# bibtab

bibtype: inproceedings
filename: fparith.bib
label: Ciminiera:1987:PMB
author: Luigi Ciminiera
title: Parallel Multipliers Based on Horizontal Compressors
crossref: Irwin:1987:PSC
pages: 63--69
month: may
monthnumber: 5
year: 1987
DOI: https://doi.org/10.1109/ARITH.1987.6158687
bibdate: Wed Nov 14 18:22:26 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 18:22:26 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Ciminiera.pdf
keywords: ARITH-8
acknowledgement: ack-nhfb
rawauthor: Luigi Ciminiera
rawtitle: Parallel Multipliers Based on Horizontal Compressors
abstract:
Two new implementations of parallel multipliers, based on iterative arrays of logic cells are presented in this paper. Both are able to compute the product of two $n$ bit numbers with a delay of $n$ cells, rather $ 2 n - 1 $ as in classical structures. The high speed operation is obtained by using pure horizontal compressors, to accelerate the horizontal signal propagation, and by adopting a suitable array structure, to shorten the vertical signal propagation. The cost and performance advantages over similar structures based on vertical compressors are discussed.

rawabstract:
Two new implementations of parallel multipliers, based on iterative arrays of logic cells are presented in this paper. Both are able to compute the product of two $n$ bit numbers with a delay of $n$ cells, rather $ 2 n - 1 $ as in classical structures. The high speed operation is obtained by using pure horizontal compressors, to accelerate the horizontal signal propagation, and by adopting a suitable array structure, to shorten the vertical signal propagation. The cost and performance advantages over similar structures based on vertical compressors are discussed.

entry:
@InProceedings{Ciminiera:1987:PMB,
  author =       "Luigi Ciminiera",
  title =        "Parallel Multipliers Based on Horizontal Compressors",
  crossref =     "Irwin:1987:PSC",
  pages =        "63--69",
  month =        may,
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158687",
  bibdate =      "Wed Nov 14 18:22:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Ciminiera.pdf",
  abstract =     "Two new implementations of parallel multipliers, based
                 on iterative arrays of logic cells are presented in
                 this paper. Both are able to compute the product of two
                 $n$ bit numbers with a delay of $n$ cells, rather $ 2 n
                 - 1 $ as in classical structures. The high speed
                 operation is obtained by using pure horizontal
                 compressors, to accelerate the horizontal signal
                 propagation, and by adopting a suitable array
                 structure, to shorten the vertical signal propagation.
                 The cost and performance advantages over similar
                 structures based on vertical compressors are
                 discussed.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}


bibtype: article
filename: fparith.bib
label: Clenshaw:1987:LIA
author: C. W. Clenshaw and Frank W. J. Olver
title: Level-Index Arithmetic Operations
journal: j-SIAM-J-NUMER-ANAL
volume: 24
number: 2
pages: 470--485
month: apr
monthnumber: 4
year: 1987
CODEN: SJNAAM
DOI: https://doi.org/10.1137/0724034
ISSN: 0036-1429 (print), 1095-7170 (electronic) OR 00361429 (print), 10957170 (electronic)
ISSNL: 0036-1429 OR 00361429
MRclass: 65G05 (65G99)
MRnumber: 881377
MRreviewer: F. Szidarovszky
bibdate: Sun Nov 12 06:18:24 2023
bibtimestamp: 2023.11.12 06:18:24 ???
fjournal: SIAM Journal on Numerical Analysis
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sinum
rawauthor: C. W. Clenshaw and Frank W. J. Olver
rawtitle: Level-Index Arithmetic Operations
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib; https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
In a recent paper the authors described a system for the internal representation of numbers in a computer, based on repeated exponentiations. The main objective in introducing this system is to eradicate the problems of overflow and underflow. The present paper supplies algorithms for performing the four basic arithmetical operations in the new system. The algorithm are accompanied by error analyses, which show that the algorithms can be executed with fixed-point arithmetic. Illustrative examples are included.

authordates:
Charles William Clenshaw (15 March 1926--23 September 2004); Frank William John Olver (15 December 1924--23 April 2013)

rawabstract:
In a recent paper the authors described a system for the internal representation of numbers in a computer, based on repeated exponentiations. The main objective in introducing this system is to eradicate the problems of overflow and underflow. The present paper supplies algorithms for performing the four basic arithmetical operations in the new system. The algorithm are accompanied by error analyses, which show that the algorithms can be executed with fixed-point arithmetic. Illustrative examples are included.

entry:
@Article{Clenshaw:1987:LIA,
  author =       "C. W. Clenshaw and Frank W. J. Olver",
  title =        "Level-Index Arithmetic Operations",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "24",
  number =       "2",
  pages =        "470--485",
  month =        apr,
  year =         "1987",
  CODEN =        "SJNAAM",
  DOI =          "https://doi.org/10.1137/0724034",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  MRclass =      "65G05 (65G99)",
  MRnumber =     "881377",
  MRreviewer =   "F. Szidarovszky",
  bibdate =      "Sun Nov 12 06:18:24 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In a recent paper the authors described a system for
                 the internal representation of numbers in a computer,
                 based on repeated exponentiations. The main objective
                 in introducing this system is to eradicate the problems
                 of overflow and underflow. The present paper supplies
                 algorithms for performing the four basic arithmetical
                 operations in the new system. The algorithm are
                 accompanied by error analyses, which show that the
                 algorithms can be executed with fixed-point arithmetic.
                 Illustrative examples are included.",
  acknowledgement = ack-nhfb,
  author-dates = "Charles William Clenshaw (15 March 1926--23 September
                 2004); Frank William John Olver (15 December 1924--23
                 April 2013)",
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
}


bibtype: inproceedings
filename: fparith.bib
label: Colagrossi:1987:NAT
author: A. Colagrossi and A. Miola
title: A Normalization Algorithm for Truncated $p$-ADIC Arithmetic
crossref: Irwin:1987:PSC
pages: 212--216
year: 1987
DOI: https://doi.org/10.1109/ARITH.1987.6158688
bibdate: Fri Nov 16 21:39:46 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.16 21:39:46 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Colagrossi_Miola.pdf
keywords: ARITH-8
acknowledgement: ack-nhfb
rawauthor: A. Colagrossi and A. Miola
rawtitle: A Normalization Algorithm for Truncated $p$-{ADIC} Arithmetic
abstract:
This paper presents a new algorithmic approach to cope with the problems related to the generation and the manipulation of the pseudo-Hensel-codes in the p-adic arithmetic. After reviewing some classical properties and the results of the Hensel code arithmetic, a new algorithm to manipulate pseudo-Hensel-codes is presented, discussed and compared with two existing methods. The lower cost of the proposed new algorithm will result from the comparison.

rawabstract:
This paper presents a new algorithmic approach to cope with the problems related to the generation and the manipulation of the pseudo-Hensel-codes in the p-adic arithmetic. After reviewing some classical properties and the results of the Hensel code arithmetic, a new algorithm to manipulate pseudo-Hensel-codes is presented, discussed and compared with two existing methods. The lower cost of the proposed new algorithm will result from the comparison.

entry:
@InProceedings{Colagrossi:1987:NAT,
  author =       "A. Colagrossi and A. Miola",
  title =        "A Normalization Algorithm for Truncated $p$-{ADIC}
                 Arithmetic",
  crossref =     "Irwin:1987:PSC",
  pages =        "212--216",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158688",
  bibdate =      "Fri Nov 16 21:39:46 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Colagrossi_Miola.pdf",
  abstract =     "This paper presents a new algorithmic approach to cope
                 with the problems related to the generation and the
                 manipulation of the pseudo-Hensel-codes in the p-adic
                 arithmetic. After reviewing some classical properties
                 and the results of the Hensel code arithmetic, a new
                 algorithm to manipulate pseudo-Hensel-codes is
                 presented, discussed and compared with two existing
                 methods. The lower cost of the proposed new algorithm
                 will result from the comparison.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}


bibtype: inproceedings
filename: fparith.bib
label: Cosnard:1987:FAC
title: The FELIN Arithmetic Coprocessor Chip
crossref: Irwin:1987:PSC
pages: 107--112
month: may
monthnumber: 5
year: 1987
DOI: https://doi.org/10.1109/ARITH.1987.6158691
bibdate: Wed Nov 14 18:22:26 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 18:22:26 ???
keywords: ARITH-8
acknowledgement: ack-nhfb
rawtitle: The {FELIN} Arithmetic Coprocessor Chip
author:
M. Cosnard and A. Guyot and B. Hochet and Jean-Michel Muller and H. Ouaouicha and P. Paul and E. Zysman

URL:
http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Cosnard_Guyot_Hochet_Muller_Ouaouicha_Paul_Zysman.pdf

abstract:
We describe a general VLSI architecture for the computation of arithmetic expressions including floating-point transcendental functions. This architecture, is divided in three parts: a communication machine, the control part of a computation machine and the operative part of this computation machine. In order to compute the most usual transcendental functions, we introduced some general algorithms, presented briefly here, including as a particular case the CORDIC scheme. Our major architecture goals were regularity, parametrization and automatic design. The final chip is designed in a 2-Alu CMOS technology, and its name is FELIN (``Fonctions ELementaires INtegrees'' is the French for ``integrated elementary functions'').

rawabstract:
We describe a general VLSI architecture for the computation of arithmetic expressions including floating-point transcendental functions. This architecture, is divided in three parts: a communication machine, the control part of a computation machine and the operative part of this computation machine. In order to compute the most usual transcendental functions, we introduced some general algorithms, presented briefly here, including as a particular case the CORDIC scheme. Our major architecture goals were regularity, parametrization and automatic design. The final chip is designed in a 2-Alu CMOS technology, and its name is FELIN (``Fonctions EL{\'e}mentaires INt{\'e}gr{\'e}es'' is the French for ``integrated elementary functions'').

rawauthor:
M. Cosnard and A. Guyot and B. Hochet and Jean-Michel Muller and H. Ouaouicha and P. Paul and E. Zysman

entry:
@InProceedings{Cosnard:1987:FAC,
  author =       "M. Cosnard and A. Guyot and B. Hochet and Jean-Michel
                 Muller and H. Ouaouicha and P. Paul and E. Zysman",
  title =        "The {FELIN} Arithmetic Coprocessor Chip",
  crossref =     "Irwin:1987:PSC",
  pages =        "107--112",
  month =        may,
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158691",
  bibdate =      "Wed Nov 14 18:22:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Cosnard_Guyot_Hochet_Muller_Ouaouicha_Paul_Zysman.pdf",
  abstract =     "We describe a general VLSI architecture for the
                 computation of arithmetic expressions including
                 floating-point transcendental functions. This
                 architecture, is divided in three parts: a
                 communication machine, the control part of a
                 computation machine and the operative part of this
                 computation machine. In order to compute the most usual
                 transcendental functions, we introduced some general
                 algorithms, presented briefly here, including as a
                 particular case the CORDIC scheme. Our major
                 architecture goals were regularity, parametrization and
                 automatic design. The final chip is designed in a 2-Alu
                 CMOS technology, and its name is FELIN (``Fonctions
                 EL{\'e}mentaires INt{\'e}gr{\'e}es'' is the French for
                 ``integrated elementary functions'').",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}


bibtype: techreport
filename: fparith.bib
label: Crockett:1987:PFF
author: Thomas W. Crockett
title: Performance of Fortran Floating-Point Operations on the Flex / 32 Multicomputer
type: ICASE Interim Report
number: 4
institution: ICASE, NASA Langley Research Center
address: Hampton, VA, USA
year: 1987
bibdate: Wed Sep 14 20:24:43 1994
bibtimestamp: 1994.09.14 20:24:43 ???
series: NASA contractor report; 178364 ICASE interim report; 4 NASA contractor report; NASA CR-178364.
keywords: Computer networks; FORTRAN (Computer program language)
acknowledgement: ack-nj
rawauthor: Thomas W. Crockett
rawtitle: Performance of {Fortran} Floating-Point Operations on the {Flex\slash 32} Multicomputer
bibsource:
https://www.math.utah.edu/pub/tex/bib/fortran2.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ovr.bib; Parallel/ovr.bib

remark:
Distributed to depository libraries in microfiche. Microfiche. [Washington, D.C.?: National Aeronautics and Space Administration], 1987. 1 microfiche.

entry:
@TechReport{Crockett:1987:PFF,
  author =       "Thomas W. Crockett",
  title =        "Performance of {Fortran} Floating-Point Operations on
                 the {Flex\slash 32} Multicomputer",
  type =         "{ICASE} Interim Report",
  number =       "4",
  institution =  "ICASE, NASA Langley Research Center",
  address =      "Hampton, VA, USA",
  pages =        "????",
  year =         "1987",
  bibdate =      "Wed Sep 14 20:24:43 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran2.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ovr.bib;
                 Parallel/ovr.bib",
  series =       "NASA contractor report; 178364 ICASE interim report; 4
                 NASA contractor report; NASA CR-178364.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  govtdocnumber = "NAS 1.26:178364 830-H-14 (MF)",
  keywords =     "Computer networks; FORTRAN (Computer program
                 language)",
  remark =       "Distributed to depository libraries in microfiche.
                 Microfiche. [Washington, D.C.?: National Aeronautics
                 and Space Administration], 1987. 1 microfiche.",
}


bibtype: incollection
filename: fparith.bib
label: Crowell:1987:FPA
author: Charles Crowell
title: Floating-point arithmetic with the TMS32020
crossref: Lin:1987:DSP
pages: 245--268
year: 1987
bibdate: Sat Nov 9 08:26:18 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.11.09 08:26:18 MST
acknowledgement: ack-nhfb
rawauthor: Charles Crowell
rawtitle: Floating-point arithmetic with the {TMS32020}
subject:
J. Computer Applications; J.2 PHYSICAL SCIENCES AND ENGINEERING; C. Computer Systems Organization; C.5 COMPUTER SYSTEM IMPLEMENTATION; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS

entry:
@InCollection{Crowell:1987:FPA,
  author =       "Charles Crowell",
  title =        "Floating-point arithmetic with the {TMS32020}",
  crossref =     "Lin:1987:DSP",
  pages =        "245--268",
  year =         "1987",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$30.67",
  acknowledgement = ack-nhfb,
  bibno =        "42623",
  catcode =      "J.2; C.5.3; G.1.0",
  CRclass =      "J.2 Mathematics and statistics; C.5.3 Microcomputers;
                 C.5.3 TMS 32010; G.1.0 General; G.1.0 Computer
                 arithmetic",
  descriptor =   "Computer Applications, PHYSICAL SCIENCES AND
                 ENGINEERING, Mathematics and statistics; Computer
                 Systems Organization, COMPUTER SYSTEM IMPLEMENTATION,
                 Microcomputers, TMS 32010; Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Computer arithmetic",
  genterm =      "MEASUREMENT; ALGORITHMS",
  guideno =      "1988-01737",
  subject =      "J. Computer Applications; J.2 PHYSICAL SCIENCES AND
                 ENGINEERING; C. Computer Systems Organization; C.5
                 COMPUTER SYSTEM IMPLEMENTATION; G. Mathematics of
                 Computing; G.1 NUMERICAL ANALYSIS",
}


bibtype: inproceedings
filename: fparith.bib
label: Demmel:1987:EAA
author: James W. Demmel
title: On error analysis in arithmetic with varying relative precision
crossref: Irwin:1987:PSC
pages: 148--152
year: 1987
DOI: https://doi.org/10.1109/ARITH.1987.6158694
bibdate: Thu Aug 23 06:14:44 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.08.23 06:14:44 ???
URL: http://www.netlib.org/na-digest/91/v91n39
keywords: ARITH-8
acknowledgement: ack-nhfb
rawauthor: James W. Demmel
rawtitle: On error analysis in arithmetic with varying relative precision
abstract:
Recently Clenshaw / Olver and Iri / Matsui proposed new floating point arithmetics which seek to eliminate overflows and underflows from most computations. Their common approach is to redistribute the available numbers to spread out the largest and smallest numbers much more thinly than in standard floating point, thus achieving a larger range at the cost of lower precision at the ends of the range. The goal of these arithmetics is to eliminate much of the effort needed to write code which is reliable despite over / underflow. In this paper we argue that for many codes this eliminated effort will reappear in the error analyses needed to ascertain or guarantee the accuracy of the computed solution. Thus reliability with respect to over / underflow has been traded for reliability with respect to roundoff. We also propose a hardware flag, analogous to the ``sticky flags'' of the IEEE binary floating point standard, to do some of this extra error analysis automatically.

remark:
Comments on SLI arithmetic proposed by Olver, Lozier, and Turner, and on Kulisch and Miranker's interval arithmetic and its implementation in IBM's ACRITH product.

rawabstract:
Recently Clenshaw\slash Olver and Iri\slash Matsui proposed new floating point arithmetics which seek to eliminate overflows and underflows from most computations. Their common approach is to redistribute the available numbers to spread out the largest and smallest numbers much more thinly than in standard floating point, thus achieving a larger range at the cost of lower precision at the ends of the range. The goal of these arithmetics is to eliminate much of the effort needed to write code which is reliable despite over\slash underflow. In this paper we argue that for many codes this eliminated effort will reappear in the error analyses needed to ascertain or guarantee the accuracy of the computed solution. Thus reliability with respect to over\slash underflow has been traded for reliability with respect to roundoff. We also propose a hardware flag, analogous to the ``sticky flags'' of the IEEE binary floating point standard, to do some of this extra error analysis automatically.

entry:
@InProceedings{Demmel:1987:EAA,
  author =       "James W. Demmel",
  title =        "On error analysis in arithmetic with varying relative
                 precision",
  crossref =     "Irwin:1987:PSC",
  pages =        "148--152",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158694",
  bibdate =      "Thu Aug 23 06:14:44 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.netlib.org/na-digest/91/v91n39",
  abstract =     "Recently Clenshaw\slash Olver and Iri\slash Matsui
                 proposed new floating point arithmetics which seek to
                 eliminate overflows and underflows from most
                 computations. Their common approach is to redistribute
                 the available numbers to spread out the largest and
                 smallest numbers much more thinly than in standard
                 floating point, thus achieving a larger range at the
                 cost of lower precision at the ends of the range. The
                 goal of these arithmetics is to eliminate much of the
                 effort needed to write code which is reliable despite
                 over\slash underflow. In this paper we argue that for
                 many codes this eliminated effort will reappear in the
                 error analyses needed to ascertain or guarantee the
                 accuracy of the computed solution. Thus reliability
                 with respect to over\slash underflow has been traded
                 for reliability with respect to roundoff. We also
                 propose a hardware flag, analogous to the ``sticky
                 flags'' of the IEEE binary floating point standard, to
                 do some of this extra error analysis automatically.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
  remark =       "Comments on SLI arithmetic proposed by Olver, Lozier,
                 and Turner, and on Kulisch and Miranker's interval
                 arithmetic and its implementation in IBM's ACRITH
                 product.",
}


bibtype: techreport
filename: fparith.bib
label: Dion:1987:MFA
author: Jeremy Dion and David Reeves Boggs and Norman P. Jouppi
title: MultiTitan: four architecture papers
institution: Digital, Western Research Laboratory
address: Palo Alto, CA, USA
pages: various
year: 1987
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: Titan (Computer)
acknowledgement: ack-nhfb
rawauthor: Jeremy Dion and David Reeves Boggs and Norman P. Jouppi
rawtitle: {MultiTitan}: four architecture papers
series:
WRL research report. Digital Equipment Corporation. Western Research Laboratory; 87-8 Digital Equipment Corporation. Western Research Laboratory. WRL research report; 87/8.

entry:
@TechReport{Dion:1987:MFA,
  author =       "Jeremy Dion and David Reeves Boggs and Norman P.
                 Jouppi",
  title =        "{MultiTitan}: four architecture papers",
  institution =  "Digital, Western Research Laboratory",
  address =      "Palo Alto, CA, USA",
  pages =        "various",
  year =         "1987",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "WRL research report. Digital Equipment Corporation.
                 Western Research Laboratory; 87-8 Digital Equipment
                 Corporation. Western Research Laboratory. WRL research
                 report; 87/8.",
  acknowledgement = ack-nhfb,
  keywords =     "Titan (Computer)",
}


bibtype: inproceedings
filename: fparith.bib
label: DuCroz:1987:DFP
author: J. Du Croz and M. Pont
title: The Development of a Floating-Point Validation Package
crossref: Irwin:1987:PSC
pages: 255--255
year: 1987
DOI: https://doi.org/10.1109/ARITH.1987.6158693
bibdate: Fri Nov 16 21:39:46 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.16 21:39:46 ???
keywords: ARITH-8
remark: Paper not received in time for publication.
acknowledgement: ack-nhfb
rawauthor: J. {Du Croz} and M. Pont
rawtitle: The Development of a Floating-Point Validation Package
entry:
@InProceedings{DuCroz:1987:DFP,
  author =       "J. {Du Croz} and M. Pont",
  title =        "The Development of a Floating-Point Validation
                 Package",
  crossref =     "Irwin:1987:PSC",
  pages =        "255--255",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158693",
  bibdate =      "Fri Nov 16 21:39:46 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
  remark =       "Paper not received in time for publication.",
}


bibtype: article
filename: fparith.bib
label: Duff:1987:EAP
author: Iain S. Duff and Jacques Laminie and Alain Lichnewsky and Francois Thomasset
title: An experiment with arithmetic precision in linear algebra computations
journal: j-INT-J-NUM-METH-FLUIDS
volume: 7
pages: 1077--1092
year: 1987
bibdate: Mon Jan 02 17:53:34 2006
bibtimestamp: 2006.01.02 17:53:34 ???
acknowledgement: ack-nhfb
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0363
rawauthor: Iain S. Duff and Jacques Laminie and Alain Lichnewsky and Fran{\c{c}}ois Thomasset
rawtitle: An experiment with arithmetic precision in linear algebra computations
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Duff:1987:EAP,
  author =       "Iain S. Duff and Jacques Laminie and Alain Lichnewsky
                 and Fran{\c{c}}ois Thomasset",
  title =        "An experiment with arithmetic precision in linear
                 algebra computations",
  journal =      j-INT-J-NUM-METH-FLUIDS,
  volume =       "7",
  number =       "????",
  pages =        "1077--1092",
  year =         "1987",
  bibdate =      "Mon Jan 02 17:53:34 2006",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0363",
}


bibtype: manual
filename: fparith.bib
label: Duhamel:1987:ASR
author: Bob Duhamel
title: Atari System Reference Manual
address: 6915 Casselberry Way, San Diego, CA 92119, USA
pages: 1077--1092
year: 1987
bibdate: Sat Mar 04 16:04:10 2006
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2006.03.04 16:04:10 ???
note: See Chapter 11: The Floating Point Arithmetic Package.
keywords: decimal floating-point arithmetic
acknowledgement: ack-nhfb
rawauthor: Bob Duhamel
rawnote: See Chapter 11: The Floating Point Arithmetic Package.
rawtitle: {Atari} System Reference Manual
URL:
http://atrey.karlin.mff.cuni.cz/~pavel/atari/atr11.html; http://web.archive.org/web/20040606074520/trident.mcs.kent.edu/~clisowsk/8bit/atrpref.html

remark:
The ROM O/S on the Atari 6502 handles decimal floating-point values stored in six-byte fields. The first byte contains the sign and an excess-64 exponent, followed by five bytes containing ten BCD digits. The O/S provides for conversion to and from ASCII string representation, to and from binary integers, add, subtract, multiple, divide, log(), log10(), exp(), exp10(), and polynomial evaluation.

entry:
@Manual{Duhamel:1987:ASR,
  author =       "Bob Duhamel",
  title =        "{Atari} System Reference Manual",
  address =      "6915 Casselberry Way, San Diego, CA 92119, USA",
  year =         "1987",
  bibdate =      "Sat Mar 04 16:04:10 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See Chapter 11: The Floating Point Arithmetic
                 Package.",
  URL =          "http://atrey.karlin.mff.cuni.cz/~pavel/atari/atr11.html;
                 http://web.archive.org/web/20040606074520/trident.mcs.kent.edu/~clisowsk/8bit/atrpref.html",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
  remark =       "The ROM O/S on the Atari 6502 handles decimal
                 floating-point values stored in six-byte fields. The
                 first byte contains the sign and an excess-64 exponent,
                 followed by five bytes containing ten BCD digits. The
                 O/S provides for conversion to and from ASCII string
                 representation, to and from binary integers, add,
                 subtract, multiple, divide, log(), log10(), exp(),
                 exp10(), and polynomial evaluation.",
}


bibtype: article
filename: fparith.bib
label: Dunham:1987:PMA
author: C. B. Dunham
title: Provably Monotone Approximations II
journal: j-SIGNUM
volume: 22
number: 3
pages: 30--31
month: jul
monthnumber: 7
year: 1987
CODEN: SNEWD6
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Tue Sep 13 09:01:31 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.13 09:01:31 ???
fjournal: ACM SIGNUM Newsletter
keywords: theory
subject: G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS, Approximation
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/signum
rawauthor: C. B. Dunham
rawtitle: Provably Monotone Approximations {II}
entry:
@Article{Dunham:1987:PMA,
  author =       "C. B. Dunham",
  title =        "Provably Monotone Approximations {II}",
  journal =      j-SIGNUM,
  volume =       "22",
  number =       "3",
  pages =        "30--31",
  month =        jul,
  year =         "1987",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Sep 13 09:01:31 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "theory",
  subject =      "G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation",
}


bibtype: article
filename: fparith.bib
label: Ercegovac:1987:FCR
author: M. D. Ercegovac and T. Lang
title: On-the-fly conversion of redundant into conventional representations
journal: j-IEEE-TRANS-COMPUT
volume: C-36
number: 7
pages: 895--897
month: jul
monthnumber: 7
year: 1987
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1987.1676986
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: M. D. Ercegovac and T. Lang
rawtitle: On-the-fly conversion of redundant into conventional representations
entry:
@Article{Ercegovac:1987:FCR,
  author =       "M. D. Ercegovac and T. Lang",
  title =        "On-the-fly conversion of redundant into conventional
                 representations",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-36",
  number =       "7",
  pages =        "895--897",
  month =        jul,
  year =         "1987",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1987.1676986",
  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/ieeetranscomput1980.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: inproceedings
filename: fparith.bib
label: Ercegovac:1987:LSC
author: Milos D. Ercegovac and Tomas Lang
title: On-Line Scheme for Computing Rotation Factors
crossref: Irwin:1987:PSC
pages: 196--203
year: 1987
DOI: https://doi.org/10.1109/ARITH.1987.6158695
bibdate: Fri Nov 16 21:39:46 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.16 21:39:46 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Ercegovac_Lang.pdf
keywords: ARITH-8
acknowledgement: ack-nhfb
rawauthor: Milo{\v{s}} D. Ercegovac and Tomas Lang
rawtitle: On-Line Scheme for Computing Rotation Factors
abstract:
An integrated radix-2 on-line algorithm for computing rotation factors for matrix transformations is presented. The inputs and outputs are in parallel form, conventional 2's complement, floating-point representation. The exponents are computed using conventional arithmetic while the significands are processed using on-line algorithms. The conventional result is obtained by using an on-the-fly conversion scheme. The rotation factors are computed in $ 9 + n $ clock cycles for $n$-bit significands. The clock period is kept small by the use of carry-save adder schemes. The implementation and performance of the algorithm are discussed.

rawabstract:
An integrated radix-2 on-line algorithm for computing rotation factors for matrix transformations is presented. The inputs and outputs are in parallel form, conventional 2's complement, floating-point representation. The exponents are computed using conventional arithmetic while the significands are processed using on-line algorithms. The conventional result is obtained by using an on-the-fly conversion scheme. The rotation factors are computed in $ 9 + n $ clock cycles for $n$-bit significands. The clock period is kept small by the use of carry-save adder schemes. The implementation and performance of the algorithm are discussed.

entry:
@InProceedings{Ercegovac:1987:LSC,
  author =       "Milo{\v{s}} D. Ercegovac and Tomas Lang",
  title =        "On-Line Scheme for Computing Rotation Factors",
  crossref =     "Irwin:1987:PSC",
  pages =        "196--203",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158695",
  bibdate =      "Fri Nov 16 21:39:46 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Ercegovac_Lang.pdf",
  abstract =     "An integrated radix-2 on-line algorithm for computing
                 rotation factors for matrix transformations is
                 presented. The inputs and outputs are in parallel form,
                 conventional 2's complement, floating-point
                 representation. The exponents are computed using
                 conventional arithmetic while the significands are
                 processed using on-line algorithms. The conventional
                 result is obtained by using an on-the-fly conversion
                 scheme. The rotation factors are computed in $ 9 + n $
                 clock cycles for $n$-bit significands. The clock period
                 is kept small by the use of carry-save adder schemes.
                 The implementation and performance of the algorithm are
                 discussed.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}


bibtype: inproceedings
filename: fparith.bib
label: Fandrianto:1987:AHS
author: Jan Fandrianto
title: Algorithms for High Speed Shared Radix 4 Division and Radix 4 Square-Root
crossref: Irwin:1987:PSC
pages: 73--79
year: 1987
DOI: https://doi.org/10.1109/ARITH.1987.6158696
bibdate: Wed Nov 14 18:22:26 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 18:22:26 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Fandrianto.pdf
keywords: ARITH-8; correct rounding; floating-point arithmetic
acknowledgement: ack-nhfb
rawauthor: Jan Fandrianto
rawtitle: Algorithms for High Speed Shared Radix 4 Division and Radix 4 Square-Root
abstract:
An algorithm to implement radix four division and radix four square-root in a shared hardware for IEEE standard for binary floating point format will be described. The algorithm is best suited to be implemented in either off-the-shelf components or being a portion of a VLSI floating-point chip. Division and square-root bits are generated by a non-restoring method while keeping the partial remainder, partial radicand, quotient and root all in redundant forms. The core iteration involves a 8-bit carry look-ahead adder, a multiplexer to convert two's complement to sign magnitude, a 19-term next quotient / root prediction PLA, a divisor / root multiple selector, and a carry save adder. At the end, two iterations of carry look-ahead adder across the length of th,e mantissa are required to generate the quotient / root in a correctly rounded form. Despite its simplicity in the hardware requirement, the algorithm takes only about 30 cycles to compute double precision division or square-root. Finally, extending the algorithm to radix eight or higher division / square-root will be discussed.

rawabstract:
An algorithm to implement radix four division and radix four square-root in a shared hardware for IEEE standard for binary floating point format will be described. The algorithm is best suited to be implemented in either off-the-shelf components or being a portion of a VLSI floating-point chip. Division and square-root bits are generated by a non-restoring method while keeping the partial remainder, partial radicand, quotient and root all in redundant forms. The core iteration involves a 8-bit carry look-ahead adder, a multiplexer to convert two's complement to sign magnitude, a 19-term next quotient\slash root prediction PLA, a divisor\slash root multiple selector, and a carry save adder. At the end, two iterations of carry look-ahead adder across the length of th,e mantissa are required to generate the quotient\slash root in a correctly rounded form. Despite its simplicity in the hardware requirement, the algorithm takes only about 30 cycles to compute double precision division or square-root. Finally, extending the algorithm to radix eight or higher division\slash square-root will be discussed.

entry:
@InProceedings{Fandrianto:1987:AHS,
  author =       "Jan Fandrianto",
  title =        "Algorithms for High Speed Shared Radix 4 Division and
                 Radix 4 Square-Root",
  crossref =     "Irwin:1987:PSC",
  pages =        "73--79",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158696",
  bibdate =      "Wed Nov 14 18:22:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Fandrianto.pdf",
  abstract =     "An algorithm to implement radix four division and
                 radix four square-root in a shared hardware for IEEE
                 standard for binary floating point format will be
                 described. The algorithm is best suited to be
                 implemented in either off-the-shelf components or being
                 a portion of a VLSI floating-point chip. Division and
                 square-root bits are generated by a non-restoring
                 method while keeping the partial remainder, partial
                 radicand, quotient and root all in redundant forms. The
                 core iteration involves a 8-bit carry look-ahead adder,
                 a multiplexer to convert two's complement to sign
                 magnitude, a 19-term next quotient\slash root
                 prediction PLA, a divisor\slash root multiple selector,
                 and a carry save adder. At the end, two iterations of
                 carry look-ahead adder across the length of th,e
                 mantissa are required to generate the quotient\slash
                 root in a correctly rounded form. Despite its
                 simplicity in the hardware requirement, the algorithm
                 takes only about 30 cycles to compute double precision
                 division or square-root. Finally, extending the
                 algorithm to radix eight or higher division\slash
                 square-root will be discussed.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8; correct rounding; floating-point arithmetic",
}


bibtype: periodical
filename: fparith.bib
label: FPS:1987:AR
author: Floating Point Systems, Inc.
title: Annual report
publisher: Floating Point Systems, Inc.
address: Portland, OR, USA
pages: various
year: 1987
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Computer industry --- United States --- Periodicals.; Floating Point Systems, Inc. --- Periodicals.
remark: Description based on: 1987.
acknowledgement: ack-nhfb
key: FPS
rawauthor: {Floating Point Systems, Inc.}
rawtitle: Annual report
entry:
@Periodical{FPS:1987:AR,
  author =       "{Floating Point Systems, Inc.}",
  key =          "FPS",
  title =        "Annual report",
  publisher =    "Floating Point Systems, Inc.",
  address =      "Portland, OR, USA",
  pages =        "various",
  year =         "1987",
  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 industry --- United States --- Periodicals.;
                 Floating Point Systems, Inc. --- Periodicals.",
  remark =       "Description based on: 1987.",
}


bibtype: article
filename: fparith.bib
label: Froggatt:1987:FPC
author: Terry Froggatt
title: Fixed-point conversion, multiplication, and division in Ada
journal: j-SIGADA-LETTERS
volume: 7
number: 1
pages: 71--81
month: jan
monthnumber: 1
year: 1987
CODEN: AALEE5
ISSN: 1094-3641 (print), 1557-9476 (electronic) OR 10943641 (print), 15579476 (electronic)
ISSNL: 1094-3641 OR 10943641
bibdate: Sat Aug 9 09:05:24 MDT 2003
bibtimestamp: 2003.08.09 09:05:24 MDT
fjournal: ACM SIGAda Ada Letters
keywords: languages; theory
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/citation.cfm?id=J32
rawauthor: Terry Froggatt
rawtitle: Fixed-point conversion, multiplication, and division in {Ada}
bibsource:
ftp://ftp.uu.net/library/bibliography; http://portal.acm.org/; http://www.adahome.com/Resources/Bibliography/articles.ref; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/sigada.bib

subject:
D.3.2 Software, PROGRAMMING LANGUAGES, Language Classifications, Ada G.1.0 Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic

entry:
@Article{Froggatt:1987:FPC,
  author =       "Terry Froggatt",
  title =        "Fixed-point conversion, multiplication, and division
                 in {Ada}",
  journal =      j-SIGADA-LETTERS,
  volume =       "7",
  number =       "1",
  pages =        "71--81",
  month =        jan # "\slash " # feb,
  year =         "1987",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Sat Aug 9 09:05:24 MDT 2003",
  bibsource =    "ftp://ftp.uu.net/library/bibliography;
                 http://portal.acm.org/;
                 http://www.adahome.com/Resources/Bibliography/articles.ref;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigada.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "languages; theory",
  subject =      "D.3.2 Software, PROGRAMMING LANGUAGES, Language
                 Classifications, Ada \\ G.1.0 Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Computer arithmetic",
}


bibtype: article
filename: fparith.bib
label: Grosse:1987:UCB
author: Eric Grosse and Cleve Moler
title: Underflow can be Harmful
journal: j-SIAM-NEWS
volume: 20
number: 6
pages: 1
year: 1987
ISSN: 0036-1437 OR 00361437
ISSNL: 0036-1437 OR 00361437
bibdate: Sat Feb 8 10:30:07 2020
bibtimestamp: 2020.02.08 10:30:07 ???
fjournal: SIAM News
acknowledgement: ack-nhfb
journalURL: https://sinews.siam.org/
rawauthor: Eric Grosse and Cleve Moler
rawtitle: Underflow can be Harmful
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/g/grosse-eric.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Grosse:1987:UCB,
  author =       "Eric Grosse and Cleve Moler",
  title =        "Underflow can be Harmful",
  journal =      j-SIAM-NEWS,
  volume =       "20",
  number =       "6",
  pages =        "1",
  year =         "1987",
  ISSN =         "0036-1437",
  ISSN-L =       "0036-1437",
  bibdate =      "Sat Feb 8 10:30:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/g/grosse-eric.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM News",
  journal-URL =  "https://sinews.siam.org/",
}


bibtype: article
filename: fparith.bib
label: Guyot:1987:WBE
author: Alain Guyot and Bertrand Hochet and Jean-Michel Muller
title: A Way to Build Efficient Carry-Skip Adders
journal: j-IEEE-TRANS-COMPUT
volume: C-36
number: 10
pages: 1144--1152
month: oct
monthnumber: 10
year: 1987
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1987.1676855
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 9 09:28:56 MDT 2011
bibtimestamp: 2011.07.09 09:28:56 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676855
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Alain Guyot and Bertrand Hochet and Jean-Michel Muller
rawtitle: A Way to Build Efficient Carry-Skip Adders
entry:
@Article{Guyot:1987:WBE,
  author =       "Alain Guyot and Bertrand Hochet and Jean-Michel
                 Muller",
  title =        "A Way to Build Efficient Carry-Skip Adders",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-36",
  number =       "10",
  pages =        "1144--1152",
  month =        oct,
  year =         "1987",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1987.1676855",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 09:28:56 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676855",
  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: Hamada:1987:NRN
author: Hozumi Hamada
title: A New Real Number Representation and Its Operation
crossref: Irwin:1987:PSC
pages: 153--157
month: may
monthnumber: 5
year: 1987
DOI: https://doi.org/10.1109/ARITH.1987.6158698
bibdate: Wed Nov 14 18:22:26 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 18:22:26 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Hamada.pdf
keywords: ARITH-8
acknowledgement: ack-nhfb
rawauthor: Hozumi Hamada
rawtitle: A New Real Number Representation and Its Operation
abstract:
A new internal representation is proposed for real numbers. It has been named URR for universal representation of real numbers. This approach is based on a bisection method which is applied to real number intervals. With this method, the point of division increases or decreases in a double exponential manner in the global range. The main characteristics of the method are as follows. First, overflow / underflow does not, in practice, occur. Second, since the data format does not depend on the length but on the value of the data, a transformation operation is virtually not needed between systems of long and short data. Finally, only one bit of resolution is lost compared with the fixed point form. In addition, arithmetic operations are slightly complicated compared with conventional representation, but they present no special difficulties. This new method is thus the most suitable internal form as an interface not only between computers but also between computers and digital systems which deal with real numbers or physical (scalar) values.

