# bibtab

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
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:16:09 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: D. K. Kostopoulos
rawtitle: An Algorithm for the Computation of Binary Logarithms
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",
  acknowledgement = ack-nj,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: techreport
filename: fparith.bib
label: 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: http://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: http://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",
  CODEN =        "ITCOB4",
  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 =          "http://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)",
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Complex arithmetic; Division; Floating-point number
                 system; Geometric; Hybrid number system processor;
                 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: http://portal.acm.org/browse_dl.cfm?idx=J89
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:
@Article{Lee:1991:FPPa,
  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-COMP-ARCH-NEWS,
  volume =       "19",
  number =       "2",
  pages =        "28--37",
  month =        apr,
  year =         "1991",
  CODEN =        "CANED2",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Fri May 12 09:40:40 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Co-published in {\em Operating Systems Review}, {\bf
                 28}(3S).",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J89",
}


bibtype: article
filename: fparith.bib
label: 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,
  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-OPER-SYS-REV,
  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/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/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: http://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 =          "http://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: http://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 =  "http://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: http://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 =  "http://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: 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: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=73596
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://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 =          "http://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 =  "http://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: http://portal.acm.org/browse_dl.cfm?idx=J89
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 =  "http://portal.acm.org/browse_dl.cfm?idx=J89",
}


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: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=2656
fjournal: IEEE Transactions on Signal Processing
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78
rawauthor: 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 =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=2656",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  keywords =     "residue arithmetic; residue number system",
  summary =      "The 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
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: IEEE Transactions on Computers
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: http://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
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/fparith.bib",
  acknowledgement = ack-nj,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: 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/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/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",
}


bibtype: article
filename: fparith.bib
label: Vassiliadis:1991:HWM
author: S. Vassiliadis and E. M. Schwarz and B. M. Sung
title: Hard-wired multipliers with encoded partial products
journal: j-IEEE-TRANS-COMPUT
volume: 40
number: 11
pages: 1181--1197
month: nov
monthnumber: 11
year: 1991
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.102823
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 12:52:24 MDT 2011
bibtimestamp: 2011.07.07 12:52:24 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=102823
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: S. Vassiliadis and E. M. Schwarz and B. M. Sung
rawtitle: Hard-wired multipliers with encoded partial products
entry:
@Article{Vassiliadis:1991:HWM,
  author =       "S. Vassiliadis and E. M. Schwarz and B. M. Sung",
  title =        "Hard-wired multipliers with encoded partial products",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "40",
  number =       "11",
  pages =        "1181--1197",
  month =        nov,
  year =         "1991",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.102823",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 12:52:24 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=102823",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: mastersthesis
filename: fparith.bib
label: Vishin:1991:FPP
author: Sanjay Vishin
title: A floating point primitive classifier for the ray casting machine
type: Typescript. Thesis (M.S.)
school: Duke University. Department of Computer Science
address: Durham, NC 27708, USA
pages: ix + 79
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: Sanjay Vishin
rawtitle: A floating point primitive classifier for the ray casting machine
keywords:
Computer graphics.; Floating-point arithmetic.; Geometry, Analytic --- Solid --- Data processing.; Image processing.

entry:
@MastersThesis{Vishin:1991:FPP,
  author =       "Sanjay Vishin",
  title =        "A floating point primitive classifier for the ray
                 casting machine",
  type =         "Typescript. Thesis ({M.S.})",
  school =       "Duke University. Department of Computer Science",
  address =      "Durham, NC 27708, USA",
  pages =        "ix + 79",
  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.; Floating-point arithmetic.;
                 Geometry, Analytic --- Solid --- Data processing.;
                 Image processing.",
}


bibtype: inproceedings
filename: fparith.bib
label: Vuillemin:1991:CTA
author: J. E. Vuillemin
title: Constant time arbitrary length synchronous binary counters
crossref: Kornerup:1991:PIS
pages: 180--183
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_Vuillemin.pdf
keywords: ARITH-10
acknowledgement: ack-nhfb
rawauthor: J. E. Vuillemin
rawtitle: Constant time arbitrary length synchronous binary counters
entry:
@InProceedings{Vuillemin:1991:CTA,
  author =       "J. E. Vuillemin",
  title =        "Constant time arbitrary length synchronous binary
                 counters",
  crossref =     "Kornerup:1991:PIS",
  pages =        "180--183",
  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_Vuillemin.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}


bibtype: article
filename: fparith.bib
label: Walter:1991:FMM
author: Colin D. Walter
title: Faster Modular Multiplication by Operand Scaling
journal: j-LECT-NOTES-COMP-SCI
volume: 576
pages: 313--??
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 11:48:11 MST 2002
bibtimestamp: 2002.02.05 11:48:11 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Colin D. Walter
rawtitle: Faster Modular Multiplication by Operand Scaling
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t0576.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/0576/05760313.htm; http://link.springer-ny.com/link/service/series/0558/papers/0576/05760313.pdf

entry:
@Article{Walter:1991:FMM,
  author =       "Colin D. Walter",
  title =        "Faster Modular Multiplication by Operand Scaling",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "576",
  pages =        "313--??",
  year =         "1991",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Feb 5 11:48:11 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t0576.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/0576/05760313.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/0576/05760313.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Wigley:1991:FMR
author: N. W. Wigley and G. A. Jullien
title: Flexible modulus residue number system for complex digital signal processing
journal: j-ELECT-LETTERS
volume: 27
number: 16
pages: 1436--1438
month: aug
monthnumber: 8
year: 1991
CODEN: ELLEAK
ISSN: 0013-5194 (print), 1350-911X (electronic) OR 00135194 (print), 1350911X (electronic)
ISSNL: 0013-5194 OR 00135194
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
URL: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=2666
fjournal: Electronics Letters
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220
rawauthor: N. W. Wigley and G. A. Jullien
rawtitle: Flexible modulus residue number system for complex digital signal processing
entry:
@Article{Wigley:1991:FMR,
  author =       "N. W. Wigley and G. A. Jullien",
  title =        "Flexible modulus residue number system for complex
                 digital signal processing",
  journal =      j-ELECT-LETTERS,
  volume =       "27",
  number =       "16",
  pages =        "1436--1438",
  month =        aug,
  year =         "1991",
  CODEN =        "ELLEAK",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=2666",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  keywords =     "residue arithmetic; residue number system",
  summary =      "The quadratic residue number system (QRNS) is often
                 used for integer calculation on complex data streams. A
                 finite polynomial ring mapping technique is presented
                 that removes the $4k + 1$ prime divisor restriction of
                 the QRNS, albeit with an \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Wigley:1991:SMR
author: N. Wigley and G. A. Jullien and D. Reaume and W. C. Miller
title: Small moduli replications in the MRRNS
crossref: Kornerup:1991:PIS
pages: 92--99
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_Wigley.pdf
keywords: ARITH-10
acknowledgement: ack-nhfb
rawauthor: N. Wigley and G. A. Jullien and D. Reaume and W. C. Miller
rawtitle: Small moduli replications in the {MRRNS}
entry:
@InProceedings{Wigley:1991:SMR,
  author =       "N. Wigley and G. A. Jullien and D. Reaume and W. C.
                 Miller",
  title =        "Small moduli replications in the {MRRNS}",
  crossref =     "Kornerup:1991:PIS",
  pages =        "92--99",
  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_Wigley.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}


bibtype: inproceedings
filename: fparith.bib
label: Williams:1991:NBC
author: Ted E. Williams and Mark A. Horowitz
crossref: Kornerup:1991:PIS
pages: 210--217
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_Williams.pdf
keywords: ARITH-10
acknowledgement: ack-nhfb
rawauthor: Ted E. Williams and Mark A. Horowitz
title:
A 160 ns 54 bit CMOS division implementation using self-timing and symmetrically overlapped SRT stages

rawtitle:
{A} 160 ns 54 bit {CMOS} division implementation using self-timing and symmetrically overlapped {SRT} stages

entry:
@InProceedings{Williams:1991:NBC,
  author =       "Ted E. Williams and Mark A. Horowitz",
  title =        "{A} 160 ns 54 bit {CMOS} division implementation using
                 self-timing and symmetrically overlapped {SRT} stages",
  crossref =     "Kornerup:1991:PIS",
  pages =        "210--217",
  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_Williams.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}


bibtype: article
filename: fparith.bib
label: Williams:1991:ZOS
author: Ted E. Williams and Mark A. Horowitz
title: A zero-overhead self-timed 160-ns 54-b CMOS divider
journal: j-IEEE-J-SOLID-STATE-CIRCUITS
volume: 26
number: 11
pages: 1651--1661
month: nov
monthnumber: 11
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: Ted E. Williams and Mark A. Horowitz
rawtitle: A zero-overhead self-timed 160-ns 54-b {CMOS} divider
entry:
@Article{Williams:1991:ZOS,
  author =       "Ted E. Williams and Mark A. Horowitz",
  title =        "A zero-overhead self-timed 160-ns 54-b {CMOS}
                 divider",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "26",
  number =       "11",
  pages =        "1651--1661",
  month =        nov,
  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: article
filename: fparith.bib
label: Winter:1991:FPA
author: Dik T. Winter
title: Floating point attributes in Ada
journal: j-SIGADA-LETTERS
volume: 11
number: 7
pages: 244--273
month: Fall
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 09:05:43 MDT 2003
bibtimestamp: 2003.08.09 09:05:43 MDT
fjournal: ACM SIGAda Ada Letters
acknowledgement: ack-nhfb
affiliation: Centrum voor Wiskunde en Inf., Amsterdam, Netherlands
corpsource: Centrum voor Wiskunde en Inf., Amsterdam, Netherlands
journalURL: http://portal.acm.org/citation.cfm?id=J32
thesaurus: Ada; Digital arithmetic; Program verification; Software portability
treatment: P Practical
rawauthor: Dik T. Winter
rawtitle: Floating point attributes in {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

abstract:
The Ada programming language offers a number of facilities to simplify the writing of portable programs. One of these is the concept of attributes. Many types and objects carry with them a set of attributes that a program may interrogate to get information about the actual implementation. The author is concerned with the set of attributes belonging to floating point types. One should hope that the floating point attributes give correct results. In fact, they are compile time constants. A little experimentation shows that that is not true. Many systems deliver incorrect attributes in a number of cases. Also, due to the inappropriate definition of some of the attributes, many attributes deliver results that are misleading. The author considers the floating point attributes the language gives and shows that indeed some definitions are inappropriate. A program that verifies the validity of the results given by a system is also presented. (3 Refs.)

keywords:
Ada; Ada programming language; compile; Compile time constants; digital arithmetic; Floating point attributes; floating point attributes; Floating point types; floating point types; Objects; objects; portability; Portable programs; portable programs; program verification; software; time constants; Types; types; Validity; validity

classcodes:
C6140D (High level languages); C6110B (Software engineering techniques); C6150G (Diagnostic, testing, debugging and evaluating systems); C5230 (Digital arithmetic methods)

rawabstract:
The Ada programming language offers a number of facilities to simplify the writing of portable programs. One of these is the concept of attributes. Many types and objects carry with them a set of attributes that a program may interrogate to get information about the actual implementation. The author is concerned with the set of attributes belonging to floating point types. One should hope that the floating point attributes give correct results. In fact, they are compile time constants. A little experimentation shows that that is not true. Many systems deliver incorrect attributes in a number of cases. Also, due to the inappropriate definition of some of the attributes, many attributes deliver results that are misleading. The author considers the floating point attributes the language gives and shows that indeed some definitions are inappropriate. A program that verifies the validity of the results given by a system is also presented. (3 Refs.)

entry:
@Article{Winter:1991:FPA,
  author =       "Dik T. Winter",
  title =        "Floating point attributes in {Ada}",
  journal =      j-SIGADA-LETTERS,
  volume =       "11",
  number =       "7",
  pages =        "244--273",
  month =        "Fall",
  year =         "1991",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Sat Aug 9 09:05:43 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",
  abstract =     "The Ada programming language offers a number of
                 facilities to simplify the writing of portable
                 programs. One of these is the concept of attributes.
                 Many types and objects carry with them a set of
                 attributes that a program may interrogate to get
                 information about the actual implementation. The author
                 is concerned with the set of attributes belonging to
                 floating point types. One should hope that the floating
                 point attributes give correct results. In fact, they
                 are compile time constants. A little experimentation
                 shows that that is not true. Many systems deliver
                 incorrect attributes in a number of cases. Also, due to
                 the inappropriate definition of some of the attributes,
                 many attributes deliver results that are misleading.
                 The author considers the floating point attributes the
                 language gives and shows that indeed some definitions
                 are inappropriate. A program that verifies the validity
                 of the results given by a system is also presented. (3
                 Refs.)",
  acknowledgement = ack-nhfb,
  affiliation =  "Centrum voor Wiskunde en Inf., Amsterdam,
                 Netherlands",
  classcodes =   "C6140D (High level languages); C6110B (Software
                 engineering techniques); C6150G (Diagnostic, testing,
                 debugging and evaluating systems); C5230 (Digital
                 arithmetic methods)",
  classification = "C5230 (Digital arithmetic methods); C6110B (Software
                 engineering techniques); C6140D (High level languages);
                 C6150G (Diagnostic, testing, debugging and evaluating
                 systems)",
  corpsource =   "Centrum voor Wiskunde en Inf., Amsterdam,
                 Netherlands",
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "Ada; Ada programming language; compile; Compile time
                 constants; digital arithmetic; Floating point
                 attributes; floating point attributes; Floating point
                 types; floating point types; Objects; objects;
                 portability; Portable programs; portable programs;
                 program verification; software; time constants; Types;
                 types; Validity; validity",
  thesaurus =    "Ada; Digital arithmetic; Program verification;
                 Software portability",
  treatment =    "P Practical",
}


bibtype: inproceedings
filename: fparith.bib
label: Wong:1991:FDU
author: Derek C. Wong and Michael J. Flynn
title: Fast division using accurate quotient approximations to reduce the number of iterations
crossref: Kornerup:1991:PIS
pages: 191--201
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_Wong.pdf
keywords: ARITH-10
acknowledgement: ack-nhfb
rawauthor: Derek C. Wong and Michael J. Flynn
rawtitle: Fast division using accurate quotient approximations to reduce the number of iterations
entry:
@InProceedings{Wong:1991:FDU,
  author =       "Derek C. Wong and Michael J. Flynn",
  title =        "Fast division using accurate quotient approximations
                 to reduce the number of iterations",
  crossref =     "Kornerup:1991:PIS",
  pages =        "191--201",
  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_Wong.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}


bibtype: article
filename: fparith.bib
label: Yan:1991:RFA
author: Tak W. Yan
title: A Rational Function Arithmetic and Simplification System in Common Lisp
journal: j-SIGSAM
volume: 25
number: 4
pages: 4--6
month: oct
monthnumber: 10
year: 1991
CODEN: SIGSBZ
ISSN: 0163-5824 (print), 1557-9492 (electronic) OR 01635824 (print), 15579492 (electronic)
ISSNL: 0163-5824 OR 01635824
bibdate: Fri Feb 8 18:27:01 MST 2002
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.02.08 18:27:01 MST
fjournal: SIGSAM Bulletin
acknowledgement: ack-nhfb
classcodes: C7310 (Mathematics); C6140D (High level languages)
corpsource: California University, Berkeley, CA, USA
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J1000
treatment: P Practical
issue: 98
rawauthor: Tak W. Yan
rawtitle: A Rational Function Arithmetic and Simplification System in {Common Lisp}
keywords:
arithmetic simplification; Common Lisp; exponentiation; freely-distributed computer algebra; LISP; Lisp prefix form; mathematics computing; multiplication; multivariate rational function; rational addition; rational expressions; symbol manipulation; system

entry:
@Article{Yan:1991:RFA,
  author =       "Tak W. Yan",
  title =        "A Rational Function Arithmetic and Simplification
                 System in {Common Lisp}",
  journal =      j-SIGSAM,
  volume =       "25",
  number =       "4",
  pages =        "4--6",
  month =        oct,
  year =         "1991",
  CODEN =        "SIGSBZ",
  ISSN =         "0163-5824 (print), 1557-9492 (electronic)",
  ISSN-L =       "0163-5824",
  bibdate =      "Fri Feb 8 18:27:01 MST 2002",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C7310 (Mathematics); C6140D (High level languages)",
  corpsource =   "California University, Berkeley, CA, USA",
  fjournal =     "SIGSAM Bulletin",
  issue =        "98",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1000",
  keywords =     "arithmetic simplification; Common Lisp;
                 exponentiation; freely-distributed computer algebra;
                 LISP; Lisp prefix form; mathematics computing;
                 multiplication; multivariate rational function;
                 rational addition; rational expressions; symbol
                 manipulation; system",
  treatment =    "P Practical",
}


bibtype: inproceedings
filename: fparith.bib
label: Yassine:1991:FAB
author: H. M. Yassine
booktitle: IEEE International Symposium on Circuits and Systems, 11--14 June 1991
title: Fast arithmetic based on residue number system architectures
volume: 5
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 2947--2950
year: 1991
DOI: https://doi.org/10.1109/ISCAS.1991.176163
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: H. M. Yassine
rawbooktitle: {IEEE} International Symposium on Circuits and Systems, 11--14 June 1991
rawtitle: Fast arithmetic based on residue number system architectures
entry:
@InProceedings{Yassine:1991:FAB,
  author =       "H. M. Yassine",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems, 11--14 June 1991",
  title =        "Fast arithmetic based on residue number system
                 architectures",
  volume =       "5",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "2947--2950",
  year =         "1991",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.1991.176163",
  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 approach is described for transforming residue
                 numbers into equivalent decimal numbers. The approach
                 is based on the periodicity inherent in residue numbers
                 and uses matrix techniques to achieve high-speed
                 residue-to-decimal conversion. In \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Yassine:1991:IMR
author: H. M. Yassine and W. R. Moore
title: Improved mixed-radix conversion for residue number system architectures
journal: Circuits, Devices and Systems, IEE Proceedings G
volume: 138
number: 1
pages: 120--124
month: feb
monthnumber: 2
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: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=2864
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: H. M. Yassine and W. R. Moore
rawtitle: Improved mixed-radix conversion for residue number system architectures
entry:
@Article{Yassine:1991:IMR,
  author =       "H. M. Yassine and W. R. Moore",
  title =        "Improved mixed-radix conversion for residue number
                 system architectures",
  journal =      "Circuits, Devices and Systems, IEE Proceedings G",
  volume =       "138",
  number =       "1",
  pages =        "120--124",
  month =        feb,
  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 =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=2864",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Processor architectures, based on arithmetic cells
                 using residue number systems, are inherently parallel,
                 modular and fault isolating. The fundamental
                 characteristic of a residue number system is its being
                 an unweighted numbering system. The authors \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Yokoo:1991:OUF
author: Hidetoshi Yokoo
crossref: Kornerup:1991:PIS
pages: 110--117
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_Yokoo.pdf
acknowledgement: ack-nhfb
affiliation: Department of Computer Science, Gunma University, Japan
thesaurus: Digital arithmetic; Number theory
rawauthor: Hidetoshi Yokoo
title:
Overflow / underflow-free floating-point number representations with self-delimiting variable-length exponent field

