# bibtab

bibtype: article
filename: fparith.bib
label: Lohninger:1985:GF
author: H. Lohninger
title: Gleitkommaarithmetik fur den 68000 toenglish Floating-point Arithmetic for the 68000 endtoenglish
journal: j-MC
volume: 2
pages: 58--64
year: 1985
ISSN: 0720-4442, 0941-777x, 0943-5409 OR 07204442, 0941777x, 09435409
bibdate: Fri Sep 16 16:30:39 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 16:30:39 ???
fjournal: MC: Die Mikrocomputer-Zeitschrift
acknowledgement: ack-nj
rawauthor: H. Lohninger
rawtitle:
{Gleitkommaarithmetik f{\"u}r den 68000} \toenglish {Floating-point Arithmetic for the 68000} \endtoenglish

entry:
@Article{Lohninger:1985:GF,
  author =       "H. Lohninger",
  title =        "{Gleitkommaarithmetik f{\"u}r den 68000} \toenglish
                 {Floating-point Arithmetic for the 68000}
                 \endtoenglish",
  journal =      j-MC,
  volume =       "2",
  pages =        "58--64",
  year =         "1985",
  ISSN =         "0720-4442, 0941-777x, 0943-5409",
  bibdate =      "Fri Sep 16 16:30:39 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: article
filename: fparith.bib
label: Lorenz:1985:AIP
author: E. Lorenz
journal: j-NACH-ELEK
volume: 35
number: 5
pages: 179--181
year: 1985
CODEN: NTELAP
ISSN: 0323-4657 OR 03234657
bibdate: Fri Sep 16 16:30:39 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 16:30:39 ???
note: The U880 is a Z80 clone microprocessor that was built in the GDR (East Germany).
fjournal: Nachrichtentechnik Elektronik
acknowledgement: ack-nj
rawauthor: E. Lorenz
rawnote: The U880 is a Z80 clone microprocessor that was built in the GDR (East Germany).
title:
Aspekte der Implementierung eines Programmpaketes zur schnellen und flexiblen Ausfuhrung von arithmetischen Operationen mit dem U880 toenglish Aspects of the Implementation of a Software Package for Fast and Flexible Execution of Arithmetic Operations on the U880 endtoenglish 

rawtitle:
{Aspekte der Implementierung eines Programmpaketes zur schnellen und flexiblen Ausf{\"u}hrung von arithmetischen Operationen mit dem U880} \toenglish {Aspects of the Implementation of a Software Package for Fast and Flexible Execution of Arithmetic Operations on the U880} \endtoenglish

entry:
@Article{Lorenz:1985:AIP,
  author =       "E. Lorenz",
  title =        "{Aspekte der Implementierung eines Programmpaketes zur
                 schnellen und flexiblen Ausf{\"u}hrung von
                 arithmetischen Operationen mit dem U880} \toenglish
                 {Aspects of the Implementation of a Software Package
                 for Fast and Flexible Execution of Arithmetic
                 Operations on the U880} \endtoenglish",
  journal =      j-NACH-ELEK,
  volume =       "35",
  number =       "5",
  pages =        "179--181",
  month =        "????",
  year =         "1985",
  CODEN =        "NTELAP",
  ISSN =         "0323-4657",
  bibdate =      "Fri Sep 16 16:30:39 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "The U880 is a Z80 clone microprocessor that was built
                 in the GDR (East Germany).",
  acknowledgement = ack-nj,
  fjournal =     "Nachrichtentechnik Elektronik",
}


bibtype: inproceedings
filename: fparith.bib
label: Luk:1985:PMC
author: Franklin T. Luk
title: A Parallel Method for Computing the Generalized Singular Value Decomposition
crossref: Hwang:1985:PSC
pages: 260--265
year: 1985
bibdate: Fri Nov 16 08:47:34 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.16 08:47:34 ???
URL: http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Luk.pdf
keywords: ARITH-7
acknowledgement: ack-nhfb
rawauthor: Franklin T. Luk
rawtitle: A Parallel Method for Computing the Generalized Singular Value Decomposition
abstract:
We describe a new parallel algorithm for computing the generalized singular value decomposition of two $ n times n $ matrices, one of which is nonsingular. Our procedure requires $ O(n) $ e time and one triangular array of $ O(n^2) $ processors.

rawabstract:
We describe a new parallel algorithm for computing the generalized singular value decomposition of two $ n \times n $ matrices, one of which is nonsingular. Our procedure requires $ O(n) $ e time and one triangular array of $ O(n^2) $ processors.

entry:
@InProceedings{Luk:1985:PMC,
  author =       "Franklin T. Luk",
  title =        "A Parallel Method for Computing the Generalized
                 Singular Value Decomposition",
  crossref =     "Hwang:1985:PSC",
  pages =        "260--265",
  year =         "1985",
  bibdate =      "Fri Nov 16 08:47:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Luk.pdf",
  abstract =     "We describe a new parallel algorithm for computing the
                 generalized singular value decomposition of two $ n
                 \times n $ matrices, one of which is nonsingular. Our
                 procedure requires $ O(n) $ e time and one triangular
                 array of $ O(n^2) $ processors.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}


bibtype: article
filename: fparith.bib
label: Majerski:1985:SRA
author: S. Majerski
title: Square-Rooting Algorithms for High-Speed Digital Circuits
journal: j-IEEE-TRANS-COMPUT
volume: C-34
number: 8
pages: 724--733
month: aug
monthnumber: 8
year: 1985
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1985.1676618
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 08:33:17 MDT 2011
bibtimestamp: 2011.07.10 08:33:17 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676618
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: S. Majerski
rawtitle: Square-Rooting Algorithms for High-Speed Digital Circuits
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib

entry:
@Article{Majerski:1985:SRA,
  author =       "S. Majerski",
  title =        "Square-Rooting Algorithms for High-Speed Digital
                 Circuits",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-34",
  number =       "8",
  pages =        "724--733",
  month =        aug,
  year =         "1985",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1985.1676618",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 08:33:17 MDT 2011",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676618",
  acknowledgement = ack-nj # "\slash " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Matula:1985:FPR
author: David W. Matula and Peter Kornerup
title: Finite Precision Rational Arithmetic: Slash Number Systems
journal: j-IEEE-TRANS-COMPUT
volume: C-34
number: 1
pages: 3--18
month: jan
monthnumber: 1
year: 1985
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1985.1676511
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Fri Nov 30 06:21:13 2007
bibtimestamp: 2007.11.30 06:21:13 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: David W. Matula and Peter Kornerup
rawtitle: Finite Precision Rational Arithmetic: Slash Number Systems
abstract:
Fraction number systems characterized by fixed-slash and floating-slash formats are specified. The structure of arithmetic over such systems is prescribed by the rounding obtained from ``best rational approximation.'' Multitiered precision hierarchies of both the fixed-slash and floating-slash type are described and analyzed with regards to their support of both exact rational and approximate real computation.

rawabstract:
Fraction number systems characterized by fixed-slash and floating-slash formats are specified. The structure of arithmetic over such systems is prescribed by the rounding obtained from ``best rational approximation.'' Multitiered precision hierarchies of both the fixed-slash and floating-slash type are described and analyzed with regards to their support of both exact rational and approximate real computation.

entry:
@Article{Matula:1985:FPR,
  author =       "David W. Matula and Peter Kornerup",
  title =        "Finite Precision Rational Arithmetic: Slash Number
                 Systems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-34",
  number =       "1",
  pages =        "3--18",
  month =        jan,
  year =         "1985",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1985.1676511",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 30 06:21:13 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  abstract =     "Fraction number systems characterized by fixed-slash
                 and floating-slash formats are specified. The structure
                 of arithmetic over such systems is prescribed by the
                 rounding obtained from ``best rational approximation.''
                 Multitiered precision hierarchies of both the
                 fixed-slash and floating-slash type are described and
                 analyzed with regards to their support of both exact
                 rational and approximate real computation.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: manual
filename: fparith.bib
label: ME:1985:FPS
title: Floating point and string listing
organization: Microprocessor Engineering
address: Southampton, UK
edition: Second
pages: 36
year: 1985
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: Electronic digital computers --- Programming.; Floating-point arithmetic.
acknowledgement: ack-nhfb
rawtitle: Floating point and string listing
entry:
@Manual{ME:1985:FPS,
  title =        "Floating point and string listing",
  organization = "Microprocessor Engineering",
  address =      "Southampton, UK",
  edition =      "Second",
  pages =        "36",
  year =         "1985",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Electronic digital computers --- Programming.;
                 Floating-point arithmetic.",
}


bibtype: article
filename: fparith.bib
label: Mithani:1985:ASN
author: D. Mithani and S. Iyer
title: Algorithm speeds nonrestoring division in microprogrammed systems
journal: j-EDN
volume: 30
number: 4
pages: 199--208
month: feb
monthnumber: 2
year: 1985
CODEN: EDNSBH
ISSN: 0012-7515, 0364-6637 OR 00127515, 03646637
bibdate: Thu Sep 15 18:42:21 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.15 18:42:21 ???
fjournal: EDN
acknowledgement: ack-nj
rawauthor: D. Mithani and S. Iyer
rawtitle: Algorithm speeds nonrestoring division in microprogrammed systems
entry:
@Article{Mithani:1985:ASN,
  author =       "D. Mithani and S. Iyer",
  title =        "Algorithm speeds nonrestoring division in
                 microprogrammed systems",
  journal =      j-EDN,
  volume =       "30",
  number =       "4",
  pages =        "199--208",
  month =        feb,
  year =         "1985",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  bibdate =      "Thu Sep 15 18:42:21 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 =     "EDN",
}


bibtype: article
filename: fparith.bib
label: Modi:1985:AIS
author: J. J. Modi and J. S. Rollett
title: An algorithm for inverse square-roots
journal: j-PARALLEL-COMPUTING
volume: 2
number: 1
pages: 69--71
month: mar
monthnumber: 3
year: 1985
CODEN: PACOEJ
DOI: https://doi.org/10.1016/0167-8191(85)90018-3
ISSN: 0167-8191 (print), 1872-7336 (electronic) OR 01678191 (print), 18727336 (electronic)
ISSNL: 0167-8191 OR 01678191
MRclass: 65W05 (65D15)
MRnumber: 86j:65195
bibdate: Mon Apr 14 12:07:40 MDT 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.04.14 12:07:40 MDT
fjournal: Parallel Computing
acknowledgement: ack-nhfb
corpsource: Department of Eng., Cambridge University, UK
journalURL: http://www.sciencedirect.com/science/journal/01678191
treatment: T Theoretical or Mathematical
rawauthor: J. J. Modi and J. S. Rollett
rawtitle: An algorithm for inverse square-roots
abstract:
An algorithm is presented for finding $ x^ 1 / 2 $, given $x$. The algorithm is designed to be particularly suited for parallel computation, in which floating-point multiplication, floating-point addition and fixed-point arithmetic can be performed simultaneously.

keywords:
fixed-point arithmetic; floating-point addition; floating-point multiplication; inverse square roots algorithm; parallel computation; parallel processing

rawabstract:
An algorithm is presented for finding $ x^{ 1 / 2} $, given $x$. The algorithm is designed to be particularly suited for parallel computation, in which floating-point multiplication, floating-point addition and fixed-point arithmetic can be performed simultaneously.

entry:
@Article{Modi:1985:AIS,
  author =       "J. J. Modi and J. S. Rollett",
  title =        "An algorithm for inverse square-roots",
  journal =      j-PARALLEL-COMPUTING,
  volume =       "2",
  number =       "1",
  pages =        "69--71",
  month =        mar,
  year =         "1985",
  CODEN =        "PACOEJ",
  DOI =          "https://doi.org/10.1016/0167-8191(85)90018-3",
  ISSN =         "0167-8191 (print), 1872-7336 (electronic)",
  ISSN-L =       "0167-8191",
  MRclass =      "65W05 (65D15)",
  MRnumber =     "86j:65195",
  bibdate =      "Mon Apr 14 12:07:40 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "An algorithm is presented for finding $ x^{ 1 / 2} $,
                 given $x$. The algorithm is designed to be particularly
                 suited for parallel computation, in which
                 floating-point multiplication, floating-point addition
                 and fixed-point arithmetic can be performed
                 simultaneously.",
  acknowledgement = ack-nhfb,
  classification = "C4290 (Other computer theory)",
  corpsource =   "Department of Eng., Cambridge University, UK",
  fjournal =     "Parallel Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01678191",
  keywords =     "fixed-point arithmetic; floating-point addition;
                 floating-point multiplication; inverse square roots
                 algorithm; parallel computation; parallel processing",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: fparith.bib
label: Moharir:1985:ESG
author: P. S. Moharir
title: Extending the Scope of Golub's Method Beyond Complex Multiplication
journal: j-IEEE-TRANS-COMPUT
volume: C-34
number: 5
pages: 484--487
month: may
monthnumber: 5
year: 1985
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1985.1676590
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 08:32:33 MDT 2011
bibtimestamp: 2011.07.10 08:32:33 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676590
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: P. S. Moharir
rawtitle: Extending the Scope of {Golub}'s Method Beyond Complex Multiplication
entry:
@Article{Moharir:1985:ESG,
  author =       "P. S. Moharir",
  title =        "Extending the Scope of {Golub}'s Method Beyond Complex
                 Multiplication",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-34",
  number =       "5",
  pages =        "484--487",
  month =        may,
  year =         "1985",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1985.1676590",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 08:32:33 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676590",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Montgomery:1985:MMT
author: Peter L. Montgomery
title: Modular Multiplication Without Trial Division
journal: j-MATH-COMPUT
volume: 44
number: 170
pages: 519--521
month: apr
monthnumber: 4
year: 1985
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 11Y16
MRnumber: 86e:11121
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
URL: http://www.jstor.org/stable/2007970
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
ajournal: Math. Comput.
corpsource: Syst. Dev. Corp., Santa Monica, CA, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Peter L. Montgomery
rawtitle: Modular Multiplication Without Trial Division
abstract:
Let $ N > 1 $. We present a method for multiplying two integers (called $N$-residues) modulo $N$ while avoiding division by $ N. N $-residues are represented in a nonstandard way, so this method is useful only if several computations are done modulo one $N$. The addition and subtraction algorithms are unchanged.

keywords:
digital arithmetic; integer; integer arithmetic; modular arithmetic; modular multiplication; multiplication; N-residue; N-residue arithmetic; number theory

classcodes:
C1160 (Combinatorial mathematics); C5230 (Digital arithmetic methods); C6130 (Data handling techniques)

rawabstract:
Let $ N > 1 $. We present a method for multiplying two integers (called $N$-residues) modulo $N$ while avoiding division by $ N. N $-residues are represented in a nonstandard way, so this method is useful only if several computations are done modulo one $N$. The addition and subtraction algorithms are unchanged.

entry:
@Article{Montgomery:1985:MMT,
  author =       "Peter L. Montgomery",
  title =        "Modular Multiplication Without Trial Division",
  journal =      j-MATH-COMPUT,
  volume =       "44",
  number =       "170",
  pages =        "519--521",
  month =        apr,
  year =         "1985",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "11Y16",
  MRnumber =     "86e:11121",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  URL =          "http://www.jstor.org/stable/2007970",
  abstract =     "Let $ N > 1 $. We present a method for multiplying two
                 integers (called $N$-residues) modulo $N$ while
                 avoiding division by $ N. N $-residues are represented
                 in a nonstandard way, so this method is useful only if
                 several computations are done modulo one $N$. The
                 addition and subtraction algorithms are unchanged.",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  classcodes =   "C1160 (Combinatorial mathematics); C5230 (Digital
                 arithmetic methods); C6130 (Data handling techniques)",
  corpsource =   "Syst. Dev. Corp., Santa Monica, CA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "digital arithmetic; integer; integer arithmetic;
                 modular arithmetic; modular multiplication;
                 multiplication; N-residue; N-residue arithmetic; number
                 theory",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: manual
filename: fparith.bib
label: Motorola:1985:MFC
title: MC68881 floating-point coprocessor user's manual
organization: Motorola, Inc.
address: Phoenix, AZ, USA
pages: various
year: 1985
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: Microprocessors --- Handbooks, manuals, etc.
remark: Spine title: MC68881 user's manual. ``MC68881 UM/AD''--Cover.
acknowledgement: ack-nhfb
rawtitle: {MC68881} floating-point coprocessor user's manual
entry:
@Manual{Motorola:1985:MFC,
  title =        "{MC68881} floating-point coprocessor user's manual",
  organization = "Motorola, Inc.",
  address =      "Phoenix, AZ, USA",
  pages =        "various",
  year =         "1985",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Microprocessors --- Handbooks, manuals, etc.",
  remark =       "Spine title: MC68881 user's manual. ``MC68881
                 UM/AD''--Cover.",
}


bibtype: book
filename: fparith.bib
label: Motorola:1985:MFP
author: Motorola
title: MC68881 Floating-Point Coprocessor User's Manual
publisher: pub-MOTOROLA
address: pub-MOTOROLA:adr
edition: Second
pages: various
year: 1985
bibdate: Fri Sep 02 23:38:03 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.02 23:38:03 ???
acknowledgement: ack-nj
rawauthor: Motorola
rawtitle: {MC68881} Floating-Point Coprocessor User's Manual
entry:
@Book{Motorola:1985:MFP,
  author =       "Motorola",
  title =        "{MC68881} Floating-Point Coprocessor User's Manual",
  publisher =    pub-MOTOROLA,
  address =      pub-MOTOROLA:adr,
  edition =      "Second",
  year =         "1985",
  bibdate =      "Fri Sep 02 23:38:03 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: Muller:1985:DBC
author: Jean-Michel Muller
title: Discrete basis and computation of elementary functions
journal: j-IEEE-TRANS-COMPUT
volume: C-34
number: 9
pages: 857--862
month: sep
monthnumber: 9
year: 1985
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1985.1676643
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
MRclass: 65D20 (65V05)
MRnumber: 87e:65016
MRreviewer: D. Zwick
bibdate: Sun Jul 10 08:33:33 MDT 2011
bibtimestamp: 2011.07.10 08:33:33 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676643
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Jean-Michel Muller
rawtitle: Discrete basis and computation of elementary functions
abstract:
We give necessary and sufficient conditions in order that the infinite product or sum of the terms of a positive decreasing sequence generates the reals in a given interval.

rawabstract:
We give necessary and sufficient conditions in order that the infinite product or sum of the terms of a positive decreasing sequence generates the reals in a given interval.

entry:
@Article{Muller:1985:DBC,
  author =       "Jean-Michel Muller",
  title =        "Discrete basis and computation of elementary
                 functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-34",
  number =       "9",
  pages =        "857--862",
  month =        sep,
  year =         "1985",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1985.1676643",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  MRclass =      "65D20 (65V05)",
  MRnumber =     "87e:65016",
  MRreviewer =   "D. Zwick",
  bibdate =      "Sun Jul 10 08:33:33 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676643",
  abstract =     "We give necessary and sufficient conditions in order
                 that the infinite product or sum of the terms of a
                 positive decreasing sequence generates the reals in a
                 given interval.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Naseem:1985:MCA
author: Asif Naseem and P. David Fisher
title: The Modified CORDIC Algorithm
crossref: Hwang:1985:PSC
pages: 144--152
year: 1985
bibdate: Wed Sep 14 20:50:04 1994
bibtimestamp: 1994.09.14 20:50:04 ???
URL: http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Naseem_Fisher.pdf
keywords: ARITH-7
acknowledgement: ack-nj
rawauthor: Asif Naseem and P. David Fisher
rawtitle: The Modified {CORDIC} Algorithm
abstract:
A Modified CORDIC Algorithm (MCA) has been developed for the evaluation of elementary arithmetic functions. MCA incorporates increased parallelism over the original CORDIC algorithm, thus, resulting in an enhanced speed of computation. This has been accomplished by decoupling the CORDIC iteration equations, and transforming the sequential nature of these equations. $n$-bit fixed point data operands are assumed and the parameter $k$ relates to the level of parallelism in the algorithm. The modified algorithm employs a $ [k + 1]n^2 $-bit ROM for lookup tables that enable elementary arithmetic functions to be evaluated in no more than $ [3 n + 2] $ and no less than $2$ time steps. The two bounds correspond to a pipelined and a parallel implementation, respectively. The formulation of the MCA can be manipulated to obtain implementations with various speed / cost characteristics. This compares to $ n(3 n + 1) / 2 $ time steps for the original CORDIC algorithm. For example, 32-bit ALU has $ k = 12 $ and $ n = 32 $; so, a 13,312-bit ROM is required to store the lookup tables, and the computation requires 98 time steps for a pipelined implementation.

rawabstract:
A Modified CORDIC Algorithm (MCA) has been developed for the evaluation of elementary arithmetic functions. MCA incorporates increased parallelism over the original CORDIC algorithm, thus, resulting in an enhanced speed of computation. This has been accomplished by decoupling the CORDIC iteration equations, and transforming the sequential nature of these equations. $n$-bit fixed point data operands are assumed and the parameter $k$ relates to the level of parallelism in the algorithm. The modified algorithm employs a $ [k + 1]n^2 $-bit ROM for lookup tables that enable elementary arithmetic functions to be evaluated in no more than $ [3 n + 2] $ and no less than $2$ time steps. The two bounds correspond to a pipelined and a parallel implementation, respectively. The formulation of the MCA can be manipulated to obtain implementations with various speed\slash cost characteristics. This compares to $ n(3 n + 1) / 2 $ time steps for the original CORDIC algorithm. For example, 32-bit ALU has $ k = 12 $ and $ n = 32 $; so, a 13,312-bit ROM is required to store the lookup tables, and the computation requires 98 time steps for a pipelined implementation.

