# bibtab

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: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=102823
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://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 =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=102823",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: mastersthesis
filename: fparith.bib
label: 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: Jean 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: Jean E. Vuillemin
rawtitle: Constant time arbitrary length synchronous binary counters
entry:
@InProceedings{Vuillemin:1991:CTA,
  author =       "Jean 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: https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=2666
fjournal: Electronics Letters
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
journalURL: https://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 =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=2666",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  keywords =     "residue arithmetic; residue number system",
  summary =      "The 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: https://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 =          "https://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: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=83650
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: https://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 =          "https://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 =  "https://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: https://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 =          "https://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: https://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 =  "https://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:
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  number =       "8",
  pages =        "58--??",
  month =        aug,
  year =         "1992",
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  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
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  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",
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  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: https://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:
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  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 =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  keywords =     "decimal floating-point arithmetic",
}


bibtype: phdthesis
filename: fparith.bib
label: Arjomand:1992:FPC
author: Ata'u'llah Arjomand
type: Ph.D. thesis
school: Yale University
address: New Haven, CT, USA
pages: 250
year: 1992
ISBN13: 979-82-08-71568-0 OR 9798208715680
MRclass: 99-05
MRnumber: 2688864
bibdate: Mon Oct 27 10:32:44 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2025.10.27 10:32:44 ???
note: Thesis (Ph.D.)--Yale University
acknowledgement: ack-nhfb
advisor: Jean-Marc Delosme
rawauthor: Ata'u'llah Arjomand
rawnote: Thesis (Ph.D.)--Yale University
title:
Fast Parallel Computation of the Singular Value Decomposition of Real Matrices Using CORDIC Arithmetic

URL:
https://www.proquest.com/dissertations-theses/fast-parallel-computation-singular-value/docview/304011601/se-2

keywords:
0405:Mathematics; 0544:Electrical engineering; 0984:Computer science; Applied sciences; Computer science; Electrical engineering; Mathematics; Pure sciences

rawtitle:
Fast Parallel Computation of the {Singular Value Decomposition} of Real Matrices Using {CORDIC} Arithmetic

entry:
@PhdThesis{Arjomand:1992:FPC,
  author =       "Ata'u'llah Arjomand",
  title =        "Fast Parallel Computation of the {Singular Value
                 Decomposition} of Real Matrices Using {CORDIC}
                 Arithmetic",
  type =         "{Ph.D.} thesis",
  school =       "Yale University",
  address =      "New Haven, CT, USA",
  pages =        "250",
  year =         "1992",
  ISBN-13 =      "979-82-08-71568-0",
  MRclass =      "99-05",
  MRnumber =     "2688864",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Thesis (Ph.D.)--Yale University",
  URL =          "https://www.proquest.com/dissertations-theses/fast-parallel-computation-singular-value/docview/304011601/se-2",
  acknowledgement = ack-nhfb,
  advisor =      "Jean-Marc Delosme",
  keywords =     "0405:Mathematics; 0544:Electrical engineering;
                 0984:Computer science; Applied sciences; Computer
                 science; Electrical engineering; Mathematics; Pure
                 sciences",
  ris-m1 =       "9314783",
  xxaddress =    "Ann Arbor, MI",
  xxpublisher =  "ProQuest LLC",
}


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: https://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: https://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 =          "https://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)",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://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:
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  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: article
filename: fparith.bib
label: Calvetti:1992:SRE
author: Daniela Calvetti
title: A Stochastic Roundoff Error Analysis for the Convolution
journal: j-MATH-COMPUT
volume: 59
number: 200
pages: 569--582
month: oct
monthnumber: 10
year: 1992
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65G05 (44A35 65T20)
MRnumber: 93a:65061
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
ajournal: Math. Comput.
classcodes: C4190 (Other numerical methods); C4110 (Error analysis in numerical methods)
corpsource: Dept. of Pure and Appl. Math., Stevens Inst. of Technol., Hoboken, NJ, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Daniela Calvetti
rawtitle: A Stochastic Roundoff Error Analysis for the Convolution
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib; JSTOR database; Theory/Matrix.bib

keywords:
accuracy; convolution; error analysis; fast Fourier transforms; Radix-2 fast Fourier transforms; roundoff errors; stochastic roundoff error analysis

entry:
@Article{Calvetti:1992:SRE,
  author =       "Daniela Calvetti",
  title =        "A Stochastic Roundoff Error Analysis for the
                 Convolution",
  journal =      j-MATH-COMPUT,
  volume =       "59",
  number =       "200",
  pages =        "569--582",
  month =        oct,
  year =         "1992",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65G05 (44A35 65T20)",
  MRnumber =     "93a:65061",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib;
                 JSTOR database; Theory/Matrix.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  classcodes =   "C4190 (Other numerical methods); C4110 (Error analysis
                 in numerical methods)",
  corpsource =   "Dept. of Pure and Appl. Math., Stevens Inst. of
                 Technol., Hoboken, NJ, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "accuracy; convolution; error analysis; fast Fourier
                 transforms; Radix-2 fast Fourier transforms; roundoff
                 errors; stochastic roundoff error analysis",
  kwds =         "nla, fft, convolution, rounding error, stochastic
                 analysis",
  treatment =    "T Theoretical or Mathematical",
}


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: https://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: https://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 =          "https://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)",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://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: https://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 =  "https://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: https://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 =  "https://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: https://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 =  "https://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: inproceedings
filename: fparith.bib
label: Dawid:1992:VIC
author: H. Dawid and H. Meyr
booktitle: [Proceedings] 1992 IEEE International Symposium on Circuits and Systems
title: VLSI implementation of the CORDIC algorithm using redundant arithmetic
volume: 3
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1089--1092 (vol. 3)
year: 1992
DOI: https://doi.org/10.1109/ISCAS.1992.230290
bibdate: Mon Oct 27 10:32:44 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2025.10.27 10:32:44 ???
acknowledgement: ack-nhfb
rawauthor: H. Dawid and H. Meyr
rawbooktitle: {[Proceedings] 1992 IEEE International Symposium on Circuits and Systems}
rawtitle: {VLSI} implementation of the {CORDIC} algorithm using redundant arithmetic
keywords:
Arithmetic; Circuits; Clocks; Computer architecture; Delay; Force control; Frequency; Signal processing algorithms; Throughput; Very large scale integration

entry:
@InProceedings{Dawid:1992:VIC,
  author =       "H. Dawid and H. Meyr",
  booktitle =    "{[Proceedings] 1992 IEEE International Symposium on
                 Circuits and Systems}",
  title =        "{VLSI} implementation of the {CORDIC} algorithm using
                 redundant arithmetic",
  volume =       "3",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1089--1092 (vol. 3)",
  year =         "1992",
  DOI =          "https://doi.org/10.1109/ISCAS.1992.230290",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Arithmetic; Circuits; Clocks; Computer architecture;
                 Delay; Force control; Frequency; Signal processing
                 algorithms; Throughput; Very large scale integration",
}


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
journalURL: https://www.sciencedirect.com/journal/microprocessing-and-microprogramming/issues
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",
  journal-URL =  "https://www.sciencedirect.com/journal/microprocessing-and-microprogramming/issues",
}