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

keywords:
ARITH-10; Exponent-significant; Floating-point number representations; Integer-fraction; Integers; Length function; Real numbers; Representation errors; Self-delimiting variable-length exponent field

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

rawtitle:
Overflow\slash underflow-free floating-point number representations with self-delimiting variable-length exponent field

entry:
@InProceedings{Yokoo:1991:OUF,
  author =       "Hidetoshi Yokoo",
  title =        "Overflow\slash underflow-free floating-point number
                 representations with self-delimiting variable-length
                 exponent field",
  crossref =     "Kornerup:1991:PIS",
  pages =        "110--117",
  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_Yokoo.pdf",
  abstract =     "A class of new floating-point representations of real
                 numbers, based on representations of the integers, is
                 described. In the class, every representation uses a
                 self-delimiting representation of the integers as a
                 variable length field, and neither overflow nor
                 underflow appears in practice. The adopted
                 representations of the integers are defined
                 systematically, so that representations of numbers
                 greater than one have both exponent-significant and
                 integer-fraction interpretations. Since representation
                 errors are characterized by the length function of an
                 underlying representation of the integers, systems
                 superior in precision can be easily selected from the
                 proposed class.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Computer Science, Gunma University,
                 Japan",
  classification = "C1160 (Combinatorial mathematics); C5230 (Digital
                 arithmetic methods)",
  keywords =     "ARITH-10; Exponent-significant; Floating-point number
                 representations; Integer-fraction; Integers; Length
                 function; Real numbers; Representation errors;
                 Self-delimiting variable-length exponent field",
  thesaurus =    "Digital arithmetic; Number theory",
}


bibtype: article
filename: fparith.bib
label: Yoshida:1991:PRT
author: N. Yoshida and E. Goto and S. Ichikawa
title: Pseudorandom Rounding for Truncated Multipliers
journal: j-IEEE-TRANS-COMPUT
volume: 40
number: 9
pages: 1065--1067
month: sep
monthnumber: 9
year: 1991
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.83650
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: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=83650
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: N. Yoshida and E. Goto and S. Ichikawa
rawtitle: Pseudorandom Rounding for Truncated Multipliers
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{Yoshida:1991:PRT,
  author =       "N. Yoshida and E. Goto and S. Ichikawa",
  title =        "Pseudorandom Rounding for Truncated Multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "40",
  number =       "9",
  pages =        "1065--1067",
  month =        sep,
  year =         "1991",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.83650",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 12:52:23 MDT 2011",
  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",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=83650",
  acknowledgement = ack-nj # "\slash " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "An economical, unbiased, overflow-free rounding scheme
                 for multiplication of multiple-precision floating-point
                 numbers is proposed. The scheme, called pseudorandom
                 rounding, saves multiplications of lower bits and makes
                 use of statistical properties \ldots{}",
}


bibtype: techreport
filename: fparith.bib
label: Yu:1991:FCF
author: Tsung Lun Yu and William B. Ribbens
number: {GLCTTR} 03-91/1
institution: Great Lakes Center for Truck Transportation Research
address: Ann Arbor, MI, USA
pages: 68
month: sep
monthnumber: 9
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: Tsung Lun Yu and William B. Ribbens
title:
A floating-point coprocessor for fault detection and isolation in electronically controlled internal combustion engines

keywords:
Fault location (Engineering); Floating-point arithmetic.; Internal combustion engines --- Defects.; Microprocessors.; Motor vehicles --- Electronic equipment.

remark:
Performed in cooperation with the University Transportation Centers Program by Vehicle Electronics Laboratory, University of Michigan.

rawtitle:
A floating-point coprocessor for fault detection and isolation in electronically controlled internal combustion engines

entry:
@TechReport{Yu:1991:FCF,
  author =       "Tsung Lun Yu and William B. Ribbens",
  title =        "A floating-point coprocessor for fault detection and
                 isolation in electronically controlled internal
                 combustion engines",
  number =       "{GLCTTR} 03-91/1",
  institution =  "Great Lakes Center for Truck Transportation Research",
  address =      "Ann Arbor, MI, USA",
  pages =        "68",
  month =        sep,
  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 =     "Fault location (Engineering); Floating-point
                 arithmetic.; Internal combustion engines --- Defects.;
                 Microprocessors.; Motor vehicles --- Electronic
                 equipment.",
  remark =       "Performed in cooperation with the University
                 Transportation Centers Program by Vehicle Electronics
                 Laboratory, University of Michigan.",
}


bibtype: article
filename: fparith.bib
label: Zelniker:1991:RCF
author: G. Zelniker and F. J. Taylor
title: A Reduced Complexity Finite Field ALU
journal: j-IEEE-TRANS-CIRCUITS-SYST
volume: 38
number: 12
pages: 1571--1573
month: dec
monthnumber: 12
year: 1991
CODEN: ICSYBT
ISSN: 0098-4094 (print), 1558-1276 (electronic) OR 00984094 (print), 15581276 (electronic)
ISSNL: 0098-4094 OR 00984094
bibdate: Fri Jun 24 19:51:42 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.06.24 19:51:42 ???
fjournal: IEEE Transactions on Circuits and Systems
keywords: arithmetic logic unit (ALU)
acknowledgement: ack-nhfb
rawauthor: G. Zelniker and F. J. Taylor
rawtitle: A Reduced Complexity Finite Field {ALU}
entry:
@Article{Zelniker:1991:RCF,
  author =       "G. Zelniker and F. J. Taylor",
  title =        "A Reduced Complexity Finite Field {ALU}",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "38",
  number =       "12",
  pages =        "1571--1573",
  month =        dec,
  year =         "1991",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Fri Jun 24 19:51:42 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  keywords =     "arithmetic logic unit (ALU)",
}


bibtype: article
filename: fparith.bib
label: Zeng:1991:AFP
author: B. Zeng and Y. Neuvo
title: Analysis of floating point roundoff errors using dummy multiplier coefficient sensitivities
journal: j-IEEE-TRANS-CIRCUITS-SYST
volume: 38
number: 6
pages: 590--601
month: jun
monthnumber: 6
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 08:40:52 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:52 MDT
fjournal: IEEE Transactions on Circuits and Systems
acknowledgement: ack-nhfb
rawauthor: B. Zeng and Y. Neuvo
rawtitle: Analysis of floating point roundoff errors using dummy multiplier coefficient sensitivities
entry:
@Article{Zeng:1991:AFP,
  author =       "B. Zeng and Y. Neuvo",
  title =        "Analysis of floating point roundoff errors using dummy
                 multiplier coefficient sensitivities",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "38",
  number =       "6",
  pages =        "590--601",
  month =        jun,
  year =         "1991",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  summary =      "A simple method for analyzing roundoff errors in
                 floating-point digital filters is presented. The method
                 is based on the coefficient sensitivities of dummy
                 multipliers with gains of one and connects the roundoff
                 error analysis to coefficient sensitive \ldots{}",
}


bibtype: phdthesis
filename: fparith.bib
label: Zeng:1991:ARR
author: Bing Zeng
title: Analysis and reduction of roundoff errors in floating-point recursive digital filters
volume: 72
type: Avhandling (doktorgrad)
school: Tampereen teknillinen korkeakoulu
address: Tampere, Finland
pages: 45 + 80
year: 1991
ISBN: 951-721-697-1 OR 9517216971
ISBN13: 978-951-721-697-5 OR 9789517216975
bibdate: Thu May 09 08:15:51 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.09 08:15:51 ???
series: Julkaisuja
acknowledgement: ack-nhfb
rawauthor: Bing Zeng
rawtitle: Analysis and reduction of roundoff errors in floating-point recursive digital filters
entry:
@PhdThesis{Zeng:1991:ARR,
  author =       "Bing Zeng",
  title =        "Analysis and reduction of roundoff errors in
                 floating-point recursive digital filters",
  volume =       "72",
  type =         "Avhandling (doktorgrad)",
  school =       "Tampereen teknillinen korkeakoulu",
  address =      "Tampere, Finland",
  pages =        "45 + 80",
  year =         "1991",
  ISBN =         "951-721-697-1",
  ISBN-13 =      "978-951-721-697-5",
  bibdate =      "Thu May 09 08:15:51 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Julkaisuja",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Zhang:1991:ADN
author: D. Zhang and G. A. Jullien and W. C. Miller and Earl Swartzlander, Jr.
title: Arithmetic for digital neural networks
crossref: Kornerup:1991:PIS
pages: 58--63
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_Zhang.pdf
keywords: ARITH-10
acknowledgement: ack-nhfb
rawauthor: D. Zhang and G. A. Jullien and W. C. Miller and Earl {Swartzlander, Jr.}
rawtitle: Arithmetic for digital neural networks
entry:
@InProceedings{Zhang:1991:ADN,
  author =       "D. Zhang and G. A. Jullien and W. C. Miller and Earl
                 {Swartzlander, Jr.}",
  title =        "Arithmetic for digital neural networks",
  crossref =     "Kornerup:1991:PIS",
  pages =        "58--63",
  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_Zhang.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}


bibtype: inproceedings
filename: fparith.bib
label: Zhang:1991:HSE
author: C. N. Zhang and H. D. Cheng
title: A high speed error correcting converter for residue number processing
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 816--820
year: 1991
DOI: https://doi.org/10.1109/CMPEUR.1991.257495
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: C. N. Zhang and H. D. Cheng
rawtitle: A high speed error correcting converter for residue number processing
booktitle:
Reliable Systems and Applications. 5th Annual European Computer Conference. Proceedings. CompEuro 91. Advanced Computer Technology, 13--16 May 1991

rawbooktitle:
Reliable Systems and Applications. 5th Annual European Computer Conference. Proceedings. {CompEuro 91}. Advanced Computer Technology, 13--16 May 1991

entry:
@InProceedings{Zhang:1991:HSE,
  author =       "C. N. Zhang and H. D. Cheng",
  booktitle =    "Reliable Systems and Applications. 5th Annual European
                 Computer Conference. Proceedings. {CompEuro 91}.
                 Advanced Computer Technology, 13--16 May 1991",
  title =        "A high speed error correcting converter for residue
                 number processing",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "816--820",
  year =         "1991",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/CMPEUR.1991.257495",
  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 novel pipelined systolic design for residue error
                 correction using the Chinese remainder theorem (CRT) is
                 described. This design has a higher throughput compared
                 to previous methods and minimum time latency. The
                 design also has overflow detection \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Zhang:1991:HSS
author: C. N. Zhang and H. D. Cheng
title: High-speed single error correcting convertor for residue number processing
journal: j-IEE-PROC-COMPUT-DIGIT-TECH
volume: 138
number: 4
pages: 177--182
month: jul
monthnumber: 7
year: 1991
CODEN: ICDTEA
DOI: https://doi.org/10.1109/78.80821
ISSN: 1350-2387 (print), 1359-7027 (electronic) OR 13502387 (print), 13597027 (electronic)
ISSNL: 1350-2387 OR 13502387
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
URL: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=2686
fjournal: IEE Proceedings. Computers and Digital Techniques
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: C. N. Zhang and H. D. Cheng
rawtitle: High-speed single error correcting convertor for residue number processing
entry:
@Article{Zhang:1991:HSS,
  author =       "C. N. Zhang and H. D. Cheng",
  title =        "High-speed single error correcting convertor for
                 residue number processing",
  journal =      j-IEE-PROC-COMPUT-DIGIT-TECH,
  volume =       "138",
  number =       "4",
  pages =        "177--182",
  month =        jul,
  year =         "1991",
  CODEN =        "ICDTEA",
  DOI =          "https://doi.org/10.1109/78.80821",
  ISSN =         "1350-2387 (print), 1359-7027 (electronic)",
  ISSN-L =       "1350-2387",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=2686",
  acknowledgement = ack-nhfb,
  fjournal =     "IEE Proceedings. Computers and Digital Techniques",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A pipelined systolic design for residue error
                 correction using the Chinese remainder theorem is
                 described which has a higher throughput compared with
                 previous methods and minimum time latency. In addition,
                 the design has the capability of overflow \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Ziv:1991:FEE
author: Abraham Ziv
title: Fast Evaluation of Elementary Mathematical Functions with Correctly Rounded Last Bit
journal: j-TOMS
volume: 17
number: 3
pages: 410--423
month: sep
monthnumber: 9
year: 1991
CODEN: ACMSCU
DOI: https://doi.org/10.1145/114697.116813
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Thu Sep 1 10:15:31 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 10:15:31 ???
URL: http://www.acm.org/pubs/citations/journals/toms/1991-17-3/p410-ziv/
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms; correct rounding; floating-point arithmetic; standardization; theory
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/toms
rawauthor: Abraham Ziv
rawtitle: Fast Evaluation of Elementary Mathematical Functions with Correctly Rounded Last Bit
subject:
bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. bf G.1.2: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation. bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency.