entry:
@InProceedings{Naseem:1985:MCA,
  author =       "Asif Naseem and P. David Fisher",
  title =        "The Modified {CORDIC} Algorithm",
  crossref =     "Hwang:1985:PSC",
  pages =        "144--152",
  year =         "1985",
  bibdate =      "Wed Sep 14 20:50:04 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Naseem_Fisher.pdf",
  abstract =     "A Modified CORDIC Algorithm (MCA) has been developed
                 for the evaluation of elementary arithmetic functions.
                 MCA incorporates increased parallelism over the
                 original CORDIC algorithm, thus, resulting in an
                 enhanced speed of computation. This has been
                 accomplished by decoupling the CORDIC iteration
                 equations, and transforming the sequential nature of
                 these equations. $n$-bit fixed point data operands are
                 assumed and the parameter $k$ relates to the level of
                 parallelism in the algorithm. The modified algorithm
                 employs a $ [k + 1]n^2 $-bit ROM for lookup tables that
                 enable elementary arithmetic functions to be evaluated
                 in no more than $ [3 n + 2] $ and no less than $2$ time
                 steps. The two bounds correspond to a pipelined and a
                 parallel implementation, respectively. The formulation
                 of the MCA can be manipulated to obtain implementations
                 with various speed\slash cost characteristics. This
                 compares to $ n(3 n + 1) / 2 $ time steps for the
                 original CORDIC algorithm. For example, 32-bit ALU has
                 $ k = 12 $ and $ n = 32 $; so, a 13,312-bit ROM is
                 required to store the lookup tables, and the
                 computation requires 98 time steps for a pipelined
                 implementation.",
  acknowledgement = ack-nj,
  keywords =     "ARITH-7",
}


bibtype: article
filename: fparith.bib
label: Neumaier:1985:IPR
author: A. Neumaier
title: Inner Product Rounding Error Analysis in the Presence of Underflow
journal: j-COMPUTING
volume: 34
number: 4
pages: 365--373
year: 1985
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
MRclass: 65G05
MRnumber: 86j:65054
bibdate: Tue Oct 12 16:33:42 MDT 1999
bibtimestamp: 1999.10.12 16:33:42 MDT
fjournal: Computing: Archiv fur informatik und numerik
acknowledgement: ack-nhfb
affiliation: Univ Freiburg, Inst fur Angewandte Mathematik, Freiburg, West Germany
journalURL: http://link.springer.com/journal/607
journalabr: Computing (Vienna/New York)
rawauthor: A. Neumaier
rawtitle: Inner Product Rounding Error Analysis in the Presence of Underflow
bibsource:
Compendex database; http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X; https://www.math.utah.edu/pub/tex/bib/fparith.bib; MathSciNet database

keywords:
computer metatheory; inner product rounding error analysis; inner products; mathematical techniques --- error analysis; underflow

entry:
@Article{Neumaier:1985:IPR,
  author =       "A. Neumaier",
  title =        "Inner Product Rounding Error Analysis in the Presence
                 of Underflow",
  journal =      j-COMPUTING,
  volume =       "34",
  number =       "4",
  pages =        "365--373",
  year =         "1985",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65G05",
  MRnumber =     "86j:65054",
  bibdate =      "Tue Oct 12 16:33:42 MDT 1999",
  bibsource =    "Compendex database;
                 http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 MathSciNet database",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ Freiburg, Inst f{\"u}r Angewandte Mathematik,
                 Freiburg, West Germany",
  classification = "723; 921",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
  journalabr =   "Computing (Vienna/New York)",
  keywords =     "computer metatheory; inner product rounding error
                 analysis; inner products; mathematical techniques ---
                 error analysis; underflow",
}


bibtype: inproceedings
filename: fparith.bib
label: Ngai:1985:RAT
author: Tin-Fook Ngai and Mary Jane Irwin
title: Regular, area-time efficient carry-lookahead adders
crossref: Hwang:1985:PSC
pages: 9--15
year: 1985
bibdate: Fri Nov 16 10:05:44 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.16 10:05:44 ???
URL: http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Ngai_Irwin.pdf
keywords: ARITH-7
acknowledgement: ack-nhfb
rawauthor: Tin-Fook Ngai and Mary Jane Irwin
rawtitle: Regular, area-time efficient carry-lookahead adders
abstract:
For fast binary addition, a carrylookahead (CLA) design is the obvious choice [OnAt83, BaJM83]. However, the direct implementation of a CLA adder in VLSI faces some undesirable limitations. Either the design lacks regularity, thus increasing the design and implementation costs, or the interconnection wires are too long, thus causing area-time inefficiency and limits on the size of addition. Brent and Kung solved the regularity problem by reformulating the carry chain computation [BrKu82]. They showed that an $n$-bit addition can be performed in time $ O(log n) $, using area $ O(n log n) $ with maximum interconnection wire length $ O(n) $. In this paper, we give an alternative $ log n $ stage design which is nearly optimum with respect to regularity, area-time efficiency, and maximum interconnection wire length.

rawabstract:
For fast binary addition, a carrylookahead (CLA) design is the obvious choice [OnAt83, BaJM83]. However, the direct implementation of a CLA adder in VLSI faces some undesirable limitations. Either the design lacks regularity, thus increasing the design and implementation costs, or the interconnection wires are too long, thus causing area-time inefficiency and limits on the size of addition. Brent and Kung solved the regularity problem by reformulating the carry chain computation [BrKu82]. They showed that an $n$-bit addition can be performed in time $ O(\log n) $, using area $ O(n \log n) $ with maximum interconnection wire length $ O(n) $. In this paper, we give an alternative $ \log n $ stage design which is nearly optimum with respect to regularity, area-time efficiency, and maximum interconnection wire length.

entry:
@InProceedings{Ngai:1985:RAT,
  author =       "Tin-Fook Ngai and Mary Jane Irwin",
  title =        "Regular, area-time efficient carry-lookahead adders",
  crossref =     "Hwang:1985:PSC",
  pages =        "9--15",
  year =         "1985",
  bibdate =      "Fri Nov 16 10:05:44 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Ngai_Irwin.pdf",
  abstract =     "For fast binary addition, a carrylookahead (CLA)
                 design is the obvious choice [OnAt83, BaJM83]. However,
                 the direct implementation of a CLA adder in VLSI faces
                 some undesirable limitations. Either the design lacks
                 regularity, thus increasing the design and
                 implementation costs, or the interconnection wires are
                 too long, thus causing area-time inefficiency and
                 limits on the size of addition. Brent and Kung solved
                 the regularity problem by reformulating the carry chain
                 computation [BrKu82]. They showed that an $n$-bit
                 addition can be performed in time $ O(\log n) $, using
                 area $ O(n \log n) $ with maximum interconnection wire
                 length $ O(n) $. In this paper, we give an alternative
                 $ \log n $ stage design which is nearly optimum with
                 respect to regularity, area-time efficiency, and
                 maximum interconnection wire length.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}


bibtype: article
filename: fparith.bib
label: Ni:1985:VRT
author: L. M. Ni and Kai Hwang
title: Vector-Reduction Techniques for Arithmetic Pipelines
journal: j-IEEE-TRANS-COMPUT
volume: C-34
number: 5
pages: 404--411
month: may
monthnumber: 5
year: 1985
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1985.1676580
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 08:32:26 MDT 2011
bibtimestamp: 2011.07.10 08:32:26 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676580
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: L. M. Ni and Kai Hwang
rawtitle: Vector-Reduction Techniques for Arithmetic Pipelines
entry:
@Article{Ni:1985:VRT,
  author =       "L. M. Ni and Kai Hwang",
  title =        "Vector-Reduction Techniques for Arithmetic Pipelines",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-34",
  number =       "5",
  pages =        "404--411",
  month =        may,
  year =         "1985",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1985.1676580",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 08:32:26 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676580",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Ohhashi:1985:HSC
author: M. Ohhashi and R. E. Schneider
title: High-Speed Computation of Unary Functions
crossref: Hwang:1985:PSC
pages: 82--85
year: 1985
bibdate: Fri Nov 16 08:47:34 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.16 08:47:34 ???
URL: http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Ohhashi_Schneider.pdf
keywords: ARITH-7
acknowledgement: ack-nhfb
rawauthor: M. Ohhashi and R. E. Schneider
rawtitle: High-Speed Computation of Unary Functions
abstract:
This paper presents an architecture for fast evaluation of unary functions such as reciprocal, square root and reciprocal square root. The theory behind the architecture has been presented in [1]. The paper shows the results of extensive simulation that have allowed us to implement the architecture with minimum chip count and maximum accuracy. The accuracy is about 8% error rate in the LSB of the chosen representation (IEEE 32-bit floating point format). This architecture allows the computation of unary functions in less than 200 nsec.

rawabstract:
This paper presents an architecture for fast evaluation of unary functions such as reciprocal, square root and reciprocal square root. The theory behind the architecture has been presented in [1]. The paper shows the results of extensive simulation that have allowed us to implement the architecture with minimum chip count and maximum accuracy. The accuracy is about 8\% error rate in the LSB of the chosen representation (IEEE 32-bit floating point format). This architecture allows the computation of unary functions in less than 200 nsec.

entry:
@InProceedings{Ohhashi:1985:HSC,
  author =       "M. Ohhashi and R. E. Schneider",
  title =        "High-Speed Computation of Unary Functions",
  crossref =     "Hwang:1985:PSC",
  pages =        "82--85",
  year =         "1985",
  bibdate =      "Fri Nov 16 08:47:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Ohhashi_Schneider.pdf",
  abstract =     "This paper presents an architecture for fast
                 evaluation of unary functions such as reciprocal,
                 square root and reciprocal square root. The theory
                 behind the architecture has been presented in [1]. The
                 paper shows the results of extensive simulation that
                 have allowed us to implement the architecture with
                 minimum chip count and maximum accuracy. The accuracy
                 is about 8\% error rate in the LSB of the chosen
                 representation (IEEE 32-bit floating point format).
                 This architecture allows the computation of unary
                 functions in less than 200 nsec.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}


bibtype: inproceedings
filename: fparith.bib
label: Oklobdzija:1985:SOS
author: Vojin G. Oklobdzija and Earl R. Barnes
title: Some Optimal Schemes for ALU Implementations in VLSI Technology
crossref: Hwang:1985:PSC
pages: 2--8
year: 1985
bibdate: Fri Nov 16 08:47:34 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.16 08:47:34 ???
URL: http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Oklobdzija_Barnes.pdf
keywords: ARITH-7
acknowledgement: ack-nhfb
rawauthor: Vojin G. Oklobdzija and Earl R. Barnes
rawtitle: Some Optimal Schemes for {ALU} Implementations in {VLSI} Technology
abstract:
An efficient scheme for carry propagation in an ALU implemented in n-MOS technology is presented. An algorithm that determines the optimum division of the carry chain of a parallel adder for various data path sizes is developed. This yields an implementation of a fast ALU which due to its regular structure occupies a modest amount of silicon. The speed of the implementation described is comparable to the carry look-ahead scheme. Our method is based on the optimization of the carry path implemented in n-MOS technology but the results can be applied to other technologies.

rawabstract:
An efficient scheme for carry propagation in an ALU implemented in n-MOS technology is presented. An algorithm that determines the optimum division of the carry chain of a parallel adder for various data path sizes is developed. This yields an implementation of a fast ALU which due to its regular structure occupies a modest amount of silicon. The speed of the implementation described is comparable to the carry look-ahead scheme. Our method is based on the optimization of the carry path implemented in n-MOS technology but the results can be applied to other technologies.

entry:
@InProceedings{Oklobdzija:1985:SOS,
  author =       "Vojin G. Oklobdzija and Earl R. Barnes",
  title =        "Some Optimal Schemes for {ALU} Implementations in
                 {VLSI} Technology",
  crossref =     "Hwang:1985:PSC",
  pages =        "2--8",
  year =         "1985",
  bibdate =      "Fri Nov 16 08:47:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Oklobdzija_Barnes.pdf",
  abstract =     "An efficient scheme for carry propagation in an ALU
                 implemented in n-MOS technology is presented. An
                 algorithm that determines the optimum division of the
                 carry chain of a parallel adder for various data path
                 sizes is developed. This yields an implementation of a
                 fast ALU which due to its regular structure occupies a
                 modest amount of silicon. The speed of the
                 implementation described is comparable to the carry
                 look-ahead scheme. Our method is based on the
                 optimization of the carry path implemented in n-MOS
                 technology but the results can be applied to other
                 technologies.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}


bibtype: book
filename: fparith.bib
label: Palmer:1985:MGN
author: John F. Palmer and Stephen P. Morse
title: Die mathematischen Grundlagen der Numerik-Prozessoren 8087 / 80287
publisher: pub-TEWI
address: pub-TEWI:adr
pages: 240
year: 1985
ISBN: 3-921803-33-0 OR 3921803330
ISBN13: 978-3-921803-33-2 OR 9783921803332
bibdate: Wed Sep 07 21:14:32 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.07 21:14:32 ???
note: German translation of em The 8087 Primer cite Palmer:1984:P.
acknowledgement: ack-nj
rawauthor: John F. Palmer and Stephen P. Morse
rawnote: German translation of {\em The 8087 Primer} \cite{Palmer:1984:P}.
rawtitle: {Die mathematischen Grundlagen der Numerik-Prozessoren 8087\slash 80287}
entry:
@Book{Palmer:1985:MGN,
  author =       "John F. Palmer and Stephen P. Morse",
  title =        "{Die mathematischen Grundlagen der Numerik-Prozessoren
                 8087\slash 80287}",
  publisher =    pub-TEWI,
  address =      pub-TEWI:adr,
  pages =        "240",
  year =         "1985",
  ISBN =         "3-921803-33-0",
  ISBN-13 =      "978-3-921803-33-2",
  LCCN =         "????",
  bibdate =      "Wed Sep 07 21:14:32 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "German translation of {\em The 8087 Primer}
                 \cite{Palmer:1984:P}.",
  acknowledgement = ack-nj,
}


bibtype: misc
filename: fparith.bib
label: Palmer:1985:PBS
author: John Palmer and Bruce Ravenel and Ravi Nave
title: Programmable Bidirectional Shifter
pages: 240
day: 2
month: apr
monthnumber: 4
year: 1985
bibdate: Sat Aug 23 06:44:00 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2025.08.23 06:44:00 ???
note: Filed 5 December 1983. See discussion cite Shirriff:2020:AMC.
URL: https://ieeemilestones.ethw.org/w/images/a/a4/Patent_Barrel_shifter_8087.pdf
acknowledgement: ack-nhfb
howpublished: US Patent 4,509,144.
rawauthor: John Palmer and Bruce Ravenel and Ravi Nave
rawnote: Filed 5 December 1983. See discussion \cite{Shirriff:2020:AMC}.
rawtitle: Programmable Bidirectional Shifter
abstract:
A programmable bidirectional shifter is disclosed comprised of a first bidirectional load and read interface circuit selectively activated for left shifts, and a similarly constituted second bidirectional load and interface circuit which is selectively activated for right shifts. The first interface circuit is coupled to a byte shift matrix while the second interface circuit is coupled to a bit shift matrix. The byte shift matrix is arranged and con figured to shift the input quantity by a multiple of bytes, namely multiples of eight bits. The bit shift matrix is similarly constituted to shift its input quantity by a selected number of bit locations up to seven consecutive places. The bit and byte shift matrices are coupled to allow bidirectional flow of signals there between. The bit and byte matrix are controlled by a bit and byte shift control circuit respectively which determines the number of bytes and bit places each matrix will actually shift.

rawabstract:
A programmable bidirectional shifter is disclosed comprised of a first bidirectional load and read interface circuit selectively activated for left shifts, and a similarly constituted second bidirectional load and interface circuit which is selectively activated for right shifts. The first interface circuit is coupled to a byte shift matrix while the second interface circuit is coupled to a bit shift matrix. The byte shift matrix is arranged and con figured to shift the input quantity by a multiple of bytes, namely multiples of eight bits. The bit shift matrix is similarly constituted to shift its input quantity by a selected number of bit locations up to seven consecutive places. The bit and byte shift matrices are coupled to allow bidirectional flow of signals there between. The bit and byte matrix are controlled by a bit and byte shift control circuit respectively which determines the number of bytes and bit places each matrix will actually shift.

entry:
@Misc{Palmer:1985:PBS,
  author =       "John Palmer and Bruce Ravenel and Ravi Nave",
  title =        "Programmable Bidirectional Shifter",
  howpublished = "US Patent 4,509,144.",
  day =          "2",
  month =        apr,
  year =         "1985",
  bibdate =      "Sat Aug 23 06:44:00 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Filed 5 December 1983. See discussion
                 \cite{Shirriff:2020:AMC}.",
  URL =          "https://ieeemilestones.ethw.org/w/images/a/a4/Patent_Barrel_shifter_8087.pdf",
  abstract =     "A programmable bidirectional shifter is disclosed
                 comprised of a first bidirectional load and read
                 interface circuit selectively activated for left
                 shifts, and a similarly constituted second
                 bidirectional load and interface circuit which is
                 selectively activated for right shifts. The first
                 interface circuit is coupled to a byte shift matrix
                 while the second interface circuit is coupled to a bit
                 shift matrix. The byte shift matrix is arranged and con
                 figured to shift the input quantity by a multiple of
                 bytes, namely multiples of eight bits. The bit shift
                 matrix is similarly constituted to shift its input
                 quantity by a selected number of bit locations up to
                 seven consecutive places. The bit and byte shift
                 matrices are coupled to allow bidirectional flow of
                 signals there between. The bit and byte matrix are
                 controlled by a bit and byte shift control circuit
                 respectively which determines the number of bytes and
                 bit places each matrix will actually shift.",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Papachristou:1985:MIR
author: Christos A. Papachristou
title: Multi-Input Residue Arithmetic Utilizing Read-Only Associate Memory
crossref: Hwang:1985:PSC
pages: 182--188
year: 1985
bibdate: Fri Nov 16 08:47:34 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.16 08:47:34 ???
URL: http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Papachristou.pdf
keywords: ARITH-7
acknowledgement: ack-nhfb
rawauthor: Christos A. Papachristou
rawtitle: Multi-Input Residue Arithmetic Utilizing Read-Only Associate Memory
abstract:
In this paper an approach to residue arithmetic is presented using Read-Only-Associative Memories (ROAMs), such as PLAs. These memories have considerable advantages for table lookup arithmetic processing over the conventional ROMs in terms of their storage and time efficiency. In residue arithmetic, the ROAM storage required largely depends on the residue recurrences in arithmetic tables modulo $M$. After reviewing recent results on the computation of recurrences, a scheme is proposed for implementing residue arithmetic based on ROAMs. The efficiency of the scheme is established by comparison to conventional ROM-based table lookup techniques. Applications to residue-to-binary number system conversion are also discussed.

rawabstract:
In this paper an approach to residue arithmetic is presented using Read-Only-Associative Memories (ROAMs), such as PLAs. These memories have considerable advantages for table lookup arithmetic processing over the conventional ROMs in terms of their storage and time efficiency. In residue arithmetic, the ROAM storage required largely depends on the residue recurrences in arithmetic tables modulo $M$. After reviewing recent results on the computation of recurrences, a scheme is proposed for implementing residue arithmetic based on ROAMs. The efficiency of the scheme is established by comparison to conventional ROM-based table lookup techniques. Applications to residue-to-binary number system conversion are also discussed.