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: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=214659
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://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 =          "https://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 =  "https://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: https://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 =          "https://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: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156540
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: M. A. Hasan and 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 =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156540",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: 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: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156539
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: M. A. Hasan and M. 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 =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156539",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: 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: https://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 =  "https://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",
}


bibtype: article
filename: fparith.bib
label: IFIF:1992:CVD
author: IFIP Working Group 2.5 (Numerical Software)
title: Comments on version 3.1 of draft ISO / IEC 10967:1991 Language Compatible Arithmetic
journal: j-SIGNUM
volume: 27
number: 1
pages: 2--3
month: jan
monthnumber: 1
year: 1992
CODEN: SNEWD6
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Tue Apr 12 07:50:21 MDT 2005
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.04.12 07:50:21 MDT
fjournal: ACM SIGNUM Newsletter
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/signum
rawauthor: {IFIP Working Group 2.5 (Numerical Software)}
rawtitle: Comments on version 3.1 of draft {ISO\slash IEC 10967:1991 Language Compatible Arithmetic}
entry:
@Article{IFIF:1992:CVD,
  author =       "{IFIP Working Group 2.5 (Numerical Software)}",
  title =        "Comments on version 3.1 of draft {ISO\slash IEC
                 10967:1991 Language Compatible Arithmetic}",
  journal =      j-SIGNUM,
  volume =       "27",
  number =       "1",
  pages =        "2--3",
  month =        jan,
  year =         "1992",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:21 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
}


bibtype: inproceedings
filename: fparith.bib
label: Jackson:1992:DTF
author: P. B. Jackson
title: Developing a toolkit for floating-point hardware in the Nuprl proof development system
crossref: Prinetto:1992:CHD
pages: 401--419
year: 1992
bibdate: Wed Dec 13 13:13:34 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.13 13:13:34 MST
acknowledgement: ack-nhfb
affiliation: Department of Computer Science, Cornell University, Ithaca, NY, USA
thesaurus: Digital arithmetic; Formal specification; Software tools; Theorem proving
rawauthor: P. B. Jackson
rawtitle: Developing a toolkit for floating-point hardware in the {Nuprl} proof development system
abstract:
Describes current work in building a toolkit of theorems, definitions and tactics in the Nuprl proof development system for the verification of floating-point hardware designs. The approach emphasizes reasoning over a wide range of levels of abstraction within a single system. For example the specification of the IEEE's floating point standard makes free use of rational arithmetic, as well as talking explicitly about the input and output bit-vectors of floating-point circuits.

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

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

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


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

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

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


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

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

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

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

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

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


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


bibtype: mastersthesis
filename: fparith.bib
label: James:1992:DRC
author: Shelton L. James
title: A distributed remote computational server
type: Thesis (M.S.)
school: University of Missouri, Columbia
address: Columbia, MO, USA
pages: vi + 183
year: 1992
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
acknowledgement: ack-nhfb
rawauthor: Shelton L. James
rawtitle: A distributed remote computational server
keywords:
Distributed operating systems (Computers); Electronic networks.; Floating-point systems.; OSI (Computer network standard)

entry:
@MastersThesis{James:1992:DRC,
  author =       "Shelton L. James",
  title =        "A distributed remote computational server",
  type =         "Thesis ({M.S.})",
  school =       "University of Missouri, Columbia",
  address =      "Columbia, MO, USA",
  pages =        "vi + 183",
  year =         "1992",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Distributed operating systems (Computers); Electronic
                 networks.; Floating-point systems.; OSI (Computer
                 network standard)",
}


bibtype: inproceedings
filename: fparith.bib
label: Johnstone:1992:RNA
author: P. Johnstone and F. E. Petry
title: Rational number approximation in higher radix floating point systems
crossref: IEEE:1992:PIS
pages: 501--504 vol.2
year: 1992
bibdate: Wed Dec 13 13:13:34 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.13 13:13:34 MST
acknowledgement: ack-nhfb
affiliation: Telerate Syst. Inc., New Orleans, LA, USA
thesaurus: Digital arithmetic
rawauthor: P. Johnstone and F. E. Petry
rawtitle: Rational number approximation in higher radix floating point systems
abstract:
Recent research has shown that hybrid non-binary floating point bases, particularly decimal-based systems, can match or exceed the error performance of more traditional binary systems. The authors address a more general question of whether such bases offer any further advantages in the domain of rational number approximation. They consider the effect of the choice of floating point base on rational number approximation in systems which exhibit the typical characteristics of floating point representations, normalized encodings, limited exponent range, and storage allocated in a fixed number of bits per datum. The frequency with which terminating and representable results can be expected is considered for binary, decimal, and other potentially interesting bases (base 30 and base 210).

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

rawabstract:
Recent research has shown that hybrid non-binary floating point bases, particularly decimal-based systems, can match or exceed the error performance of more traditional binary systems. The authors address a more general question of whether such bases offer any further advantages in the domain of rational number approximation. They consider the effect of the choice of floating point base on rational number approximation in systems which exhibit the typical characteristics of floating point representations, normalized encodings, limited exponent range, and storage allocated in a fixed number of bits per datum. The frequency with which terminating and representable results can be expected is considered for binary, decimal, and other potentially interesting bases (base 30 and base 210).

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


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


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


bibtype: article
filename: fparith.bib
label: Kahaner:1992:SJC
author: D. K. Kahaner and U. Wattenberg
title: Supercomputing-Japan: a competitive assessment
journal: j-IEEE-SPECTRUM
volume: 29
number: 9
pages: 42--47
month: sep
monthnumber: 9
year: 1992
CODEN: IEESAM
DOI: https://doi.org/10.1109/6.155708
ISSN: 0018-9235 (print), 1939-9340 (electronic) OR 00189235 (print), 19399340 (electronic)
ISSNL: 0018-9235 OR 00189235
bibdate: Thu Jan 16 07:37:23 2020
bibtimestamp: 2020.01.16 07:37:23 ???
fjournal: IEEE Spectrum
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6
rawauthor: D. K. Kahaner and U. Wattenberg
rawtitle: {Supercomputing-Japan}: a competitive assessment
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeespectrum1990.bib; https://www.math.utah.edu/pub/tex/bib/super.bib

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

entry:
@Article{Kahaner:1992:SJC,
  author =       "D. K. Kahaner and U. Wattenberg",
  title =        "{Supercomputing-Japan}: a competitive assessment",
  journal =      j-IEEE-SPECTRUM,
  volume =       "29",
  number =       "9",
  pages =        "42--47",
  month =        sep,
  year =         "1992",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/6.155708",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Thu Jan 16 07:37:23 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeespectrum1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/super.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
  keywords =     "5 to 8 GFLOPS; Arithmetic; Central Processing Unit;
                 Computer industry; Hardware; high-speed single
                 processor systems; Home computing; Information
                 technology; intuitive information processing; Japanese
                 supercomputers; Manufacturing industries; Ministry of
                 International Trade and Industry; National electric
                 code; parallel machines; Real-World Computing Program;
                 research initiatives; Supercomputers; Telephony; US
                 machines; vector processing functions",
}


bibtype: inproceedings
filename: fparith.bib
label: Kalliojarvi:1992:DRN
author: K. Kalliojarvi and Y. Neuvo
title: Distribution of roundoff noise in binary floating-point addition
crossref: White:1992:IIS
volume: 4
pages: 1796--1799
year: 1992
bibdate: Tue Dec 12 09:27:13 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.12 09:27:13 MST
acknowledgement: ack-nhfb
affiliation: Signal Process. Lab., Tampere University of Technol., Finland
bookpages: 3028
thesaurus: Digital arithmetic; Digital simulation; Roundoff errors; Signal processing
rawauthor: K. Kalliojarvi and Y. Neuvo
rawtitle: Distribution of roundoff noise in binary floating-point addition
abstract:
A method for deriving the distribution of relative round off error in addition of two binary floating-point numbers is introduced. The distribution is needed in the calculation of variance of the relative roundoff error in floating-point addition. The resulting distribution depends on the statistics of the addends and the rounding strategy chosen. As an example, the distribution is derived for the addition of two uncorrelated numbers from Gaussian distribution. The result was verified by simulation.