rawabstract:
A new internal representation is proposed for real numbers. It has been named URR for universal representation of real numbers. This approach is based on a bisection method which is applied to real number intervals. With this method, the point of division increases or decreases in a double exponential manner in the global range. The main characteristics of the method are as follows. First, overflow\slash underflow does not, in practice, occur. Second, since the data format does not depend on the length but on the value of the data, a transformation operation is virtually not needed between systems of long and short data. Finally, only one bit of resolution is lost compared with the fixed point form. In addition, arithmetic operations are slightly complicated compared with conventional representation, but they present no special difficulties. This new method is thus the most suitable internal form as an interface not only between computers but also between computers and digital systems which deal with real numbers or physical (scalar) values.

entry:
@InProceedings{Hamada:1987:NRN,
  author =       "Hozumi Hamada",
  title =        "A New Real Number Representation and Its Operation",
  crossref =     "Irwin:1987:PSC",
  pages =        "153--157",
  month =        may,
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158698",
  bibdate =      "Wed Nov 14 18:22:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Hamada.pdf",
  abstract =     "A new internal representation is proposed for real
                 numbers. It has been named URR for universal
                 representation of real numbers. This approach is based
                 on a bisection method which is applied to real number
                 intervals. With this method, the point of division
                 increases or decreases in a double exponential manner
                 in the global range. The main characteristics of the
                 method are as follows. First, overflow\slash underflow
                 does not, in practice, occur. Second, since the data
                 format does not depend on the length but on the value
                 of the data, a transformation operation is virtually
                 not needed between systems of long and short data.
                 Finally, only one bit of resolution is lost compared
                 with the fixed point form. In addition, arithmetic
                 operations are slightly complicated compared with
                 conventional representation, but they present no
                 special difficulties. This new method is thus the most
                 suitable internal form as an interface not only between
                 computers but also between computers and digital
                 systems which deal with real numbers or physical
                 (scalar) values.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}


bibtype: inproceedings
filename: fparith.bib
label: Han:1987:FAE
author: Tackdon Han and David A. Carlson
title: Fast Area-Efficient VLSI Adders
crossref: Irwin:1987:PSC
pages: 49--56
year: 1987
DOI: https://doi.org/10.1109/ARITH.1987.6158699
bibdate: Wed Nov 14 18:22:26 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 18:22:26 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Han_Carlson.pdf
keywords: ARITH-8
acknowledgement: ack-nhfb
rawauthor: Tackdon Han and David A. Carlson
rawtitle: Fast Area-Efficient {VLSI} Adders
abstract:
In this paper, we study area-time tradeoffs in VLSI for prefix computation using graph representations of this problem. Since the problem is intimately related to binary addition the results we obtain lead to the design of area-time efficient VLSI adders. This is a major goal of our work: to design em very low latency addition circuitry that is also em area efficient. To this end, we present a new graph representation for prefix computation that leads to the design of a fast, area-efficient binary adder. The new graph is a combination of previously known graph representations for prefix computation, and its area is close to known lower bounds on the VLSI area of parallel prefix graphs. Using it, we are able to design VLSI adders having area $ A = O(n log n) $ whose delay time is the lowest possible value, i.e., the fastest possible area-efficient VLSI adder.

rawabstract:
In this paper, we study area-time tradeoffs in VLSI for prefix computation using graph representations of this problem. Since the problem is intimately related to binary addition the results we obtain lead to the design of area-time efficient VLSI adders. This is a major goal of our work: to design {\em very low latency\/} addition circuitry that is also {\em area efficient}. To this end, we present a new graph representation for prefix computation that leads to the design of a fast, area-efficient binary adder. The new graph is a combination of previously known graph representations for prefix computation, and its area is close to known lower bounds on the VLSI area of parallel prefix graphs. Using it, we are able to design VLSI adders having area $ A = O(n \log n) $ whose delay time is the lowest possible value, i.e., the fastest possible area-efficient VLSI adder.

entry:
@InProceedings{Han:1987:FAE,
  author =       "Tackdon Han and David A. Carlson",
  title =        "Fast Area-Efficient {VLSI} Adders",
  crossref =     "Irwin:1987:PSC",
  pages =        "49--56",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158699",
  bibdate =      "Wed Nov 14 18:22:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Han_Carlson.pdf",
  abstract =     "In this paper, we study area-time tradeoffs in VLSI
                 for prefix computation using graph representations of
                 this problem. Since the problem is intimately related
                 to binary addition the results we obtain lead to the
                 design of area-time efficient VLSI adders. This is a
                 major goal of our work: to design {\em very low
                 latency\/} addition circuitry that is also {\em area
                 efficient}. To this end, we present a new graph
                 representation for prefix computation that leads to the
                 design of a fast, area-efficient binary adder. The new
                 graph is a combination of previously known graph
                 representations for prefix computation, and its area is
                 close to known lower bounds on the VLSI area of
                 parallel prefix graphs. Using it, we are able to design
                 VLSI adders having area $ A = O(n \log n) $ whose delay
                 time is the lowest possible value, i.e., the fastest
                 possible area-efficient VLSI adder.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}


bibtype: book
filename: fparith.bib
label: Herz-Fischler:1987:MHD
author: Roger Herz-Fischler
title: A mathematical history of division in extreme and mean ratio
publisher: Wilfrid Laurier University Press
address: Waterloo, ON, Canada
pages: xvi + 191
year: 1987
ISBN: 0-88920-152-8 OR 0889201528
ISBN13: 978-0-88920-152-1 OR 9780889201521
LCCN: A481.H47 1987
bibdate: Thu Jul 10 08:02:28 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.07.10 08:02:28 ???
acknowledgement: ack-nhfb
rawauthor: Roger Herz-Fischler
rawtitle: A mathematical history of division in extreme and mean ratio
entry:
@Book{Herz-Fischler:1987:MHD,
  author =       "Roger Herz-Fischler",
  title =        "A mathematical history of division in extreme and mean
                 ratio",
  publisher =    "Wilfrid Laurier University Press",
  address =      "Waterloo, ON, Canada",
  pages =        "xvi + 191",
  year =         "1987",
  ISBN =         "0-88920-152-8",
  ISBN-13 =      "978-0-88920-152-1",
  LCCN =         "A481.H47 1987",
  bibdate =      "Thu Jul 10 08:02:28 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$65.00",
  acknowledgement = ack-nhfb,
  libnote =      "Not yet in my library.",
}


bibtype: book
filename: fparith.bib
label: Hildebrand:1987:INA
author: Francis Begnaud Hildebrand
title: Introduction to numerical analysis
publisher: pub-DOVER
address: pub-DOVER:adr
edition: Second
pages: xiii + 669
year: 1987
ISBN: 0-486-65363-3 (paperback) OR 0486653633 (paperback)
ISBN13: 978-0-486-65363-1 (paperback) OR 9780486653631 (paperback)
LCCN: QA297 .H54 1987
bibdate: Fri Aug 20 09:19:58 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.08.20 09:19:58 MDT
URL: http://www.loc.gov/catdir/description/dover032/87005370.html
remark: Unabridged, slightly corrected republication of cite Hildebrand:1974:INA.
subject: Numerical analysis
acknowledgement: ack-nhfb
rawauthor: Francis Begnaud Hildebrand
rawtitle: Introduction to numerical analysis
entry:
@Book{Hildebrand:1987:INA,
  author =       "Francis Begnaud Hildebrand",
  title =        "Introduction to numerical analysis",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  edition =      "Second",
  pages =        "xiii + 669",
  year =         "1987",
  ISBN =         "0-486-65363-3 (paperback)",
  ISBN-13 =      "978-0-486-65363-1 (paperback)",
  LCCN =         "QA297 .H54 1987",
  bibdate =      "Fri Aug 20 09:19:58 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/description/dover032/87005370.html",
  acknowledgement = ack-nhfb,
  remark =       "Unabridged, slightly corrected republication of
                 \cite{Hildebrand:1974:INA}.",
  subject =      "Numerical analysis",
}


bibtype: article
filename: fparith.bib
label: Himmeroeder:1987:CKC
author: H.-J. Himmeroder and R. M. Toschke
journal: j-CT
volume: 1
pages: 152--158
year: 1987
ISSN: 0724-8679 OR 07248679
bibdate: Sat Feb 24 09:05:58 1996
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 09:05:58 ???
fjournal: C T: Magazin fur Computer Technik (Hannover)
acknowledgement: ack-nj
rawauthor: H.-J. Himmer{\"o}der and R. M. Toschke
title:
c't-KAT-Ce. Ein 68000-Einplatinenrechner, Teil 3: REAL-Arithmetik toenglish c't-KAT-Ce. A 68000 Single-Board Computer endtoenglish 

rawtitle:
{c't-KAT-Ce. Ein 68000-Einplatinenrechner, Teil 3: REAL-Arithmetik} \toenglish {c't-KAT-Ce. A 68000 Single-Board Computer} \endtoenglish

entry:
@Article{Himmeroeder:1987:CKC,
  author =       "H.-J. Himmer{\"o}der and R. M. Toschke",
  title =        "{c't-KAT-Ce. Ein 68000-Einplatinenrechner, Teil 3:
                 REAL-Arithmetik} \toenglish {c't-KAT-Ce. A 68000
                 Single-Board Computer} \endtoenglish",
  journal =      j-CT,
  volume =       "1",
  pages =        "152--158",
  year =         "1987",
  ISSN =         "0724-8679",
  bibdate =      "Sat Feb 24 09:05:58 1996",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "C T: Magazin f{\"u}r Computer Technik (Hannover)",
}


bibtype: inproceedings
filename: fparith.bib
label: Hochet:1987:SSL
author: Bertrand Hochet and Patrice Quinton and Yves Robert
title: Systolic Solution of Linear Systems over $ mathrm GF(p) $ with Partial Pivoting
crossref: Irwin:1987:PSC
pages: 161--168
year: 1987
DOI: https://doi.org/10.1109/ARITH.1987.6158700
bibdate: Fri Nov 16 21:39:46 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.16 21:39:46 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Hochet_Quinton_Robert.pdf
keywords: ARITH-8
acknowledgement: ack-nhfb
rawauthor: Bertrand Hochet and Patrice Quinton and Yves Robert
rawtitle: Systolic Solution of Linear Systems over {$ \mathrm {GF}(p) $} with Partial Pivoting
abstract:
We propose two systolic architectures for the Gaussian triangularization and the Gauss--Jordan diagonalization of large dense $ n times n $ matrices over $ mathrm GF(p) $, where $p$ is a prime number. The solution of large dense linear systems over $ mathrm GF(p) $ is the major computational step in various algorithms issued from arithmetic number theory and computer algebra. The two proposed architectures implement the elimination with partial pivoting, although the operation of the array remains purely systolic. The last section is devoted to the design and layout of a CMOS 8 by 8 Gauss--Jordan diagonalization systolic chip over $ mathrm GF(2) $.

rawabstract:
We propose two systolic architectures for the Gaussian triangularization and the Gauss--Jordan diagonalization of large dense $ n \times n $ matrices over $ \mathrm {GF}(p) $, where $p$ is a prime number. The solution of large dense linear systems over $ \mathrm {GF}(p) $ is the major computational step in various algorithms issued from arithmetic number theory and computer algebra. The two proposed architectures implement the elimination with partial pivoting, although the operation of the array remains purely systolic. The last section is devoted to the design and layout of a CMOS 8 by 8 Gauss--Jordan diagonalization systolic chip over $ \mathrm {GF}(2) $.

entry:
@InProceedings{Hochet:1987:SSL,
  author =       "Bertrand Hochet and Patrice Quinton and Yves Robert",
  title =        "Systolic Solution of Linear Systems over {$ \mathrm
                 {GF}(p) $} with Partial Pivoting",
  crossref =     "Irwin:1987:PSC",
  pages =        "161--168",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158700",
  bibdate =      "Fri Nov 16 21:39:46 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Hochet_Quinton_Robert.pdf",
  abstract =     "We propose two systolic architectures for the Gaussian
                 triangularization and the Gauss--Jordan diagonalization
                 of large dense $ n \times n $ matrices over $ \mathrm
                 {GF}(p) $, where $p$ is a prime number. The solution of
                 large dense linear systems over $ \mathrm {GF}(p) $ is
                 the major computational step in various algorithms
                 issued from arithmetic number theory and computer
                 algebra. The two proposed architectures implement the
                 elimination with partial pivoting, although the
                 operation of the array remains purely systolic. The
                 last section is devoted to the design and layout of a
                 CMOS 8 by 8 Gauss--Jordan diagonalization systolic chip
                 over $ \mathrm {GF}(2) $.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}


bibtype: article
filename: fparith.bib
label: Homewood:1987:ITT
author: Mark Homewood and David May and David Shepherd and Roger Shepherd
title: The IMS T800 Transputer
journal: j-IEEE-MICRO
volume: 7
number: 5
pages: 10--26
month: sep
monthnumber: 9
year: 1987
CODEN: IEMIDZ
DOI: https://doi.org/10.1109/MM.1987.305012
ISSN: 0272-1732 (print), 1937-4143 (electronic) OR 02721732 (print), 19374143 (electronic)
ISSNL: 0272-1732 OR 02721732
bibdate: Thu Dec 14 06:08:58 MST 2000
bibtimestamp: 2000.12.14 06:08:58 MST
fjournal: IEEE Micro
acknowledgement: ack-nj
affiliationaddress: Inmos Ltd, Bristol, Engl
classcodes: B1265F (Microprocessors and microcomputers); C5130 (Microprocessor chips)
corpsource: Inmos Ltd., Bristol, UK
journalURL: http://www.computer.org/csdl/mags/mi/index.html
treatment: P Practical; R Product Review
rawauthor: Mark Homewood and David May and David Shepherd and Roger Shepherd
rawtitle: The {IMS T800} Transputer
bibsource:
Compendex database; ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/fparith.bib; Parallel/transputer.bib; Science Citation Index database (1980--2000)

keywords:
architecture; capability; communication links; computer architecture; computer graphics; computer programming languages; computers, microcomputer; Design; floating-point arithmetic; floating-point unit design; graphics; IMS T800 transputer; integrated circuits, VLSI; microprocessor chips; performance; scientific computer; supercomputers; telecommunication links

entry:
@Article{Homewood:1987:ITT,
  author =       "Mark Homewood and David May and David Shepherd and
                 Roger Shepherd",
  title =        "The {IMS T800} Transputer",
  journal =      j-IEEE-MICRO,
  volume =       "7",
  number =       "5",
  pages =        "10--26",
  month =        sep # "\slash " # oct,
  year =         "1987",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/MM.1987.305012",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Thu Dec 14 06:08:58 MST 2000",
  bibsource =    "Compendex database;
                 ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 Parallel/transputer.bib; Science Citation Index
                 database (1980--2000)",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  affiliationaddress = "Inmos Ltd, Bristol, Engl",
  classcodes =   "B1265F (Microprocessors and microcomputers); C5130
                 (Microprocessor chips)",
  classification = "714; 722; 723; 921",
  corpsource =   "Inmos Ltd., Bristol, UK",
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
  keywords =     "architecture; capability; communication links;
                 computer architecture; computer graphics; computer
                 programming languages; computers, microcomputer;
                 Design; floating-point arithmetic; floating-point unit
                 design; graphics; IMS T800 transputer; integrated
                 circuits, VLSI; microprocessor chips; performance;
                 scientific computer; supercomputers; telecommunication
                 links",
  treatment =    "P Practical; R Product Review",
}


bibtype: incollection
filename: fparith.bib
label: HP:1987:IPH
author: Hewlett Packard
booktitle: HP-71 Reference Manual
title: The IEEE Proposal for Handling Math Exceptions
publisher: Hewlett Packard Company
address: Palo Alto, CA, USA
pages: 338--345
month: oct
monthnumber: 10
year: 1987
bibdate: Fri Nov 28 17:12:16 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 17:12:16 ???
URL: http://www.hpmuseum.org/
acknowledgement: ack-mfc
rawauthor: {Hewlett Packard}
rawbooktitle: {HP-71} Reference Manual
rawtitle: The {IEEE} Proposal for Handling Math Exceptions
note:
Mfg. #0071-90110, Reorder #0071-90010. First edition October 1983. Manual available from em The Museum of HP Calculators.

abstract:
The IEEE Radix Independent Floating-Point Proposal divides all of the floating-point ``exceptional events'' encountered in calculations into five classes of em math exceptions: invalid operation, division by zero, overflow, underflow, and inexact result. Associated with each math exception is a flag that is set by the HP-71 whenever an exception is encountered. These flags remain set until you clear them. Each of these flags can be accessed by its number or its name.

rawabstract:
The IEEE Radix Independent Floating-Point Proposal divides all of the floating-point ``exceptional events'' encountered in calculations into five classes of {\em math exceptions\/}: invalid operation, division by zero, overflow, underflow, and inexact result. Associated with each math exception is a flag that is set by the HP-71 whenever an exception is encountered. These flags remain set until you clear them. Each of these flags can be accessed by its number or its name.

rawnote:
Mfg. \#0071-90110, Reorder \#0071-90010. First edition October 1983. Manual available from {\em The Museum of HP Calculators}.

entry:
@InCollection{HP:1987:IPH,
  author =       "{Hewlett Packard}",
  booktitle =    "{HP-71} Reference Manual",
  title =        "The {IEEE} Proposal for Handling Math Exceptions",
  publisher =    "Hewlett Packard Company",
  address =      "Palo Alto, CA, USA",
  pages =        "338--345",
  month =        oct,
  year =         "1987",
  bibdate =      "Fri Nov 28 17:12:16 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Mfg. \#0071-90110, Reorder \#0071-90010. First edition
                 October 1983. Manual available from {\em The Museum of
                 HP Calculators}.",
  URL =          "http://www.hpmuseum.org/",
  abstract =     "The IEEE Radix Independent Floating-Point Proposal
                 divides all of the floating-point ``exceptional
                 events'' encountered in calculations into five classes
                 of {\em math exceptions\/}: invalid operation, division
                 by zero, overflow, underflow, and inexact result.
                 Associated with each math exception is a flag that is
                 set by the HP-71 whenever an exception is encountered.
                 These flags remain set until you clear them. Each of
                 these flags can be accessed by its number or its
                 name.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
}


bibtype: mastersthesis
filename: fparith.bib
label: Hu:1987:CDT
author: Timothy Hu
title: Circuit design techniques for a floating-point processor: research project
type: Master of Science, Plan II
school: University of California, Berkeley. Dept. of Electrical Engineering and Computer Sciences
address: Berkeley, CA, USA
pages: 70
year: 1987
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: Timothy Hu
rawtitle: Circuit design techniques for a floating-point processor: research project
entry:
@MastersThesis{Hu:1987:CDT,
  author =       "Timothy Hu",
  title =        "Circuit design techniques for a floating-point
                 processor: research project",
  type =         "{Master of Science, Plan II}",
  school =       "University of California, Berkeley. Dept. of
                 Electrical Engineering and Computer Sciences",
  address =      "Berkeley, CA, USA",
  pages =        "70",
  year =         "1987",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Hull:1987:TIC
author: T. E. Hull and M. S. Cohen
title: Toward an Ideal Computer Arithmetic
crossref: Irwin:1987:PSC
pages: 131--138
year: 1987
DOI: https://doi.org/10.1109/ARITH.1987.6158701
bibdate: Fri Nov 28 11:41:31 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 11:41:31 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Hull_Cohen.pdf
keywords: ARITH-8; decimal floating-point arithmetic
acknowledgement: ack-nhfb
rawauthor: T. E. Hull and M. S. Cohen
rawtitle: Toward an Ideal Computer Arithmetic
abstract:
A new computer arithmetic is described. Closely related built-in functions are included. A user's point of view is taken, so that the emphasis is on what language features are available to a user. The main new feature is flexible precision control of decimal floating-point arithmetic. It is intended that the language facilities be sufficient for describing numerical processes one might want to implement, while at the same time being simple to use, and implementable in a reasonably efficient manner. Illustrative examples are based on experience with an existing software implementation.

rawabstract:
A new computer arithmetic is described. Closely related built-in functions are included. A user's point of view is taken, so that the emphasis is on what language features are available to a user. The main new feature is flexible precision control of decimal floating-point arithmetic. It is intended that the language facilities be sufficient for describing numerical processes one might want to implement, while at the same time being simple to use, and implementable in a reasonably efficient manner. Illustrative examples are based on experience with an existing software implementation.

entry:
@InProceedings{Hull:1987:TIC,
  author =       "T. E. Hull and M. S. Cohen",
  title =        "Toward an Ideal Computer Arithmetic",
  crossref =     "Irwin:1987:PSC",
  pages =        "131--138",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158701",
  bibdate =      "Fri Nov 28 11:41:31 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Hull_Cohen.pdf",
  abstract =     "A new computer arithmetic is described. Closely
                 related built-in functions are included. A user's point
                 of view is taken, so that the emphasis is on what
                 language features are available to a user. The main new
                 feature is flexible precision control of decimal
                 floating-point arithmetic. It is intended that the
                 language facilities be sufficient for describing
                 numerical processes one might want to implement, while
                 at the same time being simple to use, and implementable
                 in a reasonably efficient manner. Illustrative examples
                 are based on experience with an existing software
                 implementation.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8; decimal floating-point arithmetic",
}


bibtype: article
filename: fparith.bib
label: IEEE:1987:ISB
author: IEEE
title: IEEE Standard for Binary Floating-Point Arithmetic
journal: j-SIGPLAN
volume: 22
number: 2
pages: 9--25
month: feb
monthnumber: 2
year: 1987
CODEN: SINODQ
DOI: https://doi.org/10.1109/IEEESTD.1985.82928
ISSN: 0362-1340 (print), 1523-2867 (print), 1558-1160 OR 03621340 (print), 15232867 (print), 15581160
ISSNL: 0362-1340 OR 03621340
bibdate: Fri Sep 09 12:55:55 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.09 12:55:55 ???
fjournal: ACM SIGPLAN Notices
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J706
rawauthor: {IEEE}
rawtitle: {IEEE} Standard for Binary Floating-Point Arithmetic
entry:
@Article{IEEE:1987:ISB,
  author =       "{IEEE}",
  title =        "{IEEE} Standard for Binary Floating-Point Arithmetic",
  journal =      j-SIGPLAN,
  volume =       "22",
  number =       "2",
  pages =        "9--25",
  month =        feb,
  year =         "1987",
  CODEN =        "SINODQ",
  DOI =          "https://doi.org/10.1109/IEEESTD.1985.82928",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Fri Sep 09 12:55:55 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 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",
}


bibtype: book
filename: fparith.bib
label: IEEE:1987:RIS
editor: IEEE
title: 854-1987 (R1994) IEEE Standard for Radix-Independent Floating-Point Arithmetic
publisher: pub-IEEE-STD
address: pub-IEEE-STD:adr
pages: 16
year: 1987
DOI: https://doi.org/10.1109/IEEESTD.1987.81037
ISBN: 1-55937-859-X OR 155937859X
ISBN13: 978-1-55937-859-8 OR 9781559378598
bibdate: Mon Apr 24 07:02:34 2000
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2000.04.24 07:02:34 ???
note: Revised 1994.
URL: http://standards.ieee.org/reading/ieee/std_public/description/busarch/854-1987_desc.html
keywords: floating point arithmetic; Floating-point arithmetic.; Standards
acknowledgement: ack-nj
raweditor: {IEEE}
rawnote: Revised 1994.
rawtitle: {854-1987 (R1994) IEEE Standard for Radix-Independent Floating-Point Arithmetic}
remark:
At head of title: An American National Standard. ``Approved March 12, 1987 IEEE Standards Board; Approved September 10, 1987 American National Standards Institute.''

entry:
@Book{IEEE:1987:RIS,
  editor =       "{IEEE}",
  title =        "{854-1987 (R1994) IEEE Standard for Radix-Independent
                 Floating-Point Arithmetic}",
  publisher =    pub-IEEE-STD,
  address =      pub-IEEE-STD:adr,
  pages =        "16",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/IEEESTD.1987.81037",
  ISBN =         "1-55937-859-X",
  ISBN-13 =      "978-1-55937-859-8",
  bibdate =      "Mon Apr 24 07:02:34 2000",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Revised 1994.",
  price =        "US\$44.00",
  URL =          "http://standards.ieee.org/reading/ieee/std_public/description/busarch/854-1987_desc.html",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  keywords =     "floating point arithmetic; Floating-point arithmetic.;
                 Standards",
  remark =       "At head of title: An American National Standard.
                 ``Approved March 12, 1987 IEEE Standards Board;
                 Approved September 10, 1987 American National Standards
                 Institute.''",
}


bibtype: mastersthesis
filename: fparith.bib
label: Jensen:1987:CIS
author: Debby Jensen
title: Control implementation for the SPUR floating point coprocessor: research project
type: Master of Science, Plan II
school: University of California, Berkeley. Dept. of Electrical Engineering and Computer Sciences
address: Berkeley, CA, USA
pages: 76
year: 1987
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: Debby Jensen
rawtitle: Control implementation for the {SPUR} floating point coprocessor: research project
entry:
@MastersThesis{Jensen:1987:CIS,
  author =       "Debby Jensen",
  title =        "Control implementation for the {SPUR} floating point
                 coprocessor: research project",
  type =         "{Master of Science, Plan II}",
  school =       "University of California, Berkeley. Dept. of
                 Electrical Engineering and Computer Sciences",
  address =      "Berkeley, CA, USA",
  pages =        "76",
  year =         "1987",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Johnson:1987:AES
author: Kenneth C. Johnson
title: Algorithm 650: Efficient Square Root Implementation on the 68000
journal: j-TOMS
volume: 13
number: 2
pages: 138--151
month: jun
monthnumber: 6
year: 1987
CODEN: ACMSCU
DOI: https://doi.org/10.1145/328512.328520
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 65D15
MRnumber: 898 489
bibdate: Thu Sep 1 10:15:42 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:15:42 ???
note: See also cite Johnson:1987:CES.
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/toms
rawauthor: Kenneth C. Johnson
rawnote: See also \cite{Johnson:1987:CES}.
rawtitle: {Algorithm 650}: Efficient Square Root Implementation on the 68000
entry:
@Article{Johnson:1987:AES,
  author =       "Kenneth C. Johnson",
  title =        "{Algorithm 650}: Efficient Square Root Implementation
                 on the 68000",
  journal =      j-TOMS,
  volume =       "13",
  number =       "2",
  pages =        "138--151",
  month =        jun,
  year =         "1987",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/328512.328520",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D15",
  MRnumber =     "898 489",
  bibdate =      "Thu Sep 1 10:15:42 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See also \cite{Johnson:1987:CES}.",
  acknowledgement = ack-nj,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: fparith.bib
label: Johnson:1987:CES
author: Kenneth C. Johnson
journal: j-TOMS
volume: 13
number: 3
pages: 320--320
month: sep
monthnumber: 9
year: 1987
CODEN: ACMSCU
DOI: https://doi.org/10.1145/29380.356210
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 320. 65D15
MRnumber: 918 582
bibdate: Sat Feb 8 10:30:18 2020
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2020.02.08 10:30:18 ???
note: See cite Johnson:1987:AES,Monahan:1987:AGC,Boisvert:1987:AAH.
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Kenneth C. Johnson
rawnote: See \cite{Johnson:1987:AES,Monahan:1987:AGC,Boisvert:1987:AAH}.
title:
Corrigendum: ``Algorithm 650: efficient square root implementation on the 68000'' [ACM Trans. Math. Software bf 13 (1987), no. 2, 138--151]

rawtitle:
Corrigendum: {``Algorithm 650: efficient square root implementation on the 68000'' [ACM Trans. Math. Software {\bf 13} (1987), no. 2, 138--151]}

entry:
@Article{Johnson:1987:CES,
  author =       "Kenneth C. Johnson",
  title =        "Corrigendum: {``Algorithm 650: efficient square root
                 implementation on the 68000'' [ACM Trans. Math.
                 Software {\bf 13} (1987), no. 2, 138--151]}",
  journal =      j-TOMS,
  volume =       "13",
  number =       "3",
  pages =        "320--320",
  month =        sep,
  year =         "1987",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/29380.356210",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "320. 65D15",
  MRnumber =     "918 582",
  bibdate =      "Sat Feb 8 10:30:18 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See
                 \cite{Johnson:1987:AES,Monahan:1987:AGC,Boisvert:1987:AAH}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: inproceedings
filename: fparith.bib
label: Kahan:1987:BCC
author: W. Kahan
title: Branch Cuts for Complex Elementary Functions or Much Ado About Nothing's Sign Bit
crossref: Iserles:1987:SAN
volume: 9
pages: 165--211
year: 1987
MRclass: 65E05
MRnumber: 88k:65027
bibdate: Sat Jan 11 17:44:01 MST 1997
bibtimestamp: 1997.01.11 17:44:01 MST
series: Inst. Math. Appl. Conf. Ser. New Ser.
URL: http://people.freebsd.org/~das/kahan86branch.pdf; http://www.cs.berkeley.edu/~dbindel/class/cs279/
acknowledgement: ack-nhfb
rawauthor: W. Kahan
rawtitle: Branch Cuts for Complex Elementary Functions or Much Ado About Nothing's Sign Bit
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-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@InProceedings{Kahan:1987:BCC,
  author =       "W. Kahan",
  title =        "Branch Cuts for Complex Elementary Functions or Much
                 Ado About Nothing's Sign Bit",
  crossref =     "Iserles:1987:SAN",
  volume =       "9",
  pages =        "165--211",
  year =         "1987",
  MRclass =      "65E05",
  MRnumber =     "88k:65027",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  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-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Inst. Math. Appl. Conf. Ser. New Ser.",
  URL =          "http://people.freebsd.org/~das/kahan86branch.pdf;
                 http://www.cs.berkeley.edu/~dbindel/class/cs279/",
  acknowledgement = ack-nhfb # " and " # ack-nj,
}


bibtype: unpublished
filename: fparith.bib
label: Kahan:1987:CWF
author: W. Kahan
title: Checking whether floating-point division is correctly rounded
pages: 165--211
year: 1987
bibdate: Mon Apr 25 05:40:03 2005
bibtimestamp: 2005.04.25 05:40:03 ???
note: Lecture notes.
keywords: correct rounding; floating-point arithmetic; rounding errors
acknowledgement: ack-nhfb
rawauthor: W. Kahan
rawnote: Lecture notes.
rawtitle: Checking whether floating-point division is correctly rounded
entry:
@Unpublished{Kahan:1987:CWF,
  author =       "W. Kahan",
  title =        "Checking whether floating-point division is correctly
                 rounded",
  year =         "1987",
  bibdate =      "Mon Apr 25 05:40:03 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Lecture notes.",
  acknowledgement = ack-nhfb,
  keywords =     "correct rounding; floating-point arithmetic; rounding
                 errors",
}


bibtype: misc
filename: fparith.bib
label: Kahan:1987:DPI
author: W. Kahan
title: Doubled-precision IEEE Standard 754 floating-point arithmetic
pages: 165--211
month: feb
monthnumber: 2
year: 1987
bibdate: Thu May 09 07:25:40 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.09 07:25:40 ???
keywords: accurate floating-point summation
remark: Cited in cite Higham:1993:AFP.
acknowledgement: ack-nhfb
howpublished: Manuscript
rawauthor: W. Kahan
rawtitle: Doubled-precision {IEEE Standard 754} floating-point arithmetic
entry:
@Misc{Kahan:1987:DPI,
  author =       "W. Kahan",
  title =        "Doubled-precision {IEEE Standard 754} floating-point
                 arithmetic",
  howpublished = "Manuscript",
  month =        feb,
  year =         "1987",
  bibdate =      "Thu May 09 07:25:40 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation",
  remark =       "Cited in \cite{Higham:1993:AFP}.",
}


bibtype: techreport
filename: fparith.bib
label: Kahan:1987:HAE
author: W. Kahan
title: Handling Arithmetic Exceptions
type: Report
institution: inst-BERKELEY-MATH-EECS
address: inst-BERKELEY-MATH-EECS:adr
pages: 165--211
day: 14
month: may
monthnumber: 5
year: 1987
bibdate: Mon Aug 26 10:42:10 2024
bibtimestamp: 2024.08.26 10:42:10 ???
URL: http://www.arithmazium.org/classroom/lib//Kahan_Handling_Arithmetic_Exceptions.pdf
acknowledgement: ack-nhfb
rawauthor: W. Kahan
rawtitle: Handling Arithmetic Exceptions
abstract:
An em Exception arises when an operation performed by a computer has to produce a result to which some people might reasonably take exception. Examples are em Division by Zero, em Overflow and Floating-Point em Underflow. Though most (but not all) exceptions must be rare, too rare to be topics cf everyday conversation, they are not so rare that computer programmers and users can ignore them altogether. This paper presents proposals, many of them now implemented on a few computers, to handle arithmetic exceptions in a generally satisfactory way at a tolerable cost. The proposals are designed to be fully compatible with concurrent, overlapped, parallel, pipelined and vectorized computing on new hardware that will be designed to support them without em precise interrupts. em Flags and em Modes are proposed to help programmers cope with exceptions; em Retrospective Diagnostics are proposed to help most of the rest of us, who aspire to use computers without having to program them. The features of IEEE Standards 754 and 854 are supported by but not obligatory for the proposals.

rawabstract:
An {\em Exception\/} arises when an operation performed by a computer has to produce a result to which some people might reasonably take exception. Examples are {\em Division by Zero}, {\em Overflow\/ } and Floating-Point {\em Underflow}. Though most (but not all) exceptions must be rare, too rare to be topics cf everyday conversation, they are not so rare that computer programmers and users can ignore them altogether. This paper presents proposals, many of them now implemented on a few computers, to handle arithmetic exceptions in a generally satisfactory way at a tolerable cost. The proposals are designed to be fully compatible with concurrent, overlapped, parallel, pipelined and vectorized computing on new hardware that will be designed to support them without {\em precise interrupts}. {\em Flags\/} and {\em Modes\/} are proposed to help programmers cope with exceptions; {\em Retrospective Diagnostics\/} are proposed to help most of the rest of us, who aspire to use computers without having to program them. The features of IEEE Standards 754 and 854 are supported by but not obligatory for the proposals.

entry:
@TechReport{Kahan:1987:HAE,
  author =       "W. Kahan",
  title =        "Handling Arithmetic Exceptions",
  type =         "Report",
  institution =  inst-BERKELEY-MATH-EECS,
  address =      inst-BERKELEY-MATH-EECS:adr,
  day =          "14",
  month =        may,
  year =         "1987",
  bibdate =      "Mon Aug 26 10:42:10 2024",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.arithmazium.org/classroom/lib//Kahan_Handling_Arithmetic_Exceptions.pdf",
  abstract =     "An {\em Exception\/} arises when an operation
                 performed by a computer has to produce a result to
                 which some people might reasonably take exception.
                 Examples are {\em Division by Zero}, {\em Overflow\/ }
                 and Floating-Point {\em Underflow}. Though most (but
                 not all) exceptions must be rare, too rare to be topics
                 cf everyday conversation, they are not so rare that
                 computer programmers and users can ignore them
                 altogether. This paper presents proposals, many of them
                 now implemented on a few computers, to handle
                 arithmetic exceptions in a generally satisfactory way
                 at a tolerable cost. The proposals are designed to be
                 fully compatible with concurrent, overlapped, parallel,
                 pipelined and vectorized computing on new hardware that
                 will be designed to support them without {\em precise
                 interrupts}. {\em Flags\/} and {\em Modes\/} are
                 proposed to help programmers cope with exceptions; {\em
                 Retrospective Diagnostics\/} are proposed to help most
                 of the rest of us, who aspire to use computers without
                 having to program them. The features of IEEE Standards
                 754 and 854 are supported by but not obligatory for the
                 proposals.",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: fparith.bib
label: Kane:1987:MRR
author: Gerry Kane
title: MIPS R2000 RISC Architecture
publisher: pub-PH
address: pub-PH:adr
pages: 165--211
year: 1987
ISBN: 0-13-584749-4 OR 0135847494
ISBN13: 978-0-13-584749-7 OR 9780135847497
LCCN: QA76.8.M52 K36 1987
bibdate: Wed Dec 15 17:51:38 1993
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1993.12.15 17:51:38 ???
acknowledgement: ack-nhfb
rawauthor: Gerry Kane
rawtitle: {MIPS R2000 RISC} Architecture
entry:
@Book{Kane:1987:MRR,
  author =       "Gerry Kane",
  title =        "{MIPS R2000 RISC} Architecture",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  year =         "1987",
  ISBN =         "0-13-584749-4",
  ISBN-13 =      "978-0-13-584749-7",
  LCCN =         "QA76.8.M52 K36 1987",
  bibdate =      "Wed Dec 15 17:51:38 1993",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Kao:1987:ISM
author: Rom-Shen Kao and Fred J. Taylor
title: Implementation of the Single Modulus Complex ALU
crossref: Irwin:1987:PSC
pages: 21--27
year: 1987
DOI: https://doi.org/10.1109/ARITH.1987.6158703
bibdate: Fri Nov 16 21:39:46 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.16 21:39:46 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Kao_Taylor.pdf
keywords: ARITH-8
acknowledgement: ack-nhfb
rawauthor: Rom-Shen Kao and Fred J. Taylor
rawtitle: Implementation of the Single Modulus Complex {ALU}
abstract:
Recently the complex residue number system, or RNS, has been a subject of intense study. One special embodiment of this theory is the single modulus complex RNS processor which suggests both implementation and performance advantages. In this paper these conjectures are tested in the context of a CMOS gate array design and are found to be valid.

rawabstract:
Recently the complex residue number system, or RNS, has been a subject of intense study. One special embodiment of this theory is the single modulus complex RNS processor which suggests both implementation and performance advantages. In this paper these conjectures are tested in the context of a CMOS gate array design and are found to be valid.

