-0-13-590464-0",
  LCCN =         "QA76.66 .S87 1991",
  bibdate =      "Mon Sep 12 08:08:01 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "A description of the Modula 3 programming language by
                 the committee that designed it, with an entertaining
                 appendix on how various design decisions were made.
                 Section 3.4 describes three floating-point interfaces
                 that provide parameters of the underlying
                 floating-point system, access primitives, and exception
                 handling.",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: Ochs:1991:NRU
author: T. Ochs
title: Numerics for the rest of us
journal: j-COMP-LANG-MAG
volume: 8
number: 10
pages: 113--127
month: oct
monthnumber: 10
year: 1991
CODEN: COMLEF
ISSN: 0749-2839 OR 07492839
bibdate: Thu Sep 1 10:15:40 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:15:40 ???
fjournal: Computer Language Magazine
acknowledgement: ack-nj
rawauthor: T. Ochs
rawtitle: Numerics for the rest of us
entry:
@Article{Ochs:1991:NRU,
  author =       "T. Ochs",
  title =        "Numerics for the rest of us",
  journal =      j-COMP-LANG-MAG,
  volume =       "8",
  number =       "10",
  pages =        "113--127",
  month =        oct,
  year =         "1991",
  CODEN =        "COMLEF",
  ISSN =         "0749-2839",
  bibdate =      "Thu Sep 1 10:15:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Computer Language Magazine",
}


bibtype: article
filename: fparith.bib
label: Ochs:1991:NTR
author: T. Ochs
title: Numeric types, representations, and other fictions
journal: j-COMP-LANG-MAG
volume: 8
number: 8
pages: 93--101
month: aug
monthnumber: 8
year: 1991
CODEN: COMLEF
ISSN: 0749-2839 OR 07492839
bibdate: Thu Sep 1 10:14:15 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 10:14:15 ???
fjournal: Computer Language Magazine
acknowledgement: ack-nj
rawauthor: T. Ochs
rawtitle: Numeric types, representations, and other fictions
entry:
@Article{Ochs:1991:NTR,
  author =       "T. Ochs",
  title =        "Numeric types, representations, and other fictions",
  journal =      j-COMP-LANG-MAG,
  volume =       "8",
  number =       "8",
  pages =        "93--101",
  month =        aug,
  year =         "1991",
  CODEN =        "COMLEF",
  ISSN =         "0749-2839",
  bibdate =      "Thu Sep 1 10:14:15 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: Ochs:1991:RF
author: T. Ochs
title: A rotten foundation
journal: j-COMP-LANG-MAG
volume: 8
number: 2
pages: 103--107
month: feb
monthnumber: 2
year: 1991
CODEN: COMLEF
ISSN: 0749-2839 OR 07492839
bibdate: Thu Sep 1 10:15:05 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 10:15:05 ???
fjournal: Computer Language Magazine
acknowledgement: ack-nj
rawauthor: T. Ochs
rawtitle: A rotten foundation
entry:
@Article{Ochs:1991:RF,
  author =       "T. Ochs",
  title =        "A rotten foundation",
  journal =      j-COMP-LANG-MAG,
  volume =       "8",
  number =       "2",
  pages =        "103--107",
  month =        feb,
  year =         "1991",
  CODEN =        "COMLEF",
  ISSN =         "0749-2839",
  bibdate =      "Thu Sep 1 10:15:05 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: Ochs:1991:SRF
author: T. Ochs
title: Son of rotten foundation: The sequel
journal: j-COMP-LANG-MAG
volume: 8
number: 3
pages: 85--91
month: mar
monthnumber: 3
year: 1991
CODEN: COMLEF
ISSN: 0749-2839 OR 07492839
bibdate: Fri Dec 08 13:04:29 1995
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 13:04:29 ???
fjournal: Computer Language Magazine
acknowledgement: ack-nj
rawauthor: T. Ochs
rawtitle: Son of rotten foundation: The sequel
entry:
@Article{Ochs:1991:SRF,
  author =       "T. Ochs",
  title =        "Son of rotten foundation: The sequel",
  journal =      j-COMP-LANG-MAG,
  volume =       "8",
  number =       "3",
  pages =        "85--91",
  month =        mar,
  year =         "1991",
  CODEN =        "COMLEF",
  ISSN =         "0749-2839",
  bibdate =      "Fri Dec 08 13:04:29 1995",
  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: OGrady:1991:HOA
author: E. Pearse O'Grady and Baek-Kyu K. Young
title: A Hardware-Oriented Algorithm for Floating-Point Function Generation
journal: j-IEEE-TRANS-COMPUT
volume: 40
number: 2
pages: 237--241
month: feb
monthnumber: 2
year: 1991
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.73596
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 12:52:19 MDT 2011
bibtimestamp: 2011.07.07 12:52:19 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=73596
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: E. Pearse O'Grady and Baek-Kyu K. Young
rawtitle: A Hardware-Oriented Algorithm for Floating-Point Function Generation
abstract:
An algorithm is presented for performing accurate, high-speed, floating-point function generation for univariate functions defined at arbitrary breakpoints. Rapid identification of the breakdown interval, which includes the input argument, is the key operation in the algorithm. A hardware implementation which makes extensive use of read / write memories illustrates the algorithm.

rawabstract:
An algorithm is presented for performing accurate, high-speed, floating-point function generation for univariate functions defined at arbitrary breakpoints. Rapid identification of the breakdown interval, which includes the input argument, is the key operation in the algorithm. A hardware implementation which makes extensive use of read\slash write memories illustrates the algorithm.

entry:
@Article{OGrady:1991:HOA,
  author =       "E. Pearse O'Grady and Baek-Kyu K. Young",
  title =        "A Hardware-Oriented Algorithm for Floating-Point
                 Function Generation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "40",
  number =       "2",
  pages =        "237--241",
  month =        feb,
  year =         "1991",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.73596",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 12:52:19 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=73596",
  abstract =     "An algorithm is presented for performing accurate,
                 high-speed, floating-point function generation for
                 univariate functions defined at arbitrary breakpoints.
                 Rapid identification of the breakdown interval, which
                 includes the input argument, is the key operation in
                 the algorithm. A hardware implementation which makes
                 extensive use of read\slash write memories illustrates
                 the algorithm.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Okabe:1991:LDC
author: Y. Okabe and N. Takagi and S. Yaima
title: Log-Depth Circuits for Elementary Functions Using Residue Number System
journal: j-ELECTRON-COMMUN-JPN
volume: 74
number: 8
pages: 31--37
year: 1991
CODEN: ECOJAL
ISSN: 0424-8368 OR 04248368
bibdate: Mon May 19 15:16:09 1997
bibtimestamp: 1997.05.19 15:16:09 ???
note: Translated from Denshi Joho Tsushin Gakkai Ronbunshi, vol.21-DI, no.9, September 1990, pp.723-728
fjournal: Electronics and communications in Japan
acknowledgement: ack-nhfb
key: OTY91
rawauthor: Y. Okabe and N. Takagi and S. Yaima
rawtitle: Log-Depth Circuits for Elementary Functions Using Residue Number System
bibsource:
ftp://ftp.ira.uka.de/pub/bibliography/Theory/arith.bib.gz; https://www.math.utah.edu/pub/tex/bib/fparith.bib

rawnote:
Translated from Denshi Joho Tsushin Gakkai Ronbunshi, vol.\ 21-DI, no.\ 9, September 1990, pp.\ 723-728

entry:
@Article{Okabe:1991:LDC,
  author =       "Y. Okabe and N. Takagi and S. Yaima",
  key =          "OTY91",
  title =        "Log-Depth Circuits for Elementary Functions Using
                 Residue Number System",
  journal =      j-ELECTRON-COMMUN-JPN,
  volume =       "74",
  number =       "8",
  pages =        "31--37",
  year =         "1991",
  CODEN =        "ECOJAL",
  ISSN =         "0424-8368",
  bibdate =      "Mon May 19 15:16:09 1997",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Theory/arith.bib.gz;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Translated from Denshi Joho Tsushin Gakkai Ronbunshi,
                 vol.\ 21-DI, no.\ 9, September 1990, pp.\ 723-728",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics and communications in Japan",
}


bibtype: inproceedings
filename: fparith.bib
label: Orup:1991:HRH
author: Holger Orup and Peter Kornerup
title: A high-radix hardware algorithm for calculating the exponential $ M^E bmod N $
crossref: Kornerup:1991:PIS
pages: 51--56
year: 1991
bibdate: Sat Nov 27 12:40:58 MST 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.27 12:40:58 MST
URL: http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Orup.pdf
keywords: ARITH-10
acknowledgement: ack-nhfb
rawauthor: Holger Orup and Peter Kornerup
rawtitle: {A} high-radix hardware algorithm for calculating the exponential {$ M^E \bmod N $}
entry:
@InProceedings{Orup:1991:HRH,
  author =       "Holger Orup and Peter Kornerup",
  title =        "{A} high-radix hardware algorithm for calculating the
                 exponential {$ M^E \bmod N $}",
  crossref =     "Kornerup:1991:PIS",
  pages =        "51--56",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Orup.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}


bibtype: article
filename: fparith.bib
label: Ozawa:1991:FND
author: K. Ozawa
title: A Fast $ O(n^2) $ Division Algorithm for Multiple-Precision Floating-Point Numbers
journal: j-INFO-PROC
volume: 14
number: 3
pages: 354--356
year: 1991
bibdate: Thu Sep 1 10:15:09 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 10:15:09 ???
acknowledgement: ack-nj
rawauthor: K. Ozawa
rawtitle: A Fast {$ O(n^2) $} Division Algorithm for Multiple-Precision Floating-Point Numbers
entry:
@Article{Ozawa:1991:FND,
  author =       "K. Ozawa",
  title =        "A Fast {$ O(n^2) $} Division Algorithm for
                 Multiple-Precision Floating-Point Numbers",
  journal =      j-INFO-PROC,
  volume =       "14",
  number =       "3",
  pages =        "354--356",
  month =        "????",
  year =         "1991",
  bibdate =      "Thu Sep 1 10:15:09 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: article
filename: fparith.bib
label: Ozawa:1991:FOD
author: K. Ozawa
title: A Fast $ O(n^2) $ Division Algorithm for Multiple-Precision Floating-Point Numbers
journal: j-J-INF-PROCESS
volume: 14
number: 3
pages: 354--356
year: 1991
CODEN: JIPRDE
ISSN: 0387-6101 OR 03876101
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: Journal of Information Processing
keywords: Fast O(n/sup 2/) division algorithm; Multiple-precision floating-point numbers; Newton method
acknowledgement: ack-nhfb
affiliation: Department of Computer Science, Coll. of Gen. Educ., Tohoku University, Miyagi, Japan
thesaurus: Algorithm theory; Digital arithmetic
rawauthor: K. Ozawa
rawtitle: A Fast {$ O(n^2) $} Division Algorithm for Multiple-Precision Floating-Point Numbers
abstract:
A fast O(n/sup 2/) algorithm is derived for the division of multiple-precision floating-point numbers, where $n$ is the number of digits in each of the numbers. This algorithm, which is a modification of the conventional pencil-and-paper technique, is as fast as the conventional $ O(n^2) $ multiplication and 2.67 times faster than the algorithm based on the Newton method.

rawabstract:
A fast O(n/sup 2/) algorithm is derived for the division of multiple-precision floating-point numbers, where $n$ is the number of digits in each of the numbers. This algorithm, which is a modification of the conventional pencil-and-paper technique, is as fast as the conventional $ O(n^2) $ multiplication and 2.67 times faster than the algorithm based on the Newton method.

