# bibtab

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: http://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: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Eberhard Lange
rawtitle: Implementation and Test of the {ACRITH} Facility in a {System}\slash 370
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/ieeetranscomput.bib

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/ieeetranscomput.bib",
  URL =          "http://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 =  "http://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: http://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 =  "http://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
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",
  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
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.08 08:08:51 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: http://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",
  acknowledgement = ack-nj,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: 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: book
filename: fparith.bib
label: Motorola:1987:MMF
author: Motorola
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
rawtitle: {MC68881\slash MC68882} Floating-Point Coprocessor User's Manual
entry:
@Book{Motorola:1987:MMF,
  author =       "Motorola",
  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
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_Olver.pdf
keywords: ARITH-8
acknowledgement: ack-nhfb
rawauthor: F. W. J. Olver
rawtitle: A Closed Computer Arithmetic
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",
  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_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,
  keywords =     "ARITH-8",
}


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
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_Olver_Turner.pdf
keywords: ARITH-8
acknowledgement: ack-nhfb
rawauthor: F. W. J. Olver and P. R. Turner
rawtitle: Implementation of Level-Index Arithmetic Using Partial Table Look-Up
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",
  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_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,
  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: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009473
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://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 =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009473",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: 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
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,
  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: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676863
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://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 =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676863",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: 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
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",
  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
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",
  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
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",
  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: http://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 =  "http://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: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676952
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://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 =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676952",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: 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: http://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 =  "http://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
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",
  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
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",
  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
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",
  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
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",
  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
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",
  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: http://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/stamp/stamp.jsp?tp=&arnumber=1676868; http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12; http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35260

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/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676868;
                 http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35260",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A 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
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",
  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: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009470
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://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 =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009470",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: 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
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",
  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
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",
  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
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:15:40 ???
fjournal: IEEE 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/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
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",
  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: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676865
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://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 =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676865",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: 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
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",
}


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: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009447
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://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 =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009447",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: 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: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009445
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://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/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009445",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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-COMP-SIM
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-COMP-SIM,
  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-COMP-SIM
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-COMP-SIM,
  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: 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: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2255
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://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 =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2255",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: 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: http://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 =          "http://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: http://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 =          "http://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
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: 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
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/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: 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: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2170
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://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 =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2170",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: techreport
filename: fparith.bib
label: 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: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2239
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://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 =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2239",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: 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
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",
}


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",
  keywords =     "computer architecture; computers, digital ---
                 Circuits; digital arithmetic; elementary functions;
                 hardwired polynomial evaluation; mathematical
                 functions; mathematical techniques; Polynomials;
                 polynomials; special-purpose circuits; VLSI
                 implementation",
  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",
  classification = "721; 722; 723; 921; C5230 (Digital arithmetic
                 methods)",
  corpsource =   "Department of Computer Science, California University,
                 Los Angeles, CA, USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "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",
  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: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2236
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://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",
  DOI =          "https://doi.org/10.1109/12.2236",
  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 =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2236",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: 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:
@Article{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,
  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: http://portal.acm.org/browse_dl.cfm?idx=J89
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 =  "http://portal.acm.org/browse_dl.cfm?idx=J89",
}


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;
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  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: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2212
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://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 =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2212",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Iacobovici:1988:HFC
author: S. Iacobovici
title: High-performance floating-point coprocessor for the NS32532 CPU
crossref: Wescon:1988:WCR
pages: 1.3/1--6
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: National Semicond. Corp., Santa Clara, CA, USA
thesaurus: Digital arithmetic; Microprocessor chips
rawauthor: S. Iacobovici
rawtitle: High-performance floating-point coprocessor for the {NS32532 CPU}
abstract:
The need to match the integer processing performance of the NS32532 CPU with the floating-point performance teams the NS32580 floating-point controller with Weitek's WTL3164 floating-point data path to achieve a peak performance of 15 MFLOPS for single- or double-precision. Using a pipelined slave protocol this solution is software compatible with existing Series 32000 software base and supports precise exception handling. Together, NS32532-NS32580-WTL3164 provide a high-performance, well-balanced solution for scientific applications, as well as number crunching, graphics and image processing.

keywords:
15 MFLOPS; Double-precision; Exception handling; Floating-point coprocessor; Graphics; Image processing; NS32532 CPU; NS32580 floating-point controller; Pipelined slave protocol; Processing performance; Scientific applications; Series 32000 software; Single precision arithmetic; WTL3164 floating-point data path

rawabstract:
The need to match the integer processing performance of the NS32532 CPU with the floating-point performance teams the NS32580 floating-point controller with Weitek's WTL3164 floating-point data path to achieve a peak performance of 15 MFLOPS for single- or double-precision. Using a pipelined slave protocol this solution is software compatible with existing Series 32000 software base and supports precise exception handling. Together, NS32532-NS32580-WTL3164 provide a high-performance, well-balanced solution for scientific applications, as well as number crunching, graphics and image processing.

entry:
@InProceedings{Iacobovici:1988:HFC,
  author =       "S. Iacobovici",
  title =        "High-performance floating-point coprocessor for the
                 {NS32532 CPU}",
  crossref =     "Wescon:1988:WCR",
  pages =        "1.3/1--6",
  year =         "1988",
  bibdate =      "Tue Dec 12 09:20:21 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The need to match the integer processing performance
                 of the NS32532 CPU with the floating-point performance
                 teams the NS32580 floating-point controller with
                 Weitek's WTL3164 floating-point data path to achieve a
                 peak performance of 15 MFLOPS for single- or
                 double-precision. Using a pipelined slave protocol this
                 solution is software compatible with existing Series
                 32000 software base and supports precise exception
                 handling. Together, NS32532-NS32580-WTL3164 provide a
                 high-performance, well-balanced solution for scientific
                 applications, as well as number crunching, graphics and
                 image processing.",
  acknowledgement = ack-nhfb,
  affiliation =  "National Semicond. Corp., Santa Clara, CA, USA",
  classification = "C5130 (Microprocessor chips); C5230 (Digital
                 arithmetic methods)",
  keywords =     "15 MFLOPS; Double-precision; Exception handling;
                 Floating-point coprocessor; Graphics; Image processing;
                 NS32532 CPU; NS32580 floating-point controller;
                 Pipelined slave protocol; Processing performance;
                 Scientific applications; Series 32000 software; Single
                 precision arithmetic; WTL3164 floating-point data
                 path",
  numericalindex = "Computer speed 1.5E+07 FLOPS",
  thesaurus =    "Digital arithmetic; Microprocessor chips",
}


bibtype: article
filename: fparith.bib
label: Iacobovici:1988:PIH
author: S. Iacobovici
title: A pipelined interface for high floating-point performance with precise exceptions
journal: j-IEEE-MICRO
volume: 8
number: 3
pages: 77--87
month: may
monthnumber: 5
year: 1988
CODEN: IEMIDZ
DOI: https://doi.org/10.1109/40.542
ISSN: 0272-1732 (print), 1937-4143 (electronic) OR 02721732 (print), 19374143 (electronic)
ISSNL: 0272-1732 OR 02721732
bibdate: Sat Jul 16 08:40:52 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:52 MDT
fjournal: IEEE Micro
acknowledgement: ack-nhfb
journalURL: http://www.computer.org/csdl/mags/mi/index.html
rawauthor: S. Iacobovici
rawtitle: A pipelined interface for high floating-point performance with precise exceptions
entry:
@Article{Iacobovici:1988:PIH,
  author =       "S. Iacobovici",
  title =        "A pipelined interface for high floating-point
                 performance with precise exceptions",
  journal =      j-IEEE-MICRO,
  volume =       "8",
  number =       "3",
  pages =        "77--87",
  month =        may # "\slash " # jun,
  year =         "1988",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/40.542",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
  summary =      "Two options are presented that were considered for a
                 pipelined interface between a central processing unit
                 (CPU) and a floating-point coprocessor (FPU), along
                 with the CPU recovery mechanisms that provide precise
                 floating-point exceptions for each \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Irwin:1988:SIP
author: M. J. Irwin
title: Special issue on parallelism in computer arithmetic
journal: j-J-PAR-DIST-COMP
volume: 5
number: 3
pages: 205--208
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 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: Pennsylvania State University, University Park, PA, USA
journalURL: http://www.sciencedirect.com/science/journal/07437315
treatment: G General Review; P Practical
rawauthor: M. J. Irwin
rawtitle: Special issue on parallelism in computer arithmetic
keywords:
computer arithmetic; digital arithmetic; lookahead adders; parallel processing; parallelism; pipelined arithmetic processors; VLSI systems

entry:
@Article{Irwin:1988:SIP,
  author =       "M. J. Irwin",
  title =        "Special issue on parallelism in computer arithmetic",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "5",
  number =       "3",
  pages =        "205--208",
  month =        jun,
  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 = "C5230 (Digital arithmetic methods); C5440
                 (Multiprocessor systems and techniques)",
  corpsource =   "Pennsylvania State University, University Park, PA,
                 USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  keywords =     "computer arithmetic; digital arithmetic; lookahead
                 adders; parallel processing; parallelism; pipelined
                 arithmetic processors; VLSI systems",
  treatment =    "G General Review; P Practical",
}


bibtype: article
filename: fparith.bib
label: Jenkins:1988:SCP
author: W. K. Jenkins and E. J. Altman
title: Self-checking properties of residue number error checkers based on mixed radix conversion
journal: j-IEEE-TRANS-CIRCUITS-SYST
volume: 35
number: 2
pages: 159--167
month: feb
monthnumber: 2
year: 1988
CODEN: ICSYBT
DOI: https://doi.org/10.1109/31.1717
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: http://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: W. K. Jenkins and E. J. Altman
rawtitle: Self-checking properties of residue number error checkers based on mixed radix conversion
entry:
@Article{Jenkins:1988:SCP,
  author =       "W. K. Jenkins and E. J. Altman",
  title =        "Self-checking properties of residue number error
                 checkers based on mixed radix conversion",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "35",
  number =       "2",
  pages =        "159--167",
  month =        feb,
  year =         "1988",
  CODEN =        "ICSYBT",
  DOI =          "https://doi.org/10.1109/31.1717",
  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 =          "http://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 =      "It has been shown previously that a mixed-radix
                 converter can be modified to perform all the essential
                 functions of an error checker for error detection and
                 correction in residue number system hardware
                 architectures. Since the computations in a \ldots{}",
}


bibtype: phdthesis
filename: fparith.bib
label: Johnstone:1988:DFP
author: Paul Johnstone
title: Decimal floating point representation
type: Thesis (Ph.D.)
school: Tulane University
address: New Orleans, LA 70118, USA
pages: vi + 101
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: Binary system (Mathematics); decimal floating-point arithmetic; Floating-point arithmetic.
acknowledgement: ack-nhfb
rawauthor: Paul Johnstone
rawtitle: Decimal floating point representation
entry:
@PhdThesis{Johnstone:1988:DFP,
  author =       "Paul Johnstone",
  title =        "Decimal floating point representation",
  type =         "Thesis ({Ph.D.})",
  school =       "Tulane University",
  address =      "New Orleans, LA 70118, USA",
  pages =        "vi + 101",
  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 =     "Binary system (Mathematics); decimal floating-point
                 arithmetic; Floating-point arithmetic.",
}


bibtype: techreport
filename: fparith.bib
label: Jouppi:1988:MFA
author: Norman Paul Jouppi and Jeremy Dion and David Reeves Boggs and Michael J. K. Nielsen
title: MultiTitan: four architecture papers
institution: Digital Western Research Laboratory
address: Palo Alto, CA, USA
edition: [Revised]
pages: various
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
series: WRL research report; 87/8
keywords: Computer architecture.; MultiTitan (Computer)
acknowledgement: ack-nhfb
rawauthor: Norman Paul Jouppi and Jeremy Dion and David Reeves Boggs and Michael J. K. Nielsen
rawtitle: {MultiTitan}: four architecture papers
remark:
``April 10, 1988.'' MultiTitan central processor unit / Norman P. Jouppi --- MultiTitan floating point unit / Norman P. Jouppi --- MultiTitan cache control unit / Jeremy Dion --- MultiTitan intra-processor bus / David Boggs, Jeremy Dion, Michael J. K. Nielsen.

entry:
@TechReport{Jouppi:1988:MFA,
  author =       "Norman Paul Jouppi and Jeremy Dion and David Reeves
                 Boggs and Michael J. K. Nielsen",
  title =        "{MultiTitan}: four architecture papers",
  institution =  "Digital Western Research Laboratory",
  address =      "Palo Alto, CA, USA",
  edition =      "[Revised]",
  pages =        "various",
  year =         "1988",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "WRL research report; 87/8",
  acknowledgement = ack-nhfb,
  keywords =     "Computer architecture.; MultiTitan (Computer)",
  remark =       "``April 10, 1988.'' MultiTitan central processor unit
                 / Norman P. Jouppi --- MultiTitan floating point unit /
                 Norman P. Jouppi --- MultiTitan cache control unit /
                 Jeremy Dion --- MultiTitan intra-processor bus / David
                 Boggs, Jeremy Dion, Michael J. K. Nielsen.",
}


bibtype: techreport
filename: fparith.bib
label: Jouppi:1988:UVS
author: Norman P. Jouppi and Jonathan Bertoni and David W. Wall
title: A unified vector / scalar floating-point architecture
type: Report
number: WRL TN-3
institution: Digital Western Research Laboratory
address: Palo Alto, CA, USA
pages: 19
year: 1988
bibdate: Thu May 09 08:38:06 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.09 08:38:06 ???
acknowledgement: ack-nhfb
rawauthor: Norman P. Jouppi and Jonathan Bertoni and David W. Wall
rawtitle: A unified vector\slash scalar floating-point architecture
entry:
@TechReport{Jouppi:1988:UVS,
  author =       "Norman P. Jouppi and Jonathan Bertoni and David W.
                 Wall",
  title =        "A unified vector\slash scalar floating-point
                 architecture",
  type =         "Report",
  number =       "WRL TN-3",
  institution =  "Digital Western Research Laboratory",
  address =      "Palo Alto, CA, USA",
  pages =        "19",
  year =         "1988",
  bibdate =      "Thu May 09 08:38:06 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: fparith.bib
label: Joy:1988:OCT
author: Edward Bennett Joy and Paul R. Beaudet and Pankaj K. Das
title: Optical communications techniques / floating point residue number system
institution: School of Electrical Engineering, Georgia Institute of Technology
address: Atlanta, GA, 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
keywords: Computer network architectures.; Computers --- Optical equipment.
acknowledgement: ack-nhfb
rawauthor: Edward Bennett Joy and Paul R. Beaudet and Pankaj K. Das
rawtitle: Optical communications techniques\slash floating point residue number system
remark:
Issued as R and D status reports [nos. 1--7], Contract funds status reports [nos. 1--8], Final technical report, and Final report, Project E-21-T01. Final technical report has author: Paul R. Beaudet. Final report has author: Pankaj K. Das. Final technical report has title: Floating point residue number system. Final report has title: New techniques in optical communications and signal processing.