entry:
@InProceedings{Kao:1987:ISM,
  author =       "Rom-Shen Kao and Fred J. Taylor",
  title =        "Implementation of the Single Modulus Complex {ALU}",
  crossref =     "Irwin:1987:PSC",
  pages =        "21--27",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158703",
  bibdate =      "Fri Nov 16 21:39:46 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Kao_Taylor.pdf",
  abstract =     "Recently the complex residue number system, or RNS,
                 has been a subject of intense study. One special
                 embodiment of this theory is the single modulus complex
                 RNS processor which suggests both implementation and
                 performance advantages. In this paper these conjectures
                 are tested in the context of a CMOS gate array design
                 and are found to be valid.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}


bibtype: inproceedings
filename: fparith.bib
label: Kirchner:1987:AVP
author: R. Kirchner and U. Kulisch
title: Arithmetic for Vector Processors
crossref: Irwin:1987:PSC
pages: 256--269
year: 1987
DOI: https://doi.org/10.1109/ARITH.1987.6158704
bibdate: Fri Nov 16 21:39:46 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.16 21:39:46 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Kirchner_Kulisch.pdf
keywords: ARITH-8
acknowledgement: ack-nhfb
rawauthor: R. Kirchner and U. Kulisch
rawtitle: Arithmetic for Vector Processors
abstract:
In electronic computers the elementary arithmetic operations are these days generally approximated by floating-point operations of highest accuracy. Vector processors and parallel computers often provide additional operations like ``multiply and add'', ``accumulate'' or ``multiply and accumulate''. Also these operations shall always deliver the correct answer whatever the data are. The user should not be obliged to execute an error analysis for operations predefined by the manufacturer. In the first part of this paper we discuss circuits which allow a fast and correct computation of sums and scalar products making use of a matrix shaped arrangement of adders and pipeline technology. In the second part a variant is discussed which permits a drastic reduction in the number of adders required. The methods discussed in this paper can also be used to build a fast arithmetic unit for micro computers in VLSI-technology.

rawabstract:
In electronic computers the elementary arithmetic operations are these days generally approximated by floating-point operations of highest accuracy. Vector processors and parallel computers often provide additional operations like ``multiply and add'', ``accumulate'' or ``multiply and accumulate''. Also these operations shall always deliver the correct answer whatever the data are. The user should not be obliged to execute an error analysis for operations predefined by the manufacturer. In the first part of this paper we discuss circuits which allow a fast and correct computation of sums and scalar products making use of a matrix shaped arrangement of adders and pipeline technology. In the second part a variant is discussed which permits a drastic reduction in the number of adders required. The methods discussed in this paper can also be used to build a fast arithmetic unit for micro computers in VLSI-technology.

entry:
@InProceedings{Kirchner:1987:AVP,
  author =       "R. Kirchner and U. Kulisch",
  title =        "Arithmetic for Vector Processors",
  crossref =     "Irwin:1987:PSC",
  pages =        "256--269",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158704",
  bibdate =      "Fri Nov 16 21:39:46 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Kirchner_Kulisch.pdf",
  abstract =     "In electronic computers the elementary arithmetic
                 operations are these days generally approximated by
                 floating-point operations of highest accuracy. Vector
                 processors and parallel computers often provide
                 additional operations like ``multiply and add'',
                 ``accumulate'' or ``multiply and accumulate''. Also
                 these operations shall always deliver the correct
                 answer whatever the data are. The user should not be
                 obliged to execute an error analysis for operations
                 predefined by the manufacturer. In the first part of
                 this paper we discuss circuits which allow a fast and
                 correct computation of sums and scalar products making
                 use of a matrix shaped arrangement of adders and
                 pipeline technology. In the second part a variant is
                 discussed which permits a drastic reduction in the
                 number of adders required. The methods discussed in
                 this paper can also be used to build a fast arithmetic
                 unit for micro computers in VLSI-technology.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}


bibtype: article
filename: fparith.bib
label: Kirchner:1987:SVS
author: Reinhard Kirchner and Ulrich Kulisch
journal: Beitrage zur angewandten Mathematik und Statistik
publisher: pub-HANSER
address: pub-HANSER:adr
pages: 139--177
year: 1987
MRclass: 68Q25 (68Q10)
MRnumber: 986 782
bibdate: Fri Dec 08 12:20:44 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 12:20:44 ???
language: German
acknowledgement: ack-nhfb
rawauthor: Reinhard Kirchner and Ulrich Kulisch
title:
Schaltungsanordnung und Verfahren zur schnellen Berechnung von Summen und Skalarprodukten von Gleitkommazahlen mit maximaler Genauigkeit mittels Pipelinetechnik. (German) [Circuit diagrams and methods for fast computation of sums and scalar products of floating point numbers with maximal accuracy via pipeline technique]

rawtitle:
{Schaltungsanordnung und Verfahren zur schnellen Berechnung von Summen und Skalarprodukten von Gleitkommazahlen mit maximaler Genauigkeit mittels Pipelinetechnik}. ({German}) [Circuit diagrams and methods for fast computation of sums and scalar products of floating point numbers with maximal accuracy via pipeline technique]

entry:
@Article{Kirchner:1987:SVS,
  author =       "Reinhard Kirchner and Ulrich Kulisch",
  title =        "{Schaltungsanordnung und Verfahren zur schnellen
                 Berechnung von Summen und Skalarprodukten von
                 Gleitkommazahlen mit maximaler Genauigkeit mittels
                 Pipelinetechnik}. ({German}) [Circuit diagrams and
                 methods for fast computation of sums and scalar
                 products of floating point numbers with maximal
                 accuracy via pipeline technique]",
  journal =      "Beitr{\"a}ge zur angewandten Mathematik und
                 Statistik",
  publisher =    pub-HANSER,
  address =      pub-HANSER:adr,
  pages =        "139--177",
  year =         "1987",
  MRclass =      "68Q25 (68Q10)",
  MRnumber =     "986 782",
  bibdate =      "Fri Dec 08 12:20:44 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
}


bibtype: article
filename: fparith.bib
label: Koopman:1987:TF
author: P. Koopman
title: Transcendental Functions
journal: j-FORTH-DIMENSIONS
volume: 9
number: 4
pages: 21--22
month: dec
monthnumber: 12
year: 1987
CODEN: FODMD5
ISSN: 0884-0822 OR 08840822
bibdate: Thu Sep 1 10:15:30 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 10:15:30 ???
fjournal: Forth Dimensions
acknowledgement: ack-nj
rawauthor: P. Koopman
rawtitle: Transcendental Functions
entry:
@Article{Koopman:1987:TF,
  author =       "P. Koopman",
  title =        "Transcendental Functions",
  journal =      j-FORTH-DIMENSIONS,
  volume =       "9",
  number =       "4",
  pages =        "21--22",
  month =        dec,
  year =         "1987",
  CODEN =        "FODMD5",
  ISSN =         "0884-0822",
  bibdate =      "Thu Sep 1 10:15:30 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 =     "Forth Dimensions",
}


bibtype: inproceedings
filename: fparith.bib
label: Kornerup:1987:BSA
author: Peter Kornerup and David W. Matula
title: A Bit-Serial Arithmetic Unit for Rational Arithmetic
crossref: Irwin:1987:PSC
pages: 204--211
year: 1987
DOI: https://doi.org/10.1109/ARITH.1987.6158705
bibdate: Fri Nov 16 21:39:46 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.16 21:39:46 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Kornerup_Matula.pdf
keywords: ARITH-8
acknowledgement: ack-nhfb
rawauthor: Peter Kornerup and David W. Matula
rawtitle: A Bit-Serial Arithmetic Unit for Rational Arithmetic
abstract:
We describe a binary implementation of an algorithm of Gosper to compute the sum, difference, product, quotient and certain rational functions of two rational operands applicable to integrated approximate and exact rational computation. The arithmetic unit we propose is an eight register computation cell with bit, serial input and output employing the binary lexicographic continued fraction (LCF) representation of the rational operands., The operands and results are processed in a most-significant-bit first on-line fashion with bit level logic leading to less delay in the computation cell when compared to operation on the full partial quotients of the standard continued fraction representation. Minimization of delay is investigated with the aim of supporting greater throughput in cascaded parallel computation with such computation cells.

rawabstract:
We describe a binary implementation of an algorithm of Gosper to compute the sum, difference, product, quotient and certain rational functions of two rational operands applicable to integrated approximate and exact rational computation. The arithmetic unit we propose is an eight register computation cell with bit, serial input and output employing the binary lexicographic continued fraction (LCF) representation of the rational operands., The operands and results are processed in a most-significant-bit first on-line fashion with bit level logic leading to less delay in the computation cell when compared to operation on the full partial quotients of the standard continued fraction representation. Minimization of delay is investigated with the aim of supporting greater throughput in cascaded parallel computation with such computation cells.

entry:
@InProceedings{Kornerup:1987:BSA,
  author =       "Peter Kornerup and David W. Matula",
  title =        "A Bit-Serial Arithmetic Unit for Rational Arithmetic",
  crossref =     "Irwin:1987:PSC",
  pages =        "204--211",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158705",
  bibdate =      "Fri Nov 16 21:39:46 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Kornerup_Matula.pdf",
  abstract =     "We describe a binary implementation of an algorithm of
                 Gosper to compute the sum, difference, product,
                 quotient and certain rational functions of two rational
                 operands applicable to integrated approximate and exact
                 rational computation. The arithmetic unit we propose is
                 an eight register computation cell with bit, serial
                 input and output employing the binary lexicographic
                 continued fraction (LCF) representation of the rational
                 operands., The operands and results are processed in a
                 most-significant-bit first on-line fashion with bit
                 level logic leading to less delay in the computation
                 cell when compared to operation on the full partial
                 quotients of the standard continued fraction
                 representation. Minimization of delay is investigated
                 with the aim of supporting greater throughput in
                 cascaded parallel computation with such computation
                 cells.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}


bibtype: phdthesis
filename: fparith.bib
label: Kraemer:1987:ISF
author: W. Kramer
type: Dissertation
school: Universitat Karlsruhe
address: Karlsruhe, Germany
year: 1987
bibdate: Fri Sep 16 16:30:41 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.16 16:30:41 ???
acknowledgement: ack-nj
authordates: 1952--2014
rawauthor: W. Kr{\"a}mer
title:
Inverse Standardfunktionen fur reelle und komplexe Intervallargumente mit a priori Fehlerabschatzungen fur beliebige Datenformate toenglish Inverse Elementary Functions for Real and Complex Interval Arguments with A-Priori Error Estimates for Arbitrary Data Formats endtoenglish 

rawtitle:
Inverse Standardfunktionen f{\"u}r reelle und komplexe Intervallargumente mit a priori Fehlerabsch{\"a}tzungen f{\"u}r beliebige Datenformate \toenglish {Inverse Elementary Functions for Real and Complex Interval Arguments with A-Priori Error Estimates for Arbitrary Data Formats} \endtoenglish

entry:
@PhdThesis{Kraemer:1987:ISF,
  author =       "W. Kr{\"a}mer",
  title =        "Inverse Standardfunktionen f{\"u}r reelle und komplexe
                 Intervallargumente mit a priori Fehlerabsch{\"a}tzungen
                 f{\"u}r beliebige Datenformate \toenglish {Inverse
                 Elementary Functions for Real and Complex Interval
                 Arguments with A-Priori Error Estimates for Arbitrary
                 Data Formats} \endtoenglish",
  type =         "Dissertation",
  school =       "Universit{\"a}t Karlsruhe",
  address =      "Karlsruhe, Germany",
  pages =        "??",
  year =         "1987",
  bibdate =      "Fri Sep 16 16:30:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  author-dates = "1952--2014",
}


bibtype: inproceedings
filename: fparith.bib
label: Kuninobu:1987:DHS
title: Design of High Speed MOS Multiplier and Divider Using Redundant Binary Representation
crossref: Irwin:1987:PSC
pages: 80--86
year: 1987
DOI: https://doi.org/10.1109/ARITH.1987.6158706
bibdate: Wed Nov 14 18:22:26 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 18:22:26 ???
keywords: ARITH-8
acknowledgement: ack-nhfb
key: KNE87
rawtitle: Design of High Speed {MOS} Multiplier and Divider Using Redundant Binary Representation
author:
Shigeo Kuninobu and Tamotsu Nishiyama and Hisakazu Edamatsu and Takashi Taniguchi and Naofumi Takagi

URL:
http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Kuninobu_Nishiyama_Edamatsu_Taniguchi_Takagi.pdf

abstract:
A high speed multiplier and divider for MOS LSI based on a new algorithm is presented. When we implement the multiplier and the divider in LSI. the features such as high speed operation, small number of transistors and easy layout are the most important factors. A computational algorithm using a redundant binary representation has several excellent features such as high speed addition operations. We improved the algorithm and the method of implementation. and designed an advanced multiplier and divider with the above mentioned features. We expect that our multiplier and divider are excellent compared with multipliers using the Booth algorithm and the Wallace tree. and with divider using the SRT method, respectively.

rawabstract:
A high speed multiplier and divider for MOS LSI based on a new algorithm is presented. When we implement the multiplier and the divider in LSI. the features such as high speed operation, small number of transistors and easy layout are the most important factors. A computational algorithm using a redundant binary representation has several excellent features such as high speed addition operations. We improved the algorithm and the method of implementation. and designed an advanced multiplier and divider with the above mentioned features. We expect that our multiplier and divider are excellent compared with multipliers using the Booth algorithm and the Wallace tree. and with divider using the SRT method, respectively.

rawauthor:
Shigeo Kuninobu and Tamotsu Nishiyama and Hisakazu Edamatsu and Takashi Taniguchi and Naofumi Takagi

entry:
@InProceedings{Kuninobu:1987:DHS,
  author =       "Shigeo Kuninobu and Tamotsu Nishiyama and Hisakazu
                 Edamatsu and Takashi Taniguchi and Naofumi Takagi",
  key =          "KNE87",
  title =        "Design of High Speed {MOS} Multiplier and Divider
                 Using Redundant Binary Representation",
  crossref =     "Irwin:1987:PSC",
  pages =        "80--86",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158706",
  bibdate =      "Wed Nov 14 18:22:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Kuninobu_Nishiyama_Edamatsu_Taniguchi_Takagi.pdf",
  abstract =     "A high speed multiplier and divider for MOS LSI based
                 on a new algorithm is presented. When we implement the
                 multiplier and the divider in LSI. the features such as
                 high speed operation, small number of transistors and
                 easy layout are the most important factors. A
                 computational algorithm using a redundant binary
                 representation has several excellent features such as
                 high speed addition operations. We improved the
                 algorithm and the method of implementation. and
                 designed an advanced multiplier and divider with the
                 above mentioned features. We expect that our multiplier
                 and divider are excellent compared with multipliers
                 using the Booth algorithm and the Wallace tree. and
                 with divider using the SRT method, respectively.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}


bibtype: article
filename: fparith.bib
label: Lange:1987:ITA
author: Eberhard Lange
title: Implementation and Test of the ACRITH Facility in a System / 370
journal: j-IEEE-TRANS-COMPUT
volume: C-36
number: 9
pages: 1088--1096
month: sep
monthnumber: 9
year: 1987
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1987.5009539
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 9 09:28:55 MDT 2011
bibtimestamp: 2011.07.09 09:28:55 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009539
fjournal: IEEE Transactions on Computers
keywords: floating-point testing
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Eberhard Lange
rawtitle: Implementation and Test of the {ACRITH} Facility in a {System}\slash 370
entry:
@Article{Lange:1987:ITA,
  author =       "Eberhard Lange",
  title =        "Implementation and Test of the {ACRITH} Facility in a
                 {System}\slash 370",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-36",
  number =       "9",
  pages =        "1088--1096",
  month =        sep,
  year =         "1987",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1987.5009539",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 09:28:55 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/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009539",
  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",
  keywords =     "floating-point testing",
}


bibtype: article
filename: fparith.bib
label: Leavitt:1987:APF
author: Randal Leavitt
title: Adjustable Precision Floating Point Arithmetic in Ada
journal: j-SIGADA-LETTERS
volume: 7
number: 5
pages: 63--78
month: sep
monthnumber: 9
year: 1987
CODEN: AALEE5
ISSN: 1094-3641 (print), 1557-9476 (electronic) OR 10943641 (print), 15579476 (electronic)
ISSNL: 1094-3641 OR 10943641
bibdate: Sat Aug 9 09:05:26 MDT 2003
bibtimestamp: 2003.08.09 09:05:26 MDT
fjournal: ACM SIGAda Ada Letters
keywords: design; performance; theory
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/citation.cfm?id=J32
rawauthor: Randal Leavitt
rawtitle: Adjustable Precision Floating Point Arithmetic in {Ada}
bibsource:
ftp://ftp.uu.net/library/bibliography; http://portal.acm.org/; http://www.adahome.com/Resources/Bibliography/articles.ref; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/sigada.bib

subject:
D.3.2 Software, PROGRAMMING LANGUAGES, Language Classifications, Ada G.1.0 Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic

entry:
@Article{Leavitt:1987:APF,
  author =       "Randal Leavitt",
  title =        "Adjustable Precision Floating Point Arithmetic in
                 {Ada}",
  journal =      j-SIGADA-LETTERS,
  volume =       "7",
  number =       "5",
  pages =        "63--78",
  month =        sep # "\slash " # oct,
  year =         "1987",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Sat Aug 9 09:05:26 MDT 2003",
  bibsource =    "ftp://ftp.uu.net/library/bibliography;
                 http://portal.acm.org/;
                 http://www.adahome.com/Resources/Bibliography/articles.ref;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigada.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "design; performance; theory",
  subject =      "D.3.2 Software, PROGRAMMING LANGUAGES, Language
                 Classifications, Ada \\ G.1.0 Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Computer arithmetic",
}


bibtype: article
filename: fparith.bib
label: Lien:1987:RCI
author: B. Lien and G. Tang
title: Reversed Chebyshev implementation of McClellan transform and its roundoff error
journal: j-IEEE-TRANS-ACOUST-SPEECH
volume: 35
number: 10
pages: 1435--1439
month: oct
monthnumber: 10
year: 1987
CODEN: IETABA
ISSN: 0096-3518 OR 00963518
bibdate: Sat Jul 16 11:25:06 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:06 MDT
fjournal: IEEE Transactions on Acoustics, Speech, and Signal Processing
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29
rawauthor: B. Lien and G. Tang
rawtitle: Reversed {Chebyshev} implementation of {McClellan} transform and its roundoff error
entry:
@Article{Lien:1987:RCI,
  author =       "B. Lien and G. Tang",
  title =        "Reversed {Chebyshev} implementation of {McClellan}
                 transform and its roundoff error",
  journal =      j-IEEE-TRANS-ACOUST-SPEECH,
  volume =       "35",
  number =       "10",
  pages =        "1435--1439",
  month =        oct,
  year =         "1987",
  CODEN =        "IETABA",
  ISSN =         "0096-3518",
  bibdate =      "Sat Jul 16 11:25:06 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Acoustics, Speech, and Signal
                 Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
  summary =      "A new structure, called the reversed Chebyshev
                 structure, for the fixed point implementation of the
                 FIR filters designed with the McClellan transformation
                 is presented. It shows the best roundoff noise
                 performance among the existing ones for both \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Lin:1987:NFP
author: Haixiang X. Lin and Henk J. Sips
title: A Novel Floating-Point Online Division Algorithm
crossref: Irwin:1987:PSC
pages: 188--195
month: may
monthnumber: 5
year: 1987
DOI: https://doi.org/10.1109/ARITH.1987.6158707
bibdate: Wed Nov 14 18:22:26 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 18:22:26 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Lin_Sips.pdf
keywords: ARITH-8
acknowledgement: ack-nhfb
rawauthor: Haixiang X. Lin and Henk J. Sips
rawtitle: A Novel Floating-Point Online Division Algorithm
abstract:
This paper describes a new online division (reciprocal) algorithm for (maximally) redundant floating-point numbers of arbitrary radix. The algorithm works for normalized, quasi-normalized, and pseudo-normalized numbers and can therefore be applied in chained online computations. The online delay of the proposed algorithm is the smallest reported so far. The algorithm consists of two steps: the first $m$ digits of the result are generated by a simple table lookup method; the remaining $ n - m $ digits are generated by using an adapted Newton--Raphson iteration method. In the second step, the online digits are created by using a fast and simple selection mechanism.

rawabstract:
This paper describes a new online division (reciprocal) algorithm for (maximally) redundant floating-point numbers of arbitrary radix. The algorithm works for normalized, quasi-normalized, and pseudo-normalized numbers and can therefore be applied in chained online computations. The online delay of the proposed algorithm is the smallest reported so far. The algorithm consists of two steps: the first $m$ digits of the result are generated by a simple table lookup method; the remaining $ n - m $ digits are generated by using an adapted Newton--Raphson iteration method. In the second step, the online digits are created by using a fast and simple selection mechanism.

entry:
@InProceedings{Lin:1987:NFP,
  author =       "Haixiang X. Lin and Henk J. Sips",
  title =        "A Novel Floating-Point Online Division Algorithm",
  crossref =     "Irwin:1987:PSC",
  pages =        "188--195",
  month =        may,
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158707",
  bibdate =      "Wed Nov 14 18:22:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Lin_Sips.pdf",
  abstract =     "This paper describes a new online division
                 (reciprocal) algorithm for (maximally) redundant
                 floating-point numbers of arbitrary radix. The
                 algorithm works for normalized, quasi-normalized, and
                 pseudo-normalized numbers and can therefore be applied
                 in chained online computations. The online delay of the
                 proposed algorithm is the smallest reported so far. The
                 algorithm consists of two steps: the first $m$ digits
                 of the result are generated by a simple table lookup
                 method; the remaining $ n - m $ digits are generated by
                 using an adapted Newton--Raphson iteration method. In
                 the second step, the online digits are created by using
                 a fast and simple selection mechanism.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}


bibtype: mastersthesis
filename: fparith.bib
label: Liu:1987:BEF
author: Zhi-Shun Alex Liu
title: Berkeley Elementary Function Test Suite: Research Project
type: Master of Science, Plan II
address: Berkeley, CA, USA
pages: 188--195
month: dec
monthnumber: 12
year: 1987
bibdate: Mon Sep 12 23:52:34 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.12 23:52:34 ???
keywords: BeEF test suite; floating-point testing
acknowledgement: ack-nj
rawauthor: Zhi-Shun Alex Liu
rawtitle: {Berkeley} Elementary Function Test Suite: Research Project
school:
Computer Science Division, Department of Electrical Engineering and Computer Science, Univerity of California at Berkeley

entry:
@MastersThesis{Liu:1987:BEF,
  author =       "Zhi-Shun Alex Liu",
  title =        "{Berkeley} Elementary Function Test Suite: Research
                 Project",
  type =         "{Master of Science, Plan II}",
  school =       "Computer Science Division, Department of Electrical
                 Engineering and Computer Science, Univerity of
                 California at Berkeley",
  address =      "Berkeley, CA, USA",
  month =        dec,
  year =         "1987",
  bibdate =      "Mon Sep 12 23:52:34 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  keywords =     "BeEF test suite; floating-point testing",
}


bibtype: article
filename: fparith.bib
label: Lo:1987:HGA
author: H.-Y. Lo and J.-L. Chen
title: A Hardwired Generalized Algorithm for Generating the Logarithm Base-$k$ by Iteration
journal: j-IEEE-TRANS-COMPUT
volume: C-36
number: 11
pages: 1363--1367
month: nov
monthnumber: 11
year: 1987
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1987.5009477
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Sep 08 08:08:51 1994
bibtimestamp: 1994.09.08 08:08:51 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: H.-Y. Lo and J.-L. Chen
rawtitle: A Hardwired Generalized Algorithm for Generating the Logarithm Base-$k$ by Iteration
entry:
@Article{Lo:1987:HGA,
  author =       "H.-Y. Lo and J.-L. Chen",
  title =        "A Hardwired Generalized Algorithm for Generating the
                 Logarithm Base-$k$ by Iteration",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-36",
  number =       "11",
  pages =        "1363--1367",
  month =        nov,
  year =         "1987",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1987.5009477",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 08 08:08:51 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  acknowledgement = ack-nj,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Maenner:1987:FIB
author: R. Maenner
title: A Fast Integer Binary Logarithm of Large Arguments
journal: j-IEEE-MICRO
volume: 7
number: 6
pages: 41--45
month: nov
monthnumber: 11
year: 1987
CODEN: IEMIDZ
DOI: https://doi.org/10.1109/MM.1987.304914
ISSN: 0272-1732 (print), 1937-4143 (electronic) OR 02721732 (print), 19374143 (electronic)
ISSNL: 0272-1732 OR 02721732
bibdate: Thu Sep 1 10:16:09 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:16:09 ???
fjournal: IEEE Micro
acknowledgement: ack-nj
journalURL: http://www.computer.org/csdl/mags/mi/index.html
rawauthor: R. Maenner
rawtitle: A Fast Integer Binary Logarithm of Large Arguments
entry:
@Article{Maenner:1987:FIB,
  author =       "R. Maenner",
  title =        "A Fast Integer Binary Logarithm of Large Arguments",
  journal =      j-IEEE-MICRO,
  volume =       "7",
  number =       "6",
  pages =        "41--45",
  month =        nov # "\slash " # dec,
  year =         "1987",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/MM.1987.304914",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  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 =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
}


bibtype: article
filename: fparith.bib
label: Magenheimer:1987:IMD
author: Daniel J. Magenheimer and Liz Peters and Karl Pettis and Dan Zuras
title: Integer multiplication and division on the HP Precision Architecture
journal: j-SIGPLAN
volume: 22
number: 10
pages: 90--99
month: oct
monthnumber: 10
year: 1987
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 09:15:15 MST 2003
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.12.14 09:15:15 MST
fjournal: ACM SIGPLAN Notices
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J706
rawauthor: Daniel J. Magenheimer and Liz Peters and Karl Pettis and Dan Zuras
rawtitle: Integer multiplication and division on the {HP Precision Architecture}
entry:
@Article{Magenheimer:1987:IMD,
  author =       "Daniel J. Magenheimer and Liz Peters and Karl Pettis
                 and Dan Zuras",
  title =        "Integer multiplication and division on the {HP
                 Precision Architecture}",
  journal =      j-SIGPLAN,
  volume =       "22",
  number =       "10",
  pages =        "90--99",
  month =        oct,
  year =         "1987",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sun Dec 14 09:15:15 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 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",
}


bibtype: article
filename: fparith.bib
label: Makarenko:1987:VMM
author: Darrell Makarenko and Jonathan Schaeffer
title: A VLSI multiprecision matrix multiplier and polynomial evaluator
journal: j-J-PAR-DIST-COMP
volume: 4
number: 6
pages: 619--628
month: dec
monthnumber: 12
year: 1987
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
affiliationaddress: Univ of Alberta, Edmonton, Alberta, Can
corpsource: Department of Computer Science, Alberta University, Edmonton, Alta., Canada
journalURL: http://www.sciencedirect.com/science/journal/07437315
journalabr: J Parallel Distrib Comput
treatment: P Practical
rawauthor: Darrell Makarenko and Jonathan Schaeffer
rawtitle: A {VLSI} multiprecision matrix multiplier and polynomial evaluator
keywords:
32 bit; 32-bit multiplication; algebra; band-matrix multiplication; bit-serial; computational complexity; computers --- Multiplying Circuits; Design; digital arithmetic; evaluations; full-matrix multiplication; integrated circuits, VLSI; linear-space evaluations; linear-time; mathematical techniques --- Polynomials; matrix; matrix multiplier; multiply and accumulate cells; multiprecision matrix multiplier; polynomial evaluator; polynomials; two dimensional array; two's complement numbers; VLSI; VLSI multiprecision; VLSI multiprecision polynomial evaluator

entry:
@Article{Makarenko:1987:VMM,
  author =       "Darrell Makarenko and Jonathan Schaeffer",
  title =        "A {VLSI} multiprecision matrix multiplier and
                 polynomial evaluator",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "4",
  number =       "6",
  pages =        "619--628",
  month =        dec,
  year =         "1987",
  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,
  affiliationaddress = "Univ of Alberta, Edmonton, Alberta, Can",
  classification = "713; 722; C4140 (Linear algebra); C4240 (Programming
                 and algorithm theory); C5230 (Digital arithmetic
                 methods)",
  corpsource =   "Department of Computer Science, Alberta University,
                 Edmonton, Alta., Canada",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "32 bit; 32-bit multiplication; algebra; band-matrix
                 multiplication; bit-serial; computational complexity;
                 computers --- Multiplying Circuits; Design; digital
                 arithmetic; evaluations; full-matrix multiplication;
                 integrated circuits, VLSI; linear-space evaluations;
                 linear-time; mathematical techniques --- Polynomials;
                 matrix; matrix multiplier; multiply and accumulate
                 cells; multiprecision matrix multiplier; polynomial
                 evaluator; polynomials; two dimensional array; two's
                 complement numbers; VLSI; VLSI multiprecision; VLSI
                 multiprecision polynomial evaluator",
  treatment =    "P Practical",
}


bibtype: inproceedings
filename: fparith.bib
label: Manzoul:1987:QCN
author: Mahmoud A. Manzoul
title: A quaternary complex number CCD adder (abstract only)
crossref: Davis:1987:PAC
pages: 434--434
year: 1987
DOI: https://doi.org/10.1145/322917.323095
bibdate: Sat Aug 22 09:06:07 2009
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2009.08.22 09:06:07 ???
acknowledgement: ack-nhfb
rawauthor: Mahmoud A. Manzoul
rawtitle: A quaternary complex number {CCD} adder (abstract only)
abstract:
Complex number arithmetic occurs frequently in digital signal processing and power systems analysis. Normally, complex numbers are given two binary words, with one word for each component (real and imaginary). Therefore, the standard binary implementation of complex numbers requires several real arithmetic operations. Besides, the two components of each complex number must be tracked down at every stage of the computation. Different digital representations for complex numbers have been proposed in an effort to reduce these problems. Knuth [1] has proposed an unconventional single component representation of complex numbers whereby the radix is chosen to be (2j) with the digit set comprised of the first four positive integers (0, 1, 2, 3). This is in contrast with the conventional two components representation with binary radix whether in Cartesian or Polar coordinates. Knuth's representation leads to simple and interesting arithmetic in the complex field [2] [3].

rawabstract:
Complex number arithmetic occurs frequently in digital signal processing and power systems analysis. Normally, complex numbers are given two binary words, with one word for each component (real and imaginary). Therefore, the standard binary implementation of complex numbers requires several real arithmetic operations. Besides, the two components of each complex number must be tracked down at every stage of the computation. Different digital representations for complex numbers have been proposed in an effort to reduce these problems. Knuth [1] has proposed an unconventional single component representation of complex numbers whereby the radix is chosen to be (2j) with the digit set comprised of the first four positive integers (0, 1, 2, 3). This is in contrast with the conventional two components representation with binary radix whether in Cartesian or Polar coordinates. Knuth's representation leads to simple and interesting arithmetic in the complex field [2] [3].

entry:
@InProceedings{Manzoul:1987:QCN,
  author =       "Mahmoud A. Manzoul",
  title =        "A quaternary complex number {CCD} adder (abstract
                 only)",
  crossref =     "Davis:1987:PAC",
  pages =        "434--434",
  year =         "1987",
  DOI =          "https://doi.org/10.1145/322917.323095",
  bibdate =      "Sat Aug 22 09:06:07 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Complex number arithmetic occurs frequently in digital
                 signal processing and power systems analysis. Normally,
                 complex numbers are given two binary words, with one
                 word for each component (real and imaginary).
                 Therefore, the standard binary implementation of
                 complex numbers requires several real arithmetic
                 operations. Besides, the two components of each complex
                 number must be tracked down at every stage of the
                 computation. Different digital representations for
                 complex numbers have been proposed in an effort to
                 reduce these problems. Knuth [1] has proposed an
                 unconventional single component representation of
                 complex numbers whereby the radix is chosen to be (2j)
                 with the digit set comprised of the first four positive
                 integers (0, 1, 2, 3). This is in contrast with the
                 conventional two components representation with binary
                 radix whether in Cartesian or Polar coordinates.
                 Knuth's representation leads to simple and interesting
                 arithmetic in the complex field [2] [3].",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Mariella:1987:IDF
author: Ray Mariella
title: Integers Don't Float
journal: j-DDJ
volume: 12
number: 12
pages: 48--??
month: dec
monthnumber: 12
year: 1987
CODEN: DDJOEB
ISSN: 1044-789X OR 1044789X
bibdate: Mon Sep 2 09:09:39 MDT 1996
bibsource: http://www.ddj.com/index/author/index.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.09.02 09:09:39 MDT
fjournal: Dr. Dobb's Journal of Software Tools
acknowledgement: ack-nhfb
rawauthor: Ray Mariella
rawtitle: Integers Don't Float
entry:
@Article{Mariella:1987:IDF,
  author =       "Ray Mariella",
  title =        "Integers Don't Float",
  journal =      j-DDJ,
  volume =       "12",
  number =       "12",
  pages =        "48--??",
  month =        dec,
  year =         "1987",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Mon Sep 2 09:09:39 MDT 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}


bibtype: article
filename: fparith.bib
label: Mays:1987:IDA
author: Michael E. Mays
title: Iterating the Division Algorithm
journal: j-FIB-QUART
volume: 25
number: 3
pages: 204--213
month: aug
monthnumber: 8
year: 1987
CODEN: FIBQAU
ISSN: 0015-0517 OR 00150517
ISSNL: 0015-0517 OR 00150517
bibdate: Thu Oct 20 18:00:58 MDT 2011
bibtimestamp: 2011.10.20 18:00:58 MDT
URL: http://www.fq.math.ca/Scanned/25-3/mays.pdf
fjournal: The Fibonacci Quarterly. Official Organ of the Fibonacci Association
acknowledgement: ack-nhfb
ajournal: Fib. Quart
journalURL: http://www.fq.math.ca/
rawauthor: Michael E. Mays
rawtitle: Iterating the Division Algorithm
bibsource:
http://www.fq.math.ca/25-3.html; https://www.math.utah.edu/pub/tex/bib/fibquart.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Mays:1987:IDA,
  author =       "Michael E. Mays",
  title =        "Iterating the Division Algorithm",
  journal =      j-FIB-QUART,
  volume =       "25",
  number =       "3",
  pages =        "204--213",
  month =        aug,
  year =         "1987",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:00:58 MDT 2011",
  bibsource =    "http://www.fq.math.ca/25-3.html;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.fq.math.ca/Scanned/25-3/mays.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}


bibtype: book
filename: fparith.bib
label: McMcusersmanual:1987:MMF
author: Motorola, Inc.
title: MC68881 / MC68882 floating-point coprocessor user's manual
publisher: pub-PH
address: pub-PH:adr
pages: various
year: 1987
ISBN: 0-13-566936-7 (pbk.) OR 0135669367 (pbk.)
ISBN13: 978-0-13-566936-5 (pbk.) OR 9780135669365 (pbk.)
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Floating-point arithmetic.; Motorola 68881 (Microprocessor); Motorola 68882 (Microprocessor)
remark: Spine title: MC68881/MC68882 user's manual. ``MC68881UM/AD REV 1''--Cover.
acknowledgement: ack-nhfb
rawauthor: {Motorola, Inc.}
rawtitle: {MC68881\slash MC68882} floating-point coprocessor user's manual
entry:
@Book{McMcusersmanual:1987:MMF,
  author =       "{Motorola, Inc.}",
  title =        "{MC68881\slash MC68882} floating-point coprocessor
                 user's manual",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "various",
  year =         "1987",
  ISBN =         "0-13-566936-7 (pbk.)",
  ISBN-13 =      "978-0-13-566936-5 (pbk.)",
  LCCN =         "????",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.; Motorola 68881
                 (Microprocessor); Motorola 68882 (Microprocessor)",
  remark =       "Spine title: MC68881/MC68882 user's manual.
                 ``MC68881UM/AD REV 1''--Cover.",
}


bibtype: article
filename: fparith.bib
label: Monahan:1987:AGC
author: John F. Monahan
title: An Algorithm for Generating Chi Random Variables
journal: j-TOMS
volume: 13
number: 2
pages: 168--172
month: jun
monthnumber: 6
year: 1987
CODEN: ACMSCU
DOI: https://doi.org/10.1145/328512.328522
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 65C10
MRnumber: 88d:65013
bibdate: Sat Nov 19 13:08:24 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.11.19 13:08:24 ???
note: See also cite Johnson:1987:CES,Monahan:1988:CAG.
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: John F. Monahan
rawnote: See also \cite{Johnson:1987:CES,Monahan:1988:CAG}.
rawtitle: An Algorithm for Generating Chi Random Variables
entry:
@Article{Monahan:1987:AGC,
  author =       "John F. Monahan",
  title =        "An Algorithm for Generating Chi Random Variables",
  journal =      j-TOMS,
  volume =       "13",
  number =       "2",
  pages =        "168--172",
  month =        jun,
  year =         "1987",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/328512.328522",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65C10",
  MRnumber =     "88d:65013",
  bibdate =      "Sat Nov 19 13:08:24 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See also \cite{Johnson:1987:CES,Monahan:1988:CAG}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: fparith.bib
label: Montgomery:1987:SPE
author: Peter L. Montgomery
title: Speeding the Pollard and elliptic curve methods of factorization
journal: j-MATH-COMPUT
volume: 48
number: 177
pages: 243--264
month: jan
monthnumber: 1
year: 1987
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 11Y05 (11A51 68Q40)
MRnumber: 88e:11130
MRreviewer: Kevin S. McCurley
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
note: See improvement cite Kim:2024:MCA.
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
ajournal: Math. Comput.
classcodes: C1160 (Combinatorial mathematics); C4240 (Programming and algorithm theory)
corpsource: Syst. Dev. Corp., Santa Monica, CA, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Peter L. Montgomery
rawnote: See improvement \cite{Kim:2024:MCA}.
rawtitle: Speeding the {Pollard} and elliptic curve methods of factorization
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib; JSTOR database

keywords:
computational complexity; elliptic curve; elliptic curve method; elliptic curve methods; factorization; Lenstra method; Monte Carlo methods; number; number theory; parametrisation; Pollard methods; polynomial preconditioning; theory; Williams method

entry:
@Article{Montgomery:1987:SPE,
  author =       "Peter L. Montgomery",
  title =        "Speeding the {Pollard} and elliptic curve methods of
                 factorization",
  journal =      j-MATH-COMPUT,
  volume =       "48",
  number =       "177",
  pages =        "243--264",
  month =        jan,
  year =         "1987",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "11Y05 (11A51 68Q40)",
  MRnumber =     "88e:11130",
  MRreviewer =   "Kevin S. McCurley",
  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/mathcomp1980.bib;
                 JSTOR database",
  note =         "See improvement \cite{Kim:2024:MCA}.",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  classcodes =   "C1160 (Combinatorial mathematics); C4240 (Programming
                 and algorithm theory)",
  corpsource =   "Syst. Dev. Corp., Santa Monica, CA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "computational complexity; elliptic curve; elliptic
                 curve method; elliptic curve methods; factorization;
                 Lenstra method; Monte Carlo methods; number; number
                 theory; parametrisation; Pollard methods; polynomial
                 preconditioning; theory; Williams method",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: techreport
filename: fparith.bib
label: Motorola:1987:MFP
author: Motorola, Inc.
title: MC68881 Floating-Point Coprocessor as a Peripheral in an M68000 System
type: Motorola Semiconductor Application Note
number: AN947/D
institution: Motorola, Inc.
address: Phoenix, AZ, USA
pages: 37
year: 1987
bibdate: Thu Nov 13 09:51:10 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2025.11.13 09:51:10 ???
acknowledgement: ack-nhfb
rawauthor: {Motorola, Inc.}
rawtitle: {MC68881} Floating-Point Coprocessor as a Peripheral in an {M68000} System
URL:
http://www.bitsavers.org/components/motorola/_appNotes/AN-0947_MC68881_Floating-Point_Coprocessor_as_a_Peripheral_in_a_M68000_System_%5BMotorola_1987_37p%5D.pdf

abstract:
The MC68881 floating-point coprocessor is a complete implementation of the proposed IEEE Standard for Binary Floating-Point Arithmetic (Task P754, Draft 10.0). All data formats, data types, operations, modes, conversions, and exception handling required in a conforming implementation of the proposed standard are supported entirely in hardware. Additionally, a full library of fast elementary transcendental functions is implemented in the hardware.