entry:
@Article{Ozawa:1991:FOD,
  author =       "K. Ozawa",
  title =        "A Fast {$ O(n^2) $} Division Algorithm for
                 Multiple-Precision Floating-Point Numbers",
  journal =      j-J-INF-PROCESS,
  volume =       "14",
  number =       "3",
  pages =        "354--356",
  month =        "????",
  year =         "1991",
  CODEN =        "JIPRDE",
  ISSN =         "0387-6101",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A fast O(n/sup 2/) algorithm is derived for the
                 division of multiple-precision floating-point numbers,
                 where $n$ is the number of digits in each of the
                 numbers. This algorithm, which is a modification of the
                 conventional pencil-and-paper technique, is as fast as
                 the conventional $ O(n^2) $ multiplication and 2.67
                 times faster than the algorithm based on the Newton
                 method.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Computer Science, Coll. of Gen. Educ.,
                 Tohoku University, Miyagi, Japan",
  classification = "C4240 (Programming and algorithm theory)",
  fjournal =     "Journal of Information Processing",
  keywords =     "Fast O(n/sup 2/) division algorithm;
                 Multiple-precision floating-point numbers; Newton
                 method",
  pubcountry =   "Japan",
  thesaurus =    "Algorithm theory; Digital arithmetic",
}


bibtype: inproceedings
filename: fparith.bib
label: Parikh:1991:RBE
author: Shrikant N. Parikh and David W. Matula
title: A redundant binary Euclidean GCD algorithm
crossref: Kornerup:1991:PIS
pages: 220--225
year: 1991
bibdate: Sat Nov 27 12:40:58 MST 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.27 12:40:58 MST
URL: http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Parikh.pdf
acknowledgement: ack-nhfb
affiliation: IBM, Westlake, TX, USA
thesaurus: Computational complexity; Digital arithmetic
rawauthor: Shrikant N. Parikh and David W. Matula
rawtitle: A redundant binary {Euclidean GCD} algorithm
abstract:
An efficient implementation of the Euclidean GCD (greatest common divisor) algorithm employing the redundant binary number system is described. The time complexity is O(n), utilizing O(n)4-2 signed 1-b adders to determine the GCD of two n-b integers. The process is similar to that used in SRT division. The efficiency of the algorithm is competitive, to within a small factor, with floating point division in terms of the number of shift and add/subtract operations. The novelty of the algorithm is based on properties derived from the proposed scheme of normalization of signed bit fractions. The implementation is well suited for systolic hardware design.

keywords:
ARITH-10; Euclidean GCD; Floating point division; Greatest common divisor; Redundant binary number system; Signed bit fractions; Systolic hardware design; Time complexity

rawabstract:
An efficient implementation of the Euclidean GCD (greatest common divisor) algorithm employing the redundant binary number system is described. The time complexity is O(n), utilizing O(n)4-2 signed 1-b adders to determine the GCD of two n-b integers. The process is similar to that used in SRT division. The efficiency of the algorithm is competitive, to within a small factor, with floating point division in terms of the number of shift and add/subtract operations. The novelty of the algorithm is based on properties derived from the proposed scheme of normalization of signed bit fractions. The implementation is well suited for systolic hardware design.

entry:
@InProceedings{Parikh:1991:RBE,
  author =       "Shrikant N. Parikh and David W. Matula",
  title =        "A redundant binary {Euclidean GCD} algorithm",
  crossref =     "Kornerup:1991:PIS",
  pages =        "220--225",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Parikh.pdf",
  abstract =     "An efficient implementation of the Euclidean GCD
                 (greatest common divisor) algorithm employing the
                 redundant binary number system is described. The time
                 complexity is O(n), utilizing O(n)4-2 signed 1-b adders
                 to determine the GCD of two n-b integers. The process
                 is similar to that used in SRT division. The efficiency
                 of the algorithm is competitive, to within a small
                 factor, with floating point division in terms of the
                 number of shift and add/subtract operations. The
                 novelty of the algorithm is based on properties derived
                 from the proposed scheme of normalization of signed bit
                 fractions. The implementation is well suited for
                 systolic hardware design.",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM, Westlake, TX, USA",
  classification = "C5230 (Digital arithmetic methods)",
  keywords =     "ARITH-10; Euclidean GCD; Floating point division;
                 Greatest common divisor; Redundant binary number
                 system; Signed bit fractions; Systolic hardware design;
                 Time complexity",
  thesaurus =    "Computational complexity; Digital arithmetic",
}


bibtype: inproceedings
filename: fparith.bib
label: Paterson:1991:SMC
author: Michael S. Paterson and Uri Zwick
title: Shallow multiplication circuits
crossref: Kornerup:1991:PIS
pages: 28--34
year: 1991
bibdate: Sat Nov 27 12:40:58 MST 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.27 12:40:58 MST
URL: http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Peterson.pdf
keywords: ARITH-10
acknowledgement: ack-nhfb
rawauthor: Michael S. Paterson and Uri Zwick
rawtitle: Shallow multiplication circuits
entry:
@InProceedings{Paterson:1991:SMC,
  author =       "Michael S. Paterson and Uri Zwick",
  title =        "Shallow multiplication circuits",
  crossref =     "Kornerup:1991:PIS",
  pages =        "28--34",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Peterson.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}


bibtype: misc
filename: fparith.bib
label: Paxson:1991:PTI
author: Vern Paxson and W. Kahan
title: A Program for Testing IEEE Binary--Decimal Conversion
pages: 28--34
month: may
monthnumber: 5
year: 1991
bibdate: Wed Jan 29 17:59:29 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.01.29 17:59:29 ???
URL: ftp://ftp.ee.lbl.gov/testbase-report.ps.Z; ftp://ftp.ee.lbl.gov/testbase.tar.Z
keywords: decimal floating-point arithmetic; floating-point testing
acknowledgement: ack-nhfb
howpublished: World-Wide Web document
rawauthor: Vern Paxson and W. Kahan
rawtitle: A Program for Testing {IEEE} Binary--Decimal Conversion
entry:
@Misc{Paxson:1991:PTI,
  author =       "Vern Paxson and W. Kahan",
  title =        "A Program for Testing {IEEE} Binary--Decimal
                 Conversion",
  howpublished = "World-Wide Web document",
  month =        may,
  year =         "1991",
  bibdate =      "Wed Jan 29 17:59:29 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://ftp.ee.lbl.gov/testbase-report.ps.Z;
                 ftp://ftp.ee.lbl.gov/testbase.tar.Z",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic; floating-point
                 testing",
}


bibtype: inproceedings
filename: fparith.bib
label: Piestrak:1991:DRG
author: Stanislaw J. Piestrak
title: Design of Residue Generators and Multioperand Modular Adders Using Carry-Save Adders
crossref: Kornerup:1991:PIS
pages: 100--107
year: 1991
bibdate: Sat Nov 17 08:46:25 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.17 08:46:25 ???
URL: http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Piestrak.pdf
keywords: ARITH-10
acknowledgement: ack-nhfb
rawauthor: Stanis{\l}aw J. Piestrak
rawtitle: Design of Residue Generators and Multioperand Modular Adders Using Carry-Save Adders
entry:
@InProceedings{Piestrak:1991:DRG,
  author =       "Stanis{\l}aw J. Piestrak",
  title =        "Design of Residue Generators and Multioperand Modular
                 Adders Using Carry-Save Adders",
  crossref =     "Kornerup:1991:PIS",
  pages =        "100--107",
  year =         "1991",
  bibdate =      "Sat Nov 17 08:46:25 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Piestrak.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}


bibtype: article
filename: fparith.bib
label: Plauger:1991:AF
author: P. J. Plauger
title: Approximating functions
journal: j-COMP-LANG-MAG
volume: 8
number: 6
pages: 17--25
month: jun
monthnumber: 6
year: 1991
CODEN: COMLEF
ISSN: 0749-2839 OR 07492839
bibdate: Thu Sep 1 10:15:40 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:15:40 ???
fjournal: Computer Language Magazine
acknowledgement: ack-nj
rawauthor: P. J. Plauger
rawtitle: Approximating functions
entry:
@Article{Plauger:1991:AF,
  author =       "P. J. Plauger",
  title =        "Approximating functions",
  journal =      j-COMP-LANG-MAG,
  volume =       "8",
  number =       "6",
  pages =        "17--25",
  month =        jun,
  year =         "1991",
  CODEN =        "COMLEF",
  ISSN =         "0749-2839",
  bibdate =      "Thu Sep 1 10:15:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Computer Language Magazine",
}


bibtype: article
filename: fparith.bib
label: Plauger:1991:EP
author: P. J. Plauger
title: Economizing polynomials
journal: j-COMP-LANG-MAG
volume: 8
number: 7
pages: 21--27
month: jul
monthnumber: 7
year: 1991
CODEN: COMLEF
ISSN: 0749-2839 OR 07492839
bibdate: Thu Sep 1 10:15:40 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:15:40 ???
fjournal: Computer Language Magazine
acknowledgement: ack-nj
rawauthor: P. J. Plauger
rawtitle: Economizing polynomials
entry:
@Article{Plauger:1991:EP,
  author =       "P. J. Plauger",
  title =        "Economizing polynomials",
  journal =      j-COMP-LANG-MAG,
  volume =       "8",
  number =       "7",
  pages =        "21--27",
  month =        jul,
  year =         "1991",
  CODEN =        "COMLEF",
  ISSN =         "0749-2839",
  bibdate =      "Thu Sep 1 10:15:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Computer Language Magazine",
}


bibtype: article
filename: fparith.bib
label: Plauger:1991:FPA
author: P. J. Plauger
title: Floating-Point Arithmetic
journal: j-EMBED-SYS-PROG
volume: 4
number: 8
pages: 95--99
month: aug
monthnumber: 8
year: 1991
CODEN: EYPRE4
ISSN: 1040-3272 OR 10403272
bibdate: Thu Sep 1 10:14:15 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 10:14:15 ???
fjournal: Embedded Systems Programming
acknowledgement: ack-nj
rawauthor: P. J. Plauger
rawtitle: Floating-Point Arithmetic
entry:
@Article{Plauger:1991:FPA,
  author =       "P. J. Plauger",
  title =        "Floating-Point Arithmetic",
  journal =      j-EMBED-SYS-PROG,
  volume =       "4",
  number =       "8",
  pages =        "95--99",
  month =        aug,
  year =         "1991",
  CODEN =        "EYPRE4",
  ISSN =         "1040-3272",
  bibdate =      "Thu Sep 1 10:14:15 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 =     "Embedded Systems Programming",
}


bibtype: article
filename: fparith.bib
label: Plauger:1991:FPP
author: P. J. Plauger
title: Floating-Point Primitives
journal: j-JCLT
volume: 3
number: 2
pages: 89--100
month: sep
monthnumber: 9
year: 1991
ISSN: 1042-5721 OR 10425721
bibdate: Thu Nov 8 14:50:36 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.08 14:50:36 ???
fjournal: The Journal of C Language Translation
acknowledgement: ack-nj
rawauthor: P. J. Plauger
rawtitle: Floating-Point Primitives
entry:
@Article{Plauger:1991:FPP,
  author =       "P. J. Plauger",
  title =        "Floating-Point Primitives",
  journal =      j-JCLT,
  volume =       "3",
  number =       "2",
  pages =        "89--100",
  month =        sep,
  year =         "1991",
  ISSN =         "1042-5721",
  bibdate =      "Thu Nov 8 14:50:36 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "The Journal of {C} Language Translation",
}


bibtype: article
filename: fparith.bib
label: Plauger:1991:HTF
author: P. J. Plauger
title: The Header tt <float.h>
journal: j-CUJ
volume: 9
type: Standard C
number: 1
pages: 9--??
month: jan
monthnumber: 1
year: 1991
ISSN: 0898-9788 OR 08989788
bibdate: Fri Aug 30 16:52:23 MDT 1996
bibsource: http://www.cuj.com/cbklist.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.08.30 16:52:23 MDT
fjournal: C Users Journal
acknowledgement: ack-nhfb
rawauthor: P. J. Plauger
rawtitle: The Header {{\tt <float.h>}}
entry:
@Article{Plauger:1991:HTF,
  author =       "P. J. Plauger",
  title =        "The Header {{\tt <float.h>}}",
  journal =      j-CUJ,
  volume =       "9",
  type =         "{Standard C}",
  number =       "1",
  pages =        "9--??",
  month =        jan,
  year =         "1991",
  ISSN =         "0898-9788",
  bibdate =      "Fri Aug 30 16:52:23 MDT 1996",
  bibsource =    "http://www.cuj.com/cbklist.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "C Users Journal",
}


bibtype: article
filename: fparith.bib
label: Plauger:1991:WW
author: P. J. Plauger
title: Washing the watchers
journal: j-COMP-LANG-MAG
volume: 8
number: 9
pages: 23--32
month: sep
monthnumber: 9
year: 1991
CODEN: COMLEF
ISSN: 0749-2839 OR 07492839
bibdate: Thu Sep 1 10:15:07 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 10:15:07 ???
fjournal: Computer Language Magazine
acknowledgement: ack-nj
rawauthor: P. J. Plauger
rawtitle: Washing the watchers
entry:
@Article{Plauger:1991:WW,
  author =       "P. J. Plauger",
  title =        "Washing the watchers",
  journal =      j-COMP-LANG-MAG,
  volume =       "8",
  number =       "9",
  pages =        "23--32",
  month =        sep,
  year =         "1991",
  CODEN =        "COMLEF",
  ISSN =         "0749-2839",
  bibdate =      "Thu Sep 1 10:15:07 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: inproceedings
filename: fparith.bib
label: Priest:1991:AAP
author: Douglas M. Priest
title: Algorithms for Arbitrary Precision Floating Point Arithmetic
crossref: Kornerup:1991:PIS
pages: 132--143
year: 1991
DOI: https://doi.org/10.1109/ARITH.1991.145549
bibdate: Sat Nov 27 12:40:58 MST 2004
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.27 12:40:58 MST
URL: http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Priest.pdf
acknowledgement: ack-nhfb
affiliation: Department of Math., California University, Berkeley, CA, USA
thesaurus: Digital arithmetic; Number theory
rawauthor: Douglas M. Priest
rawtitle: Algorithms for Arbitrary Precision Floating Point Arithmetic
abstract:
The author presents techniques for performing computations of very high accuracy using only straightforward floating-point arithmetic operations of limited precision. The validity of these techniques is proved under very general hypotheses satisfied by most implementations of floating-point arithmetic. To illustrate the applications of these techniques, an algorithm is presented which computes the intersection of a line and a line segment. The algorithm is guaranteed to correctly decide whether an intersection exists and, if so, to produce the coordinates of the intersection point accurate to full precision. The algorithm is usually quite efficient; only in a few cases does guaranteed accuracy necessitate an expensive computation.