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

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

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


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

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

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

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


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

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

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

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

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

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


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

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

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


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


bibtype: inproceedings
filename: fparith.bib
label: Kontro:1992:FAS
author: J. Kontro and K. Kalliojarvi and Y. Neuvo
title: Floating-point arithmetic in signal processing
crossref: White:1992:IIS
pages: 1784--1791 vol.4
year: 1992
bibdate: Tue Dec 12 09:27:13 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.12 09:27:13 MST
acknowledgement: ack-nhfb
affiliation: Signal Process. Lab., Tampere University of Technol., Finland
rawauthor: J. Kontro and K. Kalliojarvi and Y. Neuvo
rawtitle: Floating-point arithmetic in signal processing
abstract:
The use of floating-point arithmetic in digital signal processing is considered. An introduction to floating-point arithmetic based on the IEEE floating-point standards is given. Finite wordlength effects of these arithmetic systems are presented. Floating-point hardware is discussed. The emphasis is on audio applications. As an example, amplitude distributions and signal-to-noise ratios of quantized music are considered, and audio standards using floating-point arithmetic are presented.

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

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

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

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


bibtype: article
filename: fparith.bib
label: Kontro:1992:USF
author: J. Kontro and K. Kalliojarvi and Y. Neuvo
title: Use of Short Floating-Point Formats in Audio Applications
journal: j-IEEE-TRANS-CONSUMER-ELECTRONICS
volume: 38
number: 3
pages: 200--207
month: aug
monthnumber: 8
year: 1992
CODEN: ITCEDA
ISSN: 0098-3063 (print), 1558-4127 (electronic) OR 00983063 (print), 15584127 (electronic)
ISSNL: 0098-3063 OR 00983063
bibdate: Sat Jul 16 08:40:52 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:52 MDT
fjournal: IEEE Transactions on Consumer Electronics
acknowledgement: ack-nhfb
rawauthor: J. Kontro and K. Kalliojarvi and Y. Neuvo
rawtitle: Use of Short Floating-Point Formats in Audio Applications
entry:
@Article{Kontro:1992:USF,
  author =       "J. Kontro and K. Kalliojarvi and Y. Neuvo",
  title =        "Use of Short Floating-Point Formats in Audio
                 Applications",
  journal =      j-IEEE-TRANS-CONSUMER-ELECTRONICS,
  volume =       "38",
  number =       "3",
  pages =        "200--207",
  month =        aug,
  year =         "1992",
  CODEN =        "ITCEDA",
  ISSN =         "0098-3063 (print), 1558-4127 (electronic)",
  ISSN-L =       "0098-3063",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Consumer Electronics",
  summary =      "Use of short floating-point formats that are shorter
                 than the IEEE floating-point standard (ANSI/IEEE S+A
                 754-1985), 24+8-b, in digital audio applications is
                 studied. The performance of these formats is analyzed
                 in different parts of the digital audio \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Krishna:1992:CTA
author: H. Krishna and K.-Y. Lin and J.-D. Sun
journal: j-IEEE-TRANS-CIRCUITS-SYST-2
volume: 39
number: 1
pages: 8--17
month: jan
monthnumber: 1
year: 1992
CODEN: ICSPE5
DOI: https://doi.org/10.1109/82.204106
ISSN: 1057-7130 (print), 1558-125X (electronic) OR 10577130 (print), 1558125X (electronic)
ISSNL: 1057-7130 OR 10577130
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
URL: https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=5240
fjournal: IEEE Transactions on Circuits and Systems. 2, Analog and Digital Signal Processing
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82
rawauthor: H. Krishna and K.-Y. Lin and J.-D. Sun
title:
A coding theory approach to error control in redundant residue number systems. I. Theory and single error correction

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

entry:
@Article{Krishna:1992:CTA,
  author =       "H. Krishna and K.-Y. Lin and J.-D. Sun",
  title =        "A coding theory approach to error control in redundant
                 residue number systems. {I}. Theory and single error
                 correction",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-2,
  volume =       "39",
  number =       "1",
  pages =        "8--17",
  month =        jan,
  year =         "1992",
  CODEN =        "ICSPE5",
  DOI =          "https://doi.org/10.1109/82.204106",
  ISSN =         "1057-7130 (print), 1558-125X (electronic)",
  ISSN-L =       "1057-7130",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=5240",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems. 2, Analog
                 and Digital Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A coding theory approach to error control in redundant
                 residue number systems (RRNSs) is presented. The
                 concepts of Hamming weight, minimum distance, weight
                 distribution, and error detection and correction
                 capabilities in redundant residue number \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Krishnan:1992:CGF
author: R. Krishnan and G. A. Jullien and W. C. Miller
title: Computation of generalized FIR filter structure using the modified quadratic residue number system
journal: j-IEEE-TRANS-CIRCUITS-SYST-2
volume: 39
number: 1
pages: 58--62
month: jan
monthnumber: 1
year: 1992
CODEN: ICSPE5
DOI: https://doi.org/10.1109/82.204110
ISSN: 1057-7130 (print), 1558-125X (electronic) OR 10577130 (print), 1558125X (electronic)
ISSNL: 1057-7130 OR 10577130
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
URL: https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=5240
fjournal: IEEE Transactions on Circuits and Systems. 2, Analog and Digital Signal Processing
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82
rawauthor: R. Krishnan and G. A. Jullien and W. C. Miller
rawtitle:
Computation of generalized {FIR} filter structure using the modified quadratic residue number system

entry:
@Article{Krishnan:1992:CGF,
  author =       "R. Krishnan and G. A. Jullien and W. C. Miller",
  title =        "Computation of generalized {FIR} filter structure
                 using the modified quadratic residue number system",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-2,
  volume =       "39",
  number =       "1",
  pages =        "58--62",
  month =        jan,
  year =         "1992",
  CODEN =        "ICSPE5",
  DOI =          "https://doi.org/10.1109/82.204110",
  ISSN =         "1057-7130 (print), 1558-125X (electronic)",
  ISSN-L =       "1057-7130",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=5240",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems. 2, Analog
                 and Digital Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
  keywords =     "residue arithmetic; residue number system",
  summary =      "The systematic approach for generating the generalized
                 number theoretic FIR filter structure based on the
                 complex number theoretic z-transform is presented. A
                 step-by-step computational method that can be used in
                 the implementation and \ldots{}",
}