rawabstract:
The MC68881 floating-point coprocessor is a complete implementation of the proposed IEEE Standard for Binary Floating-Point Arithmetic (Task P754, Draft 10.0). All data formats, data types, operations, modes, conversions, and exception handling required in a conforming implementation of the proposed standard are supported entirely in hardware. Additionally, a full library of fast elementary transcendental functions is implemented in the hardware.

entry:
@TechReport{Motorola:1987:MFP,
  author =       "{Motorola, Inc.}",
  title =        "{MC68881} Floating-Point Coprocessor as a Peripheral
                 in an {M68000} System",
  type =         "Motorola Semiconductor Application Note",
  number =       "AN947/D",
  institution =  "Motorola, Inc.",
  address =      "Phoenix, AZ, USA",
  pages =        "37",
  year =         "1987",
  bibdate =      "Thu Nov 13 09:51:10 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.bitsavers.org/components/motorola/_appNotes/AN-0947_MC68881_Floating-Point_Coprocessor_as_a_Peripheral_in_a_M68000_System_%5BMotorola_1987_37p%5D.pdf",
  abstract =     "The MC68881 floating-point coprocessor is a complete
                 implementation of the proposed IEEE Standard for Binary
                 Floating-Point Arithmetic (Task P754, Draft 10.0). All
                 data formats, data types, operations, modes,
                 conversions, and exception handling required in a
                 conforming implementation of the proposed standard are
                 supported entirely in hardware. Additionally, a full
                 library of fast elementary transcendental functions is
                 implemented in the hardware.",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: fparith.bib
label: Motorola:1987:MMF
author: Motorola, Inc.
title: MC68881 / MC68882 Floating-Point Coprocessor User's Manual
publisher: pub-PH
address: pub-PH:adr
pages: various
year: 1987
ISBN: 0-13-566936-7 OR 0135669367
ISBN13: 978-0-13-566936-5 OR 9780135669365
LCCN: QA76.8.M69 M3 1987
bibdate: Fri Dec 08 13:03:15 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 13:03:15 ???
acknowledgement: ack-nhfb
rawauthor: {Motorola, Inc.}
rawtitle: {MC68881\slash MC68882} Floating-Point Coprocessor User's Manual
entry:
@Book{Motorola:1987:MMF,
  author =       "{Motorola, Inc.}",
  title =        "{MC68881\slash MC68882} Floating-Point Coprocessor
                 User's Manual",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "various",
  year =         "1987",
  ISBN =         "0-13-566936-7",
  ISBN-13 =      "978-0-13-566936-5",
  LCCN =         "QA76.8.M69 M3 1987",
  bibdate =      "Fri Dec 08 13:03:15 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: fparith.bib
label: Mutrie:1987:FEA
author: Mark P. W. Mutrie and Richard H. Bartels and Bruce W. Char
title: Floating-point error analysis using symbolic algebraic computation
type: Research report
number: CS-87-08
institution: University of Waterloo, Faculty of Mathematics
address: Waterloo, Ont., Canada
pages: 13
year: 1987
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: Roundoff errors.
remark: Supported in part by the Natural Sciences and Engineering Research Council of Canada.
acknowledgement: ack-nhfb
rawauthor: Mark P. W. Mutrie and Richard H. Bartels and Bruce W. Char
rawtitle: Floating-point error analysis using symbolic algebraic computation
entry:
@TechReport{Mutrie:1987:FEA,
  author =       "Mark P. W. Mutrie and Richard H. Bartels and Bruce W.
                 Char",
  title =        "Floating-point error analysis using symbolic algebraic
                 computation",
  type =         "Research report",
  number =       "CS-87-08",
  institution =  "University of Waterloo, Faculty of Mathematics",
  address =      "Waterloo, Ont., Canada",
  pages =        "13",
  year =         "1987",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Roundoff errors.",
  remark =       "Supported in part by the Natural Sciences and
                 Engineering Research Council of Canada.",
}


bibtype: misc
filename: fparith.bib
label: Nakano:1987:MAD
author: Hiraku Nakano
title: Method and apparatus for division using interpolation approximation
pages: 13
day: 17
month: nov
monthnumber: 11
year: 1987
bibdate: Tue Jan 08 22:36:28 2008
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2008.01.08 22:36:28 ???
URL: http://www.freepatentsonline.com/4707798.html
acknowledgement: ack-nhfb
howpublished: United States Patent 4,707,798
rawauthor: Hiraku Nakano
rawtitle: Method and apparatus for division using interpolation approximation
abstract:
A divide method and a divide apparatus for use in a data processing system. The divisor and dividend are normalized in a normalization circuit. A table unit stores a plurality of approximate reciprocal divisors and differences between adjacent approximate reciprocal divisors and is addressed by the high-order bits of the normalized divisor. The approximate reciprocal divisor read out from the table unit is, in an interpolation approximation circuit, changed into an interpolation approximated approximate reciprocal divisor in accordance with a plurality of bits following the high-order bits and the difference. A multiplication unit multiplies the interpolation approximated approximate reciprocal divisor by the normalized dividend to output a quotient.

rawabstract:
A divide method and a divide apparatus for use in a data processing system. The divisor and dividend are normalized in a normalization circuit. A table unit stores a plurality of approximate reciprocal divisors and differences between adjacent approximate reciprocal divisors and is addressed by the high-order bits of the normalized divisor. The approximate reciprocal divisor read out from the table unit is, in an interpolation approximation circuit, changed into an interpolation approximated approximate reciprocal divisor in accordance with a plurality of bits following the high-order bits and the difference. A multiplication unit multiplies the interpolation approximated approximate reciprocal divisor by the normalized dividend to output a quotient.

entry:
@Misc{Nakano:1987:MAD,
  author =       "Hiraku Nakano",
  title =        "Method and apparatus for division using interpolation
                 approximation",
  howpublished = "United States Patent 4,707,798",
  day =          "17",
  month =        nov,
  year =         "1987",
  bibdate =      "Tue Jan 08 22:36:28 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.freepatentsonline.com/4707798.html",
  abstract =     "A divide method and a divide apparatus for use in a
                 data processing system. The divisor and dividend are
                 normalized in a normalization circuit. A table unit
                 stores a plurality of approximate reciprocal divisors
                 and differences between adjacent approximate reciprocal
                 divisors and is addressed by the high-order bits of the
                 normalized divisor. The approximate reciprocal divisor
                 read out from the table unit is, in an interpolation
                 approximation circuit, changed into an interpolation
                 approximated approximate reciprocal divisor in
                 accordance with a plurality of bits following the
                 high-order bits and the difference. A multiplication
                 unit multiplies the interpolation approximated
                 approximate reciprocal divisor by the normalized
                 dividend to output a quotient.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Nelsen:1987:PSR
author: Roger B. Nelsen and James E. Schultz
title: The Probability that the ``Sum of the Rounds'' Equals the ``Round of the Sum''
journal: j-COLLEGE-MATH-J
volume: 18
number: 5
pages: 390--396
month: nov
monthnumber: 11
year: 1987
DOI: https://doi.org/10.1080/07468342.1987.11973061
ISSN: 0746-8342 (print), 1931-1346 (electronic) OR 07468342 (print), 19311346 (electronic)
ISSNL: 0746-8342 OR 07468342
bibdate: Thu Feb 14 09:50:35 MST 2019
bibtimestamp: 2019.02.14 09:50:35 MST
fjournal: College Mathematics Journal
keywords: rounding in fixed-point addition
remark: See also cite Hopkins:2016:WMN for a later independent derivation of part of this work.
acknowledgement: ack-nhfb
journalURL: https://maa.tandfonline.com/loi/ucmj20; https://www.jstor.org/journal/collmathj
onlinedate: 30 Jan 2018
rawauthor: Roger B. Nelsen and James E. Schultz
rawtitle: The Probability that the {``Sum} of the Rounds'' Equals the {``Round} of the Sum''
bibsource:
https://www.math.utah.edu/pub/tex/bib/collegemathj.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/mathgaz2010.bib

URL:
http://www.jstor.org/stable/2686963; http://www.tandfonline.com/doi/abs/10.1080/07468342.1987.11973061

entry:
@Article{Nelsen:1987:PSR,
  author =       "Roger B. Nelsen and James E. Schultz",
  title =        "The Probability that the {``Sum} of the Rounds''
                 Equals the {``Round} of the Sum''",
  journal =      j-COLLEGE-MATH-J,
  volume =       "18",
  number =       "5",
  pages =        "390--396",
  month =        nov,
  year =         "1987",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/07468342.1987.11973061",
  ISSN =         "0746-8342 (print), 1931-1346 (electronic)",
  ISSN-L =       "0746-8342",
  bibdate =      "Thu Feb 14 09:50:35 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/collegemathj.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathgaz2010.bib",
  URL =          "http://www.jstor.org/stable/2686963;
                 http://www.tandfonline.com/doi/abs/10.1080/07468342.1987.11973061",
  acknowledgement = ack-nhfb,
  fjournal =     "College Mathematics Journal",
  journal-URL =  "https://maa.tandfonline.com/loi/ucmj20;
                 https://www.jstor.org/journal/collmathj",
  keywords =     "rounding in fixed-point addition",
  onlinedate =   "30 Jan 2018",
  remark =       "See also \cite{Hopkins:2016:WMN} for a later
                 independent derivation of part of this work.",
}


bibtype: article
filename: fparith.bib
label: Obermaier:1987:SCI
author: A. Obermaier
title: Sin und cosin mit Integerarithmetik toenglish Sine and Cosine with Integer Arithmetic endtoenglish
journal: j-MC
volume: 6
pages: 108--112
year: 1987
ISSN: 0720-4442, 0941-777x, 0943-5409 OR 07204442, 0941777x, 09435409
bibdate: Fri Sep 16 16:30:41 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.16 16:30:41 ???
fjournal: MC: Die Mikrocomputer-Zeitschrift
acknowledgement: ack-nj
rawauthor: A. Obermaier
rawtitle:
{Sin und cosin mit Integerarithmetik} \toenglish {Sine and Cosine with Integer Arithmetic} \endtoenglish

entry:
@Article{Obermaier:1987:SCI,
  author =       "A. Obermaier",
  title =        "{Sin und cosin mit Integerarithmetik} \toenglish {Sine
                 and Cosine with Integer Arithmetic} \endtoenglish",
  journal =      j-MC,
  volume =       "6",
  pages =        "108--112",
  year =         "1987",
  ISSN =         "0720-4442, 0941-777x, 0943-5409",
  bibdate =      "Fri Sep 16 16:30:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "MC: Die Mikrocomputer-Zeitschrift",
}


bibtype: inproceedings
filename: fparith.bib
label: Olver:1987:CCA
author: F. W. J. Olver
title: A Closed Computer Arithmetic
crossref: Irwin:1987:PSC
pages: 139--143
month: may
monthnumber: 5
year: 1987
DOI: https://doi.org/10.1109/ARITH.1987.6158708
bibdate: Wed Nov 14 18:22:26 2007
bibtimestamp: 2007.11.14 18:22:26 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Olver.pdf
keywords: ARITH-8
remark: Reprinted in cite Olver:1990:CCA.
acknowledgement: ack-nhfb
authordates: Frank William John Olver (15 December 1924--23 April 2013)
rawauthor: F. W. J. Olver
rawtitle: A Closed Computer Arithmetic
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
Two closely related new systems of computer arithmetic are proposed. It is shown that both are closed under arithmetic operations in finite-precision arithmetic, thereby offering a permanent solution to the problems of overflow and underflow. Other advantages of the new systems pertaining to precision are described, and there is also a brief discussion of possible ways of hardware implementation.

rawabstract:
Two closely related new systems of computer arithmetic are proposed. It is shown that both are closed under arithmetic operations in finite-precision arithmetic, thereby offering a permanent solution to the problems of overflow and underflow. Other advantages of the new systems pertaining to precision are described, and there is also a brief discussion of possible ways of hardware implementation.

entry:
@InProceedings{Olver:1987:CCA,
  author =       "F. W. J. Olver",
  title =        "A Closed Computer Arithmetic",
  crossref =     "Irwin:1987:PSC",
  pages =        "139--143",
  month =        may,
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158708",
  bibdate =      "Wed Nov 14 18:22:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Olver.pdf",
  abstract =     "Two closely related new systems of computer arithmetic
                 are proposed. It is shown that both are closed under
                 arithmetic operations in finite-precision arithmetic,
                 thereby offering a permanent solution to the problems
                 of overflow and underflow. Other advantages of the new
                 systems pertaining to precision are described, and
                 there is also a brief discussion of possible ways of
                 hardware implementation.",
  acknowledgement = ack-nhfb,
  author-dates = "Frank William John Olver (15 December 1924--23 April
                 2013)",
  keywords =     "ARITH-8",
  remark =       "Reprinted in \cite{Olver:1990:CCA}.",
}


bibtype: inproceedings
filename: fparith.bib
label: Olver:1987:ILI
author: F. W. J. Olver and P. R. Turner
title: Implementation of Level-Index Arithmetic Using Partial Table Look-Up
crossref: Irwin:1987:PSC
pages: 144--147
month: may
monthnumber: 5
year: 1987
DOI: https://doi.org/10.1109/ARITH.1987.6158709
bibdate: Wed Nov 14 18:22:26 2007
bibtimestamp: 2007.11.14 18:22:26 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Olver_Turner.pdf
keywords: ARITH-8
acknowledgement: ack-nhfb
authordates: Frank William John Olver (15 December 1924--23 April 2013)
rawauthor: F. W. J. Olver and P. R. Turner
rawtitle: Implementation of Level-Index Arithmetic Using Partial Table Look-Up
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
This paper is concerned with finding fast efficient algorithms for performing level-index arithmetic. The approach used combines the advantages of parallel processing with the use of table look-up. The latter is used only for short words and the result is a potential implementation with $ li $ operation times comparable with floating-point long multiplications.

rawabstract:
This paper is concerned with finding fast efficient algorithms for performing level-index arithmetic. The approach used combines the advantages of parallel processing with the use of table look-up. The latter is used only for short words and the result is a potential implementation with $ \li $ operation times comparable with floating-point long multiplications.

entry:
@InProceedings{Olver:1987:ILI,
  author =       "F. W. J. Olver and P. R. Turner",
  title =        "Implementation of Level-Index Arithmetic Using Partial
                 Table Look-Up",
  crossref =     "Irwin:1987:PSC",
  pages =        "144--147",
  month =        may,
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158709",
  bibdate =      "Wed Nov 14 18:22:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Olver_Turner.pdf",
  abstract =     "This paper is concerned with finding fast efficient
                 algorithms for performing level-index arithmetic. The
                 approach used combines the advantages of parallel
                 processing with the use of table look-up. The latter is
                 used only for short words and the result is a potential
                 implementation with $ \li $ operation times comparable
                 with floating-point long multiplications.",
  acknowledgement = ack-nhfb,
  author-dates = "Frank William John Olver (15 December 1924--23 April
                 2013)",
  keywords =     "ARITH-8",
}


bibtype: article
filename: fparith.bib
label: Owens:1987:AC
author: Robert Michael Owens and Mary Jane Irwin
title: The Arithmetic Cube
journal: j-IEEE-TRANS-COMPUT
volume: C-36
number: 11
pages: 1342--1348
month: nov
monthnumber: 11
year: 1987
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1987.5009473
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 9 09:28:56 MDT 2011
bibtimestamp: 2011.07.09 09:28:56 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009473
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Robert Michael Owens and Mary Jane Irwin
rawtitle: The Arithmetic Cube
entry:
@Article{Owens:1987:AC,
  author =       "Robert Michael Owens and Mary Jane Irwin",
  title =        "The Arithmetic Cube",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-36",
  number =       "11",
  pages =        "1342--1348",
  month =        nov,
  year =         "1987",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1987.5009473",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 09:28:56 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009473",
  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: Papachristou:1987:ATL
author: Christos A. Papachristou
title: Associative Table Lookup Processing for Multioperand Residue Arithmetic
journal: j-J-ACM
volume: 34
number: 2
pages: 376--396
month: apr
monthnumber: 4
year: 1987
CODEN: JACOAH
ISSN: 0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)
ISSNL: 0004-5411 OR 00045411
bibdate: Sat Oct 22 00:20:03 1994
bibtimestamp: 1994.10.22 00:20:03 ???
fjournal: Journal of the ACM
acknowledgement: ack-nhfb
ajournal: J. Assoc. Comput. Mach.
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J401
rawauthor: Christos A. Papachristou
rawtitle: Associative Table Lookup Processing for Multioperand Residue Arithmetic
bibsource:
ftp://ftp.ira.uka.de/pub/bibliography/Misc/IMMD_IV.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Papachristou:1987:ATL,
  author =       "Christos A. Papachristou",
  title =        "Associative Table Lookup Processing for Multioperand
                 Residue Arithmetic",
  journal =      j-J-ACM,
  volume =       "34",
  number =       "2",
  pages =        "376--396",
  month =        apr,
  year =         "1987",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Sat Oct 22 00:20:03 1994",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Misc/IMMD_IV.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
}


bibtype: article
filename: fparith.bib
label: Parhami:1987:CTL
author: B. Parhami
title: On the Complexity of Table Lookup for Iterative Division
journal: j-IEEE-TRANS-COMPUT
volume: C-36
number: 10
pages: 1233--1236
month: oct
monthnumber: 10
year: 1987
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1987.1676863
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 9 09:28:56 MDT 2011
bibtimestamp: 2011.07.09 09:28:56 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676863
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: B. Parhami
rawtitle: On the Complexity of Table Lookup for Iterative Division
entry:
@Article{Parhami:1987:CTL,
  author =       "B. Parhami",
  title =        "On the Complexity of Table Lookup for Iterative
                 Division",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-36",
  number =       "10",
  pages =        "1233--1236",
  month =        oct,
  year =         "1987",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1987.1676863",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 09:28:56 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676863",
  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: Parhami:1987:SUC
author: Behrooz Parhami
title: Systolic Up / Down Counters with Zero and Sign Detection
crossref: Irwin:1987:PSC
pages: 174--178
year: 1987
DOI: https://doi.org/10.1109/ARITH.1987.6158710
bibdate: Wed Nov 14 18:22:26 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 18:22:26 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Parhami.pdf
keywords: ARITH-8
acknowledgement: ack-nhfb
rawauthor: Behrooz Parhami
rawtitle: Systolic Up\slash Down Counters with Zero and Sign Detection
abstract:
Although a state encoding scheme for systolic counters has been presented earlier, several important practical problems such as zero test, sign detection, overflow, underflow, and modulo-$n$ (cyclic) counting have not been dealt with adequately. In this paper, design principles for unary and binary systolic up / down counters are presented. The unary counters, which are attractive when dealing with relatively small counts, are based on the systolic stack concept. The binary counters use conventional binary number representation, with several tags associated with each bit position. The binary counter design presented can be generalized to counters with higher-radix state encodings.

rawabstract:
Although a state encoding scheme for systolic counters has been presented earlier, several important practical problems such as zero test, sign detection, overflow, underflow, and modulo-$n$ (cyclic) counting have not been dealt with adequately. In this paper, design principles for unary and binary systolic up\slash down counters are presented. The unary counters, which are attractive when dealing with relatively small counts, are based on the systolic stack concept. The binary counters use conventional binary number representation, with several tags associated with each bit position. The binary counter design presented can be generalized to counters with higher-radix state encodings.

entry:
@InProceedings{Parhami:1987:SUC,
  author =       "Behrooz Parhami",
  title =        "Systolic Up\slash Down Counters with Zero and Sign
                 Detection",
  crossref =     "Irwin:1987:PSC",
  pages =        "174--178",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158710",
  bibdate =      "Wed Nov 14 18:22:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Parhami.pdf",
  abstract =     "Although a state encoding scheme for systolic counters
                 has been presented earlier, several important practical
                 problems such as zero test, sign detection, overflow,
                 underflow, and modulo-$n$ (cyclic) counting have not
                 been dealt with adequately. In this paper, design
                 principles for unary and binary systolic up\slash down
                 counters are presented. The unary counters, which are
                 attractive when dealing with relatively small counts,
                 are based on the systolic stack concept. The binary
                 counters use conventional binary number representation,
                 with several tags associated with each bit position.
                 The binary counter design presented can be generalized
                 to counters with higher-radix state encodings.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}


bibtype: inproceedings
filename: fparith.bib
label: Peng:1987:ISM
author: Victor Peng and Sridhar Samudrala and Moshe Gavrielov
title: On the Implementation of Shifters, Multipliers, and Dividers in VLSI Floating Point Units
crossref: Irwin:1987:PSC
pages: 95--102
year: 1987
DOI: https://doi.org/10.1109/ARITH.1987.6158711
bibdate: Wed Nov 14 18:22:26 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 18:22:26 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Peng_Samudrala_Gavrielov.pdf
keywords: ARITH-8
acknowledgement: ack-nhfb
rawauthor: Victor Peng and Sridhar Samudrala and Moshe Gavrielov
rawtitle: On the Implementation of Shifters, Multipliers, and Dividers in {VLSI} Floating Point Units
abstract:
Several options for the implementation of combinatorial shifters, multipliers, and dividers for a VLSI floating point unit are presented and compared. The comparisons are made in the context of a single chip implementation in light of the constraints imposed by currently available MOS technology.

rawabstract:
Several options for the implementation of combinatorial shifters, multipliers, and dividers for a VLSI floating point unit are presented and compared. The comparisons are made in the context of a single chip implementation in light of the constraints imposed by currently available MOS technology.

entry:
@InProceedings{Peng:1987:ISM,
  author =       "Victor Peng and Sridhar Samudrala and Moshe
                 Gavrielov",
  title =        "On the Implementation of Shifters, Multipliers, and
                 Dividers in {VLSI} Floating Point Units",
  crossref =     "Irwin:1987:PSC",
  pages =        "95--102",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158711",
  bibdate =      "Wed Nov 14 18:22:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Peng_Samudrala_Gavrielov.pdf",
  abstract =     "Several options for the implementation of
                 combinatorial shifters, multipliers, and dividers for a
                 VLSI floating point unit are presented and compared.
                 The comparisons are made in the context of a single
                 chip implementation in light of the constraints imposed
                 by currently available MOS technology.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}


bibtype: article
filename: fparith.bib
label: Perlmutter:1987:A
author: D. Perlmutter and A. K.-W. Yuen
title: The 80387 and its Applications
journal: j-IEEE-MICRO
volume: 7
number: 4
pages: 42--57
month: jul
monthnumber: 7
year: 1987
CODEN: IEMIDZ
DOI: https://doi.org/10.1109/MM.1987.304880
ISSN: 0272-1732 (print), 1937-4143 (electronic) OR 02721732 (print), 19374143 (electronic)
ISSNL: 0272-1732 OR 02721732
bibdate: Wed Sep 7 22:32:00 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 22:32:00 ???
fjournal: IEEE Micro
acknowledgement: ack-nj
journalURL: http://www.computer.org/csdl/mags/mi/index.html
rawauthor: D. Perlmutter and A. K.-W. Yuen
rawtitle: The 80387 and its Applications
entry:
@Article{Perlmutter:1987:A,
  author =       "D. Perlmutter and A. K.-W. Yuen",
  title =        "The 80387 and its Applications",
  journal =      j-IEEE-MICRO,
  volume =       "7",
  number =       "4",
  pages =        "42--57",
  month =        jul # "\slash " # aug,
  year =         "1987",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/MM.1987.304880",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Wed Sep 7 22:32:00 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 Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
}


bibtype: article
filename: fparith.bib
label: Pfeiffer:1987:ADP
author: F. W. Pfeiffer
title: Automatic differentiation in PROSE
journal: j-SIGNUM
volume: 22
number: 1
pages: 2--8
month: jan
monthnumber: 1
year: 1987
CODEN: SNEWD6
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Tue Apr 12 07:50:14 MDT 2005
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.04.12 07:50:14 MDT
fjournal: ACM SIGNUM Newsletter
keywords: differentiation arithmetic; languages; point algorithm; program transformation; theory
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/signum
rawauthor: F. W. Pfeiffer
rawtitle: Automatic differentiation in {PROSE}
abstract:
A programming language is presented in which has the feature that first and second order partial derivatives of a function can be calculated using differentiation arithmetic. The language syntax allows the user to specify which variables each function is required to be differentiated with respect to. Model examples are provided.

subject:
D.3.2 Software, PROGRAMMING LANGUAGES, Language Classifications F.4.3 Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Formal Languages, Algebraic language theory

rawabstract:
A programming language is presented in which has the feature that first and second order partial derivatives of a function can be calculated using differentiation arithmetic. The language syntax allows the user to specify which variables each function is required to be differentiated with respect to. Model examples are provided.

entry:
@Article{Pfeiffer:1987:ADP,
  author =       "F. W. Pfeiffer",
  title =        "Automatic differentiation in {PROSE}",
  journal =      j-SIGNUM,
  volume =       "22",
  number =       "1",
  pages =        "2--8",
  month =        jan,
  year =         "1987",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:14 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A programming language is presented in which has the
                 feature that first and second order partial derivatives
                 of a function can be calculated using differentiation
                 arithmetic. The language syntax allows the user to
                 specify which variables each function is required to be
                 differentiated with respect to. Model examples are
                 provided.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "differentiation arithmetic; languages; point
                 algorithm; program transformation; theory",
  subject =      "D.3.2 Software, PROGRAMMING LANGUAGES, Language
                 Classifications \\ F.4.3 Theory of Computation,
                 MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Formal
                 Languages, Algebraic language theory",
}


bibtype: inproceedings
filename: fparith.bib
label: Piuri:1987:FTS
author: Vincenzo Piuri
title: Fault-Tolerant Systolic Arrays: An Approach Based upon Residue Arithmetic
crossref: Irwin:1987:PSC
pages: 230--238
year: 1987
DOI: https://doi.org/10.1109/ARITH.1987.6158712
bibdate: Fri Nov 16 21:39:46 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.16 21:39:46 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Piuri.pdf
keywords: ARITH-8
acknowledgement: ack-nhfb
rawauthor: Vincenzo Piuri
rawtitle: Fault-Tolerant Systolic Arrays: An Approach Based upon Residue Arithmetic
abstract:
Much attention has been recently given to VLSI and WSI processing arrays: systolic arrays are often adopted to execute a wide class of algorithms, e.g., for matrix arithmetic or signal and image processing. In this paper a fault-tolerant architecture is proposed to allow reliable computation of systolic arrays by using physical redundancy and residue number coding. Such architecture supplies also information for fast reconfiguration.

rawabstract:
Much attention has been recently given to VLSI and WSI processing arrays: systolic arrays are often adopted to execute a wide class of algorithms, e.g., for matrix arithmetic or signal and image processing. In this paper a fault-tolerant architecture is proposed to allow reliable computation of systolic arrays by using physical redundancy and residue number coding. Such architecture supplies also information for fast reconfiguration.

entry:
@InProceedings{Piuri:1987:FTS,
  author =       "Vincenzo Piuri",
  title =        "Fault-Tolerant Systolic Arrays: An Approach Based upon
                 Residue Arithmetic",
  crossref =     "Irwin:1987:PSC",
  pages =        "230--238",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158712",
  bibdate =      "Fri Nov 16 21:39:46 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Piuri.pdf",
  abstract =     "Much attention has been recently given to VLSI and WSI
                 processing arrays: systolic arrays are often adopted to
                 execute a wide class of algorithms, e.g., for matrix
                 arithmetic or signal and image processing. In this
                 paper a fault-tolerant architecture is proposed to
                 allow reliable computation of systolic arrays by using
                 physical redundancy and residue number coding. Such
                 architecture supplies also information for fast
                 reconfiguration.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}


bibtype: article
filename: fparith.bib
label: Prado:1987:FSR
author: J. Prado and R. Alcantara
title: A fast square-rooting algorithm using a digital signal processor
journal: j-PROC-IEEE
volume: 75
number: 2
pages: 262--264
month: feb
monthnumber: 2
year: 1987
CODEN: IEEPAD
ISSN: 0018-9219 (print), 1558-2256 (electronic) OR 00189219 (print), 15582256 (electronic)
ISSNL: 0018-9219 OR 00189219
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: Proceedings of the IEEE
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5
rawauthor: J. Prado and R. Alcantara
rawtitle: A fast square-rooting algorithm using a digital signal processor
entry:
@Article{Prado:1987:FSR,
  author =       "J. Prado and R. Alcantara",
  title =        "A fast square-rooting algorithm using a digital signal
                 processor",
  journal =      j-PROC-IEEE,
  volume =       "75",
  number =       "2",
  pages =        "262--264",
  month =        feb,
  year =         "1987",
  CODEN =        "IEEPAD",
  ISSN =         "0018-9219 (print), 1558-2256 (electronic)",
  ISSN-L =       "0018-9219",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the IEEE",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
  summary =      "The computation of square roots is required in signal
                 processing applications, such as adaptive filtering
                 using transversal filters or lattice filters, spectral
                 estimation, and many other fields of engineering
                 sciences. Actually, all the existing \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Purdy:1987:IDL
author: C. N. Purdy and G. B. Purdy
title: Integer Division in Linear Time with Bounded Fan-In
journal: j-IEEE-TRANS-COMPUT
volume: C-36
number: 5
pages: 640--644
month: may
monthnumber: 5
year: 1987
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1987.1676952
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 9 09:28:52 MDT 2011
bibtimestamp: 2011.07.09 09:28:52 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676952
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: C. N. Purdy and G. B. Purdy
rawtitle: Integer Division in Linear Time with Bounded Fan-In
entry:
@Article{Purdy:1987:IDL,
  author =       "C. N. Purdy and G. B. Purdy",
  title =        "Integer Division in Linear Time with Bounded Fan-In",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-36",
  number =       "5",
  pages =        "640--644",
  month =        may,
  year =         "1987",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1987.1676952",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 09:28:52 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676952",
  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: Rall:1987:ISC
author: L. B. Rall
title: An introduction to the scientific computing language Pascal-SC
journal: j-COMPUT-MATH-APPL
volume: 14
number: 1
pages: 53--69
year: 1987
CODEN: CMAPDK
DOI: https://doi.org/10.1016/0898-1221(87)90181-7
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Oct 13 22:36:01 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.13 22:36:01 ???
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: L. B. Rall
rawtitle: An introduction to the scientific computing language {Pascal-SC}
abstract:
Microcomputers are now widely used for small-scale scientific, engineering, and statistical computing. Pascal-SC (Pascal for Scientific Computing) is a language developed specifically for this purpose. Its most important features are: (i) accurate floating-point arithmetic for real, complex, and interval numbers, vectors, and matrices, with controlled rounding if desired; (ii) the convenience of operator notation for numerical data types and the ability to accept user-defined operators for nonstandard data types to make programs easier to write, read, and document; and (iii) compatibility with ordinary Pascal, so that Pascal programming techniques and programs already written in Pascal can be used immediately. In PascalSC, solutions of linear systems of equations, inverses of matrices, and eigenvalues and eigenvectors are computed with guaranteed error bounds, and scalar products of vectors and sums of arbitrary length of floating-point numbers are computed to the closest floating-point number, or rounded upward or downward as desired. These basic features of Pascal-SC will be described, together with some applications.

rawabstract:
Microcomputers are now widely used for small-scale scientific, engineering, and statistical computing. Pascal-SC (Pascal for Scientific Computing) is a language developed specifically for this purpose. Its most important features are: (i) accurate floating-point arithmetic for real, complex, and interval numbers, vectors, and matrices, with controlled rounding if desired; (ii) the convenience of operator notation for numerical data types and the ability to accept user-defined operators for nonstandard data types to make programs easier to write, read, and document; and (iii) compatibility with ordinary Pascal, so that Pascal programming techniques and programs already written in Pascal can be used immediately. In PascalSC, solutions of linear systems of equations, inverses of matrices, and eigenvalues and eigenvectors are computed with guaranteed error bounds, and scalar products of vectors and sums of arbitrary length of floating-point numbers are computed to the closest floating-point number, or rounded upward or downward as desired. These basic features of Pascal-SC will be described, together with some applications.

entry:
@Article{Rall:1987:ISC,
  author =       "L. B. Rall",
  title =        "An introduction to the scientific computing language
                 {Pascal-SC}",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "14",
  number =       "1",
  pages =        "53--69",
  year =         "1987",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(87)90181-7",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Oct 13 22:36:01 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Microcomputers are now widely used for small-scale
                 scientific, engineering, and statistical computing.
                 Pascal-SC (Pascal for Scientific Computing) is a
                 language developed specifically for this purpose. Its
                 most important features are: (i) accurate
                 floating-point arithmetic for real, complex, and
                 interval numbers, vectors, and matrices, with
                 controlled rounding if desired; (ii) the convenience of
                 operator notation for numerical data types and the
                 ability to accept user-defined operators for
                 nonstandard data types to make programs easier to
                 write, read, and document; and (iii) compatibility with
                 ordinary Pascal, so that Pascal programming techniques
                 and programs already written in Pascal can be used
                 immediately. In PascalSC, solutions of linear systems
                 of equations, inverses of matrices, and eigenvalues and
                 eigenvectors are computed with guaranteed error bounds,
                 and scalar products of vectors and sums of arbitrary
                 length of floating-point numbers are computed to the
                 closest floating-point number, or rounded upward or
                 downward as desired. These basic features of Pascal-SC
                 will be described, together with some applications.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: article
filename: fparith.bib
label: Rauch:1987:MCH
author: K. Rauch
journal: j-IEEE-SPECTRUM
volume: 24
number: 7
pages: 25--30
month: jul
monthnumber: 7
year: 1987
CODEN: IEESAM
DOI: https://doi.org/10.1109/MSPEC.1987.6448961
ISSN: 0018-9235 (print), 1939-9340 (electronic) OR 00189235 (print), 19399340 (electronic)
ISSNL: 0018-9235 OR 00189235
bibdate: Mon Jan 20 06:41:24 2020
bibtimestamp: 2020.01.20 06:41:24 ???
fjournal: IEEE Spectrum
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6
rawauthor: K. Rauch
title:
Math chips: How they work: Augmenting microprocessors, they speed up math operations while giving systems designers a variety of performance, cost, and integration options

keywords:
computer architecture; Coprocessors; desktop computers; digital arithmetic; math chips; mathematics coprocessors; microprocessor chips; numeric processors; operation speed; Process control; Program processors; satellite computers; standard building blocks; Standards; Workstations; workstations

rawtitle:
Math chips: How they work: Augmenting microprocessors, they speed up math operations while giving systems designers a variety of performance, cost, and integration options

entry:
@Article{Rauch:1987:MCH,
  author =       "K. Rauch",
  title =        "Math chips: How they work: Augmenting microprocessors,
                 they speed up math operations while giving systems
                 designers a variety of performance, cost, and
                 integration options",
  journal =      j-IEEE-SPECTRUM,
  volume =       "24",
  number =       "7",
  pages =        "25--30",
  month =        jul,
  year =         "1987",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/MSPEC.1987.6448961",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Mon Jan 20 06:41:24 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeespectrum1980.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
  keywords =     "computer architecture; Coprocessors; desktop
                 computers; digital arithmetic; math chips; mathematics
                 coprocessors; microprocessor chips; numeric processors;
                 operation speed; Process control; Program processors;
                 satellite computers; standard building blocks;
                 Standards; Workstations; workstations",
}


bibtype: mastersthesis
filename: fparith.bib
label: Reddy:1987:STF
author: Chakradher Ayyalaper Reddy
title: A self-testing and testable floating point divider
type: Thesis (M.S.)
school: Mississippi State University. Department of Electrical Engineering
address: Mississippi State, MS 39762, USA
pages: viii + 103
year: 1987
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: Chakradher Ayyalaper Reddy
rawtitle: A self-testing and testable floating point divider
keywords:
floating-point testing; Integrated circuits; Mississippi State University; Testing.; Very large scale integration

entry:
@MastersThesis{Reddy:1987:STF,
  author =       "Chakradher Ayyalaper Reddy",
  title =        "A self-testing and testable floating point divider",
  type =         "Thesis ({M.S.})",
  school =       "Mississippi State University. Department of Electrical
                 Engineering",
  address =      "Mississippi State, MS 39762, USA",
  pages =        "viii + 103",
  year =         "1987",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point testing; Integrated circuits;
                 Mississippi State University; Testing.; Very large
                 scale integration",
}


bibtype: inproceedings
filename: fparith.bib
label: Redinbo:1987:PCT
author: G. Robert Redinbo
title: Protecting Convolution-Type Arithmetic Array Calculations with Generalized Cyclic Codes
crossref: Irwin:1987:PSC
pages: 219--225
year: 1987
DOI: https://doi.org/10.1109/ARITH.1987.6158713
bibdate: Fri Nov 16 21:39:46 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.16 21:39:46 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Redinbo.pdf
keywords: ARITH-8
acknowledgement: ack-nhfb
rawauthor: G. Robert Redinbo
rawtitle: Protecting Convolution-Type Arithmetic Array Calculations with Generalized Cyclic Codes
abstract:
Fault-tolerance in dense high-speed arithmetic units that calculate convolutions between arrays of data is introduced through cyclic codes which are defined over the rings and fields commonly employed by such units. New systematic encoding and data manipulation techniques make the application of these generalized cyclic codes to error detection straightforward and efficient. The necessary overhead parity computations have complexity proportional to the number of parity symbols squared, whereas the error-detecting capability for both random and burst errors is directly related to this parity number'.