entry:
@InProceedings{Papachristou:1985:MIR,
  author =       "Christos A. Papachristou",
  title =        "Multi-Input Residue Arithmetic Utilizing Read-Only
                 Associate Memory",
  crossref =     "Hwang:1985:PSC",
  pages =        "182--188",
  year =         "1985",
  bibdate =      "Fri Nov 16 08:47:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Papachristou.pdf",
  abstract =     "In this paper an approach to residue arithmetic is
                 presented using Read-Only-Associative Memories (ROAMs),
                 such as PLAs. These memories have considerable
                 advantages for table lookup arithmetic processing over
                 the conventional ROMs in terms of their storage and
                 time efficiency. In residue arithmetic, the ROAM
                 storage required largely depends on the residue
                 recurrences in arithmetic tables modulo $M$. After
                 reviewing recent results on the computation of
                 recurrences, a scheme is proposed for implementing
                 residue arithmetic based on ROAMs. The efficiency of
                 the scheme is established by comparison to conventional
                 ROM-based table lookup techniques. Applications to
                 residue-to-binary number system conversion are also
                 discussed.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}


bibtype: article
filename: fparith.bib
label: Parker:1985:GCI
author: J. R. Parker
title: A General Character to Integer Conversion Method
journal: j-SPE
volume: 15
number: 8
pages: 761--766
month: aug
monthnumber: 8
year: 1985
CODEN: SPEXBL
DOI: https://doi.org/10.1002/spe.4380150804
ISSN: 0038-0644 (print), 1097-024X (electronic) OR 00380644 (print), 1097024X (electronic)
ISSNL: 0038-0644 OR 00380644
bibdate: Sat May 31 13:36:16 MDT 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/spe.bib
bibtimestamp: 1997.05.31 13:36:16 MDT
fjournal: Software --- Practice and Experience
keywords: algorithms; integer overflow detection; languages; programming techniques; type conversion
subject: D.1.m Software, PROGRAMMING TECHNIQUES, Miscellaneous
acknowledgement: ack-nhfb
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X
rawauthor: J. R. Parker
rawtitle: A General Character to Integer Conversion Method
entry:
@Article{Parker:1985:GCI,
  author =       "J. R. Parker",
  title =        "A General Character to Integer Conversion Method",
  journal =      j-SPE,
  volume =       "15",
  number =       "8",
  pages =        "761--766",
  month =        aug,
  year =         "1985",
  CODEN =        "SPEXBL",
  DOI =          "https://doi.org/10.1002/spe.4380150804",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  bibdate =      "Sat May 31 13:36:16 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/spe.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Software --- Practice and Experience",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
  keywords =     "algorithms; integer overflow detection; languages;
                 programming techniques; type conversion",
  review =       "ACM CR 8603-0209",
  subject =      "D.1.m Software, PROGRAMMING TECHNIQUES,
                 Miscellaneous",
}


bibtype: inproceedings
filename: fparith.bib
label: Pellegrino:1985:RNS
author: J. M. Pellegrino and B. M. Sadler and S. D. Casey
editor: Bruce Ronald McAvoy
title: A Residue Number System for Wideband Acousto-Optic Spectrum Analysis
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 385--390
year: 1985
DOI: https://doi.org/10.1049/el:19850252
LCCN: A367 .U46 1985eb
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
note: IEEE catalog number 85CH2209-5.
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: J. M. Pellegrino and B. M. Sadler and S. D. Casey
raweditor: Bruce Ronald McAvoy
rawnote: IEEE catalog number 85CH2209-5.
rawtitle: A Residue Number System for Wideband Acousto-Optic Spectrum Analysis
booktitle:
IEEE 1985 Ultrasonics Symposium: proceedings, October 16--18, 1985, Cathedral Hill Hotel, Van Ness at Geary, San Francisco, CA

rawbooktitle:
{IEEE 1985 Ultrasonics Symposium: proceedings, October 16--18, 1985, Cathedral Hill Hotel, Van Ness at Geary, San Francisco, CA}

entry:
@InProceedings{Pellegrino:1985:RNS,
  author =       "J. M. Pellegrino and B. M. Sadler and S. D. Casey",
  editor =       "Bruce Ronald McAvoy",
  booktitle =    "{IEEE 1985 Ultrasonics Symposium: proceedings, October
                 16--18, 1985, Cathedral Hill Hotel, Van Ness at Geary,
                 San Francisco, CA}",
  title =        "A Residue Number System for Wideband Acousto-Optic
                 Spectrum Analysis",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "385--390",
  year =         "1985",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1049/el:19850252",
  ISSN =         "????",
  LCCN =         "A367 .U46 1985eb",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE catalog number 85CH2209-5.",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
}


bibtype: phdthesis
filename: fparith.bib
label: Peralta:1985:TRN
author: Rene Caupolican Peralta
type: Thesis (Ph.D.)
school: Department of Computer Science, University of California, Berkeley
address: Berkeley, CA, USA
pages: 52
month: dec
monthnumber: 12
year: 1985
bibdate: Sat Oct 17 16:25:07 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.10.17 16:25:07 MDT
acknowledgement: ack-nhfb
rawauthor: Rene Caupolican Peralta
title:
Three results in number theory and cryptography: a new algorithm to compute square roots modulo a prime number; On the bit complexity of the discrete logarithm; A framework for the study of cryptoprotocols

keywords:
dissertations; dissertations, academic --- UCB --- computer science --- 1981--1990; University of California, Berkeley. computer science division --

rawtitle:
Three results in number theory and cryptography: a new algorithm to compute square roots modulo a prime number; On the bit complexity of the discrete logarithm; {A} framework for the study of cryptoprotocols

entry:
@PhdThesis{Peralta:1985:TRN,
  author =       "Rene Caupolican Peralta",
  title =        "Three results in number theory and cryptography: a new
                 algorithm to compute square roots modulo a prime
                 number; On the bit complexity of the discrete
                 logarithm; {A} framework for the study of
                 cryptoprotocols",
  type =         "Thesis ({Ph.D.})",
  school =       "Department of Computer Science, University of
                 California, Berkeley",
  address =      "Berkeley, CA, USA",
  pages =        "52",
  month =        dec,
  year =         "1985",
  LCCN =         "????",
  bibdate =      "Sat Oct 17 16:25:07 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "dissertations; dissertations, academic --- UCB ---
                 computer science --- 1981--1990; University of
                 California, Berkeley. computer science division --",
}


bibtype: article
filename: fparith.bib
label: Raimi:1985:FDP
author: Ralph A. Raimi
title: The First Digit Phenomenon Again
journal: j-PROC-AMER-PHIL-SOC
volume: 129
number: 2
pages: 211--219
month: jun
monthnumber: 6
year: 1985
CODEN: PAPCAA
ISSN: 0003-049X (print), 2326-9243 (electronic) OR 0003049X (print), 23269243 (electronic)
ISSNL: 0003-049X OR 0003049X
bibdate: Sat Nov 12 16:56:54 2011
bibtimestamp: 2011.11.12 16:56:54 ???
note: This paper contains strong criticism of a derivation of Benford's Law cite Logan:1978:FDP.
URL: http://www.jstor.org/stable/986989
acknowledgement: ack-nhfb
journalURL: http://www.jstor.org/journal/procamerphilsoci
rawauthor: Ralph A. Raimi
rawnote: This paper contains strong criticism of a derivation of Benford's Law \cite{Logan:1978:FDP}.
rawtitle: The First Digit Phenomenon Again
fjournal:
Proceedings of the American Philosophical Society held at Philadelphia for promoting useful knowledge

remark:
This paper contains mathematical derivations of both Stigler's Law and Benford's Law. Raimi comments on p. 217: ``the Benford law itself as a conclusion to be derived is by no means as firm as Kepler's planetary curves. Indeed, it has been pointed out by Diaconis and Freedman [D-F] [cite Diaconis:1979:RP] that a statistical analysis of Benford's announced data gives a high probability to the conjecture that he did a bit of rounding-off here and there, always in the direction of his law. The license that a physicist often takes on the path from his hypotheses to verified, observable, and repeatable conclusion is not justified here.''.

entry:
@Article{Raimi:1985:FDP,
  author =       "Ralph A. Raimi",
  title =        "The First Digit Phenomenon Again",
  journal =      j-PROC-AMER-PHIL-SOC,
  volume =       "129",
  number =       "2",
  pages =        "211--219",
  month =        jun,
  year =         "1985",
  CODEN =        "PAPCAA",
  ISSN =         "0003-049X (print), 2326-9243 (electronic)",
  ISSN-L =       "0003-049X",
  bibdate =      "Sat Nov 12 16:56:54 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "This paper contains strong criticism of a derivation
                 of Benford's Law \cite{Logan:1978:FDP}.",
  URL =          "http://www.jstor.org/stable/986989",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the {American Philosophical Society}
                 held at {Philadelphia} for promoting useful knowledge",
  journal-URL =  "http://www.jstor.org/journal/procamerphilsoci",
  remark =       "This paper contains mathematical derivations of both
                 Stigler's Law and Benford's Law. Raimi comments on p.
                 217: ``the Benford law itself as a conclusion to be
                 derived is by no means as firm as Kepler's planetary
                 curves. Indeed, it has been pointed out by Diaconis and
                 Freedman [D-F] [\cite{Diaconis:1979:RP}] that a
                 statistical analysis of Benford's announced data gives
                 a high probability to the conjecture that he did a bit
                 of rounding-off here and there, always in the direction
                 of his law. The license that a physicist often takes on
                 the path from his hypotheses to verified, observable,
                 and repeatable conclusion is not justified here.''.",
}


bibtype: article
filename: fparith.bib
label: Ramnarayan:1985:LMR
author: R. Ramnarayan and F. Taylor
title: On large moduli residue number system recursive digital filters
journal: j-IEEE-TRANS-CIRCUITS-SYST
volume: 32
number: 4
pages: 349--359
month: apr
monthnumber: 4
year: 1985
CODEN: ICSYBT
ISSN: 0098-4094 (print), 1558-1276 (electronic) OR 00984094 (print), 15581276 (electronic)
ISSNL: 0098-4094 OR 00984094
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
URL: https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23567
fjournal: IEEE Transactions on Circuits and Systems
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: R. Ramnarayan and F. Taylor
rawtitle: On large moduli residue number system recursive digital filters
entry:
@Article{Ramnarayan:1985:LMR,
  author =       "R. Ramnarayan and F. Taylor",
  title =        "On large moduli residue number system recursive
                 digital filters",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "32",
  number =       "4",
  pages =        "349--359",
  month =        apr,
  year =         "1985",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23567",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  keywords =     "residue arithmetic; residue number system",
  summary =      "The three moduli set{2^{n} - 1, 2^{n},2^{n} +
                 1}residue number system, or RNS, has recently been
                 shown to possess several attractive properties. In
                 particular, the problem of scaling is much simplified
                 through the use of an autoscale \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Rao:1985:CCC
author: T. R. N. Rao and Kasem Vathanvit
title: A Class of $ A(N + C) $ Codes and Its Properties
crossref: Hwang:1985:PSC
pages: 293--295
year: 1985
bibdate: Fri Nov 16 08:47:34 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.16 08:47:34 ???
URL: http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Rao_Vathanvit.pdf
keywords: ARITH-7
acknowledgement: ack-nhfb
rawauthor: T. R. N. Rao and Kasem Vathanvit
rawtitle: A Class of {$ A(N + C) $} Codes and Its Properties
abstract:
We discuss here a new class of arithmetic codes, called $ A(N + C) $ codes where $A$ and $C$ are constant positive integers, $N$ is information to be coded. $ A(N + C) $ codes are a special case of $ A N + B $ arithmetic codes which were first studied by Brown. $ A N $ codes are linear and cannot be used to detect unidirectional multiple errors. $ A(N + C) $ codes are non-linear and are useful for detecting and / or correcting symmetric errors, arithmetic errors and unidirectional errors. Furthermore, $ A(N + C) $ codes can be constructed to provide constant-weight, self-complementing and cyclic-code properties. It is apparent that the codes with these properties have, in some sense, broader capabilities of error detection and error correction.

rawabstract:
We discuss here a new class of arithmetic codes, called $ A(N + C) $ codes where $A$ and $C$ are constant positive integers, $N$ is information to be coded. $ A(N + C) $ codes are a special case of $ A N + B $ arithmetic codes which were first studied by Brown. $ A N $ codes are linear and cannot be used to detect unidirectional multiple errors. $ A(N + C) $ codes are non-linear and are useful for detecting and\slash or correcting symmetric errors, arithmetic errors and unidirectional errors. Furthermore, $ A(N + C) $ codes can be constructed to provide constant-weight, self-complementing and cyclic-code properties. It is apparent that the codes with these properties have, in some sense, broader capabilities of error detection and error correction.

entry:
@InProceedings{Rao:1985:CCC,
  author =       "T. R. N. Rao and Kasem Vathanvit",
  title =        "A Class of {$ A(N + C) $} Codes and Its Properties",
  crossref =     "Hwang:1985:PSC",
  pages =        "293--295",
  year =         "1985",
  bibdate =      "Fri Nov 16 08:47:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Rao_Vathanvit.pdf",
  abstract =     "We discuss here a new class of arithmetic codes,
                 called $ A(N + C) $ codes where $A$ and $C$ are
                 constant positive integers, $N$ is information to be
                 coded. $ A(N + C) $ codes are a special case of $ A N +
                 B $ arithmetic codes which were first studied by Brown.
                 $ A N $ codes are linear and cannot be used to detect
                 unidirectional multiple errors. $ A(N + C) $ codes are
                 non-linear and are useful for detecting and\slash or
                 correcting symmetric errors, arithmetic errors and
                 unidirectional errors. Furthermore, $ A(N + C) $ codes
                 can be constructed to provide constant-weight,
                 self-complementing and cyclic-code properties. It is
                 apparent that the codes with these properties have, in
                 some sense, broader capabilities of error detection and
                 error correction.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}


bibtype: inproceedings
filename: fparith.bib
label: Reed:1985:VRM
author: I. S. Reed and T. K. Truong and J. J. Chang and H. M. Shao and I. S. Hsu
title: VLSI Residue Multiplier Modulo a Fermat Number
crossref: Hwang:1985:PSC
pages: 203--206
year: 1985
bibdate: Fri Nov 16 08:47:34 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.16 08:47:34 ???
URL: http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Reed_Truong_Chang_Shao_Hsu.pdf
keywords: ARITH-7
acknowledgement: ack-nhfb
rawauthor: I. S. Reed and T. K. Truong and J. J. Chang and H. M. Shao and I. S. Hsu
rawtitle: {VLSI} Residue Multiplier Modulo a {Fermat} Number
abstract:
Multiplication is central in the implementation of Fermat number transforms (FNT) and other residue number algorithms. There is need for a good multiplication algorithm which can be realized easily on a VLSI chip. In this paper, the Leibowitz multiplier [1] is modified to realize multiplication in the ring of integers modulo a Fermat number. The advantage of this new algorithm over Leibowitz's algorithm is that Leibowitz's algorithm takes modulo after the product of multiplication is obtained. Hence time is wasted. In this new algorithm, modulo is taken in every bit operation when performing multiplication. Therefore no time is wasted in this respect. Furthermore, this algorithm requires only a sequence of cyclic shifts and additions. The design[s] for this new multiplier are regular, simple, expandable and therefore, suitable far VLSI implementation.

rawabstract:
Multiplication is central in the implementation of Fermat number transforms (FNT) and other residue number algorithms. There is need for a good multiplication algorithm which can be realized easily on a VLSI chip. In this paper, the Leibowitz multiplier [1] is modified to realize multiplication in the ring of integers modulo a Fermat number. The advantage of this new algorithm over Leibowitz's algorithm is that Leibowitz's algorithm takes modulo after the product of multiplication is obtained. Hence time is wasted. In this new algorithm, modulo is taken in every bit operation when performing multiplication. Therefore no time is wasted in this respect. Furthermore, this algorithm requires only a sequence of cyclic shifts and additions. The design[s] for this new multiplier are regular, simple, expandable and therefore, suitable far VLSI implementation.

entry:
@InProceedings{Reed:1985:VRM,
  author =       "I. S. Reed and T. K. Truong and J. J. Chang and H. M.
                 Shao and I. S. Hsu",
  title =        "{VLSI} Residue Multiplier Modulo a {Fermat} Number",
  crossref =     "Hwang:1985:PSC",
  pages =        "203--206",
  year =         "1985",
  bibdate =      "Fri Nov 16 08:47:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Reed_Truong_Chang_Shao_Hsu.pdf",
  abstract =     "Multiplication is central in the implementation of
                 Fermat number transforms (FNT) and other residue number
                 algorithms. There is need for a good multiplication
                 algorithm which can be realized easily on a VLSI chip.
                 In this paper, the Leibowitz multiplier [1] is modified
                 to realize multiplication in the ring of integers
                 modulo a Fermat number. The advantage of this new
                 algorithm over Leibowitz's algorithm is that
                 Leibowitz's algorithm takes modulo after the product of
                 multiplication is obtained. Hence time is wasted. In
                 this new algorithm, modulo is taken in every bit
                 operation when performing multiplication. Therefore no
                 time is wasted in this respect. Furthermore, this
                 algorithm requires only a sequence of cyclic shifts and
                 additions. The design[s] for this new multiplier are
                 regular, simple, expandable and therefore, suitable far
                 VLSI implementation.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}


bibtype: inproceedings
filename: fparith.bib
label: Rump:1985:HOC
author: Siegfried M. Rump
title: Higher Order Computer Arithmetic
crossref: Hwang:1985:PSC
pages: 302--308
year: 1985
bibdate: Fri Nov 16 08:47:34 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.16 08:47:34 ???
URL: http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Rump.pdf
keywords: ARITH-7
acknowledgement: ack-nhfb
rawauthor: Siegfried M. Rump
rawtitle: Higher Order Computer Arithmetic
abstract:
The floating-point arithmetic on computers is designed to approximate the corresponding operations over the real numbers as close as possible. In this paper it is shown by means of counterexamples that this need not be true for existing machines. For achieving good numerical results a floating-point arithmetic approximating the real operations as close as possible is probably best. For achieving verifications on computers, at least a precisely defined computer arithmetic is indispensable.par In this paper we first introduce the Kulisch / Miranker theory, which represents a sound basis for computer arithmetic. Each operation is precisely defined and, moreover, is of maximum accuracy. That means, the computed result is the floating-point number of the working precision closest to the infinite precise result. The theory also covers directed roundings allowing computations with intervals. These properties hold true for the floating-point numbers of single and double precision as well as for the vectors, matrices and complex extensions over those.par In the second part of the paper we demonstrate the theoretical basis for what we call 'Higher Order Computer Arithmetic'. This is an inclusion theory allowing the development of algorithms to compute bounds for the solution of various problems in numerical analysis. These bounds are automatically verified to be correct and they are of high accuracy. Very often they are of maximum accuracy, that means the left and right bounds of all components of the solution are adjacent in the floating-point screen. Moreover existence and uniqueness of a solution within the computed bounds is automatically verified by the algorithm. If this verification is not possible, a respective message is given. We develop the theory and give algorithms for the solution of systems of linear and nonlinear equations. As demonstrated by examples even for extremely ill-conditioned problems existence and uniqueness of the solution is verified within bounds of least significant bit accuracy.

rawabstract:
The floating-point arithmetic on computers is designed to approximate the corresponding operations over the real numbers as close as possible. In this paper it is shown by means of counterexamples that this need not be true for existing machines. For achieving good numerical results a floating-point arithmetic approximating the real operations as close as possible is probably best. For achieving verifications on computers, at least a precisely defined computer arithmetic is indispensable.\par In this paper we first introduce the Kulisch\slash Miranker theory, which represents a sound basis for computer arithmetic. Each operation is precisely defined and, moreover, is of maximum accuracy. That means, the computed result is the floating-point number of the working precision closest to the infinite precise result. The theory also covers directed roundings allowing computations with intervals. These properties hold true for the floating-point numbers of single and double precision as well as for the vectors, matrices and complex extensions over those.\par In the second part of the paper we demonstrate the theoretical basis for what we call 'Higher Order Computer Arithmetic'. This is an inclusion theory allowing the development of algorithms to compute bounds for the solution of various problems in numerical analysis. These bounds are automatically verified to be correct and they are of high accuracy. Very often they are of maximum accuracy, that means the left and right bounds of all components of the solution are adjacent in the floating-point screen. Moreover existence and uniqueness of a solution within the computed bounds is automatically verified by the algorithm. If this verification is not possible, a respective message is given. We develop the theory and give algorithms for the solution of systems of linear and nonlinear equations. As demonstrated by examples even for extremely ill-conditioned problems existence and uniqueness of the solution is verified within bounds of least significant bit accuracy.

entry:
@InProceedings{Rump:1985:HOC,
  author =       "Siegfried M. Rump",
  title =        "Higher Order Computer Arithmetic",
  crossref =     "Hwang:1985:PSC",
  pages =        "302--308",
  year =         "1985",
  bibdate =      "Fri Nov 16 08:47:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Rump.pdf",
  abstract =     "The floating-point arithmetic on computers is designed
                 to approximate the corresponding operations over the
                 real numbers as close as possible. In this paper it is
                 shown by means of counterexamples that this need not be
                 true for existing machines. For achieving good
                 numerical results a floating-point arithmetic
                 approximating the real operations as close as possible
                 is probably best. For achieving verifications on
                 computers, at least a precisely defined computer
                 arithmetic is indispensable.\par

                 In this paper we first introduce the Kulisch\slash
                 Miranker theory, which represents a sound basis for
                 computer arithmetic. Each operation is precisely
                 defined and, moreover, is of maximum accuracy. That
                 means, the computed result is the floating-point number
                 of the working precision closest to the infinite
                 precise result. The theory also covers directed
                 roundings allowing computations with intervals. These
                 properties hold true for the floating-point numbers of
                 single and double precision as well as for the vectors,
                 matrices and complex extensions over those.\par

                 In the second part of the paper we demonstrate the
                 theoretical basis for what we call 'Higher Order
                 Computer Arithmetic'. This is an inclusion theory
                 allowing the development of algorithms to compute
                 bounds for the solution of various problems in
                 numerical analysis. These bounds are automatically
                 verified to be correct and they are of high accuracy.
                 Very often they are of maximum accuracy, that means the
                 left and right bounds of all components of the solution
                 are adjacent in the floating-point screen. Moreover
                 existence and uniqueness of a solution within the
                 computed bounds is automatically verified by the
                 algorithm. If this verification is not possible, a
                 respective message is given. We develop the theory and
                 give algorithms for the solution of systems of linear
                 and nonlinear equations. As demonstrated by examples
                 even for extremely ill-conditioned problems existence
                 and uniqueness of the solution is verified within
                 bounds of least significant bit accuracy.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}


bibtype: article
filename: fparith.bib
label: Salomon:1985:TGF
author: D. Salomon
title: Two generalized floating-point representations
journal: j-BYTE
volume: 10
number: 9
pages: 154--158
month: sep
monthnumber: 9
year: 1985
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: D. Salomon
rawtitle: Two generalized floating-point representations
entry:
@Article{Salomon:1985:TGF,
  author =       "D. Salomon",
  title =        "Two generalized floating-point representations",
  journal =      j-BYTE,
  volume =       "10",
  number =       "9",
  pages =        "154--158",
  month =        sep,
  year =         "1985",
  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,
  fjournal =     "BYTE Magazine",
  genterm =      "ALGORITHMS; DESIGN",
  guideno =      "03372",
}


bibtype: inproceedings
filename: fparith.bib
label: Schaeffer:1985:SPE
author: Jonathan Schaeffer and Darrell Makarenko
title: Systolic Polynomial Evaluation and Matrix Multiplication with Multiple Precision
crossref: Hwang:1985:PSC
pages: 110--117
year: 1985
bibdate: Fri Nov 16 08:47:34 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.16 08:47:34 ???
URL: http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Schaeffer_Makarenko.pdf
keywords: ARITH-7
acknowledgement: ack-nhfb
rawauthor: Jonathan Schaeffer and Darrell Makarenko
rawtitle: Systolic Polynomial Evaluation and Matrix Multiplication with Multiple Precision
abstract:
The design and implementation of a systolic VLSI multi-precision polynomial evaluator and matrix multiplier is described. The use of bit-serial arithmetic allows for a very simple cell design (two registers and an accumulator) enabling a substantial number of cells to be placed on a chip. A configuration of $ N^2 $ cells can evaluate $N$ polynomials of $N$ coefficients at $N$ points and perform $N$-width band matrix multiplication and $ N times N $ full matrix multiplication, each in linear time. Using current technology, 100 polynomials of 100 coefficients can be evaluated at 100 data points with 32 bit precision in an estimated one millisecond.