entry:
@TechReport{Joy:1988:OCT,
  author =       "Edward Bennett Joy and Paul R. Beaudet and Pankaj K.
                 Das",
  title =        "Optical communications techniques\slash floating point
                 residue number system",
  institution =  "School of Electrical Engineering, Georgia Institute of
                 Technology",
  address =      "Atlanta, GA, 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",
  acknowledgement = ack-nhfb,
  keywords =     "Computer network architectures.; Computers --- Optical
                 equipment.",
  remark =       "Issued as R and D status reports [nos. 1--7], Contract
                 funds status reports [nos. 1--8], Final technical
                 report, and Final report, Project E-21-T01. Final
                 technical report has author: Paul R. Beaudet. Final
                 report has author: Pankaj K. Das. Final technical
                 report has title: Floating point residue number system.
                 Final report has title: New techniques in optical
                 communications and signal processing.",
}


bibtype: article
filename: fparith.bib
label: Juffa:1988:SAF
author: N. Juffa
title: Schnelle Algorithmen fur Sin und Cos toenglish Fast Algorithms for Sin and Cos endtoenglish
journal: j-MC
volume: 5
pages: 105--107
year: 1988
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: N. Juffa
rawtitle:
{Schnelle Algorithmen f{\"u}r Sin und Cos} \toenglish {Fast Algorithms for Sin and Cos} \endtoenglish

entry:
@Article{Juffa:1988:SAF,
  author =       "N. Juffa",
  title =        "{Schnelle Algorithmen f{\"u}r Sin und Cos} \toenglish
                 {Fast Algorithms for Sin and Cos} \endtoenglish",
  journal =      j-MC,
  volume =       "5",
  pages =        "105--107",
  year =         "1988",
  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: misc
filename: fparith.bib
label: Kahan:1988:AFP
author: William Kahan
title: Arithmazium: The Floating Point Expose
pages: 105--107
month: may
monthnumber: 5
year: 1988
bibdate: Wed Jun 05 09:50:01 2024
bibtimestamp: 2024.06.05 09:50:01 ???
URL: https://www.arithmazium.org/classroom/wk88_toc.html
acknowledgement: ack-nhfb
howpublished: Web site
rawauthor: William Kahan
rawtitle: Arithmazium: The Floating Point Expos{\'e}
note:
This site includes 27 lectures with notes and videos for CS 279 (Computer System Support for Scientific and Engineering Computation). The class handouts amount to more than 2000 pages.

rawnote:
This site includes 27 lectures with notes and videos for CS 279 (Computer System Support for Scientific and Engineering Computation). The class handouts amount to more than 2000 pages.

entry:
@Misc{Kahan:1988:AFP,
  author =       "William Kahan",
  title =        "Arithmazium: The Floating Point Expos{\'e}",
  howpublished = "Web site",
  month =        may # "\slash " # jul,
  year =         "1988",
  bibdate =      "Wed Jun 05 09:50:01 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",
  note =         "This site includes 27 lectures with notes and videos
                 for CS 279 (Computer System Support for Scientific and
                 Engineering Computation). The class handouts amount to
                 more than 2000 pages.",
  URL =          "https://www.arithmazium.org/classroom/wk88_toc.html",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: fparith.bib
label: Kahan:1988:CSS
author: W. Kahan and David Goldberg
title: Computer System Support for Scientific and Engineering Computation
type: Report
institution: inst-BERKELEY-CS
address: inst-BERKELEY-CS:adr
pages: 105--107
day: 26
month: jul
monthnumber: 7
year: 1988
bibdate: Mon Aug 26 10:39:23 2024
bibtimestamp: 2024.08.26 10:39:23 ???
note: Revised 14 June 1990.
URL: http://www.arithmazium.org/classroom/lib//Lecture_25_notes_slides.pdf
acknowledgement: ack-nhfb
rawauthor: W. Kahan and David Goldberg
rawnote: Revised 14 June 1990.
rawtitle: Computer System Support for Scientific and Engineering Computation
entry:
@TechReport{Kahan:1988:CSS,
  author =       "W. Kahan and David Goldberg",
  title =        "Computer System Support for Scientific and Engineering
                 Computation",
  type =         "Report",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  day =          "26",
  month =        jul,
  year =         "1988",
  bibdate =      "Mon Aug 26 10:39:23 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",
  note =         "Revised 14 June 1990.",
  URL =          "http://www.arithmazium.org/classroom/lib//Lecture_25_notes_slides.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Kahaner:1988:BRP
author: D. K. Kahaner
title: Benchmarks for `real' programs
journal: j-SIAM-NEWS
pages: A-61
month: nov
monthnumber: 11
year: 1988
ISSN: 0036-1437 OR 00361437
ISSNL: 0036-1437 OR 00361437
bibdate: Mon Sep 16 16:15:31 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.09.16 16:15:31 ???
fjournal: SIAM News
acknowledgement: ack-nhfb
journalURL: https://sinews.siam.org/
rawauthor: D. K. Kahaner
rawtitle: Benchmarks for `real' programs
entry:
@Article{Kahaner:1988:BRP,
  author =       "D. K. Kahaner",
  title =        "Benchmarks for `real' programs",
  journal =      j-SIAM-NEWS,
  pages =        "A-61",
  month =        nov,
  year =         "1988",
  ISSN =         "0036-1437",
  ISSN-L =       "0036-1437",
  bibdate =      "Mon Sep 16 16:15:31 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM News",
  journal-URL =  "https://sinews.siam.org/",
}


bibtype: inproceedings
filename: fparith.bib
label: Kanada:1988:VMA
author: Yasumasa Kanada
booktitle: Proceedings of Supercomputing 88. Vol. II: Science and Applications
crossref: Martin:1988:SPN
volume: 2
pages: 117--128
year: 1988
bibdate: Sat Jul 16 16:53:44 MDT 2005
bibtimestamp: 2005.07.16 16:53:44 MDT
acknowledgement: ack-nhfb
corpsource: Comput. Centre, Tokyo University, Japan
treatment: P Practical
rawauthor: Yasumasa Kanada
rawbooktitle: Proceedings of Supercomputing 88. Vol. {II}: Science and Applications
title:
Vectorization of multiple-precision arithmetic program and 201,326,000 decimal digits of $ pi $ calculation

bibsource:
https://www.math.utah.edu/pub/tex/bib/agm.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/pi.bib

abstract:
More than 200 million decimal places of $ pi $ were calculated using an arithmetic geometric mean formula independently discovered by E. Salamin and R. P. Brent in 1976. Correctness of the calculation was verified through Borwein's quartic convergent formula developed in 1983. The computation took CPU times of 5 hours 57 minutes for the main calculation and 7 hours 30 minutes for the verification calculation on the HITAC S-820 model 80 supercomputer with 256 MB of main memory and 3 GB of high speed semiconductor storage, Extended Storage, to shorten I/O time.par Computation was completed in 27th of January 1988. At that day two programs generated values up to $ 3 times 2^26 $, about 201 million. The two results agreed except for the last 21 digits. These results also agree with the 133,554,000 places of calculation of $ pi $ which was done by the author in January 1987. Compare to the record in 1987, 50% more decimal digits were calculated with about $ 1 / 6 $ of CPU time.par Computation was performed with real arithmetic based vectorized Fast Fourier Transform (FFT) multiplier and newly vectorized multiple-precision add, subtract and (single word) constant multiplication programs. Vectorizations for the later cases were realized through first order linear recurrence vector instruction on the S-820. Details of the computation and statistical tests on the first 200 million digits of $ pi - 3 $ are reported.

keywords:
arithmetic geometric mean formula; Borwein's quartic convergent formula; fast Fourier transform; fast Fourier transforms; first order linear recurrence vector instruction; HITAC S-820 model 80 supercomputer; mathematics computing; multiple-precision arithmetic program; multiplier; parallel processing; pi calculation; S-820; vectorization

rawabstract:
More than 200 million decimal places of {$ \pi $} were calculated using an arithmetic geometric mean formula independently discovered by E. Salamin and R. P. Brent in 1976. Correctness of the calculation was verified through Borwein's quartic convergent formula developed in 1983. The computation took CPU times of 5 hours 57 minutes for the main calculation and 7 hours 30 minutes for the verification calculation on the HITAC S-820 model 80 supercomputer with 256 MB of main memory and 3 GB of high speed semiconductor storage, Extended Storage, to shorten I/O time.\par Computation was completed in 27th of January 1988. At that day two programs generated values up to $ 3 \times 2^{26} $, about 201 million. The two results agreed except for the last 21 digits. These results also agree with the 133,554,000 places of calculation of $ \pi $ which was done by the author in January 1987. Compare to the record in 1987, 50\% more decimal digits were calculated with about $ 1 / 6 $ of CPU time.\par Computation was performed with real arithmetic based vectorized Fast Fourier Transform (FFT) multiplier and newly vectorized multiple-precision add, subtract and (single word) constant multiplication programs. Vectorizations for the later cases were realized through first order linear recurrence vector instruction on the S-820. Details of the computation and statistical tests on the first 200 million digits of $ \pi - 3 $ are reported.

rawtitle:
Vectorization of multiple-precision arithmetic program and 201,326,000 decimal digits of {$ \pi $} calculation

entry:
@InProceedings{Kanada:1988:VMA,
  author =       "Yasumasa Kanada",
  booktitle =    "Proceedings of Supercomputing 88. Vol. {II}: Science
                 and Applications",
  title =        "Vectorization of multiple-precision arithmetic program
                 and 201,326,000 decimal digits of {$ \pi $}
                 calculation",
  crossref =     "Martin:1988:SPN",
  volume =       "2",
  pages =        "117--128",
  year =         "1988",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 16:53:44 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib",
  abstract =     "More than 200 million decimal places of {$ \pi $} were
                 calculated using an arithmetic geometric mean formula
                 independently discovered by E. Salamin and R. P. Brent
                 in 1976. Correctness of the calculation was verified
                 through Borwein's quartic convergent formula developed
                 in 1983. The computation took CPU times of 5 hours 57
                 minutes for the main calculation and 7 hours 30 minutes
                 for the verification calculation on the HITAC S-820
                 model 80 supercomputer with 256 MB of main memory and 3
                 GB of high speed semiconductor storage, Extended
                 Storage, to shorten I/O time.\par Computation was
                 completed in 27th of January 1988. At that day two
                 programs generated values up to $ 3 \times 2^{26} $,
                 about 201 million. The two results agreed except for
                 the last 21 digits. These results also agree with the
                 133,554,000 places of calculation of $ \pi $ which was
                 done by the author in January 1987. Compare to the
                 record in 1987, 50\% more decimal digits were
                 calculated with about $ 1 / 6 $ of CPU time.\par
                 Computation was performed with real arithmetic based
                 vectorized Fast Fourier Transform (FFT) multiplier and
                 newly vectorized multiple-precision add, subtract and
                 (single word) constant multiplication programs.
                 Vectorizations for the later cases were realized
                 through first order linear recurrence vector
                 instruction on the S-820. Details of the computation
                 and statistical tests on the first 200 million digits
                 of $ \pi - 3 $ are reported.",
  acknowledgement = ack-nhfb,
  classification = "C4190 (Other numerical methods); C7310
                 (Mathematics)",
  corpsource =   "Comput. Centre, Tokyo University, Japan",
  keywords =     "arithmetic geometric mean formula; Borwein's quartic
                 convergent formula; fast Fourier transform; fast
                 Fourier transforms; first order linear recurrence
                 vector instruction; HITAC S-820 model 80 supercomputer;
                 mathematics computing; multiple-precision arithmetic
                 program; multiplier; parallel processing; pi
                 calculation; S-820; vectorization",
  sponsororg =   "IEEE; ACM SIGARCH",
  treatment =    "P Practical",
}


bibtype: inproceedings
filename: fparith.bib
label: Kanada:1988:VMP
author: Yasumasa Kanada
booktitle: Proceedings of Supercomputing 88. Vol. II: Science and Applications
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 117--128
year: 1988
bibdate: Sat Jul 16 16:53:44 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 16:53:44 MDT
acknowledgement: ack-nhfb
rawauthor: Yasumasa Kanada
rawbooktitle: Proceedings of Supercomputing 88. Vol. {II}: Science and Applications
title:
Vectorization of multiple-precision arithmetic program and 201,326,000 decimal digits of $ pi $ calculation

abstract:
More than 200 million decimal places of pi were calculated using an arithmetic geometric mean formula independently discovered by E. Salamin and R. P. Brent in 1976. Correctness of the calculation was verified through Borwein's quartic convergent formula developed in 1983. The computation took CPU times of 5 hours 57 minutes for the main calculation and 7 hours 30 minutes for the verification calculation on the HITAC S-820 model 80 supercomputer with 256 MB of main memory and 3 GB of high speed semiconductor storage, Extended Storage, to shorten I/O time.par Computation was completed in 27th of January 1988. At that day two programs generated values up to $ 3 times 2^26 $, about 201 million. The two results agreed except for the last 21 digits. These results also agree with the 133,554,000 places of calculation of $ pi $ which was done by the author in January 1987. Compare to the record in 1987, 50% more decimal digits were calculated with about $ 1 / 6 $ of CPU time.par Computation was performed with real arithmetic based vectorized Fast Fourier Transform (FFT) multiplier and newly vectorized multiple-precision add, subtract and (single word) constant multiplication programs. Vectorizations for the later cases were realized through first order linear recurrence vector instruction on the S-820. Dertails of the computation and statistical tests on the first 200 million digits of $ pi - 3 $ are reported.