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


bibtype: inproceedings
filename: fparith.bib
label: Kutuso:1992:EMO
author: K. N. Kutuso and H. M. Yassine
booktitle: Proceedings of the 35th Midwest Symposium on Circuits and Systems, 1992
title: Effect of moduli ordering of mixed radix conversion methods in residue number systems
volume: 1
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 678--680
year: 1992
DOI: https://doi.org/10.1109/MWSCAS.1992.271232
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: K. N. Kutuso and H. M. Yassine
rawbooktitle: Proceedings of the 35th Midwest Symposium on Circuits and Systems, 1992
rawtitle: Effect of moduli ordering of mixed radix conversion methods in residue number systems
entry:
@InProceedings{Kutuso:1992:EMO,
  author =       "K. N. Kutuso and H. M. Yassine",
  booktitle =    "Proceedings of the 35th Midwest Symposium on Circuits
                 and Systems, 1992",
  title =        "Effect of moduli ordering of mixed radix conversion
                 methods in residue number systems",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "678--680",
  year =         "1992",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/MWSCAS.1992.271232",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "The effect of moduli ordering in different methods for
                 converting residue numbers to decimal numbers using the
                 mixed radix approach is investigated. The number of
                 operations involved in the conversion process of
                 residue numbers to their decimal \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Lacroix:1992:DDM
author: A. Lacroix and F. Hartwig
title: Distribution densities of the mantissa and exponent of floating point numbers
crossref: White:1992:IIS
pages: 1792--1795 vol.4
year: 1992
bibdate: Tue Dec 12 09:27:13 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.12 09:27:13 MST
note: 6 vol.
acknowledgement: ack-nhfb
affiliation: Inst. fuer Angewandte Phys., J. W. Goethe-University, Frankfurt am Main, Germany
thesaurus: Digital arithmetic; Digital filters; Roundoff errors; Signal processing
rawauthor: A. Lacroix and F. Hartwig
rawnote: 6 vol.
rawtitle: Distribution densities of the mantissa and exponent of floating point numbers
abstract:
The relations between the probability densities of real numbers and the corresponding mantissa and exponent densities in the floating point number format are investigated. Assumptions about continuity of the probability density of real numbers lead to certain restrictions in terms of the density of the mantissa. A few real number densities of practical importance were treated analytically and experimentally. During arithmetic operations like addition and multiplication which are essential for signal processing the operand density is altered. The effect concerning the densities of mantissa and exponent of the result is discussed. The reciprocal density of the mantissas plays a central role. Applications in roundoff-noise-analysis of signal processing with finite wordlength are considered. (5 Refs.)

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

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

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


bibtype: article
filename: fparith.bib
label: Lang:1992:HRS
author: T. Lang and P. Montuschi
title: Higher radix square root with prescaling
journal: j-IEEE-TRANS-COMPUT
volume: 41
number: 8
pages: 996--1009
month: aug
monthnumber: 8
year: 1992
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.156542
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 10:49:19 MDT 2011
bibtimestamp: 2011.07.07 10:49:19 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156542
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: T. Lang and P. Montuschi
rawtitle: Higher radix square root with prescaling
entry:
@Article{Lang:1992:HRS,
  author =       "T. Lang and P. Montuschi",
  title =        "Higher radix square root with prescaling",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "8",
  pages =        "996--1009",
  month =        aug,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.156542",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 10:49:19 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156542",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "A scheme for performing higher radix square root based
                 on prescaling of the radicand is presented to reduce
                 the complexity of the result-digit selection. The
                 scheme requires several steps, namely multiplication
                 for prescaling the radicand, square \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Lee:1992:ACR
author: J. H. M. Lee and M. H. van Emden
title: Adapting $ rm CLP(sc R) $ to floating-point arithmetic
journal: Fifth generation computer systems, vol 1
volume: 2
publisher: Ohm
address: Tokyo, Japan
pages: 996--1003
year: 1992
MRclass: 68N15 (68N17 68Q40)
MRnumber: 93m:68027
bibdate: Fri Dec 8 08:24:13 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 08:24:13 ???
acknowledgement: ack-nhfb
rawauthor: J. H. M. Lee and M. H. {van Emden}
rawtitle: Adapting {$ {\rm CLP}(\sc {R}) $} to floating-point arithmetic
entry:
@Article{Lee:1992:ACR,
  author =       "J. H. M. Lee and M. H. {van Emden}",
  title =        "Adapting {$ {\rm CLP}(\sc {R}) $} to floating-point
                 arithmetic",
  journal =      "Fifth generation computer systems, vol 1",
  volume =       "2",
  publisher =    "Ohm",
  address =      "Tokyo, Japan",
  pages =        "996--1003",
  year =         "1992",
  MRclass =      "68N15 (68N17 68Q40)",
  MRnumber =     "93m:68027",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Lee:1992:FPP
author: K. Lee
title: On the Floating Point Performance of the i860 Microprocessor
journal: j-INT-J-HIGH-SPEED-COMPUTING
volume: 4
number: 4
pages: 251--268
month: dec
monthnumber: 12
year: 1992
CODEN: IHSCEZ
ISSN: 0129-0533 OR 01290533
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
fjournal: International Journal of High Speed Computing
acknowledgement: ack-nhfb
journalURL: http://www.worldscientific.com/worldscinet/ijhsc
rawauthor: K. Lee
rawtitle: On the Floating Point Performance of the i860 Microprocessor
entry:
@Article{Lee:1992:FPP,
  author =       "K. Lee",
  title =        "On the Floating Point Performance of the i860
                 Microprocessor",
  journal =      j-INT-J-HIGH-SPEED-COMPUTING,
  volume =       "4",
  number =       "4",
  pages =        "251--268",
  month =        dec,
  year =         "1992",
  CODEN =        "IHSCEZ",
  ISSN =         "0129-0533",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of High Speed Computing",
  journal-URL =  "http://www.worldscientific.com/worldscinet/ijhsc",
}


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


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

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


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


bibtype: inproceedings
filename: fparith.bib
label: Liu:1992:QBS
author: K. J. R. Liu and E. Frantzeskakis
booktitle: Workshop on VLSI Signal Processing, V, 1992
title: Qrd-based Square Root Free and Division Free Algorithms and Architectures
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 459--468
year: 1992
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: K. J. R. Liu and E. Frantzeskakis
rawbooktitle: Workshop on {VLSI} Signal Processing, V, 1992
rawtitle: Qrd-based Square Root Free and Division Free Algorithms and Architectures
entry:
@InProceedings{Liu:1992:QBS,
  author =       "K. J. R. Liu and E. Frantzeskakis",
  booktitle =    "Workshop on {VLSI} Signal Processing, V, 1992",
  title =        "Qrd-based Square Root Free and Division Free
                 Algorithms and Architectures",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "459--468",
  year =         "1992",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Not \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Lozier:1992:RPC
author: D. W. Lozier and P. R. Turner
journal: j-COMPUTING
volume: 48
number: 3-4
pages: 239--258 (or 239--257??)
year: 1992
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
MRclass: 65Y05 (65-04 65G05)
MRnumber: 93e:65161
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
fjournal: Computing: Archiv fur informatik und numerik
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/607
rawauthor: D. W. Lozier and P. R. Turner
title:
Robust Parallel Computation in Floating-Point and SLI Arithmetic. Robuste Parallel-Verarbeitung in Gleitkomma-und SLI-Arithmetik

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

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


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

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

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

entry:
@Article{Lozier:1992:RPV,
  author =       "D. W. Lozier and P. R. Turner",
  title =        "{Robuste Parallel-Verarbeitung in Gleitkomma- und
                 SLI-Arithmetik}. ({German}) [{Robust} Parallel
                 Computation in Floating-Point and {SLI} Arithmetic]",
  journal =      j-COMPUTING,
  volume =       "48",
  number =       "3--4",
  pages =        "239--257",
  month =        sep,
  year =         "1992",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65Y05 (65-04 65G05)",
  MRnumber =     "93e:65161",
  bibdate =      "Mon Oct 11 20:38:38 MDT 1999",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
                 https://www.math.utah.edu/pub/tex/bib/computing.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 MathSciNet database; OCLC Contents1st database",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  language =     "German",
}


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

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

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

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


bibtype: article
filename: fparith.bib
label: Lu:1992:NDA
author: M. Lu and J.-S. Chiang
title: A novel division algorithm for the residue number system
journal: j-IEEE-TRANS-COMPUT
volume: 41
number: 8
pages: 1026--1032
month: aug
monthnumber: 8
year: 1992
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.156545
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 10:49:19 MDT 2011
bibtimestamp: 2011.07.07 10:49:19 MDT
fjournal: IEEE Transactions on Computers
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: M. Lu and J.-S. Chiang
rawtitle: A novel division algorithm for the residue number system
URL:
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4052; https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156545

entry:
@Article{Lu:1992:NDA,
  author =       "M. Lu and J.-S. Chiang",
  title =        "A novel division algorithm for the residue number
                 system",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "8",
  pages =        "1026--1032",
  month =        aug,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.156545",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 10:49:19 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4052;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156545",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A novel general algorithm for signed number division
                 in the residue number system (RNS) is presented. The
                 parity checking technique used for sign and overflow
                 detection in this algorithm is more efficient and
                 practical than conventional methods. \ldots{}",
}