rawabstract:
Fault-tolerance in dense high-speed arithmetic units that calculate convolutions between arrays of data is introduced through cyclic codes which are defined over the rings and fields commonly employed by such units. New systematic encoding and data manipulation techniques make the application of these generalized cyclic codes to error detection straightforward and efficient. The necessary overhead parity computations have complexity proportional to the number of parity symbols squared, whereas the error-detecting capability for both random and burst errors is directly related to this parity number'.

entry:
@InProceedings{Redinbo:1987:PCT,
  author =       "G. Robert Redinbo",
  title =        "Protecting Convolution-Type Arithmetic Array
                 Calculations with Generalized Cyclic Codes",
  crossref =     "Irwin:1987:PSC",
  pages =        "219--225",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158713",
  bibdate =      "Fri Nov 16 21:39:46 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Redinbo.pdf",
  abstract =     "Fault-tolerance in dense high-speed arithmetic units
                 that calculate convolutions between arrays of data is
                 introduced through cyclic codes which are defined over
                 the rings and fields commonly employed by such units.
                 New systematic encoding and data manipulation
                 techniques make the application of these generalized
                 cyclic codes to error detection straightforward and
                 efficient. The necessary overhead parity computations
                 have complexity proportional to the number of parity
                 symbols squared, whereas the error-detecting capability
                 for both random and burst errors is directly related to
                 this parity number'.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}


bibtype: article
filename: fparith.bib
label: Rehmer:1987:DIM
author: Karl Rehmer
title: Development and Implementation of the Magnavox Generic Ada Basic Mathematics Package
journal: j-SIGADA-LETTERS
volume: 7
number: 3
pages: 73--83
month: may
monthnumber: 5
year: 1987
CODEN: AALEE5
ISSN: 1094-3641 (print), 1557-9476 (electronic) OR 10943641 (print), 15579476 (electronic)
ISSNL: 1094-3641 OR 10943641
bibdate: Sat Aug 9 09:05:25 MDT 2003
bibtimestamp: 2003.08.09 09:05:25 MDT
fjournal: ACM SIGAda Ada Letters
keywords: design; floating point, real arithmetic; languages; theory; verification
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/citation.cfm?id=J32
rawauthor: Karl Rehmer
rawtitle: Development and Implementation of the {Magnavox} Generic {Ada} Basic Mathematics Package
bibsource:
ftp://ftp.uu.net/library/bibliography; http://portal.acm.org/; http://www.adahome.com/Resources/Bibliography/articles.ref; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/sigada.bib

subject:
D.2.2 Software, SOFTWARE ENGINEERING, Tools and Techniques, Software libraries D.3.2 Software, PROGRAMMING LANGUAGES, Language Classifications, Ada G.4 Mathematics of Computing, MATHEMATICAL SOFTWARE

entry:
@Article{Rehmer:1987:DIM,
  author =       "Karl Rehmer",
  title =        "Development and Implementation of the {Magnavox}
                 Generic {Ada} Basic Mathematics Package",
  journal =      j-SIGADA-LETTERS,
  volume =       "7",
  number =       "3",
  pages =        "73--83",
  month =        may # "\slash " # jun,
  year =         "1987",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Sat Aug 9 09:05:25 MDT 2003",
  bibsource =    "ftp://ftp.uu.net/library/bibliography;
                 http://portal.acm.org/;
                 http://www.adahome.com/Resources/Bibliography/articles.ref;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigada.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "design; floating point, real arithmetic; languages;
                 theory; verification",
  subject =      "D.2.2 Software, SOFTWARE ENGINEERING, Tools and
                 Techniques, Software libraries \\ D.3.2 Software,
                 PROGRAMMING LANGUAGES, Language Classifications, Ada
                 \\
                 G.4 Mathematics of Computing, MATHEMATICAL SOFTWARE",
}


bibtype: inproceedings
filename: fparith.bib
label: Robertson:1987:EDC
author: James E. Robertson
crossref: Irwin:1987:PSC
pages: 226--229
year: 1987
DOI: https://doi.org/10.1109/ARITH.1987.6158714
bibdate: Fri Nov 16 21:39:46 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.16 21:39:46 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Robertson.pdf
keywords: ARITH-8
acknowledgement: ack-nhfb
rawauthor: James E. Robertson
title:
Error-Detection and Correction for Addition and Subtraction through Use of Higher Radix Extensions of Hamming Codes

abstract:
The properties of Hamming codes for error detection and correction can be extended from the binary parity check to addition, modulo $ 2 r $. Malfunctions in hardware during addition, modulo $ 2 r $, can be detected and corrected. Since carry-save and signed-digit addition, radix $r$, are included in addition, modulo $ 2 r $, this extension of Hamming codes makes possible new techniques for detection and correction of hardware malfunctions during signed-digit and carry-save addition.

rawabstract:
The properties of Hamming codes for error detection and correction can be extended from the binary parity check to addition, modulo $ 2 r $. Malfunctions in hardware during addition, modulo $ 2 r $, can be detected and corrected. Since carry-save and signed-digit addition, radix $r$, are included in addition, modulo $ 2 r $, this extension of Hamming codes makes possible new techniques for detection and correction of hardware malfunctions during signed-digit and carry-save addition.

rawtitle:
Error-Detection and Correction for Addition and Subtraction through Use of Higher Radix Extensions of {Hamming} Codes

entry:
@InProceedings{Robertson:1987:EDC,
  author =       "James E. Robertson",
  title =        "Error-Detection and Correction for Addition and
                 Subtraction through Use of Higher Radix Extensions of
                 {Hamming} Codes",
  crossref =     "Irwin:1987:PSC",
  pages =        "226--229",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158714",
  bibdate =      "Fri Nov 16 21:39:46 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Robertson.pdf",
  abstract =     "The properties of Hamming codes for error detection
                 and correction can be extended from the binary parity
                 check to addition, modulo $ 2 r $. Malfunctions in
                 hardware during addition, modulo $ 2 r $, can be
                 detected and corrected. Since carry-save and
                 signed-digit addition, radix $r$, are included in
                 addition, modulo $ 2 r $, this extension of Hamming
                 codes makes possible new techniques for detection and
                 correction of hardware malfunctions during signed-digit
                 and carry-save addition.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}


bibtype: article
filename: fparith.bib
label: Rolfe:1987:FIS
author: Timothy J. Rolfe
title: On a Fast Integer Square Root Algorithm
journal: j-SIGNUM
volume: 22
number: 4
pages: 6--11
month: oct
monthnumber: 10
year: 1987
CODEN: SNEWD6
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Thu Sep 1 10:15:42 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:15:42 ???
fjournal: ACM SIGNUM Newsletter
keywords: algorithms; performance; theory
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/signum
rawauthor: Timothy J. Rolfe
rawtitle: On a Fast Integer Square Root Algorithm
subject:
F.2.1 Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Number-theoretic computations

entry:
@Article{Rolfe:1987:FIS,
  author =       "Timothy J. Rolfe",
  title =        "On a Fast Integer Square Root Algorithm",
  journal =      j-SIGNUM,
  volume =       "22",
  number =       "4",
  pages =        "6--11",
  month =        oct,
  year =         "1987",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Thu Sep 1 10:15:42 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "algorithms; performance; theory",
  subject =      "F.2.1 Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Number-theoretic computations",
}


bibtype: article
filename: fparith.bib
label: Rysavy:1987:MSC
author: M. Rysavy
title: MISHA --- a system for calculations with arbitrary arithmetic precision
journal: j-COMP-PHYS-COMM
volume: 47
number: 2--3
pages: 351--359
month: nov
monthnumber: 11
year: 1987
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(87)90120-2
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Mon Feb 13 10:28:21 MST 2012
bibtimestamp: 2012.02.13 10:28:21 MST
URL: http://www.sciencedirect.com/science/article/pii/0010465587901202
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: M. Rysav{\'y}
rawtitle: {MISHA} --- a system for calculations with arbitrary arithmetic precision
bibsource:
https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Rysavy:1987:MSC,
  author =       "M. Rysav{\'y}",
  title =        "{MISHA} --- a system for calculations with arbitrary
                 arithmetic precision",
  journal =      j-COMP-PHYS-COMM,
  volume =       "47",
  number =       "2--3",
  pages =        "351--359",
  month =        nov # "\slash " # dec,
  year =         "1987",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(87)90120-2",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 10:28:21 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465587901202",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: article
filename: fparith.bib
label: Scheidt:1987:DFP
author: J. K. Scheidt and C. W. Schelin
title: Distributions of floating point numbers
journal: j-COMPUTING
volume: 38
number: 4
pages: 315--324
year: 1987
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
MRclass: 65G10
MRnumber: 88g:65046
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 ???
fjournal: Computing: Archiv fur informatik und numerik
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/607
reviewer: J. A. Grant
rawauthor: J. K. Scheidt and C. W. Schelin
rawtitle: Distributions of floating point numbers
entry:
@Article{Scheidt:1987:DFP,
  author =       "J. K. Scheidt and C. W. Schelin",
  title =        "Distributions of floating point numbers",
  journal =      j-COMPUTING,
  volume =       "38",
  number =       "4",
  pages =        "315--324",
  year =         "1987",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65G10",
  MRnumber =     "88g:65046",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  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",
  reviewer =     "J. A. Grant",
}


bibtype: inproceedings
filename: fparith.bib
label: Scherson:1987:VCO
author: Isaac D. Scherson and Yiming Ma
title: Vector Computations on Orthogonal Memory Access Multiprocessor System
crossref: Irwin:1987:PSC
pages: 28--36
year: 1987
DOI: https://doi.org/10.1109/ARITH.1987.6158715
bibdate: Fri Nov 16 21:39:46 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.16 21:39:46 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Scherson_Ma.pdf
acknowledgement: ack-nhfb
rawauthor: Isaac D. Scherson and Yiming Ma
rawtitle: Vector Computations on Orthogonal Memory Access Multiprocessor System
abstract:
An Orthogonal Memory Access system allows a multiplicity of processors to concurrently access distinct rows or columns of a rectangular array of data elements. The resulting tightly-coupled multi-processing system is feasible with current technology and has even been suggested for VLSI as a ``reduced mesh''. In this paper we introduce the architecture and concentrate on its application to a number of basic vector and. numerical computations. Matrix multiplication, L-U decomposition. polynomial evaluation and solutions to linear systems and partial differential equations, all show a speed-up of $ O(n) $ for a $n$-processor system. The flexibility in the choice of the number of PEs makes the architecture a strong competitor in the world of special-purpose parallel systems. Actually, we prove that the machine exhibits the same performance as any other system with the same number of processors within a factor of 3.

keywords:
ARITH-8; numerical analysis; parallel algorithms; parallel architecture; performance analysis; time complexity

rawabstract:
An Orthogonal Memory Access system allows a multiplicity of processors to concurrently access distinct rows or columns of a rectangular array of data elements. The resulting tightly-coupled multi-processing system is feasible with current technology and has even been suggested for VLSI as a ``reduced mesh''. In this paper we introduce the architecture and concentrate on its application to a number of basic vector and. numerical computations. Matrix multiplication, L-U decomposition. polynomial evaluation and solutions to linear systems and partial differential equations, all show a speed-up of $ O(n) $ for a $n$-processor system. The flexibility in the choice of the number of PEs makes the architecture a strong competitor in the world of special-purpose parallel systems. Actually, we prove that the machine exhibits the same performance as any other system with the same number of processors within a factor of 3.

entry:
@InProceedings{Scherson:1987:VCO,
  author =       "Isaac D. Scherson and Yiming Ma",
  title =        "Vector Computations on Orthogonal Memory Access
                 Multiprocessor System",
  crossref =     "Irwin:1987:PSC",
  pages =        "28--36",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158715",
  bibdate =      "Fri Nov 16 21:39:46 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Scherson_Ma.pdf",
  abstract =     "An Orthogonal Memory Access system allows a
                 multiplicity of processors to concurrently access
                 distinct rows or columns of a rectangular array of data
                 elements. The resulting tightly-coupled
                 multi-processing system is feasible with current
                 technology and has even been suggested for VLSI as a
                 ``reduced mesh''. In this paper we introduce the
                 architecture and concentrate on its application to a
                 number of basic vector and. numerical computations.
                 Matrix multiplication, L-U decomposition. polynomial
                 evaluation and solutions to linear systems and partial
                 differential equations, all show a speed-up of $ O(n) $
                 for a $n$-processor system. The flexibility in the
                 choice of the number of PEs makes the architecture a
                 strong competitor in the world of special-purpose
                 parallel systems. Actually, we prove that the machine
                 exhibits the same performance as any other system with
                 the same number of processors within a factor of 3.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8; numerical analysis; parallel algorithms;
                 parallel architecture; performance analysis; time
                 complexity",
}


bibtype: inproceedings
filename: fparith.bib
label: Schumacher:1987:CAI
author: Gunter Schumacher
title: Computer Arithmetic and Ill-Conditioned Algebraic Problems
crossref: Irwin:1987:PSC
pages: 270--276
year: 1987
DOI: https://doi.org/10.1109/ARITH.1987.6158716
bibdate: Fri Nov 16 21:39:46 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.16 21:39:46 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Schumacher.pdf
abstract: n/a
keywords: ARITH-8
remark: Text illegible because of large white streak on each page.
acknowledgement: ack-nhfb
rawabstract: n/a
rawauthor: G{\"u}nter Schumacher
rawtitle: Computer Arithmetic and Ill-Conditioned Algebraic Problems
entry:
@InProceedings{Schumacher:1987:CAI,
  author =       "G{\"u}nter Schumacher",
  title =        "Computer Arithmetic and Ill-Conditioned Algebraic
                 Problems",
  crossref =     "Irwin:1987:PSC",
  pages =        "270--276",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158716",
  bibdate =      "Fri Nov 16 21:39:46 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Schumacher.pdf",
  abstract =     "n/a",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
  remark =       "Text illegible because of large white streak on each
                 page.",
}


bibtype: inproceedings
filename: fparith.bib
label: Sharma:1987:ATE
author: Ramautar Sharma
title: Area-Time Efficient Arithmetic Elements for VLSI Systems
crossref: Irwin:1987:PSC
pages: 58--62
year: 1987
DOI: https://doi.org/10.1109/ARITH.1987.6158717
bibdate: Fri Nov 16 21:39:46 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.16 21:39:46 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Sharma.pdf
keywords: ARITH-8
acknowledgement: ack-nhfb
rawauthor: Ramautar Sharma
rawtitle: Area-Time Efficient Arithmetic Elements for {VLSI} Systems
abstract:
Algorithms for the high speed binary arithmetic operations of addition and multiplication in a VLSI environment are analyzed for area-time efficiency. It is shown that some schemes for addition and multiplication, although good for stand-alone designs, fail to provide both area and time efficiencies simultaneously. Solutions that yield area-time efficient practical implementations of these arithmetic functions are described.

rawabstract:
Algorithms for the high speed binary arithmetic operations of addition and multiplication in a VLSI environment are analyzed for area-time efficiency. It is shown that some schemes for addition and multiplication, although good for stand-alone designs, fail to provide both area and time efficiencies simultaneously. Solutions that yield area-time efficient practical implementations of these arithmetic functions are described.

entry:
@InProceedings{Sharma:1987:ATE,
  author =       "Ramautar Sharma",
  title =        "Area-Time Efficient Arithmetic Elements for {VLSI}
                 Systems",
  crossref =     "Irwin:1987:PSC",
  pages =        "58--62",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158717",
  bibdate =      "Fri Nov 16 21:39:46 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Sharma.pdf",
  abstract =     "Algorithms for the high speed binary arithmetic
                 operations of addition and multiplication in a VLSI
                 environment are analyzed for area-time efficiency. It
                 is shown that some schemes for addition and
                 multiplication, although good for stand-alone designs,
                 fail to provide both area and time efficiencies
                 simultaneously. Solutions that yield area-time
                 efficient practical implementations of these arithmetic
                 functions are described.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}


bibtype: inproceedings
filename: fparith.bib
label: Shenoy:1987:AST
author: A. Shenoy and R. Kumaresan
booktitle: IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP '87
title: An accurate scaling technique in improved residue number system arithmetic
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1414--1417
year: 1987
DOI: https://doi.org/10.1109/TC.1987.1676868
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
fjournal: IEEE Transactions on Computers
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
rawauthor: A. Shenoy and R. Kumaresan
rawbooktitle: {IEEE} International Conference on Acoustics, Speech, and Signal Processing, {ICASSP '87}
rawtitle: An accurate scaling technique in improved residue number system arithmetic
entry:
@InProceedings{Shenoy:1987:AST,
  author =       "A. Shenoy and R. Kumaresan",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing, {ICASSP '87}",
  title =        "An accurate scaling technique in improved residue
                 number system arithmetic",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1414--1417",
  month =        "????",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/TC.1987.1676868",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A fast and accurate magnitude scaling technique in the
                 residue number system (RNS) is proposed. This technique
                 obtains the residues of the scaled integer, when scaled
                 by a product of a subset of the moduli, in
                 approximately log n cycles, where n is \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Shyu:1987:CIM
author: H. C. Shyu and T. K. Truong and I. S. Reed
journal: j-IEEE-TRANS-COMPUT
volume: C-36
number: 10
pages: 1255--1258
month: oct
monthnumber: 10
year: 1987
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1987.1676868
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 9 09:28:56 MDT 2011
bibtimestamp: 2011.07.09 09:28:56 MDT
fjournal: IEEE Transactions on Computers
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: H. C. Shyu and T. K. Truong and I. S. Reed
title:
A Complex Integer Multiplier Using the Quadratic-Polynomial Residue Number System with Numbers of Form $ 22 n + 1 $

URL:
http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12; http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35260; https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676868

rawtitle:
A Complex Integer Multiplier Using the Quadratic-Polynomial Residue Number System with Numbers of Form $ 22 n + 1 $

entry:
@Article{Shyu:1987:CIM,
  author =       "H. C. Shyu and T. K. Truong and I. S. Reed",
  title =        "A Complex Integer Multiplier Using the
                 Quadratic-Polynomial Residue Number System with Numbers
                 of Form $ 22 n + 1 $",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-36",
  number =       "10",
  pages =        "1255--1258",
  month =        oct,
  year =         "1987",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1987.1676868",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 09:28:56 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35260;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676868",
  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 quadratic-polynomial Fermat residue number system
                 (QFNS) can be used to compute the complex
                 multiplications needed to perform a DFT. The advantage
                 of such a QFNS is that complex multiplication can be
                 accomplished with only two integer \ldots{}",
}


bibtype: incollection
filename: fparith.bib
label: Simar:1987:FPA
author: R. Simar, Jr.
title: Floating-point arithmetic with the TMS32010
crossref: Lin:1987:DSP
pages: 213--244
year: 1987
bibdate: Sat Nov 9 08:26:18 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.11.09 08:26:18 MST
acknowledgement: ack-nhfb
rawauthor: R. {Simar, Jr.}
rawtitle: Floating-point arithmetic with the {TMS32010}
subject:
J. Computer Applications; J.2 PHYSICAL SCIENCES AND ENGINEERING; C. Computer Systems Organization; C.5 COMPUTER SYSTEM IMPLEMENTATION; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS

entry:
@InCollection{Simar:1987:FPA,
  author =       "R. {Simar, Jr.}",
  title =        "Floating-point arithmetic with the {TMS32010}",
  crossref =     "Lin:1987:DSP",
  pages =        "213--244",
  year =         "1987",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  bibno =        "42622",
  catcode =      "J.2; C.5.3; G.1.0",
  CRclass =      "J.2 Mathematics and statistics; C.5.3 Microcomputers;
                 C.5.3 TMS 32010; G.1.0 General; G.1.0 Computer
                 arithmetic",
  descriptor =   "Computer Applications, PHYSICAL SCIENCES AND
                 ENGINEERING, Mathematics and statistics; Computer
                 Systems Organization, COMPUTER SYSTEM IMPLEMENTATION,
                 Microcomputers, TMS 32010; Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Computer arithmetic",
  genterm =      "MEASUREMENT; ALGORITHMS",
  guideno =      "1988-01736",
  pubcite =      "Englewood Cliffs, NJ",
  pubname =      "Prentice-Hall, Inc.",
  subject =      "J. Computer Applications; J.2 PHYSICAL SCIENCES AND
                 ENGINEERING; C. Computer Systems Organization; C.5
                 COMPUTER SYSTEM IMPLEMENTATION; G. Mathematics of
                 Computing; G.1 NUMERICAL ANALYSIS",
}


bibtype: inproceedings
filename: fparith.bib
label: Smith:1987:SAE
author: S. G. Smith and P. B. Denyer
title: Synthesis of Area-Efficient VLSI Architectures for Vector and Matrix Multiplication
crossref: Irwin:1987:PSC
pages: 13--20
year: 1987
DOI: https://doi.org/10.1109/ARITH.1987.6158718
bibdate: Fri Nov 16 21:39:46 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.16 21:39:46 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Smith_Denyer.pdf
keywords: ARITH-8
acknowledgement: ack-nhfb
rawauthor: S. G. Smith and P. B. Denyer
rawtitle: Synthesis of Area-Efficient {VLSI} Architectures for Vector and Matrix Multiplication
abstract:
A methodology is presented for synthesis of area-efficient, high-performance VLSI modules for vector and matrix multiplication. Three fundamental computational elements are employed in the composition of these architectures: memory register, multiplexer (1-from-2 data selector), and carry-save add-shift computer. Two's complement serial / parallel carry-save accumulation provides performance, while the use of symmetric-coded distributed arithmetic eliminates redundant computation to effect area-savings.

rawabstract:
A methodology is presented for synthesis of area-efficient, high-performance VLSI modules for vector and matrix multiplication. Three fundamental computational elements are employed in the composition of these architectures: memory register, multiplexer (1-from-2 data selector), and carry-save add-shift computer. Two's complement serial\slash parallel carry-save accumulation provides performance, while the use of symmetric-coded distributed arithmetic eliminates redundant computation to effect area-savings.

entry:
@InProceedings{Smith:1987:SAE,
  author =       "S. G. Smith and P. B. Denyer",
  title =        "Synthesis of Area-Efficient {VLSI} Architectures for
                 Vector and Matrix Multiplication",
  crossref =     "Irwin:1987:PSC",
  pages =        "13--20",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158718",
  bibdate =      "Fri Nov 16 21:39:46 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Smith_Denyer.pdf",
  abstract =     "A methodology is presented for synthesis of
                 area-efficient, high-performance VLSI modules for
                 vector and matrix multiplication. Three fundamental
                 computational elements are employed in the composition
                 of these architectures: memory register, multiplexer
                 (1-from-2 data selector), and carry-save add-shift
                 computer. Two's complement serial\slash parallel
                 carry-save accumulation provides performance, while the
                 use of symmetric-coded distributed arithmetic
                 eliminates redundant computation to effect
                 area-savings.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}


bibtype: incollection
filename: fparith.bib
label: Spangler:1987:RMM
author: R. A. Spangler
title: Revealing the mystery---the machine and how it functions
crossref: Anbar:1987:CM
pages: 9--46
year: 1987
bibdate: Sat Nov 9 08:26:18 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.11.09 08:26:18 MST
subject: C. Computer Systems Organization; C.0 GENERAL; B. Hardware; B.0 GENERAL
acknowledgement: ack-nhfb
affiliation: State University of New York at Buffalo, Buffalo
reviewer: E. Mallach
rawauthor: R. A. Spangler
rawtitle: Revealing the mystery---the machine and how it functions
entry:
@InCollection{Spangler:1987:RMM,
  author =       "R. A. Spangler",
  title =        "Revealing the mystery---the machine and how it
                 functions",
  crossref =     "Anbar:1987:CM",
  pages =        "9--46",
  year =         "1987",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "State University of New York at Buffalo, Buffalo",
  bibno =        "22925",
  catcode =      "C.0; B.0",
  content =      "In this paper, the author tries to describe the way a
                 digital computer works: from gates, through
                 instructions, data encoding, and interrupts, to
                 peripherals of more than a dozen types. He tries to do
                 this in 29 pages plus a nine-page appendix on
                 semiconductor technology. He tries to do it for an
                 audience described in the book's foreword as \par

                 (1) physicians who were educated in the pre-computer
                 era, (2) medical students and house staff being
                 educated now, (3) computer professionals interested in
                 medical applications, and (4) readers outside of the
                 medical profession and the computer science community
                 who are interested in the role of automation in health
                 care.\par

                 This is a tall order. The paper comes impressively
                 close to filling it. In clearly-written prose, Spangler
                 takes the reader through the overall structure of a
                 computer; its major components; information, binary
                 numbers (including floating point), and character
                 codes; word length issues; gates, combinatorial
                 circuits and flip-flops; instruction sets, including
                 subroutines and interrupts; and peripheral devices,
                 with emphasis on mass storage.\par

                 A necessary byproduct of covering all this material in
                 such a short space is a condensed, economical writing
                 style. Statements are made and concept",
  CRnumber =     "8802-0079",
  descriptor =   "Computer Systems Organization, GENERAL; Hardware,
                 GENERAL",
  genterm =      "DESIGN",
  pubcite =      "Rockville, MD",
  pubname =      "Computer Science Press, Inc.",
  reviewer =     "E. Mallach",
  subject =      "C. Computer Systems Organization; C.0 GENERAL; B.
                 Hardware; B.0 GENERAL",
  waffil =       "State University of New York at Buffalo, Buffalo",
}


bibtype: manual
filename: fparith.bib
label: Sun:1987:SAM
title: The SPARC Architecture Manual
organization: pub-SUN
address: pub-SUN:adr
edition: Part No: 800-1399-07
pages: 9--46
month: aug
monthnumber: 8
year: 1987
bibdate: Wed Sep 14 23:02:18 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.14 23:02:18 ???
acknowledgement: ack-nhfb
key: Sun Microsystems
rawtitle: The {SPARC} Architecture Manual
entry:
@Manual{Sun:1987:SAM,
  key =          "Sun Microsystems",
  title =        "The {SPARC} Architecture Manual",
  organization = pub-SUN,
  address =      pub-SUN:adr,
  edition =      "Part No: 800-1399-07",
  month =        aug # " 8",
  year =         "1987",
  bibdate =      "Wed Sep 14 23:02:18 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Takagi:1987:LED
author: Naofumi Takagi and Shuzo Yajima
journal: j-IEEE-TRANS-COMPUT
volume: C-36
number: 11
pages: 1310--1317
month: nov
monthnumber: 11
year: 1987
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1987.5009470
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 9 09:28:56 MDT 2011
bibtimestamp: 2011.07.09 09:28:56 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009470
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Naofumi Takagi and Shuzo Yajima
title:
On-Line Error-Detectable High-Speed Multiplier Using Redundant Binary Representation and Three-Rail Logic

rawtitle:
On-Line Error-Detectable High-Speed Multiplier Using Redundant Binary Representation and Three-Rail Logic

entry:
@Article{Takagi:1987:LED,
  author =       "Naofumi Takagi and Shuzo Yajima",
  title =        "On-Line Error-Detectable High-Speed Multiplier Using
                 Redundant Binary Representation and Three-Rail Logic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-36",
  number =       "11",
  pages =        "1310--1317",
  month =        nov,
  year =         "1987",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1987.5009470",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 09:28:56 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009470",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: phdthesis
filename: fparith.bib
label: Takagi:1987:SHA
author: Naofumi Takagi
title: Studies on Hardware Algorithms for Arithmetic Operations with a Redundant Binary Adder
type: PhD dissertation
school: Department of Information Sciences, Faculty of Engineering, Kyoto University
address: Kyoto, Japan
pages: vii + 150
month: aug
monthnumber: 8
year: 1987
bibdate: Thu Nov 13 06:14:34 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2025.11.13 06:14:34 ???
acknowledgement: ack-nhfb
rawauthor: Naofumi Takagi
rawtitle: Studies on Hardware Algorithms for Arithmetic Operations with a Redundant Binary Adder
URL:
http://hdl.handle.net/2433/154053; https://repository.kulib.kyoto-u.ac.jp/server/api/core/bitstreams/b38960be-ee22-458e-9899-ed77db01155e/content;

TOC:
Abstract / i Table of Contents / v 1: Introduction / 1 1.1 Backgrounds / 1 1.2 Outline of the Thesis / 4 2: Preliminaries / 8 2.1 Binary Number System / 8 2.2 Computation Model / 8 2.3 Redundant Binary Representation 2.3.1 Redundant Binary Representation / 10 2.3.2 Carry-Propagation-Free Addition / 11 2.3.3 Redundant Binary to Binary Conversion / 15 2.3.4 Special Redundant Binary Numbers / 16 3: A Multiplication Hardware Algorithm with a Redundant Binary Addition Tree / 19 3.1 Introduction / 19 3.2 A Multiplication Hardware Algorithm / 19 3.2.1 Algorithm / 21 3.2.2 Analysis of the Algorithm / 25 3.3 A Multiplier Based on the Algorithm 3.3.1 Multiplier Recoding and Partial Product Generation / 27 3.3.2 A Multiplier Based on the Algorithm / 30 3.3.3 The Depth and the Gate Count of the Multiplier / 33 3.4 Computation of Other Arithmetic Functions Using the Multiplier 3.4.1 Redundant Binary Multiplier Receding / 35 3.4.2 Computation of Other Arithmetic Functions / 36 3.5 Remarks and Discussions / 39 4: A Subtract-and-Shift Division Hardware Algorithm / 42 4.1 Introduction / 42 4.2 A Division Hardware Algorithm / 44 4.2.1 Algorithm / 44 4.2.2 Analysis of the Algorithm / 47 4.3 A Divider Based on the Algorithm / 51 4.4 Remarks and Discussions / 56 4.A A Proof of the Correctness of the Algorithm / 57 5: A Subtract-and-Shift Square Root Hardware Algorithm / 60 5.1 Introduction / 60 5.2 A Square Root Hardware Algorithm / 62 5.2.1 Algorithm / 62 5.2.2 Analysis of the Algorithm / 67 5.3 A Square Root Circuit Based on the Algorithm / 69 5.4 Remarks and Discussions / 70 5.A A Proof of the Correctness of the Algorithm / 71 6: Hardware Algorithms for Elementary Functions / 75 6.1 Introduction / 75 6.2 Hardware Algorithms Based on the CORDIC Method / 77 6.2.1 Principle of the CORDIC Method / 77 6.2.2 A Hardware Algorithm for Computing Sines and Cosines / 80 6.2.3 A Hardware Algorithm for Computing Arctangents / 87 6.3 Hardware Algorithms Based on the STL Method / 91 6.3.1 Principle of the STL Method / 91 6.3.2 A Hardware Algorithm for Computing Logarithms / 92 6.3.3 A Hardware Algorithm for Computing Exponentials / 97 6.4 Remarks and Discussions / 101 7: Design of Self-Checking Arithmetic Circuits by Means of the Three-Rail Logic / 103 7.1 Introduction / 103 7.2 Design of Self-Checking Arithmetic Circuits / 106 7.3 A Design of a Self-Checking Multiplier / 112 7.4 Remarks and Discussions / 119 8: Redundant Coding Schemes for Several Algebraic Systems / 121 8.1 Introduction / 121 8.2 Coding Schemes and Local Computability / 122 8.3 A Redundant Coding Scheme for a Residue Class and a Hardware Algorithm for Modular Addition / 124 8.4 Redundant Coding Schemes for Other Algebraic Systems / 129 8.5 Remarks and Discussions / 132 9: Conclusion / 135 Acknowledgments / 138

rawTOC:
Abstract / i \\ Table of Contents / v \\ \\ 1: Introduction / 1 \\ 1.1 Backgrounds / 1 \\ 1.2 Outline of the Thesis / 4 \\ \\ 2: Preliminaries / 8 \\ 2.1 Binary Number System / 8 \\ 2.2 Computation Model / 8 \\ 2.3 Redundant Binary Representation \\ 2.3.1 Redundant Binary Representation / 10 \\ 2.3.2 Carry-Propagation-Free Addition / 11 \\ 2.3.3 Redundant Binary to Binary Conversion / 15 \\ 2.3.4 Special Redundant Binary Numbers / 16 \\ \\ 3: A Multiplication Hardware Algorithm with a Redundant Binary Addition Tree / 19 \\ 3.1 Introduction / 19 \\ 3.2 A Multiplication Hardware Algorithm / 19 \\ 3.2.1 Algorithm / 21 \\ 3.2.2 Analysis of the Algorithm / 25 \\ 3.3 A Multiplier Based on the Algorithm \\ 3.3.1 Multiplier Recoding and Partial Product Generation / 27 \\ 3.3.2 A Multiplier Based on the Algorithm / 30 \\ 3.3.3 The Depth and the Gate Count of the Multiplier / 33 \\ 3.4 Computation of Other Arithmetic Functions Using the Multiplier \\ 3.4.1 Redundant Binary Multiplier Receding / 35 \\ 3.4.2 Computation of Other Arithmetic Functions / 36 \\ 3.5 Remarks and Discussions / 39 \\ \\ 4: A Subtract-and-Shift Division Hardware Algorithm / 42 \\ 4.1 Introduction / 42 \\ 4.2 A Division Hardware Algorithm / 44 \\ 4.2.1 Algorithm / 44 \\ 4.2.2 Analysis of the Algorithm / 47 \\ 4.3 A Divider Based on the Algorithm / 51 \\ 4.4 Remarks and Discussions / 56 \\ 4.A A Proof of the Correctness of the Algorithm / 57 \\ \\ 5: A Subtract-and-Shift Square Root Hardware Algorithm / 60 \\ 5.1 Introduction / 60 \\ 5.2 A Square Root Hardware Algorithm / 62 \\ 5.2.1 Algorithm / 62 \\ 5.2.2 Analysis of the Algorithm / 67 \\ 5.3 A Square Root Circuit Based on the Algorithm / 69 \\ 5.4 Remarks and Discussions / 70 \\ 5.A A Proof of the Correctness of the Algorithm / 71 \\ \\ 6: Hardware Algorithms for Elementary Functions / 75 \\ 6.1 Introduction / 75 \\ 6.2 Hardware Algorithms Based on the CORDIC Method / 77 \\ 6.2.1 Principle of the CORDIC Method / 77 \\ 6.2.2 A Hardware Algorithm for Computing Sines and Cosines / 80 \\ 6.2.3 A Hardware Algorithm for Computing Arctangents / 87 \\ 6.3 Hardware Algorithms Based on the STL Method / 91 \\ 6.3.1 Principle of the STL Method / 91 \\ 6.3.2 A Hardware Algorithm for Computing Logarithms / 92 \\ 6.3.3 A Hardware Algorithm for Computing Exponentials / 97 \\ 6.4 Remarks and Discussions / 101 \\ \\ 7: Design of Self-Checking Arithmetic Circuits by Means of the Three-Rail Logic / 103 \\ 7.1 Introduction / 103 \\ 7.2 Design of Self-Checking Arithmetic Circuits / 106 \\ 7.3 A Design of a Self-Checking Multiplier / 112 \\ 7.4 Remarks and Discussions / 119 \\ \\ 8: Redundant Coding Schemes for Several Algebraic Systems / 121 \\ 8.1 Introduction / 121 \\ 8.2 Coding Schemes and Local Computability / 122 \\ 8.3 A Redundant Coding Scheme for a Residue Class and a Hardware Algorithm for Modular Addition / 124 \\ 8.4 Redundant Coding Schemes for Other Algebraic Systems / 129 \\ 8.5 Remarks and Discussions / 132 \\ \\ 9: Conclusion / 135 \\ Acknowledgments / 138

entry:
@PhdThesis{Takagi:1987:SHA,
  author =       "Naofumi Takagi",
  title =        "Studies on Hardware Algorithms for Arithmetic
                 Operations with a Redundant Binary Adder",
  type =         "{PhD} dissertation",
  school =       "Department of Information Sciences, Faculty of
                 Engineering, Kyoto University",
  address =      "Kyoto, Japan",
  pages =        "vii + 150",
  month =        aug,
  year =         "1987",
  bibdate =      "Thu Nov 13 06:14:34 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://hdl.handle.net/2433/154053;
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  acknowledgement = ack-nhfb,
  tableofcontents = "Abstract / i \\
                 Table of Contents / v \\
                 \\
                 1: Introduction / 1 \\
                 1.1 Backgrounds / 1 \\
                 1.2 Outline of the Thesis / 4 \\
                 \\
                 2: Preliminaries / 8 \\
                 2.1 Binary Number System / 8 \\
                 2.2 Computation Model / 8 \\
                 2.3 Redundant Binary Representation \\
                 2.3.1 Redundant Binary Representation / 10 \\
                 2.3.2 Carry-Propagation-Free Addition / 11 \\
                 2.3.3 Redundant Binary to Binary Conversion / 15 \\
                 2.3.4 Special Redundant Binary Numbers / 16 \\
                 \\
                 3: A Multiplication Hardware Algorithm with a Redundant
                 Binary Addition Tree / 19 \\
                 3.1 Introduction / 19 \\
                 3.2 A Multiplication Hardware Algorithm / 19 \\
                 3.2.1 Algorithm / 21 \\
                 3.2.2 Analysis of the Algorithm / 25 \\
                 3.3 A Multiplier Based on the Algorithm \\
                 3.3.1 Multiplier Recoding and Partial Product
                 Generation / 27 \\
                 3.3.2 A Multiplier Based on the Algorithm / 30 \\
                 3.3.3 The Depth and the Gate Count of the Multiplier /
                 33 \\
                 3.4 Computation of Other Arithmetic Functions Using the
                 Multiplier \\
                 3.4.1 Redundant Binary Multiplier Receding / 35 \\
                 3.4.2 Computation of Other Arithmetic Functions / 36
                 \\
                 3.5 Remarks and Discussions / 39 \\
                 \\
                 4: A Subtract-and-Shift Division Hardware Algorithm /
                 42 \\
                 4.1 Introduction / 42 \\
                 4.2 A Division Hardware Algorithm / 44 \\
                 4.2.1 Algorithm / 44 \\
                 4.2.2 Analysis of the Algorithm / 47 \\
                 4.3 A Divider Based on the Algorithm / 51 \\
                 4.4 Remarks and Discussions / 56 \\
                 4.A A Proof of the Correctness of the Algorithm / 57
                 \\
                 \\
                 5: A Subtract-and-Shift Square Root Hardware Algorithm
                 / 60 \\
                 5.1 Introduction / 60 \\
                 5.2 A Square Root Hardware Algorithm / 62 \\
                 5.2.1 Algorithm / 62 \\
                 5.2.2 Analysis of the Algorithm / 67 \\
                 5.3 A Square Root Circuit Based on the Algorithm / 69
                 \\
                 5.4 Remarks and Discussions / 70 \\
                 5.A A Proof of the Correctness of the Algorithm / 71
                 \\
                 \\
                 6: Hardware Algorithms for Elementary Functions / 75
                 \\
                 6.1 Introduction / 75 \\
                 6.2 Hardware Algorithms Based on the CORDIC Method / 77
                 \\
                 6.2.1 Principle of the CORDIC Method / 77 \\
                 6.2.2 A Hardware Algorithm for Computing Sines and
                 Cosines / 80 \\
                 6.2.3 A Hardware Algorithm for Computing Arctangents /
                 87 \\
                 6.3 Hardware Algorithms Based on the STL Method / 91
                 \\
                 6.3.1 Principle of the STL Method / 91 \\
                 6.3.2 A Hardware Algorithm for Computing Logarithms /
                 92 \\
                 6.3.3 A Hardware Algorithm for Computing Exponentials /
                 97 \\
                 6.4 Remarks and Discussions / 101 \\
                 \\
                 7: Design of Self-Checking Arithmetic Circuits by Means
                 of the Three-Rail Logic / 103 \\
                 7.1 Introduction / 103 \\
                 7.2 Design of Self-Checking Arithmetic Circuits / 106
                 \\
                 7.3 A Design of a Self-Checking Multiplier / 112 \\
                 7.4 Remarks and Discussions / 119 \\
                 \\
                 8: Redundant Coding Schemes for Several Algebraic
                 Systems / 121 \\
                 8.1 Introduction / 121 \\
                 8.2 Coding Schemes and Local Computability / 122 \\
                 8.3 A Redundant Coding Scheme for a Residue Class and a
                 Hardware Algorithm for Modular Addition / 124 \\
                 8.4 Redundant Coding Schemes for Other Algebraic
                 Systems / 129 \\
                 8.5 Remarks and Discussions / 132 \\
                 \\
                 9: Conclusion / 135 \\
                 Acknowledgments / 138",
}