rawabstract:
More than 200 million decimal places of {\pi} were calculated using an arithmetic geometric mean formula independently discovered by E. Salamin and R. P. Brent in 1976. Correctness of the calculation was verified through Borwein's quartic convergent formula developed in 1983. The computation took CPU times of 5 hours 57 minutes for the main calculation and 7 hours 30 minutes for the verification calculation on the HITAC S-820 model 80 supercomputer with 256 MB of main memory and 3 GB of high speed semiconductor storage, Extended Storage, to shorten I/O time.\par Computation was completed in 27th of January 1988. At that day two programs generated values up to $ 3 \times 2^{26} $, about 201 million. The two results agreed except for the last 21 digits. These results also agree with the 133,554,000 places of calculation of $ \pi $ which was done by the author in January 1987. Compare to the record in 1987, 50\% more decimal digits were calculated with about $ 1 / 6 $ of CPU time.\par Computation was performed with real arithmetic based vectorized Fast Fourier Transform (FFT) multiplier and newly vectorized multiple-precision add, subtract and (single word) constant multiplication programs. Vectorizations for the later cases were realized through first order linear recurrence vector instruction on the S-820. Dertails of the computation and statistical tests on the first 200 million digits of $ \pi - 3 $ are reported.

rawtitle:
Vectorization of multiple-precision arithmetic program and 201,326,000 decimal digits of {$ \pi $} calculation

entry:
@InProceedings{Kanada:1988:VMP,
  author =       "Yasumasa Kanada",
  booktitle =    "Proceedings of Supercomputing 88. Vol. {II}: Science
                 and Applications",
  title =        "Vectorization of multiple-precision arithmetic program
                 and 201,326,000 decimal digits of {$ \pi $}
                 calculation",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "117--128",
  year =         "1988",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 16:53:44 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "More than 200 million decimal places of {\pi} were
                 calculated using an arithmetic geometric mean formula
                 independently discovered by E. Salamin and R. P. Brent
                 in 1976. Correctness of the calculation was verified
                 through Borwein's quartic convergent formula developed
                 in 1983. The computation took CPU times of 5 hours 57
                 minutes for the main calculation and 7 hours 30 minutes
                 for the verification calculation on the HITAC S-820
                 model 80 supercomputer with 256 MB of main memory and 3
                 GB of high speed semiconductor storage, Extended
                 Storage, to shorten I/O time.\par

                 Computation was completed in 27th of January 1988. At
                 that day two programs generated values up to $ 3 \times
                 2^{26} $, about 201 million. The two results agreed
                 except for the last 21 digits. These results also agree
                 with the 133,554,000 places of calculation of $ \pi $
                 which was done by the author in January 1987. Compare
                 to the record in 1987, 50\% more decimal digits were
                 calculated with about $ 1 / 6 $ of CPU
                 time.\par

                 Computation was performed with real arithmetic based
                 vectorized Fast Fourier Transform (FFT) multiplier and
                 newly vectorized multiple-precision add, subtract and
                 (single word) constant multiplication programs.
                 Vectorizations for the later cases were realized
                 through first order linear recurrence vector
                 instruction on the S-820. Dertails of the computation
                 and statistical tests on the first 200 million digits
                 of $ \pi - 3 $ are reported.",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Kida:1988:FPP
author: H. Kida and M. Watabe and T. Nakamikawa and S. Morinaga and S. Kawasaki and H. Inayoshi
title: A floating point processing unit for the GMICRO CPU
crossref: Sakamura:1988:TPO
pages: 301--316
year: 1988
DOI: https://doi.org/10.1007/978-4-431-68081-9_21
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
acknowledgement: ack-nhfb
affiliation: Hitachi Ltd., Tokyo, Japan
bookpages: xi + 384
thesaurus: Computer architecture; Microprocessor chips
rawauthor: H. Kida and M. Watabe and T. Nakamikawa and S. Morinaga and S. Kawasaki and H. Inayoshi
rawtitle: A floating point processing unit for the {GMICRO} {CPU}
abstract:
Describes the architecture and implementation of a newly developed floating point processing unit (FPU). It was developed as a high performance 32-bit coprocessor of the 32-bit GMICRO microprocessor, which satisfies the IEEE 754 Standard for Binary Floating-Point Arithmetic. High performance was achieved by the high speed coprocessor's interface with the GMICRO CPU and the pipeline processing. The coprocessor's interface was designed to minimize CPU-FPU communication overhead caused by transferring commands, operands and coprocessor information. Furthermore, to improve operation speed, the FPU performs pipeline processing named command pipeline. The FPU has three main elements, the bus control unit, format conversion unit, and execution control unit. In order to perform high speed calculations, each element in the chip is designed to operate in parallel. (5 Refs.)

keywords:
32 Bit; Coprocessor; Floating point processing unit; FPU; GMICRO CPU; GMICRO microprocessor; IEEE 754; Standard for Binary Floating-Point Arithmetic

rawabstract:
Describes the architecture and implementation of a newly developed floating point processing unit (FPU). It was developed as a high performance 32-bit coprocessor of the 32-bit GMICRO microprocessor, which satisfies the IEEE 754 Standard for Binary Floating-Point Arithmetic. High performance was achieved by the high speed coprocessor's interface with the GMICRO CPU and the pipeline processing. The coprocessor's interface was designed to minimize CPU-FPU communication overhead caused by transferring commands, operands and coprocessor information. Furthermore, to improve operation speed, the FPU performs pipeline processing named command pipeline. The FPU has three main elements, the bus control unit, format conversion unit, and execution control unit. In order to perform high speed calculations, each element in the chip is designed to operate in parallel. (5 Refs.)

entry:
@InProceedings{Kida:1988:FPP,
  author =       "H. Kida and M. Watabe and T. Nakamikawa and S.
                 Morinaga and S. Kawasaki and H. Inayoshi",
  title =        "A floating point processing unit for the {GMICRO}
                 {CPU}",
  crossref =     "Sakamura:1988:TPO",
  bookpages =    "xi + 384",
  pages =        "301--316",
  year =         "1988",
  DOI =          "https://doi.org/10.1007/978-4-431-68081-9_21",
  bibdate =      "Tue Dec 12 09:17:24 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Describes the architecture and implementation of a
                 newly developed floating point processing unit (FPU).
                 It was developed as a high performance 32-bit
                 coprocessor of the 32-bit GMICRO microprocessor, which
                 satisfies the IEEE 754 Standard for Binary
                 Floating-Point Arithmetic. High performance was
                 achieved by the high speed coprocessor's interface with
                 the GMICRO CPU and the pipeline processing. The
                 coprocessor's interface was designed to minimize
                 CPU-FPU communication overhead caused by transferring
                 commands, operands and coprocessor information.
                 Furthermore, to improve operation speed, the FPU
                 performs pipeline processing named command pipeline.
                 The FPU has three main elements, the bus control unit,
                 format conversion unit, and execution control unit. In
                 order to perform high speed calculations, each element
                 in the chip is designed to operate in parallel. (5
                 Refs.)",
  acknowledgement = ack-nhfb,
  affiliation =  "Hitachi Ltd., Tokyo, Japan",
  classification = "C5220 (Computer architecture)",
  confdate =     "1988",
  conflocation = "Japan",
  keywords =     "32 Bit; Coprocessor; Floating point processing unit;
                 FPU; GMICRO CPU; GMICRO microprocessor; IEEE 754;
                 Standard for Binary Floating-Point Arithmetic",
  numericalindex = "Word length 3.2E+01 bit",
  pubcountry =   "Japan",
  thesaurus =    "Computer architecture; Microprocessor chips",
}


bibtype: article
filename: fparith.bib
label: Kirchner:1988:AAV
author: R. Kirchner and U. Kulisch
title: Accurate arithmetic for vector processors
journal: j-J-PAR-DIST-COMP
volume: 5
number: 3
pages: 250--270
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 Kaiserslautern, West Ger
corpsource: Fachbereich Inf., Kaiserslautern University, West Germany
journalURL: http://www.sciencedirect.com/science/journal/07437315
journalabr: J Parallel Distrib Comput
treatment: P Practical
rawauthor: R. Kirchner and U. Kulisch
rawtitle: Accurate arithmetic for vector processors
keywords:
arithmetic operations; Computational Methods; computer systems, digital --- Parallel Processing; computers; computers, digital; computers, microcomputer; digital arithmetic; dot products; implementation techniques; local memory; microcomputers; parallel; parallel processing; pipelined compound operations; sums; vector processors; VLSI technology

entry:
@Article{Kirchner:1988:AAV,
  author =       "R. Kirchner and U. Kulisch",
  title =        "Accurate arithmetic for vector processors",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "5",
  number =       "3",
  pages =        "250--270",
  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 Kaiserslautern, West Ger",
  classification = "721; 722; 723; C5230 (Digital arithmetic methods);
                 C5440 (Multiprocessor systems and techniques)",
  corpsource =   "Fachbereich Inf., Kaiserslautern University, West
                 Germany",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "arithmetic operations; Computational Methods; computer
                 systems, digital --- Parallel Processing; computers;
                 computers, digital; computers, microcomputer; digital
                 arithmetic; dot products; implementation techniques;
                 local memory; microcomputers; parallel; parallel
                 processing; pipelined compound operations; sums; vector
                 processors; VLSI technology",
  treatment =    "P Practical",
}


bibtype: article
filename: fparith.bib
label: Knuth:1988:FM
author: Donald E. Knuth
title: Fibonacci multiplication
journal: j-APPL-MATH-LETT
volume: 1
number: 1
pages: 57--60
year: 1988
CODEN: AMLEEL
ISSN: 0893-9659 (print), 1873-5452 (electronic) OR 08939659 (print), 18735452 (electronic)
ISSNL: 0893-9659 OR 08939659
MRclass: 11B39
MRnumber: 89f:11031
MRreviewer: W. Herget
bibdate: Fri Mar 22 18:03:29 MST 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; MathSciNet database
bibtimestamp: 2002.03.22 18:03:29 MST
fjournal: Applied Mathematics Letters
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08939659
rawauthor: Donald E. Knuth
rawtitle: {Fibonacci} multiplication
entry:
@Article{Knuth:1988:FM,
  author =       "Donald E. Knuth",
  title =        "{Fibonacci} multiplication",
  journal =      j-APPL-MATH-LETT,
  volume =       "1",
  number =       "1",
  pages =        "57--60",
  year =         "1988",
  CODEN =        "AMLEEL",
  ISSN =         "0893-9659 (print), 1873-5452 (electronic)",
  ISSN-L =       "0893-9659",
  MRclass =      "11B39",
  MRnumber =     "89f:11031",
  MRreviewer =   "W. Herget",
  bibdate =      "Fri Mar 22 18:03:29 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 MathSciNet database",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08939659",
}


bibtype: article
filename: fparith.bib
label: Kornerup:1988:LAU
author: Peter Kornerup and David W. Matula
title: An on-line arithmetic unit for bit-pipelined rational arithmetic
journal: j-J-PAR-DIST-COMP
volume: 5
number: 3
pages: 310--330
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: Odense Univ, Odense, Den
corpsource: Odense University, Denmark
journalURL: http://www.sciencedirect.com/science/journal/07437315
journalabr: J Parallel Distrib Comput
treatment: P Practical
rawauthor: Peter Kornerup and David W. Matula
rawtitle: An on-line arithmetic unit for bit-pipelined rational arithmetic
keywords:
algorithm of Gosper; Algorithms; binary version; bit-pipelined rational arithmetic; computer metatheory --- Binary Sequences; computer programming; computers, digital --- Computational Methods; difference; digital arithmetic; functions; mathematical techniques --- Algorithms; on-line arithmetic unit; online arithmetic unit; product; quotient; rational; sum

entry:
@Article{Kornerup:1988:LAU,
  author =       "Peter Kornerup and David W. Matula",
  title =        "An on-line arithmetic unit for bit-pipelined rational
                 arithmetic",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "5",
  number =       "3",
  pages =        "310--330",
  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 = "Odense Univ, Odense, Den",
  classification = "722; 723; 921; C5230 (Digital arithmetic methods)",
  corpsource =   "Odense University, Denmark",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "algorithm of Gosper; Algorithms; binary version;
                 bit-pipelined rational arithmetic; computer metatheory
                 --- Binary Sequences; computer programming; computers,
                 digital --- Computational Methods; difference; digital
                 arithmetic; functions; mathematical techniques ---
                 Algorithms; on-line arithmetic unit; online arithmetic
                 unit; product; quotient; rational; sum",
  treatment =    "P Practical",
}


bibtype: inproceedings
filename: fparith.bib
label: Krishnan:1988:IRN
author: R. Krishnan
booktitle: IEEE International Symposium on Circuits and Systems, 7--9 June 1988
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1297--1300
year: 1988
DOI: https://doi.org/10.1109/ISCAS.1988.15166
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: R. Krishnan
rawbooktitle: {IEEE} International Symposium on Circuits and Systems, 7--9 June 1988
title:
Implementation of recursive and nonrecursive digital filters using the single multiplexed ROM in the quadratic residue number system

rawtitle:
Implementation of recursive and nonrecursive digital filters using the single multiplexed {ROM} in the quadratic residue number system