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

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

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


bibtype: misc
filename: fparith.bib
label: Lynch:1992:HSD
author: T. Lynch and S. McIntyre and K. Tseng and S. Shaw and T. Hurson
title: High speed divider with square root capability
pages: 137--145
year: 1992
bibdate: Thu Apr 2 08:38:35 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.04.02 08:38:35 ???
note: U.S. Patent No. 5,128,891.
acknowledgement: ack-sfo
rawauthor: T. Lynch and S. McIntyre and K. Tseng and S. Shaw and T. Hurson
rawnote: U.S. Patent No. 5,128,891.
rawtitle: High speed divider with square root capability
entry:
@Misc{Lynch:1992:HSD,
  author =       "T. Lynch and S. McIntyre and K. Tseng and S. Shaw and
                 T. Hurson",
  title =        "High speed divider with square root capability",
  year =         "1992",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "U.S. Patent No. 5,128,891.",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Madrid:1992:MBA
author: P. E. Madrid and B. Millar and E. E. Swartzlander
editor: Dwight Hill
title: Modified Booth algorithm for high radix multiplication
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 118--212
year: 1992
DOI: https://doi.org/10.1109/ICCD.1992.276194
ISSN: 1063-6404 OR 10636404
LCCN: TK7888.4 .I35 1992
bibdate: Thu Nov 13 10:39:44 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2025.11.13 10:39:44 ???
URL: https://ieeexplore.ieee.org/document/276194/
acknowledgement: ack-nhfb
bookpages: xvii + 605
rawauthor: P. E. Madrid and B. Millar and E. E. Swartzlander
raweditor: Dwight Hill
rawtitle: Modified {Booth} algorithm for high radix multiplication
booktitle:
Proceedings of the 1992 IEEE International Conference on Computer Design: VLSI in Computers & Processors, 11--14 October 1992, Cambridge, MA, USA

ISBN:
0-8186-3110-4 (paperback), 0-8186-3111-2 (microfiche), 0-8186-3112-0 OR 0818631104 (paperback), 0818631112 (microfiche), 0818631120

ISBN13:
978-0-8186-3110-8, 978-0-8186-3111-5, 978-0-8186-3112-2 OR 9780818631108, 9780818631115, 9780818631122

rawbooktitle:
Proceedings of the {1992 IEEE International Conference on Computer Design: VLSI in Computers \& Processors, 11--14 October 1992, Cambridge, MA, USA}

entry:
@InProceedings{Madrid:1992:MBA,
  author =       "P. E. Madrid and B. Millar and E. E. Swartzlander",
  editor =       "Dwight Hill",
  booktitle =    "Proceedings of the {1992 IEEE International Conference
                 on Computer Design: VLSI in Computers \& Processors,
                 11--14 October 1992, Cambridge, MA, USA}",
  title =        "Modified {Booth} algorithm for high radix
                 multiplication",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  bookpages =    "xvii + 605",
  pages =        "118--212",
  year =         "1992",
  DOI =          "https://doi.org/10.1109/ICCD.1992.276194",
  ISBN =         "0-8186-3110-4 (paperback), 0-8186-3111-2 (microfiche),
                 0-8186-3112-0",
  ISBN-13 =      "978-0-8186-3110-8, 978-0-8186-3111-5,
                 978-0-8186-3112-2",
  ISSN =         "1063-6404",
  LCCN =         "TK7888.4 .I35 1992",
  bibdate =      "Thu Nov 13 10:39:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/document/276194/",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Maguire:1992:MD
author: J. Maguire
title: MC8810: Datapath
crossref: Juj:1992:NCR
pages: 193--197
year: 1992
bibdate: Wed Sep 7 22:32:42 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.07 22:32:42 ???
acknowledgement: ack-nj
rawauthor: J. Maguire
rawtitle: {MC8810}: Datapath
entry:
@InProceedings{Maguire:1992:MD,
  author =       "J. Maguire",
  title =        "{MC8810}: Datapath",
  crossref =     "Juj:1992:NCR",
  pages =        "193--197",
  year =         "1992",
  bibdate =      "Wed Sep 7 22:32:42 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: mastersthesis
filename: fparith.bib
label: Makhdumi:1992:CCS
author: Shazia Makhdumi
title: Comparison of current switch bipolar circuits for high performance floating point arithmetic
type: Thesis (M.S.)
school: Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science
address: Cambridge, MA, USA
pages: 107
year: 1992
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
acknowledgement: ack-nhfb
rawauthor: Shazia Makhdumi
rawtitle: Comparison of current switch bipolar circuits for high performance floating point arithmetic
entry:
@MastersThesis{Makhdumi:1992:CCS,
  author =       "Shazia Makhdumi",
  title =        "Comparison of current switch bipolar circuits for high
                 performance floating point arithmetic",
  type =         "Thesis ({M.S.})",
  school =       "Massachusetts Institute of Technology, Dept. of
                 Electrical Engineering and Computer Science",
  address =      "Cambridge, MA, USA",
  pages =        "107",
  year =         "1992",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: fparith.bib
label: Mar:1992:DSP
editor: Amy Mar
title: Digital signal processing applications using the ADSP-2100 family
publisher: pub-PH
address: pub-PH:adr
year: 1992
ISBN: 0-13-219726-X (vol. 1), 0-13-178567-2 (vol. 2) OR 013219726X (vol. 1), 0131785672 (vol. 2)
LCCN: TK5102.9 .D53 1992
bibdate: Sat Jan 15 05:58:58 MST 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2005.01.15 05:58:58 MST
subject: Signal processing; Digital techniques; Microprocessors
acknowledgement: ack-nhfb
raweditor: Amy Mar
rawtitle: Digital signal processing applications using the {ADSP}-2100 family
ISBN13:
978-0-13-219726-7 (vol. 1), 978-0-13-178567-0 (vol. 2) OR 9780132197267 (vol. 1), 9780131785670 (vol. 2)

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

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


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


bibtype: techreport
filename: fparith.bib
label: MenissierMorain:1992:CNR
author: V. Menissier-Morain
title: CAML numbers reference manual
number: 141
institution: Inst. Nat. Recherche Inf. Autom.
address: Le Chesnay, France
pages: 157
month: jul
monthnumber: 7
year: 1992
bibdate: Tue Dec 12 09:27:13 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.12 09:27:13 MST
acknowledgement: ack-nhfb
thesaurus: Digital arithmetic; Functional programming; High level languages; Mathematics computing
rawauthor: V. M{\'e}nissier-Morain
rawtitle: {CAML} numbers reference manual
abstract:
An overview is given of the arithmetic of the functional language CAML V3.1. This arithmetic includes floating point numbers, arbitrary large integers and rationals and a complete set of primitives. Its implementation relies on the efficient BigNum package (J.-C. Herve et al., 1989).