keywords:
accurate floating-point summation; ARITH-10; coordinates; floating point arithmetic; intersection point; line intersection; line segment

rawabstract:
The author presents techniques for performing computations of very high accuracy using only straightforward floating-point arithmetic operations of limited precision. The validity of these techniques is proved under very general hypotheses satisfied by most implementations of floating-point arithmetic. To illustrate the applications of these techniques, an algorithm is presented which computes the intersection of a line and a line segment. The algorithm is guaranteed to correctly decide whether an intersection exists and, if so, to produce the coordinates of the intersection point accurate to full precision. The algorithm is usually quite efficient; only in a few cases does guaranteed accuracy necessitate an expensive computation.

entry:
@InProceedings{Priest:1991:AAP,
  author =       "Douglas M. Priest",
  title =        "Algorithms for Arbitrary Precision Floating Point
                 Arithmetic",
  crossref =     "Kornerup:1991:PIS",
  pages =        "132--143",
  year =         "1991",
  DOI =          "https://doi.org/10.1109/ARITH.1991.145549",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  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/arith10/papers/ARITH10_Priest.pdf",
  abstract =     "The author presents techniques for performing
                 computations of very high accuracy using only
                 straightforward floating-point arithmetic operations of
                 limited precision. The validity of these techniques is
                 proved under very general hypotheses satisfied by most
                 implementations of floating-point arithmetic. To
                 illustrate the applications of these techniques, an
                 algorithm is presented which computes the intersection
                 of a line and a line segment. The algorithm is
                 guaranteed to correctly decide whether an intersection
                 exists and, if so, to produce the coordinates of the
                 intersection point accurate to full precision. The
                 algorithm is usually quite efficient; only in a few
                 cases does guaranteed accuracy necessitate an expensive
                 computation.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "Department of Math., California University, Berkeley,
                 CA, USA",
  classification = "C1160 (Combinatorial mathematics); C5230 (Digital
                 arithmetic methods)",
  keywords =     "accurate floating-point summation; ARITH-10;
                 coordinates; floating point arithmetic; intersection
                 point; line intersection; line segment",
  thesaurus =    "Digital arithmetic; Number theory",
}


bibtype: article
filename: fparith.bib
label: Pugh:1991:TFV
author: Kenneth Pugh and Hugo Calleens
title: tt floats Versus tt doubles
journal: j-CUJ
volume: 9
type: Questions and Answers
number: 6
pages: 117--??
month: jun
monthnumber: 6
year: 1991
ISSN: 0898-9788 OR 08989788
bibdate: Fri Aug 30 16:52:23 MDT 1996
bibsource: http://www.cuj.com/cbklist.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.08.30 16:52:23 MDT
fjournal: C Users Journal
acknowledgement: ack-nhfb
rawauthor: Kenneth Pugh and Hugo Calleens
rawtitle: {{\tt float}}s Versus {{\tt double}}s
entry:
@Article{Pugh:1991:TFV,
  author =       "Kenneth Pugh and Hugo Calleens",
  title =        "{{\tt float}}s Versus {{\tt double}}s",
  journal =      j-CUJ,
  volume =       "9",
  type =         "Questions and Answers",
  number =       "6",
  pages =        "117--??",
  month =        jun,
  year =         "1991",
  ISSN =         "0898-9788",
  bibdate =      "Fri Aug 30 16:52:23 MDT 1996",
  bibsource =    "http://www.cuj.com/cbklist.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "C Users Journal",
}


bibtype: techreport
filename: fparith.bib
label: Quach:1991:DIS
author: N. Quach and M. Flynn
title: Design and implementation of the SNAP floating-point adder
type: Technical Report
number: CSL-TR-91-501
institution: Computer Systems Laboratory, Stanford University
address: Stanford, CA, USA
pages: 117--??
month: dec
monthnumber: 12
year: 1991
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: Design and implementation of the {SNAP} floating-point adder
entry:
@TechReport{Quach:1991:DIS,
  author =       "N. Quach and M. Flynn",
  title =        "Design and implementation of the {SNAP} floating-point
                 adder",
  type =         "Technical Report",
  number =       "CSL-TR-91-501",
  institution =  "Computer Systems Laboratory, Stanford University",
  address =      "Stanford, CA, USA",
  month =        dec,
  year =         "1991",
  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: techreport
filename: fparith.bib
label: Quach:1991:FIR
author: N. Quach and N. Takagi and M. J. Flynn
title: On Fast IEEE Rounding
type: Technical Report
number: CSL-TR-91-459
institution: Stanford University
address: Stanford, CA, USA
pages: v + 27
month: jan
monthnumber: 1
year: 1991
bibdate: Sun Dec 10 14:08:33 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.10 14:08:33 ???
URL: http://i.stanford.edu/pub/cstr/reports/csl/tr/91/459/CSL-TR-91-459.pdf
acknowledgement: ack-nhfb
rawauthor: N. Quach and N. Takagi and M. J. Flynn
rawtitle: On Fast {IEEE} Rounding
abstract:
A systematic general rounding procedure is proposed. This procedure consists of 2 steps: constructing a rounding table and selecting a prediction scheme. Optimization guidelines are given in each step to minimize the hardware used. This procedure-based rounding method has the additional advantage that verification and generalization are trivial. Two rounding hardware models are described. The first is shown to be identical to that reported by Santoro, et al. The second is more powerful, providing solutions where the first fails. Applying this approach to the IEEE rounding modes for high-speed conventional binary multipliers reveals that round to infinity is more difficult to implement than the round to nearest mode; more adders are potentially needed. Round to zero requires the least amount of hardware. A generalization of this procedure to redundant binary multipliers reveals two major advantages over conventional binary multipliers. First, the computation of the sticky bit consumes considerably less hardware. Second, implementing round to positive and minus infinity modes does not require the examination of the sticky bit, removing a possible worst-case path. A generalization of this approach to addition produces a similar solution to that reported by Quach and Flynn. Although generalizable to other kinds of rounding as well as other arithmetic operations, we only treat the case of IEEE rounding for addition and multiplication; IEEE rounding because it is the current standard on rounding, addition and multiplication because they are the most frequently used arithmetic operations in a typical scientific computation.

keywords:
high-speed floating-point adders; high-speed parallel multipliers; IEEE rounding; redundant binary multipliers; redundant binary representation

rawabstract:
A systematic general rounding procedure is proposed. This procedure consists of 2 steps: constructing a rounding table and selecting a prediction scheme. Optimization guidelines are given in each step to minimize the hardware used. This procedure-based rounding method has the additional advantage that verification and generalization are trivial. Two rounding hardware models are described. The first is shown to be identical to that reported by Santoro, et al. The second is more powerful, providing solutions where the first fails. Applying this approach to the IEEE rounding modes for high-speed conventional binary multipliers reveals that round to infinity is more difficult to implement than the round to nearest mode; more adders are potentially needed. Round to zero requires the least amount of hardware. A generalization of this procedure to redundant binary multipliers reveals two major advantages over conventional binary multipliers. First, the computation of the sticky bit consumes considerably less hardware. Second, implementing round to positive and minus infinity modes does not require the examination of the sticky bit, removing a possible worst-case path. A generalization of this approach to addition produces a similar solution to that reported by Quach and Flynn. Although generalizable to other kinds of rounding as well as other arithmetic operations, we only treat the case of IEEE rounding for addition and multiplication; IEEE rounding because it is the current standard on rounding, addition and multiplication because they are the most frequently used arithmetic operations in a typical scientific computation.

entry:
@TechReport{Quach:1991:FIR,
  author =       "N. Quach and N. Takagi and M. J. Flynn",
  title =        "On Fast {IEEE} Rounding",
  type =         "Technical Report",
  number =       "CSL-TR-91-459",
  institution =  "Stanford University",
  address =      "Stanford, CA, USA",
  pages =        "v + 27",
  month =        jan,
  year =         "1991",
  bibdate =      "Sun Dec 10 14:08:33 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://i.stanford.edu/pub/cstr/reports/csl/tr/91/459/CSL-TR-91-459.pdf",
  abstract =     "A systematic general rounding procedure is proposed.
                 This procedure consists of 2 steps: constructing a
                 rounding table and selecting a prediction scheme.
                 Optimization guidelines are given in each step to
                 minimize the hardware used. This procedure-based
                 rounding method has the additional advantage that
                 verification and generalization are trivial. Two
                 rounding hardware models are described. The first is
                 shown to be identical to that reported by Santoro, et
                 al. The second is more powerful, providing solutions
                 where the first fails. Applying this approach to the
                 IEEE rounding modes for high-speed conventional binary
                 multipliers reveals that round to infinity is more
                 difficult to implement than the round to nearest mode;
                 more adders are potentially needed. Round to zero
                 requires the least amount of hardware. A generalization
                 of this procedure to redundant binary multipliers
                 reveals two major advantages over conventional binary
                 multipliers. First, the computation of the sticky bit
                 consumes considerably less hardware. Second,
                 implementing round to positive and minus infinity modes
                 does not require the examination of the sticky bit,
                 removing a possible worst-case path. A generalization
                 of this approach to addition produces a similar
                 solution to that reported by Quach and Flynn. Although
                 generalizable to other kinds of rounding as well as
                 other arithmetic operations, we only treat the case of
                 IEEE rounding for addition and multiplication; IEEE
                 rounding because it is the current standard on
                 rounding, addition and multiplication because they are
                 the most frequently used arithmetic operations in a
                 typical scientific computation.",
  acknowledgement = ack-nhfb,
  keywords =     "high-speed floating-point adders; high-speed parallel
                 multipliers; IEEE rounding; redundant binary
                 multipliers; redundant binary representation",
}


bibtype: techreport
filename: fparith.bib
label: Quach:1991:LOP
author: N. T. Quach and M. J. Flynn
title: Leading one prediction --- implementation, generalization, and application
type: Technical Report
number: CSL-TR-91-463
institution: Computer Systems Laboratory, Stanford University
address: Stanford, CA, USA
pages: v + 27
month: mar
monthnumber: 3
year: 1991
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. T. Quach and M. J. Flynn
rawtitle: Leading one prediction --- implementation, generalization, and application
entry:
@TechReport{Quach:1991:LOP,
  author =       "N. T. Quach and M. J. Flynn",
  title =        "Leading one prediction --- implementation,
                 generalization, and application",
  type =         "Technical Report",
  number =       "CSL-TR-91-463",
  institution =  "Computer Systems Laboratory, Stanford University",
  address =      "Stanford, CA, USA",
  month =        mar,
  year =         "1991",
  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: Raja:1991:NDT
author: Paruvachi V. R. Raja
title: Novel Design Techniques for RNS Systolic VLSI Arrays
journal: j-LECT-NOTES-COMP-SCI
volume: 507
pages: 206--??
year: 1991
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Mon May 13 08:51:55 MDT 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.05.13 08:51:55 MDT
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Paruvachi V. R. Raja
rawtitle: Novel Design Techniques for {RNS} Systolic {VLSI} Arrays
entry:
@Article{Raja:1991:NDT,
  author =       "Paruvachi V. R. Raja",
  title =        "Novel Design Techniques for {RNS} Systolic {VLSI}
                 Arrays",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "507",
  pages =        "206--??",
  year =         "1991",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Mon May 13 08:51:55 MDT 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: inproceedings
filename: fparith.bib
label: Rao:1991:ARN
author: B. D. Rao
title: Analysis of roundoff noise in floating point digital filters
volume: 3
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1893--1896
year: 1991
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: B. D. Rao
rawtitle: Analysis of roundoff noise in floating point digital filters
booktitle:
Acoustics, Speech, and Signal Processing, 1991. ICASSP-91., 1991 International Conference on. 14--17 April 1991