entry:
@InProceedings{Krishnan:1988:IRN,
  author =       "R. Krishnan",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems, 7--9 June 1988",
  title =        "Implementation of recursive and nonrecursive digital
                 filters using the single multiplexed {ROM} in the
                 quadratic residue number system",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1297--1300",
  year =         "1988",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.1988.15166",
  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 =      "Recursive and nonrecursive digital filters have been
                 implemented using the proposed single-multiplexed
                 dual-clock computational module (SDCM) in the bit-slice
                 architecture. The amount of memory requirements has
                 been reduced to 50\% required for the \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Krishnan:1988:SCR
author: R. Krishnan
booktitle: International Conference on Acoustics, Speech, and Signal Processing, ICASSP-88, 11--14 April 1988
volume: 3
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1842--1845
year: 1988
DOI: https://doi.org/10.1109/ICASSP.1988.196981
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: R. Krishnan
title:
A single-channel ROM-based complex digital filter implementation in the quadratic residue number systems

rawbooktitle:
International Conference on Acoustics, Speech, and Signal Processing, {ICASSP-88, 11--14} April 1988

rawtitle:
A single-channel {ROM}-based complex digital filter implementation in the quadratic residue number systems

entry:
@InProceedings{Krishnan:1988:SCR,
  author =       "R. Krishnan",
  booktitle =    "International Conference on Acoustics, Speech, and
                 Signal Processing, {ICASSP-88, 11--14} April 1988",
  title =        "A single-channel {ROM}-based complex digital filter
                 implementation in the quadratic residue number
                 systems",
  volume =       "3",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1842--1845",
  year =         "1988",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ICASSP.1988.196981",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "The implementation of complex digital filters using
                 the quadratic residue number system (QRNs) and modified
                 quadratic residue number system (MQRNS) is considered.
                 These QRNS/MQRNS-based filter architectures are
                 memory-intensive because the lookup- \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Lai:1988:FAI
author: K. Lai and J. Valerio
title: The floating-point architecture of Intel's 80960
crossref: Wescon:1988:WCR
pages: 1.5/1--3
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: Intel Corp., Hillsboro, OR, USA
thesaurus: Computer architecture; Digital arithmetic; Microprocessor chips
rawauthor: K. Lai and J. Valerio
rawtitle: The floating-point architecture of {Intel's 80960}
abstract:
The Intel 80960KB is a microprocessor with hardware floating-point support integrated on-chip. In a departure from previous microprocessors, the 80960KB incorporates full floating-point support within the processor instead of relying on a coprocessor. As floating-point speeds increase, the off-chip coprocessor interface becomes a significant performance bottleneck. Additionally, component and system cost, board space, and cleanliness of architecture are other good reasons to have on-chip floating-point support. The implementation delivers accurate results with good performance: 1.1 single-precision Linpack MFLOPS, and 4.1 single-precision mega-Whetstones per second. (0 Refs.)

keywords:
1.1 MFLOPS; Board space; Cleanliness; Component costs; Floating-point architecture; Intel 80960KB; Linpack; Microprocessor; On-chip floating-point support; Performance; System cost

rawabstract:
The Intel 80960KB is a microprocessor with hardware floating-point support integrated on-chip. In a departure from previous microprocessors, the 80960KB incorporates full floating-point support within the processor instead of relying on a coprocessor. As floating-point speeds increase, the off-chip coprocessor interface becomes a significant performance bottleneck. Additionally, component and system cost, board space, and cleanliness of architecture are other good reasons to have on-chip floating-point support. The implementation delivers accurate results with good performance: 1.1 single-precision Linpack MFLOPS, and 4.1 single-precision mega-Whetstones per second. (0 Refs.)

entry:
@InProceedings{Lai:1988:FAI,
  author =       "K. Lai and J. Valerio",
  title =        "The floating-point architecture of {Intel's 80960}",
  crossref =     "Wescon:1988:WCR",
  pages =        "1.5/1--3",
  year =         "1988",
  bibdate =      "Tue Dec 12 09:20:21 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The Intel 80960KB is a microprocessor with hardware
                 floating-point support integrated on-chip. In a
                 departure from previous microprocessors, the 80960KB
                 incorporates full floating-point support within the
                 processor instead of relying on a coprocessor. As
                 floating-point speeds increase, the off-chip
                 coprocessor interface becomes a significant performance
                 bottleneck. Additionally, component and system cost,
                 board space, and cleanliness of architecture are other
                 good reasons to have on-chip floating-point support.
                 The implementation delivers accurate results with good
                 performance: 1.1 single-precision Linpack MFLOPS, and
                 4.1 single-precision mega-Whetstones per second. (0
                 Refs.)",
  acknowledgement = ack-nhfb,
  affiliation =  "Intel Corp., Hillsboro, OR, USA",
  classification = "C5130 (Microprocessor chips); C5220 (Computer
                 architecture); C5230 (Digital arithmetic methods)",
  keywords =     "1.1 MFLOPS; Board space; Cleanliness; Component costs;
                 Floating-point architecture; Intel 80960KB; Linpack;
                 Microprocessor; On-chip floating-point support;
                 Performance; System cost",
  numericalindex = "Computer speed 1.1E+06 FLOPS",
  thesaurus =    "Computer architecture; Digital arithmetic;
                 Microprocessor chips",
}


bibtype: inproceedings
filename: fparith.bib
label: Lai:1988:IFS
author: K. Lai and J. Valerio
title: Integrated floating-point solution for the Intel 80960KB
crossref: Midcon:1988:MCP
pages: 249--251
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: Intel Corp., Hillsboro, OR, USA
thesaurus: Digital arithmetic; Microprocessor chips
rawauthor: K. Lai and J. Valerio
rawtitle: Integrated floating-point solution for the {Intel 80960KB}
abstract:
The Intel 80960KB is a microprocessor with hardware floating-point support integrated on-chip. In a departure from previous microprocessors, the 80960KB incorporates full floating-point support within the processor instead of relying on a coprocessor. As floating-point speeds increase, the off-chip coprocessor interface becomes a significant performance bottleneck. Additionally, component and system cost, board space, and cleanliness of architecture are other good reasons to have on-chip floating-point support. The implementation delivers accurate results with good performance: 1.1 single precision Linpack MFLOPS, and 4.1 single precision mega Whetstones per second. (0 Refs.)

keywords:
Floating-point support; Integrated floating point; Intel 80960KB; Microprocessor; Onchip floating point

rawabstract:
The Intel 80960KB is a microprocessor with hardware floating-point support integrated on-chip. In a departure from previous microprocessors, the 80960KB incorporates full floating-point support within the processor instead of relying on a coprocessor. As floating-point speeds increase, the off-chip coprocessor interface becomes a significant performance bottleneck. Additionally, component and system cost, board space, and cleanliness of architecture are other good reasons to have on-chip floating-point support. The implementation delivers accurate results with good performance: 1.1 single precision Linpack MFLOPS, and 4.1 single precision mega Whetstones per second. (0 Refs.)

entry:
@InProceedings{Lai:1988:IFS,
  author =       "K. Lai and J. Valerio",
  title =        "Integrated floating-point solution for the {Intel
                 80960KB}",
  crossref =     "Midcon:1988:MCP",
  pages =        "249--251",
  year =         "1988",
  bibdate =      "Tue Dec 12 09:20:21 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The Intel 80960KB is a microprocessor with hardware
                 floating-point support integrated on-chip. In a
                 departure from previous microprocessors, the 80960KB
                 incorporates full floating-point support within the
                 processor instead of relying on a coprocessor. As
                 floating-point speeds increase, the off-chip
                 coprocessor interface becomes a significant performance
                 bottleneck. Additionally, component and system cost,
                 board space, and cleanliness of architecture are other
                 good reasons to have on-chip floating-point support.
                 The implementation delivers accurate results with good
                 performance: 1.1 single precision Linpack MFLOPS, and
                 4.1 single precision mega Whetstones per second. (0
                 Refs.)",
  acknowledgement = ack-nhfb,
  affiliation =  "Intel Corp., Hillsboro, OR, USA",
  classification = "C5130 (Microprocessor chips)",
  keywords =     "Floating-point support; Integrated floating point;
                 Intel 80960KB; Microprocessor; Onchip floating point",
  thesaurus =    "Digital arithmetic; Microprocessor chips",
}


bibtype: article
filename: fparith.bib
label: Lawson:1988:SRR
author: Charles L. Lawson
title: Series reversion as the reversed chain rule
journal: j-SIGNUM
volume: 23
number: 1
pages: 7--9
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 Apr 12 07:50:16 MDT 2005
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.04.12 07:50:16 MDT
fjournal: ACM SIGNUM Newsletter
keywords: design; differentiation arithmetic; implicit functions; languages; theory
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/signum
rawauthor: Charles L. Lawson
rawtitle: Series reversion as the reversed chain rule
abstract:
Lawson gives Fortran subroutines for differentiation arithmetic. A subroutine SWPRO for products corresponds to Chang's ATS [Chang74a]. The chain rule is implemented by repeated calls to SWPRO. Series reversion for implicit functions is implemented by reversing the chain rule. An application is given to Keppler's equation, $ M - E + e sin (E) = 0 $.

subject:
D.3.3 Software, PROGRAMMING LANGUAGES, Language Constructs, Modules, packages G.4 Mathematics of Computing, MATHEMATICAL SOFTWARE D.3.3 Software, PROGRAMMING LANGUAGES, Language Constructs, Procedures, functions, and subroutines

rawabstract:
Lawson gives Fortran subroutines for differentiation arithmetic. A subroutine SWPRO for products corresponds to Chang's ATS [Chang74a]. The chain rule is implemented by repeated calls to SWPRO. Series reversion for implicit functions is implemented by reversing the chain rule. An application is given to Keppler's equation, $ M - E + e \sin (E) = 0 $.

entry:
@Article{Lawson:1988:SRR,
  author =       "Charles L. Lawson",
  title =        "Series reversion as the reversed chain rule",
  journal =      j-SIGNUM,
  volume =       "23",
  number =       "1",
  pages =        "7--9",
  month =        jan,
  year =         "1988",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:16 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Lawson gives Fortran subroutines for differentiation
                 arithmetic. A subroutine SWPRO for products corresponds
                 to Chang's ATS [Chang74a]. The chain rule is
                 implemented by repeated calls to SWPRO. Series
                 reversion for implicit functions is implemented by
                 reversing the chain rule. An application is given to
                 Keppler's equation, $ M - E + e \sin (E) = 0 $.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "design; differentiation arithmetic; implicit
                 functions; languages; theory",
  subject =      "D.3.3 Software, PROGRAMMING LANGUAGES, Language
                 Constructs, Modules, packages \\ G.4 Mathematics of
                 Computing, MATHEMATICAL SOFTWARE \\ D.3.3 Software,
                 PROGRAMMING LANGUAGES, Language Constructs, Procedures,
                 functions, and subroutines",
}


bibtype: techreport
filename: fparith.bib
label: Liu:1988:BEF
author: Zhi-Shun Alex Liu
title: Berkeley Elementary Function Test Suite
address: Berkeley, CA, USA
pages: ii + 59
day: 30
month: dec
monthnumber: 12
year: 1988
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 ???
URL: http://www.netlib.org/fp/ucbtest.tgz; http://www.ucbtest.org/zaliu-papers/zaliu-beef-doc.pdf
keywords: BeEF test suite; floating-point testing
acknowledgement: ack-nj
rawauthor: Zhi-Shun Alex Liu
rawtitle: {Berkeley} Elementary Function Test Suite
institution:
Computer Science Division, Department of Electrical Engineering and Computer Science, Univerity of California at Berkeley

abstract:
A suite of programs is presented to test how accurately the elementary transcendental functions exp, log, sin, cos and atan have been implemented in a computer's run-time library. The suite is written in the language C and designed to run on any computer with binary floating-point arithmetic rounded in a reasonable way. The suite makes no appeal to extra-precise arithmetic; the tests use only whatever arithmetic capabilities are present in the environment where the transcendental functions are to be used. Despite this limitation, the tests run fast and deliver indication of accuracy to within a small fraction of an ULP (Unit in the Last Place) of the functions under test. This account includes the proofs of the test suite's claims to accuracy.

rawabstract:
A suite of programs is presented to test how accurately the elementary transcendental functions exp, log, sin, cos and atan have been implemented in a computer's run-time library. The suite is written in the language C and designed to run on any computer with binary floating-point arithmetic rounded in a reasonable way. The suite makes no appeal to extra-precise arithmetic; the tests use only whatever arithmetic capabilities are present in the environment where the transcendental functions are to be used. Despite this limitation, the tests run fast and deliver indication of accuracy to within a small fraction of an ULP (Unit in the Last Place) of the functions under test. This account includes the proofs of the test suite's claims to accuracy.