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

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

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


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


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

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


bibtype: article
filename: fparith.bib
label: Mikami:1992:NDO
author: N. Mikami and M. Kobayashi and Y. Yokoyama
title: A New DSP-Oriented Algorithm for Calculation of the Square Root Using a Nonlinear Digital Filter
journal: j-IEEE-TRANS-SIG-PROC
volume: 40
number: 7
pages: 1663--1669
month: jul
monthnumber: 7
year: 1992
CODEN: ITPRED
ISSN: 1053-587X (print), 1941-0476 (electronic) OR 1053587X (print), 19410476 (electronic)
ISSNL: 1053-587X OR 1053587X
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
fjournal: IEEE Transactions on Signal Processing
acknowledgement: ack-nj
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78
rawauthor: N. Mikami and M. Kobayashi and Y. Yokoyama
rawtitle: A New {DSP}-Oriented Algorithm for Calculation of the Square Root Using a Nonlinear Digital Filter
entry:
@Article{Mikami:1992:NDO,
  author =       "N. Mikami and M. Kobayashi and Y. Yokoyama",
  title =        "A New {DSP}-Oriented Algorithm for Calculation of the
                 Square Root Using a Nonlinear Digital Filter",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "40",
  number =       "7",
  pages =        "1663--1669",
  month =        jul,
  year =         "1992",
  CODEN =        "ITPRED",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  summary =      "A high-speed algorithm for calculating the square root
                 is proposed. This algorithm, which can be regarded as
                 calculation of the step response of a kind of nonlinear
                 IIR filter, requires no divisions. Therefore, it is
                 suitable for a VLSI digital \ldots{}",
}


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


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

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

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

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


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


bibtype: article
filename: fparith.bib
label: Moore:1992:PRP
author: David L. Moore
title: Programming the 29050 (RISC programming)
journal: j-DDJ
volume: 17
number: 1
pages: 34, 36, 38, 40, 42
month: jan
monthnumber: 1
year: 1992
CODEN: DDJOEB
ISSN: 1044-789X OR 1044789X
bibdate: Tue Sep 10 10:06:23 MDT 1996
bibsource: http://www.ddj.com/index/author/index.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.09.10 10:06:23 MDT
fjournal: Dr. Dobb's Journal of Software Tools
acknowledgement: ack-nhfb
thesaurus: Assembly language; Microprogramming; Reduced instruction set computing
rawauthor: David L. Moore
rawtitle: Programming the 29050 ({RISC} programming)
keywords:
29000 Family; AM29050; Assembly language programming; Flat address space; Floating-point operations; Registers; RISC processors

entry:
@Article{Moore:1992:PRP,
  author =       "David L. Moore",
  title =        "Programming the 29050 ({RISC} programming)",
  journal =      j-DDJ,
  volume =       "17",
  number =       "1",
  pages =        "34, 36, 38, 40, 42",
  month =        jan,
  year =         "1992",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Tue Sep 10 10:06:23 MDT 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C5220 (Computer architecture); C6110 (Systems
                 analysis and programming); C6140B (Machine-oriented
                 languages)",
  fjournal =     "Dr. Dobb's Journal of Software Tools",
  keywords =     "29000 Family; AM29050; Assembly language programming;
                 Flat address space; Floating-point operations;
                 Registers; RISC processors",
  thesaurus =    "Assembly language; Microprogramming; Reduced
                 instruction set computing",
}


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

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

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


bibtype: article
filename: fparith.bib
label: Mou:1992:OSA
author: Z.-J. Mou and F. Jutand
title: `Overturned-stairs' adder trees and multiplier design
journal: j-IEEE-TRANS-COMPUT
volume: 41
number: 8
pages: 940--948
month: aug
monthnumber: 8
year: 1992
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.156536
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 10:49:19 MDT 2011
bibtimestamp: 2011.07.07 10:49:19 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156536
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Z.-J. Mou and F. Jutand
rawtitle: {`Overturned-stairs'} adder trees and multiplier design
entry:
@Article{Mou:1992:OSA,
  author =       "Z.-J. Mou and F. Jutand",
  title =        "{`Overturned-stairs'} adder trees and multiplier
                 design",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "8",
  pages =        "940--948",
  month =        aug,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.156536",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 10:49:19 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156536",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


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

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

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


bibtype: phdthesis
filename: fparith.bib
label: Mutrie:1992:TSS
author: Mark P. W. Mutrie
title: Towards a symbolic system for floating-point error analysis
type: Thesis (Ph.D.)
publisher: National Library of Canada = Bibliotheque nationale du Canada
school: University of Waterloo
address: Waterloo, ON, Canada
pages: 284--293
year: 1992
ISBN: 0-315-72486-2 OR 0315724862
ISBN13: 978-0-315-72486-0 OR 9780315724860
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
note: 8 microfiches. University Microfilms order no. UMI00359027
series: Canadian theses = Theses canadiennes
acknowledgement: ack-nhfb
rawauthor: Mark P. W. Mutrie
rawnote: 8 microfiches. University Microfilms order no. UMI00359027
rawtitle: Towards a symbolic system for floating-point error analysis
entry:
@PhdThesis{Mutrie:1992:TSS,
  author =       "Mark P. W. Mutrie",
  title =        "Towards a symbolic system for floating-point error
                 analysis",
  type =         "Thesis ({Ph.D.})",
  publisher =    "National Library of Canada = Bibliotheque nationale du
                 Canada",
  school =       "University of Waterloo",
  address =      "Waterloo, ON, Canada",
  year =         "1992",
  ISBN =         "0-315-72486-2",
  ISBN-13 =      "978-0-315-72486-0",
  LCCN =         "????",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "8 microfiches. University Microfilms order no.
                 UMI00359027",
  series =       "Canadian theses = Theses canadiennes",
  acknowledgement = ack-nhfb,
}


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

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

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

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

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

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


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

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

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


bibtype: article
filename: fparith.bib
label: Ng:1992:ARH
author: K. C. Ng
title: Argument Reduction for Huge Arguments: Good to the Last Bit
journal: SunPro
pages: 365--372
day: 13
month: jul
monthnumber: 7
year: 1992
bibdate: Thu Sep 1 10:16:08 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:16:08 ???
note: Work in progress.
URL: http://www.validlab.com/arg.pdf
keywords: range reduction
acknowledgement: ack-nj
rawauthor: K. C. Ng
rawnote: Work in progress.
rawtitle: Argument Reduction for Huge Arguments: Good to the Last Bit
entry:
@Article{Ng:1992:ARH,
  author =       "K. C. Ng",
  title =        "Argument Reduction for Huge Arguments: Good to the
                 Last Bit",
  journal =      "SunPro",
  volume =       "??",
  number =       "??",
  day =          "13",
  month =        jul,
  year =         "1992",
  bibdate =      "Thu Sep 1 10:16:08 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Work in progress.",
  URL =          "http://www.validlab.com/arg.pdf",
  acknowledgement = ack-nj,
  keywords =     "range reduction",
}