rawbooktitle:
Acoustics, Speech, and Signal Processing, 1991. {ICASSP-91., 1991} International Conference on. 14--17 April 1991

entry:
@InProceedings{Rao:1991:ARN,
  author =       "B. D. Rao",
  booktitle =    "Acoustics, Speech, and Signal Processing, 1991.
                 {ICASSP-91., 1991} International Conference on. 14--17
                 April 1991",
  title =        "Analysis of roundoff noise in floating point digital
                 filters",
  volume =       "3",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1893--1896",
  year =         "1991",
  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 systematic approach for the analysis of roundoff
                 noise in floating point digital filters is presented.
                 The analysis is based on a high level model developed
                 to deal with the errors in the inner product operation.
                 The model consists of an efficient \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Rees:1991:RRA
author: Jonathan Rees and William Clinger and others
title: The revised$^4$ report on the algorithmic language Scheme
journal: ACM SIGPLAN Lisp Pointers
volume: 4
number: 3
pages: 1--55
month: jul
monthnumber: 7
year: 1991
bibdate: Wed Jan 29 16:50:56 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.01.29 16:50:56 ???
acknowledgement: ack-nhfb
rawauthor: Jonathan Rees and William Clinger and others
rawtitle: The revised$^4$ report on the algorithmic language {Scheme}
remark:
From cite Steele:2004:RHP: ``the result [of a binary-to-decimal conversion] is expressed using the minimum number of digitsldots ''

entry:
@Article{Rees:1991:RRA,
  author =       "Jonathan Rees and William Clinger and others",
  title =        "The revised$^4$ report on the algorithmic language
                 {Scheme}",
  journal =      "ACM SIGPLAN Lisp Pointers",
  volume =       "4",
  number =       "3",
  pages =        "1--55",
  month =        jul # "\slash " # sep,
  year =         "1991",
  bibdate =      "Wed Jan 29 16:50:56 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "From \cite{Steele:2004:RHP}: ``the result [of a
                 binary-to-decimal conversion] is expressed using the
                 minimum number of digits\ldots{}''",
}


bibtype: article
filename: fparith.bib
label: Rump:1991:CAI
author: Siegfried M. Rump
title: A Class of Arbitrarily Ill-Conditioned Floating-Point Matrices
journal: j-SIAM-J-MAT-ANA-APPL
volume: 12
number: 4
pages: 645--653
month: oct
monthnumber: 10
year: 1991
CODEN: SJMAEL
ISSN: 0895-4798 (print), 1095-7162 (electronic) OR 08954798 (print), 10957162 (electronic)
ISSNL: 0895-4798 OR 08954798
MRclass: 65F35 (15A12 65G05)
MRnumber: 92d:65076
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: SIAM Journal on Matrix Analysis and Applications
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/simax
rawauthor: Siegfried M. Rump
rawtitle: A Class of Arbitrarily Ill-Conditioned Floating-Point Matrices
entry:
@Article{Rump:1991:CAI,
  author =       "Siegfried M. Rump",
  title =        "A Class of Arbitrarily Ill-Conditioned Floating-Point
                 Matrices",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "12",
  number =       "4",
  pages =        "645--653",
  month =        oct,
  year =         "1991",
  CODEN =        "SJMAEL",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "65F35 (15A12 65G05)",
  MRnumber =     "92d:65076",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}


bibtype: article
filename: fparith.bib
label: Scott:1991:MCS
author: T. J. Scott
title: Mathematics and computer science at odds over real numbers
journal: j-SIGCSE
volume: 23
number: 1
pages: 130--139
month: mar
monthnumber: 3
year: 1991
CODEN: SIGSD3
ISSN: 0097-8418 (print), 2331-3927 (electronic) OR 00978418 (print), 23313927 (electronic)
bibdate: Tue Dec 12 09:20:21 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.12 09:20:21 MST
note: 22nd SIGCSE Technical Symposium on Computer Science Education.
fjournal: SIGCSE Bulletin (ACM Special Interest Group on Computer Science Education)
acknowledgement: ack-nhfb
affiliation: Department of Computer Science, Western Illinois University, Macomb, IL, USA
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J688
thesaurus: Computer science education; Data structures; Digital arithmetic; Educational courses; Number theory
rawauthor: T. J. Scott
rawnote: 22nd SIGCSE Technical Symposium on Computer Science Education.
rawtitle: Mathematics and computer science at odds over real numbers
abstract:
Discusses the `real numbers' data type as implemented by `floating point' numbers. Floating point implementations and a theorem that characterizes their truncations are presented. A teachable floating point system is presented, chosen so that most problems can be worked out with paper and pencil. Then major differences between floating point number systems and the continuous real number system are presented. Important floating point formats are next discussed. Two examples derived from actual computing practice on mainframes, minicomputers, and PCs are presented. The paper concludes with a discussion of where floating point arithmetic should be taught in standard courses in the ACM curriculum.

keywords:
ACM curriculum; Computer science; Floating point arithmetic; Floating point formats; Floating point number systems; Real number data types; Standard courses; Teaching; Truncations

rawabstract:
Discusses the `real numbers' data type as implemented by `floating point' numbers. Floating point implementations and a theorem that characterizes their truncations are presented. A teachable floating point system is presented, chosen so that most problems can be worked out with paper and pencil. Then major differences between floating point number systems and the continuous real number system are presented. Important floating point formats are next discussed. Two examples derived from actual computing practice on mainframes, minicomputers, and PCs are presented. The paper concludes with a discussion of where floating point arithmetic should be taught in standard courses in the ACM curriculum.

entry:
@Article{Scott:1991:MCS,
  author =       "T. J. Scott",
  title =        "Mathematics and computer science at odds over real
                 numbers",
  journal =      j-SIGCSE,
  volume =       "23",
  number =       "1",
  pages =        "130--139",
  month =        mar,
  year =         "1991",
  CODEN =        "SIGSD3",
  ISSN =         "0097-8418 (print), 2331-3927 (electronic)",
  bibdate =      "Tue Dec 12 09:20:21 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "22nd SIGCSE Technical Symposium on Computer Science
                 Education.",
  abstract =     "Discusses the `real numbers' data type as implemented
                 by `floating point' numbers. Floating point
                 implementations and a theorem that characterizes their
                 truncations are presented. A teachable floating point
                 system is presented, chosen so that most problems can
                 be worked out with paper and pencil. Then major
                 differences between floating point number systems and
                 the continuous real number system are presented.
                 Important floating point formats are next discussed.
                 Two examples derived from actual computing practice on
                 mainframes, minicomputers, and PCs are presented. The
                 paper concludes with a discussion of where floating
                 point arithmetic should be taught in standard courses
                 in the ACM curriculum.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Computer Science, Western Illinois
                 University, Macomb, IL, USA",
  classification = "C0220 (Education and training); C5230 (Digital
                 arithmetic methods)",
  confdate =     "7-8 March 1991",
  conflocation = "San Antonio, TX, USA",
  confsponsor =  "ACM",
  fjournal =     "SIGCSE Bulletin (ACM Special Interest Group on
                 Computer Science Education)",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J688",
  keywords =     "ACM curriculum; Computer science; Floating point
                 arithmetic; Floating point formats; Floating point
                 number systems; Real number data types; Standard
                 courses; Teaching; Truncations",
  thesaurus =    "Computer science education; Data structures; Digital
                 arithmetic; Educational courses; Number theory",
}


bibtype: techreport
filename: fparith.bib
label: Seznec:1991:OCE
author: Andre Seznec and Karl Courtel
title: OPAC: a cost-effective floating-point coprocessor = Le coprocessor numerique OPAC
institution: Institut National de Recherche en Informatique et en Automatique
address: Le Chesnay, France
pages: 24
year: 1991
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Floating-point arithmetic.; Microprocessors.
acknowledgement: ack-nhfb
rawauthor: Andre Seznec and Karl Courtel
rawtitle: {OPAC}: a cost-effective floating-point coprocessor = Le coprocessor num{\'e}rique {OPAC}
series:
Rapports de recherche. Institut National de Recherche en Informatique et en Automatique; 1461 Rapports de recherche (Institut national de recherche en informatique et en automatique (France)); 1461.

remark:
Abstracts in English and French. ``Mai 1991.'' Abstract: ``The effective performance of RISC microprocessors on numerical applications remains on the order of a few megaflops/s. In this paper, we show that the static addressing of the registers in standard RISC floating-point coprocessors is one of the main bottleneck [sic] for performance. In the architecture of the coprocessor OPAC, we propose an alternative using only FIFO queues for storing intermediate results and reusable operands. Performance close to multiplication-accumulation every cycle is expected on a large set of numerical applications at a reasonable hardware cost.'' Supported in part by the CNRS PRC-AMN Supported in part by the French Ministry of Defense.

entry:
@TechReport{Seznec:1991:OCE,
  author =       "Andre Seznec and Karl Courtel",
  title =        "{OPAC}: a cost-effective floating-point coprocessor =
                 Le coprocessor num{\'e}rique {OPAC}",
  institution =  "Institut National de Recherche en Informatique et en
                 Automatique",
  address =      "Le Chesnay, France",
  pages =        "24",
  year =         "1991",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Rapports de recherche. Institut National de Recherche
                 en Informatique et en Automatique; 1461 Rapports de
                 recherche (Institut national de recherche en
                 informatique et en automatique (France)); 1461.",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.; Microprocessors.",
  remark =       "Abstracts in English and French. ``Mai 1991.''
                 Abstract: ``The effective performance of RISC
                 microprocessors on numerical applications remains on
                 the order of a few megaflops/s. In this paper, we show
                 that the static addressing of the registers in standard
                 RISC floating-point coprocessors is one of the main
                 bottleneck [sic] for performance. In the architecture
                 of the coprocessor OPAC, we propose an alternative
                 using only FIFO queues for storing intermediate results
                 and reusable operands. Performance close to
                 multiplication-accumulation every cycle is expected on
                 a large set of numerical applications at a reasonable
                 hardware cost.'' Supported in part by the CNRS PRC-AMN
                 Supported in part by the French Ministry of Defense.",
}


bibtype: techreport
filename: fparith.bib
label: Seznec:1991:OFP
author: Andre Seznec and Karl Courtel
type: Rapports de recherche
number: 1555
institution: Institut National de Recherche en Informatique et en Automatique
address: Le Chesnay, France
pages: 27
year: 1991
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.; Kernel functions.; Parallel programming (Computer science)
acknowledgement: ack-nhfb
rawauthor: Andre Seznec and Karl Courtel
title:
OPAC: a floating-point coprocessor dedicated to compute-bound kernels = OPAC: un coprocesseur flottant dedie au calcul matriciel

remark:
Abstracts in English and French. ``October 7, 1991.'' Abstract: ``In various application domains, programmers are not specialists of parallel programming, but are demanding for performance that cannot be reached without using parallelism. Nevertheless, in many applications, the main part of the computations may be encapsulated in compute-bounds kernels with [sic] exhibit high potential parallelism. Achieving high performance on compute-bound primitives at a low hardware cost has became [sic] an important challenge. In this paper, we present the architecture of the OPAC floating-point operator. OPAC has been designed in order to be the basic cell in a multi-cell floating-point coprocessor dedicated to the execution of the most useful compute-bound kernels. The peak performance of one floating-point multiply-add per cycle per cell obtained on the OPAC prototype may be approached in a microprocessor environment on a multi-cell OPAC floating-point coprocessor on a large set of numerical applications.'' Supported in part by the French ministry of defense. Supported in part by the CNRS (PRC-ANM and GCIS)