entry:
@TechReport{Liu:1988:BEF,
  author =       "Zhi-Shun Alex Liu",
  title =        "{Berkeley} Elementary Function Test Suite",
  institution =  "Computer Science Division, Department of Electrical
                 Engineering and Computer Science, Univerity of
                 California at Berkeley",
  address =      "Berkeley, CA, USA",
  pages =        "ii + 59",
  day =          "30",
  month =        dec,
  year =         "1988",
  bibdate =      "Mon Sep 12 23:52:34 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.netlib.org/fp/ucbtest.tgz;
                 http://www.ucbtest.org/zaliu-papers/zaliu-beef-doc.pdf",
  abstract =     "A suite of programs is presented to test how
                 accurately the elementary transcendental functions exp,
                 log, sin, cos and atan have been implemented in a
                 computer's run-time library. The suite is written in
                 the language C and designed to run on any computer with
                 binary floating-point arithmetic rounded in a
                 reasonable way. The suite makes no appeal to
                 extra-precise arithmetic; the tests use only whatever
                 arithmetic capabilities are present in the environment
                 where the transcendental functions are to be used.
                 Despite this limitation, the tests run fast and deliver
                 indication of accuracy to within a small fraction of an
                 ULP (Unit in the Last Place) of the functions under
                 test. This account includes the proofs of the test
                 suite's claims to accuracy.",
  acknowledgement = ack-nj,
  keywords =     "BeEF test suite; floating-point testing",
}


bibtype: inproceedings
filename: fparith.bib
label: Lu:1988:MCF
author: P. Y. Lu and A. Jain and J. Kung and P. H. Ang
title: A 30-MFLOP 32b CMOS Floating-Point Processor
crossref: IEEE:1988:IIS
pages: 28, 29, 285
year: 1988
bibdate: Fri Dec 08 13:04:40 1995
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 13:04:40 ???
acknowledgement: ack-nj
rawauthor: P. Y. Lu and A. Jain and J. Kung and P. H. Ang
rawtitle: A 30-{MFLOP} 32b {CMOS} Floating-Point Processor
entry:
@InProceedings{Lu:1988:MCF,
  author =       "P. Y. Lu and A. Jain and J. Kung and P. H. Ang",
  title =        "A 30-{MFLOP} 32b {CMOS} Floating-Point Processor",
  crossref =     "IEEE:1988:IIS",
  pages =        "28, 29, 285",
  year =         "1988",
  bibdate =      "Fri Dec 08 13:04:40 1995",
  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: Luk:1988:AAB
author: Franklin T. Luk and Haesun Park
title: An analysis of algorithm-based fault tolerance techniques
journal: j-J-PAR-DIST-COMP
volume: 5
number: 2
pages: 172--184
month: apr
monthnumber: 4
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: Cornell Univ, Ithaca, NY, USA
corpsource: Sch. of Electr. Eng., Cornell University, Ithaca, NY, USA
journalURL: http://www.sciencedirect.com/science/journal/07437315
journalabr: J Parallel Distrib Comput
treatment: T Theoretical or Mathematical
rawauthor: Franklin T. Luk and Haesun Park
rawtitle: An analysis of algorithm-based fault tolerance techniques
keywords:
algorithm-based fault tolerance; analysis; computation; computer programming --- Algorithms; computer systems, digital; decomposition; error analysis; Fault Tolerant Capability; fault tolerant computing; floating point error; Gaussian elimination; Gaussian elimination with pairwise pivoting; LU; lu decomposition; matrix algebra; pairwise pivoting; qr decomposition; QR decomposition; rank-one perturbation; rounding errors; roundoff errors; systolic array; transient error; unified checksum scheme

entry:
@Article{Luk:1988:AAB,
  author =       "Franklin T. Luk and Haesun Park",
  title =        "An analysis of algorithm-based fault tolerance
                 techniques",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "5",
  number =       "2",
  pages =        "172--184",
  month =        apr,
  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 = "Cornell Univ, Ithaca, NY, USA",
  classification = "722; 723; C4110 (Error analysis in numerical
                 methods); C4140 (Linear algebra); C5230 (Digital
                 arithmetic methods); C5470 (Performance evaluation and
                 testing)",
  corpsource =   "Sch. of Electr. Eng., Cornell University, Ithaca, NY,
                 USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "algorithm-based fault tolerance; analysis;
                 computation; computer programming --- Algorithms;
                 computer systems, digital; decomposition; error
                 analysis; Fault Tolerant Capability; fault tolerant
                 computing; floating point error; Gaussian elimination;
                 Gaussian elimination with pairwise pivoting; LU; lu
                 decomposition; matrix algebra; pairwise pivoting; qr
                 decomposition; QR decomposition; rank-one perturbation;
                 rounding errors; roundoff errors; systolic array;
                 transient error; unified checksum scheme",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: mastersthesis
filename: fparith.bib
label: Lyu:1988:PFP
author: Chung-nan Lyu
title: Pipelined floating point divider with built-in testing circuits
type: Thesis (M.S.)
school: Ohio University
address: Athens, OH, USA
pages: 90
month: jun
monthnumber: 6
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 testing; parallel processing (electronic computers)
acknowledgement: ack-nhfb
rawauthor: Chung-nan Lyu
rawtitle: Pipelined floating point divider with built-in testing circuits
entry:
@MastersThesis{Lyu:1988:PFP,
  author =       "Chung-nan Lyu",
  title =        "Pipelined floating point divider with built-in testing
                 circuits",
  type =         "Thesis ({M.S.})",
  school =       "Ohio University",
  address =      "Athens, OH, USA",
  pages =        "90",
  month =        jun,
  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 testing; parallel processing
                 (electronic computers)",
}


bibtype: article
filename: fparith.bib
label: Magenheimer:1988:IMD
author: Daniel J. Magenheimer and Liz Peters and Karl W. Peters and Dan Zuras
title: Integer Multiplication and Division on the HP Precision Architecture
journal: j-IEEE-TRANS-COMPUT
volume: 37
number: 8
pages: 980--990
month: aug
monthnumber: 8
year: 1988
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.2248
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Aug 04 16:38:15 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.08.04 16:38:15 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Daniel J. Magenheimer and Liz Peters and Karl W. Peters and Dan Zuras
rawtitle: Integer Multiplication and Division on the {HP Precision Architecture}
entry:
@Article{Magenheimer:1988:IMD,
  author =       "Daniel J. Magenheimer and Liz Peters and Karl W.
                 Peters and Dan Zuras",
  title =        "Integer Multiplication and Division on the {HP
                 Precision Architecture}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "37",
  number =       "8",
  pages =        "980--990",
  month =        aug,
  year =         "1988",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.2248",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Aug 04 16:38:15 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Marchyulaitis:1988:SRN
author: Saulyus Marchyulaui tis
journal: Statist. Problemy Upravleniya
volume: 82
pages: 57--68
year: 1988
MRclass: 65G05 (65C20)
MRnumber: 89k:65056
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 ???
keywords: accurate floating-point summation
language: Russian
acknowledgement: ack-nhfb
rawauthor: Saulyus Marchyula{\u\i}tis
title:
Summation of real numbers in arithmetic with a floating point. A probability approach to determining the variance of absolute round-off error. (Russian)

rawtitle:
Summation of real numbers in arithmetic with a floating point. {A} probability approach to determining the variance of absolute round-off error. ({Russian})

entry:
@Article{Marchyulaitis:1988:SRN,
  author =       "Saulyus Marchyula{\u\i}tis",
  title =        "Summation of real numbers in arithmetic with a
                 floating point. {A} probability approach to determining
                 the variance of absolute round-off error. ({Russian})",
  journal =      "Statist. Problemy Upravleniya",
  volume =       "82",
  pages =        "57--68",
  year =         "1988",
  MRclass =      "65G05 (65C20)",
  MRnumber =     "89k:65056",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation",
  language =     "Russian",
}


bibtype: article
filename: fparith.bib
label: Maurer:1988:DVW
author: P. M. Maurer
title: Design Verification of the WE 32106 Math Accelerator Unit
journal: j-IEEE-DES-TEST-COMPUT
volume: 5
number: 3
pages: 11--21
month: jun
monthnumber: 6
year: 1988
ISSN: 0740-7475 (print), 1558-1918 (electronic) OR 07407475 (print), 15581918 (electronic)
ISSNL: 0740-7475 OR 07407475
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 Design & Test of Computers
acknowledgement: ack-nj
rawauthor: P. M. Maurer
rawtitle: Design Verification of the {WE} 32106 Math Accelerator Unit
entry:
@Article{Maurer:1988:DVW,
  author =       "P. M. Maurer",
  title =        "Design Verification of the {WE} 32106 Math Accelerator
                 Unit",
  journal =      j-IEEE-DES-TEST-COMPUT,
  volume =       "5",
  number =       "3",
  pages =        "11--21",
  month =        jun,
  year =         "1988",
  ISSN =         "0740-7475 (print), 1558-1918 (electronic)",
  ISSN-L =       "0740-7475",
  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 Design \& Test of Computers",
}


bibtype: article
filename: fparith.bib
label: McLellan:1988:DCF
author: E. J. McLellan and G. M. Wolrich and R. A. J. Yodlowski
title: Development of the CVAX floating-point chip
journal: j-DEC-TECH-J
number: 7
pages: 109--120
month: aug
monthnumber: 8
year: 1988
CODEN: DTJOEL
ISSN: 0898-901X OR 0898901X
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: Digital Technical Journal
acknowledgement: ack-nj
rawauthor: E. J. McLellan and G. M. Wolrich and R. A. J. Yodlowski
rawtitle: Development of the {CVAX} floating-point chip
entry:
@Article{McLellan:1988:DCF,
  author =       "E. J. McLellan and G. M. Wolrich and R. A. J.
                 Yodlowski",
  title =        "Development of the {CVAX} floating-point chip",
  journal =      j-DEC-TECH-J,
  volume =       "??",
  number =       "7",
  pages =        "109--120",
  month =        aug,
  year =         "1988",
  CODEN =        "DTJOEL",
  ISSN =         "0898-901X",
  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 =     "Digital Technical Journal",
}


bibtype: inproceedings
filename: fparith.bib
label: Melear:1988:IFP
author: C. Melear
title: An integrated floating point unit for a RISC architecture
crossref: Wescon:1988:WCR
pages: 1.2/1--8
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: Motorola, Austin, TX, USA
thesaurus: Digital arithmetic; Microprocessor chips; Reduced instruction set computing
rawauthor: C. Melear
rawtitle: An integrated floating point unit for a {RISC} architecture
abstract:
RISC architectures require multiple bus structures that allow for instructions, operands, and results to all travel about the processor on each clock cycle. Thus, by putting the floating point unit on these multiple bus structures, it can receive instructions and operands on each clock cycle. Some number of cycles later, as more floating point instructions are issued, floating point results can also be sent out on the destination bus, yielding burst execution rates equal to the clock rate. The present clock rate is 20 MHz and will be increased eventually to the 40 MHz area. At 20 MHz, sustained execution rates of 7 MFLOPS are typical. Performance rates of 10.5 MWhetstones have also been demonstrated (20 MHz clock). The floating point unit is only one part of the RISC processor. By combining all the aspects of software, memory system interfacing and high performance hardware like the 88100 floating point unit, mainframe performance moves one step closer to the desktop computer world.

keywords:
20 MHz; 7 MFLOPS; 88100 Floating point unit; Burst execution rates; Clock cycle; Clock rate; Desktop computer; Execution rates; Memory system interfacing; Multiple bus structures; Performance rates; RISC architecture

rawabstract:
RISC architectures require multiple bus structures that allow for instructions, operands, and results to all travel about the processor on each clock cycle. Thus, by putting the floating point unit on these multiple bus structures, it can receive instructions and operands on each clock cycle. Some number of cycles later, as more floating point instructions are issued, floating point results can also be sent out on the destination bus, yielding burst execution rates equal to the clock rate. The present clock rate is 20 MHz and will be increased eventually to the 40 MHz area. At 20 MHz, sustained execution rates of 7 MFLOPS are typical. Performance rates of 10.5 MWhetstones have also been demonstrated (20 MHz clock). The floating point unit is only one part of the RISC processor. By combining all the aspects of software, memory system interfacing and high performance hardware like the 88100 floating point unit, mainframe performance moves one step closer to the desktop computer world.

entry:
@InProceedings{Melear:1988:IFP,
  author =       "C. Melear",
  title =        "An integrated floating point unit for a {RISC}
                 architecture",
  crossref =     "Wescon:1988:WCR",
  pages =        "1.2/1--8",
  year =         "1988",
  bibdate =      "Tue Dec 12 09:20:21 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "RISC architectures require multiple bus structures
                 that allow for instructions, operands, and results to
                 all travel about the processor on each clock cycle.
                 Thus, by putting the floating point unit on these
                 multiple bus structures, it can receive instructions
                 and operands on each clock cycle. Some number of cycles
                 later, as more floating point instructions are issued,
                 floating point results can also be sent out on the
                 destination bus, yielding burst execution rates equal
                 to the clock rate. The present clock rate is 20 MHz and
                 will be increased eventually to the 40 MHz area. At 20
                 MHz, sustained execution rates of 7 MFLOPS are typical.
                 Performance rates of 10.5 MWhetstones have also been
                 demonstrated (20 MHz clock). The floating point unit is
                 only one part of the RISC processor. By combining all
                 the aspects of software, memory system interfacing and
                 high performance hardware like the 88100 floating point
                 unit, mainframe performance moves one step closer to
                 the desktop computer world.",
  acknowledgement = ack-nhfb,
  affiliation =  "Motorola, Austin, TX, USA",
  classification = "C5130 (Microprocessor chips); C5220 (Computer
                 architecture); C5230 (Digital arithmetic methods)",
  keywords =     "20 MHz; 7 MFLOPS; 88100 Floating point unit; Burst
                 execution rates; Clock cycle; Clock rate; Desktop
                 computer; Execution rates; Memory system interfacing;
                 Multiple bus structures; Performance rates; RISC
                 architecture",
  numericalindex = "Frequency 2.0E+07 Hz; Computer speed 7.0E+06 FLOPS",
  thesaurus =    "Digital arithmetic; Microprocessor chips; Reduced
                 instruction set computing",
}


bibtype: article
filename: fparith.bib
label: Milnikel:1988:SRF
author: R. Milnikel and R. Wollenberg
journal: j-ELECTRONIK
volume: 8
pages: 114--1122
year: 1988
CODEN: EKRKAR
ISSN: 0013-5658 OR 00135658
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: Elektronik
acknowledgement: ack-nj
rawauthor: R. Milnikel and R. Wollenberg
title:
Schnelles Radizierverfahren fur Gleitkommazahlen im IEEE-Format toenglish Fast Square-rooting method for Floating-point Numbers in IEEE Format endtoenglish 

rawtitle:
{Schnelles Radizierverfahren f{\"u}r Gleitkommazahlen im IEEE-Format} \toenglish {Fast Square-rooting method for Floating-point Numbers in IEEE Format} \endtoenglish