bibtype: article
filename: fparith.bib
label: Taylor:1987:RAI
author: Fred J. Taylor
title: A residue arithmetic implementation of the FFT
journal: j-J-PAR-DIST-COMP
volume: 4
number: 2
pages: 191--208
month: apr
monthnumber: 4
year: 1987
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
affiliationaddress: Univ of Florida, Gainesville, FL, USA
corpsource: Department of Electr. Eng., Coll. of Eng., Florida University, Gainesville, FL, USA
journalURL: http://www.sciencedirect.com/science/journal/07437315
journalabr: J Parallel Distrib Comput
treatment: T Theoretical or Mathematical; X Experimental
rawauthor: Fred J. Taylor
rawtitle: A residue arithmetic implementation of the {FFT}
keywords:
complex arithmetic; complexity; computational complexity; computer metatheory; computerised signal processing; digital arithmetic; discrete Fourier transform (DFT); evaluation; Fast Fourier Transforms; fast Fourier transforms; FFT; FFT system; management system; mathematical techniques; mathematical transformations; performance; residue arithmetic; residue arithmetic number system; sign; sign management; single-modulus complex residue number system; speed

entry:
@Article{Taylor:1987:RAI,
  author =       "Fred J. Taylor",
  title =        "A residue arithmetic implementation of the {FFT}",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "4",
  number =       "2",
  pages =        "191--208",
  month =        apr,
  year =         "1987",
  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,
  affiliationaddress = "Univ of Florida, Gainesville, FL, USA",
  classification = "723; 921; C4190 (Other numerical methods); C4240
                 (Programming and algorithm theory); C5230 (Digital
                 arithmetic methods); C5260 (Digital signal processing);
                 C5470 (Performance evaluation and testing)",
  corpsource =   "Department of Electr. Eng., Coll. of Eng., Florida
                 University, Gainesville, FL, USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "complex arithmetic; complexity; computational
                 complexity; computer metatheory; computerised signal
                 processing; digital arithmetic; discrete Fourier
                 transform (DFT); evaluation; Fast Fourier Transforms;
                 fast Fourier transforms; FFT; FFT system; management
                 system; mathematical techniques; mathematical
                 transformations; performance; residue arithmetic;
                 residue arithmetic number system; sign; sign
                 management; single-modulus complex residue number
                 system; speed",
  treatment =    "T Theoretical or Mathematical; X Experimental",
}


bibtype: article
filename: fparith.bib
label: Thompson:1987:FME
author: T. Thompson
title: Fast Math --- a first look at Motorola's 68882 math coprocessor
journal: j-BYTE
volume: 12
number: 12
pages: 120--121
month: dec
monthnumber: 12
year: 1987
CODEN: BYTEDJ
ISSN: 0360-5280 (print), 1082-7838 (electronic) OR 03605280 (print), 10827838 (electronic)
ISSNL: 0360-5280 OR 03605280
bibdate: Wed Sep 7 22:32:00 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 22:32:00 ???
fjournal: BYTE Magazine
acknowledgement: ack-nj
rawauthor: T. Thompson
rawtitle: Fast Math --- a first look at {Motorola}'s 68882 math coprocessor
entry:
@Article{Thompson:1987:FME,
  author =       "T. Thompson",
  title =        "Fast Math --- a first look at {Motorola}'s 68882 math
                 coprocessor",
  journal =      j-BYTE,
  volume =       "12",
  number =       "12",
  pages =        "120--121",
  month =        dec,
  year =         "1987",
  CODEN =        "BYTEDJ",
  ISSN =         "0360-5280 (print), 1082-7838 (electronic)",
  ISSN-L =       "0360-5280",
  bibdate =      "Wed Sep 7 22:32:00 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 =     "BYTE Magazine",
}


bibtype: article
filename: fparith.bib
label: Thompson:1987:IEF
author: P. Thompson
title: Implementing an Elementary Function Library
journal: j-SIGNUM
volume: 22
number: 2
pages: 2--5
month: apr
monthnumber: 4
year: 1987
CODEN: SNEWD6
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Thu Sep 1 10:15:30 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 10:15:30 ???
fjournal: ACM SIGNUM Newsletter
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/signum
rawauthor: P. Thompson
rawtitle: Implementing an Elementary Function Library
entry:
@Article{Thompson:1987:IEF,
  author =       "P. Thompson",
  title =        "Implementing an Elementary Function Library",
  journal =      j-SIGNUM,
  volume =       "22",
  number =       "2",
  pages =        "2--5",
  month =        apr,
  year =         "1987",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Thu Sep 1 10:15:30 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
}


bibtype: inproceedings
filename: fparith.bib
label: Tu:1987:RLD
author: Paul K. G. Tu and Milos D. Ercegovac
title: A Radix-4 On-Line Division Algorithm
crossref: Irwin:1987:PSC
pages: 181--187
year: 1987
DOI: https://doi.org/10.1109/ARITH.1987.6158719
bibdate: Fri Nov 16 21:39:46 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.16 21:39:46 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Tu_Ercegovac.pdf
keywords: ARITH-8
acknowledgement: ack-nhfb
rawauthor: Paul K. G. Tu and Milo{\v{s}} D. Ercegovac
rawtitle: A Radix-4 On-Line Division Algorithm
abstract:
We present an on-line algorithm for radix-4 floating point division. The divisor is first transformed in to a range such that the quotient digits are computed as a function of the scaled partial remainder only.

rawabstract:
We present an on-line algorithm for radix-4 floating point division. The divisor is first transformed in to a range such that the quotient digits are computed as a function of the scaled partial remainder only.

entry:
@InProceedings{Tu:1987:RLD,
  author =       "Paul K. G. Tu and Milo{\v{s}} D. Ercegovac",
  title =        "A Radix-4 On-Line Division Algorithm",
  crossref =     "Irwin:1987:PSC",
  pages =        "181--187",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158719",
  bibdate =      "Fri Nov 16 21:39:46 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Tu_Ercegovac.pdf",
  abstract =     "We present an on-line algorithm for radix-4 floating
                 point division. The divisor is first transformed in to
                 a range such that the quotient digits are computed as a
                 function of the scaled partial remainder only.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}


bibtype: article
filename: fparith.bib
label: Turner:1987:DDI
author: Peter R. Turner
title: The Distribution of l.s.d. and Its Implications for Computer Design
journal: j-MATH-GAZ
volume: 71
number: 455
pages: 26--31
month: mar
monthnumber: 3
year: 1987
CODEN: MAGAAS
DOI: https://doi.org/10.2307/3616283
ISSN: 0025-5572 (print), 2056-6328 (electronic) OR 00255572 (print), 20566328 (electronic)
bibdate: Tue Oct 30 23:36:58 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.10.30 23:36:58 ???
fjournal: Mathematical Gazette
keywords: Benford's Law; Law of Anomalous Numbers; logarithmic distribution; overflow; underflow; Zipf's Law
acknowledgement: ack-nhfb
journalURL: http://www.m-a.org.uk/jsp/index.jsp?lnk=620
rawauthor: Peter R. Turner
rawtitle: The Distribution of l.s.d. and Its Implications for Computer Design
entry:
@Article{Turner:1987:DDI,
  author =       "Peter R. Turner",
  title =        "The Distribution of l.s.d. and Its Implications for
                 Computer Design",
  journal =      j-MATH-GAZ,
  volume =       "71",
  number =       "455",
  pages =        "26--31",
  month =        mar,
  year =         "1987",
  CODEN =        "MAGAAS",
  DOI =          "https://doi.org/10.2307/3616283",
  ISSN =         "0025-5572 (print), 2056-6328 (electronic)",
  bibdate =      "Tue Oct 30 23:36:58 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Gazette",
  journal-URL =  "http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
  keywords =     "Benford's Law; Law of Anomalous Numbers; logarithmic
                 distribution; overflow; underflow; Zipf's Law",
}


bibtype: inproceedings
filename: fparith.bib
label: Umeo:1987:DTO
author: Hiroshi Umeo
title: A Design of Time-Optimum and Register-Number-Minimum Systolic Convolver
crossref: Irwin:1987:PSC
pages: 5--12
year: 1987
DOI: https://doi.org/10.1109/ARITH.1987.6158720
bibdate: Fri Nov 16 21:39:46 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.16 21:39:46 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Umeo.pdf
keywords: ARITH-8
acknowledgement: ack-nhfb
rawauthor: Hiroshi Umeo
rawtitle: A Design of Time-Optimum and Register-Number-Minimum Systolic Convolver
abstract:
We present an optimum bit-parallel / word-sequential systolic convolver. Our design is the best one among the previous many convolvers in the sense that its optimality in time and space performances is simultaneously attained without augmenting any global control, broadcasting, preloading, and / or multi sequential or parallel I/O ports, which were allowed in most of the previous designs. As an application of our convolver we give a systolic polynomial divider which can compute the polynomial division in exactly $ n + O(1) $ steps on $ [min (n - m, m) / 2] + O(1) $ systolic cells, for the division of any degree n polynomial by any degree $m$ polynomial ($ n geq m $).

rawabstract:
We present an optimum bit-parallel\slash word-sequential systolic convolver. Our design is the best one among the previous many convolvers in the sense that its optimality in time and space performances is simultaneously attained without augmenting any global control, broadcasting, preloading, and\slash or multi sequential or parallel I/O ports, which were allowed in most of the previous designs. As an application of our convolver we give a systolic polynomial divider which can compute the polynomial division in exactly $ n + O(1) $ steps on $ [\min (n - m, m) / 2] + O(1) $ systolic cells, for the division of any degree n polynomial by any degree $m$ polynomial ($ n \geq m $).

entry:
@InProceedings{Umeo:1987:DTO,
  author =       "Hiroshi Umeo",
  title =        "A Design of Time-Optimum and Register-Number-Minimum
                 Systolic Convolver",
  crossref =     "Irwin:1987:PSC",
  pages =        "5--12",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158720",
  bibdate =      "Fri Nov 16 21:39:46 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Umeo.pdf",
  abstract =     "We present an optimum bit-parallel\slash
                 word-sequential systolic convolver. Our design is the
                 best one among the previous many convolvers in the
                 sense that its optimality in time and space
                 performances is simultaneously attained without
                 augmenting any global control, broadcasting,
                 preloading, and\slash or multi sequential or parallel
                 I/O ports, which were allowed in most of the previous
                 designs. As an application of our convolver we give a
                 systolic polynomial divider which can compute the
                 polynomial division in exactly $ n + O(1) $ steps on $
                 [\min (n - m, m) / 2] + O(1) $ systolic cells, for the
                 division of any degree n polynomial by any degree $m$
                 polynomial ($ n \geq m $).",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}


bibtype: article
filename: fparith.bib
label: Ushio:1987:CRE
author: T. Ushio and C. Hsu
title: Chaotic rounding error in digital control systems
journal: j-IEEE-TRANS-CIRCUITS-SYST
volume: 34
number: 2
pages: 133--139
month: feb
monthnumber: 2
year: 1987
CODEN: ICSYBT
ISSN: 0098-4094 (print), 1558-1276 (electronic) OR 00984094 (print), 15581276 (electronic)
ISSNL: 0098-4094 OR 00984094
bibdate: Sat Jul 16 11:25:03 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:03 MDT
fjournal: IEEE Transactions on Circuits and Systems
acknowledgement: ack-nhfb
rawauthor: T. Ushio and C. Hsu
rawtitle: Chaotic rounding error in digital control systems
entry:
@Article{Ushio:1987:CRE,
  author =       "T. Ushio and C. Hsu",
  title =        "Chaotic rounding error in digital control systems",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "34",
  number =       "2",
  pages =        "133--139",
  month =        feb,
  year =         "1987",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Sat Jul 16 11:25:03 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  summary =      "Chaotic behavior due to the round-off effect in
                 digital control systems is called the chaotic rounding
                 error. First, we model digital control systems with
                 finite-wordlength digital compensators by mixed
                 mappings. A mixed mapping system is described
                 \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Vachss:1987:CMF
author: R. Vachss
title: The Cordic Magnification Function
journal: j-IEEE-MICRO
volume: 7
number: 5
pages: 83--84
month: sep
monthnumber: 9
year: 1987
CODEN: IEMIDZ
DOI: https://doi.org/10.1109/MM.1987.305021
ISSN: 0272-1732 (print), 1937-4143 (electronic) OR 02721732 (print), 19374143 (electronic)
ISSNL: 0272-1732 OR 02721732
bibdate: Thu Sep 1 10:15:40 1994
bibtimestamp: 1994.09.01 10:15:40 ???
fjournal: IEEE Micro
acknowledgement: ack-nj
journalURL: http://www.computer.org/csdl/mags/mi/index.html
rawauthor: R. Vachss
rawtitle: The {Cordic} Magnification Function
entry:
@Article{Vachss:1987:CMF,
  author =       "R. Vachss",
  title =        "The {Cordic} Magnification Function",
  journal =      j-IEEE-MICRO,
  volume =       "7",
  number =       "5",
  pages =        "83--84",
  month =        sep # "\slash " # oct,
  year =         "1987",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/MM.1987.305021",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Thu Sep 1 10:15:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
}


bibtype: article
filename: fparith.bib
label: Vitek:1987:EFA
author: V. Vitek
title: Enumeration in floating-point arithmetic
journal: ASR - Bulletin INORGA
volume: 21
number: 6
pages: 301--305
year: 1987
ISSN: 0231-8954 OR 02318954
bibdate: Tue Dec 12 09:17:24 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.12 09:17:24 MST
keywords: Algebraic operations; Computer representation; Floating-point arithmetic; Overflow; Underflow
acknowledgement: ack-nhfb
thesaurus: Carry logic; Digital arithmetic; Error handling
rawauthor: V. Vitek
rawtitle: Enumeration in floating-point arithmetic
abstract:
The paper studies the computer representation of numbers in floating-point arithmetic and algebraic operations with these numbers with respect to the validity of basic algebraic laws. Methods for the handling of emergency situations are given: overflow and underflow, illustrated using the example of the computation of a member of the binomial expansion. (6 Refs.)

rawabstract:
The paper studies the computer representation of numbers in floating-point arithmetic and algebraic operations with these numbers with respect to the validity of basic algebraic laws. Methods for the handling of emergency situations are given: overflow and underflow, illustrated using the example of the computation of a member of the binomial expansion. (6 Refs.)

entry:
@Article{Vitek:1987:EFA,
  author =       "V. Vitek",
  title =        "Enumeration in floating-point arithmetic",
  journal =      "ASR - Bulletin INORGA",
  volume =       "21",
  number =       "6",
  pages =        "301--305",
  month =        "????",
  year =         "1987",
  ISSN =         "0231-8954",
  bibdate =      "Tue Dec 12 09:17:24 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The paper studies the computer representation of
                 numbers in floating-point arithmetic and algebraic
                 operations with these numbers with respect to the
                 validity of basic algebraic laws. Methods for the
                 handling of emergency situations are given: overflow
                 and underflow, illustrated using the example of the
                 computation of a member of the binomial expansion. (6
                 Refs.)",
  acknowledgement = ack-nhfb,
  classification = "C5230 (Digital arithmetic methods)",
  keywords =     "Algebraic operations; Computer representation;
                 Floating-point arithmetic; Overflow; Underflow",
  pubcountry =   "Czechoslovakia",
  thesaurus =    "Carry logic; Digital arithmetic; Error handling",
}


bibtype: inproceedings
filename: fparith.bib
label: Wang:1987:EEF
author: Kai Hwang and H. C. Wang and Z. Xu
title: Evaluating Elementary Functions with Chebyshev Polynomials on Pipeline Nets
crossref: Irwin:1987:PSC
pages: 121--128
year: 1987
DOI: https://doi.org/10.1109/ARITH.1987.6158702
bibdate: Fri Nov 16 21:39:46 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.16 21:39:46 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Hwang_Wang_Xu.pdf
keywords: ARITH-8
acknowledgement: ack-nhfb
rawauthor: Kai Hwang and H. C. Wang and Z. Xu
rawtitle: Evaluating Elementary Functions with {Chebyshev} Polynomials on Pipeline Nets
abstract:
Fast evaluation of vector-valued elementary functions plays a vital role in many real-time applications. In this paper, we present a pipeline networking approach to designing a Chebyshev polynomial evaluator for the fast evaluation of elementary functions over a string of arguments. In particular, pipeline nets are employed to perform the preprocessing and postprocessing of various elementary functions to boost the overall system performance. Design tradeoffs are analyzed among representational accuracy, processing speed and hardware complexity.

rawabstract:
Fast evaluation of vector-valued elementary functions plays a vital role in many real-time applications. In this paper, we present a pipeline networking approach to designing a Chebyshev polynomial evaluator for the fast evaluation of elementary functions over a string of arguments. In particular, pipeline nets are employed to perform the preprocessing and postprocessing of various elementary functions to boost the overall system performance. Design tradeoffs are analyzed among representational accuracy, processing speed and hardware complexity.

entry:
@InProceedings{Wang:1987:EEF,
  author =       "Kai Hwang and H. C. Wang and Z. Xu",
  title =        "Evaluating Elementary Functions with {Chebyshev}
                 Polynomials on Pipeline Nets",
  crossref =     "Irwin:1987:PSC",
  pages =        "121--128",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158702",
  bibdate =      "Fri Nov 16 21:39:46 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Hwang_Wang_Xu.pdf",
  abstract =     "Fast evaluation of vector-valued elementary functions
                 plays a vital role in many real-time applications. In
                 this paper, we present a pipeline networking approach
                 to designing a Chebyshev polynomial evaluator for the
                 fast evaluation of elementary functions over a string
                 of arguments. In particular, pipeline nets are employed
                 to perform the preprocessing and postprocessing of
                 various elementary functions to boost the overall
                 system performance. Design tradeoffs are analyzed among
                 representational accuracy, processing speed and
                 hardware complexity.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}


bibtype: manual
filename: fparith.bib
label: WeitekCorporation:1987:WFP
title: WTL 1167 floating point coprocessor: preliminary data
organization: Weitek Corporation
address: Sunnyvale, CA, USA
pages: 54
year: 1987
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Floating-point arithmetic.; Intel 80386 (Microprocessor) --- Programming.
remark: August 1988.
acknowledgement: ack-nhfb
rawtitle: {WTL} 1167 floating point coprocessor: preliminary data
entry:
@Manual{WeitekCorporation:1987:WFP,
  title =        "{WTL} 1167 floating point coprocessor: preliminary
                 data",
  organization = "{Weitek Corporation}",
  address =      "Sunnyvale, CA, USA",
  pages =        "54",
  year =         "1987",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.; Intel 80386
                 (Microprocessor) --- Programming.",
  remark =       "August 1988.",
}


bibtype: mastersthesis
filename: fparith.bib
label: Williams:1987:FPL
author: Robert Leslie Williams
title: A floating point loop engine architecture using pattern generation
type: Thesis (M.S.)
school: University of New Mexico
address: Albuquerque, NM, USA
pages: ix + 92
year: 1987
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Computer architecture.; Computer engineering.
acknowledgement: ack-nhfb
rawauthor: Robert Leslie Williams
rawtitle: A floating point loop engine architecture using pattern generation
entry:
@MastersThesis{Williams:1987:FPL,
  author =       "Robert Leslie Williams",
  title =        "A floating point loop engine architecture using
                 pattern generation",
  type =         "Thesis ({M.S.})",
  school =       "University of New Mexico",
  address =      "Albuquerque, NM, USA",
  pages =        "ix + 92",
  year =         "1987",
  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 architecture.; Computer engineering.",
}


bibtype: inproceedings
filename: fparith.bib
label: Williams:1987:STC
author: T. E. Williams and M. Horowitz and R. L. Alverson and T. S. Yang
title: A self-timed chip for division
crossref: Losleben:1987:ARV
pages: 75--96
year: 1987
bibdate: Mon Sep 16 16:35:03 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.09.16 16:35:03 ???
acknowledgement: ack-nhfb
rawauthor: T. E. Williams and M. Horowitz and R. L. Alverson and T. S. Yang
rawtitle: A self-timed chip for division
entry:
@InProceedings{Williams:1987:STC,
  author =       "T. E. Williams and M. Horowitz and R. L. Alverson and
                 T. S. Yang",
  title =        "A self-timed chip for division",
  crossref =     "Losleben:1987:ARV",
  pages =        "75--96",
  year =         "1987",
  bibdate =      "Mon Sep 16 16:35:03 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Wu:1987:FDS
author: I-Chen Wu
title: A Fast $1$-D Serial-Parallel Systolic Multiplier
journal: j-IEEE-TRANS-COMPUT
volume: C-36
number: 10
pages: 1243--1247
month: oct
monthnumber: 10
year: 1987
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1987.1676865
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 9 09:28:56 MDT 2011
bibtimestamp: 2011.07.09 09:28:56 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676865
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: I-Chen Wu
rawtitle: A Fast {$1$-D} Serial-Parallel Systolic Multiplier
entry:
@Article{Wu:1987:FDS,
  author =       "I-Chen Wu",
  title =        "A Fast {$1$-D} Serial-Parallel Systolic Multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-36",
  number =       "10",
  pages =        "1243--1247",
  month =        oct,
  year =         "1987",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1987.1676865",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 09:28:56 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676865",
  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: Wu:1987:TRF
author: Chwan-Ghia Wu and Lih-Ren Tzeng and Tien-Shou Wu
title: Time-Redundant Fault-Masking in ALUs
crossref: Irwin:1987:PSC
pages: 239--243
year: 1987
bibdate: Fri Nov 16 21:39:46 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.16 21:39:46 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Wu_Cheng_Wu.pdf
keywords: ARITH-8
remark: This paper is missing from the IEEE Xplore database, so its DOI and text are not available there.
acknowledgement: ack-nhfb
rawauthor: Chwan-Ghia Wu and Lih-Ren Tzeng and Tien-Shou Wu
rawtitle: Time-Redundant Fault-Masking in {ALUs}
abstract:
A new error correction scheme for bit-sliced ALUs is presented. The method adopted for fault location is an extension of a concurrent error detection scheme called RESO (Recomputing with Shifted Operands). The term bit-slice is used in the generic sense and the length of the slice may be one or more bits. The proposed scheme requires two consecutive computation steps for normal operations and the possible locations of faults, if any, can be located provided that the failures are confined to a certain number of adjacent bit-slices. The fault-free bit-slices of the ALU are thus figured out. The final and effective computation is then carried out through those identified fault-free bit-slices. A circular structure is proposed to realize this concept.

rawabstract:
A new error correction scheme for bit-sliced ALUs is presented. The method adopted for fault location is an extension of a concurrent error detection scheme called RESO (Recomputing with Shifted Operands). The term bit-slice is used in the generic sense and the length of the slice may be one or more bits. The proposed scheme requires two consecutive computation steps for normal operations and the possible locations of faults, if any, can be located provided that the failures are confined to a certain number of adjacent bit-slices. The fault-free bit-slices of the ALU are thus figured out. The final and effective computation is then carried out through those identified fault-free bit-slices. A circular structure is proposed to realize this concept.

entry:
@InProceedings{Wu:1987:TRF,
  author =       "Chwan-Ghia Wu and Lih-Ren Tzeng and Tien-Shou Wu",
  title =        "Time-Redundant Fault-Masking in {ALUs}",
  crossref =     "Irwin:1987:PSC",
  pages =        "239--243",
  year =         "1987",
  bibdate =      "Fri Nov 16 21:39:46 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Wu_Cheng_Wu.pdf",
  abstract =     "A new error correction scheme for bit-sliced ALUs is
                 presented. The method adopted for fault location is an
                 extension of a concurrent error detection scheme called
                 RESO (Recomputing with Shifted Operands). The term
                 bit-slice is used in the generic sense and the length
                 of the slice may be one or more bits. The proposed
                 scheme requires two consecutive computation steps for
                 normal operations and the possible locations of faults,
                 if any, can be located provided that the failures are
                 confined to a certain number of adjacent bit-slices.
                 The fault-free bit-slices of the ALU are thus figured
                 out. The final and effective computation is then
                 carried out through those identified fault-free
                 bit-slices. A circular structure is proposed to realize
                 this concept.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
  remark =       "This paper is missing from the IEEE Xplore database,
                 so its DOI and text are not available there.",
}


bibtype: article
filename: fparith.bib
label: Zaccone:1987:ENP
author: Richard J. Zaccone and Jesse L. Barlow
title: Eliminating the Normalization Problem in Digit On-Line Arithmetic
journal: j-IEEE-TRANS-COMPUT
volume: C-36
number: 1
pages: 36--46
month: jan
monthnumber: 1
year: 1987
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1987.5009447
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 9 09:28:49 MDT 2011
bibtimestamp: 2011.07.09 09:28:49 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009447
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Richard J. Zaccone and Jesse L. Barlow
rawtitle: Eliminating the Normalization Problem in Digit On-Line Arithmetic
entry:
@Article{Zaccone:1987:ENP,
  author =       "Richard J. Zaccone and Jesse L. Barlow",
  title =        "Eliminating the Normalization Problem in Digit On-Line
                 Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-36",
  number =       "1",
  pages =        "36--46",
  month =        jan,
  year =         "1987",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1987.5009447",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 09:28:49 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009447",
  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: Zurawski:1987:DHS
author: J. H. P. Zurawski and J. B. Gosling
title: Design of a High-Speed Square Root Multiply and Divide Unit
journal: j-IEEE-TRANS-COMPUT
volume: C-36
number: 1
pages: 13--23
month: jan
monthnumber: 1
year: 1987
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1987.5009445
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 9 09:28:49 MDT 2011
bibtimestamp: 2011.07.09 09:28:49 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009445
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: J. H. P. Zurawski and J. B. Gosling
rawtitle: Design of a High-Speed Square Root Multiply and Divide Unit
entry:
@Article{Zurawski:1987:DHS,
  author =       "J. H. P. Zurawski and J. B. Gosling",
  title =        "Design of a High-Speed Square Root Multiply and Divide
                 Unit",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-36",
  number =       "1",
  pages =        "13--23",
  month =        jan,
  year =         "1987",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1987.5009445",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 09:28:49 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009445",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: book
filename: fparith.bib
label: Aberth:1988:PNA
author: Oliver Aberth
title: Precise Numerical Analysis
publisher: pub-WCB
address: pub-WCB:adr
pages: x + 225
year: 1988
ISBN: 0-697-06760-2 OR 0697067602
ISBN13: 978-0-697-06760-9 OR 9780697067609
LCCN: QA297 .A28 1988
bibdate: Thu Nov 8 14:50:32 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.08 14:50:32 ???
acknowledgement: ack-nj
rawauthor: Oliver Aberth
rawtitle: Precise Numerical Analysis
abstract:
Aberth addresses elementary issues of precise floating point computations using variable precision range arithmetic. Numbers are represented as a variable precision number $ pm $ a range. Rational arithmetic is also considered. Chapters are devoted to begin enumerate item rootfinding, item polynomial rootfinding, item numerical linear algebra, item differentiation and integration, and item ordinary differential equations. end enumerate Differentiation is handled by a codelist approach like [Rall81a], and applications to Taylor series are given. Interval techniques for ordinary differential equations are based on using an it a priori bound to capture remainder terms. Several methods are illustrated, including Taylor series methods.

keywords:
differentiation; differentiation arithmetic; general numerical analysis; integration; interval techniques; linear algebra; ordinary differential equations.; variable precision arithmetic

rawabstract:
Aberth addresses elementary issues of precise floating point computations using variable precision range arithmetic. Numbers are represented as a variable precision number $ \pm $ a range. Rational arithmetic is also considered. Chapters are devoted to \begin{enumerate} \item rootfinding, \item polynomial rootfinding, \item numerical linear algebra, \item differentiation and integration, and \item ordinary differential equations. \end{enumerate} Differentiation is handled by a codelist approach like [Rall81a], and applications to Taylor series are given. Interval techniques for ordinary differential equations are based on using an {\it a priori\/} bound to capture remainder terms. Several methods are illustrated, including Taylor series methods.

entry:
@Book{Aberth:1988:PNA,
  author =       "Oliver Aberth",
  title =        "Precise Numerical Analysis",
  publisher =    pub-WCB,
  address =      pub-WCB:adr,
  pages =        "x + 225",
  year =         "1988",
  ISBN =         "0-697-06760-2",
  ISBN-13 =      "978-0-697-06760-9",
  LCCN =         "QA297 .A28 1988",
  bibdate =      "Thu Nov 8 14:50:32 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Aberth addresses elementary issues of precise floating
                 point computations using variable precision range
                 arithmetic. Numbers are represented as a variable
                 precision number $ \pm $ a range. Rational arithmetic
                 is also considered. Chapters are devoted to
                 \begin{enumerate} \item rootfinding, \item polynomial
                 rootfinding, \item numerical linear algebra, \item
                 differentiation and integration, and \item ordinary
                 differential equations. \end{enumerate} Differentiation
                 is handled by a codelist approach like [Rall81a], and
                 applications to Taylor series are given. Interval
                 techniques for ordinary differential equations are
                 based on using an {\it a priori\/} bound to capture
                 remainder terms. Several methods are illustrated,
                 including Taylor series methods.",
  acknowledgement = ack-nj,
  comment =      "Text for a one semester, junior level course in
                 numerical analysis. Includes PC disk with software
                 written in PBASIC. Sound introductory level discussion
                 of code lists and error capture techniques.",
  keywords =     "differentiation; differentiation arithmetic; general
                 numerical analysis; integration; interval techniques;
                 linear algebra; ordinary differential equations.;
                 variable precision arithmetic",
}


bibtype: article
filename: fparith.bib
label: Alt:1988:FEP
author: Rene Alt
journal: j-MATH-COMPUT-SIMUL
volume: 30
number: 6
pages: 505--517
year: 1988
CODEN: MCSIDR
ISSN: 0378-4754 (print), 1872-7166 (electronic) OR 03784754 (print), 18727166 (electronic)
ISSNL: 0378-4754 OR 03784754
MRclass: 65G05 (65F10)
MRnumber: 90f:65067
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 ???
fjournal: Mathematics and Computers in Simulation
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03784754
reviewer: D. Bini
rawauthor: Ren{\'e} Alt
title:
Floating-point error propagation in iterative methods. Stochastic methods in round-off error analysis

rawtitle:
Floating-point error propagation in iterative methods. Stochastic methods in round-off error analysis

entry:
@Article{Alt:1988:FEP,
  author =       "Ren{\'e} Alt",
  title =        "Floating-point error propagation in iterative methods.
                 Stochastic methods in round-off error analysis",
  journal =      j-MATH-COMPUT-SIMUL,
  volume =       "30",
  number =       "6",
  pages =        "505--517",
  year =         "1988",
  CODEN =        "MCSIDR",
  ISSN =         "0378-4754 (print), 1872-7166 (electronic)",
  ISSN-L =       "0378-4754",
  MRclass =      "65G05 (65F10)",
  MRnumber =     "90f:65067",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics and Computers in Simulation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784754",
  reviewer =     "D. Bini",
}


bibtype: article
filename: fparith.bib
label: Alt:1988:FPE
author: R. Alt
title: Floating-point error propagation in iterative methods
journal: j-MATH-COMPUT-SIMUL
volume: 30
number: 6
pages: 505--517
month: dec
monthnumber: 12
year: 1988
CODEN: MCSIDR
ISSN: 0378-4754 (print), 1872-7166 (electronic) OR 03784754 (print), 18727166 (electronic)
ISSNL: 0378-4754 OR 03784754
bibdate: Sat Nov 9 08:26:18 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.11.09 08:26:18 MST
fjournal: Mathematics and Computers in Simulation
subject: G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03784754
rawauthor: R. Alt
rawtitle: Floating-point error propagation in iterative methods
entry:
@Article{Alt:1988:FPE,
  author =       "R. Alt",
  title =        "Floating-point error propagation in iterative
                 methods",
  journal =      j-MATH-COMPUT-SIMUL,
  volume =       "30",
  number =       "6",
  pages =        "505--517",
  month =        dec,
  year =         "1988",
  CODEN =        "MCSIDR",
  ISSN =         "0378-4754 (print), 1872-7166 (electronic)",
  ISSN-L =       "0378-4754",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  bibno =        "56847",
  catcode =      "G.1.0",
  CRclass =      "G.1.0 General; G.1.0 Computer arithmetic",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Computer arithmetic",
  fjournal =     "Mathematics and Computers in Simulation",
  genterm =      "THEORY; ALGORITHMS",
  guideno =      "1988-12109",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784754",
  journalabbrev = "Math. Comput. Simul.",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}


bibtype: article
filename: fparith.bib
label: AMD:1988:IFP
author: Advanced Micro Devices
title: IEEE floating-point format
journal: j-MICROPROC-MICROSYS
volume: 12
number: 1
pages: 13--23
month: jan
monthnumber: 1
year: 1988
CODEN: MIMID5
ISSN: 0141-9331 (print), 1872-9436 (electronic) OR 01419331 (print), 18729436 (electronic)
ISSNL: 0141-9331 OR 01419331
bibdate: Sat Nov 9 08:26:18 MST 2002
bibtimestamp: 2002.11.09 08:26:18 MST
fjournal: Microprocessors and Microsystems
acknowledgement: ack-nj
rawauthor: {Advanced Micro Devices}
rawtitle: {IEEE} floating-point format
bibsource:
ACM Computing Archive CD-ROM database (1991); ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib

subject:
mathematics of computing, numerical analysis, general, computer arithmetic; computing milieux, the computer industry, standards

entry:
@Article{AMD:1988:IFP,
  author =       "{Advanced Micro Devices}",
  title =        "{IEEE} floating-point format",
  journal =      j-MICROPROC-MICROSYS,
  volume =       "12",
  number =       "1",
  pages =        "13--23",
  month =        jan # "\slash " # feb,
  year =         "1988",
  CODEN =        "MIMID5",
  ISSN =         "0141-9331 (print), 1872-9436 (electronic)",
  ISSN-L =       "0141-9331",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 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,
  bibno =        "23",
  categories =   "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 K. Computing Milieux; K.1 THE COMPUTER INDUSTRY; G.1.0
                 General; G.1.0 Computer arithmetic; K.1 Standards",
  content =      "DESIGN; STANDARDIZATION; THEORY",
  CRnumber =     "1988-12470",
  fjournal =     "Microprocessors and Microsystems",
  guideno =      "1",
  subject =      "mathematics of computing, numerical analysis, general,
                 computer arithmetic; computing milieux, the computer
                 industry, standards",
  wsub =         "Jesse L. Barlow",
}


bibtype: article
filename: fparith.bib
label: An:1988:CRE
author: S. H. An and K. Yao
journal: j-IEEE-TRANS-CIRCUITS-SYST
volume: 35
number: 2
pages: 241--246
month: feb
monthnumber: 2
year: 1988
CODEN: ICSYBT
ISSN: 0098-4094 (print), 1558-1276 (electronic) OR 00984094 (print), 15581276 (electronic)
ISSNL: 0098-4094 OR 00984094
bibdate: Sat Jul 16 11:25:06 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:06 MDT
fjournal: IEEE Transactions on Circuits and Systems
acknowledgement: ack-nhfb
rawauthor: S. H. An and K. Yao
title:
Convergent and roundoff error properties of reflection coefficients in adaptive spatial recursive least squares lattice algorithm

rawtitle:
Convergent and roundoff error properties of reflection coefficients in adaptive spatial recursive least squares lattice algorithm

entry:
@Article{An:1988:CRE,
  author =       "S. H. An and K. Yao",
  title =        "Convergent and roundoff error properties of reflection
                 coefficients in adaptive spatial recursive least
                 squares lattice algorithm",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "35",
  number =       "2",
  pages =        "241--246",
  month =        feb,
  year =         "1988",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Sat Jul 16 11:25:06 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  summary =      "The spatial recursive least-squares lattice (RLSL)
                 algorithm is considered and the convergent properties
                 as well as the finite-precision roundoff effects of the
                 reflection coefficients are studied in detail. It is
                 shown that when the forgetting \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Anderson:1988:MRE
author: Ned Anderson
title: Minimum relative error approximations for $ 1 / t $
journal: j-NUM-MATH
volume: 54
number: 2
pages: 117--124
month: nov
monthnumber: 11
year: 1988
CODEN: NUMMA7
DOI: https://doi.org/10.1007/BF01396969
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
MRclass: 65D15
MRnumber: 90a:65037
MRreviewer: Mariano Gasca
bibdate: Mon May 26 11:49:34 MDT 1997
bibtimestamp: 1997.05.26 11:49:34 MDT
fjournal: Numerische Mathematik
acknowledgement: ack-nhfb
corpsource: Corp. Res., Digital Equipment Corp., Hudson, MA, USA
journalURL: http://link.springer.com/journal/211
treatment: T Theoretical or Mathematical
rawauthor: Ned Anderson
rawtitle: Minimum relative error approximations for $ 1 / t $
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/nummath.bib