entry:
@Article{Ziv:1991:FEE,
  author =       "Abraham Ziv",
  title =        "Fast Evaluation of Elementary Mathematical Functions
                 with Correctly Rounded Last Bit",
  journal =      j-TOMS,
  volume =       "17",
  number =       "3",
  pages =        "410--423",
  month =        sep,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/114697.116813",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Sep 1 10:15:31 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-3/p410-ziv/",
  acknowledgement = ack-nj,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; correct rounding; floating-point
                 arithmetic; standardization; theory",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Numerical algorithms. {\bf G.1.2}:
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Efficiency.",
}


bibtype: article
filename: fparith.bib
label: Acha:1992:LOF
author: J. I. Acha and J. Calvo
title: Low-frequency oscillator for floating-point digital signal processor chips
journal: j-ELECT-LETTERS
volume: 28
number: 17
pages: 1582--??
month: aug
monthnumber: 8
year: 1992
CODEN: ELLEAK
ISSN: 0013-5194 (print), 1350-911X (electronic) OR 00135194 (print), 1350911X (electronic)
ISSNL: 0013-5194 OR 00135194
bibdate: 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 Letters
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220
rawauthor: J. I. Acha and J. Calvo
rawtitle: Low-frequency oscillator for floating-point digital signal processor chips
entry:
@Article{Acha:1992:LOF,
  author =       "J. I. Acha and J. Calvo",
  title =        "Low-frequency oscillator for floating-point digital
                 signal processor chips",
  journal =      j-ELECT-LETTERS,
  volume =       "28",
  number =       "17",
  pages =        "1582--??",
  month =        aug,
  year =         "1992",
  CODEN =        "ELLEAK",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  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 Letters",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
}


bibtype: article
filename: fparith.bib
label: Anonymous:1992:FPa
author: Anonymous
title: Floating Point
journal: j-COMPUT-AIDED-ENG
volume: 11
number: 8
pages: 58--??
month: aug
monthnumber: 8
year: 1992
CODEN: CCAEDJ
ISSN: 0733-3536 (print), 2162-1365 (electronic) OR 07333536 (print), 21621365 (electronic)
ISSNL: 0733-3536 OR 07333536
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
abstract: OpenGL: The NeWs of 3D Graphics?
fjournal: Computer-aided engineering: CAE
acknowledgement: ack-nhfb
rawabstract: OpenGL: The NeWs of 3D Graphics?
rawauthor: Anonymous
rawtitle: Floating Point
entry:
@Article{Anonymous:1992:FPa,
  author =       "Anonymous",
  title =        "Floating Point",
  journal =      j-COMPUT-AIDED-ENG,
  volume =       "11",
  number =       "8",
  pages =        "58--??",
  month =        aug,
  year =         "1992",
  CODEN =        "CCAEDJ",
  ISSN =         "0733-3536 (print), 2162-1365 (electronic)",
  ISSN-L =       "0733-3536",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "OpenGL: The NeWs of 3D Graphics?",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer-aided engineering: CAE",
}


bibtype: article
filename: fparith.bib
label: Anonymous:1992:FPb
author: Anonymous
title: Floating Point
journal: j-COMPUT-AIDED-ENG
volume: 11
number: 11
pages: 62--??
month: nov
monthnumber: 11
year: 1992
CODEN: CCAEDJ
ISSN: 0733-3536 (print), 2162-1365 (electronic) OR 07333536 (print), 21621365 (electronic)
ISSNL: 0733-3536 OR 07333536
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
abstract: Software with a View.
fjournal: Computer-aided engineering: CAE
acknowledgement: ack-nhfb
rawabstract: Software with a View.
rawauthor: Anonymous
rawtitle: Floating Point
entry:
@Article{Anonymous:1992:FPb,
  author =       "Anonymous",
  title =        "Floating Point",
  journal =      j-COMPUT-AIDED-ENG,
  volume =       "11",
  number =       "11",
  pages =        "62--??",
  month =        nov,
  year =         "1992",
  CODEN =        "CCAEDJ",
  ISSN =         "0733-3536 (print), 2162-1365 (electronic)",
  ISSN-L =       "0733-3536",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Software with a View.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer-aided engineering: CAE",
}


bibtype: article
filename: fparith.bib
label: Anonymous:1992:FPc
author: Anonymous
title: Floating Point
journal: j-COMPUT-AIDED-ENG
volume: 11
number: 10
pages: 101--??
month: oct
monthnumber: 10
year: 1992
CODEN: CCAEDJ
ISSN: 0733-3536 (print), 2162-1365 (electronic) OR 07333536 (print), 21621365 (electronic)
ISSNL: 0733-3536 OR 07333536
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
abstract: A Helping Hand for FEA.
fjournal: Computer-aided engineering: CAE
acknowledgement: ack-nhfb
rawabstract: A Helping Hand for FEA.
rawauthor: Anonymous
rawtitle: Floating Point
entry:
@Article{Anonymous:1992:FPc,
  author =       "Anonymous",
  title =        "Floating Point",
  journal =      j-COMPUT-AIDED-ENG,
  volume =       "11",
  number =       "10",
  pages =        "101--??",
  month =        oct,
  year =         "1992",
  CODEN =        "CCAEDJ",
  ISSN =         "0733-3536 (print), 2162-1365 (electronic)",
  ISSN-L =       "0733-3536",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A Helping Hand for FEA.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer-aided engineering: CAE",
}


bibtype: manual
filename: fparith.bib
label: ANSI:ftn92
title: American National Standard Programming Language Fortran Extended X3.198--1992
organization: pub-ANSI
address: pub-ANSI:adr
pages: 101--??
year: 1992
bibdate: Sat Feb 8 10:28:55 2020
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/master.bib
bibtimestamp: 2020.02.08 10:28:55 ???
acknowledgement: ack-nhfb
rawtitle: {American National Standard Programming Language Fortran Extended X3.198--1992}
entry:
@Manual{ANSI:ftn92,
  title =        "{American National Standard Programming Language
                 Fortran Extended X3.198--1992}",
  organization = pub-ANSI,
  address =      pub-ANSI:adr,
  year =         "1992",
  bibdate =      "Sat Feb 8 10:28:55 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  acknowledgement = ack-nhfb,
  xxnote =       "This US Standard is identical to the international
                 standard, ISO 1539:1991. See also
                 \cite{Adams:1992:FHC,Brainerd:1990:PGF,Counihan:1991:F,Metcalf:1990:FE}.",
}


bibtype: article
filename: fparith.bib
label: Arazi:1992:BDC
author: B. Arazi and D. Naccache
title: Binary-to-Decimal Conversion Based on the Divisibility of $ 2^8 - 1 $ by 5
journal: j-ELECT-LETTERS
volume: 28
number: 3
pages: 2151--2152
month: nov
monthnumber: 11
year: 1992
CODEN: ELLEAK
ISSN: 0013-5194 (print), 1350-911X (electronic) OR 00135194 (print), 1350911X (electronic)
ISSNL: 0013-5194 OR 00135194
bibdate: Thu Sep 1 10:16:11 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:16:11 ???
fjournal: Electronics Letters
keywords: decimal floating-point arithmetic
acknowledgement: ack-nj
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220
rawauthor: B. Arazi and D. Naccache
rawtitle: Binary-to-Decimal Conversion Based on the Divisibility of $ 2^8 - 1 $ by 5
entry:
@Article{Arazi:1992:BDC,
  author =       "B. Arazi and D. Naccache",
  title =        "Binary-to-Decimal Conversion Based on the Divisibility
                 of $ 2^8 - 1 $ by 5",
  journal =      j-ELECT-LETTERS,
  volume =       "28",
  number =       "3",
  pages =        "2151--2152",
  month =        nov,
  year =         "1992",
  CODEN =        "ELLEAK",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Thu Sep 1 10:16:11 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Electronics Letters",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  keywords =     "decimal floating-point arithmetic",
}


bibtype: article
filename: fparith.bib
label: Arnold:1992:AFI
author: M. G. Arnold and T. A. Bailey and J. R. Cowles and M. D. Winkel
title: Applying features of IEEE 754 to sign / logarithm arithmetic
journal: j-IEEE-TRANS-COMPUT
volume: 41
number: 8
pages: 1040--1050
month: aug
monthnumber: 8
year: 1992
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.156547
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 10:49:19 MDT 2011
bibtimestamp: 2011.07.07 10:49:19 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156547
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
affiliation: Department of Computer Science, Wyoming University, Laramie, WY, USA
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
thesaurus: Digital arithmetic; Number theory; Standards
rawauthor: M. G. Arnold and T. A. Bailey and J. R. Cowles and M. D. Winkel
rawtitle: Applying features of {IEEE 754} to sign\slash logarithm arithmetic
abstract:
Various features found in standard floating point arithmetic (IEEE 754) are examined in light of their appropriateness for sign/logarithm arithmetic. The emphasis is on a 32-b word size comparable to IEEE 754 single precision, although other word sizes are possible. A multilayer sign/logarithm format is considered. The lowest layer, similar to previous implementations, would provide only normalized representations but would not provide representations for zero, denormalized values, infinities, and NaNs. The highest layer would provide most of the features found in IEEE 754, including zeros, denormalized values, infinities, and NaNs. Novel algorithms for implementing logarithmic denormalized arithmetic are presented. Simulation results show that the error characteristics of the proposed logarithmic denormalized arithmetic algorithms are similar to those of the denormalized floating point arithmetic in IEEE 754.

keywords:
32 Bit; Denormalized values; IEEE 754; Infinities; Logarithmic denormalized arithmetic algorithms; Multilayer sign/logarithm format; NaNs; Sign/logarithm arithmetic; Standard floating point arithmetic; Zeros

rawabstract:
Various features found in standard floating point arithmetic (IEEE 754) are examined in light of their appropriateness for sign/logarithm arithmetic. The emphasis is on a 32-b word size comparable to IEEE 754 single precision, although other word sizes are possible. A multilayer sign/logarithm format is considered. The lowest layer, similar to previous implementations, would provide only normalized representations but would not provide representations for zero, denormalized values, infinities, and NaNs. The highest layer would provide most of the features found in IEEE 754, including zeros, denormalized values, infinities, and NaNs. Novel algorithms for implementing logarithmic denormalized arithmetic are presented. Simulation results show that the error characteristics of the proposed logarithmic denormalized arithmetic algorithms are similar to those of the denormalized floating point arithmetic in IEEE 754.

entry:
@Article{Arnold:1992:AFI,
  author =       "M. G. Arnold and T. A. Bailey and J. R. Cowles and M.
                 D. Winkel",
  title =        "Applying features of {IEEE 754} to sign\slash
                 logarithm arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "8",
  pages =        "1040--1050",
  month =        aug,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.156547",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 10:49:19 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156547",
  abstract =     "Various features found in standard floating point
                 arithmetic (IEEE 754) are examined in light of their
                 appropriateness for sign/logarithm arithmetic. The
                 emphasis is on a 32-b word size comparable to IEEE 754
                 single precision, although other word sizes are
                 possible. A multilayer sign/logarithm format is
                 considered. The lowest layer, similar to previous
                 implementations, would provide only normalized
                 representations but would not provide representations
                 for zero, denormalized values, infinities, and NaNs.
                 The highest layer would provide most of the features
                 found in IEEE 754, including zeros, denormalized
                 values, infinities, and NaNs. Novel algorithms for
                 implementing logarithmic denormalized arithmetic are
                 presented. Simulation results show that the error
                 characteristics of the proposed logarithmic
                 denormalized arithmetic algorithms are similar to those
                 of the denormalized floating point arithmetic in IEEE
                 754.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Computer Science, Wyoming University,
                 Laramie, WY, USA",
  ajournal =     "IEEE Trans. Comput.",
  classification = "B0250 (Combinatorial mathematics); B1265B (Logic
                 circuits); C1160 (Combinatorial mathematics); C5230
                 (Digital arithmetic methods)",
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "32 Bit; Denormalized values; IEEE 754; Infinities;
                 Logarithmic denormalized arithmetic algorithms;
                 Multilayer sign/logarithm format; NaNs; Sign/logarithm
                 arithmetic; Standard floating point arithmetic; Zeros",
  numericalindex = "Word length 3.2E+01 bit",
  thesaurus =    "Digital arithmetic; Number theory; Standards",
}


bibtype: techreport
filename: fparith.bib
label: Bailey:1992:ATF
author: David H. Bailey
title: Automatic Translation of Fortran Programs to Multiprecision
type: RNR Technical Report
number: RNR-91-025
institution: NAS Applied Research Branch, NASA Ames Research Center
address: Moffett Field, CA 94035
pages: 1040--1050
day: 17
month: apr
monthnumber: 4
year: 1992
bibdate: Mon Sep 12 23:55:57 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.12 23:55:57 ???
acknowledgement: ack-nhfb
rawauthor: David H. Bailey
rawtitle: Automatic Translation of {Fortran} Programs to Multiprecision
entry:
@TechReport{Bailey:1992:ATF,
  author =       "David H. Bailey",
  title =        "Automatic Translation of {Fortran} Programs to
                 Multiprecision",
  type =         "{RNR} Technical Report",
  number =       "RNR-91-025",
  institution =  "NAS Applied Research Branch, NASA Ames Research
                 Center",
  address =      "Moffett Field, CA 94035",
  day =          "17",
  month =        apr,
  year =         "1992",
  bibdate =      "Mon Sep 12 23:55:57 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: fparith.bib
label: Bailey:1992:PHP
author: David H. Bailey
title: A Portable High Performance Multiprecision Package
type: RNR Technical Report
number: RNR-90-022
institution: NAS Applied Research Branch, NASA Ames Research Center
address: Moffett Field, CA 94035
pages: 1040--1050
day: 29
month: may
monthnumber: 5
year: 1992
bibdate: Mon Sep 12 23:56:03 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.12 23:56:03 ???
acknowledgement: ack-nhfb
rawauthor: David H. Bailey
rawtitle: A Portable High Performance Multiprecision Package
entry:
@TechReport{Bailey:1992:PHP,
  author =       "David H. Bailey",
  title =        "A Portable High Performance Multiprecision Package",
  type =         "{RNR} Technical Report",
  number =       "RNR-90-022",
  institution =  "NAS Applied Research Branch, NASA Ames Research
                 Center",
  address =      "Moffett Field, CA 94035",
  day =          "29",
  month =        may,
  year =         "1992",
  bibdate =      "Mon Sep 12 23:56:03 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Baker:1992:LCE
author: H. G. Baker
title: Less Complex Elementary Functions
journal: j-SIGPLAN
volume: 27
number: 11
pages: 15--16
month: nov
monthnumber: 11
year: 1992
CODEN: SINODQ
ISSN: 0362-1340 (print), 1523-2867 (print), 1558-1160 OR 03621340 (print), 15232867 (print), 15581160
ISSNL: 0362-1340 OR 03621340
bibdate: Thu Sep 08 08:11:27 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.08 08:11:27 ???
fjournal: ACM SIGPLAN Notices
acknowledgement: ack-nj
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J706
rawauthor: H. G. Baker
rawtitle: Less Complex Elementary Functions
entry:
@Article{Baker:1992:LCE,
  author =       "H. G. Baker",
  title =        "Less Complex Elementary Functions",
  journal =      j-SIGPLAN,
  volume =       "27",
  number =       "11",
  pages =        "15--16",
  month =        nov,
  year =         "1992",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Thu Sep 08 08:11:27 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
}


bibtype: article
filename: fparith.bib
label: Bakhrakh:1992:NIF
title: Numerical investigation of floating-point arithmetic operations. (Russian)
journal: j-PROGRAMMIROVANIE
volume: 6
pages: 13--17
year: 1992
CODEN: PROGD3
ISSN: 0132-3474, 0361-7688 OR 01323474, 03617688
MRclass: 65G05
MRnumber: 1 227 941
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 ???
note: English translation appears in cite Bakhrakh:1993:NIF.
fjournal: Programmirovanie
language: Russian
acknowledgement: ack-nhfb
rawnote: English translation appears in \cite{Bakhrakh:1993:NIF}.
rawtitle: Numerical investigation of floating-point arithmetic operations. ({Russian})
author:
S. M. Bakhrakh and S. V. Velichko and N. E. Pilipchatin and V. F. Spiridonov and E. G. Sukhov and Yu. G. Fedorova and V. I. Kheifets

rawauthor:
S. M. Bakhrakh and S. V. Velichko and N. E. Pilipchatin and V. F. Spiridonov and E. G. Sukhov and Yu. G. Fedorova and V. I. Kheifets

entry:
@Article{Bakhrakh:1992:NIF,
  author =       "S. M. Bakhrakh and S. V. Velichko and N. E.
                 Pilipchatin and V. F. Spiridonov and E. G. Sukhov and
                 Yu. G. Fedorova and V. I. Kheifets",
  title =        "Numerical investigation of floating-point arithmetic
                 operations. ({Russian})",
  journal =      j-PROGRAMMIROVANIE,
  volume =       "6",
  pages =        "13--17",
  year =         "1992",
  CODEN =        "PROGD3",
  ISSN =         "0132-3474, 0361-7688",
  MRclass =      "65G05",
  MRnumber =     "1 227 941",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "English translation appears in
                 \cite{Bakhrakh:1993:NIF}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Programmirovanie",
  language =     "Russian",
}


bibtype: techreport
filename: fparith.bib
label: Bewick:1992:BMU
author: G. Bewick and M. J. Flynn
title: Binary multiplication using partially redundant multiples
type: Technical Report
number: CSL-TR-92-528
institution: Computer Systems Laboratory, Stanford University
address: Stanford, CA, USA
pages: 13--17
month: jun
monthnumber: 6
year: 1992
bibdate: Thu Apr 2 08:38:35 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.04.02 08:38:35 ???
acknowledgement: ack-sfo
rawauthor: G. Bewick and M. J. Flynn
rawtitle: Binary multiplication using partially redundant multiples
entry:
@TechReport{Bewick:1992:BMU,
  author =       "G. Bewick and M. J. Flynn",
  title =        "Binary multiplication using partially redundant
                 multiples",
  type =         "Technical Report",
  number =       "CSL-TR-92-528",
  institution =  "Computer Systems Laboratory, Stanford University",
  address =      "Stanford, CA, USA",
  month =        jun,
  year =         "1992",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
}


bibtype: techreport
filename: fparith.bib
label: Blair:1992:PMD
author: M. Blair and S. Obenski and P. Bridickas
title: Patriot missile defense: Software problem led to system failure at Dhahran, Saudi Arabia
type: Report
number: GAO/IMTEC-92-26
institution: Information Management and Technology Division, United States General Accounting Office
address: Washington, DC, USA
pages: 13--17
year: 1992
bibdate: Sat Apr 01 07:34:33 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2017.04.01 07:34:33 ???
URL: http://www.gao.gov/assets/220/215614.pdf; http://www.gao.gov/products/IMTEC-92-26
acknowledgement: ack-nhfb
rawauthor: M. Blair and S. Obenski and P. Bridickas
rawtitle: {Patriot} missile defense: Software problem led to system failure at {Dhahran, Saudi Arabia}
abstract:
Pursuant to a congressional request, GAO reviewed the facts associated with the failure of a Patriot missile defense system in Dhahran, Saudi Arabia, during Operation Desert Storm.par GAO found that: (1) the Patriot battery at Dhahran failed to track and intercept a Scud missile due to a software problem in the system's weapons control computer; (2) the software problem caused an inaccurate tracking calculation which became worse the longer the system operated; (3) at the time of the incident, the battery had operated continuously for over 100 hours and the inaccuracy was serious enough to cause the system to look in the wrong place for the incoming Scud; (4) two weeks before the incident, Army officials received Israeli data indicating some loss in accuracy after the system had been running for 8 consecutive hours; (5) the Army had never used the Patriot to defend against tactical ballistic missiles or expected the Patriot to operate continuously for long periods of time; and (6) Army officials modified the software, but the new software did not reach Dhahran until the day after the incident. ldots The precision of a computer's calculations depends on the number of bits in its registers. Since the Patriot's registers are only 24 bits long, precision beyond 24 bits is not possible unless the software is specifically written to adjust for such hardware limitations. Computers built today have registers that contain as many as 64 bits, permitting calculations with far greater precision. ldots During the conflict the Patriot's software was modified six times. Patriots had to be shut down for at least 1 to 2 hours to install each software modification.