rawabstract:
The design and implementation of a systolic VLSI multi-precision polynomial evaluator and matrix multiplier is described. The use of bit-serial arithmetic allows for a very simple cell design (two registers and an accumulator) enabling a substantial number of cells to be placed on a chip. A configuration of $ N^2 $ cells can evaluate $N$ polynomials of $N$ coefficients at $N$ points and perform $N$-width band matrix multiplication and $ N \times N $ full matrix multiplication, each in linear time. Using current technology, 100 polynomials of 100 coefficients can be evaluated at 100 data points with 32 bit precision in an estimated one millisecond.

entry:
@InProceedings{Schaeffer:1985:SPE,
  author =       "Jonathan Schaeffer and Darrell Makarenko",
  title =        "Systolic Polynomial Evaluation and Matrix
                 Multiplication with Multiple Precision",
  crossref =     "Hwang:1985:PSC",
  pages =        "110--117",
  year =         "1985",
  bibdate =      "Fri Nov 16 08:47:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Schaeffer_Makarenko.pdf",
  abstract =     "The design and implementation of a systolic VLSI
                 multi-precision polynomial evaluator and matrix
                 multiplier is described. The use of bit-serial
                 arithmetic allows for a very simple cell design (two
                 registers and an accumulator) enabling a substantial
                 number of cells to be placed on a chip. A configuration
                 of $ N^2 $ cells can evaluate $N$ polynomials of $N$
                 coefficients at $N$ points and perform $N$-width band
                 matrix multiplication and $ N \times N $ full matrix
                 multiplication, each in linear time. Using current
                 technology, 100 polynomials of 100 coefficients can be
                 evaluated at 100 data points with 32 bit precision in
                 an estimated one millisecond.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}


bibtype: article
filename: fparith.bib
label: Schoof:1985:ECF
author: Rene Schoof
title: Elliptic Curves Over Finite Fields and the Computation of Square Roots $ operatorname mod p $
journal: j-MATH-COMPUT
volume: 44
number: 170
pages: 483--494
month: apr
monthnumber: 4
year: 1985
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 11Y16 (11G20 14G15)
MRnumber: 86e:11122
MRreviewer: Karl Rubin
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
ajournal: Math. Comput.
corpsource: Amsterdam University, Netherlands
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Ren{\'e} Schoof
rawtitle: Elliptic Curves Over Finite Fields and the Computation of Square Roots $ \operatorname {mod} p $
keywords:
computational complexity; deterministic algorithm; elliptic curve; F/sub q/-points; finite fields; function evaluation; number theory; square roots mod p; Weierstrass equation

classcodes:
B0250 (Combinatorial mathematics); B0290D (Functional analysis); C1160 (Combinatorial mathematics); C4120 (Functional analysis); C4240 (Programming and algorithm theory)

entry:
@Article{Schoof:1985:ECF,
  author =       "Ren{\'e} Schoof",
  title =        "Elliptic Curves Over Finite Fields and the Computation
                 of Square Roots $ \operatorname {mod} p $",
  journal =      j-MATH-COMPUT,
  volume =       "44",
  number =       "170",
  pages =        "483--494",
  month =        apr,
  year =         "1985",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "11Y16 (11G20 14G15)",
  MRnumber =     "86e:11122",
  MRreviewer =   "Karl Rubin",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  classcodes =   "B0250 (Combinatorial mathematics); B0290D (Functional
                 analysis); C1160 (Combinatorial mathematics); C4120
                 (Functional analysis); C4240 (Programming and algorithm
                 theory)",
  corpsource =   "Amsterdam University, Netherlands",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "computational complexity; deterministic algorithm;
                 elliptic curve; F/sub q/-points; finite fields;
                 function evaluation; number theory; square roots mod p;
                 Weierstrass equation",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: book
filename: fparith.bib
label: Scott:1985:CNS
author: Norman R. Scott
title: Computer Number Systems and Arithmetic
publisher: pub-PH
address: pub-PH:adr
pages: x + 254
year: 1985
ISBN: 0-13-164211-1 OR 0131642111
ISBN13: 978-0-13-164211-9 OR 9780131642119
LCCN: QA76.9.C62 S38 1985
bibdate: Thu Sep 1 10:14:05 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:14:05 ???
acknowledgement: ack-nj
rawauthor: Norman R. Scott
rawtitle: Computer Number Systems and Arithmetic
entry:
@Book{Scott:1985:CNS,
  author =       "Norman R. Scott",
  title =        "Computer Number Systems and Arithmetic",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "x + 254",
  year =         "1985",
  ISBN =         "0-13-164211-1",
  ISBN-13 =      "978-0-13-164211-9",
  LCCN =         "QA76.9.C62 S38 1985",
  bibdate =      "Thu Sep 1 10:14:05 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: Shah:1985:PHS
author: A. Shah and M. Sid-Ahmed and G. Jullien
journal: j-IEEE-TRANS-CIRCUITS-SYST
volume: 32
number: 3
pages: 285--288
month: mar
monthnumber: 3
year: 1985
CODEN: ICSYBT
ISSN: 0098-4094 (print), 1558-1276 (electronic) OR 00984094 (print), 15581276 (electronic)
ISSNL: 0098-4094 OR 00984094
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
URL: https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23566
fjournal: IEEE Transactions on Circuits and Systems
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: A. Shah and M. Sid-Ahmed and G. Jullien
title:
A proposed hardware structure for two-dimensional recursive digital filters using the residue number system

rawtitle:
A proposed hardware structure for two-dimensional recursive digital filters using the residue number system

entry:
@Article{Shah:1985:PHS,
  author =       "A. Shah and M. Sid-Ahmed and G. Jullien",
  title =        "A proposed hardware structure for two-dimensional
                 recursive digital filters using the residue number
                 system",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "32",
  number =       "3",
  pages =        "285--288",
  month =        mar,
  year =         "1985",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23566",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A hardware structure is proposed for implementing
                 two-dimensional ($2$-D) recursive digital filters based
                 on the residue number system (RNS). The parallel
                 pipelined structure arising from the use of RNS
                 arithmetic facilitates video bandwidth filtering.
                 \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Shimada:1985:NAC
author: R. Shimada and Y. Ohkura and J. Aoe
title: Nonbinary Arithmetic AN Codes Using Odd Radix Expressions
journal: j-IEEE-TRANS-COMPUT
volume: C-34
number: 11
pages: 1050--1056
month: nov
monthnumber: 11
year: 1985
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1985.1676538
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 08:33:37 MDT 2011
bibtimestamp: 2011.07.10 08:33:37 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676538
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: R. Shimada and Y. Ohkura and J. Aoe
rawtitle: Nonbinary Arithmetic {AN} Codes Using Odd Radix Expressions
entry:
@Article{Shimada:1985:NAC,
  author =       "R. Shimada and Y. Ohkura and J. Aoe",
  title =        "Nonbinary Arithmetic {AN} Codes Using Odd Radix
                 Expressions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-34",
  number =       "11",
  pages =        "1050--1056",
  month =        nov,
  year =         "1985",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1985.1676538",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 08:33:37 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676538",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Smith:1985:DFI
author: S. P. Smith and H. C. Torng
title: Design of a Faster Inner Product Processor
crossref: Hwang:1985:PSC
pages: 38--43
year: 1985
bibdate: Fri Nov 16 08:47:34 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.16 08:47:34 ???
URL: http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Smith_Torng.pdf
keywords: ARITH-7
acknowledgement: ack-nhfb
rawauthor: S. P. Smith and H. C. Torng
rawtitle: Design of a Faster Inner Product Processor
abstract:
This paper presents the design of a fast inner product processor, with appreciably reduced latency and cost. The inner product processor is implemented with a tree of carry propagate or carry save adders; this tree is obtained with the incorporation of three innovations in the conventional multiply/add tree:par (1) The leaf-multipliers are expanded into adder subtrees, thus achieving an $ O(log N b) $ latency, where $N$ denotes the number of elements in a vector and $b$ the number of bits in each element.par (2) The partial products, to be summed in producing an inner product, are reordered according to their ``minimum alignments'' bringing approximately a 20% saving in hardware.par (3) The reordering also truncates the carry propagation chain in the final propagation stage by $ 2 log b - 1 $ positions, significantly reducing the latency further. A form of the Baugh and Wooley algorithm is adopted to implement two's complement notation with changes only in peripheral hardware.

rawabstract:
This paper presents the design of a fast inner product processor, with appreciably reduced latency and cost. The inner product processor is implemented with a tree of carry propagate or carry save adders; this tree is obtained with the incorporation of three innovations in the conventional multiply/add tree:\par (1) The leaf-multipliers are expanded into adder subtrees, thus achieving an $ O(\log N b) $ latency, where $N$ denotes the number of elements in a vector and $b$ the number of bits in each element.\par (2) The partial products, to be summed in producing an inner product, are reordered according to their ``minimum alignments'' bringing approximately a 20\% saving in hardware.\par (3) The reordering also truncates the carry propagation chain in the final propagation stage by $ 2 \log b - 1 $ positions, significantly reducing the latency further. A form of the Baugh and Wooley algorithm is adopted to implement two's complement notation with changes only in peripheral hardware.

entry:
@InProceedings{Smith:1985:DFI,
  author =       "S. P. Smith and H. C. Torng",
  title =        "Design of a Faster Inner Product Processor",
  crossref =     "Hwang:1985:PSC",
  pages =        "38--43",
  year =         "1985",
  bibdate =      "Fri Nov 16 08:47:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Smith_Torng.pdf",
  abstract =     "This paper presents the design of a fast inner product
                 processor, with appreciably reduced latency and cost.
                 The inner product processor is implemented with a tree
                 of carry propagate or carry save adders; this tree is
                 obtained with the incorporation of three innovations in
                 the conventional multiply/add tree:\par

                 (1) The leaf-multipliers are expanded into adder
                 subtrees, thus achieving an $ O(\log N b) $ latency,
                 where $N$ denotes the number of elements in a vector
                 and $b$ the number of bits in each element.\par

                 (2) The partial products, to be summed in producing an
                 inner product, are reordered according to their
                 ``minimum alignments'' bringing approximately a 20\%
                 saving in hardware.\par

                 (3) The reordering also truncates the carry propagation
                 chain in the final propagation stage by $ 2 \log b - 1
                 $ positions, significantly reducing the latency
                 further. A form of the Baugh and Wooley algorithm is
                 adopted to implement two's complement notation with
                 changes only in peripheral hardware.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}


bibtype: article
filename: fparith.bib
label: Smith:1985:FIP
author: S. P. Smith and H. C. Torng
title: A fast inner product processor based on equal alignments
journal: j-J-PAR-DIST-COMP
volume: 2
number: 4
pages: 376--390
month: nov
monthnumber: 11
year: 1985
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: P Practical
rawauthor: S. P. Smith and H. C. Torng
rawtitle: A fast inner product processor based on equal alignments
keywords:
adder subtrees; Algorithms; alignments; Baugh and Wooley algorithm; carry-; carry-propagate adder tree; computer metatheory --- Boolean Algebra; computer programming; computers --- Multiplying Circuits; digital arithmetic; equal alignments; fast inner product processor; free of carry-propagate or carry-save adders; inner product processor; integrated circuits, VLSI; leaf-multipliers; matrix algebra; matrix multiplications; microprocessor chips; minimum; satellite computers; save adders; special purpose computers; two's complement notation; VLSI

entry:
@Article{Smith:1985:FIP,
  author =       "S. P. Smith and H. C. Torng",
  title =        "A fast inner product processor based on equal
                 alignments",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "2",
  number =       "4",
  pages =        "376--390",
  month =        nov,
  year =         "1985",
  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 = "713; 723; 921; B0290H (Linear algebra); B1265F
                 (Microprocessors and microcomputers); B2570
                 (Semiconductor integrated circuits); C4140 (Linear
                 algebra); C5130 (Microprocessor chips); C5230 (Digital
                 arithmetic methods)",
  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 =     "adder subtrees; Algorithms; alignments; Baugh and
                 Wooley algorithm; carry-; carry-propagate adder tree;
                 computer metatheory --- Boolean Algebra; computer
                 programming; computers --- Multiplying Circuits;
                 digital arithmetic; equal alignments; fast inner
                 product processor; free of carry-propagate or
                 carry-save adders; inner product processor; integrated
                 circuits, VLSI; leaf-multipliers; matrix algebra;
                 matrix multiplications; microprocessor chips; minimum;
                 satellite computers; save adders; special purpose
                 computers; two's complement notation; VLSI",
  treatment =    "P Practical",
}


bibtype: techreport
filename: fparith.bib
label: Spafford:1985:RAS
author: Eugene Howard Spafford
title: A report on the accuracy of some floating point math functions on selected computers
institution: School of Information and Computer Science, Georgia Institute of Technology
address: Atlanta, GA, USA
pages: 26
year: 1985
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: GIT-ICS; 85/06
keywords: Operating systems (Computers)
acknowledgement: ack-nhfb
rawauthor: Eugene Howard Spafford
rawtitle: A report on the accuracy of some floating point math functions on selected computers
entry:
@TechReport{Spafford:1985:RAS,
  author =       "Eugene Howard Spafford",
  title =        "A report on the accuracy of some floating point math
                 functions on selected computers",
  institution =  "School of Information and Computer Science, Georgia
                 Institute of Technology",
  address =      "Atlanta, GA, USA",
  pages =        "26",
  year =         "1985",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "GIT-ICS; 85/06",
  acknowledgement = ack-nhfb,
  keywords =     "Operating systems (Computers)",
}


bibtype: article
filename: fparith.bib
label: Sreedharan:1985:ASS
author: J. Sreedharan and A. Dhurkadas
title: 8086 algorithm solves square roots
journal: j-EDN
volume: 30
number: 7
pages: 272
month: apr
monthnumber: 4
year: 1985
CODEN: EDNSBH
ISSN: 0012-7515, 0364-6637 OR 00127515, 03646637
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: EDN
acknowledgement: ack-nj
rawauthor: J. Sreedharan and A. Dhurkadas
rawtitle: 8086 algorithm solves square roots
entry:
@Article{Sreedharan:1985:ASS,
  author =       "J. Sreedharan and A. Dhurkadas",
  title =        "8086 algorithm solves square roots",
  journal =      j-EDN,
  volume =       "30",
  number =       "7",
  pages =        "272",
  month =        apr,
  year =         "1985",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  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 =     "EDN",
}


bibtype: article
filename: fparith.bib
label: Stewart:1985:NCD
author: G. W. Stewart
title: A Note on Complex Division
journal: j-TOMS
volume: 11
number: 3
pages: 238--241
month: sep
monthnumber: 9
year: 1985
CODEN: ACMSCU
DOI: https://doi.org/10.1145/214408.214414
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Fri Aug 26 23:38:15 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.08.26 23:38:15 ???
note: See also cite Stewart:1986:CNC.
URL: http://www.acm.org/pubs/citations/journals/toms/1985-11-3/p238-stewart/
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms; complex arithmetic; computer arithmetic; na
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: G. W. Stewart
rawnote: See also \cite{Stewart:1986:CNC}.
rawtitle: A Note on Complex Division
abstract:
An algorithm for computing the quotient of two complex numbers is modified to make it more robust in the presence of underflows.

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

rawabstract:
An algorithm for computing the quotient of two complex numbers is modified to make it more robust in the presence of underflows.

entry:
@Article{Stewart:1985:NCD,
  author =       "G. W. Stewart",
  title =        "A Note on Complex Division",
  journal =      j-TOMS,
  volume =       "11",
  number =       "3",
  pages =        "238--241",
  month =        sep,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/214408.214414",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Aug 26 23:38:15 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See also \cite{Stewart:1986:CNC}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1985-11-3/p238-stewart/",
  abstract =     "An algorithm for computing the quotient of two complex
                 numbers is modified to make it more robust in the
                 presence of underflows.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; complex arithmetic; computer arithmetic;
                 na",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Numerical algorithms. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Reliability and robustness.",
}


bibtype: article
filename: fparith.bib
label: Stummel:1985:FEA
author: Friedrich Stummel
title: Forward error analysis of Gaussian elimination. I. Error and residual estimates
journal: j-NUM-MATH
volume: 46
number: 3
pages: 365--395
year: 1985
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
MRclass: 65G05 (65F10)
MRnumber: 87d:65054a
MRreviewer: Karl-Heinz Bachmann
bibdate: Mon May 26 11:49:34 MDT 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.05.26 11:49:34 MDT
fjournal: Numerische Mathematik
acknowledgement: ack-nhfb
corpsource: Fachbereich Math., Johann Wolfgang Goethe-University, Frankfurt, West Germany
journalURL: http://link.springer.com/journal/211
treatment: T Theoretical or Mathematical
rawauthor: Friedrich Stummel
rawtitle: Forward error analysis of {Gaussian} elimination. {I}. Error and residual estimates
keywords:
absolute errors; arithmetic floating-point operations; associated optimal component-wise error; coefficient matrices; condition numbers; data perturbations; error analysis; error estimates; first order approximations; forward error analysis; Gaussian elimination; general linear algebraic systems; linearization method; matrix norms; perturbation theory; residual estimates; rounding errors; superposition; vector norms

entry:
@Article{Stummel:1985:FEA,
  author =       "Friedrich Stummel",
  title =        "Forward error analysis of {Gaussian} elimination. {I}.
                 Error and residual estimates",
  journal =      j-NUM-MATH,
  volume =       "46",
  number =       "3",
  pages =        "365--395",
  year =         "1985",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65G05 (65F10)",
  MRnumber =     "87d:65054a",
  MRreviewer =   "Karl-Heinz Bachmann",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "B0290B (Error analysis in numerical methods); C4110
                 (Error analysis in numerical methods)",
  corpsource =   "Fachbereich Math., Johann Wolfgang Goethe-University,
                 Frankfurt, West Germany",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "absolute errors; arithmetic floating-point operations;
                 associated optimal component-wise error; coefficient
                 matrices; condition numbers; data perturbations; error
                 analysis; error estimates; first order approximations;
                 forward error analysis; Gaussian elimination; general
                 linear algebraic systems; linearization method; matrix
                 norms; perturbation theory; residual estimates;
                 rounding errors; superposition; vector norms",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: inproceedings
filename: fparith.bib
label: Swartzlander:1985:AHS
author: Earl Swartzlander, Jr. and John Eldon
title: Arithmetic for High Speed FFT Implementation
crossref: Hwang:1985:PSC
pages: 223--230
year: 1985
bibdate: Fri Nov 16 08:47:34 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.16 08:47:34 ???
URL: http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Swartzlander_Eldon.pdf
keywords: ARITH-7
acknowledgement: ack-nhfb
rawauthor: Earl {Swartzlander, Jr.} and John Eldon
rawtitle: Arithmetic for High Speed {FFT} Implementation
abstract:
This paper describes recent progress in the implementation of high speed spectrum analysis systems with state-of-the-art commercial and semi-custom VLSI circuits. Initial efforts are producing Fast Fourier Transform (FFT) and inverse FFT processors that operate at data rates of up to 40 MHz (complex). The current implementation computes transforms of up to 16,384 points in length by means of the radix 4 pipeline FFT algorithm. The interstage reordering is performed by delay commutators implemented with semi-custom VLSI, while the arithmetic is performed by commercial single chip 22 bit floating point adders and multipliers. This paper explains the pipeline FFT implementation and focuses attention on the arithmetic used to realize the design.

rawabstract:
This paper describes recent progress in the implementation of high speed spectrum analysis systems with state-of-the-art commercial and semi-custom VLSI circuits. Initial efforts are producing Fast Fourier Transform (FFT) and inverse FFT processors that operate at data rates of up to 40 MHz (complex). The current implementation computes transforms of up to 16,384 points in length by means of the radix 4 pipeline FFT algorithm. The interstage reordering is performed by delay commutators implemented with semi-custom VLSI, while the arithmetic is performed by commercial single chip 22 bit floating point adders and multipliers. This paper explains the pipeline FFT implementation and focuses attention on the arithmetic used to realize the design.