rawtitle:
{OPAC}: a floating-point coprocessor dedicated to compute-bound kernels = {OPAC}: un coprocesseur flottant dedi{\'e} au calcul matriciel

entry:
@TechReport{Seznec:1991:OFP,
  author =       "Andre Seznec and Karl Courtel",
  title =        "{OPAC}: a floating-point coprocessor dedicated to
                 compute-bound kernels = {OPAC}: un coprocesseur
                 flottant dedi{\'e} au calcul matriciel",
  type =         "Rapports de recherche",
  number =       "1555",
  institution =  "Institut National de Recherche en Informatique et en
                 Automatique",
  address =      "Le Chesnay, France",
  pages =        "27",
  year =         "1991",
  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.; Kernel functions.; Parallel
                 programming (Computer science)",
  remark =       "Abstracts in English and French. ``October 7, 1991.''
                 Abstract: ``In various application domains, programmers
                 are not specialists of parallel programming, but are
                 demanding for performance that cannot be reached
                 without using parallelism. Nevertheless, in many
                 applications, the main part of the computations may be
                 encapsulated in compute-bounds kernels with [sic]
                 exhibit high potential parallelism. Achieving high
                 performance on compute-bound primitives at a low
                 hardware cost has became [sic] an important challenge.
                 In this paper, we present the architecture of the OPAC
                 floating-point operator. OPAC has been designed in
                 order to be the basic cell in a multi-cell
                 floating-point coprocessor dedicated to the execution
                 of the most useful compute-bound kernels. The peak
                 performance of one floating-point multiply-add per
                 cycle per cell obtained on the OPAC prototype may be
                 approached in a microprocessor environment on a
                 multi-cell OPAC floating-point coprocessor on a large
                 set of numerical applications.'' Supported in part by
                 the French ministry of defense. Supported in part by
                 the CNRS (PRC-ANM and GCIS)",
}


bibtype: article
filename: fparith.bib
label: Shaeffer:1991:HEP
journal: j-IEEE-TRANS-NUCL-SCI
volume: 38
number: 6
pages: 1421--1428
month: dec
monthnumber: 12
year: 1991
CODEN: IRNSAM
ISSN: 0018-9499 (print), 1558-1578 (electronic) OR 00189499 (print), 15581578 (electronic)
ISSNL: 0018-9499 OR 00189499
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 Nuclear Science
keywords: floating-point testing
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=23
author:
D. L. Shaeffer and J. R. Kimbrough and S. M. Denton and J. L. Kaschmitter and J. W. Wilburn and R. W. Davis and N. J. Colella and D. B. Holtkamp

title:
High energy proton SEU test results for the commercially available MIPS R3000 microprocessor and R3010 floating point unit

rawauthor:
D. L. Shaeffer and J. R. Kimbrough and S. M. Denton and J. L. Kaschmitter and J. W. Wilburn and R. W. Davis and N. J. Colella and D. B. Holtkamp

rawtitle:
High energy proton {SEU} test results for the commercially available {MIPS R3000} microprocessor and {R3010} floating point unit

entry:
@Article{Shaeffer:1991:HEP,
  author =       "D. L. Shaeffer and J. R. Kimbrough and S. M. Denton
                 and J. L. Kaschmitter and J. W. Wilburn and R. W. Davis
                 and N. J. Colella and D. B. Holtkamp",
  title =        "High energy proton {SEU} test results for the
                 commercially available {MIPS R3000} microprocessor and
                 {R3010} floating point unit",
  journal =      j-IEEE-TRANS-NUCL-SCI,
  volume =       "38",
  number =       "6",
  pages =        "1421--1428",
  month =        dec,
  year =         "1991",
  CODEN =        "IRNSAM",
  ISSN =         "0018-9499 (print), 1558-1578 (electronic)",
  ISSN-L =       "0018-9499",
  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 Nuclear Science",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=23",
  keywords =     "floating-point testing",
  summary =      "Proton single event upset (SEU) cross sections and
                 proton total dose hardness of commercially available
                 MIPS R3000 microprocessors (CPU) and R3010 floating
                 point units (FPU) were obtained by exposing these parts
                 to 256 MeV protons from the linear accelerator
                 \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Shand:1991:HSL
author: M. Shand and P. Bertin and J. Vuillemin
title: Hardware speedups in long integer multiplication
journal: j-COMP-ARCH-NEWS
volume: 19
number: 1
pages: 106--113
month: mar
monthnumber: 3
year: 1991
CODEN: CANED2
ISSN: 0163-5964 (print), 1943-5851 (electronic) OR 01635964 (print), 19435851 (electronic)
ISSNL: 0163-5964 OR 01635964
bibdate: Fri May 12 09:40:33 MDT 2006
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2006.05.12 09:40:33 MDT
fjournal: ACM SIGARCH Computer Architecture News
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/sigarch
rawauthor: M. Shand and P. Bertin and J. Vuillemin
rawtitle: Hardware speedups in long integer multiplication
entry:
@Article{Shand:1991:HSL,
  author =       "M. Shand and P. Bertin and J. Vuillemin",
  title =        "Hardware speedups in long integer multiplication",
  journal =      j-COMP-ARCH-NEWS,
  volume =       "19",
  number =       "1",
  pages =        "106--113",
  month =        mar,
  year =         "1991",
  CODEN =        "CANED2",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Fri May 12 09:40:33 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 =  "https://dl.acm.org/loi/sigarch",
}


bibtype: book
filename: fparith.bib
label: Siewiorek:1991:AST
author: Daniel P. Siewiorek and Philip John Koopman, Jr.
title: The Architecture of Supercomputers --- Titan, A Case Study
publisher: pub-ACADEMIC
address: pub-ACADEMIC:adr
pages: xvii + 202
year: 1991
ISBN: 0-12-643060-8 OR 0126430608
ISBN13: 978-0-12-643060-8 OR 9780126430608
LCCN: QA76.5 S536 1991
bibdate: Sun Jan 23 17:54:38 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.01.23 17:54:38 ???
acknowledgement: ack-nhfb
rawauthor: Daniel P. Siewiorek and Philip John {Koopman, Jr.}
rawtitle: The Architecture of Supercomputers\emdash Titan, {A} Case Study
entry:
@Book{Siewiorek:1991:AST,
  author =       "Daniel P. Siewiorek and Philip John {Koopman, Jr.}",
  title =        "The Architecture of Supercomputers\emdash Titan, {A}
                 Case Study",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xvii + 202",
  year =         "1991",
  ISBN =         "0-12-643060-8",
  ISBN-13 =      "978-0-12-643060-8",
  LCCN =         "QA76.5 S536 1991",
  bibdate =      "Sun Jan 23 17:54:38 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Skavantzos:1991:PRN
author: A. Skavantzos and F. J. Taylor
title: On the polynomial residue number system [digital signal processing]
journal: j-IEEE-TRANS-SIG-PROC
volume: 39
number: 2
pages: 376--382
month: feb
monthnumber: 2
year: 1991
CODEN: ITPRED
DOI: https://doi.org/10.1109/78.80821
ISSN: 1053-587X (print), 1941-0476 (electronic) OR 1053587X (print), 19410476 (electronic)
ISSNL: 1053-587X OR 1053587X
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
URL: https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=2656
fjournal: IEEE Transactions on Signal Processing
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78
rawauthor: A. Skavantzos and F. J. Taylor
rawtitle: On the polynomial residue number system [digital signal processing]
entry:
@Article{Skavantzos:1991:PRN,
  author =       "A. Skavantzos and F. J. Taylor",
  title =        "On the polynomial residue number system [digital
                 signal processing]",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "39",
  number =       "2",
  pages =        "376--382",
  month =        feb,
  year =         "1991",
  CODEN =        "ITPRED",
  DOI =          "https://doi.org/10.1109/78.80821",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=2656",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  keywords =     "residue arithmetic; residue number system",
  summary =      "The theory of the polynomial residue number system
                 (PRNS), a system in which totally parallel polynomial
                 multiplication can be achieved provided that the
                 arithmetic takes place in some carefully chosen ring,
                 is examined. Such a system is defined by \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Smith:1991:AFP
author: David M. Smith
title: Algorithm 693: A FORTRAN Package for Floating-Point Multiple-Precision Arithmetic
journal: j-TOMS
volume: 17
number: 2
pages: 273--283
month: jun
monthnumber: 6
year: 1991
CODEN: ACMSCU
DOI: https://doi.org/10.1145/108556.108585
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Wed Dec 13 18:36:25 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.13 18:36:25 ???
URL: http://www.acm.org/pubs/citations/journals/toms/1991-17-2/p273-smith/
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
affiliation: Loyola Marymount University, Los Angeles, CA, USA
journalURL: https://dl.acm.org/loi/toms
thesaurus: Digital arithmetic; Function approximation; Mathematics computing; Software packages; Subroutines
rawauthor: David M. Smith
rawtitle: {Algorithm 693}: {A FORTRAN} Package for Floating-Point Multiple-Precision Arithmetic
abstract:
FM is a collection of FORTRAN-77 routines which performs floating-point multiple-precision arithmetic and elementary functions. Results are almost always correctly rounded, and due to improved algorithms used for elementary functions, reasonable efficiency is obtained.

keywords:
Accuracy; correct rounding; Elementary functions; floating-point arithmetic; Floating-point multiple-precision arithmetic; FM; FORTRAN-77 routines; Mathematical library; Portable software; Rounding off

subject:
bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. bf D.3.2: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN 77.

rawabstract:
FM is a collection of FORTRAN-77 routines which performs floating-point multiple-precision arithmetic and elementary functions. Results are almost always correctly rounded, and due to improved algorithms used for elementary functions, reasonable efficiency is obtained.

entry:
@Article{Smith:1991:AFP,
  author =       "David M. Smith",
  title =        "{Algorithm 693}: {A FORTRAN} Package for
                 Floating-Point Multiple-Precision Arithmetic",
  journal =      j-TOMS,
  volume =       "17",
  number =       "2",
  pages =        "273--283",
  month =        jun,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/108556.108585",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Dec 13 18:36:25 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-2/p273-smith/",
  abstract =     "FM is a collection of FORTRAN-77 routines which
                 performs floating-point multiple-precision arithmetic
                 and elementary functions. Results are almost always
                 correctly rounded, and due to improved algorithms used
                 for elementary functions, reasonable efficiency is
                 obtained.",
  acknowledgement = ack-nhfb,
  affiliation =  "Loyola Marymount University, Los Angeles, CA, USA",
  classification = "C4130 (Interpolation and function approximation);
                 C5230 (Digital arithmetic methods); C7310
                 (Mathematics)",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Accuracy; correct rounding; Elementary functions;
                 floating-point arithmetic; Floating-point
                 multiple-precision arithmetic; FM; FORTRAN-77 routines;
                 Mathematical library; Portable software; Rounding off",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Numerical algorithms. {\bf D.3.2}:
                 Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN 77.",
  thesaurus =    "Digital arithmetic; Function approximation;
                 Mathematics computing; Software packages; Subroutines",
}


bibtype: article
filename: fparith.bib
label: Sorensen:1991:OEC
author: D. C. Sorensen and Ping Tak Peter Tang
title: On the Orthogonality of Eigenvectors Computed by Divide and Conquer Techniques
journal: j-SIAM-J-NUMER-ANAL
volume: 28
number: 6
pages: 1752--1775
month: dec
monthnumber: 12
year: 1991
CODEN: SJNAAM
ISSN: 0036-1429 (print), 1095-7170 (electronic) OR 00361429 (print), 10957170 (electronic)
ISSNL: 0036-1429 OR 00361429
MRclass: 65F15 (65G05)
MRnumber: 92h:65065
bibdate: Fri Oct 16 06:57:22 MDT 1998
bibtimestamp: 1998.10.16 06:57:22 MDT
fjournal: SIAM Journal on Numerical Analysis
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sinum
rawauthor: D. C. Sorensen and Ping Tak Peter Tang
rawtitle: On the Orthogonality of Eigenvectors Computed by Divide and Conquer Techniques
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database; Parallel/par.lin.alg.bib; Theory/Matrix.bib

note:
Pages 1759--1761 discuss implementation of useful primitives for higher-precision arithmetic: DPAdd2(), DPAdd3(), DPDiv().

rawnote:
Pages 1759--1761 discuss implementation of useful primitives for higher-precision arithmetic: DPAdd2(), DPAdd3(), DPDiv().