remark:
From the report: ``Because of the way the Patriot computer performs its calculations and the fact that its registers are only 24 bits long, the conversion of time from an integer to a real number cannot be any more precise than 24 bits. This conversion results in a loss of precision causing a less accurate time calculation. The effect of this inaccuracy on the range gate's calculation is directly proportional to the target's velocity and the length of time the system has been running. Consequently, performing the conversion after the Patriot has been running continuously for extended periods causes the range gate to shift away from the center of the target, making it less likely that the target, in this case a Scud, will be successfully intercepted. ldots On February 25, Alpha Battery had been in operation for over 100 consecutive hours. Because the system had been on so long, the resulting inaccuracy in the time calculation caused the range gate to shift so much that the system could not track the incoming Scud. Consequently, Alpha Battery did not engage the Scud, which then struck an Army barracks and killed 28 American soldiers.''

rawabstract:
Pursuant to a congressional request, GAO reviewed the facts associated with the failure of a Patriot missile defense system in Dhahran, Saudi Arabia, during Operation Desert Storm.\par GAO found that: (1) the Patriot battery at Dhahran failed to track and intercept a Scud missile due to a software problem in the system's weapons control computer; (2) the software problem caused an inaccurate tracking calculation which became worse the longer the system operated; (3) at the time of the incident, the battery had operated continuously for over 100 hours and the inaccuracy was serious enough to cause the system to look in the wrong place for the incoming Scud; (4) two weeks before the incident, Army officials received Israeli data indicating some loss in accuracy after the system had been running for 8 consecutive hours; (5) the Army had never used the Patriot to defend against tactical ballistic missiles or expected the Patriot to operate continuously for long periods of time; and (6) Army officials modified the software, but the new software did not reach Dhahran until the day after the incident. \ldots{} The precision of a computer's calculations depends on the number of bits in its registers. Since the Patriot's registers are only 24 bits long, precision beyond 24 bits is not possible unless the software is specifically written to adjust for such hardware limitations. Computers built today have registers that contain as many as 64 bits, permitting calculations with far greater precision. \ldots{} During the conflict the Patriot's software was modified six times. Patriots had to be shut down for at least 1 to 2 hours to install each software modification.

entry:
@TechReport{Blair:1992:PMD,
  author =       "M. Blair and S. Obenski and P. Bridickas",
  title =        "{Patriot} missile defense: Software problem led to
                 system failure at {Dhahran, Saudi Arabia}",
  type =         "Report",
  number =       "GAO/IMTEC-92-26",
  institution =  "Information Management and Technology Division, United
                 States General Accounting Office",
  address =      "Washington, DC, USA",
  year =         "1992",
  bibdate =      "Sat Apr 01 07:34:33 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.gao.gov/assets/220/215614.pdf;
                 http://www.gao.gov/products/IMTEC-92-26",
  abstract =     "Pursuant to a congressional request, GAO reviewed the
                 facts associated with the failure of a Patriot missile
                 defense system in Dhahran, Saudi Arabia, during
                 Operation Desert Storm.\par

                 GAO found that: (1) the Patriot battery at Dhahran
                 failed to track and intercept a Scud missile due to a
                 software problem in the system's weapons control
                 computer; (2) the software problem caused an inaccurate
                 tracking calculation which became worse the longer the
                 system operated; (3) at the time of the incident, the
                 battery had operated continuously for over 100 hours
                 and the inaccuracy was serious enough to cause the
                 system to look in the wrong place for the incoming
                 Scud; (4) two weeks before the incident, Army officials
                 received Israeli data indicating some loss in accuracy
                 after the system had been running for 8 consecutive
                 hours; (5) the Army had never used the Patriot to
                 defend against tactical ballistic missiles or expected
                 the Patriot to operate continuously for long periods of
                 time; and (6) Army officials modified the software, but
                 the new software did not reach Dhahran until the day
                 after the incident. \ldots{} The precision of a
                 computer's calculations depends on the number of bits
                 in its registers. Since the Patriot's registers are
                 only 24 bits long, precision beyond 24 bits is not
                 possible unless the software is specifically written to
                 adjust for such hardware limitations. Computers built
                 today have registers that contain as many as 64 bits,
                 permitting calculations with far greater precision.
                 \ldots{} During the conflict the Patriot's software was
                 modified six times. Patriots had to be shut down for at
                 least 1 to 2 hours to install each software
                 modification.",
  acknowledgement = ack-nhfb,
  remark =       "From the report: ``Because of the way the Patriot
                 computer performs its calculations and the fact that
                 its registers are only 24 bits long, the conversion of
                 time from an integer to a real number cannot be any
                 more precise than 24 bits. This conversion results in a
                 loss of precision causing a less accurate time
                 calculation. The effect of this inaccuracy on the range
                 gate's calculation is directly proportional to the
                 target's velocity and the length of time the system has
                 been running. Consequently, performing the conversion
                 after the Patriot has been running continuously for
                 extended periods causes the range gate to shift away
                 from the center of the target, making it less likely
                 that the target, in this case a Scud, will be
                 successfully intercepted. \ldots{} On February 25,
                 Alpha Battery had been in operation for over 100
                 consecutive hours. Because the system had been on so
                 long, the resulting inaccuracy in the time calculation
                 caused the range gate to shift so much that the system
                 could not track the incoming Scud. Consequently, Alpha
                 Battery did not engage the Scud, which then struck an
                 Army barracks and killed 28 American soldiers.''",
  xxremark =     "Report of integer overflow in a timer that made the
                 guidance system erroneous; the ultimate solution proved
                 to be to reboot the guidance computer every few hours,
                 before the overflow.",
}


bibtype: article
filename: fparith.bib
label: Bohlender:1992:PAF
author: G. Bohlender and D. Cordes and A. Knofel and U. Kulisch and R. Lohner and W. V. Walter
title: Proposal for Accurate Floating-Point Vector Arithmetic
journal: j-MATH-SCI-ENG
volume: 189
pages: 87--104
year: 1992
CODEN: MTSEAT
ISSN: 0076-5392 OR 00765392
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: Mathematics in Science and Engineering
acknowledgement: ack-nhfb
rawauthor: G. Bohlender and D. Cordes and A. Kn{\"o}fel and U. Kulisch and R. Lohner and W. V. Walter
rawtitle: Proposal for Accurate Floating-Point Vector Arithmetic
entry:
@Article{Bohlender:1992:PAF,
  author =       "G. Bohlender and D. Cordes and A. Kn{\"o}fel and U.
                 Kulisch and R. Lohner and W. V. Walter",
  title =        "Proposal for Accurate Floating-Point Vector
                 Arithmetic",
  journal =      j-MATH-SCI-ENG,
  volume =       "189",
  number =       "??",
  pages =        "87--104",
  year =         "1992",
  CODEN =        "MTSEAT",
  ISSN =         "0076-5392",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics in Science and Engineering",
}


bibtype: article
filename: fparith.bib
label: Borwein:1992:MHP
author: Jonathan M. Borwein and Mark A. Limber
title: Maple as a High Precision Calculator
journal: j-MAPLE-TECH-NEWS
volume: 0
number: 8
pages: 39--44
month: Fall
year: 1992
ISSN: 1061-5733 OR 10615733
ISSNL: 1061-5733 OR 10615733
bibdate: Fri May 09 22:33:19 1997
bibtimestamp: 1997.05.09 22:33:19 ???
URL: http://www.can.nl/Systems_and_Packages/Per_Purpose/General/Maple/mtn/mtn8.html
fjournal: Maple technical newsletter
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://web.mit.edu/maple/www/plibrary/mtn.html
rawauthor: Jonathan M. Borwein and Mark A. Limber
rawtitle: {Maple} as a High Precision Calculator
ORCID: Borwein, Jonathan/0000-0002-1263-0646
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/maple-tech.bib

entry:
@Article{Borwein:1992:MHP,
  author =       "Jonathan M. Borwein and Mark A. Limber",
  title =        "{Maple} as a High Precision Calculator",
  journal =      j-MAPLE-TECH-NEWS,
  volume =       "0",
  number =       "8",
  pages =        "39--44",
  month =        "Fall",
  year =         "1992",
  ISSN =         "1061-5733",
  ISSN-L =       "1061-5733",
  bibdate =      "Fri May 09 22:33:19 1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/maple-tech.bib",
  URL =          "http://www.can.nl/Systems_and_Packages/Per_Purpose/General/Maple/mtn/mtn8.html",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Maple technical newsletter",
  journal-URL =  "http://web.mit.edu/maple/www/plibrary/mtn.html",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: fparith.bib
label: Brosgol:1992:ADA
author: Benjamin M. Brosgol and Robert I. Eachus and David E. Emery
title: An Ada Decimal Arithmetic Capability
journal: CrossTalk: The Journal of Defense Software Engineering
volume: 36
publisher: Software Technology Support Center
address: Hill AFB, Odgen, UT, USA
pages: 39--44
month: sep
monthnumber: 9
year: 1992
bibdate: Fri Nov 28 16:01:38 2003
bibsource: http://www.stsc.hill.af.mil/crosstalk/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 16:01:38 ???
URL: http://www.iste.uni-stuttgart.de/ps/AdaBasis/pal_1195/ada/ajpo/work-grp/ev-team/ev-info/summary.txt
keywords: decimal floating-point arithmetic
acknowledgement: ack-mfc
rawauthor: Benjamin M. Brosgol and Robert I. Eachus and David E. Emery
rawtitle: An {Ada} Decimal Arithmetic Capability
entry:
@Article{Brosgol:1992:ADA,
  author =       "Benjamin M. Brosgol and Robert I. Eachus and David E.
                 Emery",
  title =        "An {Ada} Decimal Arithmetic Capability",
  journal =      "CrossTalk: The Journal of Defense Software
                 Engineering",
  volume =       "36",
  publisher =    "Software Technology Support Center",
  address =      "Hill AFB, Odgen, UT, USA",
  month =        sep,
  year =         "1992",
  bibdate =      "Fri Nov 28 16:01:38 2003",
  bibsource =    "http://www.stsc.hill.af.mil/crosstalk/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.iste.uni-stuttgart.de/ps/AdaBasis/pal_1195/ada/ajpo/work-grp/ev-team/ev-info/summary.txt",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
  pagecount =    "8 (approx)",
  xxCODEN =      "none",
  xxISSN =       "none",
}


bibtype: inproceedings
filename: fparith.bib
label: Brosgol:1992:DAA
author: Benjamin M. Brosgol and Robert I. Eachus and David E. Emery
title: Decimal arithmetic in Ada
crossref: Katwijk:1992:AMT
pages: 138--149
year: 1992
DOI: https://doi.org/10.1007/3-540-55585-4_1
bibdate: Thu Aug 07 17:11:50 2008
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2008.08.07 17:11:50 ???
keywords: decimal floating-point arithmetic
acknowledgement: ack-nhfb
rawauthor: Benjamin M. Brosgol and Robert I. Eachus and David E. Emery
rawtitle: Decimal arithmetic in {Ada}
entry:
@InProceedings{Brosgol:1992:DAA,
  author =       "Benjamin M. Brosgol and Robert I. Eachus and David E.
                 Emery",
  title =        "Decimal arithmetic in {Ada}",
  crossref =     "Katwijk:1992:AMT",
  pages =        "138--149",
  year =         "1992",
  DOI =          "https://doi.org/10.1007/3-540-55585-4_1",
  bibdate =      "Thu Aug 07 17:11:50 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}


bibtype: inproceedings
filename: fparith.bib
label: Clarkson:1992:SED
author: K. L. Clarkson
title: Safe and effective determinant evaluation
crossref: IEEE:1992:ASF
pages: 387--395
year: 1992
bibdate: Tue Nov 22 05:54:53 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.11.22 05:54:53 ???
keywords: accurate floating-point summation
acknowledgement: ack-nhfb
rawauthor: K. L. Clarkson
rawtitle: Safe and effective determinant evaluation
entry:
@InProceedings{Clarkson:1992:SED,
  author =       "K. L. Clarkson",
  title =        "Safe and effective determinant evaluation",
  crossref =     "IEEE:1992:ASF",
  pages =        "387--395",
  year =         "1992",
  bibdate =      "Tue Nov 22 05:54:53 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation",
}


bibtype: article
filename: fparith.bib
label: Cosentino:1992:AMJ
author: R. J. Cosentino and J. J. Vaccaro
title: Adaptation of the Mactaggart and Jack Complex Multiplication Algorithm for Floating-Point Operators
journal: j-IEEE-TRANS-COMPUT
volume: 41
number: 10
pages: 1324--1326
month: oct
monthnumber: 10
year: 1992
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.166608
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 10:49:20 MDT 2011
bibtimestamp: 2011.07.07 10:49:20 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=166608
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
affiliation: Mitre Corp., Bedford, MA, USA
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
thesaurus: Digital arithmetic
rawauthor: R. J. Cosentino and J. J. Vaccaro
abstract:
With a suitable treatment of the exponents in the input operands, a hardware implementation of the Mactaggart and Jack fixed-point complex multiplication algorithm can also calculate a floating-point product with no loss in accuracy from the greater dynamic range of the floating-point inputs. This floating-point technique can be extended to any sum to two products operation, such as encountered in matrix multiplication and vector cross-products.

keywords:
Floating-point operators; Hardware implementation; Jack complex multiplication algorithm; Mactaggart complex multiplication; Matrix multiplication; Vector cross-products

rawabstract:
With a suitable treatment of the exponents in the input operands, a hardware implementation of the Mactaggart and Jack fixed-point complex multiplication algorithm can also calculate a floating-point product with no loss in accuracy from the greater dynamic range of the floating-point inputs. This floating-point technique can be extended to any sum to two products operation, such as encountered in matrix multiplication and vector cross-products.