entry:
@InProceedings{Swartzlander:1985:AHS,
  author =       "Earl {Swartzlander, Jr.} and John Eldon",
  title =        "Arithmetic for High Speed {FFT} Implementation",
  crossref =     "Hwang:1985:PSC",
  pages =        "223--230",
  year =         "1985",
  bibdate =      "Fri Nov 16 08:47:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Swartzlander_Eldon.pdf",
  abstract =     "This paper describes recent progress in the
                 implementation of high speed spectrum analysis systems
                 with state-of-the-art commercial and semi-custom VLSI
                 circuits. Initial efforts are producing Fast Fourier
                 Transform (FFT) and inverse FFT processors that operate
                 at data rates of up to 40 MHz (complex). The current
                 implementation computes transforms of up to 16,384
                 points in length by means of the radix 4 pipeline FFT
                 algorithm. The interstage reordering is performed by
                 delay commutators implemented with semi-custom VLSI,
                 while the arithmetic is performed by commercial single
                 chip 22 bit floating point adders and multipliers. This
                 paper explains the pipeline FFT implementation and
                 focuses attention on the arithmetic used to realize the
                 design.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}


bibtype: manual
filename: fparith.bib
label: Symbolics:1985:RGS
title: Reference Guide to Symbolics-Lisp
organization: Symbolics, Inc.
address: Cambridge, MA, USA
pages: 223--230
month: mar
monthnumber: 3
year: 1985
bibdate: Wed Jan 29 17:06:41 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.01.29 17:06:41 ???
remark: From cite Steele:2004:RHP: ``The number of digits printed is the `correct' numberldots ''
acknowledgement: ack-nhfb
rawtitle: Reference Guide to {Symbolics-Lisp}
entry:
@Manual{Symbolics:1985:RGS,
  title =        "Reference Guide to {Symbolics-Lisp}",
  organization = "Symbolics, Inc.",
  address =      "Cambridge, MA, USA",
  month =        mar,
  year =         "1985",
  bibdate =      "Wed Jan 29 17:06:41 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "From \cite{Steele:2004:RHP}: ``The number of digits
                 printed is the `correct' number\ldots{}''",
}


bibtype: article
filename: fparith.bib
label: Takagi:1985:HSV
author: N. Takagi and H. Yasuura and S. Yajima
title: High-speed VLSI multiplication algorithm with a redundant binary addition tree
journal: j-IEEE-TRANS-COMPUT
volume: C-34
number: 9
pages: 789--796
year: 1985
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1985.1676634
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Mon Sep 16 16:29:25 2002
bibtimestamp: 2002.09.16 16:29:25 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: N. Takagi and H. Yasuura and S. Yajima
rawtitle: High-speed {VLSI} multiplication algorithm with a redundant binary addition tree
entry:
@Article{Takagi:1985:HSV,
  author =       "N. Takagi and H. Yasuura and S. Yajima",
  title =        "High-speed {VLSI} multiplication algorithm with a
                 redundant binary addition tree",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-34",
  number =       "9",
  pages =        "789--796",
  year =         "1985",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1985.1676634",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Sep 16 16:29:25 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Takeda:1985:SCB
author: K. Takeda and F. Ishino and Y. Ito and T. Nakashima
title: A single-chip 80-bit floating point processor
journal: j-IEEE-J-SOLID-STATE-CIRCUITS
volume: 20
number: 5
pages: 986--992
month: oct
monthnumber: 10
year: 1985
CODEN: IJSCBC
ISSN: 0018-9200 (print), 1558-173X (electronic) OR 00189200 (print), 1558173X (electronic)
ISSNL: 0018-9200 OR 00189200
bibdate: Sat Jul 16 08:40:53 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:53 MDT
fjournal: IEEE Journal of Solid-State Circuits
acknowledgement: ack-nhfb
rawauthor: K. Takeda and F. Ishino and Y. Ito and T. Nakashima
rawtitle: A single-chip 80-bit floating point processor
entry:
@Article{Takeda:1985:SCB,
  author =       "K. Takeda and F. Ishino and Y. Ito and T. Nakashima",
  title =        "A single-chip 80-bit floating point processor",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "20",
  number =       "5",
  pages =        "986--992",
  month =        oct,
  year =         "1985",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  summary =      "A single-chip 80-bit floating point VLSI processor
                 capable of performing 5.6 million floating point
                 operations per second has been realized using
                 1.2-$\mu$m n-well CMOS technology. The processor
                 handles 80-bit double-extended floating point data
                 \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Taniguchi:1985:TDI
author: Kenji Taniguchi
title: Three Dimensional IC's and Application to High Speed Image Processor
crossref: Hwang:1985:PSC
pages: 216--222
year: 1985
bibdate: Fri Nov 16 08:47:34 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.16 08:47:34 ???
URL: http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Taniguchi.pdf
keywords: ARITH-7
acknowledgement: ack-nhfb
rawauthor: Kenji Taniguchi
rawtitle: Three Dimensional {IC}'s and Application to High Speed Image Processor
abstract:
Present state-of-the-art 3-D IC fabrication technologies are reviewed. Both short interconnection wiring inherent to 3-D structure and parallel processing architecture offer high performance for 3-D integrated circuit. An idea of a high speed image sensor composed of six layers is proposed.

rawabstract:
Present state-of-the-art 3-D IC fabrication technologies are reviewed. Both short interconnection wiring inherent to 3-D structure and parallel processing architecture offer high performance for 3-D integrated circuit. An idea of a high speed image sensor composed of six layers is proposed.

entry:
@InProceedings{Taniguchi:1985:TDI,
  author =       "Kenji Taniguchi",
  title =        "Three Dimensional {IC}'s and Application to High Speed
                 Image Processor",
  crossref =     "Hwang:1985:PSC",
  pages =        "216--222",
  year =         "1985",
  bibdate =      "Fri Nov 16 08:47:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Taniguchi.pdf",
  abstract =     "Present state-of-the-art 3-D IC fabrication
                 technologies are reviewed. Both short interconnection
                 wiring inherent to 3-D structure and parallel
                 processing architecture offer high performance for 3-D
                 integrated circuit. An idea of a high speed image
                 sensor composed of six layers is proposed.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}


bibtype: article
filename: fparith.bib
label: Taylor:1985:HFP
author: F. Taylor
title: A hybrid floating-point logarithmic number system processor
journal: j-IEEE-TRANS-CIRCUITS-SYST
volume: 32
number: 1
pages: 92--95
month: jan
monthnumber: 1
year: 1985
CODEN: ICSYBT
ISSN: 0098-4094 (print), 1558-1276 (electronic) OR 00984094 (print), 15581276 (electronic)
ISSNL: 0098-4094 OR 00984094
bibdate: Sat Jul 16 08:40:53 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:53 MDT
fjournal: IEEE Transactions on Circuits and Systems
acknowledgement: ack-nhfb
rawauthor: F. Taylor
rawtitle: A hybrid floating-point logarithmic number system processor
entry:
@Article{Taylor:1985:HFP,
  author =       "F. Taylor",
  title =        "A hybrid floating-point logarithmic number system
                 processor",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "32",
  number =       "1",
  pages =        "92--95",
  month =        jan,
  year =         "1985",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Sat Jul 16 08:40:53 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 attributes of the traditional floating-point
                 processor and the logarithmic number system are
                 combined. The result is a hybrid system which offers
                 some advantages over the familiar floating-point
                 system. The new system, called the(FU)^{2}",
}


bibtype: inproceedings
filename: fparith.bib
label: Taylor:1985:MER
author: Fred J. Taylor
title: A More Efficient Residue Arithmetic Implementation of the FFT
crossref: Hwang:1985:PSC
pages: 243--250
year: 1985
bibdate: Fri Nov 16 08:47:34 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.16 08:47:34 ???
URL: http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Taylor1.pdf
keywords: ARITH-7
acknowledgement: ack-nhfb
rawauthor: Fred J. Taylor
rawtitle: A More Efficient Residue Arithmetic Implementation of the {FFT}
abstract:
After 20 years, the FFT remains restricted in its real time capabilities. To overcome this throughput obstacle, fast residue arithmetic units are studied based on several recent innovations in the field of complex finite rings. A dedicated machine is designed which makes use of these new results and is compared to conventional FFT designs. Using high speed semiconductor memory to implement the required residue arithmetic mappings, speed and complexity metrics of a basic FFT unit are shown to be improved. However, the derived architecture and arithmetic introduce a new and challenging set of magnitude scaling problems. They are resolved with the result being an integrated residue arithmetic FFT system capable of supporting very high real time data rates.

rawabstract:
After 20 years, the FFT remains restricted in its real time capabilities. To overcome this throughput obstacle, fast residue arithmetic units are studied based on several recent innovations in the field of complex finite rings. A dedicated machine is designed which makes use of these new results and is compared to conventional FFT designs. Using high speed semiconductor memory to implement the required residue arithmetic mappings, speed and complexity metrics of a basic FFT unit are shown to be improved. However, the derived architecture and arithmetic introduce a new and challenging set of magnitude scaling problems. They are resolved with the result being an integrated residue arithmetic FFT system capable of supporting very high real time data rates.

entry:
@InProceedings{Taylor:1985:MER,
  author =       "Fred J. Taylor",
  title =        "A More Efficient Residue Arithmetic Implementation of
                 the {FFT}",
  crossref =     "Hwang:1985:PSC",
  pages =        "243--250",
  year =         "1985",
  bibdate =      "Fri Nov 16 08:47:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Taylor1.pdf",
  abstract =     "After 20 years, the FFT remains restricted in its real
                 time capabilities. To overcome this throughput
                 obstacle, fast residue arithmetic units are studied
                 based on several recent innovations in the field of
                 complex finite rings. A dedicated machine is designed
                 which makes use of these new results and is compared to
                 conventional FFT designs. Using high speed
                 semiconductor memory to implement the required residue
                 arithmetic mappings, speed and complexity metrics of a
                 basic FFT unit are shown to be improved. However, the
                 derived architecture and arithmetic introduce a new and
                 challenging set of magnitude scaling problems. They are
                 resolved with the result being an integrated residue
                 arithmetic FFT system capable of supporting very high
                 real time data rates.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}


bibtype: article
filename: fparith.bib
label: Taylor:1985:RFU
author: F. J. Taylor and G. Papadourakis and A. Skavantzos and A. Stouraitis
title: A Radix-4 FFT Using Complex RNS Arithmetic
journal: j-IEEE-TRANS-COMPUT
volume: C-34
number: 6
pages: 573--576
month: jun
monthnumber: 6
year: 1985
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1985.5009414
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 08:32:52 MDT 2011
bibtimestamp: 2011.07.10 08:32:52 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009414
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: F. J. Taylor and G. Papadourakis and A. Skavantzos and A. Stouraitis
rawtitle: A Radix-4 {FFT} Using Complex {RNS} Arithmetic
entry:
@Article{Taylor:1985:RFU,
  author =       "F. J. Taylor and G. Papadourakis and A. Skavantzos and
                 A. Stouraitis",
  title =        "A Radix-4 {FFT} Using Complex {RNS} Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-34",
  number =       "6",
  pages =        "573--576",
  month =        jun,
  year =         "1985",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1985.5009414",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 08:32:52 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009414",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Taylor:1985:RSD
author: George S. Taylor
crossref: Hwang:1985:PSC
pages: 64--71
year: 1985
bibdate: Thu Apr 2 08:38:35 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.04.02 08:38:35 ???
URL: http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Taylor.pdf
keywords: ARITH-7
acknowledgement: ack-sfo
rawauthor: George S. Taylor
title:
Radix 16 SRT dividers with overlapped quotient selection stages: a 225 Nanosecond Double Precision Divider for the S-1 Mark IIB

abstract:
This paper compares the three simplest SRT division methods by using them to design a divider that produces four quotient bits per cycle (radix 16). The three methods are distinguished by the number of bits found per stage of quotient selection logic:par (a) one bit per stage (radix 2) with quotient digits chosen from the set $ - 1, 0, 1 $,par (b) two bits per stage (radix 4) with quotient digits $ - 2, - 1, 0, 1, 2 $, orpar (c) two bits per stage (radix 4) with quotient digits $ - 3, - 2, - 1, 0, 1, 2, 3 $.par For each method, we compare several ways to overlap multiple stages of quotient selection logic and we consider both irredundant and redundant (carry-save) representations for the remainder.par The cost and performance of each alternative is evaluated in terms a specific ECL gate array technology. We find that we can build a 15% faster divider with radix four stages than with radix two stages, for about the same amount of hardware. Between the two radix 4 alternatives, method (c) offers more speed than method (b) at the cost of 20% more hardware.par A radix 16 divider using method (b) has been built for the S-1 Mark IIB computer under development at Lawrence Livermore Laboratory. This divider consists of eight ECL gate arrays and has a 12.5 nanosecond cycle time. It performs IEEE single and double precision floating point division in 150 and 225 nanoseconds, respectively, the shortest times reported for any general purpose computer.

rawabstract:
This paper compares the three simplest SRT division methods by using them to design a divider that produces four quotient bits per cycle (radix 16). The three methods are distinguished by the number of bits found per stage of quotient selection logic:\par (a) one bit per stage (radix 2) with quotient digits chosen from the set $ \{ - 1, 0, 1 \} $,\par (b) two bits per stage (radix 4) with quotient digits $ \{ - 2, - 1, 0, 1, 2 \} $, or\par (c) two bits per stage (radix 4) with quotient digits $ \{ - 3, - 2, - 1, 0, 1, 2, 3 \} $.\par For each method, we compare several ways to overlap multiple stages of quotient selection logic and we consider both irredundant and redundant (carry-save) representations for the remainder.\par The cost and performance of each alternative is evaluated in terms a specific ECL gate array technology. We find that we can build a 15\% faster divider with radix four stages than with radix two stages, for about the same amount of hardware. Between the two radix 4 alternatives, method (c) offers more speed than method (b) at the cost of 20\% more hardware.\par A radix 16 divider using method (b) has been built for the S-1 Mark IIB computer under development at Lawrence Livermore Laboratory. This divider consists of eight ECL gate arrays and has a 12.5 nanosecond cycle time. It performs IEEE single and double precision floating point division in 150 and 225 nanoseconds, respectively, the shortest times reported for any general purpose computer.

rawtitle:
Radix 16 {SRT} dividers with overlapped quotient selection stages: a 225 Nanosecond Double Precision Divider for the {S-1 Mark IIB}

entry:
@InProceedings{Taylor:1985:RSD,
  author =       "George S. Taylor",
  title =        "Radix 16 {SRT} dividers with overlapped quotient
                 selection stages: a 225 Nanosecond Double Precision
                 Divider for the {S-1 Mark IIB}",
  crossref =     "Hwang:1985:PSC",
  pages =        "64--71",
  year =         "1985",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Taylor.pdf",
  abstract =     "This paper compares the three simplest SRT division
                 methods by using them to design a divider that produces
                 four quotient bits per cycle (radix 16). The three
                 methods are distinguished by the number of bits found
                 per stage of quotient selection logic:\par

                 (a) one bit per stage (radix 2) with quotient digits
                 chosen from the set $ \{ - 1, 0, 1 \} $,\par

                 (b) two bits per stage (radix 4) with quotient digits $
                 \{ - 2, - 1, 0, 1, 2 \} $, or\par

                 (c) two bits per stage (radix 4) with quotient digits $
                 \{ - 3, - 2, - 1, 0, 1, 2, 3 \} $.\par

                 For each method, we compare several ways to overlap
                 multiple stages of quotient selection logic and we
                 consider both irredundant and redundant (carry-save)
                 representations for the remainder.\par

                 The cost and performance of each alternative is
                 evaluated in terms a specific ECL gate array
                 technology. We find that we can build a 15\% faster
                 divider with radix four stages than with radix two
                 stages, for about the same amount of hardware. Between
                 the two radix 4 alternatives, method (c) offers more
                 speed than method (b) at the cost of 20\% more
                 hardware.\par

                 A radix 16 divider using method (b) has been built for
                 the S-1 Mark IIB computer under development at Lawrence
                 Livermore Laboratory. This divider consists of eight
                 ECL gate arrays and has a 12.5 nanosecond cycle time.
                 It performs IEEE single and double precision floating
                 point division in 150 and 225 nanoseconds,
                 respectively, the shortest times reported for any
                 general purpose computer.",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  keywords =     "ARITH-7",
}


bibtype: mastersthesis
filename: fparith.bib
label: Tesnow:1985:IDS
author: Kurt Alan Tesnow
title: Implementation of the digital simulation of a synchronous machine using a floating-point processor
type: Thesis (M.S.)
school: Department of Electrical Engineering and Applied Physics, Case Western Reserve University
address: Cleveland, OH 44106, USA
pages: vii + 255
year: 1985
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: Kurt Alan Tesnow
rawtitle: Implementation of the digital simulation of a synchronous machine using a floating-point processor
entry:
@MastersThesis{Tesnow:1985:IDS,
  author =       "Kurt Alan Tesnow",
  title =        "Implementation of the digital simulation of a
                 synchronous machine using a floating-point processor",
  type =         "Thesis ({M.S.})",
  school =       "Department of Electrical Engineering and Applied
                 Physics, Case Western Reserve University",
  address =      "Cleveland, OH 44106, USA",
  pages =        "vii + 255",
  year =         "1985",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: fparith.bib
label: Thies:1985:NPE
author: Klaus-Dieter Thies
publisher: pub-TEWI
address: pub-TEWI:adr
pages: 355
year: 1985
ISBN: 3-921803-53-5 OR 3921803535
ISBN13: 978-3-921803-53-0 OR 9783921803530
bibdate: Sat Nov 09 10:08:28 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.11.09 10:08:28 ???
acknowledgement: ack-nj
rawauthor: Klaus-Dieter Thies
title:
Die 8087 / 80287 numerischen Prozessor Erweiterungen fur 8086 / 80286 Systeme toenglish The 8087 / 80287 Numeric Processor Extension for 8086 / 80286 Systems endtoenglish 

rawtitle:
{Die 8087\slash 80287 numerischen Prozessor Erweiterungen f{\"u}r 8086\slash 80286 Systeme} \toenglish {The 8087\slash 80287 Numeric Processor Extension for 8086\slash 80286 Systems} \endtoenglish

entry:
@Book{Thies:1985:NPE,
  author =       "Klaus-Dieter Thies",
  title =        "{Die 8087\slash 80287 numerischen Prozessor
                 Erweiterungen f{\"u}r 8086\slash 80286 Systeme}
                 \toenglish {The 8087\slash 80287 Numeric Processor
                 Extension for 8086\slash 80286 Systems} \endtoenglish",
  publisher =    pub-TEWI,
  address =      pub-TEWI:adr,
  pages =        "355",
  year =         "1985",
  ISBN =         "3-921803-53-5",
  ISBN-13 =      "978-3-921803-53-0",
  LCCN =         "????",
  bibdate =      "Sat Nov 09 10:08:28 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: Tsuji:1985:REF
author: Kumiko Tsuji
title: Round-off errors in floating-point additions
journal: j-MEM-FAC-SCI-KYUSHU-UNIV-A
volume: 39
number: 2
pages: 209--225
year: 1985
CODEN: MFKAAF
ISSN: 0373-6385 (print), 1883-2172 (electronic) OR 03736385 (print), 18832172 (electronic)
ISSNL: 0373-6385 OR 03736385
MRclass: 65G05 (65-04)
MRnumber: 86j: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 ???
acknowledgement: ack-nhfb
reviewer: Aurel Galantai
rawauthor: Kumiko Tsuji
rawtitle: Round-off errors in floating-point additions
fjournal:
Memoirs of the Faculty of Science, Kyushu Imperial University. Series A, Mathematics = Kyushu Teikoku Daigaku Rigakubu kiyo

entry:
@Article{Tsuji:1985:REF,
  author =       "Kumiko Tsuji",
  title =        "Round-off errors in floating-point additions",
  journal =      j-MEM-FAC-SCI-KYUSHU-UNIV-A,
  volume =       "39",
  number =       "2",
  pages =        "209--225",
  year =         "1985",
  CODEN =        "MFKAAF",
  ISSN =         "0373-6385 (print), 1883-2172 (electronic)",
  ISSN-L =       "0373-6385",
  MRclass =      "65G05 (65-04)",
  MRnumber =     "86j:65056",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Memoirs of the Faculty of Science, Kyushu Imperial
                 University. Series A, Mathematics = Kyushu Teikoku
                 Daigaku Rigakubu kiyo",
  reviewer =     "Aur{\'e}l Gal{\'a}ntai",
}


bibtype: inproceedings
filename: fparith.bib
label: vonGudenberg:1985:FPC
author: J. W. von Gudenberg
title: Floating-point computation in PASCAL-SC with verified results
crossref: Buchberger:1985:PEE
pages: 322--324
year: 1985
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: J. W. von Gudenberg
rawtitle: Floating-point computation in {PASCAL-SC} with verified results
subject:
G. Mathematics of Computing; G.4 MATHEMATICAL SOFTWARE; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS

entry:
@InProceedings{vonGudenberg:1985:FPC,
  author =       "J. W. von Gudenberg",
  title =        "Floating-point computation in {PASCAL-SC} with
                 verified results",
  crossref =     "Buchberger:1985:PEE",
  pages =        "322--324",
  year =         "1985",
  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,
  catcode =      "G; G.1.0",
  CRclass =      "G.1.0 General; G.1.0 Computer arithmetic",
  descriptor =   "Mathematics of Computing, MATHEMATICAL SOFTWARE;
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Computer arithmetic",
  genterm =      "THEORY; VERIFICATION; ALGORITHMS",
  guideno =      "12475",
  subject =      "G. Mathematics of Computing; G.4 MATHEMATICAL
                 SOFTWARE; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS",
}


bibtype: article
filename: fparith.bib
label: Williamson:1985:NAB
author: D. Williamson and S. Sridharan and P. McCrea
title: A new approach for block floating-point arithmetic in recursive filters
journal: j-IEEE-TRANS-CIRCUITS-SYST
volume: 32
number: 7
pages: 719--722
month: jul
monthnumber: 7
year: 1985
CODEN: ICSYBT
ISSN: 0098-4094 (print), 1558-1276 (electronic) OR 00984094 (print), 15581276 (electronic)
ISSNL: 0098-4094 OR 00984094
bibdate: Sat Jul 16 08:40:53 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:53 MDT
fjournal: IEEE Transactions on Circuits and Systems
acknowledgement: ack-nhfb
rawauthor: D. Williamson and S. Sridharan and P. McCrea
rawtitle: A new approach for block floating-point arithmetic in recursive filters
entry:
@Article{Williamson:1985:NAB,
  author =       "D. Williamson and S. Sridharan and P. McCrea",
  title =        "A new approach for block floating-point arithmetic in
                 recursive filters",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "32",
  number =       "7",
  pages =        "719--722",
  month =        jul,
  year =         "1985",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  summary =      "An approach to block floating-point arithmetic in
                 recursive second-order direct form digital filters is
                 proposed. Used in conjunction with residue (or error)
                 feedback, the method gives improved scaling and
                 roundoff noise properties compared to an \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Yun:1985:BPS
author: David Y. Y. Yun and Chang N. Zhang
title: Binary Paradigm and Systolic Array Implementation for Residue Arithmetic
crossref: Hwang:1985:PSC
pages: 189--193
year: 1985
bibdate: Fri Nov 16 08:47:34 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.16 08:47:34 ???
URL: http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Yun_Zhang.pdf
keywords: ARITH-7
acknowledgement: ack-nhfb
rawauthor: David Y. Y. Yun and Chang N. Zhang
rawtitle: Binary Paradigm and Systolic Array Implementation for Residue Arithmetic
abstract:
The problem of residue, or modular, arithmetic is fundamental to symbolic and algebraic computation, coding theory and applications, as well as to error-free arithmetic computations. This paper describes novel algorithms that can lead to efficient hardware for arithmetic operations in residue domains. One of the main achievements is in allowing the flexibility of changing moduli. The technology of systolic array has been used to implement one of the most representative operations, the modular multiplier. It is shown that a linear systolic array can compute $N$ modular products in time $ O(N) $ with constant number of cells.