entry:
@Article{Milnikel:1988:SRF,
  author =       "R. Milnikel and R. Wollenberg",
  title =        "{Schnelles Radizierverfahren f{\"u}r Gleitkommazahlen
                 im IEEE-Format} \toenglish {Fast Square-rooting method
                 for Floating-point Numbers in IEEE Format}
                 \endtoenglish",
  journal =      j-ELECTRONIK,
  volume =       "8",
  pages =        "114--1122",
  year =         "1988",
  CODEN =        "EKRKAR",
  ISSN =         "0013-5658",
  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 =     "Elektronik",
}


bibtype: article
filename: fparith.bib
label: Monahan:1988:CAG
author: John F. Monahan
title: Corrigendum: ``An Algorithm for Generating Chi Random Variables''
journal: j-TOMS
volume: 14
number: 1
pages: 111--111
month: mar
monthnumber: 3
year: 1988
CODEN: ACMSCU
DOI: https://doi.org/10.1145/42288.356228
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 111. 65C10
MRnumber: 89d:65006, 88d:65013
bibdate: Fri Mar 28 10:45:16 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.03.28 10:45:16 ???
note: See cite Monahan:1987:AGC.
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: John F. Monahan
rawnote: See \cite{Monahan:1987:AGC}.
rawtitle: Corrigendum: ``{An} Algorithm for Generating Chi Random Variables''
entry:
@Article{Monahan:1988:CAG,
  author =       "John F. Monahan",
  title =        "Corrigendum: ``{An} Algorithm for Generating Chi
                 Random Variables''",
  journal =      j-TOMS,
  volume =       "14",
  number =       "1",
  pages =        "111--111",
  month =        mar,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/42288.356228",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "111. 65C10",
  MRnumber =     "89d:65006, 88d:65013",
  bibdate =      "Fri Mar 28 10:45:16 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Monahan:1987:AGC}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: manual
filename: fparith.bib
label: Motorola:1988:GPF
title: 96-bit general purpose floating-point digital-signal processor technical summary
organization: Motorola, Inc.
address: Phoenix, AZ, USA
pages: 23
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
series: Motorola semiconductor technical data
keywords: Integrated circuits.; Signal processing --- Digital techniques.
remark: Caption title. ``BR574/D.''
acknowledgement: ack-nhfb
rawtitle: 96-bit general purpose floating-point digital-signal processor technical summary
entry:
@Manual{Motorola:1988:GPF,
  title =        "96-bit general purpose floating-point digital-signal
                 processor technical summary",
  organization = "Motorola, Inc.",
  address =      "Phoenix, AZ, USA",
  pages =        "23",
  year =         "1988",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Motorola semiconductor technical data",
  acknowledgement = ack-nhfb,
  keywords =     "Integrated circuits.; Signal processing --- Digital
                 techniques.",
  remark =       "Caption title. ``BR574/D.''",
}


bibtype: book
filename: fparith.bib
label: Motorola:1988:MFP
author: Motorola, Inc.Staff
title: MC 68881 and 68882 Floating-Point Coprocessor User's Manual
publisher: pub-PH
address: pub-PH:adr
pages: 23
month: feb
monthnumber: 2
year: 1988
ISBN: 0-13-566936-7 OR 0135669367
ISBN13: 978-0-13-566936-5 OR 9780135669365
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
language: eng
acknowledgement: ack-nhfb
rawauthor: {Motorola, Inc.Staff}
rawtitle: {MC} 68881 and 68882 Floating-Point Coprocessor User's Manual
entry:
@Book{Motorola:1988:MFP,
  author =       "{Motorola, Inc.Staff}",
  title =        "{MC} 68881 and 68882 Floating-Point Coprocessor User's
                 Manual",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  month =        feb,
  year =         "1988",
  ISBN =         "0-13-566936-7",
  ISBN-13 =      "978-0-13-566936-5",
  LCCN =         "????",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$22.50",
  acknowledgement = ack-nhfb,
  language =     "eng",
}


bibtype: article
filename: fparith.bib
label: Nakamura:1988:SCP
author: S. Nakamura and K.-Y. Chu
title: A single chip parallel multiplier by MOS technology
journal: j-IEEE-TRANS-COMPUT
volume: 37
number: 3
pages: 274--282
month: mar
monthnumber: 3
year: 1988
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.2164
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: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2164
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: S. Nakamura and K.-Y. Chu
rawtitle: A single chip parallel multiplier by {MOS} technology
entry:
@Article{Nakamura:1988:SCP,
  author =       "S. Nakamura and K.-Y. Chu",
  title =        "A single chip parallel multiplier by {MOS}
                 technology",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "37",
  number =       "3",
  pages =        "274--282",
  month =        mar,
  year =         "1988",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.2164",
  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 =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2164",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Nikolos:1988:EDT
author: D. Nikolos and A. M. Paschalis and G. Philokyprou
title: Efficient design of totally self-checking checkers for all low-cost arithmetic codes
journal: j-IEEE-TRANS-COMPUT
volume: 37
number: 7
pages: 807--814
month: jul
monthnumber: 7
year: 1988
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.2226
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: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2226
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: D. Nikolos and A. M. Paschalis and G. Philokyprou
rawtitle: Efficient design of totally self-checking checkers for all low-cost arithmetic codes
entry:
@Article{Nikolos:1988:EDT,
  author =       "D. Nikolos and A. M. Paschalis and G. Philokyprou",
  title =        "Efficient design of totally self-checking checkers for
                 all low-cost arithmetic codes",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "37",
  number =       "7",
  pages =        "807--814",
  month =        jul,
  year =         "1988",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.2226",
  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 =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2226",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Normand:1988:PSP
author: J. M. Normand
title: Percola: a special purpose programmable 64-bit floating-point processor
crossref: ACM:1988:ICS
pages: 55--65
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
URL: http://doi.acm.org/10.1145/55364.55370
acknowledgement: ack-nhfb
affiliation: Centre d'Etudes Nucleaires, Saclay, France
rawauthor: J. M. Normand
rawtitle: {Percola}: a special purpose programmable 64-bit floating-point processor
subject:
G. Mathematics of Computing; G.3 PROBABILITY AND STATISTICS; C. Computer Systems Organization; C.5 COMPUTER SYSTEM IMPLEMENTATION; C. Computer Systems Organization; C.5 COMPUTER SYSTEM IMPLEMENTATION; J. Computer Applications; J.2 PHYSICAL SCIENCES AND ENGINEERING; G. Mathematics of Computing; G.3 PROBABILITY AND STATISTICS; B. Hardware; B.6 LOGIC DESIGN

entry:
@InProceedings{Normand:1988:PSP,
  author =       "J. M. Normand",
  title =        "{Percola}: a special purpose programmable 64-bit
                 floating-point processor",
  crossref =     "ACM:1988:ICS",
  pages =        "55--65",
  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",
  price =        "US\$49.00",
  URL =          "http://doi.acm.org/10.1145/55364.55370",
  acknowledgement = ack-nhfb,
  affiliation =  "Centre d'Etudes Nucl{\'e}aires, Saclay, France",
  bibno =        "55370",
  catcode =      "G.3; C.5.1; C.5.3; J.2; G.3; B.6.3",
  CRclass =      "G.3 Random number generation; C.5.1 Large and Medium
                 (``Mainframe'') Computers; C.5.1 Super (very large)
                 computers; C.5.3 Microcomputers; C.5.3 Motorola 68000;
                 J.2 Physics; G.3 Statistical computing; B.6.3 Design
                 Aids; B.6.3 Optimization",
  descriptor =   "Mathematics of Computing, PROBABILITY AND STATISTICS,
                 Random number generation; Computer Systems
                 Organization, COMPUTER SYSTEM IMPLEMENTATION, Large and
                 Medium (``Mainframe'') Computers, Super (very large)
                 computers; Computer Systems Organization, COMPUTER
                 SYSTEM IMPLEMENTATION, Microcomputers, Motorola 68000;
                 Computer Applications, PHYSICAL SCIENCES AND
                 ENGINEERING, Physics; Mathematics of Computing,
                 PROBABILITY AND STATISTICS, Statistical computing;
                 Hardware, LOGIC DESIGN, Design Aids, Optimization",
  genterm =      "ALGORITHMS; DESIGN",
  guideno =      "1988-15563",
  subject =      "G. Mathematics of Computing; G.3 PROBABILITY AND
                 STATISTICS; C. Computer Systems Organization; C.5
                 COMPUTER SYSTEM IMPLEMENTATION; C. Computer Systems
                 Organization; C.5 COMPUTER SYSTEM IMPLEMENTATION; J.
                 Computer Applications; J.2 PHYSICAL SCIENCES AND
                 ENGINEERING; G. Mathematics of Computing; G.3
                 PROBABILITY AND STATISTICS; B. Hardware; B.6 LOGIC
                 DESIGN",
  waffil =       "Rennes",
  wauthedit =    "Lenfant, J.",
  wsub =         "Conference Proceedings",
}


bibtype: article
filename: fparith.bib
label: Oklobdzija:1988:IAV
author: Vojin G. Oklobdzija and Earl R. Barnes
title: On implementing addition in VLSI technology
journal: j-J-PAR-DIST-COMP
volume: 5
number: 6
pages: 716--728
month: dec
monthnumber: 12
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: Yorktown Heights, NY, USA
corpsource: IBM Thomas J. Watson Res. Center, Yorktown Heights, NY, USA
journalURL: http://www.sciencedirect.com/science/journal/07437315
journalabr: J Parallel Distrib Comput
treatment: P Practical
rawauthor: Vojin G. Oklobdzija and Earl R. Barnes
rawtitle: On implementing addition in {VLSI} technology
keywords:
addition; Arithmetic Algorithms; arithmetic algorithms; carry-lookahead; CMOS integrated circuits; CMOS technology; Computer Aided Design; Computer Programming--Algorithms; digital arithmetic; estimates; integrated; Integrated Circuits, VLSI; logic circuits; logic design; Logic Levels; logic levels; quick; recurrence solver schemes; Semiconductor Devices, MOS; Single-chip VLSI Processor; VLSI; VLSI Implementation; VLSI technology; VLSI-; VLSI-cmos Technology

entry:
@Article{Oklobdzija:1988:IAV,
  author =       "Vojin G. Oklobdzija and Earl R. Barnes",
  title =        "On implementing addition in {VLSI} technology",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "5",
  number =       "6",
  pages =        "716--728",
  month =        dec,
  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 = "Yorktown Heights, NY, USA",
  classification = "713; 714; 723; B1265B (Logic circuits); B2570D (CMOS
                 integrated circuits); C5210 (Logic design methods);
                 C5230 (Digital arithmetic methods)",
  corpsource =   "IBM Thomas J. Watson Res. Center, Yorktown Heights,
                 NY, USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "addition; Arithmetic Algorithms; arithmetic
                 algorithms; carry-lookahead; CMOS integrated circuits;
                 CMOS technology; Computer Aided Design; Computer
                 Programming--Algorithms; digital arithmetic; estimates;
                 integrated; Integrated Circuits, VLSI; logic circuits;
                 logic design; Logic Levels; logic levels; quick;
                 recurrence solver schemes; Semiconductor Devices, MOS;
                 Single-chip VLSI Processor; VLSI; VLSI Implementation;
                 VLSI technology; VLSI-; VLSI-cmos Technology",
  treatment =    "P Practical",
}


bibtype: inproceedings
filename: fparith.bib
label: Papadourakis:1988:VDP
author: G. M. Papadourakis and J. Condorodis
title: A VLSI design of processing element for reconfigurable systolic architectures based on LNS
volume: 4
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 2080--2083
year: 1988
bibdate: Sat Jul 16 16:14:38 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 16:14:38 MDT
acknowledgement: ack-nhfb
rawauthor: G. M. Papadourakis and J. Condorodis
rawtitle: A {VLSI} design of processing element for reconfigurable systolic architectures based on {LNS}
booktitle:
1988 International Conference on Acoustics, Speech, and Signal Processing: ICASSP-88, 11--14 April 1988

rawbooktitle:
1988 International Conference on Acoustics, Speech, and Signal Processing: {ICASSP-88, 11--14} April 1988

entry:
@InProceedings{Papadourakis:1988:VDP,
  author =       "G. M. Papadourakis and J. Condorodis",
  booktitle =    "1988 International Conference on Acoustics, Speech,
                 and Signal Processing: {ICASSP-88, 11--14} April 1988",
  title =        "A {VLSI} design of processing element for
                 reconfigurable systolic architectures based on {LNS}",
  volume =       "4",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "2080--2083",
  year =         "1988",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 16:14:38 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "The design and development of a processing element
                 (PE) in an orthogonal systolic architecture, using the
                 state of the art in VLSI technology, is presented. The
                 goal was to create a high-speed, high-precision PE
                 which would be adaptive to a highly \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Papamichalis:1988:TFP
author: P. Papamichalis and R. Simar, Jr.
title: The TMS320C30 Floating-Point Digital Signal Processor
journal: j-IEEE-MICRO
volume: 8
number: 6
pages: 13--29
month: nov
monthnumber: 11
year: 1988
CODEN: IEMIDZ
DOI: https://doi.org/10.1109/40.16778
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
rawauthor: P. Papamichalis and R. {Simar, Jr.}
rawtitle: The {TMS320C30} Floating-Point Digital Signal Processor
entry:
@Article{Papamichalis:1988:TFP,
  author =       "P. Papamichalis and R. {Simar, Jr.}",
  title =        "The {TMS320C30} Floating-Point Digital Signal
                 Processor",
  journal =      j-IEEE-MICRO,
  volume =       "8",
  number =       "6",
  pages =        "13--29",
  month =        nov # "\slash " # dec,
  year =         "1988",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/40.16778",
  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 320C30 is a fast processor with a large memory
                 space and floating-point-arithmetic capabilities. The
                 authors describe the 320C30 architecture in detail,
                 discussing both the internal organization of the device
                 and the external interfaces. They also \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Perlman:1988:AFP
author: R. M. Perlman
title: The Am29027 --- a floating-point accelerator for the Am29000 streamlined instruction processor
crossref: Wescon:1988:WCR
pages: 1.4/1--7
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: Adv. Micro Devices, Sunnyale, CA, USA
thesaurus: Digital arithmetic; Microprocessor chips; Pipeline processing; Reduced instruction set computing
rawauthor: R. M. Perlman
rawtitle: The {Am29027} --- a floating-point accelerator for the {Am29000} streamlined instruction processor
abstract:
The Am29000, a 32-bit RISC processor, sets new standards of performance for integer processing. A 25 MHz Am29000 with cache can achieve in excess of 35600 Dhrystones. Even with simple video DRAM memory, the Am29000 has a performance of 24300 Dhrystones. Although the Am29000 contains no hardware dedicated to floating-point computation, it can emulate floating-point operations in software at speeds that were heretofore achieved only by dedicated floating-point coprocessors. For numerically-intensive applications, the Am29000 can be augmented with the Am29027 arithmetic accelerator. The Am29027 is a single-chip floating-point unit that performs single-, double-, and mixed-precision operations, and completely implements IEEE standard 754 for those operations supported. The Am29027 offers two operating modes: a low-latency mode, for scalar operations, and a pipeline mode, for vector and matrix calculations. When configured in pipeline mode, the AM29027 can achieve a peak throughput of 16 MFLOPS.