entry:
@Article{Sorensen:1991:OEC,
  author =       "D. C. Sorensen and Ping Tak Peter Tang",
  title =        "On the Orthogonality of Eigenvectors Computed by
                 Divide and Conquer Techniques",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "28",
  number =       "6",
  pages =        "1752--1775",
  month =        dec,
  year =         "1991",
  CODEN =        "SJNAAM",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  MRclass =      "65F15 (65G05)",
  MRnumber =     "92h:65065",
  bibdate =      "Fri Oct 16 06:57:22 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database; Parallel/par.lin.alg.bib;
                 Theory/Matrix.bib",
  note =         "Pages 1759--1761 discuss implementation of useful
                 primitives for higher-precision arithmetic: DPAdd2(),
                 DPAdd3(), DPDiv().",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
  kwds =         "nla, eig, prll, symmetric matrix",
}


bibtype: phdthesis
filename: fparith.bib
label: Sparmann:1991:SBT
author: U. Sparmann
title: Structure Based Test Methods for Arithmetic Circuits
type: Ph.D. thesis
school: Computer Science Department, University of Saarland
address: Saarbrucken, Germany
pages: 1752--1775
year: 1991
bibdate: Tue Mar 13 10:30:20 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.03.13 10:30:20 ???
note: In German.
keywords: floating-point testing
remark: Cited in cite Mueller:2000:CAC.
acknowledgement: ack-nhfb
rawauthor: U. Sparmann
rawnote: In German.
rawtitle: Structure Based Test Methods for Arithmetic Circuits
entry:
@PhdThesis{Sparmann:1991:SBT,
  author =       "U. Sparmann",
  title =        "Structure Based Test Methods for Arithmetic Circuits",
  type =         "{Ph.D.} thesis",
  school =       "Computer Science Department, University of Saarland",
  address =      "Saarbr{\"u}cken, Germany",
  year =         "1991",
  bibdate =      "Tue Mar 13 10:30:20 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "In German.",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point testing",
  remark =       "Cited in \cite{Mueller:2000:CAC}.",
}


bibtype: article
filename: fparith.bib
label: Squire:1991:ANS
author: Jon S. Squire
title: Ada numerics standardization and testing
journal: j-SIGADA-LETTERS
volume: 11
number: 7
address: New York, NY, USA
pages: 1--286
year: 1991
CODEN: AALEE5
ISSN: 1094-3641 (print), 1557-9476 (electronic) OR 10943641 (print), 15579476 (electronic)
ISSNL: 1094-3641 OR 10943641
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 SIGAda Ada Letters
keywords: Ada (Computer program language); floating-point testing
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/citation.cfm?id=J32
rawauthor: Jon S. Squire
rawtitle: {Ada} numerics standardization and testing
remark:
A special edition from SIGAda ldots presented by SIGAda Numerics Working Group and Ada-Europe Numerics Working Group and ISO- IEC/JTC1/SC22/WG9 Numerics Rapporteur Group.

TOC:
Introduction to the proposed standard for the elementary functions in Ada / Kenneth W. Dritz Proposed standard for a generic package of elementary functions for Ada / edited by Kenneth W. Dritz Rationale for the proposed standard for a generic package of elementary functions for Ada; Proposed standard for a generic package of primitive functions for Ada; Rationale for the proposed standard for a generic package of primitive functions for Ada / Kenneth W. Dritz Proposed standard for packages of real and complex type declarations and basic operations for Ada (including vector and matrix types) / edited by Graham S. Hodgson Rationale for the proposed standard for packages of real and complex type declarations and basic operations for Ada (including vector and matrix types) / Graham S. Hodgson. Proposed standard for a generic package of complex elementary functions / edited by Jon S. Squire Rationale for the proposed standard for a generic package of complex elementary functions / Jon S. Squire A portable generic elementary function package in Ada and an accurate test suite / Ping Tak Peter Tang Towards validation of generic elementary functions and other standard Ada numerics packages / Jon S. Squire Floating point attributes in Ada / Dik T. Winter An Ada math library for real-time avionics / Donald A. Celarier and Donald W. Sando Predefined floating point type names, uniformity rapporteur group UI-48 / edited by Jon S. Squire.

rawTOC:
Introduction to the proposed standard for the elementary functions in Ada / Kenneth W. Dritz\\ Proposed standard for a generic package of elementary functions for Ada / edited by Kenneth W. Dritz\\ Rationale for the proposed standard for a generic package of elementary functions for Ada; Proposed standard for a generic package of primitive functions for Ada; Rationale for the proposed standard for a generic package of primitive functions for Ada / Kenneth W. Dritz\\ Proposed standard for packages of real and complex type declarations and basic operations for Ada (including vector and matrix types) / edited by Graham S. Hodgson\\ Rationale for the proposed standard for packages of real and complex type declarations and basic operations for Ada (including vector and matrix types) / Graham S. Hodgson. Proposed standard for a generic package of complex elementary functions / edited by Jon S. Squire \\ Rationale for the proposed standard for a generic package of complex elementary functions / Jon S. Squire \\ A portable generic elementary function package in Ada and an accurate test suite / Ping Tak Peter Tang \\ Towards validation of generic elementary functions and other standard Ada numerics packages / Jon S. Squire\\ Floating point attributes in Ada / Dik T. Winter\\ An Ada math library for real-time avionics / Donald A. Celarier and Donald W. Sando\\ Predefined floating point type names, uniformity rapporteur group UI-48 / edited by Jon S. Squire.

entry:
@Article{Squire:1991:ANS,
  author =       "Jon S. Squire",
  title =        "{Ada} numerics standardization and testing",
  journal =      j-SIGADA-LETTERS,
  volume =       "11",
  number =       "7",
  address =      "New York, NY, USA",
  pages =        "1--286",
  year =         "1991",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  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 SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "Ada (Computer program language); floating-point
                 testing",
  remark =       "A special edition from SIGAda \ldots{} presented by
                 SIGAda Numerics Working Group and Ada-Europe Numerics
                 Working Group and ISO- IEC/JTC1/SC22/WG9 Numerics
                 Rapporteur Group.",
  tableofcontents = "Introduction to the proposed standard for the
                 elementary functions in Ada / Kenneth W. Dritz\\
                 Proposed standard for a generic package of elementary
                 functions for Ada / edited by Kenneth W. Dritz\\
                 Rationale for the proposed standard for a generic
                 package of elementary functions for Ada; Proposed
                 standard for a generic package of primitive functions
                 for Ada; Rationale for the proposed standard for a
                 generic package of primitive functions for Ada /
                 Kenneth W. Dritz\\
                 Proposed standard for packages of real and complex type
                 declarations and basic operations for Ada (including
                 vector and matrix types) / edited by Graham S.
                 Hodgson\\
                 Rationale for the proposed standard for packages of
                 real and complex type declarations and basic operations
                 for Ada (including vector and matrix types) / Graham S.
                 Hodgson. Proposed standard for a generic package of
                 complex elementary functions / edited by Jon S. Squire
                 \\
                 Rationale for the proposed standard for a generic
                 package of complex elementary functions / Jon S. Squire
                 \\
                 A portable generic elementary function package in Ada
                 and an accurate test suite / Ping Tak Peter Tang \\
                 Towards validation of generic elementary functions and
                 other standard Ada numerics packages / Jon S. Squire\\
                 Floating point attributes in Ada / Dik T. Winter\\
                 An Ada math library for real-time avionics / Donald A.
                 Celarier and Donald W. Sando\\
                 Predefined floating point type names, uniformity
                 rapporteur group UI-48 / edited by Jon S. Squire.",
}


bibtype: inproceedings
filename: fparith.bib
label: Steidley:1991:FPA
author: C. W. Steidley
title: Floating point arithmetic basic exercises in mathematical reasoning for computer science majors
crossref: ASEE:1991:CCW
pages: 191--197 vol.1
year: 1991
bibdate: Tue Dec 12 09:27:13 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.12 09:27:13 MST
keywords: Computer science majors; Computers; Floating point arithmetic; Mathematical reasoning
acknowledgement: ack-nhfb
affiliation: Central Washington University, Ellensburg, WA, USA
thesaurus: Computer science education; Digital arithmetic
rawauthor: C. W. Steidley
rawtitle: Floating point arithmetic basic exercises in mathematical reasoning for computer science majors
abstract:
The author gives examples demonstrating how an unsuspecting user of floating point arithmetic on computers may be misled by results. Specifically, there are cases where the fundamental rules of arithmetic break down. Thus, it is even more imperative that fledgling computer scientists have some insight into the machinations of floating point arithmetic on computers.

rawabstract:
The author gives examples demonstrating how an unsuspecting user of floating point arithmetic on computers may be misled by results. Specifically, there are cases where the fundamental rules of arithmetic break down. Thus, it is even more imperative that fledgling computer scientists have some insight into the machinations of floating point arithmetic on computers.

entry:
@InProceedings{Steidley:1991:FPA,
  author =       "C. W. Steidley",
  title =        "Floating point arithmetic basic exercises in
                 mathematical reasoning for computer science majors",
  crossref =     "ASEE:1991:CCW",
  pages =        "191--197 vol.1",
  year =         "1991",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The author gives examples demonstrating how an
                 unsuspecting user of floating point arithmetic on
                 computers may be misled by results. Specifically, there
                 are cases where the fundamental rules of arithmetic
                 break down. Thus, it is even more imperative that
                 fledgling computer scientists have some insight into
                 the machinations of floating point arithmetic on
                 computers.",
  acknowledgement = ack-nhfb,
  affiliation =  "Central Washington University, Ellensburg, WA, USA",
  classification = "C0220 (Education and training); C5230 (Digital
                 arithmetic methods)",
  keywords =     "Computer science majors; Computers; Floating point
                 arithmetic; Mathematical reasoning",
  thesaurus =    "Computer science education; Digital arithmetic",
}


bibtype: article
filename: fparith.bib
label: Takagi:1991:RCM
author: N. Takagi and T. Asada and S. Yajima
title: Redundant CORDIC Methods with a Constant Scale Factor for Sine and Cosine Computation
journal: j-IEEE-TRANS-COMPUT
volume: C-40
number: 9
pages: 989--995
month: sep
monthnumber: 9
year: 1991
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.83660
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Sep 1 10:15:40 1994
bibtimestamp: 1994.09.01 10:15:40 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: N. Takagi and T. Asada and S. Yajima
rawtitle: Redundant {CORDIC} Methods with a Constant Scale Factor for Sine and Cosine Computation
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib

entry:
@Article{Takagi:1991:RCM,
  author =       "N. Takagi and T. Asada and S. Yajima",
  title =        "Redundant {CORDIC} Methods with a Constant Scale
                 Factor for Sine and Cosine Computation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-40",
  number =       "9",
  pages =        "989--995",
  month =        sep,
  year =         "1991",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.83660",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 1 10:15:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  acknowledgement = ack-nj,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Takagi:1991:RMM
author: Naofumi Takagi
crossref: Kornerup:1991:PIS
pages: 35--42
year: 1991
bibdate: Sat Nov 27 12:40:58 MST 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.27 12:40:58 MST
URL: http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Takagi.pdf
keywords: ARITH-10
acknowledgement: ack-nhfb
rawauthor: Naofumi Takagi
title:
A radix-$4$ modular multiplication hardware algorithm efficient for iterative modular multiplications

rawtitle:
{A} radix-$4$ modular multiplication hardware algorithm efficient for iterative modular multiplications

entry:
@InProceedings{Takagi:1991:RMM,
  author =       "Naofumi Takagi",
  title =        "{A} radix-$4$ modular multiplication hardware
                 algorithm efficient for iterative modular
                 multiplications",
  crossref =     "Kornerup:1991:PIS",
  pages =        "35--42",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Takagi.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}