rawabstract:
The problem of residue, or modular, arithmetic is fundamental to symbolic and algebraic computation, coding theory and applications, as well as to error-free arithmetic computations. This paper describes novel algorithms that can lead to efficient hardware for arithmetic operations in residue domains. One of the main achievements is in allowing the flexibility of changing moduli. The technology of systolic array has been used to implement one of the most representative operations, the modular multiplier. It is shown that a linear systolic array can compute $N$ modular products in time $ O(N) $ with constant number of cells.

entry:
@InProceedings{Yun:1985:BPS,
  author =       "David Y. Y. Yun and Chang N. Zhang",
  title =        "Binary Paradigm and Systolic Array Implementation for
                 Residue Arithmetic",
  crossref =     "Hwang:1985:PSC",
  pages =        "189--193",
  year =         "1985",
  bibdate =      "Fri Nov 16 08:47:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Yun_Zhang.pdf",
  abstract =     "The problem of residue, or modular, arithmetic is
                 fundamental to symbolic and algebraic computation,
                 coding theory and applications, as well as to
                 error-free arithmetic computations. This paper
                 describes novel algorithms that can lead to efficient
                 hardware for arithmetic operations in residue domains.
                 One of the main achievements is in allowing the
                 flexibility of changing moduli. The technology of
                 systolic array has been used to implement one of the
                 most representative operations, the modular multiplier.
                 It is shown that a linear systolic array can compute
                 $N$ modular products in time $ O(N) $ with constant
                 number of cells.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}


bibtype: inproceedings
filename: fparith.bib
label: Zaccone:1985:INR
author: Richar J. Zaccone and Jesse L. Barlow
title: Improved Normalization Results for Digit On-Line Arithmetic
crossref: Hwang:1985:PSC
pages: 20--27
year: 1985
bibdate: Wed Nov 14 18:06:21 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 18:06:21 ???
URL: http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Zaccone_Barlow.pdf
keywords: ARITH-7
acknowledgement: ack-nhfb
rawauthor: Richar J. Zaccone and Jesse L. Barlow
rawtitle: Improved Normalization Results for Digit On-Line Arithmetic
abstract:
In digit on-line arithmetic, operands are introduced 1 digit at a time. After the first few operand digits have been introduced. the result begins to appear a digit at a time. This feature of digit on-line arithmetic allows a significant amount of overlapping of arithmetic operations.par Digit on-line arithmetic can sometimes produce unnormalized results. This can present a problem for the divide and square root algorithms. If the divisor and radicand are highly unnormalized, these algorithms will not produce the correct results. Two advances in overcoming this problem are presented. First, several techniques for producing results that are closer to being normalized are developed. Second, it is shown that normalized results are not necessary for divide and square root to work properly. Combining these results yields algorithms that will always give the correct results.

rawabstract:
In digit on-line arithmetic, operands are introduced 1 digit at a time. After the first few operand digits have been introduced. the result begins to appear a digit at a time. This feature of digit on-line arithmetic allows a significant amount of overlapping of arithmetic operations.\par Digit on-line arithmetic can sometimes produce unnormalized results. This can present a problem for the divide and square root algorithms. If the divisor and radicand are highly unnormalized, these algorithms will not produce the correct results. Two advances in overcoming this problem are presented. First, several techniques for producing results that are closer to being normalized are developed. Second, it is shown that normalized results are not necessary for divide and square root to work properly. Combining these results yields algorithms that will always give the correct results.

entry:
@InProceedings{Zaccone:1985:INR,
  author =       "Richar J. Zaccone and Jesse L. Barlow",
  title =        "Improved Normalization Results for Digit On-Line
                 Arithmetic",
  crossref =     "Hwang:1985:PSC",
  pages =        "20--27",
  year =         "1985",
  bibdate =      "Wed Nov 14 18:06:21 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Zaccone_Barlow.pdf",
  abstract =     "In digit on-line arithmetic, operands are introduced 1
                 digit at a time. After the first few operand digits
                 have been introduced. the result begins to appear a
                 digit at a time. This feature of digit on-line
                 arithmetic allows a significant amount of overlapping
                 of arithmetic operations.\par

                 Digit on-line arithmetic can sometimes produce
                 unnormalized results. This can present a problem for
                 the divide and square root algorithms. If the divisor
                 and radicand are highly unnormalized, these algorithms
                 will not produce the correct results. Two advances in
                 overcoming this problem are presented. First, several
                 techniques for producing results that are closer to
                 being normalized are developed. Second, it is shown
                 that normalized results are not necessary for divide
                 and square root to work properly. Combining these
                 results yields algorithms that will always give the
                 correct results.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}


bibtype: inproceedings
filename: fparith.bib
label: Zadrozny:1985:AFP
author: Wlodzimierz Zadrozny
title: Axiomatizations of Floating Point Arithmetics
crossref: Hwang:1985:PSC
pages: 74--81
year: 1985
bibdate: Fri Nov 16 08:47:34 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.16 08:47:34 ???
URL: http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Zadrozny.pdf
keywords: ARITH-7
acknowledgement: ack-nhfb
rawauthor: W{\l}odzimierz Zadro{\'z}ny
rawtitle: Axiomatizations of Floating Point Arithmetics
abstract:
We present a universal scheme for axiomatizing floating point arithmetic. The schema can be used to axiomatize any floating point arithmetic. It consists of a labeled graph with vertices describing some arithmetical properties and edges containing appropriate axioms. The language of floating point arithmetic is developed gradually in this scheme. The scheme can provide a vehicle for studying and implementing various versions of floating point arithmetic.

rawabstract:
We present a universal scheme for axiomatizing floating point arithmetic. The schema can be used to axiomatize any floating point arithmetic. It consists of a labeled graph with vertices describing some arithmetical properties and edges containing appropriate axioms. The language of floating point arithmetic is developed gradually in this scheme. The scheme can provide a vehicle for studying and implementing various versions of floating point arithmetic.

entry:
@InProceedings{Zadrozny:1985:AFP,
  author =       "W{\l}odzimierz Zadro{\'z}ny",
  title =        "Axiomatizations of Floating Point Arithmetics",
  crossref =     "Hwang:1985:PSC",
  pages =        "74--81",
  year =         "1985",
  bibdate =      "Fri Nov 16 08:47:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Zadrozny.pdf",
  abstract =     "We present a universal scheme for axiomatizing
                 floating point arithmetic. The schema can be used to
                 axiomatize any floating point arithmetic. It consists
                 of a labeled graph with vertices describing some
                 arithmetical properties and edges containing
                 appropriate axioms. The language of floating point
                 arithmetic is developed gradually in this scheme. The
                 scheme can provide a vehicle for studying and
                 implementing various versions of floating point
                 arithmetic.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}


bibtype: article
filename: fparith.bib
label: Zorpette:1985:BBN
author: Glenn Zorpette
journal: j-IEEE-SPECTRUM
volume: 22
number: 9
pages: 65--71
month: sep
monthnumber: 9
year: 1985
CODEN: IEESAM
DOI: https://doi.org/10.1109/MSPEC.1985.6370815
ISSN: 0018-9235 (print), 1939-9340 (electronic) OR 00189235 (print), 19399340 (electronic)
ISSNL: 0018-9235 OR 00189235
bibdate: Mon Jan 20 06:41:24 2020
bibtimestamp: 2020.01.20 06:41:24 ???
fjournal: IEEE Spectrum
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6
rawauthor: Glenn Zorpette
title:
The beauty of 32 bits: This near-optimum bit width has unprecedented potential for the well-informed designer of microprocessor-based systems

bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeespectrum1980.bib

keywords:
32 bit microprocessor chip; Companies; Computers; dynamic RAM; floating-point arithmetic; mainframes; memory management; microprocessor chips; Microprocessors; Pipeline processing; pipelining; processing rates; Random access memory; Registers; Sun; very large scale integration; VLSI

rawtitle:
The beauty of 32 bits: This near-optimum bit width has unprecedented potential for the well-informed designer of microprocessor-based systems

entry:
@Article{Zorpette:1985:BBN,
  author =       "Glenn Zorpette",
  title =        "The beauty of 32 bits: This near-optimum bit width has
                 unprecedented potential for the well-informed designer
                 of microprocessor-based systems",
  journal =      j-IEEE-SPECTRUM,
  volume =       "22",
  number =       "9",
  pages =        "65--71",
  month =        sep,
  year =         "1985",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/MSPEC.1985.6370815",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Mon Jan 20 06:41:24 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeespectrum1980.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
  keywords =     "32 bit microprocessor chip; Companies; Computers;
                 dynamic RAM; floating-point arithmetic; mainframes;
                 memory management; microprocessor chips;
                 Microprocessors; Pipeline processing; pipelining;
                 processing rates; Random access memory; Registers; Sun;
                 very large scale integration; VLSI",
}


bibtype: techreport
filename: fparith.bib
label: Adams:1986:FSSa
author: Glenn D. Adams
title: Functional specification and simulation of a floating point co-processor for SPUR [1]
type: Report
number: UCB/CSD 87/311
institution: University of California. Computer Science Division
address: Berkeley, CA.
pages: 52
year: 1986
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: Sponsored by DARPA. Monitored by Naval Electronic Systems Command.
acknowledgement: ack-nhfb
rawauthor: Glenn D. Adams
rawtitle: Functional specification and simulation of a floating point co-processor for {SPUR} [1]
keywords:
Computer architecture.; Floating-point arithmetic.; Integrated circuits --- Design and construction.

entry:
@TechReport{Adams:1986:FSSa,
  author =       "Glenn D. Adams",
  title =        "Functional specification and simulation of a floating
                 point co-processor for {SPUR} [1]",
  type =         "Report",
  number =       "UCB/CSD 87/311",
  institution =  "University of California. Computer Science Division",
  address =      "Berkeley, CA.",
  pages =        "52",
  year =         "1986",
  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.; Floating-point arithmetic.;
                 Integrated circuits --- Design and construction.",
  remark =       "Sponsored by DARPA. Monitored by Naval Electronic
                 Systems Command.",
}


bibtype: mastersthesis
filename: fparith.bib
label: Adams:1986:FSSb
author: Glenn D. Adams
title: Functional specification and simulation of a floating point co-processor for SPUR: research project
type: Master of Science, Plan II
school: University of California, Berkeley. Dept. of Electrical and Engineering and Computer Sciences
address: Berkeley, CA.
pages: various
year: 1986
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: Glenn D. Adams
rawtitle:
Functional specification and simulation of a floating point co-processor for {SPUR}: research project

entry:
@MastersThesis{Adams:1986:FSSb,
  author =       "Glenn D. Adams",
  title =        "Functional specification and simulation of a floating
                 point co-processor for {SPUR}: research project",
  type =         "{Master of Science, Plan II}",
  school =       "University of California, Berkeley. Dept. of
                 Electrical and Engineering and Computer Sciences",
  address =      "Berkeley, CA.",
  pages =        "various",
  year =         "1986",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Agarwal:1986:NSV
title: New Scalar and Vector Elementary Functions for the IBM System / 370
journal: j-IBM-JRD
volume: 30
number: 2
pages: 126--144
month: mar
monthnumber: 3
year: 1986
CODEN: IBMJAE
DOI: https://doi.org/10.1147/rd.302.0126
ISSN: 0018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)
ISSNL: 0018-8646 OR 00188646
MRclass: 76W05
MRnumber: 840 341
bibdate: Sat Jan 11 17:44:01 MST 1997
bibtimestamp: 1997.01.11 17:44:01 MST
note: See clarification cite Agarwal:1987:CNS.
fjournal: IBM Journal of Research and Development
acknowledgement: ack-nhfb
ajournal: IBM J. Res. Develop.
classcodes: C6140D (High level languages); C7310 (Mathematics computing)
corpsource: IBM Res. Div., Yorktown Heights, NY, USA
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520
journalabr: IBM J Res Dev
treatment: N New Development; P Practical
rawnote: See clarification \cite{Agarwal:1987:CNS}.
rawtitle: New Scalar and Vector Elementary Functions for the {IBM System\slash 370}
author:
Ramesh C. Agarwal and James W. Cooley and Fred G. Gustavson and James B. Shearer and Gordon Slishman and Bryant Tuckerman

bibsource:
Compendex database; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib

abstract:
Algorithms have been developed to compute short-and long-precision elementary functions: SIN, COS, TAN, COTAN, LOG, LOG10, EXP, POWER, SQRT, ATAN, ASIN, ACOS, ATAN2, and CABS, in scalar (28 functions) and vector (22 functions) mode. They have been implemented as part of the new VS FORTRAN library recently announced along with the IBM 3090 Vector Facility. These algorithms are essentially table-based algorithms. An important feature of these algorithms is that they produce bitwise-identical results on scalar and vector System / 370 machines. Of these, for five functions the computed value result is always the correctly rounded value of the infinite-precision result. For the rest of the functions, the value returned is one of the two floating-point neighbors bordering the infinite-precision result, which implies exact results if they are machine-representable. For the five correctly rounded elementary functions, scalar and vector algorithms are designed independently to optimize performance in each case.

keywords:
ACOS; Algorithms; algorithms; ASIN; ATAN; ATAN2; bitwise-identical results; CABS; computer metatheory; computer programming; computer programming languages --- fortran; COS; COTAN; design; elementary functions; EXP; FORTRAN; fortran library; functions; IBM computers; IBM System/370; infinite-precision result; LOG; LOG10; mainframes; measurement; performance; POWER; scalar elementary functions; SIN; SQRT; subroutines; table-based algorithms; TAN; vector elementary; VS FORTRAN library

subject:
C.4 Computer Systems Organization, PERFORMANCE OF SYSTEMS I.1.2 Computing Methodologies, ALGEBRAIC MANIPULATION, Algorithms F.3.3 Theory of Computation, LOGICS AND MEANINGS OF PROGRAMS, Studies of Program Constructs, Functional constructs C.1.2 Computer Systems Organization, PROCESSOR ARCHITECTURES, Multiple Data Stream Architectures (Multiprocessors), Array and vector processors

rawabstract:
Algorithms have been developed to compute short-and long-precision elementary functions: SIN, COS, TAN, COTAN, LOG, LOG10, EXP, POWER, SQRT, ATAN, ASIN, ACOS, ATAN2, and CABS, in scalar (28 functions) and vector (22 functions) mode. They have been implemented as part of the new VS FORTRAN library recently announced along with the IBM 3090 Vector Facility. These algorithms are essentially table-based algorithms. An important feature of these algorithms is that they produce bitwise-identical results on scalar and vector System\slash 370 machines. Of these, for five functions the computed value result is always the correctly rounded value of the infinite-precision result. For the rest of the functions, the value returned is one of the two floating-point neighbors bordering the infinite-precision result, which implies exact results if they are machine-representable. For the five correctly rounded elementary functions, scalar and vector algorithms are designed independently to optimize performance in each case.

rawauthor:
Ramesh C. Agarwal and James W. Cooley and Fred G. Gustavson and James B. Shearer and Gordon Slishman and Bryant Tuckerman

entry:
@Article{Agarwal:1986:NSV,
  author =       "Ramesh C. Agarwal and James W. Cooley and Fred G.
                 Gustavson and James B. Shearer and Gordon Slishman and
                 Bryant Tuckerman",
  title =        "New Scalar and Vector Elementary Functions for the
                 {IBM System\slash 370}",
  journal =      j-IBM-JRD,
  volume =       "30",
  number =       "2",
  pages =        "126--144",
  month =        mar,
  year =         "1986",
  CODEN =        "IBMJAE",
  DOI =          "https://doi.org/10.1147/rd.302.0126",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  MRclass =      "76W05",
  MRnumber =     "840 341",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib",
  note =         "See clarification \cite{Agarwal:1987:CNS}.",
  abstract =     "Algorithms have been developed to compute short-and
                 long-precision elementary functions: SIN, COS, TAN,
                 COTAN, LOG, LOG10, EXP, POWER, SQRT, ATAN, ASIN, ACOS,
                 ATAN2, and CABS, in scalar (28 functions) and vector
                 (22 functions) mode. They have been implemented as part
                 of the new VS FORTRAN library recently announced along
                 with the IBM 3090 Vector Facility. These algorithms are
                 essentially table-based algorithms. An important
                 feature of these algorithms is that they produce
                 bitwise-identical results on scalar and vector
                 System\slash 370 machines. Of these, for five functions
                 the computed value result is always the correctly
                 rounded value of the infinite-precision result. For the
                 rest of the functions, the value returned is one of the
                 two floating-point neighbors bordering the
                 infinite-precision result, which implies exact results
                 if they are machine-representable. For the five
                 correctly rounded elementary functions, scalar and
                 vector algorithms are designed independently to
                 optimize performance in each case.",
  accepted =     "2 December 1985",
  acknowledgement = ack-nhfb,
  ajournal =     "IBM J. Res. Develop.",
  classcodes =   "C6140D (High level languages); C7310 (Mathematics
                 computing)",
  classification = "723",
  corpsource =   "IBM Res. Div., Yorktown Heights, NY, USA",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  journalabr =   "IBM J Res Dev",
  keywords =     "ACOS; Algorithms; algorithms; ASIN; ATAN; ATAN2;
                 bitwise-identical results; CABS; computer metatheory;
                 computer programming; computer programming languages
                 --- fortran; COS; COTAN; design; elementary functions;
                 EXP; FORTRAN; fortran library; functions; IBM
                 computers; IBM System/370; infinite-precision result;
                 LOG; LOG10; mainframes; measurement; performance;
                 POWER; scalar elementary functions; SIN; SQRT;
                 subroutines; table-based algorithms; TAN; vector
                 elementary; VS FORTRAN library",
  received =     "5 November 1985",
  remark-1 =     "Numerous figures show errors in ulps, in either linear
                 or logarithmic scales, as dot plots over a range of
                 arguments, an idea that the authors credit to a
                 suggestion by Cleve Moler, then consulting with IBM
                 Palo Alto labs; such plots are used extensively in
                 \cite{Beebe:2017:MFC}.",
  remark-2 =     "From pages 128--129: ``A great deal of satisfaction
                 was obtained from the fact that five of the intrinsic
                 functions reported here always deliver correctly
                 rounded results; these are SQRT, DSQRT, CABS, CDABS,
                 and EXP. One important aspect of this is that correctly
                 rounded results were obtained with surprisingly little
                 sacrifice in performance.''",
  remark-3 =     "From page 132: ``Our CABS and CDABS functions satisfy
                 $\e/u < 0.5$ (this can also be called a half-ulp
                 criterion). They have best-possible rounding, except
                 that unavoidably there are cases when $| e/u | = 0.5$,
                 in which case it would be equally correct to round
                 downward or upward; we choose to round upward. This is
                 consistent with the System/370 definition of
                 rounding.''",
  remark-4 =     "From pages 134--135: ``Tuckerman's condition is of
                 historic significance, as its use allowed us to produce
                 IBM's first elementary function that delivered
                 correctly rounded results for all arguments.''",
  remark-5 =     "From page 137: ``X**2.0 usually produces a correctly
                 rounded value, while X*X always produces the truncated
                 value of $X^2$ .''",
  remark-6 =     "From page 139: ``Generating precise times is
                 difficult, since seemingly inconsequential changes in
                 the timing procedure may have a noticeable effect on
                 the measured times. For example, on the 3081KX the
                 performance of the STM [store multiple] and LM [load
                 multiple] instructions is severely degraded near page
                 boundaries. This means that in the rare event that the
                 save area of a subroutine is near a page boundary, the
                 speed of execution of the subroutine will be
                 substantially decreased.''",
  subject =      "C.4 Computer Systems Organization, PERFORMANCE OF
                 SYSTEMS \\ I.1.2 Computing Methodologies, ALGEBRAIC
                 MANIPULATION, Algorithms \\ F.3.3 Theory of
                 Computation, LOGICS AND MEANINGS OF PROGRAMS, Studies
                 of Program Constructs, Functional constructs \\ C.1.2
                 Computer Systems Organization, PROCESSOR ARCHITECTURES,
                 Multiple Data Stream Architectures (Multiprocessors),
                 Array and vector processors",
  treatment =    "N New Development; P Practical",
}