bibtype: inproceedings
filename: fparith.bib
label: Nishimura:1992:FPR
author: S. Nishimura
booktitle: Proceedings of the 35th Midwest Symposium on Circuits and Systems, 1992
title: A fixed-point roundoff error analysis of adaptive notch filters
volume: 1
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 373--376
year: 1992
bibdate: Sat Jul 16 11:25:07 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:07 MDT
acknowledgement: ack-nhfb
rawauthor: S. Nishimura
rawbooktitle: Proceedings of the 35th Midwest Symposium on Circuits and Systems, 1992
rawtitle: A fixed-point roundoff error analysis of adaptive notch filters
entry:
@InProceedings{Nishimura:1992:FPR,
  author =       "S. Nishimura",
  booktitle =    "Proceedings of the 35th Midwest Symposium on Circuits
                 and Systems, 1992",
  title =        "A fixed-point roundoff error analysis of adaptive
                 notch filters",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "373--376",
  year =         "1992",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:07 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Methods to analyze the convergence and steady-state
                 characteristics of an adaptive notch filter when the
                 effects of fixed-point arithmetic are taken into
                 account are presented. The adaptive detection of a
                 sinusoid with white Gaussian noise is \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Obaidat:1992:DMA
author: Mohammad S. Obaidat and Saleh A. Bleha
title: A Decimal Multiplication Algorithm for Microcomputers
journal: j-COMPUT-ELECTR-ENG
volume: 18
number: 5
pages: 357--363
month: sep
monthnumber: 9
year: 1992
CODEN: CPEEBQ
ISSN: 0045-7906 (print), 1879-0755 (electronic) OR 00457906 (print), 18790755 (electronic)
ISSNL: 0045-7906 OR 00457906
bibdate: Thu Sep 1 10:16:11 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:16:11 ???
fjournal: Computers and Electrical Engineering
keywords: decimal floating-point arithmetic
acknowledgement: ack-nj
rawauthor: Mohammad S. Obaidat and Saleh A. Bleha
rawtitle: A Decimal Multiplication Algorithm for Microcomputers
entry:
@Article{Obaidat:1992:DMA,
  author =       "Mohammad S. Obaidat and Saleh A. Bleha",
  title =        "A Decimal Multiplication Algorithm for
                 Microcomputers",
  journal =      j-COMPUT-ELECTR-ENG,
  volume =       "18",
  number =       "5",
  pages =        "357--363",
  month =        sep,
  year =         "1992",
  CODEN =        "CPEEBQ",
  ISSN =         "0045-7906 (print), 1879-0755 (electronic)",
  ISSN-L =       "0045-7906",
  bibdate =      "Thu Sep 1 10:16:11 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Computers and Electrical Engineering",
  keywords =     "decimal floating-point arithmetic",
}


bibtype: article
filename: fparith.bib
label: Ochs:1992:SIR
author: T. Ochs
title: This sine is also right!
journal: j-COMP-LANG-MAG
volume: 9
number: 1
pages: 89--93
month: jan
monthnumber: 1
year: 1992
CODEN: COMLEF
ISSN: 0749-2839 OR 07492839
bibdate: Thu Sep 01 10:44:04 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:44:04 ???
fjournal: Computer Language Magazine
acknowledgement: ack-nj
rawauthor: T. Ochs
rawtitle: This sine is also right!
entry:
@Article{Ochs:1992:SIR,
  author =       "T. Ochs",
  title =        "This sine is also right!",
  journal =      j-COMP-LANG-MAG,
  volume =       "9",
  number =       "1",
  pages =        "89--93",
  month =        jan,
  year =         "1992",
  CODEN =        "COMLEF",
  ISSN =         "0749-2839",
  bibdate =      "Thu Sep 01 10:44:04 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Computer Language Magazine",
}


bibtype: article
filename: fparith.bib
label: Okada:1992:AQE
author: Kazuho Okada and Yasuaki Kuroe
journal: j-ELECT-COMM-JAPAN-3-FUND-ELECT-SCI
volume: 75
number: 6
pages: 1--??
month: jun
monthnumber: 6
year: 1992
CODEN: ECJSER
ISSN: 1042-0967 (print), 1520-6440 (electronic) OR 10420967 (print), 15206440 (electronic)
ISSNL: 1042-0967 OR 10420967
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
fjournal: Electronics and communications in Japan. Part 3, Fundamental electronic science
acknowledgement: ack-nhfb
rawauthor: Kazuho Okada and Yasuaki Kuroe
title:
Analysis of Quantization Errors in Digital Control Systems Using Floating-Point Arithmetic--Considering Computational Order in Controller

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

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


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

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


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


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


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

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


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


bibtype: article
filename: fparith.bib
label: Pichat:1992:SFR
author: Michele Pichat
title: Sets of floating-point results associated with an algebraic algorithm
journal: Computational and applied mathematics, I (Dublin, 1991)
pages: 409--418
year: 1992
MRclass: 68M07 (65G05)
MRnumber: 93m:68010
bibdate: Fri Dec 8 08:24:13 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 08:24:13 ???
acknowledgement: ack-nhfb
rawauthor: Mich{\`e}le Pichat
rawtitle: Sets of floating-point results associated with an algebraic algorithm
entry:
@Article{Pichat:1992:SFR,
  author =       "Mich{\`e}le Pichat",
  title =        "Sets of floating-point results associated with an
                 algebraic algorithm",
  journal =      "Computational and applied mathematics, I (Dublin,
                 1991)",
  pages =        "409--418",
  year =         "1992",
  MRclass =      "68M07 (65G05)",
  MRnumber =     "93m:68010",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


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

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

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

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

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

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


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

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

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


bibtype: inproceedings
filename: fparith.bib
label: Posch:1992:RNS
author: K. C. Posch and R. Posch
booktitle: Proceedings of the Fourth IEEE Symposium on Parallel and Distributed Processing 1992
title: Residue number systems: a key to parallelism in public key cryptography
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 432--435
year: 1992
DOI: https://doi.org/10.1109/SPDP.1992.242713
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: K. C. Posch and R. Posch
rawbooktitle: Proceedings of the Fourth {IEEE} Symposium on Parallel and Distributed Processing 1992
rawtitle: Residue number systems: a key to parallelism in public key cryptography
entry:
@InProceedings{Posch:1992:RNS,
  author =       "K. C. Posch and R. Posch",
  booktitle =    "Proceedings of the Fourth {IEEE} Symposium on Parallel
                 and Distributed Processing 1992",
  title =        "Residue number systems: a key to parallelism in public
                 key cryptography",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "432--435",
  year =         "1992",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/SPDP.1992.242713",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Public key cryptography and parallel algorithms are
                 considered. Special attention is paid to algorithms
                 using long integer modulo arithmetic. A modification of
                 the commonly known RSA algorithm is taken as a
                 candidate. So far all implementations have \ldots{}",
}


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


bibtype: phdthesis
filename: fparith.bib
label: Priest:1992:PFP
author: Douglas M. Priest
type: Thesis (Ph.D. in Mathematics)
school: Department of Computer Science, University of California, Berkeley
address: Berkeley, CA, USA
pages: iv + 136
month: dec
monthnumber: 12
year: 1992
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
note: UMI order number GAX93-30692.
URL: ftp://ftp.icsi.berkeley.edu/pub/theory/priest-thesis.ps.Z
acknowledgement: ack-nhfb
rawauthor: Douglas M. Priest
rawnote: UMI order number GAX93-30692.
title:
On Properties of Floating Point Arithmetics: Numerical Stability and the Cost of Accurate Computations

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

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

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

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

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

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

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


bibtype: article
filename: fparith.bib
label: Quach:1992:HSA
author: N. T. Quach and M. J. Flynn
title: High-speed addition in CMOS
journal: j-IEEE-TRANS-COMPUT
volume: 41
number: 12
pages: 1612--1615
month: dec
monthnumber: 12
year: 1992
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.214671
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Apr 2 08:38:35 1998
bibtimestamp: 1998.04.02 08:38:35 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-sfo
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: N. T. Quach and M. J. Flynn
rawtitle: High-speed addition in {CMOS}
entry:
@Article{Quach:1992:HSA,
  author =       "N. T. Quach and M. J. Flynn",
  title =        "High-speed addition in {CMOS}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "12",
  pages =        "1612--1615",
  month =        dec,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.214671",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