bibtype: techreport
filename: fparith.bib
label: Tang:1991:TLAa
author: Ping Tak Peter Tang
title: Table-Lookup Algorithms for Elementary Functions and Their Error Analysis
type: Technical Report
number: MCS-P194-1190
institution: Argonne National Laboratory
address: Argonne, IL, USA
year: 1991
bibdate: Thu Jan 30 16:25:10 2020
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2020.01.30 16:25:10 ???
acknowledgement: ack-nhfb
rawauthor: Ping Tak Peter Tang
rawtitle: Table-Lookup Algorithms for Elementary Functions and Their Error Analysis
entry:
@TechReport{Tang:1991:TLAa,
  author =       "Ping Tak Peter Tang",
  title =        "Table-Lookup Algorithms for Elementary Functions and
                 Their Error Analysis",
  type =         "Technical Report",
  number =       "MCS-P194-1190",
  institution =  "Argonne National Laboratory",
  address =      "Argonne, IL, USA",
  pages =        "????",
  year =         "1991",
  bibdate =      "Thu Jan 30 16:25:10 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Tang:1991:TLAb
author: Ping Tak Peter Tang
title: Table-Lookup Algorithms for Elementary Functions and Their Error Analysis
crossref: Kornerup:1991:PIS
pages: 232--236
year: 1991
bibdate: Sat Nov 27 12:40:58 MST 2004
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.27 12:40:58 MST
URL: http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Tang.pdf
keywords: ARITH-10
acknowledgement: ack-nj
rawauthor: Ping Tak Peter Tang
rawtitle: Table-Lookup Algorithms for Elementary Functions and Their Error Analysis
entry:
@InProceedings{Tang:1991:TLAb,
  author =       "Ping Tak Peter Tang",
  title =        "Table-Lookup Algorithms for Elementary Functions and
                 Their Error Analysis",
  crossref =     "Kornerup:1991:PIS",
  pages =        "232--236",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  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/arith10/papers/ARITH10_Tang.pdf",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  keywords =     "ARITH-10",
}


bibtype: inproceedings
filename: fparith.bib
label: Taylor:1991:TFA
author: V. E. Taylor and A. Ranade and D. G. Messerschmitt
title: Three-dimensional finite-element analyses: implications for computer architectures
crossref: IEEE:1991:PSA
pages: 786--795
year: 1991
bibdate: Wed Apr 15 16:28:01 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.04.15 16:28:01 MDT
acknowledgement: ack-nhfb
corpsource: Department of Electr. Eng. and Computer Science, California University, Berkeley, CA, USA
treatment: P Practical; T Theoretical or Mathematical
rawauthor: V. E. Taylor and A. Ranade and D. G. Messerschmitt
rawtitle: Three-dimensional finite-element analyses: implications for computer architectures
keywords:
columns; computer architectures; data path design; data structure; data structures; finite element analysis; floating-point units; matrix algebra; memory bandwidth; parallel architectures; parallel programming; programming theory; rows; sparse matrices; sparsity pattern

entry:
@InProceedings{Taylor:1991:TFA,
  author =       "V. E. Taylor and A. Ranade and D. G. Messerschmitt",
  title =        "Three-dimensional finite-element analyses:
                 implications for computer architectures",
  crossref =     "IEEE:1991:PSA",
  pages =        "786--795",
  year =         "1991",
  bibdate =      "Wed Apr 15 16:28:01 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C4140 (Linear algebra); C4185 (Finite element
                 analysis); C4240P (Parallel programming and algorithm
                 theory); C5220P (Parallel architecture); C6110P
                 (Parallel programming); C6120 (File organisation)",
  corpsource =   "Department of Electr. Eng. and Computer Science,
                 California University, Berkeley, CA, USA",
  keywords =     "columns; computer architectures; data path design;
                 data structure; data structures; finite element
                 analysis; floating-point units; matrix algebra; memory
                 bandwidth; parallel architectures; parallel
                 programming; programming theory; rows; sparse matrices;
                 sparsity pattern",
  sponsororg =   "IEEE; ACM",
  treatment =    "P Practical; T Theoretical or Mathematical",
}


bibtype: article
filename: fparith.bib
label: teRiele:1991:NLB
author: H. J. J. te Riele
title: A new lower bound for the de Bruijn-Newman constant
journal: j-NUM-MATH
volume: 58
number: 6
pages: 661--667
year: 1991
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
MRclass: 30D10 (11M26 30D15 65E05)
MRnumber: 92c:30030
MRreviewer: George L. Csordas
bibdate: Mon May 26 11:49:34 MDT 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.05.26 11:49:34 MDT
fjournal: Numerische Mathematik
acknowledgement: ack-nhfb
corpsource: Centre for Math. and Computer Science, Amsterdam, Netherlands
journalURL: http://link.springer.com/journal/211
treatment: T Theoretical or Mathematical
rawauthor: H. J. J. {te Riele}
rawtitle: A new lower bound for the {de Bruijn-Newman} constant
keywords:
complex zeros; de Bruijn-Newman constant; high-precision floating-point computations; integral equations; Jensen polynomial; lover bound; polynomials; Riemann hypothesis; Sturm sequence

entry:
@Article{teRiele:1991:NLB,
  author =       "H. J. J. {te Riele}",
  title =        "A new lower bound for the {de Bruijn-Newman}
                 constant",
  journal =      j-NUM-MATH,
  volume =       "58",
  number =       "6",
  pages =        "661--667",
  year =         "1991",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "30D10 (11M26 30D15 65E05)",
  MRnumber =     "92c:30030",
  MRreviewer =   "George L. Csordas",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "B0290F (Interpolation and function approximation);
                 B0290R (Integral equations); C4130 (Interpolation and
                 function approximation); C4180 (Integral equations)",
  corpsource =   "Centre for Math. and Computer Science, Amsterdam,
                 Netherlands",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "complex zeros; de Bruijn-Newman constant;
                 high-precision floating-point computations; integral
                 equations; Jensen polynomial; lover bound; polynomials;
                 Riemann hypothesis; Sturm sequence",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: manual
filename: fparith.bib
label: TI:1991:TDH
title: TMS34082 designer's handbook
organization: Texas Instruments Incorporated
address: Dallas, TX, USA
edition: Revised
pages: various
year: 1991
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
remark: ``Datapath VLSI products''--Cover. ``2564007-9721 revision A, May 1991''--T.p.
acknowledgement: ack-nhfb
rawtitle: {TMS34082} designer's handbook
keywords:
Computer graphics --- Equipment and supplies.; Floating-point arithmetic --- Computer simulation.; Integrated circuits --- Very large scale integration --- Handbooks,; manuals, etc.

entry:
@Manual{TI:1991:TDH,
  title =        "{TMS34082} designer's handbook",
  organization = "{Texas Instruments Incorporated}",
  address =      "Dallas, TX, USA",
  edition =      "Revised",
  pages =        "various",
  year =         "1991",
  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 graphics --- Equipment and supplies.;
                 Floating-point arithmetic --- Computer simulation.;
                 Integrated circuits --- Very large scale integration
                 --- Handbooks,; manuals, etc.",
  remark =       "``Datapath VLSI products''--Cover. ``2564007-9721
                 revision A, May 1991''--T.p.",
}


bibtype: manual
filename: fparith.bib
label: TI:1991:TFDa
title: TMS320 floating-point DSP optimizing C compiler user's guide
organization: Texas Instruments Incorporated
address: Dallas, TX, USA
edition: Revised
pages: various
year: 1991
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
remark: ``Microprocessor development systems''--Cover. ``2576391-9721 revision A, October 1991''--T.p.
acknowledgement: ack-nhfb
rawtitle: {TMS320} floating-point {DSP} optimizing {C} compiler user's guide
keywords:
Compilers (Computer programs).; manuals, etc.; Signal processing --- Digital techniques --- Equipment and; supplies.; Texas Instruments TMS320 series microprocessors --- Handbooks

entry:
@Manual{TI:1991:TFDa,
  title =        "{TMS320} floating-point {DSP} optimizing {C} compiler
                 user's guide",
  organization = "{Texas Instruments Incorporated}",
  address =      "Dallas, TX, USA",
  edition =      "Revised",
  pages =        "various",
  year =         "1991",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Compilers (Computer programs).; manuals, etc.; Signal
                 processing --- Digital techniques --- Equipment and;
                 supplies.; Texas Instruments TMS320 series
                 microprocessors --- Handbooks",
  remark =       "``Microprocessor development systems''--Cover.
                 ``2576391-9721 revision A, October 1991''--T.p.",
}


bibtype: manual
filename: fparith.bib
label: TI:1991:TFDb
title: TMS320 floating-point DSP assembly language tools user's guide
organization: Texas Instruments Incorporated
address: Dallas, TX, USA
edition: Revised
pages: various
year: 1991
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
remark: ``Microprocessor development systems''--Cover. ``2576328-9721 revision A, September 1991''--T.p.
acknowledgement: ack-nhfb
rawtitle: {TMS320} floating-point {DSP} assembly language tools user's guide
keywords:
Assembler language (Computer program language).; Handbooks, manuals, etc.; Signal processing --- Digital techniques --- Equipment and; supplies.; Texas Instruments TMS320 series microprocessors --- Programming --

entry:
@Manual{TI:1991:TFDb,
  title =        "{TMS320} floating-point {DSP} assembly language tools
                 user's guide",
  organization = "{Texas Instruments Incorporated}",
  address =      "Dallas, TX, USA",
  edition =      "Revised",
  pages =        "various",
  year =         "1991",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Assembler language (Computer program language).;
                 Handbooks, manuals, etc.; Signal processing --- Digital
                 techniques --- Equipment and; supplies.; Texas
                 Instruments TMS320 series microprocessors ---
                 Programming --",
  remark =       "``Microprocessor development systems''--Cover.
                 ``2576328-9721 revision A, September 1991''--T.p.",
}


bibtype: manual
filename: fparith.bib
label: TI:1991:TST
title: TMS34082 software tool kit user's guide
organization: Texas Instruments Incorporated
address: Dallas
edition: 2547321-9721 revision.
pages: various
year: 1991
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 storage devices.; TMS34082 Floating-Point Processor.
remark: ``Datapath VLSI products''--Cover. ``SSCA001''--P. [4] of cover.
acknowledgement: ack-nhfb
rawtitle: {TMS34082} software tool kit user's guide
entry:
@Manual{TI:1991:TST,
  title =        "{TMS34082} software tool kit user's guide",
  organization = "Texas Instruments Incorporated",
  address =      "Dallas",
  edition =      "2547321-9721 revision.",
  pages =        "various",
  year =         "1991",
  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 storage devices.; TMS34082 Floating-Point
                 Processor.",
  remark =       "``Datapath VLSI products''--Cover. ``SSCA001''--P. [4]
                 of cover.",
}


bibtype: inproceedings
filename: fparith.bib
label: Tomabechi:1991:DMD
author: N. Tomabechi
booktitle: IEEE International Symposium on Circuits and Systems, 11--14 June 1991
title: Design method of defect-tolerant WSI systems based on the residue number system
volume: 5
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 3082--3085
year: 1991
DOI: https://doi.org/10.1109/ISCAS.1991.176199
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: N. Tomabechi
rawbooktitle: {IEEE} International Symposium on Circuits and Systems, 11--14 June 1991
rawtitle: Design method of defect-tolerant {WSI} systems based on the residue number system
entry:
@InProceedings{Tomabechi:1991:DMD,
  author =       "N. Tomabechi",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems, 11--14 June 1991",
  title =        "Design method of defect-tolerant {WSI} systems based
                 on the residue number system",
  volume =       "5",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "3082--3085",
  year =         "1991",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.1991.176199",
  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 design method is proposed for defect-tolerant WSI
                 arithmetic systems based on the RNS (residue number
                 system). The yield analysis has shown that the features
                 of the RNS are very well suited for the defect recovery
                 of WSIs. In the RNS, addition and \ldots{}",
}


bibtype: techreport
filename: fparith.bib
label: Tsang:1991:SDC
author: Annie Tsang and Manfred Olschanowsky
title: A Study of DataBase 2 Customer Queries
type: Technical Report
number: TR 03.413
institution: IBM Santa Teresa Laboratory
address: San Jose, CA, USA
pages: 3082--3085
month: apr
monthnumber: 4
year: 1991
bibdate: Mon Mar 06 08:07:19 2006
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2006.03.06 08:07:19 ???
keywords: decimal floating-point arithmetic
acknowledgement: ack-nhfb
rawauthor: Annie Tsang and Manfred Olschanowsky
rawtitle: A Study of {DataBase 2} Customer Queries
remark:
This report surveys the numeric data types used in commercial databases by 51 major organizations, and finds that 98.6% of the numeric data are decimal.