bibtype: book
filename: fparith.bib
label: Apple:1986:ANM
author: Apple Computer, Inc. and Don Reed
title: Apple Numerics Manual
publisher: pub-AW
address: pub-AW:adr
pages: vii + 295
year: 1986
ISBN: 0-201-17741-2 OR 0201177412
ISBN13: 978-0-201-17741-1 OR 9780201177411
LCCN: QA297 .A66; QA76.8.A662 A59 1986
bibdate: Thu Nov 29 23:38:40 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; melvyl.cdlib.org:210/CDL90
bibtimestamp: 2007.11.29 23:38:40 MST
note: See also cite Apple:1988:ANM,Apple:1994:IMP.
keywords: SANE (Standard Apple Numeric Environment)
remark: Standard Apple Numeric Environment for all Macintosh and Apple II computers.
subject: Numerical calculations; Computer programs; Apple computer
acknowledgement: ack-nhfb
rawauthor: {Apple Computer, Inc.} and Don Reed
rawnote: See also \cite{Apple:1988:ANM,Apple:1994:IMP}.
rawtitle: {Apple} Numerics Manual
entry:
@Book{Apple:1986:ANM,
  author =       "{Apple Computer, Inc.} and Don Reed",
  title =        "{Apple} Numerics Manual",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  pages =        "vii + 295",
  year =         "1986",
  ISBN =         "0-201-17741-2",
  ISBN-13 =      "978-0-201-17741-1",
  LCCN =         "QA297 .A66; QA76.8.A662 A59 1986",
  bibdate =      "Thu Nov 29 23:38:40 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  note =         "See also \cite{Apple:1988:ANM,Apple:1994:IMP}.",
  acknowledgement = ack-nhfb,
  keywords =     "SANE (Standard Apple Numeric Environment)",
  remark =       "Standard Apple Numeric Environment for all Macintosh
                 and Apple II computers.",
  subject =      "Numerical calculations; Computer programs; Apple
                 computer",
}


bibtype: article
filename: fparith.bib
label: Ardalan:1986:FPE
author: S. Ardalan
title: Floating-point error analysis of recursive least-squares and least-mean-squares adaptive filters
journal: j-IEEE-TRANS-CIRCUITS-SYST
volume: 33
number: 12
pages: 1192--1208
month: dec
monthnumber: 12
year: 1986
CODEN: ICSYBT
ISSN: 0098-4094 (print), 1558-1276 (electronic) OR 00984094 (print), 15581276 (electronic)
ISSNL: 0098-4094 OR 00984094
bibdate: Sat Jul 16 08:40:53 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:53 MDT
fjournal: IEEE Transactions on Circuits and Systems
acknowledgement: ack-nhfb
rawauthor: S. Ardalan
rawtitle: Floating-point error analysis of recursive least-squares and least-mean-squares adaptive filters
entry:
@Article{Ardalan:1986:FPE,
  author =       "S. Ardalan",
  title =        "Floating-point error analysis of recursive
                 least-squares and least-mean-squares adaptive filters",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "33",
  number =       "12",
  pages =        "1192--1208",
  month =        dec,
  year =         "1986",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  summary =      "A floating-point error analysis of the Recursive Least
                 Squares (RLS) and Least-Mean-Squares (LMS) algorithms
                 is presented. Both the prewindowed growing memory RLS
                 algorithm (lambda = 1) for stationary systems and the
                 exponentially windowed RLS \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Bayoumi:1986:LBV
author: Magdy A. Bayoumi
title: Lower bounds for VLSI implementation of residue number system architectures
journal: j-INTEGRATION-VLSI-J
volume: 4
number: 3
pages: 263--269
month: sep
monthnumber: 9
year: 1986
CODEN: IVJODL
DOI: https://doi.org/10.1016/0167-9260(86)90004-0
ISSN: 0167-9260 (print), 1872-7522 (electronic) OR 01679260 (print), 18727522 (electronic)
ISSNL: 0167-9260 OR 01679260
bibdate: Thu Nov 18 09:57:37 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.11.18 09:57:37 ???
fjournal: Integration, the VLSI journal
keywords: area-time complexity; lower bounds; RNS; VLSI
acknowledgement: ack-nhfb
journalURL: https://www.sciencedirect.com/journal/integration/issues
rawauthor: Magdy A. Bayoumi
rawtitle: Lower bounds for {VLSI} implementation of residue number system architectures
abstract:
Since the number of components that can fit on a single chip is large and rapidly growing, the asymptotic analysis and computational complexity have become applicable to the VLSI systems. We propose a model of computation devoted to VLSI structures based on Residue Number System (RNS). The developed model employs the `cut theorem' which has been used by most of the abstract VLSI models. It is not as general as other reported models, but it gives tighter lower bounds and more accurate measures of performance for RNS structures. This computational model relates the area and time complexities with the inherent properties of RNS, the moduli size and the dynamic range. The model supports the look-up table implementation approach and it is technology-independent.

rawabstract:
Since the number of components that can fit on a single chip is large and rapidly growing, the asymptotic analysis and computational complexity have become applicable to the VLSI systems. We propose a model of computation devoted to VLSI structures based on Residue Number System (RNS). The developed model employs the `cut theorem' which has been used by most of the abstract VLSI models. It is not as general as other reported models, but it gives tighter lower bounds and more accurate measures of performance for RNS structures. This computational model relates the area and time complexities with the inherent properties of RNS, the moduli size and the dynamic range. The model supports the look-up table implementation approach and it is technology-independent.

entry:
@Article{Bayoumi:1986:LBV,
  author =       "Magdy A. Bayoumi",
  title =        "Lower bounds for {VLSI} implementation of residue
                 number system architectures",
  journal =      j-INTEGRATION-VLSI-J,
  volume =       "4",
  number =       "3",
  pages =        "263--269",
  month =        sep,
  year =         "1986",
  CODEN =        "IVJODL",
  DOI =          "https://doi.org/10.1016/0167-9260(86)90004-0",
  ISSN =         "0167-9260 (print), 1872-7522 (electronic)",
  ISSN-L =       "0167-9260",
  bibdate =      "Thu Nov 18 09:57:37 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Since the number of components that can fit on a
                 single chip is large and rapidly growing, the
                 asymptotic analysis and computational complexity have
                 become applicable to the VLSI systems. We propose a
                 model of computation devoted to VLSI structures based
                 on Residue Number System (RNS). The developed model
                 employs the `cut theorem' which has been used by most
                 of the abstract VLSI models. It is not as general as
                 other reported models, but it gives tighter lower
                 bounds and more accurate measures of performance for
                 RNS structures. This computational model relates the
                 area and time complexities with the inherent properties
                 of RNS, the moduli size and the dynamic range. The
                 model supports the look-up table implementation
                 approach and it is technology-independent.",
  acknowledgement = ack-nhfb,
  fjournal =     "Integration, the VLSI journal",
  journal-URL =  "https://www.sciencedirect.com/journal/integration/issues",
  keywords =     "area-time complexity; lower bounds; RNS; VLSI",
}


bibtype: inproceedings
filename: fparith.bib
label: Beims:1986:FPP
author: B. Beims
title: The Floating-Point Performance Standard Gets Even Faster!
crossref: Wescon:1986:WCR
pages: 35/1/1--13
year: 1986
bibdate: Wed Sep 14 19:13:54 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.14 19:13:54 ???
acknowledgement: ack-nj
rawauthor: B. Beims
rawtitle: The Floating-Point Performance Standard Gets Even Faster!
entry:
@InProceedings{Beims:1986:FPP,
  author =       "B. Beims",
  title =        "The Floating-Point Performance Standard Gets Even
                 Faster!",
  crossref =     "Wescon:1986:WCR",
  pages =        "35/1/1--13",
  year =         "1986",
  bibdate =      "Wed Sep 14 19:13:54 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: inproceedings
filename: fparith.bib
label: Berger:1986:NNF
author: P. A. Berger
title: The National NS32381 Floating Point Slave Processor
crossref: Wescon:1986:WCR
pages: 35/2/1--6
year: 1986
bibdate: Mon Sep 12 08:32:02 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.12 08:32:02 ???
acknowledgement: ack-nj
rawauthor: P. A. Berger
rawtitle: The {National NS32381} Floating Point Slave Processor
entry:
@InProceedings{Berger:1986:NNF,
  author =       "P. A. Berger",
  title =        "The {National NS32381} Floating Point Slave
                 Processor",
  crossref =     "Wescon:1986:WCR",
  pages =        "35/2/1--6",
  year =         "1986",
  bibdate =      "Mon Sep 12 08:32:02 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: Bernstein:1986:MIC
author: Robert L. Bernstein
title: Multiplication by Integer Constants
journal: j-SPE
volume: 16
number: 7
pages: 641--652
month: jul
monthnumber: 7
year: 1986
CODEN: SPEXBL
DOI: https://doi.org/10.1002/spe.4380160704
ISSN: 0038-0644 (print), 1097-024X (electronic) OR 00380644 (print), 1097024X (electronic)
ISSNL: 0038-0644 OR 00380644
bibdate: Sat May 31 13:36:16 MDT 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.05.31 13:36:16 MDT
fjournal: Software---Practice and Experience
acknowledgement: ack-nhfb
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X
rawauthor: Robert L. Bernstein
rawtitle: Multiplication by Integer Constants
abstract:
Methods are given for finding a sequence of `add', `subtract' and `shift' instructions to multiply the contents of a register by an integer constant. Each method generalizes the previous one and requires only a few intermediate or scratch registers. A variation of the last method is used in the PL.8 compiler and uses an unnoticeable amount of the overall compile time. Some statistics roughly indicating the effectiveness of the methods are presented.

rawabstract:
Methods are given for finding a sequence of `add', `subtract' and `shift' instructions to multiply the contents of a register by an integer constant. Each method generalizes the previous one and requires only a few intermediate or scratch registers. A variation of the last method is used in the PL.8 compiler and uses an unnoticeable amount of the overall compile time. Some statistics roughly indicating the effectiveness of the methods are presented.

entry:
@Article{Bernstein:1986:MIC,
  author =       "Robert L. Bernstein",
  title =        "Multiplication by Integer Constants",
  journal =      j-SPE,
  volume =       "16",
  number =       "7",
  pages =        "641--652",
  month =        jul,
  year =         "1986",
  CODEN =        "SPEXBL",
  DOI =          "https://doi.org/10.1002/spe.4380160704",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  bibdate =      "Sat May 31 13:36:16 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Methods are given for finding a sequence of `add',
                 `subtract' and `shift' instructions to multiply the
                 contents of a register by an integer constant. Each
                 method generalizes the previous one and requires only a
                 few intermediate or scratch registers. A variation of
                 the last method is used in the PL.8 compiler and uses
                 an unnoticeable amount of the overall compile time.
                 Some statistics roughly indicating the effectiveness of
                 the methods are presented.",
  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: Campbell:1986:NSR
author: R. A. Campbell
title: NS32000 Square Roots
journal: j-DDJ
volume: 11
number: 3
pages: 122--123, 106
month: mar
monthnumber: 3
year: 1986
CODEN: DDJOEB
ISSN: 1044-789X OR 1044789X
bibdate: Fri Dec 08 13:05:56 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 13:05:56 ???
fjournal: Dr. Dobb's Journal of Software Tools
acknowledgement: ack-nj
rawauthor: R. A. Campbell
rawtitle: {NS32000} Square Roots
entry:
@Article{Campbell:1986:NSR,
  author =       "R. A. Campbell",
  title =        "{NS32000} Square Roots",
  journal =      j-DDJ,
  volume =       "11",
  number =       "3",
  pages =        "122--123, 106",
  month =        mar,
  year =         "1986",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Fri Dec 08 13:05:56 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 =     "Dr. Dobb's Journal of Software Tools",
}


bibtype: article
filename: fparith.bib
label: Campbell:1986:SS
author: R. A. Campbell
title: In Search of a Sine
journal: j-DDJ
volume: 11
number: 12
pages: 30--32
month: dec
monthnumber: 12
year: 1986
CODEN: DDJOEB
ISSN: 1044-789X OR 1044789X
bibdate: Thu Sep 1 10:15:57 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 10:15:57 ???
fjournal: Dr. Dobb's Journal of Software Tools
acknowledgement: ack-nj
rawauthor: R. A. Campbell
rawtitle: In Search of a Sine
entry:
@Article{Campbell:1986:SS,
  author =       "R. A. Campbell",
  title =        "In Search of a Sine",
  journal =      j-DDJ,
  volume =       "11",
  number =       "12",
  pages =        "30--32",
  month =        dec,
  year =         "1986",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Thu Sep 1 10:15:57 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 =     "Dr. Dobb's Journal of Software Tools",
}


bibtype: mastersthesis
filename: fparith.bib
label: Cao:1986:BFP
author: Hai Cao
title: A bit-slice floating point processor
type: Project (M.S., Electrical and Electronic Engineering)
school: California State University
address: Sacramento, CA, USA
pages: vii + 104
year: 1986
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
note: Karl E. Stoffers, Chairperson.
keywords: Bit slice microprocessors.
acknowledgement: ack-nhfb
rawauthor: Hai Cao
rawnote: Karl E. Stoffers, Chairperson.
rawtitle: A bit-slice floating point processor
entry:
@MastersThesis{Cao:1986:BFP,
  author =       "Hai Cao",
  title =        "A bit-slice floating point processor",
  type =         "Project ({M.S., Electrical and Electronic
                 Engineering})",
  school =       "California State University",
  address =      "Sacramento, CA, USA",
  pages =        "vii + 104",
  year =         "1986",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Karl E. Stoffers, Chairperson.",
  acknowledgement = ack-nhfb,
  keywords =     "Bit slice microprocessors.",
}


bibtype: article
filename: fparith.bib
label: Cathey:1986:LEI
author: J. Cathey
title: Letter to the editor [Integer Square Root]
journal: j-DDJ
volume: 11
number: 8
pages: 14, 82--85
month: aug
monthnumber: 8
year: 1986
CODEN: DDJOEB
ISSN: 1044-789X OR 1044789X
bibdate: Thu Sep 08 07:59:25 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.08 07:59:25 ???
fjournal: Dr. Dobb's Journal of Software Tools
acknowledgement: ack-nj
rawauthor: J. Cathey
rawtitle: Letter to the editor [Integer Square Root]
entry:
@Article{Cathey:1986:LEI,
  author =       "J. Cathey",
  title =        "Letter to the editor [Integer Square Root]",
  journal =      j-DDJ,
  volume =       "11",
  number =       "8",
  pages =        "14, 82--85",
  month =        aug,
  year =         "1986",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Thu Sep 08 07:59:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}


bibtype: inproceedings
filename: fparith.bib
label: Chadha:1986:IHP
author: K. Chadha
title: Intel 80387: high performance, single chip numerics coprocessor for the 80386
crossref: Wescon:1986:WCR
pages: 35/4/1--5
year: 1986
bibdate: Wed Sep 7 22:31:45 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 22:31:45 ???
acknowledgement: ack-nj
rawauthor: K. Chadha
rawtitle: {Intel} 80387: high performance, single chip numerics coprocessor for the 80386
entry:
@InProceedings{Chadha:1986:IHP,
  author =       "K. Chadha",
  title =        "{Intel} 80387: high performance, single chip numerics
                 coprocessor for the 80386",
  crossref =     "Wescon:1986:WCR",
  pages =        "35/4/1--5",
  year =         "1986",
  bibdate =      "Wed Sep 7 22:31:45 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: Chakraborti:1986:IMR
author: N. B. Chakraborti and J. S. Soundararajan and A. L. N. Reddy
title: An Implementation of Mixed-Radix Conversion for Residue Number Applications
journal: j-IEEE-TRANS-COMPUT
volume: C-35
number: 8
pages: 762--764
month: aug
monthnumber: 8
year: 1986
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1986.1676829
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 9 14:09:51 MDT 2011
bibtimestamp: 2011.07.09 14:09:51 MDT
fjournal: IEEE Transactions on Computers
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: N. B. Chakraborti and J. S. Soundararajan and A. L. N. Reddy
rawtitle: An Implementation of Mixed-Radix Conversion for Residue Number Applications
URL:
http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12; http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35258; https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676829

entry:
@Article{Chakraborti:1986:IMR,
  author =       "N. B. Chakraborti and J. S. Soundararajan and A. L. N.
                 Reddy",
  title =        "An Implementation of Mixed-Radix Conversion for
                 Residue Number Applications",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-35",
  number =       "8",
  pages =        "762--764",
  month =        aug,
  year =         "1986",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1986.1676829",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 14:09:51 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35258;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676829",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A method of residue number system (RNS) conversion to
                 mixed-radix (MR) representation is presented. This
                 method is found to be cost-effective and efficient,
                 particularly for moduli size 4/5 bits. A comparison of
                 conversion times and hardware \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Chowdary:1986:APR
author: N. Chowdary and W. Steenaart
title: Accumulation of product roundoff errors in modified FFT's
journal: j-IEEE-TRANS-CIRCUITS-SYST
volume: 33
number: 1
pages: 103--107
month: jan
monthnumber: 1
year: 1986
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: N. Chowdary and W. Steenaart
rawtitle: Accumulation of product roundoff errors in modified {FFT}'s
entry:
@Article{Chowdary:1986:APR,
  author =       "N. Chowdary and W. Steenaart",
  title =        "Accumulation of product roundoff errors in modified
                 {FFT}'s",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "33",
  number =       "1",
  pages =        "103--107",
  month =        jan,
  year =         "1986",
  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 =      "In this paper, expressions are derived for the mean
                 square error in modified radix-2 FFT algorithms. To
                 reduce the mean square error at the output of a special
                 purpose, high-speed low-order(n {leq} 32)FFT processor
                 implemented in fixed- \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Clenshaw:1986:GEL
author: C. W. Clenshaw and Daniel W. Lozier and F. W. J. Olver and P. R. Turner
title: Generalized Exponential and Logarithmic Functions
journal: j-COMPUT-MATH-APPL
volume: 12
number: 5--6
pages: 1091--1101
month: sep
monthnumber: 9
year: 1986
CODEN: CMAPDK
DOI: https://doi.org/10.1016/0898-1221(86)90233-6
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
MRclass: 33A70 (39B10 65G05)
MRnumber: MR0871348 (88a:33027)
bibdate: Fri Jul 09 06:27:26 2004
bibtimestamp: 2004.07.09 06:27:26 ???
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: C. W. Clenshaw and Daniel W. Lozier and F. W. J. Olver and P. R. Turner
rawtitle: Generalized Exponential and Logarithmic Functions
abstract:
Generalizations of the exponential and logarithmic functions are defined and an investigation is made of two possible versions of these functions. Some applications are described, including computer arithmetic, properties of very large and very small numbers, and the determination of functional roots.

rawabstract:
Generalizations of the exponential and logarithmic functions are defined and an investigation is made of two possible versions of these functions. Some applications are described, including computer arithmetic, properties of very large and very small numbers, and the determination of functional roots.