keywords:
approximation theory; functional equation; geometric convergence rates; iterative methods; minimum relative error approximations; polynomial approximations; polynomials

entry:
@Article{Anderson:1988:MRE,
  author =       "Ned Anderson",
  title =        "Minimum relative error approximations for $ 1 / t $",
  journal =      j-NUM-MATH,
  volume =       "54",
  number =       "2",
  pages =        "117--124",
  month =        nov,
  year =         "1988",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF01396969",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65D15",
  MRnumber =     "90a:65037",
  MRreviewer =   "Mariano Gasca",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/nummath.bib",
  acknowledgement = ack-nhfb,
  classification = "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  corpsource =   "Corp. Res., Digital Equipment Corp., Hudson, MA, USA",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "approximation theory; functional equation; geometric
                 convergence rates; iterative methods; minimum relative
                 error approximations; polynomial approximations;
                 polynomials",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: fparith.bib
label: Anonymous:1988:IGI
author: Anonymous
title: IMACS-GAMM international symposium on computer arithmetic and self-validating numerical methods
journal: j-MATH-COMPUT-SIMUL
volume: 30
number: 6
pages: 572--572
month: dec
monthnumber: 12
year: 1988
CODEN: MCSIDR
DOI: https://doi.org/10.1016/0378-4754(88)90091-2
ISSN: 0378-4754 (print), 1872-7166 (electronic) OR 03784754 (print), 18727166 (electronic)
ISSNL: 0378-4754 OR 03784754
bibdate: Mon Aug 18 16:03:57 MDT 2025
bibtimestamp: 2025.08.18 16:03:57 MDT
URL: https://www.sciencedirect.com/science/article/pii/0378475488900912
fjournal: Mathematics and Computers in Simulation
acknowledgement: ack-nhfb
ajournal: Math. Comput. Simul.
journalURL: https://www.sciencedirect.com/science/journal/03784754
rawauthor: Anonymous
rawtitle: {IMACS-GAMM} international symposium on computer arithmetic and self-validating numerical methods
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/mathcomputsimul1980.bib

entry:
@Article{Anonymous:1988:IGI,
  author =       "Anonymous",
  title =        "{IMACS-GAMM} international symposium on computer
                 arithmetic and self-validating numerical methods",
  journal =      j-MATH-COMPUT-SIMUL,
  volume =       "30",
  number =       "6",
  pages =        "572--572",
  month =        dec,
  year =         "1988",
  CODEN =        "MCSIDR",
  DOI =          "https://doi.org/10.1016/0378-4754(88)90091-2",
  ISSN =         "0378-4754 (print), 1872-7166 (electronic)",
  ISSN-L =       "0378-4754",
  bibdate =      "Mon Aug 18 16:03:57 MDT 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomputsimul1980.bib",
  URL =          "https://www.sciencedirect.com/science/article/pii/0378475488900912",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput. Simul.",
  fjournal =     "Mathematics and Computers in Simulation",
  journal-URL =  "https://www.sciencedirect.com/science/journal/03784754",
}


bibtype: book
filename: fparith.bib
label: Apple:1988:ANM
author: Apple Computer, Inc.
title: Apple Numerics Manual
publisher: pub-AW
address: pub-AW:adr
edition: Second
pages: xxvi + 294
year: 1988
ISBN: 0-201-17738-2 OR 0201177382
ISBN13: 978-0-201-17738-1 OR 9780201177381
LCCN: QA76.8.A662 A767 1988
bibdate: Wed Sep 07 21:06:52 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.07 21:06:52 ???
series: The Apple technical library
acknowledgement: ack-nhfb
rawauthor: {Apple Computer, Inc.}
rawtitle: {Apple} Numerics Manual
keywords:
Apple II (computer) --- programming; computation by computer systems --- floating point representation; Macintosh (computer) --- programming; numerical calculations --- data processing; SANE (Standard Apple Numeric Environment)

entry:
@Book{Apple:1988:ANM,
  author =       "{Apple Computer, Inc.}",
  title =        "{Apple} Numerics Manual",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  edition =      "Second",
  pages =        "xxvi + 294",
  year =         "1988",
  ISBN =         "0-201-17738-2",
  ISBN-13 =      "978-0-201-17738-1",
  LCCN =         "QA76.8.A662 A767 1988",
  bibdate =      "Wed Sep 07 21:06:52 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$29.95",
  series =       "The Apple technical library",
  acknowledgement = ack-nhfb,
  keywords =     "Apple II (computer) --- programming; computation by
                 computer systems --- floating point representation;
                 Macintosh (computer) --- programming; numerical
                 calculations --- data processing; SANE (Standard Apple
                 Numeric Environment)",
}


bibtype: article
filename: fparith.bib
label: Bailey:1988:EHS
author: David H. Bailey
title: Extra high speed matrix multiplication on the Cray-2
journal: j-SIAM-J-SCI-STAT-COMP
volume: 9
number: 3
pages: 603--607
month: may
monthnumber: 5
year: 1988
CODEN: SIJCD4
DOI: https://doi.org/10.1137/0909040
ISSN: 0196-5204 OR 01965204
ISSNL: 0196-5204 OR 01965204
MRclass: 65F30 (65G05 65W05)
MRnumber: 937 496
bibdate: Mon Mar 31 10:00:04 MDT 2014
bibtimestamp: 2014.03.31 10:00:04 MDT
fjournal: SIAM Journal on Scientific and Statistical Computing
acknowledgement: ack-nhfb
corpsource: Ames Res. Center, NASA, Moffett Field, CA, USA
journalURL: http://epubs.siam.org/loi/sijcd4
onlinedate: May 1988
treatment: P Practical
rawauthor: David H. Bailey
rawtitle: Extra high speed matrix multiplication on the {Cray-2}
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/siamjscistatcomp.bib

keywords:
Cray-2; floating-point operations; library routines; mathematics computing; matrix algebra; matrix multiplication; memory bank contention; numerical stability

entry:
@Article{Bailey:1988:EHS,
  author =       "David H. Bailey",
  title =        "Extra high speed matrix multiplication on the
                 {Cray-2}",
  journal =      j-SIAM-J-SCI-STAT-COMP,
  volume =       "9",
  number =       "3",
  pages =        "603--607",
  month =        may,
  year =         "1988",
  CODEN =        "SIJCD4",
  DOI =          "https://doi.org/10.1137/0909040",
  ISSN =         "0196-5204",
  ISSN-L =       "0196-5204",
  MRclass =      "65F30 (65G05 65W05)",
  MRnumber =     "937 496",
  bibdate =      "Mon Mar 31 10:00:04 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscistatcomp.bib",
  acknowledgement = ack-nhfb,
  classification = "C7310 (Mathematics)",
  corpsource =   "Ames Res. Center, NASA, Moffett Field, CA, USA",
  fjournal =     "SIAM Journal on Scientific and Statistical Computing",
  journal-URL =  "http://epubs.siam.org/loi/sijcd4",
  keywords =     "Cray-2; floating-point operations; library routines;
                 mathematics computing; matrix algebra; matrix
                 multiplication; memory bank contention; numerical
                 stability",
  onlinedate =   "May 1988",
  treatment =    "P Practical",
}


bibtype: inproceedings
filename: fparith.bib
label: Bandyopadhyay:1988:SAF
author: S. Bandyopadhyay and G. A. Jullien and A. Sengupta
booktitle: Proceedings of the International Conference on Systolic Arrays, 1988. 25--27 May 1988
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 577--586
year: 1988
DOI: https://doi.org/10.1109/ARRAYS.1988.18094
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: S. Bandyopadhyay and G. A. Jullien and A. Sengupta
rawbooktitle: Proceedings of the International Conference on Systolic Arrays, 1988. 25--27 May 1988
title:
A systolic array for fault tolerant digital signal processing using a residue number system approach

rawtitle:
A systolic array for fault tolerant digital signal processing using a residue number system approach

entry:
@InProceedings{Bandyopadhyay:1988:SAF,
  author =       "S. Bandyopadhyay and G. A. Jullien and A. Sengupta",
  booktitle =    "Proceedings of the International Conference on
                 Systolic Arrays, 1988. 25--27 May 1988",
  title =        "A systolic array for fault tolerant digital signal
                 processing using a residue number system approach",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "577--586",
  year =         "1988",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ARRAYS.1988.18094",
  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 =      "Fault detection and correction using the Chinese
                 remainder theorem for decoding is investigated. It is
                 shown that this approach is well suited for
                 implementation by VLSI circuits for digital signal
                 processing using systolic architectures. A systolic
                 \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Banning:1988:PRF
author: Craig Banning
title: Perfectly Rounded Floats
journal: j-CUJ
volume: 6
number: 2
pages: 14--??
month: feb
monthnumber: 2
year: 1988
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: Craig Banning
rawtitle: Perfectly Rounded Floats
entry:
@Article{Banning:1988:PRF,
  author =       "Craig Banning",
  title =        "Perfectly Rounded Floats",
  journal =      j-CUJ,
  volume =       "6",
  number =       "2",
  pages =        "14--??",
  month =        feb,
  year =         "1988",
  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: Barany:1988:FEI
author: T. E. Barany
title: Fast evaluation of integer roots in microcontroller systems
journal: j-MICROPROC-MICROSYS
volume: 12
number: 6
pages: 341--344
month: jul
monthnumber: 7
year: 1988
CODEN: MIMID5
ISSN: 0141-9331 (print), 1872-9436 (electronic) OR 01419331 (print), 18729436 (electronic)
ISSNL: 0141-9331 OR 01419331
bibdate: Fri Dec 08 13:06:02 1995
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 13:06:02 ???
fjournal: Microprocessors and Microsystems
acknowledgement: ack-nj
rawauthor: T. E. Barany
rawtitle: Fast evaluation of integer roots in microcontroller systems
entry:
@Article{Barany:1988:FEI,
  author =       "T. E. Barany",
  title =        "Fast evaluation of integer roots in microcontroller
                 systems",
  journal =      j-MICROPROC-MICROSYS,
  volume =       "12",
  number =       "6",
  pages =        "341--344",
  month =        jul # "--" # aug,
  year =         "1988",
  CODEN =        "MIMID5",
  ISSN =         "0141-9331 (print), 1872-9436 (electronic)",
  ISSN-L =       "0141-9331",
  bibdate =      "Fri Dec 08 13:06:02 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Microprocessors and Microsystems",
}


bibtype: techreport
filename: fparith.bib
label: Barlow:1988:EAU
author: Jesse Louis Barlow and Richard J. Zaccone
title: Error analysis in unnormalized floating point arithmetic
type: Technical report
number: CS-88-33
institution: Pennsylvania State University, Department of Computer Science
address: University Park, PA, USA
pages: 12
year: 1988
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Floating-point arithmetic.
remark: Supported by the National Science Foundation. Supported by the Office of Naval Research.
acknowledgement: ack-nhfb
rawauthor: Jesse Louis Barlow and Richard J. Zaccone
rawtitle: Error analysis in unnormalized floating point arithmetic
entry:
@TechReport{Barlow:1988:EAU,
  author =       "Jesse Louis Barlow and Richard J. Zaccone",
  title =        "Error analysis in unnormalized floating point
                 arithmetic",
  type =         "Technical report",
  number =       "CS-88-33",
  institution =  "Pennsylvania State University, Department of Computer
                 Science",
  address =      "University Park, PA, USA",
  pages =        "12",
  year =         "1988",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.",
  remark =       "Supported by the National Science Foundation.
                 Supported by the Office of Naval Research.",
}


bibtype: techreport
filename: fparith.bib
label: Barlowe:1988:EAU
author: Jesse L. Barlowe
title: Error analysis in unnormalized floating point arithmetic
type: Technical report
number: CS-88-10
institution: Pennsylvania State University, Department of Computer Science
address: University Park, PA, USA
pages: 14
year: 1988
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Computer arithmetic.; Errors.
remark: Supported by the National Science Foundation. Supported by the Office of Naval Research.
acknowledgement: ack-nhfb
rawauthor: Jesse L. Barlowe
rawtitle: Error analysis in unnormalized floating point arithmetic
entry:
@TechReport{Barlowe:1988:EAU,
  author =       "Jesse L. Barlowe",
  title =        "Error analysis in unnormalized floating point
                 arithmetic",
  type =         "Technical report",
  number =       "CS-88-10",
  institution =  "Pennsylvania State University, Department of Computer
                 Science",
  address =      "University Park, PA, USA",
  pages =        "14",
  year =         "1988",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer arithmetic.; Errors.",
  remark =       "Supported by the National Science Foundation.
                 Supported by the Office of Naval Research.",
}


bibtype: inproceedings
filename: fparith.bib
label: BenChorin:1988:NPC
author: S. Ben-Chorin
title: NS32532-NS32580 processor cluster delivers high floating-point performance
crossref: Midcon:1988:MCP
pages: 243--248
year: 1988
bibdate: Tue Dec 12 09:20:21 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.12 09:20:21 MST
acknowledgement: ack-nhfb
affiliation: Nat. Semicond. Corp., Santa Clara, CA, USA
thesaurus: Computer architecture; Microprocessor chips
rawauthor: S. Ben-Chorin
rawtitle: {NS32532-NS32580} processor cluster delivers high floating-point performance
abstract:
The NS32580 Floating-Point Controller (FPC) teams with Weitek's WTL3164 Floating-Point Data Path (FPDP) device and the NS32532 CPU to achieve a floating-point performance that complements the NS32532's 15 MIPS peak-integer performance. Due to a pipelined coprocessor interface and the floating-point controller design, this processor cluster achieves a peak floating-point performance of 15 MFLOPs for both single-precision (32-bit) and double-precision (64-bit) floating-point instructions, such as add, subtract and multiply. This high-performance is accomplished without sacrificing software compatibility with the previous Series 32000 processor clusters, including precise floating-point exceptions.

keywords:
Floating-Point Controller; Floating-Point Data Path; Floating-point performance; NS32532 CPU; NS32580; Pipelined coprocessor interface; Processor cluster; WTL3164

rawabstract:
The NS32580 Floating-Point Controller (FPC) teams with Weitek's WTL3164 Floating-Point Data Path (FPDP) device and the NS32532 CPU to achieve a floating-point performance that complements the NS32532's 15 MIPS peak-integer performance. Due to a pipelined coprocessor interface and the floating-point controller design, this processor cluster achieves a peak floating-point performance of 15 MFLOPs for both single-precision (32-bit) and double-precision (64-bit) floating-point instructions, such as add, subtract and multiply. This high-performance is accomplished without sacrificing software compatibility with the previous Series 32000 processor clusters, including precise floating-point exceptions.

entry:
@InProceedings{BenChorin:1988:NPC,
  author =       "S. Ben-Chorin",
  title =        "{NS32532-NS32580} processor cluster delivers high
                 floating-point performance",
  crossref =     "Midcon:1988:MCP",
  pages =        "243--248",
  year =         "1988",
  bibdate =      "Tue Dec 12 09:20:21 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The NS32580 Floating-Point Controller (FPC) teams with
                 Weitek's WTL3164 Floating-Point Data Path (FPDP) device
                 and the NS32532 CPU to achieve a floating-point
                 performance that complements the NS32532's 15 MIPS
                 peak-integer performance. Due to a pipelined
                 coprocessor interface and the floating-point controller
                 design, this processor cluster achieves a peak
                 floating-point performance of 15 MFLOPs for both
                 single-precision (32-bit) and double-precision (64-bit)
                 floating-point instructions, such as add, subtract and
                 multiply. This high-performance is accomplished without
                 sacrificing software compatibility with the previous
                 Series 32000 processor clusters, including precise
                 floating-point exceptions.",
  acknowledgement = ack-nhfb,
  affiliation =  "Nat. Semicond. Corp., Santa Clara, CA, USA",
  classification = "C5130 (Microprocessor chips); C5220 (Computer
                 architecture)",
  keywords =     "Floating-Point Controller; Floating-Point Data Path;
                 Floating-point performance; NS32532 CPU; NS32580;
                 Pipelined coprocessor interface; Processor cluster;
                 WTL3164",
  thesaurus =    "Computer architecture; Microprocessor chips",
}


bibtype: inproceedings
filename: fparith.bib
label: Bewick:1988:ANB
author: G. Bewick and P. Song and G. De Micheli and M. Flynn
title: Approaching a nanosecond: a 32-bit adder
crossref: IEEE:1988:PII
pages: 221--226
year: 1988
DOI: https://doi.org/10.1109/ICCD.1988.25695
bibdate: Mon Dec 24 09:52:15 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.12.24 09:52:15 ???
acknowledgement: ack-nhfb
rawauthor: G. Bewick and P. Song and G. De Micheli and M. Flynn
rawtitle: Approaching a nanosecond: a 32-bit adder
entry:
@InProceedings{Bewick:1988:ANB,
  author =       "G. Bewick and P. Song and G. De Micheli and M. Flynn",
  title =        "Approaching a nanosecond: a 32-bit adder",
  crossref =     "IEEE:1988:PII",
  pages =        "221--226",
  year =         "1988",
  DOI =          "https://doi.org/10.1109/ICCD.1988.25695",
  bibdate =      "Mon Dec 24 09:52:15 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Birman:1988:DHS
author: M. Birman and G. Chu and L. Hu and J. McLeod and N. Bedard and F. Ware and L. Torban and C. M. Lim
title: Design of a high-speed arithmetic datapath
crossref: IEEE:1988:PII
pages: 214--216
year: 1988
bibdate: Wed Sep 7 22:32:00 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 22:32:00 ???
acknowledgement: ack-nj
rawauthor: M. Birman and G. Chu and L. Hu and J. McLeod and N. Bedard and F. Ware and L. Torban and C. M. Lim
rawtitle: Design of a high-speed arithmetic datapath
entry:
@InProceedings{Birman:1988:DHS,
  author =       "M. Birman and G. Chu and L. Hu and J. McLeod and N.
                 Bedard and F. Ware and L. Torban and C. M. Lim",
  title =        "Design of a high-speed arithmetic datapath",
  crossref =     "IEEE:1988:PII",
  pages =        "214--216",
  year =         "1988",
  bibdate =      "Wed Sep 7 22:32:00 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: Blaker:1988:FPB
author: David Mark Blaker
title: Floating point bit-sequential arithmetic units
type: Thesis (M.S.)
school: Lehigh University
address: Bethlehem, PA, USA
pages: vi + 73
year: 1988
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Computer arithmetic.; Floating-point arithmetic.
acknowledgement: ack-nhfb
rawauthor: David Mark Blaker
rawtitle: Floating point bit-sequential arithmetic units
entry:
@MastersThesis{Blaker:1988:FPB,
  author =       "David Mark Blaker",
  title =        "Floating point bit-sequential arithmetic units",
  type =         "Thesis ({M.S.})",
  school =       "Lehigh University",
  address =      "Bethlehem, PA, USA",
  pages =        "vi + 73",
  year =         "1988",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer arithmetic.; Floating-point arithmetic.",
}


bibtype: article
filename: fparith.bib
label: Bohlender:1988:IFA
author: Gerd Bohlender
title: Is floating-point arithmetic still adequate?
journal: Systems analysis and simulation
volume: 46
publisher: Akademie-Verlag
address: Berlin, Germany
pages: 105--108
year: 1988
MRclass: 68N15 (65G99)
MRnumber: 976 389
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 ???
acknowledgement: ack-nhfb
rawauthor: Gerd Bohlender
rawtitle: Is floating-point arithmetic still adequate?
entry:
@Article{Bohlender:1988:IFA,
  author =       "Gerd Bohlender",
  title =        "Is floating-point arithmetic still adequate?",
  journal =      "Systems analysis and simulation",
  volume =       "46",
  publisher =    "Akademie-Verlag",
  address =      "Berlin, Germany",
  pages =        "105--108",
  year =         "1988",
  MRclass =      "68N15 (65G99)",
  MRnumber =     "976 389",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  xxjournal =    "Math. Res.",
  xxx =          "I (Berlin, 1988)",
}


bibtype: techreport
filename: fparith.bib
label: Bose:1988:VDT
author: Bidyut Kumar Bose
title: VLSI design techniques for floating-point computation
type: Report
number: UCB/CSD 88/469
institution: University of California, Berkeley, Computer Science Division
address: Berkeley, CA, USA
pages: vi + 173
year: 1988
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Floating-point arithmetic.; Integrated circuits --- Very large scale integration.
acknowledgement: ack-nhfb
rawauthor: Bidyut Kumar Bose
rawtitle: {VLSI} design techniques for floating-point computation
entry:
@TechReport{Bose:1988:VDT,
  author =       "Bidyut Kumar Bose",
  title =        "{VLSI} design techniques for floating-point
                 computation",
  type =         "Report",
  number =       "UCB/CSD 88/469",
  institution =  "University of California, Berkeley, Computer Science
                 Division",
  address =      "Berkeley, CA, USA",
  pages =        "vi + 173",
  year =         "1988",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.; Integrated circuits ---
                 Very large scale integration.",
}


bibtype: mastersthesis
filename: fparith.bib
label: Brooks:1988:VIF
author: Kelvin R. Brooks
title: The VLSI implementation of a floating-point multiplier
type: Thesis (M.S.)
school: North Carolina A&T State University
address: Greensboro, NC, USA
pages: x + 78
year: 1988
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: Electric engineering.; Integrated circuits --- Very large scale integration.
acknowledgement: ack-nhfb
rawauthor: Kelvin R. Brooks
rawtitle: The {VLSI} implementation of a floating-point multiplier
entry:
@MastersThesis{Brooks:1988:VIF,
  author =       "Kelvin R. Brooks",
  title =        "The {VLSI} implementation of a floating-point
                 multiplier",
  type =         "Thesis ({M.S.})",
  school =       "North Carolina A\&T State University",
  address =      "Greensboro, NC, USA",
  pages =        "x + 78",
  year =         "1988",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Electric engineering.; Integrated circuits --- Very
                 large scale integration.",
}


bibtype: article
filename: fparith.bib
label: Brosnan:1988:MED
author: T. J. Brosnan and N. R. Strader II
title: Modular error detection for bit-serial multiplication
journal: j-IEEE-TRANS-COMPUT
volume: 37
number: 9
pages: 1043--1052
month: sep
monthnumber: 9
year: 1988
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.2255
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 9 08:33:28 MDT 2011
bibtimestamp: 2011.07.09 08:33:28 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2255
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: T. J. Brosnan and N. R. {Strader II}
rawtitle: Modular error detection for bit-serial multiplication
entry:
@Article{Brosnan:1988:MED,
  author =       "T. J. Brosnan and N. R. {Strader II}",
  title =        "Modular error detection for bit-serial
                 multiplication",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "37",
  number =       "9",
  pages =        "1043--1052",
  month =        sep,
  year =         "1988",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.2255",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 08:33:28 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2255",
  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: Byington:1988:HGB
author: Carl Byington
title: How to get better floating-point results
journal: j-BYTE
volume: 13
number: 3
pages: 229--236
month: mar
monthnumber: 3
year: 1988
CODEN: BYTEDJ
ISSN: 0360-5280 (print), 1082-7838 (electronic) OR 03605280 (print), 10827838 (electronic)
ISSNL: 0360-5280 OR 03605280
bibdate: Sat Nov 9 08:26:18 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.11.09 08:26:18 MST
fjournal: BYTE Magazine
acknowledgement: ack-nhfb
rawauthor: Carl Byington
rawtitle: How to get better floating-point results
subject:
C. Computer Systems Organization; C.5 COMPUTER SYSTEM IMPLEMENTATION; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; D. Software; D.1 PROGRAMMING TECHNIQUES

entry:
@Article{Byington:1988:HGB,
  author =       "Carl Byington",
  title =        "How to get better floating-point results",
  journal =      j-BYTE,
  volume =       "13",
  number =       "3",
  pages =        "229--236",
  month =        mar,
  year =         "1988",
  CODEN =        "BYTEDJ",
  ISSN =         "0360-5280 (print), 1082-7838 (electronic)",
  ISSN-L =       "0360-5280",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  bibno =        "44973",
  catcode =      "C.5.3; G.1.0; D.1.m",
  CRclass =      "C.5.3 Microcomputers; G.1.0 General; G.1.0 Computer
                 arithmetic; D.1.m Miscellaneous",
  descriptor =   "Computer Systems Organization, COMPUTER SYSTEM
                 IMPLEMENTATION, Microcomputers; Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Computer
                 arithmetic; Software, PROGRAMMING TECHNIQUES,
                 Miscellaneous",
  fjournal =     "BYTE Magazine",
  genterm =      "DESIGN; RELIABILITY",
  guideno =      "1988-05276",
  subject =      "C. Computer Systems Organization; C.5 COMPUTER SYSTEM
                 IMPLEMENTATION; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS; D. Software; D.1 PROGRAMMING
                 TECHNIQUES",
}


bibtype: article
filename: fparith.bib
label: Callahan:1988:EII
author: D. Callahan and J. Cocke and K. Kennedy
title: Estimating interlock and improving balance for pipelined architectures
journal: j-J-PAR-DIST-COMP
volume: 5
number: 4
pages: 334--358
month: aug
monthnumber: 8
year: 1988
CODEN: JPDCER
ISSN: 0743-7315 (print), 1096-0848 (electronic) OR 07437315 (print), 10960848 (electronic)
ISSNL: 0743-7315 OR 07437315
bibdate: Sat Apr 12 17:13:17 MDT 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.04.12 17:13:17 MDT
fjournal: Journal of Parallel and Distributed Computing
acknowledgement: ack-nhfb
corpsource: Department of Computer Science, Rice University, Houston, TX, USA
journalURL: http://www.sciencedirect.com/science/journal/07437315
treatment: P Practical
rawauthor: D. Callahan and J. Cocke and K. Kennedy
rawtitle: Estimating interlock and improving balance for pipelined architectures
keywords:
arithmetic; bandwidth; digital arithmetic; DO loops; execution order constraints; fine-grain parallelism; floating-point; memory; parallel architectures; pipeline; pipeline balance; pipeline interlock; pipelined architectures; processing

entry:
@Article{Callahan:1988:EII,
  author =       "D. Callahan and J. Cocke and K. Kennedy",
  title =        "Estimating interlock and improving balance for
                 pipelined architectures",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "5",
  number =       "4",
  pages =        "334--358",
  month =        aug,
  year =         "1988",
  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 = "C5220 (Computer architecture); C5230 (Digital
                 arithmetic methods)",
  corpsource =   "Department of Computer Science, Rice University,
                 Houston, TX, USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  keywords =     "arithmetic; bandwidth; digital arithmetic; DO loops;
                 execution order constraints; fine-grain parallelism;
                 floating-point; memory; parallel architectures;
                 pipeline; pipeline balance; pipeline interlock;
                 pipelined architectures; processing",
  treatment =    "P Practical",
}


bibtype: article
filename: fparith.bib
label: Capocelli:1988:EVN
author: R. M. Capocelli and R. Giancarlo
journal: j-IEEE-TRANS-CIRCUITS-SYST
volume: 35
number: 11
pages: 1425--1430
month: nov
monthnumber: 11
year: 1988
CODEN: ICSYBT
DOI: https://doi.org/10.1109/31.14466
ISSN: 0098-4094 (print), 1558-1276 (electronic) OR 00984094 (print), 15581276 (electronic)
ISSNL: 0098-4094 OR 00984094
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=565
fjournal: IEEE Transactions on Circuits and Systems
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: R. M. Capocelli and R. Giancarlo
title:
Efficient VLSI networks for converting an integer from binary system to residue number system and vice versa

rawtitle:
Efficient {VLSI} networks for converting an integer from binary system to residue number system and vice versa

entry:
@Article{Capocelli:1988:EVN,
  author =       "R. M. Capocelli and R. Giancarlo",
  title =        "Efficient {VLSI} networks for converting an integer
                 from binary system to residue number system and vice
                 versa",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "35",
  number =       "11",
  pages =        "1425--1430",
  month =        nov,
  year =         "1988",
  CODEN =        "ICSYBT",
  DOI =          "https://doi.org/10.1109/31.14466",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  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=565",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  keywords =     "residue arithmetic; residue number system",
  summary =      "VLSI networks for converting integers from binary to
                 residue number systems are presented Both direct and
                 reverse conversion are treated. The networks are
                 improvements, with respect to area or time or both, of
                 previously proposed \ldots{}",
}


bibtype: techreport
filename: fparith.bib
label: Cappello:1988:SSSa
author: Peter R. Cappello and Willard L. Miranker
title: Systolic super summation with reduced hardware
type: Technical report
number: TRCS88-27
institution: University of California, Santa Barbara, College of Engineering Department of Computer Science
address: Santa Barbara, CA, USA
pages: 8
year: 1988
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: accurate floating-point summation; computer science --- mathematics; floating-point arithmetic
acknowledgement: ack-nhfb
rawauthor: Peter R. Cappello and Willard L. Miranker
rawtitle: Systolic super summation with reduced hardware
remark:
``A principle limitation in accuracy for scientific computation performed with floating-point arithmetic may be traced to the computation of repeated sums, such as those which arise in inner products. A design is proposed for a systolic super summer, a cellular piece of hardware for the summation of floating-point numbers. The apparatus receives floating-point summands, converting them into a fixed-point form by a sieve-like cellular array. The emerging fixed-point numbers then are summed in a pipelined array of long accumulators. The architectural regularity of the sieve makes it ideal for implementation in VLSI circuit technology.'' Supported by the Office of Naval Research.

entry:
@TechReport{Cappello:1988:SSSa,
  author =       "Peter R. Cappello and Willard L. Miranker",
  title =        "Systolic super summation with reduced hardware",
  type =         "Technical report",
  number =       "TRCS88-27",
  institution =  "University of California, Santa Barbara, College of
                 Engineering Department of Computer Science",
  address =      "Santa Barbara, CA, USA",
  pages =        "8",
  year =         "1988",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation; computer science
                 --- mathematics; floating-point arithmetic",
  remark =       "``A principle limitation in accuracy for scientific
                 computation performed with floating-point arithmetic
                 may be traced to the computation of repeated sums, such
                 as those which arise in inner products. A design is
                 proposed for a systolic super summer, a cellular piece
                 of hardware for the summation of floating-point
                 numbers. The apparatus receives floating-point
                 summands, converting them into a fixed-point form by a
                 sieve-like cellular array. The emerging fixed-point
                 numbers then are summed in a pipelined array of long
                 accumulators. The architectural regularity of the sieve
                 makes it ideal for implementation in VLSI circuit
                 technology.'' Supported by the Office of Naval
                 Research.",
}


bibtype: misc
filename: fparith.bib
label: Cappello:1988:SSSb
author: Peter R. Cappello and Willard L. Miranker
title: Systolic super summation device
pages: 8
day: 14
month: jun
monthnumber: 6
year: 1988
bibdate: Mon Dec 29 16:20:01 2008
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2008.12.29 16:20:01 ???
URL: http://www.patentstorm.us/patents/4751665/fulltext.html
acknowledgement: ack-nhfb
howpublished: US Patent 4751665
rawauthor: Peter R. Cappello and Willard L. Miranker
rawtitle: Systolic super summation device
abstract:
A cellular architecture for a systolic super summer for high throughput performance of repeated sums of floating-point numbers. The summer receives pipelined inputs of streams of summands, converts the floating-point summands into a fixed-point form by a sieve-like pipelined cellular network, and sums the emerging fixed-point numbers in a corresponding network of extremely long accumulators. The throughput per unit area of the hardware approaches that of a tree network, but without the long wires and signal propagation that are intrinsic to tree networks.

rawabstract:
A cellular architecture for a systolic super summer for high throughput performance of repeated sums of floating-point numbers. The summer receives pipelined inputs of streams of summands, converts the floating-point summands into a fixed-point form by a sieve-like pipelined cellular network, and sums the emerging fixed-point numbers in a corresponding network of extremely long accumulators. The throughput per unit area of the hardware approaches that of a tree network, but without the long wires and signal propagation that are intrinsic to tree networks.

entry:
@Misc{Cappello:1988:SSSb,
  author =       "Peter R. Cappello and Willard L. Miranker",
  title =        "Systolic super summation device",
  howpublished = "US Patent 4751665",
  day =          "14",
  month =        jun,
  year =         "1988",
  bibdate =      "Mon Dec 29 16:20:01 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.patentstorm.us/patents/4751665/fulltext.html",
  abstract =     "A cellular architecture for a systolic super summer
                 for high throughput performance of repeated sums of
                 floating-point numbers. The summer receives pipelined
                 inputs of streams of summands, converts the
                 floating-point summands into a fixed-point form by a
                 sieve-like pipelined cellular network, and sums the
                 emerging fixed-point numbers in a corresponding network
                 of extremely long accumulators. The throughput per unit
                 area of the hardware approaches that of a tree network,
                 but without the long wires and signal propagation that
                 are intrinsic to tree networks.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Capps:1988:OAL
author: C. David Capps and R. Aaron Falk and Theodore L. Houk
title: Optical Arithmetic / Logic Unit Based on Residue Arithmetic and Symbolic Substitution
journal: j-APPL-OPTICS
volume: 27
number: 9
pages: 1682--1686
month: may
monthnumber: 5
year: 1988
CODEN: APOPAI
ISSN: 0003-6935 OR 00036935
bibdate: Fri Jun 24 18:13:20 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.06.24 18:13:20 ???
fjournal: Applied Optics
acknowledgement: ack-nhfb
journalURL: http://www.osapublishing.org/ao/browse.cfm
rawauthor: C. David Capps and R. Aaron Falk and Theodore L. Houk
rawtitle: Optical Arithmetic\slash Logic Unit Based on Residue Arithmetic and Symbolic Substitution
abstract:
There has been difficulty in achieving a fully parallel, digital optical adder or multiplier. The primary obstacle is the carry operation inherent in any fixed-radix number system. The concepts of residue number representation and symbolic substitution can be combined to produce a parallel optical arithmetic/logic unit.

rawabstract:
There has been difficulty in achieving a fully parallel, digital optical adder or multiplier. The primary obstacle is the carry operation inherent in any fixed-radix number system. The concepts of residue number representation and symbolic substitution can be combined to produce a parallel optical arithmetic/logic unit.