entry:
@TechReport{Tsang:1991:SDC,
  author =       "Annie Tsang and Manfred Olschanowsky",
  title =        "A Study of {DataBase 2} Customer Queries",
  type =         "Technical Report",
  number =       "TR 03.413",
  institution =  "IBM Santa Teresa Laboratory",
  address =      "San Jose, CA, USA",
  month =        apr,
  year =         "1991",
  bibdate =      "Mon Mar 06 08:07:19 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
  remark =       "This report surveys the numeric data types used in
                 commercial databases by 51 major organizations, and
                 finds that 98.6\% of the numeric data are decimal.",
}


bibtype: article
filename: fparith.bib
label: Tsubokawa:1991:FEA
author: Hiroshi Tsubokawa and Hajime Kubota and Shigeo Tsujii
title: Floating-Point Error Analysis for Recursive Least-Square Algorithm Using UD Factorization
journal: j-ELECT-COMM-JAPAN-3-FUND-ELECT-SCI
volume: 74
number: 6
pages: 1--10
year: 1991
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: Hiroshi Tsubokawa and Hajime Kubota and Shigeo Tsujii
rawtitle: Floating-Point Error Analysis for Recursive Least-Square Algorithm Using {UD} Factorization
entry:
@Article{Tsubokawa:1991:FEA,
  author =       "Hiroshi Tsubokawa and Hajime Kubota and Shigeo
                 Tsujii",
  title =        "Floating-Point Error Analysis for Recursive
                 Least-Square Algorithm Using {UD} Factorization",
  journal =      j-ELECT-COMM-JAPAN-3-FUND-ELECT-SCI,
  volume =       "74",
  number =       "6",
  pages =        "1--10",
  year =         "1991",
  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: inproceedings
filename: fparith.bib
label: Tu:1991:ALA
author: Paul K.-G. Tu and Milos D. Ercegovac
title: Application of on-line arithmetic algorithms to the SVD computation: preliminary results
crossref: Kornerup:1991:PIS
pages: 246--255
year: 1991
bibdate: Sat Nov 27 12:40:58 MST 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.27 12:40:58 MST
URL: http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Tu.pdf
acknowledgement: ack-nhfb
affiliation: IBM Corp., Austin, TX, USA
thesaurus: Digital arithmetic
rawauthor: Paul K.-G. Tu and Milo{\v{s}} D. Ercegovac
rawtitle: Application of on-line arithmetic algorithms to the {SVD} computation: preliminary results
abstract:
A scheme for the singular value decomposition (SVD) problem, based on online arithmetic, is discussed. The design, using radix-2 floating-point online operations, implemented in the LSI HCMOS gate-array technology, is compared with a compatible conventional arithmetic implementation. The preliminary results indicate that the proposed online approach achieves a speedup of 2.4-3.2 with respect to the conventional solutions, with 1.3-5.5 more gates and more than 6 times fewer interconnections.

keywords:
ARITH-10; Floating-point online operations; Online; Online arithmetic; Radix-2; Singular value decomposition

rawabstract:
A scheme for the singular value decomposition (SVD) problem, based on online arithmetic, is discussed. The design, using radix-2 floating-point online operations, implemented in the LSI HCMOS gate-array technology, is compared with a compatible conventional arithmetic implementation. The preliminary results indicate that the proposed online approach achieves a speedup of 2.4-3.2 with respect to the conventional solutions, with 1.3-5.5 more gates and more than 6 times fewer interconnections.

entry:
@InProceedings{Tu:1991:ALA,
  author =       "Paul K.-G. Tu and Milo{\v{s}} D. Ercegovac",
  title =        "Application of on-line arithmetic algorithms to the
                 {SVD} computation: preliminary results",
  crossref =     "Kornerup:1991:PIS",
  pages =        "246--255",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Tu.pdf",
  abstract =     "A scheme for the singular value decomposition (SVD)
                 problem, based on online arithmetic, is discussed. The
                 design, using radix-2 floating-point online operations,
                 implemented in the LSI HCMOS gate-array technology, is
                 compared with a compatible conventional arithmetic
                 implementation. The preliminary results indicate that
                 the proposed online approach achieves a speedup of
                 2.4-3.2 with respect to the conventional solutions,
                 with 1.3-5.5 more gates and more than 6 times fewer
                 interconnections.",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM Corp., Austin, TX, USA",
  classification = "C5230 (Digital arithmetic methods)",
  keywords =     "ARITH-10; Floating-point online operations; Online;
                 Online arithmetic; Radix-2; Singular value
                 decomposition",
  thesaurus =    "Digital arithmetic",
}


bibtype: article
filename: fparith.bib
label: Tu:1991:GAI
author: Paul K.-G. Tu and Milos D. Ercegovac
title: Gate Array Implementation of On-Line Algorithms for Floating-Point Operations
journal: j-J-VLSI-SIGNAL-PROC
volume: 3
number: 4
pages: 307--318
month: oct
monthnumber: 10
year: 1991
CODEN: JVSPED
DOI: https://doi.org/10.1007/BF00936903
ISSN: 0922-5773 (print), 1573-109x (electronic) OR 09225773 (print), 1573109x (electronic)
ISSNL: 0922-5773 OR 09225773
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: Journal of VLSI Signal Processing
acknowledgement: ack-nhfb
rawauthor: Paul K.-G. Tu and Milo{\v{s}} D. Ercegovac
rawtitle: Gate Array Implementation of On-Line Algorithms for Floating-Point Operations
abstract:
We present gate array designs of on-line arithmetic units for radix-2 floating-point addition, multiplication and division operations. Performance and complexity characteristics of the implementations of on-line arithmetic units are discussed and compared with those of the compatible conventional floating-point algorithms implemented in the same technology.

rawabstract:
We present gate array designs of on-line arithmetic units for radix-2 floating-point addition, multiplication and division operations. Performance and complexity characteristics of the implementations of on-line arithmetic units are discussed and compared with those of the compatible conventional floating-point algorithms implemented in the same technology.

entry:
@Article{Tu:1991:GAI,
  author =       "Paul K.-G. Tu and Milo{\v{s}} D. Ercegovac",
  title =        "Gate Array Implementation of On-Line Algorithms for
                 Floating-Point Operations",
  journal =      j-J-VLSI-SIGNAL-PROC,
  volume =       "3",
  number =       "4",
  pages =        "307--318",
  month =        oct,
  year =         "1991",
  CODEN =        "JVSPED",
  DOI =          "https://doi.org/10.1007/BF00936903",
  ISSN =         "0922-5773 (print), 1573-109x (electronic)",
  ISSN-L =       "0922-5773",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We present gate array designs of on-line arithmetic
                 units for radix-2 floating-point addition,
                 multiplication and division operations. Performance and
                 complexity characteristics of the implementations of
                 on-line arithmetic units are discussed and compared
                 with those of the compatible conventional
                 floating-point algorithms implemented in the same
                 technology.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of VLSI Signal Processing",
}


bibtype: inproceedings
filename: fparith.bib
label: Turner:1991:IAE
author: Peter R. Turner
title: Implementation and analysis of extended SLI operations
crossref: Kornerup:1991:PIS
pages: 118--126
year: 1991
bibdate: Sat Nov 27 12:40:58 MST 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.27 12:40:58 MST
URL: http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Turner.pdf
keywords: ARITH-10
acknowledgement: ack-nhfb
rawauthor: Peter R. Turner
rawtitle: Implementation and analysis of extended {SLI} operations
entry:
@InProceedings{Turner:1991:IAE,
  author =       "Peter R. Turner",
  title =        "Implementation and analysis of extended {SLI}
                 operations",
  crossref =     "Kornerup:1991:PIS",
  pages =        "118--126",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Turner.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}


bibtype: article
filename: fparith.bib
label: Umemura:1991:FNL
author: K. Umemura
title: Floating-point number LISP
journal: j-SPE
volume: 21
number: 10
pages: 1015--1026
month: oct
monthnumber: 10
year: 1991
CODEN: SPEXBL
ISSN: 0038-0644 (print), 1097-024X (electronic) OR 00380644 (print), 1097024X (electronic)
ISSNL: 0038-0644 OR 00380644
bibdate: Tue Dec 12 09:26:54 MST 1995
bibtimestamp: 1995.12.12 09:26:54 MST
fjournal: Software---Practice and Experience
acknowledgement: ack-nhfb
affiliation: Software Labs., NTT Corp., Tokyo, Japan
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X
thesaurus: Digital arithmetic; LISP; Mathematics computing; Symbol manipulation
rawauthor: K. Umemura
rawtitle: Floating-point number {LISP}
bibsource:
https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
A floating-point-number-oriented LISP has been developed. Though it performs type checking on every numeric operation, it runs as fast as Fortran for simple differential-equation problems. The author describes the implementation, provides some measurements of its efficiency and discusses the feasibility of this type of implementation.

keywords:
Floating-point-number-oriented LISP; Numeric operation; Simple differential-equation problems; Type checking

rawabstract:
A floating-point-number-oriented LISP has been developed. Though it performs type checking on every numeric operation, it runs as fast as Fortran for simple differential-equation problems. The author describes the implementation, provides some measurements of its efficiency and discusses the feasibility of this type of implementation.

entry:
@Article{Umemura:1991:FNL,
  author =       "K. Umemura",
  title =        "Floating-point number {LISP}",
  journal =      j-SPE,
  volume =       "21",
  number =       "10",
  pages =        "1015--1026",
  month =        oct,
  year =         "1991",
  CODEN =        "SPEXBL",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  bibdate =      "Tue Dec 12 09:26:54 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A floating-point-number-oriented LISP has been
                 developed. Though it performs type checking on every
                 numeric operation, it runs as fast as Fortran for
                 simple differential-equation problems. The author
                 describes the implementation, provides some
                 measurements of its efficiency and discusses the
                 feasibility of this type of implementation.",
  acknowledgement = ack-nhfb,
  affiliation =  "Software Labs., NTT Corp., Tokyo, Japan",
  classification = "C5230 (Digital arithmetic methods); C6130 (Data
                 handling techniques); C6140D (High level languages);
                 C7310 (Mathematics)",
  fjournal =     "Software---Practice and Experience",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
  keywords =     "Floating-point-number-oriented LISP; Numeric
                 operation; Simple differential-equation problems; Type
                 checking",
  pubcountry =   "UK",
  thesaurus =    "Digital arithmetic; LISP; Mathematics computing;
                 Symbol manipulation",
}


bibtype: article
filename: fparith.bib
label: Umemura:1991:FPN
author: Kyoji Umemura
title: Floating-point Number LISP
journal: j-SPE
volume: 21
number: 10
pages: 1015--1026
month: oct
monthnumber: 10
year: 1991
CODEN: SPEXBL
ISSN: 0038-0644 (print), 1097-024X (electronic) OR 00380644 (print), 1097024X (electronic)
ISSNL: 0038-0644 OR 00380644
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: Software---Practice and Experience
acknowledgement: ack-nhfb
affiliation: Software Labs., NTT Corp., Tokyo, Japan
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X
thesaurus: Digital arithmetic; LISP; Mathematics computing; Symbol manipulation
rawauthor: Kyoji Umemura
rawtitle: Floating-point Number {LISP}
abstract:
A floating-point-number-oriented LISP has been developed. Though it performs type checking on every numeric operation, it runs as fast as Fortran for simple differential-equation problems. The author describes the implementation, provides some measurements of its efficiency and discusses the feasibility of this type of implementation.

keywords:
Floating-point-number-oriented LISP; Numeric operation; Simple differential-equation problems; Type checking

entry:
@Article{Umemura:1991:FPN,
  author =       "Kyoji Umemura",
  title =        "Floating-point Number {LISP}",
  journal =      j-SPE,
  volume =       "21",
  number =       "10",
  pages =        "1015--1026",
  month =        oct,
  year =         "1991",
  CODEN =        "SPEXBL",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A floating-point-number-oriented LISP has been
                 developed. Though it performs type checking on every
                 numeric operation, it runs as fast as Fortran for
                 simple differential-equation problems. The author
                 describes the implementation, provides some
                 measurements of its efficiency and discusses the
                 feasibility of this type of implementation.",
  acknowledgement = ack-nhfb,
  affiliation =  "Software Labs., NTT Corp., Tokyo, Japan",
  classification = "C5230 (Digital arithmetic methods); C6130 (Data
                 handling techniques); C6140D (High level languages);
                 C7310 (Mathematics)",
  fjournal =     "Software---Practice and Experience",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
  keywords =     "Floating-point-number-oriented LISP; Numeric
                 operation; Simple differential-equation problems; Type
                 checking",
  pubcountry =   "UK",
  thesaurus =    "Digital arithmetic; LISP; Mathematics computing;
                 Symbol manipulation",
}