rawtitle:
Adaptation of the {Mactaggart} and {Jack} Complex Multiplication Algorithm for Floating-Point Operators

entry:
@Article{Cosentino:1992:AMJ,
  author =       "R. J. Cosentino and J. J. Vaccaro",
  title =        "Adaptation of the {Mactaggart} and {Jack} Complex
                 Multiplication Algorithm for Floating-Point Operators",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "10",
  pages =        "1324--1326",
  month =        oct,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.166608",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 10:49:20 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=166608",
  abstract =     "With a suitable treatment of the exponents in the
                 input operands, a hardware implementation of the
                 Mactaggart and Jack fixed-point complex multiplication
                 algorithm can also calculate a floating-point product
                 with no loss in accuracy from the greater dynamic range
                 of the floating-point inputs. This floating-point
                 technique can be extended to any sum to two products
                 operation, such as encountered in matrix multiplication
                 and vector cross-products.",
  acknowledgement = ack-nhfb,
  affiliation =  "Mitre Corp., Bedford, MA, USA",
  ajournal =     "IEEE Trans. Comput.",
  classification = "C5230 (Digital arithmetic methods)",
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Floating-point operators; Hardware implementation;
                 Jack complex multiplication algorithm; Mactaggart
                 complex multiplication; Matrix multiplication; Vector
                 cross-products",
  summary =      "With a suitable treatment of the exponents in the
                 input operands, a hardware implementation of the
                 Mactaggart and Jack fixed-point complex multiplication
                 algorithm can also calculate a floating-point product
                 with no loss in accuracy from the greater \ldots{}",
  thesaurus =    "Digital arithmetic",
}


bibtype: article
filename: fparith.bib
label: Dao-Trong:1992:SCI
author: S. Dao-Trong and K. Helwig
title: A single-chip IBM System / 390 floating-point processor in CMOS
journal: j-IBM-JRD
volume: 36
number: 4
pages: 733--749
month: jul
monthnumber: 7
year: 1992
CODEN: IBMJAE
ISSN: 0018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)
ISSNL: 0018-8646 OR 00188646
bibdate: Wed Sep 7 22:32:42 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.07 22:32:42 ???
fjournal: IBM Journal of Research and Development
acknowledgement: ack-nj
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520
rawauthor: S. Dao-Trong and K. Helwig
rawtitle: A single-chip {IBM System}\slash 390 floating-point processor in {CMOS}
entry:
@Article{Dao-Trong:1992:SCI,
  author =       "S. Dao-Trong and K. Helwig",
  title =        "A single-chip {IBM System}\slash 390 floating-point
                 processor in {CMOS}",
  journal =      j-IBM-JRD,
  volume =       "36",
  number =       "4",
  pages =        "733--749",
  month =        jul,
  year =         "1992",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Wed Sep 7 22:32:42 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}


bibtype: article
filename: fparith.bib
label: Dao-Trong:1992:SIS
author: S. Dao-Trong and K. Helwig
title: A single-chip IBM System / 390 floating-point processor in CMOS
journal: j-IBM-JRD
volume: 36
number: 4
pages: 733--750
month: jul
monthnumber: 7
year: 1992
CODEN: IBMJAE
ISSN: 0018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)
ISSNL: 0018-8646 OR 00188646
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: IBM Journal of Research and Development
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520
rawauthor: S. Dao-Trong and K. Helwig
rawtitle: A single-chip {IBM} System\slash 390 floating-point processor in {CMOS}
entry:
@Article{Dao-Trong:1992:SIS,
  author =       "S. Dao-Trong and K. Helwig",
  title =        "A single-chip {IBM} System\slash 390 floating-point
                 processor in {CMOS}",
  journal =      j-IBM-JRD,
  volume =       "36",
  number =       "4",
  pages =        "733--750",
  month =        jul,
  year =         "1992",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}


bibtype: article
filename: fparith.bib
label: DaoTrong:1992:SIS
author: S. Dao-Trong and K. Helwig
title: A single-chip IBM system / 390 floating-point processor in CMOS
journal: j-IBM-JRD
volume: 36
number: 4
pages: 733--749
month: jul
monthnumber: 7
year: 1992
CODEN: IBMJAE
ISSN: 0018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)
ISSNL: 0018-8646 OR 00188646
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: IBM Journal of Research and Development
acknowledgement: ack-nhfb
affiliation: IBM Germany, Boeblingen, Germany
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520
rawauthor: S. Dao-Trong and K. Helwig
rawtitle: A single-chip {IBM} system\slash 390 floating-point processor in {CMOS}
abstract:
A floating-point processor with the IBM System/390 architecture is implemented in one CMOS VLSI chip containing over 70000 cells (equivalent inverters), using a transistor channel length of 0.5 mu m. All floating-point instructions are hard-wired, including the binary integer multiplications. The chip is implemented in a 1- mu m technology with three layers of metal. All circuits are realized in standard cells except for a floating-point register and a multiplier array macro, which are custom designed to save chip area. Instructions are performed in a five-stage pipeline with a maximum operating frequency of 37 MHz. The chip measures 12.7 mm*12.7 mm, and dissipates 2 W. It is part of the chip set which forms the core of the IBM Enterprise System/9000 Type 9221 entry-level models.

keywords:
37 MHz; Binary integer multiplications; Chip set; CMOS; Equivalent inverters; Five-stage pipeline; IBM Enterprise System/9000; Single-chip IBM system/390 floating-point processor; Transistor channel length

thesaurus:
CMOS integrated circuits; Digital arithmetic; Equipment evaluation; IBM computers; Microprocessor chips

rawabstract:
A floating-point processor with the IBM System/390 architecture is implemented in one CMOS VLSI chip containing over 70000 cells (equivalent inverters), using a transistor channel length of 0.5 mu m. All floating-point instructions are hard-wired, including the binary integer multiplications. The chip is implemented in a 1- mu m technology with three layers of metal. All circuits are realized in standard cells except for a floating-point register and a multiplier array macro, which are custom designed to save chip area. Instructions are performed in a five-stage pipeline with a maximum operating frequency of 37 MHz. The chip measures 12.7 mm*12.7 mm, and dissipates 2 W. It is part of the chip set which forms the core of the IBM Enterprise System/9000 Type 9221 entry-level models.

entry:
@Article{DaoTrong:1992:SIS,
  author =       "S. Dao-Trong and K. Helwig",
  title =        "A single-chip {IBM} system\slash 390 floating-point
                 processor in {CMOS}",
  journal =      j-IBM-JRD,
  volume =       "36",
  number =       "4",
  pages =        "733--749",
  month =        jul,
  year =         "1992",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A floating-point processor with the IBM System/390
                 architecture is implemented in one CMOS VLSI chip
                 containing over 70000 cells (equivalent inverters),
                 using a transistor channel length of 0.5 mu m. All
                 floating-point instructions are hard-wired, including
                 the binary integer multiplications. The chip is
                 implemented in a 1- mu m technology with three layers
                 of metal. All circuits are realized in standard cells
                 except for a floating-point register and a multiplier
                 array macro, which are custom designed to save chip
                 area. Instructions are performed in a five-stage
                 pipeline with a maximum operating frequency of 37 MHz.
                 The chip measures 12.7 mm*12.7 mm, and dissipates 2 W.
                 It is part of the chip set which forms the core of the
                 IBM Enterprise System/9000 Type 9221 entry-level
                 models.",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM Germany, Boeblingen, Germany",
  classification = "B1265F (Microprocessors and microcomputers); B2570D
                 (CMOS integrated circuits); C5130 (Microprocessor
                 chips); C5230 (Digital arithmetic methods)",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  keywords =     "37 MHz; Binary integer multiplications; Chip set;
                 CMOS; Equivalent inverters; Five-stage pipeline; IBM
                 Enterprise System/9000; Single-chip IBM system/390
                 floating-point processor; Transistor channel length",
  numericalindex = "Frequency 3.7E+07 Hz",
  thesaurus =    "CMOS integrated circuits; Digital arithmetic;
                 Equipment evaluation; IBM computers; Microprocessor
                 chips",
}


bibtype: mastersthesis
filename: fparith.bib
label: Daumas:1992:BIR
author: Marc Daumas
title: Basis for the implementation of a reliable dot product
type: Master's Thesis
school: Southern Methodist University
address: Dallas, Texas
pages: 733--749
year: 1992
bibdate: Wed Nov 24 12:42:59 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.24 12:42:59 ???
acknowledgement: ack-nhfb
rawauthor: Marc Daumas
rawtitle: Basis for the implementation of a reliable dot product
entry:
@MastersThesis{Daumas:1992:BIR,
  author =       "Marc Daumas",
  title =        "Basis for the implementation of a reliable dot
                 product",
  type =         "{Master}'s Thesis",
  school =       "Southern Methodist University",
  address =      "Dallas, Texas",
  year =         "1992",
  bibdate =      "Wed Nov 24 12:42:59 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Davarakis:1992:PPA
author: C. T. Davarakis and D. G. Maritsas
title: A Probabilistic Parallel Associative Search and Query Set of Algorithms
journal: j-J-PAR-DIST-COMP
volume: 14
number: 1
pages: 37--49
month: jan
monthnumber: 1
year: 1992
CODEN: JPDCER
ISSN: 0743-7315 (print), 1096-0848 (electronic) OR 07437315 (print), 10960848 (electronic)
ISSNL: 0743-7315 OR 07437315
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: Computer Technology Inst
affiliationaddress: Patras, Greece
corpsource: Department of Comput. Eng., Comput. Technol. Inst., Patras, Greece
journalURL: http://www.sciencedirect.com/science/journal/07437315
journalabr: J Parallel Distrib Comput
treatment: A Application; P Practical
rawauthor: C. T. Davarakis and D. G. Maritsas
rawtitle: A Probabilistic Parallel Associative Search and Query Set of Algorithms
keywords:
Algorithms; arithmetic applications; Associative searching; Computer Programming; computing; Data Storage, Digital--Associative; digital arithmetic; extrema algorithm; extrema queries; generic associative process; heuristic programming; heuristics; high performance systems; Mathematical Techniques--Heuristic; mathematics; multilayer associative process; parallel algorithms; parallel associative search; parallel threshold; performance evaluation; Primitive algorithms; primitive algorithms; probabilistic; Probability; query set of algorithms; symbol manipulation; symbolic applications; threshold searches; time performance

entry:
@Article{Davarakis:1992:PPA,
  author =       "C. T. Davarakis and D. G. Maritsas",
  title =        "A Probabilistic Parallel Associative Search and Query
                 Set of Algorithms",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "14",
  number =       "1",
  pages =        "37--49",
  month =        jan,
  year =         "1992",
  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 =  "Computer Technology Inst",
  affiliationaddress = "Patras, Greece",
  classification = "723; 921; 922; C1230 (Artificial intelligence);
                 C4240P (Parallel programming and algorithm theory);
                 C5470 (Performance evaluation and testing); C7310
                 (Mathematics)",
  corpsource =   "Department of Comput. Eng., Comput. Technol. Inst.,
                 Patras, Greece",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "Algorithms; arithmetic applications; Associative
                 searching; Computer Programming; computing; Data
                 Storage, Digital--Associative; digital arithmetic;
                 extrema algorithm; extrema queries; generic associative
                 process; heuristic programming; heuristics; high
                 performance systems; Mathematical
                 Techniques--Heuristic; mathematics; multilayer
                 associative process; parallel algorithms; parallel
                 associative search; parallel threshold; performance
                 evaluation; Primitive algorithms; primitive algorithms;
                 probabilistic; Probability; query set of algorithms;
                 symbol manipulation; symbolic applications; threshold
                 searches; time performance",
  treatment =    "A Application; P Practical",
}


bibtype: inproceedings
filename: fparith.bib
label: Dawid:1992:BSC
author: H. Dawid and G. Fettweis
title: Bit-level systolic carry-save array division
crossref: IEEE:1992:GCG
pages: 484--488 vol.1
year: 1992
bibdate: Tue Dec 12 09:27:13 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.12 09:27:13 MST
acknowledgement: ack-nhfb
affiliation: Aachen University of Technol., Germany
thesaurus: Digital arithmetic; Systolic arrays
rawauthor: H. Dawid and G. Fettweis
rawtitle: Bit-level systolic carry-save array division
abstract:
A bit-level systolic carry-save division array that allows bit-level pipelining, just as for carry-save array multipliers, is presented. This architecture leads to very fast, efficient and regular division implementations as needed in digital signal processing (DSP) applications such as speech processing or cryptography. The architecture is very well suited for integer division as well as for the division of normalized fixed-point mantissas used in floating-point number system implementations.

keywords:
Bit-level pipelining; Carry-save array multipliers; Cryptography; Digital signal processing; DSP; Floating-point number system; Integer division; Normalized fixed-point mantissas; Speech processing; Systolic carry-save array division

rawabstract:
A bit-level systolic carry-save division array that allows bit-level pipelining, just as for carry-save array multipliers, is presented. This architecture leads to very fast, efficient and regular division implementations as needed in digital signal processing (DSP) applications such as speech processing or cryptography. The architecture is very well suited for integer division as well as for the division of normalized fixed-point mantissas used in floating-point number system implementations.

entry:
@InProceedings{Dawid:1992:BSC,
  author =       "H. Dawid and G. Fettweis",
  title =        "Bit-level systolic carry-save array division",
  crossref =     "IEEE:1992:GCG",
  pages =        "484--488 vol.1",
  year =         "1992",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A bit-level systolic carry-save division array that
                 allows bit-level pipelining, just as for carry-save
                 array multipliers, is presented. This architecture
                 leads to very fast, efficient and regular division
                 implementations as needed in digital signal processing
                 (DSP) applications such as speech processing or
                 cryptography. The architecture is very well suited for
                 integer division as well as for the division of
                 normalized fixed-point mantissas used in floating-point
                 number system implementations.",
  acknowledgement = ack-nhfb,
  affiliation =  "Aachen University of Technol., Germany",
  classification = "B1265B (Logic circuits); C5130 (Microprocessor
                 chips); C5230 (Digital arithmetic methods); C5260
                 (Digital signal processing)",
  keywords =     "Bit-level pipelining; Carry-save array multipliers;
                 Cryptography; Digital signal processing; DSP;
                 Floating-point number system; Integer division;
                 Normalized fixed-point mantissas; Speech processing;
                 Systolic carry-save array division",
  thesaurus =    "Digital arithmetic; Systolic arrays",
}


bibtype: article
filename: fparith.bib
label: Dawson:1992:RLS
author: Jeffrey Dawson and Mary Payne and Craig Schaffert
title: The Role of LIA-1 in Software Portability
journal: j-SIGNUM
volume: 27
number: 4
pages: 9--12
month: oct
monthnumber: 10
year: 1992
CODEN: SNEWD6
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Tue Apr 12 07:50:22 MDT 2005
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.04.12 07:50:22 MDT
fjournal: ACM SIGNUM Newsletter
acknowledgement: ack-nhfb
affiliation: Digital Equipment Corp., Maynard, MA, USA
journalURL: https://dl.acm.org/loi/signum
thesaurus: Mathematics computing; Software portability; Standards
rawauthor: Jeffrey Dawson and Mary Payne and Craig Schaffert
rawtitle: The Role of {LIA-1} in Software Portability
note:
LIA is now an International Standard, ISO/IEC 10967-1:1994; it is ``92 pages of small print, densely mathematical, not counting 8 pages of front matter, and it is not available electronically.'' Its adoption has been rather controversial.

abstract:
The second committee draft of language independent arithmetic-Part 1: Integer and floating point arithmetic is now available. This document was formerly called the Language Compatible Arithmetic Standard (LCAS) and is now referred to as LIA-1. This draft was prepared by ISO/IEC JTC1/SC22/WG11, with assistance from standards committees in several countries. The authors explain the goals of the standard and methods for achieving those goals. They present them to clear up previous misunderstandings, misconceptions, and misrepresentations of the purpose of the standard. (0 Refs.)

keywords:
Floating point arithmetic; Integer arithmetic; ISO/IEC JTC1/SC22/WG11; Language independent arithmetic; LIA-1; Software portability; Standard

rawabstract:
The second committee draft of language independent arithmetic-Part 1: Integer and floating point arithmetic is now available. This document was formerly called the Language Compatible Arithmetic Standard (LCAS) and is now referred to as LIA-1. This draft was prepared by ISO/IEC JTC1/SC22/WG11, with assistance from standards committees in several countries. The authors explain the goals of the standard and methods for achieving those goals. They present them to clear up previous misunderstandings, misconceptions, and misrepresentations of the purpose of the standard. (0 Refs.)

rawnote:
LIA is now an International Standard, ISO/IEC 10967-1:1994; it is ``92 pages of small print, densely mathematical, not counting 8 pages of front matter, and it is not available electronically.'' Its adoption has been rather controversial.

entry:
@Article{Dawson:1992:RLS,
  author =       "Jeffrey Dawson and Mary Payne and Craig Schaffert",
  title =        "The Role of {LIA-1} in Software Portability",
  journal =      j-SIGNUM,
  volume =       "27",
  number =       "4",
  pages =        "9--12",
  month =        oct,
  year =         "1992",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:22 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "LIA is now an International Standard, ISO/IEC
                 10967-1:1994; it is ``92 pages of small print, densely
                 mathematical, not counting 8 pages of front matter, and
                 it is not available electronically.'' Its adoption has
                 been rather controversial.",
  abstract =     "The second committee draft of language independent
                 arithmetic-Part 1: Integer and floating point
                 arithmetic is now available. This document was formerly
                 called the Language Compatible Arithmetic Standard
                 (LCAS) and is now referred to as LIA-1. This draft was
                 prepared by ISO/IEC JTC1/SC22/WG11, with assistance
                 from standards committees in several countries. The
                 authors explain the goals of the standard and methods
                 for achieving those goals. They present them to clear
                 up previous misunderstandings, misconceptions, and
                 misrepresentations of the purpose of the standard. (0
                 Refs.)",
  acknowledgement = ack-nhfb,
  affiliation =  "Digital Equipment Corp., Maynard, MA, USA",
  classification = "C0310F (Software development management); C6110B
                 (Software engineering techniques); C7310
                 (Mathematics)",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "Floating point arithmetic; Integer arithmetic; ISO/IEC
                 JTC1/SC22/WG11; Language independent arithmetic; LIA-1;
                 Software portability; Standard",
  thesaurus =    "Mathematics computing; Software portability;
                 Standards",
}


bibtype: book
filename: fparith.bib
label: DEC:1992:AAH
author: Digital Equipment Corporation
title: Alpha Architecture Handbook
publisher: pub-DP
address: pub-DP:adr
pages: 9--12
year: 1992
bibdate: Mon Jan 18 15:08:40 1993
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1993.01.18 15:08:40 ???
acknowledgement: ack-nhfb
rawauthor: Digital Equipment Corporation
rawtitle: {Alpha} Architecture Handbook
entry:
@Book{DEC:1992:AAH,
  author =       "Digital Equipment Corporation",
  title =        "{Alpha} Architecture Handbook",
  publisher =    pub-DP,
  address =      pub-DP:adr,
  year =         "1992",
  bibdate =      "Mon Jan 18 15:08:40 1993",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: fparith.bib
label: Demmel:1992:LWN
author: James Demmel
title: LAPACK working note 49 draft: a specification for floating point parallel prefix
type: Technical report
number: CS-92-167
institution: University of Tennessee, Computer Science Dept.
address: Knoxville, TN, USA
pages: 8 + 1
month: may
monthnumber: 5
year: 1992
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Linear algebraic groups.
acknowledgement: ack-nhfb
rawauthor: James Demmel
rawtitle: {LAPACK} working note 49 draft: a specification for floating point parallel prefix
abstract:
Parallel prefix is a useful operation for various linear algebra operations, including solving bidiagonal systems of equations and finding the eigenvalues of a symmetric tridiagonal matrix. However, the simplest implementations of parallel prefix for the operations of scalar floating point add and scalar floating point multiply are inadequate to solve these important problems. This is because they are too susceptible to over/underflow, and because they apparently cannot solve the general two term recurrence needed to find eigenvalues. In this note we propose a specification for parallel prefix operations overcoming these drawbacks.