keywords:
16 MFLOPS; 32 Bit; Am29000 streamlined instruction processor; Am29027 arithmetic accelerator; Cache; Floating-point operations; IEEE standard 754; Low-latency mode; Matrix calculations; Mixed-precision operations; Pipeline mode; RISC processor; Scalar operations; Vector calculations; Video DRAM memory

rawabstract:
The Am29000, a 32-bit RISC processor, sets new standards of performance for integer processing. A 25 MHz Am29000 with cache can achieve in excess of 35600 Dhrystones. Even with simple video DRAM memory, the Am29000 has a performance of 24300 Dhrystones. Although the Am29000 contains no hardware dedicated to floating-point computation, it can emulate floating-point operations in software at speeds that were heretofore achieved only by dedicated floating-point coprocessors. For numerically-intensive applications, the Am29000 can be augmented with the Am29027 arithmetic accelerator. The Am29027 is a single-chip floating-point unit that performs single-, double-, and mixed-precision operations, and completely implements IEEE standard 754 for those operations supported. The Am29027 offers two operating modes: a low-latency mode, for scalar operations, and a pipeline mode, for vector and matrix calculations. When configured in pipeline mode, the AM29027 can achieve a peak throughput of 16 MFLOPS.

entry:
@InProceedings{Perlman:1988:AFP,
  author =       "R. M. Perlman",
  title =        "The {Am29027} --- a floating-point accelerator for the
                 {Am29000} streamlined instruction processor",
  crossref =     "Wescon:1988:WCR",
  pages =        "1.4/1--7",
  year =         "1988",
  bibdate =      "Tue Dec 12 09:20:21 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The Am29000, a 32-bit RISC processor, sets new
                 standards of performance for integer processing. A 25
                 MHz Am29000 with cache can achieve in excess of 35600
                 Dhrystones. Even with simple video DRAM memory, the
                 Am29000 has a performance of 24300 Dhrystones. Although
                 the Am29000 contains no hardware dedicated to
                 floating-point computation, it can emulate
                 floating-point operations in software at speeds that
                 were heretofore achieved only by dedicated
                 floating-point coprocessors. For numerically-intensive
                 applications, the Am29000 can be augmented with the
                 Am29027 arithmetic accelerator. The Am29027 is a
                 single-chip floating-point unit that performs single-,
                 double-, and mixed-precision operations, and completely
                 implements IEEE standard 754 for those operations
                 supported. The Am29027 offers two operating modes: a
                 low-latency mode, for scalar operations, and a pipeline
                 mode, for vector and matrix calculations. When
                 configured in pipeline mode, the AM29027 can achieve a
                 peak throughput of 16 MFLOPS.",
  acknowledgement = ack-nhfb,
  affiliation =  "Adv. Micro Devices, Sunnyale, CA, USA",
  classification = "C5130 (Microprocessor chips); C5230 (Digital
                 arithmetic methods)",
  keywords =     "16 MFLOPS; 32 Bit; Am29000 streamlined instruction
                 processor; Am29027 arithmetic accelerator; Cache;
                 Floating-point operations; IEEE standard 754;
                 Low-latency mode; Matrix calculations; Mixed-precision
                 operations; Pipeline mode; RISC processor; Scalar
                 operations; Vector calculations; Video DRAM memory",
  numericalindex = "Word length 3.2E+01 bit; Computer speed 1.6E+07
                 FLOPS",
  thesaurus =    "Digital arithmetic; Microprocessor chips; Pipeline
                 processing; Reduced instruction set computing",
}


bibtype: article
filename: fparith.bib
label: Pichat:1988:APC
author: M. A. Pichat
journal: j-MATH-COMP-SIM
volume: 30
number: 6
pages: 541--552
year: 1988
CODEN: MCSIDR
ISSN: 0378-4754 (print), 1872-7166 (electronic) OR 03784754 (print), 18727166 (electronic)
ISSNL: 0378-4754 OR 03784754
MRclass: 65G05
MRnumber: 90d:65090
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: Luciano Biasini
rawauthor: M. A. Pichat
title:
All possible computed results in correct floating-point summation. Stochastic methods in round-off error analysis

rawtitle:
All possible computed results in correct floating-point summation. Stochastic methods in round-off error analysis

entry:
@Article{Pichat:1988:APC,
  author =       "M. A. Pichat",
  title =        "All possible computed results in correct
                 floating-point summation. Stochastic methods in
                 round-off error analysis",
  journal =      j-MATH-COMP-SIM,
  volume =       "30",
  number =       "6",
  pages =        "541--552",
  year =         "1988",
  CODEN =        "MCSIDR",
  ISSN =         "0378-4754 (print), 1872-7166 (electronic)",
  ISSN-L =       "0378-4754",
  MRclass =      "65G05",
  MRnumber =     "90d:65090",
  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 =     "Luciano Biasini",
}


bibtype: mastersthesis
filename: fparith.bib
label: Pier:1988:IPA
author: Richard Michael Pier
title: An IBM PC / AT-based floating point imaging workstation architecture
type: Thesis (M.S.E.E.)
school: University of Washington
address: Seattle, WA, USA
pages: vi + 35
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
acknowledgement: ack-nhfb
rawauthor: Richard Michael Pier
rawtitle: An {IBM PC\slash AT}-based floating point imaging workstation architecture
keywords:
Computer architecture.; IBM Personal Computer AT.; Image processing --- Equipment and supplies.; Microcomputer workstations.

entry:
@MastersThesis{Pier:1988:IPA,
  author =       "Richard Michael Pier",
  title =        "An {IBM PC\slash AT}-based floating point imaging
                 workstation architecture",
  type =         "Thesis ({M.S.E.E.})",
  school =       "University of Washington",
  address =      "Seattle, WA, USA",
  pages =        "vi + 35",
  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 architecture.; IBM Personal Computer AT.;
                 Image processing --- Equipment and supplies.;
                 Microcomputer workstations.",
}


bibtype: article
filename: fparith.bib
label: Pitas:1988:FPE
author: I. Pitas and M. G. Strintzis
title: Floating point error analysis of two-dimensional, fast Fourier transform algorithms
journal: j-IEEE-TRANS-CIRCUITS-SYST
volume: 35
number: 1
pages: 112--115
month: jan
monthnumber: 1
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 08:40:52 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:52 MDT
fjournal: IEEE Transactions on Circuits and Systems
acknowledgement: ack-nhfb
rawauthor: I. Pitas and M. G. Strintzis
rawtitle: Floating point error analysis of two-dimensional, fast {Fourier} transform algorithms
entry:
@Article{Pitas:1988:FPE,
  author =       "I. Pitas and M. G. Strintzis",
  title =        "Floating point error analysis of two-dimensional, fast
                 {Fourier} transform algorithms",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "35",
  number =       "1",
  pages =        "112--115",
  month =        jan,
  year =         "1988",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  summary =      "Floating-point error is conducted for three algorithms
                 commonly used for the calculation of two-dimensional
                 fast Fourier transforms (FFTs), namely, the
                 conventional row-column FFT, the vector-radix FFT, and
                 the polynomial-transform FFT. The respective \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Plauger:1988:PFP
author: P. J. Plauger
title: Properties of floating-point arithmetic
journal: j-COMP-LANG-MAG
volume: 5
number: 3
pages: 17--22
month: mar
monthnumber: 3
year: 1988
CODEN: COMLEF
ISSN: 0749-2839 OR 07492839
bibdate: Thu Sep 1 10:14:15 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:14:15 ???
fjournal: Computer Language Magazine
acknowledgement: ack-nj
rawauthor: P. J. Plauger
rawtitle: Properties of floating-point arithmetic
entry:
@Article{Plauger:1988:PFP,
  author =       "P. J. Plauger",
  title =        "Properties of floating-point arithmetic",
  journal =      j-COMP-LANG-MAG,
  volume =       "5",
  number =       "3",
  pages =        "17--22",
  month =        mar,
  year =         "1988",
  CODEN =        "COMLEF",
  ISSN =         "0749-2839",
  bibdate =      "Thu Sep 1 10:14:15 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Computer Language Magazine",
}


bibtype: inproceedings
filename: fparith.bib
label: Prandolini:1988:VIB
author: R. Prandolini and S. Sridharan
crossref: IREE:1988:AMC
pages: 33--40
year: 1988
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
acknowledgement: ack-nhfb
affiliation: Sch. of Electr. and Electron. Syst. Eng., Queensland Inst. of Technol., Brisbane, Qld., Australia
thesaurus: Digital filters; Digital signal processing chips; VLSI
rawauthor: R. Prandolini and S. Sridharan
title:
VLSI implementation of a block floating point coprocessor for the TMS320 fixed point digital signal processor

abstract:
The design of a co-processor which can be interfaced to the TMS32020 fixed-point digital signal processor is described. The co-processor enables efficient implementation of block floating-point arithmetic for digital filtering using the TMS32020.

keywords:
Block floating point coprocessor; Block floating-point arithmetic; Digital filtering; TMS320 fixed point digital signal processor; VLSI implementation

rawabstract:
The design of a co-processor which can be interfaced to the TMS32020 fixed-point digital signal processor is described. The co-processor enables efficient implementation of block floating-point arithmetic for digital filtering using the TMS32020.

rawtitle:
{VLSI} implementation of a block floating point coprocessor for the {TMS320} fixed point digital signal processor

entry:
@InProceedings{Prandolini:1988:VIB,
  author =       "R. Prandolini and S. Sridharan",
  title =        "{VLSI} implementation of a block floating point
                 coprocessor for the {TMS320} fixed point digital signal
                 processor",
  crossref =     "IREE:1988:AMC",
  pages =        "33--40",
  year =         "1988",
  bibdate =      "Tue Dec 12 09:17:24 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The design of a co-processor which can be interfaced
                 to the TMS32020 fixed-point digital signal processor is
                 described. The co-processor enables efficient
                 implementation of block floating-point arithmetic for
                 digital filtering using the TMS32020.",
  acknowledgement = ack-nhfb,
  affiliation =  "Sch. of Electr. and Electron. Syst. Eng., Queensland
                 Inst. of Technol., Brisbane, Qld., Australia",
  classification = "B1265F (Microprocessors and microcomputers); B1270F
                 (Digital filters); B2570 (Semiconductor integrated
                 circuits); C5130 (Microprocessor chips); C5240 (Digital
                 filters); C5260 (Digital signal processing)",
  keywords =     "Block floating point coprocessor; Block floating-point
                 arithmetic; Digital filtering; TMS320 fixed point
                 digital signal processor; VLSI implementation",
  thesaurus =    "Digital filters; Digital signal processing chips;
                 VLSI",
}


bibtype: article
filename: fparith.bib
label: Prather:1988:CET
author: R. E. Prather
title: Comparison and Extension of Theories of Zipf and Halstead
journal: j-COMP-J
volume: 31
number: 3
pages: 248--252
month: jun
monthnumber: 6
year: 1988
CODEN: CMPJA6
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
bibdate: Tue Mar 25 13:51:56 MST 1997
bibtimestamp: 1997.03.25 13:51:56 MST
fjournal: The Computer Journal
acknowledgement: ack-nhfb
affiliation: Trinity Univ, San Antonio, TX, USA
affiliationaddress: Trinity Univ, San Antonio, TX, USA
classcodes: C6110B (Software engineering techniques)
corpsource: Comput. and Inf. Sci., Trinity University, San Antonio, TX, USA
journalURL: http://comjnl.oxfordjournals.org/
treatment: T Theoretical or Mathematical
rawauthor: R. E. Prather
rawtitle: Comparison and Extension of Theories of {Zipf} and {Halstead}
bibsource:
Compendex database; http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/248.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/249.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/250.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/251.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/252.tif

keywords:
behavioural psychology; computer programming; computer software; empirical law; Halstead metrics; Halstead's hypothesis; length estimates; Measurements; probabilistic hypothesis; process; programming; software engineering; software metrication; software science; Zipf metrics; Zipf's law