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


bibtype: article
filename: fparith.bib
label: Rao:1992:FPA
author: B. D. Rao
title: Floating point arithmetic and digital filters
journal: j-IEEE-TRANS-SIG-PROC
volume: 40
number: 1
pages: 85--95
month: jan
monthnumber: 1
year: 1992
CODEN: ITPRED
ISSN: 1053-587X (print), 1941-0476 (electronic) OR 1053587X (print), 19410476 (electronic)
ISSNL: 1053-587X OR 1053587X
bibdate: Sat Jul 16 08:40:52 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:52 MDT
fjournal: IEEE Transactions on Signal Processing
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78
rawauthor: B. D. Rao
rawtitle: Floating point arithmetic and digital filters
entry:
@Article{Rao:1992:FPA,
  author =       "B. D. Rao",
  title =        "Floating point arithmetic and digital filters",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "40",
  number =       "1",
  pages =        "85--95",
  month =        jan,
  year =         "1992",
  CODEN =        "ITPRED",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  summary =      "The roundoff noise properties of floating point
                 digital filters are examined. To make the analysis
                 tractable, a high level model to deal with the errors
                 in the inner product operation is developed. This model
                 establishes a broad connection between \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Rix:1992:CBF
author: B. Rix and D. Timmermann and H. Hahn and B. J. Hosticka
booktitle: 1992 Proceedings of the IEEE Custom Integrated Circuits Conference
title: A CORDIC-based Floating-point Arithmetic Unit
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 30.3.1--30.3.4
year: 1992
DOI: https://doi.org/10.1109/CICC.1992.591874
bibdate: Mon Oct 27 10:32:44 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2025.10.27 10:32:44 ???
acknowledgement: ack-nhfb
rawauthor: B. Rix and D. Timmermann and H. Hahn and B. J. Hosticka
rawbooktitle: {1992 Proceedings of the IEEE Custom Integrated Circuits Conference}
rawtitle: A {CORDIC}-based Floating-point Arithmetic Unit
keywords:
Adders; Floating-point arithmetic; Generators; Microelectronics; Pipelines; Registers; Routing; Throughput; Transistors; Vectors

entry:
@InProceedings{Rix:1992:CBF,
  author =       "B. Rix and D. Timmermann and H. Hahn and B. J.
                 Hosticka",
  booktitle =    "{1992 Proceedings of the IEEE Custom Integrated
                 Circuits Conference}",
  title =        "A {CORDIC}-based Floating-point Arithmetic Unit",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "30.3.1--30.3.4",
  year =         "1992",
  DOI =          "https://doi.org/10.1109/CICC.1992.591874",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Adders; Floating-point arithmetic; Generators;
                 Microelectronics; Pipelines; Registers; Routing;
                 Throughput; Transistors; Vectors",
}


bibtype: inproceedings
filename: fparith.bib
label: Rix:1992:CFA
author: B. Rix and D. Timmermann and H. Hahn and B. J. Hosticka
title: A CORDIC-based floating-point arithmetic unit
crossref: IEEE:1992:PIC
pages: 30.3/1--4
year: 1992
bibdate: Tue Dec 12 09:27:13 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.12 09:27:13 MST
acknowledgement: ack-nhfb
affiliation: Department of Electr. Eng., Duisburg University, Germany
bookpages: 766
thesaurus: CMOS integrated circuits; Digital arithmetic; Digital signal processing chips
rawauthor: B. Rix and D. Timmermann and H. Hahn and B. J. Hosticka
rawtitle: A {CORDIC}-based floating-point arithmetic unit
abstract:
A floating-point arithmetic unit based on the CORDIC algorithm is described. It computes a wide range of arithmetic, trigonometric, and hyperbolic functions and achieves a normalized peak performance of 220 MFLOPS. The unit is implemented in 1.6- mu m double-metal CMOS technology and packaged in a 280-pin PGA.

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

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

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


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


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


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


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


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


bibtype: article
filename: fparith.bib
label: Seznec:1992:OFC
author: A. Seznec and K. Courtel
title: OPAC: a Floating-Point Coprocessor Dedicated to Compute-Bound Kernels
journal: j-COMP-ARCH-NEWS
volume: 20
number: 2
pages: 427--427
month: may
monthnumber: 5
year: 1992
CODEN: CANED2
ISSN: 0163-5964 (print), 1943-5851 (electronic) OR 01635964 (print), 19435851 (electronic)
ISSNL: 0163-5964 OR 01635964
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
fjournal: ACM SIGARCH Computer Architecture News
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/sigarch
rawauthor: A. Seznec and K. Courtel
rawtitle: {OPAC}: a Floating-Point Coprocessor Dedicated to Compute-Bound Kernels
entry:
@Article{Seznec:1992:OFC,
  author =       "A. Seznec and K. Courtel",
  title =        "{OPAC}: a Floating-Point Coprocessor Dedicated to
                 Compute-Bound Kernels",
  journal =      j-COMP-ARCH-NEWS,
  volume =       "20",
  number =       "2",
  pages =        "427--427",
  month =        may,
  year =         "1992",
  CODEN =        "CANED2",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "https://dl.acm.org/loi/sigarch",
}


bibtype: article
filename: fparith.bib
label: Simar:1992:FPP
title: Floating-Point Processors Join Forces in Parallel Processing Architectures
journal: j-IEEE-MICRO
volume: 12
number: 4
pages: 60--69
month: jul
monthnumber: 7
year: 1992
CODEN: IEMIDZ
DOI: https://doi.org/10.1109/40.149737
ISSN: 0272-1732 (print), 1937-4143 (electronic) OR 02721732 (print), 19374143 (electronic)
ISSNL: 0272-1732 OR 02721732
bibdate: Sat Jul 16 08:40:52 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:52 MDT
fjournal: IEEE Micro
acknowledgement: ack-nhfb
journalURL: http://www.computer.org/csdl/mags/mi/index.html
rawtitle: Floating-Point Processors Join Forces in Parallel Processing Architectures
author:
Ray Simar, Jr. and Peter Koeppen and Jerald Leach and Steve Marshall and Dave Francis and Greg Mekras and Jeffrey Rosenstrauch and Scott Anderson

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

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

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

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


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

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

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

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

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


bibtype: article
filename: fparith.bib
label: Skavantzos:1992:DCM
author: A. Skavantzos and T. Stouraitis
title: Decomposition of complex multipliers using polynomial encoding
journal: j-IEEE-TRANS-COMPUT
volume: 41
number: 10
pages: 1331--1333
month: oct
monthnumber: 10
year: 1992
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.166610
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 10:49:20 MDT 2011
bibtimestamp: 2011.07.07 10:49:20 MDT
note: See comments cite Katti:1994:CDC.
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=166610
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: A. Skavantzos and T. Stouraitis
rawnote: See comments \cite{Katti:1994:CDC}.
rawtitle: Decomposition of complex multipliers using polynomial encoding
entry:
@Article{Skavantzos:1992:DCM,
  author =       "A. Skavantzos and T. Stouraitis",
  title =        "Decomposition of complex multipliers using polynomial
                 encoding",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "10",
  pages =        "1331--1333",
  month =        oct,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.166610",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 10:49:20 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  note =         "See comments \cite{Katti:1994:CDC}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=166610",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Skavantzos:1992:NMM
author: A. Skavantzos and P. B. Rao
title: New multipliers modulo $ 2^N - 1 $
journal: j-IEEE-TRANS-COMPUT
volume: 41
number: 8
pages: 957--961
month: aug
monthnumber: 8
year: 1992
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.156538
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 10:49:19 MDT 2011
bibtimestamp: 2011.07.07 10:49:19 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156538
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: A. Skavantzos and P. B. Rao
rawtitle: New multipliers modulo {$ 2^N - 1 $}
entry:
@Article{Skavantzos:1992:NMM,
  author =       "A. Skavantzos and P. B. Rao",
  title =        "New multipliers modulo {$ 2^N - 1 $}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "8",
  pages =        "957--961",
  month =        aug,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.156538",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 10:49:19 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156538",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