rawabstract:
Parallel prefix is a useful operation for various linear algebra operations, including solving bidiagonal systems of equations and finding the eigenvalues of a symmetric tridiagonal matrix. However, the simplest implementations of parallel prefix for the operations of scalar floating point add and scalar floating point multiply are inadequate to solve these important problems. This is because they are too susceptible to over/underflow, and because they apparently cannot solve the general two term recurrence needed to find eigenvalues. In this note we propose a specification for parallel prefix operations overcoming these drawbacks.

entry:
@TechReport{Demmel:1992:LWN,
  author =       "James Demmel",
  title =        "{LAPACK} working note 49 draft: a specification for
                 floating point parallel prefix",
  type =         "Technical report",
  number =       "CS-92-167",
  institution =  "University of Tennessee, Computer Science Dept.",
  address =      "Knoxville, TN, USA",
  pages =        "8 + 1",
  month =        may,
  year =         "1992",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Parallel prefix is a useful operation for various
                 linear algebra operations, including solving bidiagonal
                 systems of equations and finding the eigenvalues of a
                 symmetric tridiagonal matrix. However, the simplest
                 implementations of parallel prefix for the operations
                 of scalar floating point add and scalar floating point
                 multiply are inadequate to solve these important
                 problems. This is because they are too susceptible to
                 over/underflow, and because they apparently cannot
                 solve the general two term recurrence needed to find
                 eigenvalues. In this note we propose a specification
                 for parallel prefix operations overcoming these
                 drawbacks.",
  acknowledgement = ack-nhfb,
  keywords =     "Linear algebraic groups.",
}


bibtype: techreport
filename: fparith.bib
label: Demmel:1992:SFP
author: J. Demmel
title: A Specification for Floating Point Parallel Prefix
type: LAPACK Working Note
number: 49
institution: inst-UT-CS
address: inst-UT-CS:adr
pages: 8 + 1
month: may
monthnumber: 5
year: 1992
bibdate: Fri Apr 22 17:06:37 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.04.22 17:06:37 ???
note: UT-CS-92-167, May 1992.
URL: http://www.netlib.org/lapack/lawns/lawn49.ps; http://www.netlib.org/lapack/lawnspdf/lawn49.pdf
acknowledgement: ack-nhfb
rawauthor: J. Demmel
rawnote: UT-CS-92-167, May 1992.
rawtitle: A Specification for Floating Point Parallel Prefix
entry:
@TechReport{Demmel:1992:SFP,
  author =       "J. Demmel",
  title =        "A Specification for Floating Point Parallel Prefix",
  type =         "LAPACK Working Note",
  number =       "49",
  institution =  inst-UT-CS,
  address =      inst-UT-CS:adr,
  month =        may,
  year =         "1992",
  bibdate =      "Fri Apr 22 17:06:37 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "UT-CS-92-167, May 1992.",
  URL =          "http://www.netlib.org/lapack/lawns/lawn49.ps;
                 http://www.netlib.org/lapack/lawnspdf/lawn49.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Devine:1992:RTT
author: M. L. Devine
title: Real time trigonometric function evaluation
journal: j-MICROPROC-MICROSYS
volume: 16
number: 8
pages: 417--425
month: aug
monthnumber: 8
year: 1992
CODEN: MIMID5
ISSN: 0141-9331 (print), 1872-9436 (electronic) OR 01419331 (print), 18729436 (electronic)
ISSNL: 0141-9331 OR 01419331
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
bibtimestamp: 1994.09.01 10:16:09 ???
fjournal: Microprocessors and Microsystems
acknowledgement: ack-nj
rawauthor: M. L. Devine
rawtitle: Real time trigonometric function evaluation
entry:
@Article{Devine:1992:RTT,
  author =       "M. L. Devine",
  title =        "Real time trigonometric function evaluation",
  journal =      j-MICROPROC-MICROSYS,
  volume =       "16",
  number =       "8",
  pages =        "417--425",
  month =        aug,
  year =         "1992",
  CODEN =        "MIMID5",
  ISSN =         "0141-9331 (print), 1872-9436 (electronic)",
  ISSN-L =       "0141-9331",
  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",
  acknowledgement = ack-nj,
  fjournal =     "Microprocessors and Microsystems",
}


bibtype: article
filename: fparith.bib
label: Dimauro:1992:NMF
author: G. Dimauro and S. Impedovo and G. Pirlo
title: A new magnitude function for fast numbers comparison in the residue number system
journal: j-MICROPROC-MICROPROG
volume: 35
number: 1--2
pages: 97--104
month: sep
monthnumber: 9
year: 1992
CODEN: MMICDT
DOI: https://doi.org/10.1016/0165-6074(92)90300-V
ISSN: 0165-6074 (print), 1878-7061 (electronic) OR 01656074 (print), 18787061 (electronic)
ISSNL: 0165-6074 OR 01656074
bibdate: Thu Nov 18 09:52:10 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.11.18 09:52:10 ???
fjournal: Microprocessing and Microprogramming
acknowledgement: ack-nhfb
rawauthor: G. Dimauro and S. Impedovo and G. Pirlo
rawtitle: A new magnitude function for fast numbers comparison in the residue number system
abstract:
In this paper a new magnitude function, called the `diagonal function', has been defined from a Residue Number System to the integers. The `diagonal function' provides an efficient technique for fast magnitude comparison of numbers in the residue representation. The superiority of this technique with respect to the approaches based on the Chinese Remainder Theorem and on the Mixed Radix Transformation is shown.

rawabstract:
In this paper a new magnitude function, called the `diagonal function', has been defined from a Residue Number System to the integers. The `diagonal function' provides an efficient technique for fast magnitude comparison of numbers in the residue representation. The superiority of this technique with respect to the approaches based on the Chinese Remainder Theorem and on the Mixed Radix Transformation is shown.

entry:
@Article{Dimauro:1992:NMF,
  author =       "G. Dimauro and S. Impedovo and G. Pirlo",
  title =        "A new magnitude function for fast numbers comparison
                 in the residue number system",
  journal =      j-MICROPROC-MICROPROG,
  volume =       "35",
  number =       "1--2",
  pages =        "97--104",
  month =        sep,
  year =         "1992",
  CODEN =        "MMICDT",
  DOI =          "https://doi.org/10.1016/0165-6074(92)90300-V",
  ISSN =         "0165-6074 (print), 1878-7061 (electronic)",
  ISSN-L =       "0165-6074",
  bibdate =      "Thu Nov 18 09:52:10 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In this paper a new magnitude function, called the
                 `diagonal function', has been defined from a Residue
                 Number System to the integers. The `diagonal function'
                 provides an efficient technique for fast magnitude
                 comparison of numbers in the residue representation.
                 The superiority of this technique with respect to the
                 approaches based on the Chinese Remainder Theorem and
                 on the Mixed Radix Transformation is shown.",
  acknowledgement = ack-nhfb,
  fjournal =     "Microprocessing and Microprogramming",
}


bibtype: mastersthesis
filename: fparith.bib
label: Du:1992:CAB
author: Sihai Du
title: Cellular automata based floating-point adder and multiplier with a single transition rule
type: Thesis (M.S.C.E.)
school: Wright State University
address: Dayton, OH, USA
pages: ix + 68
year: 1992
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Cellular automata --- Research.; Computer Simulation.; Floating-point arithmetic --- Research.
acknowledgement: ack-nhfb
rawauthor: Sihai Du
rawtitle: Cellular automata based floating-point adder and multiplier with a single transition rule
entry:
@MastersThesis{Du:1992:CAB,
  author =       "Sihai Du",
  title =        "Cellular automata based floating-point adder and
                 multiplier with a single transition rule",
  type =         "Thesis ({M.S.C.E.})",
  school =       "Wright State University",
  address =      "Dayton, OH, USA",
  pages =        "ix + 68",
  year =         "1992",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Cellular automata --- Research.; Computer Simulation.;
                 Floating-point arithmetic --- Research.",
}


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


bibtype: inproceedings
filename: fparith.bib
label: Duprat:1992:DOF
author: J. Duprat and M. Fiallos-Aguilar and Jean-Michel Muller and H. J. Yeh
title: Delays of on-line floating point operators in borrow-save representation
crossref: Quinton:1992:APV
pages: 273--278
year: 1992
bibdate: Wed Dec 13 13:13:34 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.13 13:13:34 MST
acknowledgement: ack-nhfb
affiliation: Ecole Normale Superieure de Lyon, France
thesaurus: Delays; Digital arithmetic; Pipeline processing
rawauthor: J. Duprat and M. Fiallos-Aguilar and Jean-Michel Muller and H. J. Yeh
rawtitle: Delays of on-line floating point operators in borrow-save representation
abstract:
On-line computation using redundant notations to represent numbers is an interesting field of computer arithmetic. In these systems, different operators can operate together in a digit level pipelining mode. In integer or fixed-point format, implementations of the main operations have been proposed. This paper focuses on a floating point format. The authors show that, more so in addition than in multiplication, critical loss of information due to the variation of the length of the mantissas can be avoided by partial normalizations. Furthermore, these normalizations do not break the circulation of the digit though they do delay the operations even more.

keywords:
Borrow-save representation; Computer arithmetic; Delays; Digit level pipelining mode; Floating point format; Mantissas; On-line floating point operators; Partial normalizations; Redundant notations

rawabstract:
On-line computation using redundant notations to represent numbers is an interesting field of computer arithmetic. In these systems, different operators can operate together in a digit level pipelining mode. In integer or fixed-point format, implementations of the main operations have been proposed. This paper focuses on a floating point format. The authors show that, more so in addition than in multiplication, critical loss of information due to the variation of the length of the mantissas can be avoided by partial normalizations. Furthermore, these normalizations do not break the circulation of the digit though they do delay the operations even more.

entry:
@InProceedings{Duprat:1992:DOF,
  author =       "J. Duprat and M. Fiallos-Aguilar and Jean-Michel
                 Muller and H. J. Yeh",
  title =        "Delays of on-line floating point operators in
                 borrow-save representation",
  crossref =     "Quinton:1992:APV",
  pages =        "273--278",
  year =         "1992",
  bibdate =      "Wed Dec 13 13:13:34 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "On-line computation using redundant notations to
                 represent numbers is an interesting field of computer
                 arithmetic. In these systems, different operators can
                 operate together in a digit level pipelining mode. In
                 integer or fixed-point format, implementations of the
                 main operations have been proposed. This paper focuses
                 on a floating point format. The authors show that, more
                 so in addition than in multiplication, critical loss of
                 information due to the variation of the length of the
                 mantissas can be avoided by partial normalizations.
                 Furthermore, these normalizations do not break the
                 circulation of the digit though they do delay the
                 operations even more.",
  acknowledgement = ack-nhfb,
  affiliation =  "Ecole Normale Superieure de Lyon, France",
  classification = "C5230 (Digital arithmetic methods); C5440
                 (Multiprocessor systems and techniques)",
  keywords =     "Borrow-save representation; Computer arithmetic;
                 Delays; Digit level pipelining mode; Floating point
                 format; Mantissas; On-line floating point operators;
                 Partial normalizations; Redundant notations",
  thesaurus =    "Delays; Digital arithmetic; Pipeline processing",
}


bibtype: article
filename: fparith.bib
label: Duprat:1992:SPF
author: J. Duprat and M. Fiallos Aguilar
journal: j-LECT-NOTES-COMP-SCI
number: 634
pages: 707--712
year: 1992
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: J. Duprat and M. Fiallos Aguilar
title:
On the Simulation of Pipelining of Fully Digit On-Line Floating-Point Adder Networks on Massively Parallel Computers

rawtitle:
On the Simulation of Pipelining of Fully Digit On-Line Floating-Point Adder Networks on Massively Parallel Computers

entry:
@Article{Duprat:1992:SPF,
  author =       "J. Duprat and M. Fiallos Aguilar",
  title =        "On the Simulation of Pipelining of Fully Digit On-Line
                 Floating-Point Adder Networks on Massively Parallel
                 Computers",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "??",
  number =       "634",
  pages =        "707--712",
  year =         "1992",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Ercegovac:1992:FRC
author: M. D. Ercegovac and T. Lang
title: On-the-fly rounding [computing arithmetic]
journal: j-IEEE-TRANS-COMPUT
volume: 41
number: 12
pages: 1497--1503
month: dec
monthnumber: 12
year: 1992
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.214659
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 10:49:21 MDT 2011
bibtimestamp: 2011.07.07 10:49:21 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=214659
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: M. D. Ercegovac and T. Lang
rawtitle: On-the-fly rounding [computing arithmetic]
abstract:
In implementations of operations based on digit-recurrence algorithms such as division, left-to-right multiplication and square root, the result is obtained in digit-serial form, from most significant digit to least significant. To reduce the complexity of the result-digit selection and allow the use of redundant addition, the result-digit has values from a signed-digit set. As a consequence, the result has to be converted to conventional representation, which can be done on-the-fly as the digits are produced, without the use of a carry-propagate adder. The authors describe three ways to modify this conversion process so that the result is rounded. The resulting operation is fast because no carry-propagate addition is needed. The schemes described apply also to online arithmetic operations.

rawabstract:
In implementations of operations based on digit-recurrence algorithms such as division, left-to-right multiplication and square root, the result is obtained in digit-serial form, from most significant digit to least significant. To reduce the complexity of the result-digit selection and allow the use of redundant addition, the result-digit has values from a signed-digit set. As a consequence, the result has to be converted to conventional representation, which can be done on-the-fly as the digits are produced, without the use of a carry-propagate adder. The authors describe three ways to modify this conversion process so that the result is rounded. The resulting operation is fast because no carry-propagate addition is needed. The schemes described apply also to online arithmetic operations.