entry:
@Article{Prather:1988:CET,
  author =       "R. E. Prather",
  title =        "Comparison and Extension of Theories of {Zipf} and
                 {Halstead}",
  journal =      j-COMP-J,
  volume =       "31",
  number =       "3",
  pages =        "248--252",
  month =        jun,
  year =         "1988",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Mar 25 13:51:56 MST 1997",
  bibsource =    "Compendex database;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/248.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/249.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/250.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/251.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/252.tif",
  acknowledgement = ack-nhfb,
  affiliation =  "Trinity Univ, San Antonio, TX, USA",
  affiliationaddress = "Trinity Univ, San Antonio, TX, USA",
  classcodes =   "C6110B (Software engineering techniques)",
  classification = "723",
  corpsource =   "Comput. and Inf. Sci., Trinity University, San
                 Antonio, TX, USA",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "behavioural psychology; computer programming; computer
                 software; empirical law; Halstead metrics; Halstead's
                 hypothesis; length estimates; Measurements;
                 probabilistic hypothesis; process; programming;
                 software engineering; software metrication; software
                 science; Zipf metrics; Zipf's law",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: book
filename: fparith.bib
label: Press:1988:NRC
author: W. H. Press and B. P. Flannery and S. A. Teukolsky and W. T. Vetterling
title: Numerical Recipes in C: The Art of Scientific Computing
publisher: pub-CAMBRIDGE
address: pub-CAMBRIDGE:adr
pages: xxii + 735
year: 1988
ISBN: 0-521-43724-5 OR 0521437245
ISBN13: 978-0-521-43724-0 OR 9780521437240
LCCN: QA76.73.C15 N865 1988
bibdate: Thu Sep 01 10:34:42 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 10:34:42 ???
acknowledgement: ack-nj
rawauthor: W. H. Press and B. P. Flannery and S. A. Teukolsky and W. T. Vetterling
rawtitle: Numerical Recipes in {C}: The Art of Scientific Computing
entry:
@Book{Press:1988:NRC,
  author =       "W. H. Press and B. P. Flannery and S. A. Teukolsky and
                 W. T. Vetterling",
  title =        "Numerical Recipes in {C}: The Art of Scientific
                 Computing",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "xxii + 735",
  year =         "1988",
  ISBN =         "0-521-43724-5",
  ISBN-13 =      "978-0-521-43724-0",
  LCCN =         "QA76.73.C15 N865 1988",
  bibdate =      "Thu Sep 01 10:34:42 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: mastersthesis
filename: fparith.bib
label: Rajanala:1988:ISP
author: Arunkumar V. Rajanala
type: Thesis (M.S.)
school: Oregon State University
address: Corvallis, OR, USA
pages: 77
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.; Microprocessors.
acknowledgement: ack-nhfb
rawauthor: Arunkumar V. Rajanala
title:
IEEE 754 single precision standard compatible floating point processor implemented using silicon compiler technology

rawtitle:
{IEEE 754} single precision standard compatible floating point processor implemented using silicon compiler technology

entry:
@MastersThesis{Rajanala:1988:ISP,
  author =       "Arunkumar V. Rajanala",
  title =        "{IEEE 754} single precision standard compatible
                 floating point processor implemented using silicon
                 compiler technology",
  type =         "Thesis ({M.S.})",
  school =       "Oregon State University",
  address =      "Corvallis, OR, USA",
  pages =        "77",
  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.; Microprocessors.",
}


bibtype: inproceedings
filename: fparith.bib
label: Randal:1988:FPC
author: V. T. Randal and J. L. Schmalzel and A. P. Shepherd
title: Floating-Point Computation Using a Microcontroller
crossref: Harris:1988:PAI
pages: 1243--1244
year: 1988
bibdate: Wed Sep 07 22:02:38 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.07 22:02:38 ???
acknowledgement: ack-nj
rawauthor: V. T. Randal and J. L. Schmalzel and A. P. Shepherd
rawtitle: Floating-Point Computation Using a Microcontroller
entry:
@InProceedings{Randal:1988:FPC,
  author =       "V. T. Randal and J. L. Schmalzel and A. P. Shepherd",
  title =        "Floating-Point Computation Using a Microcontroller",
  crossref =     "Harris:1988:PAI",
  pages =        "1243--1244",
  year =         "1988",
  bibdate =      "Wed Sep 07 22:02:38 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: Razaz:1988:TPM
author: M. Razaz and J. L. Schonfelder
title: Test Procedures for Measurement of Floating-Point Characteristics of Computing Environments
journal: j-COMP-J
volume: 31
number: 1
pages: 12--16
month: feb
monthnumber: 2
year: 1988
CODEN: CMPJA6
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
bibdate: Tue Mar 25 13:51:56 MST 1997
bibsource: Compendex database; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.03.25 13:51:56 MST
fjournal: The Computer Journal
acknowledgement: ack-nhfb
affiliation: Univ of Birmingham, Birmingham, Engl
affiliationaddress: Univ of Birmingham, Birmingham, Engl
classcodes: C5470 (Performance evaluation and testing)
corpsource: Department of Electron. and Electr. Eng., Birmingham University, UK
journalURL: http://comjnl.oxfordjournals.org/
treatment: P Practical
rawauthor: M. Razaz and J. L. Schonfelder
rawtitle: Test Procedures for Measurement of Floating-Point Characteristics of Computing Environments
keywords:
arithmetic; arithmetic processors; CDC; computer testing; computers, digital; computing environments; conversion test; DEC; digital arithmetic; floating-point arithmetic; floating-point characteristics; floating-point testing; IBM; ICL; mantissa; minimum representable number; nominal decimal; normalisation base; number representation; operations; parameters; performance evaluation; precision; precision-dependent; procedures; representation test; test; Testing

entry:
@Article{Razaz:1988:TPM,
  author =       "M. Razaz and J. L. Schonfelder",
  title =        "Test Procedures for Measurement of Floating-Point
                 Characteristics of Computing Environments",
  journal =      j-COMP-J,
  volume =       "31",
  number =       "1",
  pages =        "12--16",
  month =        feb,
  year =         "1988",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Mar 25 13:51:56 MST 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ of Birmingham, Birmingham, Engl",
  affiliationaddress = "Univ of Birmingham, Birmingham, Engl",
  classcodes =   "C5470 (Performance evaluation and testing)",
  classification = "723",
  corpsource =   "Department of Electron. and Electr. Eng., Birmingham
                 University, UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "arithmetic; arithmetic processors; CDC; computer
                 testing; computers, digital; computing environments;
                 conversion test; DEC; digital arithmetic;
                 floating-point arithmetic; floating-point
                 characteristics; floating-point testing; IBM; ICL;
                 mantissa; minimum representable number; nominal
                 decimal; normalisation base; number representation;
                 operations; parameters; performance evaluation;
                 precision; precision-dependent; procedures;
                 representation test; test; Testing",
  treatment =    "P Practical",
}


bibtype: inproceedings
filename: fparith.bib
label: Ries:1988:MFP
author: P. S. Ries
title: An 8 MFLOP Floating-Point Coprocessor for a RISC Microprocessor
crossref: Electro:1988:ECR
pages: 48/1/1--8
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: P. S. Ries
rawtitle: An 8 {MFLOP} Floating-Point Coprocessor for a {RISC} Microprocessor
entry:
@InProceedings{Ries:1988:MFP,
  author =       "P. S. Ries",
  title =        "An 8 {MFLOP} Floating-Point Coprocessor for a {RISC}
                 Microprocessor",
  crossref =     "Electro:1988:ECR",
  pages =        "48/1/1--8",
  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: article
filename: fparith.bib
label: Robertazzi:1988:BOF
author: T. G. Robertazzi and S. C. Schwartz
title: Best ``Ordering'' for Floating-Point Addition
journal: j-TOMS
volume: 14
number: 1
pages: 101--110
month: mar
monthnumber: 3
year: 1988
CODEN: ACMSCU
DOI: https://doi.org/10.1145/42288.42343
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 65G99 (65V05)
MRnumber: 89b:65117
bibdate: Sat Nov 19 13:08:22 1994
bibtimestamp: 1994.11.19 13:08:22 ???
URL: http://www.acm.org/pubs/citations/journals/toms/1988-14-1/p101-robertazzi/
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: accurate floating-point summation; algorithms; performance
acknowledgement: ack-nhfb
affiliation: State University of New York at Stony Brook, Stony Brook; Princeton University, Princeton, NJ
journalURL: https://dl.acm.org/loi/toms
reviewer: Jesse L. Barlow
rawauthor: T. G. Robertazzi and S. C. Schwartz
rawtitle: Best {``Ordering''} for Floating-Point Addition
bibsource:
ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib

subject:
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.1.0 Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic

entry:
@Article{Robertazzi:1988:BOF,
  author =       "T. G. Robertazzi and S. C. Schwartz",
  title =        "Best {``Ordering''} for Floating-Point Addition",
  journal =      j-TOMS,
  volume =       "14",
  number =       "1",
  pages =        "101--110",
  month =        mar,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/42288.42343",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65G99 (65V05)",
  MRnumber =     "89b:65117",
  bibdate =      "Sat Nov 19 13:08:22 1994",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1988-14-1/p101-robertazzi/",
  acknowledgement = ack-nhfb,
  affiliation =  "State University of New York at Stony Brook, Stony
                 Brook; Princeton University, Princeton, NJ",
  bibno =        "42343",
  catcode =      "G.1.0",
  content =      "This paper compares a variety of methods for
                 accumulating a floating-point sum. Wilkinson pointed
                 out that if we compute the $\sum^n_{i = 1} x_i$ in
                 strictly increasing order in magnitude of the $x_i$,
                 then we obtain a better bound on the rounding error
                 than if the sum is computed in random order
                 [1].\par

                 The authors discuss five different accumulation
                 strategies. They compare these accumulation strategies
                 for when the $x_i$ are uniformly distributed and for
                 when they are exponentially distributed. First they
                 compare a random order for summing the $x_i$, summing
                 in decreasing order of magnitude, and summing in
                 increasing order of magnitude. Not surprisingly,
                 summing in increasing order of magnitude is the best
                 and summing in decreasing order of magnitude is the
                 worst. In fact, it is not difficult to show this for
                 any class of distributions where the mean and variance
                 exist.\par

                 The interesting results in the paper concern two other
                 accumulation strategies. Both of these are shown to be
                 better than summing in increasing order of magnitude
                 for both the uniform and exponential distribution.
                 Fortunately, one of these strategies is the tree sum
                 (or fan-in sum) that is often used in parallel
                 computation. The paper calls this strategy the
                 ``adjacency'' ordering.",
  CRclass =      "G.1.0 General; G.1.0 Computer arithmetic",
  CRnumber =     "8810-0794",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Computer arithmetic",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  genterm =      "ALGORITHMS; PERFORMANCE",
  journal-URL =  "https://dl.acm.org/loi/toms",
  journalabbrev = "ACM Trans. Math. Softw.",
  keywords =     "accurate floating-point summation; algorithms;
                 performance",
  review =       "ACM CR 8810-0794",
  reviewer =     "Jesse L. Barlow",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G.1.0 Mathematics of Computing, NUMERICAL ANALYSIS,
                 General, Computer arithmetic",
}


bibtype: article
filename: fparith.bib
label: Rowen:1988:MRF
author: Chris Rowen and Mark Johnson and Paul Ries
title: The MIPS R3010 Floating-Point Coprocessor
journal: j-IEEE-MICRO
volume: 8
number: 3
pages: 53--62
month: may
monthnumber: 5
year: 1988
CODEN: IEMIDZ
DOI: https://doi.org/10.1109/40.540
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
bibtimestamp: 2005.07.16 08:40:52 MDT
fjournal: IEEE Micro
acknowledgement: ack-nj
affiliationaddress: MIPS Computer Systems, Sunnyvale, CA, USA
corpsource: MIPS Comput. Syst., Sunnyvale, CA, USA
journalURL: http://www.computer.org/csdl/mags/mi/index.html
treatment: P Practical
rawauthor: Chris Rowen and Mark Johnson and Paul Ries
rawtitle: The {MIPS R3010} Floating-Point Coprocessor
bibsource:
Compendex database; garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/fparith.bib; Science Citation Index database (1980--2000)

keywords:
32-bit R31010 floating-point coprocessor; accelerator chip; computer architecture; computer systems, digital --- Parallel Processing; computers, microcomputer; Design; design techniques; digital arithmetic; floating-point; instruction set computing; integrated circuits, VLSI; microprocessor chips; million instruction per second (MIPS) processor; MIPS R3010 floating-point coprocessor; reduced; reduced-instruction-set-computer; reduced-instruction-set-computer (RISC); VLSI

classcodes:
B1265F (Microprocessors and microcomputers); B2570 (Semiconductor integrated circuits); C5130 (Microprocessor chips); C5220 (Computer architecture); C5230 (Digital arithmetic methods)

entry:
@Article{Rowen:1988:MRF,
  author =       "Chris Rowen and Mark Johnson and Paul Ries",
  title =        "The {MIPS R3010} Floating-Point Coprocessor",
  journal =      j-IEEE-MICRO,
  volume =       "8",
  number =       "3",
  pages =        "53--62",
  month =        may # "\slash " # jun,
  year =         "1988",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/40.540",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "Compendex database;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 Science Citation Index database (1980--2000)",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  affiliationaddress = "MIPS Computer Systems, Sunnyvale, CA, USA",
  classcodes =   "B1265F (Microprocessors and microcomputers); B2570
                 (Semiconductor integrated circuits); C5130
                 (Microprocessor chips); C5220 (Computer architecture);
                 C5230 (Digital arithmetic methods)",
  classification = "714; 722; 723",
  corpsource =   "MIPS Comput. Syst., Sunnyvale, CA, USA",
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
  keywords =     "32-bit R31010 floating-point coprocessor; accelerator
                 chip; computer architecture; computer systems, digital
                 --- Parallel Processing; computers, microcomputer;
                 Design; design techniques; digital arithmetic;
                 floating-point; instruction set computing; integrated
                 circuits, VLSI; microprocessor chips; million
                 instruction per second (MIPS) processor; MIPS R3010
                 floating-point coprocessor; reduced;
                 reduced-instruction-set-computer;
                 reduced-instruction-set-computer (RISC); VLSI",
  summary =      "A description is given of the R3010 floating-point
                 accelerator chip, a coprocessor that is based on
                 advanced reduced-instruction-set-computer (RISC)
                 architecture and VLSI design techniques and provides
                 high-speed floating-point operation. The 75000-
                 \ldots{}",
  treatment =    "P Practical",
  xxauthor =     "C. Rowen and P. Ries and M. Johnson",
}