entry:
@Article{Capps:1988:OAL,
  author =       "C. David Capps and R. Aaron Falk and Theodore L.
                 Houk",
  title =        "Optical Arithmetic\slash Logic Unit Based on Residue
                 Arithmetic and Symbolic Substitution",
  journal =      j-APPL-OPTICS,
  volume =       "27",
  number =       "9",
  pages =        "1682--1686",
  month =        may,
  year =         "1988",
  CODEN =        "APOPAI",
  ISSN =         "0003-6935",
  bibdate =      "Fri Jun 24 18:13:20 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "There has been difficulty in achieving a fully
                 parallel, digital optical adder or multiplier. The
                 primary obstacle is the carry operation inherent in any
                 fixed-radix number system. The concepts of residue
                 number representation and symbolic substitution can be
                 combined to produce a parallel optical arithmetic/logic
                 unit.",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Optics",
  journal-URL =  "http://www.osapublishing.org/ao/browse.cfm",
}


bibtype: article
filename: fparith.bib
label: Cardarilli:1988:SPD
author: G. C. Cardarilli and R. Lojacono and G. Martinelli and M. Salerno
title: Structurally passive digital filters in residue number systems
journal: j-IEEE-TRANS-CIRCUITS-SYST
volume: 35
number: 2
pages: 149--158
month: feb
monthnumber: 2
year: 1988
CODEN: ICSYBT
DOI: https://doi.org/10.1109/31.1716
ISSN: 0098-4094 (print), 1558-1276 (electronic) OR 00984094 (print), 15581276 (electronic)
ISSNL: 0098-4094 OR 00984094
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=107
fjournal: IEEE Transactions on Circuits and Systems
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: G. C. Cardarilli and R. Lojacono and G. Martinelli and M. Salerno
rawtitle: Structurally passive digital filters in residue number systems
entry:
@Article{Cardarilli:1988:SPD,
  author =       "G. C. Cardarilli and R. Lojacono and G. Martinelli and
                 M. Salerno",
  title =        "Structurally passive digital filters in residue number
                 systems",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "35",
  number =       "2",
  pages =        "149--158",
  month =        feb,
  year =         "1988",
  CODEN =        "ICSYBT",
  DOI =          "https://doi.org/10.1109/31.1716",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  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=107",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  keywords =     "residue arithmetic; residue number system",
  summary =      "The possibility of realizing structural passive
                 digital filters in terms of residue number systems
                 (RNS) is considered. For this purpose, an algorithm is
                 proposed for realizing the RNS rotator, which
                 represents the basic element of these filters.
                 \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Cavallaro:1988:CAS
author: Joseph R. Cavallaro and Franklin T. Luk
title: CORDIC arithmetic for an SVD processor
journal: j-J-PAR-DIST-COMP
volume: 5
number: 3
pages: 271--290
month: jun
monthnumber: 6
year: 1988
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
bibtimestamp: 1997.04.12 19:06:31 MDT
fjournal: Journal of Parallel and Distributed Computing
acknowledgement: ack-nhfb
affiliationaddress: Cornell Univ, Ithaca, NY, USA
corpsource: Sch. of Electr. Eng., Cornell University, NY, USA
journalURL: http://www.sciencedirect.com/science/journal/07437315
journalabr: J Parallel Distrib Comput
treatment: P Practical
rawauthor: Joseph R. Cavallaro and Franklin T. Luk
rawtitle: {CORDIC} arithmetic for an {SVD} processor
bibsource:
Compendex database; https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

keywords:
Algorithms; computer architecture; computer programming; computers, digital --- Computational Methods; CORDIC arithmetic; Decomposition; digital arithmetic; hardware division; inverse tangents; mathematical techniques --- Algorithms; parallel processing; real-time; rotations; signal processing applications; Singular Value; singular value decomposition; special-purpose arithmetic techniques; square root; SVD processor; vector; vector rotations; VLSI implementation

entry:
@Article{Cavallaro:1988:CAS,
  author =       "Joseph R. Cavallaro and Franklin T. Luk",
  title =        "{CORDIC} arithmetic for an {SVD} processor",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "5",
  number =       "3",
  pages =        "271--290",
  month =        jun,
  year =         "1988",
  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/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliationaddress = "Cornell Univ, Ithaca, NY, USA",
  classification = "721; 722; 723; 921; C5230 (Digital arithmetic
                 methods); C5440 (Multiprocessor systems and
                 techniques)",
  corpsource =   "Sch. of Electr. Eng., Cornell University, NY, USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "Algorithms; computer architecture; computer
                 programming; computers, digital --- Computational
                 Methods; CORDIC arithmetic; Decomposition; digital
                 arithmetic; hardware division; inverse tangents;
                 mathematical techniques --- Algorithms; parallel
                 processing; real-time; rotations; signal processing
                 applications; Singular Value; singular value
                 decomposition; special-purpose arithmetic techniques;
                 square root; SVD processor; vector; vector rotations;
                 VLSI implementation",
  treatment =    "P Practical",
}


bibtype: inproceedings
filename: fparith.bib
label: Cavallaro:1988:FPC
author: J. R. Cavallaro and F. T. Luk
booktitle: Proceedings 1988 IEEE International Conference on Computer Design: VLSI
title: Floating point CORDIC for matrix computations
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 40--42
year: 1988
DOI: https://doi.org/10.1109/ICCD.1988.25655
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: J. R. Cavallaro and F. T. Luk
rawbooktitle: {Proceedings 1988 IEEE International Conference on Computer Design: VLSI}
rawtitle: Floating point {CORDIC} for matrix computations
keywords:
Adders; Equations; Floating-point arithmetic; Hardware; Matrix decomposition; Read only memory; Registers; Signal processing algorithms; Singular value decomposition; Very large scale integration

entry:
@InProceedings{Cavallaro:1988:FPC,
  author =       "J. R. Cavallaro and F. T. Luk",
  booktitle =    "{Proceedings 1988 IEEE International Conference on
                 Computer Design: VLSI}",
  title =        "Floating point {CORDIC} for matrix computations",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "40--42",
  year =         "1988",
  DOI =          "https://doi.org/10.1109/ICCD.1988.25655",
  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; Equations; Floating-point arithmetic;
                 Hardware; Matrix decomposition; Read only memory;
                 Registers; Signal processing algorithms; Singular value
                 decomposition; Very large scale integration",
}


bibtype: article
filename: fparith.bib
label: Chaitin:1988:RA
author: Gregory J. Chaitin
title: Randomness in Arithmetic
journal: j-SCI-AMER
volume: 259
number: 1
pages: 80--85 (Intl. ed. 52--57)
month: jul
monthnumber: 7
year: 1988
CODEN: SCAMAC
DOI: https://doi.org/10.1038/scientificamerican0788-80
ISSN: 0036-8733 (print), 1946-7087 (electronic) OR 00368733 (print), 19467087 (electronic)
ISSNL: 0036-8733 OR 00368733
bibdate: Wed May 22 15:04:14 MDT 2013
bibtimestamp: 2013.05.22 15:04:14 MDT
URL: http://www.nature.com/scientificamerican/journal/v259/n1/pdf/scientificamerican0788-80.pdf
fjournal: Scientific American
remark: (VBI-001989)
acknowledgement: ack-nhfb
journalURL: http://www.nature.com/scientificamerican
rawauthor: Gregory J. Chaitin
rawtitle: Randomness in Arithmetic
bibsource:
Distributed/QLD/1988.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/sciam1980.bib

keywords:
algorithmic information theory; computability theory; halting problem; incompleteness theorem; number theory; Pascal's triangle; randomness

entry:
@Article{Chaitin:1988:RA,
  author =       "Gregory J. Chaitin",
  title =        "Randomness in Arithmetic",
  journal =      j-SCI-AMER,
  volume =       "259",
  number =       "1",
  pages =        "80--85 (Intl. ed. 52--57)",
  month =        jul,
  year =         "1988",
  CODEN =        "SCAMAC",
  DOI =          "https://doi.org/10.1038/scientificamerican0788-80",
  ISSN =         "0036-8733 (print), 1946-7087 (electronic)",
  ISSN-L =       "0036-8733",
  bibdate =      "Wed May 22 15:04:14 MDT 2013",
  bibsource =    "Distributed/QLD/1988.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sciam1980.bib",
  URL =          "http://www.nature.com/scientificamerican/journal/v259/n1/pdf/scientificamerican0788-80.pdf",
  acknowledgement = ack-nhfb,
  country =      "USA",
  date =         "01/07/93",
  descriptors =  "Randomness; Arithmetic",
  enum =         "9449",
  fjournal =     "Scientific American",
  journal-URL =  "http://www.nature.com/scientificamerican",
  keywords =     "algorithmic information theory; computability theory;
                 halting problem; incompleteness theorem; number theory;
                 Pascal's triangle; randomness",
  remark =       "(VBI-001989)",
  xxnewdata =    "1998.01.30",
}


bibtype: article
filename: fparith.bib
label: Chen:1988:GCM
author: M. C. Chen
title: The generation of a class of multipliers: synthesizing highly parallel algorithms in VLSI
journal: j-IEEE-TRANS-COMPUT
volume: 37
number: 3
pages: 329--338
month: mar
monthnumber: 3
year: 1988
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.2170
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 9 08:33:25 MDT 2011
bibtimestamp: 2011.07.09 08:33:25 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2170
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: M. C. Chen
rawtitle: The generation of a class of multipliers: synthesizing highly parallel algorithms in {VLSI}
entry:
@Article{Chen:1988:GCM,
  author =       "M. C. Chen",
  title =        "The generation of a class of multipliers: synthesizing
                 highly parallel algorithms in {VLSI}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "37",
  number =       "3",
  pages =        "329--338",
  month =        mar,
  year =         "1988",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.2170",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 08:33:25 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2170",
  acknowledgement = 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: Cheng:1988:ATM
author: Kuo-kuang Cheng and Robert R. Seban
title: Algorithm theory and the microarchitecture of an optimal VLSI floating point divider
address: Tempe, AZ, USA
pages: 17
year: 1988
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
remark: ``December 22, 1988.''
acknowledgement: ack-nhfb
rawauthor: Kuo-kuang Cheng and Robert R. Seban
rawtitle: Algorithm theory and the microarchitecture of an optimal {VLSI} floating point divider
institution:
Department of Computer Science, College of Engineering and Applied Sciences, Arizona State University

series:
CR-R; 89028 TR; 88-032 Report (Arizona State University. College of Engineering and Applied Sciences); 89:28. Technical report (Arizona State University. Department of Computer Science); 88-032.

entry:
@TechReport{Cheng:1988:ATM,
  author =       "Kuo-kuang Cheng and Robert R. Seban",
  title =        "Algorithm theory and the microarchitecture of an
                 optimal {VLSI} floating point divider",
  institution =  "Department of Computer Science, College of Engineering
                 and Applied Sciences, Arizona State University",
  address =      "Tempe, AZ, USA",
  pages =        "17",
  year =         "1988",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "CR-R; 89028 TR; 88-032 Report (Arizona State
                 University. College of Engineering and Applied
                 Sciences); 89:28. Technical report (Arizona State
                 University. Department of Computer Science); 88-032.",
  acknowledgement = ack-nhfb,
  remark =       "``December 22, 1988.''",
}


bibtype: article
filename: fparith.bib
label: Cody:1988:AMS
author: W. J. Cody
title: Algorithm 665: MACHAR: a Subroutine to Dynamically Determine Machine Parameters
journal: j-TOMS
volume: 14
number: 4
pages: 303--311
month: dec
monthnumber: 12
year: 1988
CODEN: ACMSCU
DOI: https://doi.org/10.1145/50063.51907
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sun Sep 04 22:33:58 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.04 22:33:58 ???
URL: http://www.acm.org/pubs/citations/journals/toms/1988-14-4/p303-cody/
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/toms
rawauthor: W. J. Cody
rawtitle: {Algorithm 665}: {MACHAR}: a Subroutine to Dynamically Determine Machine Parameters
subject:
bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Portability. bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic.

entry:
@Article{Cody:1988:AMS,
  author =       "W. J. Cody",
  title =        "{Algorithm 665}: {MACHAR}: a Subroutine to Dynamically
                 Determine Machine Parameters",
  journal =      j-TOMS,
  volume =       "14",
  number =       "4",
  pages =        "303--311",
  month =        dec,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/50063.51907",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 22:33:58 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/1988-14-4/p303-cody/",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Portability. {\bf G.1.0}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Computer
                 arithmetic.",
}


bibtype: incollection
filename: fparith.bib
label: Cody:1988:FPS
author: W. J. Cody
title: Floating-point standards --- theory and practice
crossref: Moore:1988:RCR
pages: 99--107
year: 1988
bibdate: Sat Nov 9 08:26:18 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.11.09 08:26:18 MST
subject: B. Hardware; B.7 INTEGRATED CIRCUITS; K. Computing Milieux; K.1 THE COMPUTER INDUSTRY
acknowledgement: ack-nhfb
affiliation: Argonne National Laboratory, Argonne, IL
rawauthor: W. J. Cody
rawtitle: Floating-point standards --- theory and practice
entry:
@InCollection{Cody:1988:FPS,
  author =       "W. J. Cody",
  title =        "Floating-point standards --- theory and practice",
  crossref =     "Moore:1988:RCR",
  pages =        "99--107",
  year =         "1988",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Argonne National Laboratory, Argonne, IL",
  bibno =        "60186",
  catcode =      "B.7.1; K.1",
  CRclass =      "B.7.1 Types and Design Styles; K.1 Standards",
  descriptor =   "Hardware, INTEGRATED CIRCUITS, Types and Design
                 Styles; Computing Milieux, THE COMPUTER INDUSTRY,
                 Standards",
  genterm =      "THEORY; RELIABILITY; STANDARDIZATION; RELIABILITY",
  guideno =      "1988-01977",
  subject =      "B. Hardware; B.7 INTEGRATED CIRCUITS; K. Computing
                 Milieux; K.1 THE COMPUTER INDUSTRY",
  waffil =       "Ohio State University, Columbus",
}


bibtype: article
filename: fparith.bib
label: Cosentino:1988:FTS
author: R. J. Cosentino
title: Fault tolerance in a systolic residue arithmetic processor array
journal: j-IEEE-TRANS-COMPUT
volume: 37
number: 7
pages: 886--890
month: jul
monthnumber: 7
year: 1988
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.2239
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 9 08:33:27 MDT 2011
bibtimestamp: 2011.07.09 08:33:27 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2239
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: R. J. Cosentino
rawtitle: Fault tolerance in a systolic residue arithmetic processor array
entry:
@Article{Cosentino:1988:FTS,
  author =       "R. J. Cosentino",
  title =        "Fault tolerance in a systolic residue arithmetic
                 processor array",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "37",
  number =       "7",
  pages =        "886--890",
  month =        jul,
  year =         "1988",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.2239",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 08:33:27 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2239",
  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: Davila:1988:FPA
author: J. M. Davila and A. J. Phillips and D. Tabak
title: Floating Point Arithmetic on a RISC
journal: j-MICROPROC-MICROPROG
volume: 23
number: 1--5
pages: 179--184
month: mar
monthnumber: 3
year: 1988
CODEN: MMICDT
ISSN: 0165-6074 (print), 1878-7061 (electronic) OR 01656074 (print), 18787061 (electronic)
ISSNL: 0165-6074 OR 01656074
bibdate: Thu Sep 1 10:15:06 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 10:15:06 ???
fjournal: Microprocessing and Microprogramming
acknowledgement: ack-nj
journalURL: https://www.sciencedirect.com/journal/microprocessing-and-microprogramming/issues
rawauthor: J. M. Davila and A. J. Phillips and D. Tabak
rawtitle: Floating Point Arithmetic on a {RISC}
entry:
@Article{Davila:1988:FPA,
  author =       "J. M. Davila and A. J. Phillips and D. Tabak",
  title =        "Floating Point Arithmetic on a {RISC}",
  journal =      j-MICROPROC-MICROPROG,
  volume =       "23",
  number =       "1--5",
  pages =        "179--184",
  month =        mar,
  year =         "1988",
  CODEN =        "MMICDT",
  ISSN =         "0165-6074 (print), 1878-7061 (electronic)",
  ISSN-L =       "0165-6074",
  bibdate =      "Thu Sep 1 10:15:06 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 =     "Microprocessing and Microprogramming",
  journal-URL =  "https://www.sciencedirect.com/journal/microprocessing-and-microprogramming/issues",
}


bibtype: inproceedings
filename: fparith.bib
label: deLange:1988:OFP
author: A. A. J. de Lange and A. J. van der Hoeven and E. F. Deprettere and J. Bu
booktitle: 1988., IEEE International Symposium on Circuits and Systems
title: An optimal floating-point pipeline CMOS CORDIC processor
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 2043--2047 (vol. 3)
year: 1988
DOI: https://doi.org/10.1109/ISCAS.1988.15343
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: A. A. J. de Lange and A. J. van der Hoeven and E. F. Deprettere and J. Bu
rawbooktitle: {1988., IEEE International Symposium on Circuits and Systems}
rawtitle: An optimal floating-point pipeline {CMOS} {CORDIC} processor
keywords:
Algorithm design and analysis; Analytical models; Circuit simulation; CMOS process; Design methodology; Macrocell networks; Pipelines; Signal processing algorithms; Silicon compiler; Very large scale integration

entry:
@InProceedings{deLange:1988:OFP,
  author =       "A. A. J. de Lange and A. J. van der Hoeven and E. F.
                 Deprettere and J. Bu",
  booktitle =    "{1988., IEEE International Symposium on Circuits and
                 Systems}",
  title =        "An optimal floating-point pipeline {CMOS} {CORDIC}
                 processor",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "2043--2047 (vol. 3)",
  year =         "1988",
  DOI =          "https://doi.org/10.1109/ISCAS.1988.15343",
  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 =     "Algorithm design and analysis; Analytical models;
                 Circuit simulation; CMOS process; Design methodology;
                 Macrocell networks; Pipelines; Signal processing
                 algorithms; Silicon compiler; Very large scale
                 integration",
}


bibtype: mastersthesis
filename: fparith.bib
label: Duerksen:1988:CAP
author: Joel L. Duerksen
type: Thesis (M.S.)
school: Department of Computer Science, Ball State University
address: Muncie, IN 47306, USA
pages: ix + 206
year: 1988
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Algorithms.; Computer graphics.
acknowledgement: ack-nhfb
rawauthor: Joel L. Duerksen
title:
A comparative analysis of the performance of floating point and integer based line drawing algorithms for raster displays

rawtitle:
A comparative analysis of the performance of floating point and integer based line drawing algorithms for raster displays

entry:
@MastersThesis{Duerksen:1988:CAP,
  author =       "Joel L. Duerksen",
  title =        "A comparative analysis of the performance of floating
                 point and integer based line drawing algorithms for
                 raster displays",
  type =         "Thesis ({M.S.})",
  school =       "Department of Computer Science, Ball State
                 University",
  address =      "Muncie, IN 47306, USA",
  pages =        "ix + 206",
  year =         "1988",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Algorithms.; Computer graphics.",
}


bibtype: article
filename: fparith.bib
label: Dunham:1988:PMA
author: C. B. Dunham
title: Provably Monotone Approximations III
journal: j-SIGNUM
volume: 23
number: 1
pages: 10--10
month: jan
monthnumber: 1
year: 1988
CODEN: SNEWD6
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Tue Sep 13 09:05:50 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.13 09:05:50 ???
fjournal: ACM SIGNUM Newsletter
keywords: theory
subject: G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS, Approximation
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/signum
rawauthor: C. B. Dunham
rawtitle: Provably Monotone Approximations {III}
entry:
@Article{Dunham:1988:PMA,
  author =       "C. B. Dunham",
  title =        "Provably Monotone Approximations {III}",
  journal =      j-SIGNUM,
  volume =       "23",
  number =       "1",
  pages =        "10--10",
  month =        jan,
  year =         "1988",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Sep 13 09:05:50 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "theory",
  subject =      "G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation",
}


bibtype: article
filename: fparith.bib
label: Duprat:1988:HPE
author: Jean Duprat and Jean-Michel Muller
title: Hardwired polynomial evaluation
journal: j-J-PAR-DIST-COMP
volume: 5
number: 3
pages: 291--309
month: jun
monthnumber: 6
year: 1988
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
affiliationaddress: CNRS, Grenoble, Fr
corpsource: Inst. Nat. Polytech. de Grenoble, France
journalURL: http://www.sciencedirect.com/science/journal/07437315
journalabr: J Parallel Distrib Comput
treatment: P Practical
rawauthor: Jean Duprat and Jean-Michel Muller
rawtitle: Hardwired polynomial evaluation
keywords:
computer architecture; computers, digital --- Circuits; digital arithmetic; elementary functions; hardwired polynomial evaluation; mathematical functions; mathematical techniques; Polynomials; polynomials; special-purpose circuits; VLSI implementation

entry:
@Article{Duprat:1988:HPE,
  author =       "Jean Duprat and Jean-Michel Muller",
  title =        "Hardwired polynomial evaluation",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "5",
  number =       "3",
  pages =        "291--309",
  month =        jun,
  year =         "1988",
  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,
  affiliationaddress = "CNRS, Grenoble, Fr",
  classification = "721; 722; 723; 921; C4130 (Interpolation and
                 function approximation); C5230 (Digital arithmetic
                 methods)",
  corpsource =   "Inst. Nat. Polytech. de Grenoble, France",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
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  treatment =    "P Practical",
}


bibtype: inproceedings
filename: fparith.bib
label: Ercegovac:1988:LAD
author: M. D. Ercegovac and T. Lang
title: On-Line Arithmetic: a Design Methodology and Applications in Digital Signal Processing
crossref: Brodersen:1988:VSP
volume: 3
pages: 252--263
year: 1988
bibdate: Fri Dec 08 10:42:22 2006
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2006.12.08 10:42:22 ???
note: Reprinted in cite [66--77]Swartzlander:1990:CAb.
acknowledgement: ack-nhfb
rawauthor: M. D. Ercegovac and T. Lang
rawnote: Reprinted in \cite[66--77]{Swartzlander:1990:CAb}.
rawtitle: On-Line Arithmetic: a Design Methodology and Applications in Digital Signal Processing
entry:
@InProceedings{Ercegovac:1988:LAD,
  author =       "M. D. Ercegovac and T. Lang",
  title =        "On-Line Arithmetic: a Design Methodology and
                 Applications in Digital Signal Processing",
  crossref =     "Brodersen:1988:VSP",
  volume =       "3",
  pages =        "252--263",
  year =         "1988",
  bibdate =      "Fri Dec 08 10:42:22 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[66--77]{Swartzlander:1990:CAb}.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Ercegovac:1988:LSC
author: Milos D. Ercegovac and Tomas Lang
title: On-line scheme for computing rotation factors
journal: j-J-PAR-DIST-COMP
volume: 5
number: 3
pages: 209--227
month: jun
monthnumber: 6
year: 1988
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
affiliationaddress: Univ of California, Los Angeles, CA, USA
corpsource: Department of Computer Science, California University, Los Angeles, CA, USA
journalURL: http://www.sciencedirect.com/science/journal/07437315
journalabr: J Parallel Distrib Comput
treatment: P Practical; T Theoretical or Mathematical
rawauthor: Milo{\v{s}} D. Ercegovac and Tomas Lang
rawtitle: On-line scheme for computing rotation factors
keywords:
algorithm; Algorithms; clock period; computer programming; computers, digital --- Computational Methods; computing rotation factors; digital arithmetic; floating-point; low-precision estimates; mathematical techniques --- Algorithms; matrix transformations; on-line algorithm; online scheme; radix-2 online; representation; rotation factors computing; systolic arrays

entry:
@Article{Ercegovac:1988:LSC,
  author =       "Milo{\v{s}} D. Ercegovac and Tomas Lang",
  title =        "On-line scheme for computing rotation factors",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "5",
  number =       "3",
  pages =        "209--227",
  month =        jun,
  year =         "1988",
  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,
  affiliationaddress = "Univ of California, Los Angeles, CA, USA",
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  corpsource =   "Department of Computer Science, California University,
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  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
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  keywords =     "algorithm; Algorithms; clock period; computer
                 programming; computers, digital --- Computational
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                 mathematical techniques --- Algorithms; matrix
                 transformations; on-line algorithm; online scheme;
                 radix-2 online; representation; rotation factors
                 computing; systolic arrays",
  treatment =    "P Practical; T Theoretical or Mathematical",
}


bibtype: article
filename: fparith.bib
label: Fam:1988:ECM
author: A. T. Fam
title: Efficient complex matrix multiplication
journal: j-IEEE-TRANS-COMPUT
volume: 37
number: 7
pages: 877--879
month: jul
monthnumber: 7
year: 1988
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.2236
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 9 08:33:27 MDT 2011
bibtimestamp: 2011.07.09 08:33:27 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2236
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: A. T. Fam
rawtitle: Efficient complex matrix multiplication
entry:
@Article{Fam:1988:ECM,
  author =       "A. T. Fam",
  title =        "Efficient complex matrix multiplication",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "37",
  number =       "7",
  pages =        "877--879",
  month =        jul,
  year =         "1988",
  CODEN =        "ITCOB4",
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  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 08:33:27 MDT 2011",
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  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: Farnum:1988:CSF
author: Charles Farnum
title: Compiler Support for Floating-Point Computation
journal: j-SPE
volume: 18
number: 7
pages: 701--709
month: jul
monthnumber: 7
year: 1988
CODEN: SPEXBL
ISSN: 0038-0644 (print), 1097-024X (electronic) OR 00380644 (print), 1097024X (electronic)
ISSNL: 0038-0644 OR 00380644
bibdate: Sat May 24 19:46:39 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.05.24 19:46:39 ???
fjournal: Software---Practice and Experience
acknowledgement: ack-nhfb
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X
rawauthor: Charles Farnum
rawtitle: Compiler Support for Floating-Point Computation
entry:
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  author =       "Charles Farnum",
  title =        "Compiler Support for Floating-Point Computation",
  journal =      j-SPE,
  volume =       "18",
  number =       "7",
  pages =        "701--709",
  month =        jul,
  year =         "1988",
  CODEN =        "SPEXBL",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  bibdate =      "Sat May 24 19:46:39 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Software---Practice and Experience",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
}


bibtype: article
filename: fparith.bib
label: Fiske:1988:RAP
author: S. Fiske and W. J. Dally
title: The reconfigurable arithmetic processor
journal: j-COMP-ARCH-NEWS
volume: 16
number: 2
pages: 30--36
month: may
monthnumber: 5
year: 1988
CODEN: CANED2
ISSN: 0163-5964 (print), 1943-5851 (electronic) OR 01635964 (print), 19435851 (electronic)
ISSNL: 0163-5964 OR 01635964
bibdate: Fri May 12 09:40:45 MDT 2006
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2006.05.12 09:40:45 MDT
fjournal: ACM SIGARCH Computer Architecture News
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/sigarch
rawauthor: S. Fiske and W. J. Dally
rawtitle: The reconfigurable arithmetic processor
entry:
@Article{Fiske:1988:RAP,
  author =       "S. Fiske and W. J. Dally",
  title =        "The reconfigurable arithmetic processor",
  journal =      j-COMP-ARCH-NEWS,
  volume =       "16",
  number =       "2",
  pages =        "30--36",
  month =        may,
  year =         "1988",
  CODEN =        "CANED2",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Fri May 12 09:40:45 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: Fitzpatrick:1988:PVF
author: S. Fitzpatrick
journal: Electronique Industrielle
volume: 148
pages: 30--32
day: 15
month: sep
monthnumber: 9
year: 1988
bibdate: Sat Oct 24 15:01:51 1998
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.10.24 15:01:51 ???
acknowledgement: ack-nj
rawauthor: S. Fitzpatrick
title:
Processeur a virgule flottante a 33 Mflops toenglish 33 Mflops Floating-Point Processor endtoenglish 

rawtitle:
Processeur {\`a} virgule flottante {\`a} 33 {Mflops} \toenglish {33 Mflops Floating-Point Processor} \endtoenglish

entry:
@Article{Fitzpatrick:1988:PVF,
  author =       "S. Fitzpatrick",
  title =        "Processeur {\`a} virgule flottante {\`a} 33 {Mflops}
                 \toenglish {33 Mflops Floating-Point Processor}
                 \endtoenglish",
  journal =      "Electronique Industrielle",
  volume =       "148",
  pages =        "30--32",
  day =          "15",
  month =        sep,
  year =         "1988",
  bibdate =      "Sat Oct 24 15:01:51 1998",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: Fuccio:1988:DAS
title: The DSP32C: AT&T's Second-Generation Floating-Point Digital Signal Processor
journal: j-IEEE-MICRO
volume: 8
number: 6
pages: 30--48
month: nov
monthnumber: 11
year: 1988
CODEN: IEMIDZ
DOI: https://doi.org/10.1109/40.16779
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: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:52 MDT
fjournal: IEEE Micro
acknowledgement: ack-nj
journalURL: http://www.computer.org/csdl/mags/mi/index.html
rawtitle: The {DSP32C}: {AT\&T}'s Second-Generation Floating-Point Digital Signal Processor
author:
M. L. Fuccio and R. N. Gadenz and C. J. Garen and J. M. Huser and B. Ng and S. P. Pekarich and K. D. Ulery

rawauthor:
M. L. Fuccio and R. N. Gadenz and C. J. Garen and J. M. Huser and B. Ng and S. P. Pekarich and K. D. Ulery

entry:
@Article{Fuccio:1988:DAS,
  author =       "M. L. Fuccio and R. N. Gadenz and C. J. Garen and J.
                 M. Huser and B. Ng and S. P. Pekarich and K. D. Ulery",
  title =        "The {DSP32C}: {AT\&T}'s Second-Generation
                 Floating-Point Digital Signal Processor",
  journal =      j-IEEE-MICRO,
  volume =       "8",
  number =       "6",
  pages =        "30--48",
  month =        nov # "\slash " # dec,
  year =         "1988",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/40.16779",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
  summary =      "The WEDSP32C high-performance, programmable digital
                 signal processor supports 32-bit floating-point
                 arithmetic and is upwardly compatible with its
                 predecessor, the WEDSP32. Because it is implemented in
                 0.75-$\mu$m (effective channel length) CMOS technology
                 \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Gibson:1988:GBA
author: J. K. Gibson
title: A generalisation of Brickell's algorithm for fast modular multiplication
journal: j-BIT
volume: 28
number: 4
pages: 755--763
month: dec
monthnumber: 12
year: 1988
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01954895
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
MRclass: 68Q25 (68P25 68U99)
MRnumber: 89m:68058
MRreviewer: Ricardo Baeza-Yates
bibdate: Wed Jan 4 18:52:20 MST 2006
bibtimestamp: 2006.01.04 18:52:20 MST
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=28&issue=4&spage=755
fjournal: BIT (Nordisk tidskrift for informationsbehandling)
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: J. K. Gibson
rawtitle: A generalisation of {Brickell}'s algorithm for fast modular multiplication
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=28&issue=4; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Gibson:1988:GBA,
  author =       "J. K. Gibson",
  title =        "A generalisation of {Brickell}'s algorithm for fast
                 modular multiplication",
  journal =      j-BIT,
  volume =       "28",
  number =       "4",
  pages =        "755--763",
  month =        dec,
  year =         "1988",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01954895",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "68Q25 (68P25 68U99)",
  MRnumber =     "89m:68058",
  MRreviewer =   "Ricardo Baeza-Yates",
  bibdate =      "Wed Jan 4 18:52:20 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=28&issue=4;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=28&issue=4&spage=755",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}


bibtype: article
filename: fparith.bib
label: Grehan:1988:BBL
author: R. Grehan and T. Thompson
title: Borland beefs up its languages
journal: j-BYTE
volume: 13
number: 10
pages: 151--154
month: oct
monthnumber: 10
year: 1988
CODEN: BYTEDJ
ISSN: 0360-5280 (print), 1082-7838 (electronic) OR 03605280 (print), 10827838 (electronic)
ISSNL: 0360-5280 OR 03605280
bibdate: Thu Sep 12 17:54:09 MDT 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.09.12 17:54:09 MDT
fjournal: BYTE Magazine
acknowledgement: ack-nhfb
thesaurus: C language; Pascal; Program assemblers; Program compilers; Program debugging; Software packages
rawauthor: R. Grehan and T. Thompson
rawtitle: {Borland} beefs up its languages
keywords:
Borland International; Built-in source-level debuggers; Command-line interface version; Expanded memory; Floating-point emulation; High-speed assembler; In-line assembly language support; Integrated development environment; Line-oriented environment; Premier development languages; Stand-alone debugger; TASM; Turbo Assembler; Turbo C; Turbo Debugger; Turbo language; Turbo Pascal

entry:
@Article{Grehan:1988:BBL,
  author =       "R. Grehan and T. Thompson",
  title =        "{Borland} beefs up its languages",
  journal =      j-BYTE,
  volume =       "13",
  number =       "10",
  pages =        "151--154",
  month =        oct,
  year =         "1988",
  CODEN =        "BYTEDJ",
  ISSN =         "0360-5280 (print), 1082-7838 (electronic)",
  ISSN-L =       "0360-5280",
  bibdate =      "Thu Sep 12 17:54:09 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C6140D (High level languages); C6150C (Compilers,
                 interpreters and other processors); C6150G (Diagnostic,
                 testing, debugging and evaluating systems)",
  fjournal =     "BYTE Magazine",
  keywords =     "Borland International; Built-in source-level
                 debuggers; Command-line interface version; Expanded
                 memory; Floating-point emulation; High-speed assembler;
                 In-line assembly language support; Integrated
                 development environment; Line-oriented environment;
                 Premier development languages; Stand-alone debugger;
                 TASM; Turbo Assembler; Turbo C; Turbo Debugger; Turbo
                 language; Turbo Pascal",
  thesaurus =    "C language; Pascal; Program assemblers; Program
                 compilers; Program debugging; Software packages",
}


bibtype: article
filename: fparith.bib
label: Grehan:1988:FPCa
author: Rick Grehan
title: Floating-Point Without a Coprocessor
journal: j-BYTE
volume: 13
number: 9
pages: 313--319
month: sep
monthnumber: 9
year: 1988
CODEN: BYTEDJ
ISSN: 0360-5280 (print), 1082-7838 (electronic) OR 03605280 (print), 10827838 (electronic)
ISSNL: 0360-5280 OR 03605280
bibdate: Sat Nov 9 08:26:18 MST 2002
bibtimestamp: 2002.11.09 08:26:18 MST
fjournal: BYTE Magazine
acknowledgement: ack-nj
rawauthor: Rick Grehan
rawtitle: Floating-Point Without a Coprocessor
bibsource:
ACM Computing Archive CD-ROM database (1991); ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib

subject:
C. Computer Systems Organization; C.3 SPECIAL-PURPOSE AND APPLICATION-BASED SYSTEMS; G. Mathematics of Computing; G.0 GENERAL

entry:
@Article{Grehan:1988:FPCa,
  author =       "Rick Grehan",
  title =        "Floating-Point Without a Coprocessor",
  journal =      j-BYTE,
  volume =       "13",
  number =       "9",
  pages =        "313--319",
  month =        sep,
  year =         "1988",
  CODEN =        "BYTEDJ",
  ISSN =         "0360-5280 (print), 1082-7838 (electronic)",
  ISSN-L =       "0360-5280",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 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,
  bibno =        "47602",
  catcode =      "C.3; G.0",
  descriptor =   "Computer Systems Organization, SPECIAL-PURPOSE AND
                 APPLICATION-BASED SYSTEMS; Mathematics of Computing,
                 GENERAL",
  fjournal =     "BYTE Magazine",
  genterm =      "DESIGN; THEORY; MANAGEMENT",
  guideno =      "1988-05346",
  subject =      "C. Computer Systems Organization; C.3 SPECIAL-PURPOSE
                 AND APPLICATION-BASED SYSTEMS; G. Mathematics of
                 Computing; G.0 GENERAL",
}


bibtype: article
filename: fparith.bib
label: Grehan:1988:FPCb
author: R. Grehan
title: Floating-Point Without a Coprocessor, Part 2
journal: j-BYTE
volume: 13
number: 10
pages: 293--297 (or 293--298??)
month: oct
monthnumber: 10
year: 1988
CODEN: BYTEDJ
ISSN: 0360-5280 (print), 1082-7838 (electronic) OR 03605280 (print), 10827838 (electronic)
ISSNL: 0360-5280 OR 03605280
bibdate: Thu Sep 12 17:54:09 MDT 1996
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.09.12 17:54:09 MDT
fjournal: BYTE Magazine
acknowledgement: ack-nj
thesaurus: Input-output programs; Mathematics computing; Number theory; Programming; Software packages
rawauthor: R. Grehan
rawtitle: Floating-Point Without a Coprocessor, Part 2
keywords:
Addition; Binary floating-point mathematics package; Division; Floating-point accumulators; Floating-point number manipulation; Maths chip emulation; Multiplication; Number input/output; Primary math operations; Pseudocode routines; Subtraction

entry:
@Article{Grehan:1988:FPCb,
  author =       "R. Grehan",
  title =        "Floating-Point Without a Coprocessor, Part 2",
  journal =      j-BYTE,
  volume =       "13",
  number =       "10",
  pages =        "293--297 (or 293--298??)",
  month =        oct,
  year =         "1988",
  CODEN =        "BYTEDJ",
  ISSN =         "0360-5280 (print), 1082-7838 (electronic)",
  ISSN-L =       "0360-5280",
  bibdate =      "Thu Sep 12 17:54:09 MDT 1996",
  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,
  classification = "C1160 (Combinatorial mathematics); C6110 (Systems
                 analysis and programming); C7310 (Mathematics)",
  fjournal =     "BYTE Magazine",
  keywords =     "Addition; Binary floating-point mathematics package;
                 Division; Floating-point accumulators; Floating-point
                 number manipulation; Maths chip emulation;
                 Multiplication; Number input/output; Primary math
                 operations; Pseudocode routines; Subtraction",
  thesaurus =    "Input-output programs; Mathematics computing; Number
                 theory; Programming; Software packages",
}


bibtype: mastersthesis
filename: fparith.bib
label: Helminen:1988:AFP
author: Brenda K. Helminen
title: An analysis of the floating point and communication performance of the FPS T-Series hypercube
type: Thesis (M.S.)
school: Michigan Technological University
address: Houghton, MI, USA
pages: viii + 69
year: 1988
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: Michigan Technological University. --- Theses (M.S.).; MTU Computer Science. --- Thesis (M.S.).
acknowledgement: ack-nhfb
rawauthor: Brenda K. Helminen
rawtitle: An analysis of the floating point and communication performance of the {FPS} {T-Series} hypercube
entry:
@MastersThesis{Helminen:1988:AFP,
  author =       "Brenda K. Helminen",
  title =        "An analysis of the floating point and communication
                 performance of the {FPS} {T-Series} hypercube",
  type =         "Thesis ({M.S.})",
  school =       "Michigan Technological University",
  address =      "Houghton, MI, USA",
  pages =        "viii + 69",
  year =         "1988",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Michigan Technological University. --- Theses
                 ({M.S.}).; MTU Computer Science. --- Thesis ({M.S.}).",
}


bibtype: mastersthesis
filename: fparith.bib
label: Ho:1988:ADI
author: Naven Chuen Wing Ho
title: Analysis and design of an instantaneous floating point amplifier
type: Thesis (M.S.)
school: Department of Electrical Engineering, Cullen College of Engineering, University of Houston
address: Houston, TX, USA
pages: xv + 185
year: 1988
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: Amplifiers (Electronics); Seismic waves --- Data processing.
acknowledgement: ack-nhfb
rawauthor: Naven Chuen Wing Ho
rawtitle: Analysis and design of an instantaneous floating point amplifier
entry:
@MastersThesis{Ho:1988:ADI,
  author =       "Naven Chuen Wing Ho",
  title =        "Analysis and design of an instantaneous floating point
                 amplifier",
  type =         "Thesis ({M.S.})",
  school =       "Department of Electrical Engineering, Cullen College
                 of Engineering, University of Houston",
  address =      "Houston, TX, USA",
  pages =        "xv + 185",
  year =         "1988",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Amplifiers (Electronics); Seismic waves --- Data
                 processing.",
}


bibtype: book
filename: fparith.bib
label: Holt:1988:BR
title: Beyond RISC --- An Essential Guide to Hewlett--Packard Precision Architecture
publisher: pub-SRNI
address: pub-SRNI:adr
pages: xvii + 342
year: 1988
ISBN: 0-9618813-7-2 OR 0961881372
ISBN13: 978-0-9618813-7-5 OR 9780961881375
LCCN: QA76.8.H66 B49 1988
bibdate: Thu Sep 15 11:34:06 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.15 11:34:06 ???
acknowledgement: ack-nhfb
rawtitle: Beyond {RISC}\emdash An Essential Guide to Hewlett--Packard Precision Architecture
editor:
Wayne E. Holt and Steven M. Cooper and Jason M. Goertz and Scott E. Levine and Joanna L. Mosher and Stanley R. Sieler, Jr. and Jacques Van Damme

raweditor:
Wayne E. Holt and Steven M. Cooper and Jason M. Goertz and Scott E. Levine and Joanna L. Mosher and Stanley R. {Sieler, Jr.} and Jacques {Van Damme}

entry:
@Book{Holt:1988:BR,
  editor =       "Wayne E. Holt and Steven M. Cooper and Jason M. Goertz
                 and Scott E. Levine and Joanna L. Mosher and Stanley R.
                 {Sieler, Jr.} and Jacques {Van Damme}",
  title =        "Beyond {RISC}\emdash An Essential Guide to
                 Hewlett--Packard Precision Architecture",
  publisher =    pub-SRNI,
  address =      pub-SRNI:adr,
  pages =        "xvii + 342",
  year =         "1988",
  ISBN =         "0-9618813-7-2",
  ISBN-13 =      "978-0-9618813-7-5",
  LCCN =         "QA76.8.H66 B49 1988",
  bibdate =      "Thu Sep 15 11:34:06 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Hsu:1988:CVA
author: I. S. Hsu and T. K. Truong and L. J. Deutsch and I. S. Reed
title: A comparison of VLSI architecture of finite field multipliers using dual, normal, or standard bases
journal: j-IEEE-TRANS-COMPUT
volume: 37
number: 6
pages: 735--739
month: jun
monthnumber: 6
year: 1988
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.2212
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 9 08:33:27 MDT 2011
bibtimestamp: 2011.07.09 08:33:27 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2212
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: I. S. Hsu and T. K. Truong and L. J. Deutsch and I. S. Reed
rawtitle:
A comparison of {VLSI} architecture of finite field multipliers using dual, normal, or standard bases

entry:
@Article{Hsu:1988:CVA,
  author =       "I. S. Hsu and T. K. Truong and L. J. Deutsch and I. S.
                 Reed",
  title =        "A comparison of {VLSI} architecture of finite field
                 multipliers using dual, normal, or standard bases",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "37",
  number =       "6",
  pages =        "735--739",
  month =        jun,
  year =         "1988",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.2212",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 08:33:27 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2212",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