entry:
@Article{Ercegovac:1992:FRC,
  author =       "M. D. Ercegovac and T. Lang",
  title =        "On-the-fly rounding [computing arithmetic]",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "12",
  pages =        "1497--1503",
  month =        dec,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.214659",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 10:49:21 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=214659",
  abstract =     "In implementations of operations based on
                 digit-recurrence algorithms such as division,
                 left-to-right multiplication and square root, the
                 result is obtained in digit-serial form, from most
                 significant digit to least significant. To reduce the
                 complexity of the result-digit selection and allow the
                 use of redundant addition, the result-digit has values
                 from a signed-digit set. As a consequence, the result
                 has to be converted to conventional representation,
                 which can be done on-the-fly as the digits are
                 produced, without the use of a carry-propagate adder.
                 The authors describe three ways to modify this
                 conversion process so that the result is rounded. The
                 resulting operation is fast because no carry-propagate
                 addition is needed. The schemes described apply also to
                 online arithmetic operations.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Fagin:1992:LIM
author: Barry S. Fagin
title: Large Integer Multiplication on Hypercubes
journal: j-J-PAR-DIST-COMP
volume: 14
number: 4
pages: 426--430
month: apr
monthnumber: 4
year: 1992
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: Thayer Sch. of Eng., Dartmouth Coll., Hanover, NH, USA
journalURL: http://www.sciencedirect.com/science/journal/07437315
treatment: T Theoretical or Mathematical
rawauthor: Barry S. Fagin
rawtitle: Large Integer Multiplication on Hypercubes
keywords:
Connection Machine; digital arithmetic; Fermat Number Transform; hypercube networks; hypercubes; integer multiplication; parallel algorithms; polynomial transforms; transforms

entry:
@Article{Fagin:1992:LIM,
  author =       "Barry S. Fagin",
  title =        "Large Integer Multiplication on Hypercubes",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "14",
  number =       "4",
  pages =        "426--430",
  month =        apr,
  year =         "1992",
  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 = "C4230M (Multiprocessor interconnection); C4240P
                 (Parallel programming and algorithm theory); C5230
                 (Digital arithmetic methods)",
  corpsource =   "Thayer Sch. of Eng., Dartmouth Coll., Hanover, NH,
                 USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  keywords =     "Connection Machine; digital arithmetic; Fermat Number
                 Transform; hypercube networks; hypercubes; integer
                 multiplication; parallel algorithms; polynomial
                 transforms; transforms",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: fparith.bib
label: Filanovsky:1992:SCA
author: I. M. Filanovsky and H. P. Baltes
title: Simple CMOS analog square-rooting and squaring circuits
journal: j-IEEE-TRANS-CIRCUITS-SYST-I-FUNDAM-THEORY-APPL
volume: 39
number: 4
pages: 312--315
month: apr
monthnumber: 4
year: 1992
CODEN: ITCAEX
ISSN: 1057-7122 (print), 1558-1268 (electronic) OR 10577122 (print), 15581268 (electronic)
ISSNL: 1057-7122 OR 10577122
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
fjournal: IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=81
rawauthor: I. M. Filanovsky and H. P. Baltes
rawtitle: Simple {CMOS} analog square-rooting and squaring circuits
entry:
@Article{Filanovsky:1992:SCA,
  author =       "I. M. Filanovsky and H. P. Baltes",
  title =        "Simple {CMOS} analog square-rooting and squaring
                 circuits",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-I-FUNDAM-THEORY-APPL,
  volume =       "39",
  number =       "4",
  pages =        "312--315",
  month =        apr,
  year =         "1992",
  CODEN =        "ITCAEX",
  ISSN =         "1057-7122 (print), 1558-1268 (electronic)",
  ISSN-L =       "1057-7122",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems I:
                 Fundamental Theory and Applications",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=81",
  summary =      "Two closely related CMOS circuits are described. In
                 the first circuit, the input signal is a current, and
                 the output is a voltage proportional to the square root
                 of input current. In the second circuit, the input is a
                 voltage, and the output is the \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Fujii:1992:FCL
author: H. Fujii and C. Hori and T. Takada and N. Hatanaka and T. Demura and G. Ootomo
title: A Floating-Point Cell Library and a 100-MFLOPS Image Signal Processor
journal: j-IEEE-J-SOLID-STATE-CIRCUITS
volume: 27
number: 7
pages: 1080--1088
month: jul
monthnumber: 7
year: 1992
CODEN: IJSCBC
ISSN: 0018-9200 (print), 1558-173X (electronic) OR 00189200 (print), 1558173X (electronic)
ISSNL: 0018-9200 OR 00189200
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
fjournal: IEEE Journal of Solid-State Circuits
acknowledgement: ack-nhfb
rawauthor: H. Fujii and C. Hori and T. Takada and N. Hatanaka and T. Demura and G. Ootomo
rawtitle: A Floating-Point Cell Library and a {100-MFLOPS} Image Signal Processor
entry:
@Article{Fujii:1992:FCL,
  author =       "H. Fujii and C. Hori and T. Takada and N. Hatanaka and
                 T. Demura and G. Ootomo",
  title =        "A Floating-Point Cell Library and a {100-MFLOPS} Image
                 Signal Processor",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "27",
  number =       "7",
  pages =        "1080--1088",
  month =        jul,
  year =         "1992",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
}


bibtype: article
filename: fparith.bib
label: Fujii:1992:FPC
author: H. Fujii and C. Hori and T. Takada and N. Hatanaka and T. Demura and G. Ootomo
title: A floating-point cell library and a 100-Mflops image signal processor
journal: j-IEEE-J-SOLID-STATE-CIRCUITS
volume: 27
number: 7
pages: 1080--1088
month: jul
monthnumber: 7
year: 1992
CODEN: IJSCBC
ISSN: 0018-9200 (print), 1558-173X (electronic) OR 00189200 (print), 1558173X (electronic)
ISSNL: 0018-9200 OR 00189200
bibdate: Sat Jul 16 08:40:52 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:52 MDT
fjournal: IEEE Journal of Solid-State Circuits
acknowledgement: ack-nhfb
rawauthor: H. Fujii and C. Hori and T. Takada and N. Hatanaka and T. Demura and G. Ootomo
rawtitle: A floating-point cell library and a {100-Mflops} image signal processor
entry:
@Article{Fujii:1992:FPC,
  author =       "H. Fujii and C. Hori and T. Takada and N. Hatanaka and
                 T. Demura and G. Ootomo",
  title =        "A floating-point cell library and a {100-Mflops} image
                 signal processor",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "27",
  number =       "7",
  pages =        "1080--1088",
  month =        jul,
  year =         "1992",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  summary =      "A novel floating-point cell library for image signal
                 processors that includes a floating-point arithmetic
                 logic unit (ALU), a floating-point multiplier (MPY), an
                 instruction RAM, and a data register file is
                 considered. It has been designed for high-speed
                 \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Gamberger:1992:IIM
author: D. Gamberger
title: Inversion of integer matrices in residue number system
journal: j-IEE-PROC-COMPUT-DIGIT-TECH
volume: 139
number: 5
pages: 465--468
month: sep
monthnumber: 9
year: 1992
CODEN: ICDTEA
DOI: https://doi.org/10.1109/78.157231
ISSN: 1350-2387 (print), 1359-7027 (electronic) OR 13502387 (print), 13597027 (electronic)
ISSNL: 1350-2387 OR 13502387
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
URL: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4186
fjournal: IEE Proceedings. Computers and Digital Techniques
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: D. Gamberger
rawtitle: Inversion of integer matrices in residue number system
entry:
@Article{Gamberger:1992:IIM,
  author =       "D. Gamberger",
  title =        "Inversion of integer matrices in residue number
                 system",
  journal =      j-IEE-PROC-COMPUT-DIGIT-TECH,
  volume =       "139",
  number =       "5",
  pages =        "465--468",
  month =        sep,
  year =         "1992",
  CODEN =        "ICDTEA",
  DOI =          "https://doi.org/10.1109/78.157231",
  ISSN =         "1350-2387 (print), 1359-7027 (electronic)",
  ISSN-L =       "1350-2387",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4186",
  acknowledgement = ack-nhfb,
  fjournal =     "IEE Proceedings. Computers and Digital Techniques",
  keywords =     "residue arithmetic; residue number system",
  summary =      "The presented algorithm makes use of the recently
                 introduced incompletely specified residue number
                 system. This system enables the operations necessary in
                 the inversion process to be done quickly, completely in
                 parallel for different moduli, even if \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Goldberg:1992:DFD
author: D. Goldberg
title: The design of floating-point data types
journal: j-LOPLAS
volume: 1
number: 2
pages: 138--151
month: jun
monthnumber: 6
year: 1992
CODEN: ALPSE8
ISSN: 1057-4514 (print), 1557-7384 (electronic) OR 10574514 (print), 15577384 (electronic)
ISSNL: 1057-4514 OR 10574514
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: ACM Letters on Programming Languages and Systems
acknowledgement: ack-nhfb
affiliation: Xerox Palo Alto Res. Center, CA, USA
thesaurus: Data structures; Digital arithmetic
rawauthor: D. Goldberg
rawtitle: The design of floating-point data types
abstract:
The issues involved in designing the floating-point part of a programming language are discussed. Looking at the language specifications for most existing languages might suggest that this design involves only trivial issues, such as whether to have one or two types of REALs or how to name the functions that convert from INTEGER to REAL. It is shown that there are more significant semantic issues involved. After discussing the tradeoffs for the major design decisions, they are illustrated by presenting the design of the floating-point part of the Modula-3 language.

keywords:
Design; Floating-point data types; Language specifications; Modula-3 language; Programming language; REALs

rawabstract:
The issues involved in designing the floating-point part of a programming language are discussed. Looking at the language specifications for most existing languages might suggest that this design involves only trivial issues, such as whether to have one or two types of REALs or how to name the functions that convert from INTEGER to REAL. It is shown that there are more significant semantic issues involved. After discussing the tradeoffs for the major design decisions, they are illustrated by presenting the design of the floating-point part of the Modula-3 language.

entry:
@Article{Goldberg:1992:DFD,
  author =       "D. Goldberg",
  title =        "The design of floating-point data types",
  journal =      j-LOPLAS,
  volume =       "1",
  number =       "2",
  pages =        "138--151",
  month =        jun,
  year =         "1992",
  CODEN =        "ALPSE8",
  ISSN =         "1057-4514 (print), 1557-7384 (electronic)",
  ISSN-L =       "1057-4514",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The issues involved in designing the floating-point
                 part of a programming language are discussed. Looking
                 at the language specifications for most existing
                 languages might suggest that this design involves only
                 trivial issues, such as whether to have one or two
                 types of REALs or how to name the functions that
                 convert from INTEGER to REAL. It is shown that there
                 are more significant semantic issues involved. After
                 discussing the tradeoffs for the major design
                 decisions, they are illustrated by presenting the
                 design of the floating-point part of the Modula-3
                 language.",
  acknowledgement = ack-nhfb,
  affiliation =  "Xerox Palo Alto Res. Center, CA, USA",
  classification = "C6120 (File organisation)",
  fjournal =     "ACM Letters on Programming Languages and Systems",
  keywords =     "Design; Floating-point data types; Language
                 specifications; Modula-3 language; Programming
                 language; REALs",
  thesaurus =    "Data structures; Digital arithmetic",
}


bibtype: article
filename: fparith.bib
label: Gray:1992:UMF
author: A. Gray and R. Knill
title: Using Mathematica to Find Closed Form Expressions for Approximations to the Square Root of $x$
journal: j-MATHEMATICA-EDUC
volume: 1
number: 4
pages: 12--13
month: Summer
year: 1992
ISSN: 1065-2965 OR 10652965
bibdate: Sat Apr 6 16:22:43 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.04.06 16:22:43 ???
fjournal: Mathematica in Education
acknowledgement: ack-ble
rawauthor: A. Gray and R. Knill
rawtitle: Using {Mathematica} to Find Closed Form Expressions for Approximations to the Square Root of $x$
entry:
@Article{Gray:1992:UMF,
  author =       "A. Gray and R. Knill",
  title =        "Using {Mathematica} to Find Closed Form Expressions
                 for Approximations to the Square Root of $x$",
  journal =      j-MATHEMATICA-EDUC,
  volume =       "1",
  number =       "4",
  pages =        "12--13",
  month =        "Summer",
  year =         "1992",
  ISSN =         "1065-2965",
  bibdate =      "Sat Apr 6 16:22:43 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-ble,
  fjournal =     "Mathematica in Education",
}


bibtype: inproceedings
filename: fparith.bib
label: Hartwig:1992:AFQ
author: F. Hartwig and A. Lacroix
title: Analysis of floating-point quantization errors using stochastic models
crossref: Vandewalle:1992:SPV
pages: 247--250 vol.1
year: 1992
bibdate: Tue Dec 12 09:29:07 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.12 09:29:07 MST
acknowledgement: ack-nhfb
affiliation: Inst. fur Angewandte Phys., J. W. Goethe-University, Frankfurt am Main, Germany
rawauthor: F. Hartwig and A. Lacroix
rawtitle: Analysis of floating-point quantization errors using stochastic models
abstract:
Some results concerning the single quantizer with limited exponent wordlength are presented. In addition to roundoff, the authors present a generalization for magnitude truncation. The method is also applied to digital filters. The theoretical results are tested in comparison with simulation results.

keywords:
Digital filters; Digital signal processing devices; Floating-point quantization errors; Limited exponent wordlength; Magnitude truncation; Roundoff; Simulation results; Stochastic models; Theoretical results

thesaurus:
Analogue-digital conversion; Digital arithmetic; Digital filters; Error analysis; Signal processing; Stochastic processes

rawabstract:
Some results concerning the single quantizer with limited exponent wordlength are presented. In addition to roundoff, the authors present a generalization for magnitude truncation. The method is also applied to digital filters. The theoretical results are tested in comparison with simulation results.

entry:
@InProceedings{Hartwig:1992:AFQ,
  author =       "F. Hartwig and A. Lacroix",
  title =        "Analysis of floating-point quantization errors using
                 stochastic models",
  crossref =     "Vandewalle:1992:SPV",
  pages =        "247--250 vol.1",
  year =         "1992",
  bibdate =      "Tue Dec 12 09:29:07 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Some results concerning the single quantizer with
                 limited exponent wordlength are presented. In addition
                 to roundoff, the authors present a generalization for
                 magnitude truncation. The method is also applied to
                 digital filters. The theoretical results are tested in
                 comparison with simulation results.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. fur Angewandte Phys., J. W. Goethe-University,
                 Frankfurt am Main, Germany",
  classification = "B0240Z (Other and miscellaneous); B0290B (Error
                 analysis in numerical methods); B1265H (A/D and D/A
                 convertors); B6140 (Signal processing and detection);
                 C1140Z (Other and miscellaneous); C5230 (Digital
                 arithmetic methods); C5240 (Digital filters)",
  keywords =     "Digital filters; Digital signal processing devices;
                 Floating-point quantization errors; Limited exponent
                 wordlength; Magnitude truncation; Roundoff; Simulation
                 results; Stochastic models; Theoretical results",
  thesaurus =    "Analogue-digital conversion; Digital arithmetic;
                 Digital filters; Error analysis; Signal processing;
                 Stochastic processes",
}


bibtype: inproceedings
filename: fparith.bib
label: Hartwig:1992:MFA
author: F. Hartwig and A. Lacroix
title: Multi-operand floating-point addition utilizing operand sorting
crossref: White:1992:IIS
pages: 1800--1803 vol.4
year: 1992
bibdate: Tue Dec 12 09:27:13 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.12 09:27:13 MST
acknowledgement: ack-nhfb
affiliation: Inst. fuer Angewandte Phys., J. W. Goethe-University, Frankfurt am Main, Germany
thesaurus: Digital arithmetic; Signal processing; Sorting
rawauthor: F. Hartwig and A. Lacroix
rawtitle: Multi-operand floating-point addition utilizing operand sorting
abstract:
In many signal processing applications repeated additions have to be calculated with a considerable number of operands. It is known that proper sorting of operands has a positive influence on the precision of the result of multioperand floating-point additions. This is investigated for different operand statistics and for proper sorting strategies. In addition to successive addition techniques, adder trees are included in the investigation. The densities of the addition errors for different floating-point addition methods are compared.

keywords:
Adder trees; Addition errors densities; Floating-point addition; Floating-point addition methods; Multioperand floating-point additions; Operand sorting; Operand statistics; Repeated additions; Signal processing; Sorting strategies; Successive addition techniques

rawabstract:
In many signal processing applications repeated additions have to be calculated with a considerable number of operands. It is known that proper sorting of operands has a positive influence on the precision of the result of multioperand floating-point additions. This is investigated for different operand statistics and for proper sorting strategies. In addition to successive addition techniques, adder trees are included in the investigation. The densities of the addition errors for different floating-point addition methods are compared.

entry:
@InProceedings{Hartwig:1992:MFA,
  author =       "F. Hartwig and A. Lacroix",
  title =        "Multi-operand floating-point addition utilizing
                 operand sorting",
  crossref =     "White:1992:IIS",
  pages =        "1800--1803 vol.4",
  year =         "1992",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In many signal processing applications repeated
                 additions have to be calculated with a considerable
                 number of operands. It is known that proper sorting of
                 operands has a positive influence on the precision of
                 the result of multioperand floating-point additions.
                 This is investigated for different operand statistics
                 and for proper sorting strategies. In addition to
                 successive addition techniques, adder trees are
                 included in the investigation. The densities of the
                 addition errors for different floating-point addition
                 methods are compared.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. fuer Angewandte Phys., J. W. Goethe-University,
                 Frankfurt am Main, Germany",
  classification = "C1260 (Information theory); C5230 (Digital
                 arithmetic methods); C5260 (Digital signal processing);
                 C6130 (Data handling techniques)",
  keywords =     "Adder trees; Addition errors densities; Floating-point
                 addition; Floating-point addition methods; Multioperand
                 floating-point additions; Operand sorting; Operand
                 statistics; Repeated additions; Signal processing;
                 Sorting strategies; Successive addition techniques",
  thesaurus =    "Digital arithmetic; Signal processing; Sorting",
}


bibtype: article
filename: fparith.bib
label: Hasan:1992:BSS
author: M. A. Hasan and V. K. Bhargava
title: Bit-serial systolic divider and multiplier for finite fields $ mathrm GF(2^m) $
journal: j-IEEE-TRANS-COMPUT
volume: 41
number: 8
pages: 972--980
month: aug
monthnumber: 8
year: 1992
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.156540
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 10:49:19 MDT 2011
bibtimestamp: 2011.07.07 10:49:19 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156540
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: M. A. Hasan and V. K. Bhargava
rawtitle: Bit-serial systolic divider and multiplier for finite fields {$ \mathrm {GF}(2^m) $}
entry:
@Article{Hasan:1992:BSS,
  author =       "M. A. Hasan and V. K. Bhargava",
  title =        "Bit-serial systolic divider and multiplier for finite
                 fields {$ \mathrm {GF}(2^m) $}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "8",
  pages =        "972--980",
  month =        aug,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.156540",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 10:49:19 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156540",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Hasan:1992:MCL
author: M. A. Hasan and M. Wang and V. K. Bhargava
journal: j-IEEE-TRANS-COMPUT
volume: 41
number: 8
pages: 962--971
month: aug
monthnumber: 8
year: 1992
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.156539
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 10:49:19 MDT 2011
bibtimestamp: 2011.07.07 10:49:19 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156539
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: M. A. Hasan and M. Wang and V. K. Bhargava
title:
Modular construction of low complexity parallel multipliers for a class of finite fields $ mathrm GF(2^m) $

rawtitle:
Modular construction of low complexity parallel multipliers for a class of finite fields {$ \mathrm {GF}(2^m) $}

entry:
@Article{Hasan:1992:MCL,
  author =       "M. A. Hasan and M. Wang and V. K. Bhargava",
  title =        "Modular construction of low complexity parallel
                 multipliers for a class of finite fields {$ \mathrm
                 {GF}(2^m) $}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "8",
  pages =        "962--971",
  month =        aug,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.156539",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 10:49:19 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156539",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Hegeman:1992:AF
author: Frederick W. Hegeman
title: Arithmetic In Factorial-Base
journal: j-CUJ
volume: 10
number: 2
pages: 73--??
month: feb
monthnumber: 2
year: 1992
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: Frederick W. Hegeman
rawtitle: Arithmetic In Factorial-Base
entry:
@Article{Hegeman:1992:AF,
  author =       "Frederick W. Hegeman",
  title =        "Arithmetic In Factorial-Base",
  journal =      j-CUJ,
  volume =       "10",
  number =       "2",
  pages =        "73--??",
  month =        feb,
  year =         "1992",
  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: Hoehfeld:1992:LLN
author: M. Hoehfeld and S. E. Fahlman
title: Learning with limited numerical precision using the cascade-correlation algorithm
journal: j-IEEE-TRANS-NEURAL-NETW
volume: 3
number: 4
pages: 602--611
month: jul
monthnumber: 7
year: 1992
CODEN: ITNNEP
DOI: https://doi.org/10.1109/72.143374
ISSN: 1045-9227 (print), 1941-0093 (electronic) OR 10459227 (print), 19410093 (electronic)
ISSNL: 1045-9227 OR 10459227
bibdate: Fri Sep 22 17:49:00 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.22 17:49:00 ???
fjournal: IEEE Transactions on Neural Networks
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=72
rawauthor: M. Hoehfeld and S. E. Fahlman
rawtitle: Learning with limited numerical precision using the cascade-correlation algorithm
entry:
@Article{Hoehfeld:1992:LLN,
  author =       "M. Hoehfeld and S. E. Fahlman",
  title =        "Learning with limited numerical precision using the
                 cascade-correlation algorithm",
  journal =      j-IEEE-TRANS-NEURAL-NETW,
  volume =       "3",
  number =       "4",
  pages =        "602--611",
  month =        jul,
  year =         "1992",
  CODEN =        "ITNNEP",
  DOI =          "https://doi.org/10.1109/72.143374",
  ISSN =         "1045-9227 (print), 1941-0093 (electronic)",
  ISSN-L =       "1045-9227",
  bibdate =      "Fri Sep 22 17:49:00 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Neural Networks",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=72",
}


bibtype: inproceedings
filename: fparith.bib
label: Hoff:1992:FCH
author: J. R. Hoff and G. W. Foster
title: A full custom, high speed, floating point adder
crossref: Alley:1992:CRI
pages: 450 vol.1
year: 1992
bibdate: Tue Dec 12 09:29:07 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.12 09:29:07 MST
acknowledgement: ack-nhfb
affiliation: Fermilab, Batavia, IL, USA
thesaurus: Adders; Digital arithmetic; Nuclear electronics; Physics computing; Pipeline processing
rawauthor: J. R. Hoff and G. W. Foster
rawtitle: A full custom, high speed, floating point adder
abstract:
Summary form only. A high-speed pipelined floating point adder for use by the Solenoidal Detector Collaboration (SDC) at the Superconducting Super Collider (SSC) is discussed. The adder uses a unique floating point format. The chip is designed to be a two-stage pipeline and to operate at a peak speed of at least 63 MHz. Static rather than dynamic logic was desired, to permit operation at lower speeds and to ease system testing. The chip is implemented using Orbit Semiconductor's 1.2 mu m n-well process. Simulations indicate that the device will operate at 63 MHz. Initial testing performed at Fermilab, limited by test equipment, indicates speeds of at least 63 MHz, with some tests demonstrating speeds in excess of 150 MHz.

keywords:
150 MHz; 63 MHz; Fermilab; Floating point adder; High speed; Orbit Semiconductor; Pipelined; SDC; Simulation; Static logic; System testing; Testing; Two-stage pipeline

rawabstract:
Summary form only. A high-speed pipelined floating point adder for use by the Solenoidal Detector Collaboration (SDC) at the Superconducting Super Collider (SSC) is discussed. The adder uses a unique floating point format. The chip is designed to be a two-stage pipeline and to operate at a peak speed of at least 63 MHz. Static rather than dynamic logic was desired, to permit operation at lower speeds and to ease system testing. The chip is implemented using Orbit Semiconductor's 1.2 mu m n-well process. Simulations indicate that the device will operate at 63 MHz. Initial testing performed at Fermilab, limited by test equipment, indicates speeds of at least 63 MHz, with some tests demonstrating speeds in excess of 150 MHz.

entry:
@InProceedings{Hoff:1992:FCH,
  author =       "J. R. Hoff and G. W. Foster",
  title =        "A full custom, high speed, floating point adder",
  crossref =     "Alley:1992:CRI",
  pages =        "450 vol.1",
  year =         "1992",
  bibdate =      "Tue Dec 12 09:29:07 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Summary form only. A high-speed pipelined floating
                 point adder for use by the Solenoidal Detector
                 Collaboration (SDC) at the Superconducting Super
                 Collider (SSC) is discussed. The adder uses a unique
                 floating point format. The chip is designed to be a
                 two-stage pipeline and to operate at a peak speed of at
                 least 63 MHz. Static rather than dynamic logic was
                 desired, to permit operation at lower speeds and to
                 ease system testing. The chip is implemented using
                 Orbit Semiconductor's 1.2 mu m n-well process.
                 Simulations indicate that the device will operate at 63
                 MHz. Initial testing performed at Fermilab, limited by
                 test equipment, indicates speeds of at least 63 MHz,
                 with some tests demonstrating speeds in excess of 150
                 MHz.",
  acknowledgement = ack-nhfb,
  affiliation =  "Fermilab, Batavia, IL, USA",
  classification = "A2980C (Computer systems); B1265B (Logic circuits);
                 B7430 (Counting circuits and electronics); C5120 (Logic
                 and switching circuits); C5230 (Digital arithmetic
                 methods); C7320 (Physics and Chemistry)",
  keywords =     "150 MHz; 63 MHz; Fermilab; Floating point adder; High
                 speed; Orbit Semiconductor; Pipelined; SDC; Simulation;
                 Static logic; System testing; Testing; Two-stage
                 pipeline",
  numericalindex = "Frequency 6.3E+07 Hz; Frequency 1.5E+08 Hz",
  thesaurus =    "Adders; Digital arithmetic; Nuclear electronics;
                 Physics computing; Pipeline processing",
}


bibtype: article
filename: fparith.bib
label: Hohfeld:1992:PRN
author: Markus Hohfeld and Scott E. Fahlman
title: Probabilistic rounding in neural network learning with limited precision
journal: j-NEUROCOMPUTING
volume: 4
number: 6
pages: 291--299
month: dec
monthnumber: 12
year: 1992
CODEN: NRCGEO
DOI: https://doi.org/10.1016/0925-2312(92)90014-g
ISSN: 0925-2312 (print), 1872-8286 (electronic) OR 09252312 (print), 18728286 (electronic)
ISSNL: 0925-2312 OR 09252312
bibdate: Fri Sep 22 17:46:22 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.22 17:46:22 ???
fjournal: Neurocomputing
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/09252312
rawauthor: Markus H{\"o}hfeld and Scott E. Fahlman
rawtitle: Probabilistic rounding in neural network learning with limited precision
entry:
@Article{Hohfeld:1992:PRN,
  author =       "Markus H{\"o}hfeld and Scott E. Fahlman",
  title =        "Probabilistic rounding in neural network learning with
                 limited precision",
  journal =      j-NEUROCOMPUTING,
  volume =       "4",
  number =       "6",
  pages =        "291--299",
  month =        dec,
  year =         "1992",
  CODEN =        "NRCGEO",
  DOI =          "https://doi.org/10.1016/0925-2312(92)90014-g",
  ISSN =         "0925-2312 (print), 1872-8286 (electronic)",
  ISSN-L =       "0925-2312",
  bibdate =      "Fri Sep 22 17:46:22 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Neurocomputing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/09252312",
}


bibtype: article
filename: fparith.bib
label: Horiguchi:1992:FNR
author: Hiroshi Horiguchi and Tsutomu Tayama
title: Floating-Point Numbers and Real Numbers II
journal: j-ADV-SOFT-SCI-TECH
volume: 3
pages: 151--156
year: 1992
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
rawtitle: Floating-Point Numbers and Real Numbers {II}
entry:
@Article{Horiguchi:1992:FNR,
  author =       "Hiroshi Horiguchi and Tsutomu Tayama",
  title =        "Floating-Point Numbers and Real Numbers {II}",
  journal =      j-ADV-SOFT-SCI-TECH,
  volume =       "3",
  number =       "??",
  pages =        "151--156",
  year =         "1992",
  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: mastersthesis
filename: fparith.bib
label: Hoyt:1992:MFP
author: Brian S. Hoyt
title: The Macintosh floating point arithmetic visualization system
type: Thesis (M.S.--Electrical Engineering)
school: Bucknell University
address: Lewisburg, PA, USA
pages: ix + 88
year: 1992
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
acknowledgement: ack-nhfb
rawauthor: Brian S. Hoyt
rawtitle: The {Macintosh} floating point arithmetic visualization system
note:
Supervised by Richard J. Zaccone. Describes the design, development, implementation, and use of MacFavs (Macintosh Floating point arithmetic visualization system). MacFavs uses simulation, visual displays, and animations to allow students to see actual machine representations of floating point numbers.

keywords:
Floating-point arithmetic.; Macintosh (Computer); Numerical analysis --- Computer-assisted instruction.

rawnote:
Supervised by Richard J. Zaccone. Describes the design, development, implementation, and use of MacFavs (Macintosh Floating point arithmetic visualization system). MacFavs uses simulation, visual displays, and animations to allow students to see actual machine representations of floating point numbers.

entry:
@MastersThesis{Hoyt:1992:MFP,
  author =       "Brian S. Hoyt",
  title =        "The {Macintosh} floating point arithmetic
                 visualization system",
  type =         "Thesis ({M.S.--Electrical Engineering})",
  school =       "Bucknell University",
  address =      "Lewisburg, PA, USA",
  pages =        "ix + 88",
  year =         "1992",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Supervised by Richard J. Zaccone. Describes the
                 design, development, implementation, and use of MacFavs
                 (Macintosh Floating point arithmetic visualization
                 system). MacFavs uses simulation, visual displays, and
                 animations to allow students to see actual machine
                 representations of floating point numbers.",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.; Macintosh (Computer);
                 Numerical analysis --- Computer-assisted instruction.",
}


bibtype: article
filename: fparith.bib
label: Hudak:1992:RPL
title: Report on the programming language Haskell: a non-strict, purely functional language (Version 1.2)
journal: j-SIGPLAN
volume: 27
number: 5
pages: Ri--Rx, R1--R163
month: may
monthnumber: 5
year: 1992
CODEN: SINODQ
ISSN: 0362-1340 (print), 1523-2867 (print), 1558-1160 OR 03621340 (print), 15232867 (print), 15581160
ISSNL: 0362-1340 OR 03621340
bibdate: Sun Dec 14 09:16:21 MST 2003
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.12.14 09:16:21 MST
fjournal: ACM SIGPLAN Notices
acknowledgement: ack-nhfb
affiliation: Yale University, New Haven, CT, USA
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J706
thesaurus: Functional programming; High level languages
author:
Paul Hudak and Simon Peyton Jones and Philip Wadler and Brian Boutel and Jon Fairbairn and Joseph Fasel and Maria M. Guzman and Kevin Hammond and John Hughes and Thomas Johnsson and Dick Kieburtz and Rishiyur Nikhil and Will Partain and John Peterson

abstract:
Haskell is a general purpose, purely functional programming language incorporating many recent innovations in programming language research, including higher-order functions, non-strict semantics, static polymorphic typing, user-defined algebraic datatypes, pattern-matching, list comprehensions, a module system, and a rich set of primitive datatypes, including lists, arrays, arbitrary and fixed precision integers, and floating-point numbers. Haskell is both the culmination and solidification of many years of research on functional languages-the design has been influenced by languages as old as ISWIM and as new as Miranda. The report defines the syntax for Haskell programs and an informal abstract semantics for the meaning of such programs.

keywords:
Abstract semantics; Arrays; Fixed precision integers; Floating-point numbers; Functional programming language; Haskell; Higher-order functions; List comprehensions; Lists; Module system; Non-strict semantics; Pattern-matching; Primitive datatypes; Static polymorphic typing; Syntax; User-defined algebraic datatypes

rawabstract:
Haskell is a general purpose, purely functional programming language incorporating many recent innovations in programming language research, including higher-order functions, non-strict semantics, static polymorphic typing, user-defined algebraic datatypes, pattern-matching, list comprehensions, a module system, and a rich set of primitive datatypes, including lists, arrays, arbitrary and fixed precision integers, and floating-point numbers. Haskell is both the culmination and solidification of many years of research on functional languages-the design has been influenced by languages as old as ISWIM and as new as Miranda. The report defines the syntax for Haskell programs and an informal abstract semantics for the meaning of such programs.

rawauthor:
Paul Hudak and Simon Peyton Jones and Philip Wadler and Brian Boutel and Jon Fairbairn and Joseph Fasel and Mar{\'\i}a M. Guzm{\'a}n and Kevin Hammond and John Hughes and Thomas Johnsson and Dick Kieburtz and Rishiyur Nikhil and Will Partain and John Peterson

rawtitle:
Report on the programming language {Haskell}: a non-strict, purely functional language (Version 1.2)

entry:
@Article{Hudak:1992:RPL,
  author =       "Paul Hudak and Simon Peyton Jones and Philip Wadler
                 and Brian Boutel and Jon Fairbairn and Joseph Fasel and
                 Mar{\'\i}a M. Guzm{\'a}n and Kevin Hammond and John
                 Hughes and Thomas Johnsson and Dick Kieburtz and
                 Rishiyur Nikhil and Will Partain and John Peterson",
  title =        "Report on the programming language {Haskell}: a
                 non-strict, purely functional language (Version 1.2)",
  journal =      j-SIGPLAN,
  volume =       "27",
  number =       "5",
  pages =        "Ri--Rx, R1--R163",
  month =        may,
  year =         "1992",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sun Dec 14 09:16:21 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Haskell is a general purpose, purely functional
                 programming language incorporating many recent
                 innovations in programming language research, including
                 higher-order functions, non-strict semantics, static
                 polymorphic typing, user-defined algebraic datatypes,
                 pattern-matching, list comprehensions, a module system,
                 and a rich set of primitive datatypes, including lists,
                 arrays, arbitrary and fixed precision integers, and
                 floating-point numbers. Haskell is both the culmination
                 and solidification of many years of research on
                 functional languages-the design has been influenced by
                 languages as old as ISWIM and as new as Miranda. The
                 report defines the syntax for Haskell programs and an
                 informal abstract semantics for the meaning of such
                 programs.",
  acknowledgement = ack-nhfb,
  affiliation =  "Yale University, New Haven, CT, USA",
  classification = "C6140D (High level languages)",
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "Abstract semantics; Arrays; Fixed precision integers;
                 Floating-point numbers; Functional programming
                 language; Haskell; Higher-order functions; List
                 comprehensions; Lists; Module system; Non-strict
                 semantics; Pattern-matching; Primitive datatypes;
                 Static polymorphic typing; Syntax; User-defined
                 algebraic datatypes",
  thesaurus =    "Functional programming; High level languages",
}