entry:
@Article{Clenshaw:1986:GEL,
  author =       "C. W. Clenshaw and Daniel W. Lozier and F. W. J. Olver
                 and P. R. Turner",
  title =        "Generalized Exponential and Logarithmic Functions",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "12",
  number =       "5--6",
  pages =        "1091--1101",
  month =        sep # "\slash " # dec,
  year =         "1986",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(86)90233-6",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  MRclass =      "33A70 (39B10 65G05)",
  MRnumber =     "MR0871348 (88a:33027)",
  bibdate =      "Fri Jul 09 06:27:26 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Generalizations of the exponential and logarithmic
                 functions are defined and an investigation is made of
                 two possible versions of these functions. Some
                 applications are described, including computer
                 arithmetic, properties of very large and very small
                 numbers, and the determination of functional roots.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: article
filename: fparith.bib
label: Clenshaw:1986:UAR
author: C. W. Clenshaw and F. W. J. Olver
title: Unrestricted algorithms for reciprocals and square roots
journal: j-BIT
volume: 26
number: 4
pages: 475--492
month: dec
monthnumber: 12
year: 1986
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01935054
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
MRclass: 65D20
MRnumber: 87k:65019
MRreviewer: Luciano Biasini
bibdate: Wed Jan 4 18:52:19 MST 2006
bibtimestamp: 2006.01.04 18:52:19 MST
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=26&issue=4&spage=475
fjournal: BIT (Nordisk tidskrift for informationsbehandling)
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: C. W. Clenshaw and F. W. J. Olver
rawtitle: Unrestricted algorithms for reciprocals and square roots
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=26&issue=4; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Clenshaw:1986:UAR,
  author =       "C. W. Clenshaw and F. W. J. Olver",
  title =        "Unrestricted algorithms for reciprocals and square
                 roots",
  journal =      j-BIT,
  volume =       "26",
  number =       "4",
  pages =        "475--492",
  month =        dec,
  year =         "1986",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01935054",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65D20",
  MRnumber =     "87k:65019",
  MRreviewer =   "Luciano Biasini",
  bibdate =      "Wed Jan 4 18:52:19 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=26&issue=4;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=26&issue=4&spage=475",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  xxpages =      "476--492??",
}


bibtype: phdthesis
filename: fparith.bib
label: Coonen:1986:CPS
author: Jerome Toby Coonen
title: Contributions to a proposed standard for binary floating-point arithmetic
type: Thesis (Ph.D.)
school: University of California, Berkeley
address: Berkeley, CA, USA
pages: various
year: 1986
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)
acknowledgement: ack-nhfb
rawauthor: Jerome Toby Coonen
rawtitle: Contributions to a proposed standard for binary floating-point arithmetic
entry:
@PhdThesis{Coonen:1986:CPS,
  author =       "Jerome Toby Coonen",
  title =        "Contributions to a proposed standard for binary
                 floating-point arithmetic",
  type =         "Thesis ({Ph.D.})",
  school =       "University of California, Berkeley",
  address =      "Berkeley, CA, USA",
  pages =        "various",
  year =         "1986",
  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)",
}


bibtype: mastersthesis
filename: fparith.bib
label: Crowell:1986:ECU
author: Deborah Susan Crowell
title: Error-free computation using multiple-modulus residue arithmetic
type: Thesis (M.S.)
school: University of Tennessee, Knoxville
address: Knoxville, TN, USA
pages: vi + 106
year: 1986
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: Deborah Susan Crowell
rawtitle: Error-free computation using multiple-modulus residue arithmetic
keywords:
Algorithms.; Approximation theory --- Data processing.; Floating-point arithmetic.; Modular arithmetic.

entry:
@MastersThesis{Crowell:1986:ECU,
  author =       "Deborah Susan Crowell",
  title =        "Error-free computation using multiple-modulus residue
                 arithmetic",
  type =         "Thesis ({M.S.})",
  school =       "University of Tennessee, Knoxville",
  address =      "Knoxville, TN, USA",
  pages =        "vi + 106",
  year =         "1986",
  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.; Approximation theory --- Data
                 processing.; Floating-point arithmetic.; Modular
                 arithmetic.",
}


bibtype: article
filename: fparith.bib
label: Curtis:1986:CPL
author: T. W. Curtis and Paul Allison and James A. Howard
title: A CORDIC Processor for Laser Trimming
journal: j-IEEE-MICRO
volume: 6
number: 3
pages: 61--71
month: may
monthnumber: 5
year: 1986
CODEN: IEMIDZ
DOI: https://doi.org/10.1109/MM.1986.304680
ISSN: 0272-1732 (print), 1937-4143 (electronic) OR 02721732 (print), 19374143 (electronic)
ISSNL: 0272-1732 OR 02721732
bibdate: Thu Sep 08 00:48:52 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.08 00:48:52 ???
fjournal: IEEE Micro
acknowledgement: ack-nhfb
journalURL: http://www.computer.org/csdl/mags/mi/index.html
rawauthor: T. W. Curtis and Paul Allison and James A. Howard
rawtitle: A {CORDIC} Processor for Laser Trimming
keywords:
Computer errors; Computer interfaces; Control systems; Error correction; Laser beam cutting; Optical control; Weight control

entry:
@Article{Curtis:1986:CPL,
  author =       "T. W. Curtis and Paul Allison and James A. Howard",
  title =        "A {CORDIC} Processor for Laser Trimming",
  journal =      j-IEEE-MICRO,
  volume =       "6",
  number =       "3",
  pages =        "61--71",
  month =        may # "\slash " # jun,
  year =         "1986",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/MM.1986.304680",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Thu Sep 08 00:48:52 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
  keywords =     "Computer errors; Computer interfaces; Control systems;
                 Error correction; Laser beam cutting; Optical control;
                 Weight control",
}


bibtype: inproceedings
filename: fparith.bib
label: Desrosiers:1986:CFP
author: B. Desrosiers and J.-L. Peter and C. Sitbon
title: Custom Floating Point Chip Designed with a Cohesive Structured Method
crossref: IEEE:1986:PII
pages: 402--405
year: 1986
bibdate: Wed Sep 7 22:31:45 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 22:31:45 ???
acknowledgement: ack-nj
rawauthor: B. Desrosiers and J.-L. Peter and C. Sitbon
rawtitle: Custom Floating Point Chip Designed with a Cohesive Structured Method
entry:
@InProceedings{Desrosiers:1986:CFP,
  author =       "B. Desrosiers and J.-L. Peter and C. Sitbon",
  title =        "Custom Floating Point Chip Designed with a Cohesive
                 Structured Method",
  crossref =     "IEEE:1986:PII",
  pages =        "402--405",
  year =         "1986",
  bibdate =      "Wed Sep 7 22:31:45 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: inproceedings
filename: fparith.bib
label: DuCroz:1986:FFP
author: J. Du Croz
title: FPV -- a Floating-Point Validation Package
crossref: Unicom:1986:SQA
pages: 47--55
year: 1986
bibdate: Thu Sep 01 11:58:18 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 11:58:18 ???
acknowledgement: ack-nj
rawauthor: J. Du Croz
rawtitle: {FPV} -- a Floating-Point Validation Package
entry:
@InProceedings{DuCroz:1986:FFP,
  author =       "J. Du Croz",
  title =        "{FPV} -- a Floating-Point Validation Package",
  crossref =     "Unicom:1986:SQA",
  pages =        "47--55",
  year =         "1986",
  bibdate =      "Thu Sep 01 11:58:18 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: Dutka:1986:SRT
author: Jacques Dutka
title: On square roots and their representations
journal: j-ARCH-HIST-EXACT-SCI
volume: 36
number: 1
pages: 21--39
month: mar
monthnumber: 3
year: 1986
CODEN: AHESAN
DOI: https://doi.org/10.1007/BF00357439
ISSN: 0003-9519 (print), 1432-0657 (electronic) OR 00039519 (print), 14320657 (electronic)
ISSNL: 0003-9519 OR 00039519
MRclass: 01A05 (11-03 11A63)
MRnumber: 863340 (87m:01003)
MRreviewer: Donald Cook
bibdate: Fri Feb 4 21:50:24 MST 2011
bibtimestamp: 2011.02.04 21:50:24 MST
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0003-9519&volume=36&issue=1&spage=21
fjournal: Archive for History of Exact Sciences
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/407
rawauthor: Jacques Dutka
rawtitle: On square roots and their representations
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0003-9519&volume=36&issue=1; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Dutka:1986:SRT,
  author =       "Jacques Dutka",
  title =        "On square roots and their representations",
  journal =      j-ARCH-HIST-EXACT-SCI,
  volume =       "36",
  number =       "1",
  pages =        "21--39",
  month =        mar,
  year =         "1986",
  CODEN =        "AHESAN",
  DOI =          "https://doi.org/10.1007/BF00357439",
  ISSN =         "0003-9519 (print), 1432-0657 (electronic)",
  ISSN-L =       "0003-9519",
  MRclass =      "01A05 (11-03 11A63)",
  MRnumber =     "863340 (87m:01003)",
  MRreviewer =   "Donald Cook",
  bibdate =      "Fri Feb 4 21:50:24 MST 2011",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0003-9519&volume=36&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0003-9519&volume=36&issue=1&spage=21",
  acknowledgement = ack-nhfb,
  fjournal =     "Archive for History of Exact Sciences",
  journal-URL =  "http://link.springer.com/journal/407",
  MRtitle =      "On square roots and their representations",
}


bibtype: article
filename: fparith.bib
label: Dutta:1986:IMF
author: U. Dutta and D. Bhattacharya and A. D. Sarma
title: Implementation of Multibyte Floating Point Arithmetic in 8-bit Microprocessor
journal: j-MECH-ENG-BULL
volume: 17
number: 3
pages: 104--113
month: sep
monthnumber: 9
year: 1986
CODEN: MEGBBQ
ISSN: 0379-5527 OR 03795527
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: Mechanical Engineering Bulletin
acknowledgement: ack-nj
rawauthor: U. Dutta and D. Bhattacharya and A. D. Sarma
rawtitle: Implementation of Multibyte Floating Point Arithmetic in 8-bit Microprocessor
entry:
@Article{Dutta:1986:IMF,
  author =       "U. Dutta and D. Bhattacharya and A. D. Sarma",
  title =        "Implementation of Multibyte Floating Point Arithmetic
                 in 8-bit Microprocessor",
  journal =      j-MECH-ENG-BULL,
  volume =       "17",
  number =       "3",
  pages =        "104--113",
  month =        sep,
  year =         "1986",
  CODEN =        "MEGBBQ",
  ISSN =         "0379-5527",
  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 =     "Mechanical Engineering Bulletin",
}


bibtype: article
filename: fparith.bib
label: Feldstein:1986:OUS
author: Alan Feldstein and Peter Turner
title: Overflow, underflow, and severe loss of significance in floating-point addition and subtraction
journal: j-IMA-J-NUMER-ANAL
volume: 6
number: 2
pages: 241--251
month: apr
monthnumber: 4
year: 1986
CODEN: IJNADH
ISSN: 0272-4979 (print), 1464-3642 (electronic) OR 02724979 (print), 14643642 (electronic)
ISSNL: 0272-4979 OR 02724979
MRclass: 65G05
MRnumber: 89h:65065
bibdate: Sat Dec 23 14:52:49 2000
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2000.12.23 14:52:49 ???
fjournal: IMA Journal of Numerical Analysis
keywords: Benford's Law; Law of Anomalous Numbers; logarithmic distribution; overflow; underflow; Zipf's Law
acknowledgement: ack-nhfb
journalURL: http://imajna.oxfordjournals.org/content/by/year
rawauthor: Alan Feldstein and Peter Turner
rawtitle: Overflow, underflow, and severe loss of significance in floating-point addition and subtraction
abstract:
In this paper it is shown that, under the assumption of the logarithmic distribution of numbers, floating-point addition and subtraction can result in overflow or underflow with alarming frequency?--a frequency that increases rapidly with machine speed unless the range of the exponent is also increased. If numbers are assumed to be distributed in accordance with Sweeney's (1965) experiments, then severe loss of significance occurs with large probability in floating point subtraction. These results have implications for computer design and lead to the suggestion of a long word format which will reduce the risks to acceptable levels.

rawabstract:
In this paper it is shown that, under the assumption of the logarithmic distribution of numbers, floating-point addition and subtraction can result in overflow or underflow with alarming frequency?--a frequency that increases rapidly with machine speed unless the range of the exponent is also increased. If numbers are assumed to be distributed in accordance with Sweeney's (1965) experiments, then severe loss of significance occurs with large probability in floating point subtraction. These results have implications for computer design and lead to the suggestion of a long word format which will reduce the risks to acceptable levels.

entry:
@Article{Feldstein:1986:OUS,
  author =       "Alan Feldstein and Peter Turner",
  title =        "Overflow, underflow, and severe loss of significance
                 in floating-point addition and subtraction",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "6",
  number =       "2",
  pages =        "241--251",
  month =        apr,
  year =         "1986",
  CODEN =        "IJNADH",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  MRclass =      "65G05",
  MRnumber =     "89h:65065",
  bibdate =      "Sat Dec 23 14:52:49 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In this paper it is shown that, under the assumption
                 of the logarithmic distribution of numbers,
                 floating-point addition and subtraction can result in
                 overflow or underflow with alarming frequency?--a
                 frequency that increases rapidly with machine speed
                 unless the range of the exponent is also increased. If
                 numbers are assumed to be distributed in accordance
                 with Sweeney's (1965) experiments, then severe loss of
                 significance occurs with large probability in floating
                 point subtraction. These results have implications for
                 computer design and lead to the suggestion of a long
                 word format which will reduce the risks to acceptable
                 levels.",
  acknowledgement = ack-nhfb,
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
  keywords =     "Benford's Law; Law of Anomalous Numbers; logarithmic
                 distribution; overflow; underflow; Zipf's Law",
}


bibtype: article
filename: fparith.bib
label: Ferro:1986:DTF
author: F. Ferro
title: DSP tackles floating-point arithmetic
journal: j-COMP-DESIGN
volume: 25
number: 15
pages: 53--56
day: 15
month: aug
monthnumber: 8
year: 1986
CODEN: CMPDAM
ISSN: 0010-4566 OR 00104566
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: Computer Design
subject: B. Hardware; B.7 INTEGRATED CIRCUITS
acknowledgement: ack-nhfb
rawauthor: F. Ferro
rawtitle: {DSP} tackles floating-point arithmetic
entry:
@Article{Ferro:1986:DTF,
  author =       "F. Ferro",
  title =        "{DSP} tackles floating-point arithmetic",
  journal =      j-COMP-DESIGN,
  volume =       "25",
  number =       "15",
  pages =        "53--56",
  day =          "15",
  month =        aug,
  year =         "1986",
  CODEN =        "CMPDAM",
  ISSN =         "0010-4566",
  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 =        "16915",
  catcode =      "B.7.1",
  CRclass =      "B.7.1 Types and Design Styles; B.7.1 Advanced
                 technologies",
  descriptor =   "Hardware, INTEGRATED CIRCUITS, Types and Design
                 Styles, Advanced technologies",
  fjournal =     "Computer Design",
  genterm =      "DESIGN",
  guideno =      "1986-04012",
  journalabbrev = "Comput. Des.",
  subject =      "B. Hardware; B.7 INTEGRATED CIRCUITS",
}


bibtype: article
filename: fparith.bib
label: Gavrielov:1986:NFP
author: Moshe Gavrielov and Lev Epstein
title: The NS32081 Floating-Point Unit --- Architecture and Implementation
journal: j-IEEE-MICRO
volume: 6
number: 2
pages: 6--12
month: mar
monthnumber: 3
year: 1986
CODEN: IEMIDZ
DOI: https://doi.org/10.1109/MM.1986.304737
ISSN: 0272-1732 (print), 1937-4143 (electronic) OR 02721732 (print), 19374143 (electronic)
ISSNL: 0272-1732 OR 02721732
bibdate: Thu Dec 14 06:08:58 MST 2000
bibtimestamp: 2000.12.14 06:08:58 MST
fjournal: IEEE Micro
acknowledgement: ack-nj
affiliationaddress: Digital Equipment Corp, Hudson, MA, USA
corpsource: Digital Equipment Corp., Hudson, MA, USA
journalURL: http://www.computer.org/csdl/mags/mi/index.html
treatment: P Practical; R Product Review
rawauthor: Moshe Gavrielov and Lev Epstein
rawtitle: The {NS32081} Floating-Point Unit --- Architecture and Implementation
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:
binary floating point arithmetic; binary floating-; brand; carry propagation circuit; chip design; computer architecture; computers, microcomputer; Construction; data storage, semiconductor; digital arithmetic; digital devices; field effect; floating-point operations; high-speed; IEEE standard; integrated circuits; internal structure; logic circuit implementations; microcode; microprocessor chips; NMOS processor; ns32081 floating-point processor; NS32081 floating-point unit; parallel multiway-; point arithmetic; processor concept; semiconductor devices, MOS; slave; slave processor; software package; standards

classcodes:
B1265F (Microprocessors and microcomputers); B2570F (Other MOS integrated circuits); C5130 (Microprocessor chips); C5220 (Computer architecture); C5230 (Digital arithmetic methods)

entry:
@Article{Gavrielov:1986:NFP,
  author =       "Moshe Gavrielov and Lev Epstein",
  title =        "The {NS32081} Floating-Point Unit --- Architecture and
                 Implementation",
  journal =      j-IEEE-MICRO,
  volume =       "6",
  number =       "2",
  pages =        "6--12",
  month =        mar # "\slash " # apr,
  year =         "1986",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/MM.1986.304737",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Thu Dec 14 06:08:58 MST 2000",
  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 = "Digital Equipment Corp, Hudson, MA, USA",
  classcodes =   "B1265F (Microprocessors and microcomputers); B2570F
                 (Other MOS integrated circuits); C5130 (Microprocessor
                 chips); C5220 (Computer architecture); C5230 (Digital
                 arithmetic methods)",
  classification = "713; 714; 721; 722; 723; 902",
  corpsource =   "Digital Equipment Corp., Hudson, MA, USA",
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
  keywords =     "binary floating point arithmetic; binary floating-;
                 brand; carry propagation circuit; chip design; computer
                 architecture; computers, microcomputer; Construction;
                 data storage, semiconductor; digital arithmetic;
                 digital devices; field effect; floating-point
                 operations; high-speed; IEEE standard; integrated
                 circuits; internal structure; logic circuit
                 implementations; microcode; microprocessor chips; NMOS
                 processor; ns32081 floating-point processor; NS32081
                 floating-point unit; parallel multiway-; point
                 arithmetic; processor concept; semiconductor devices,
                 MOS; slave; slave processor; software package;
                 standards",
  treatment =    "P Practical; R Product Review",
  xxtitle =      "The {NS32081} Floating-point Unit",
}


bibtype: article
filename: fparith.bib
label: Grappel:1986:SRA
author: R. D. Grappel
title: Square-root algorithm is fast and simple
journal: j-EDN
volume: 31
number: 8
pages: 248--248
month: apr
monthnumber: 4
year: 1986
CODEN: EDNSBH
ISSN: 0012-7515, 0364-6637 OR 00127515, 03646637
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: EDN
acknowledgement: ack-nj
rawauthor: R. D. Grappel
rawtitle: Square-root algorithm is fast and simple
entry:
@Article{Grappel:1986:SRA,
  author =       "R. D. Grappel",
  title =        "Square-root algorithm is fast and simple",
  journal =      j-EDN,
  volume =       "31",
  number =       "8",
  pages =        "248--248",
  month =        apr,
  year =         "1986",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  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 =     "EDN",
}


bibtype: article
filename: fparith.bib
label: Gustafson:1986:AHV
author: John L. Gustafson and Stuart Hawkinson and Ken Scott
title: The architecture of a homogeneous vector supercomputer
journal: j-J-PAR-DIST-COMP
volume: 3
number: 3
pages: 297--304
month: sep
monthnumber: 9
year: 1986
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: Floating Point Systems Inc, Beaverton, OR, USA
corpsource: Floating Point Syst. Inc., Beaverton, OR, USA
journalURL: http://www.sciencedirect.com/science/journal/07437315
journalabr: J Parallel Distrib Comput
treatment: P Practical
rawauthor: John L. Gustafson and Stuart Hawkinson and Ken Scott
rawtitle: The architecture of a homogeneous vector supercomputer
keywords:
12 MFLOPS; 64-bit floating-point; 96 MFLOPS; arithmetic; binary n-cube; computer architecture; computer systems, digital; dual-ported memory design; Floating Point; homogeneous vector supercomputer; interconnection scheme; multiprocessing; parallel; parallel architecture; parallel architectures; parallel machines; Parallel Processing; pipeline processing; pipeline vector arithmetic; pipelined vector arithmetic; programming; software development; supercomputer; Systems; technology; vector processing; VLSI

entry:
@Article{Gustafson:1986:AHV,
  author =       "John L. Gustafson and Stuart Hawkinson and Ken Scott",
  title =        "The architecture of a homogeneous vector
                 supercomputer",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "3",
  number =       "3",
  pages =        "297--304",
  month =        sep,
  year =         "1986",
  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 = "Floating Point Systems Inc, Beaverton, OR, USA",
  classification = "722; 723; C5220 (Computer architecture); C5440
                 (Multiprocessor systems and techniques); C6110 (Systems
                 analysis and programming)",
  corpsource =   "Floating Point Syst. Inc., Beaverton, OR, USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "12 MFLOPS; 64-bit floating-point; 96 MFLOPS;
                 arithmetic; binary n-cube; computer architecture;
                 computer systems, digital; dual-ported memory design;
                 Floating Point; homogeneous vector supercomputer;
                 interconnection scheme; multiprocessing; parallel;
                 parallel architecture; parallel architectures; parallel
                 machines; Parallel Processing; pipeline processing;
                 pipeline vector arithmetic; pipelined vector
                 arithmetic; programming; software development;
                 supercomputer; Systems; technology; vector processing;
                 VLSI",
  treatment =    "P Practical",
}


bibtype: book
filename: fparith.bib
label: Hamming:1986:NMS
author: R. W. (Richard Wesley) Hamming
title: Numerical methods for scientists and engineers
publisher: pub-DOVER
address: pub-DOVER:adr
edition: Second
pages: ix + 721
year: 1986
ISBN: 0-486-65241-6 (paperback) OR 0486652416 (paperback)
ISBN13: 978-0-486-65241-2 (paperback) OR 9780486652412 (paperback)
LCCN: QA297 .H28 1986
bibdate: Fri Aug 20 09:12:08 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.08.20 09:12:08 MDT
URL: http://www.loc.gov/catdir/description/dover032/86016226.html
remark: Reprint of cite Hamming:1973:NMS.
subject: numerical analysis; data processing
acknowledgement: ack-nhfb
rawauthor: R. W. (Richard Wesley) Hamming
rawtitle: Numerical methods for scientists and engineers
entry:
@Book{Hamming:1986:NMS,
  author =       "R. W. (Richard Wesley) Hamming",
  title =        "Numerical methods for scientists and engineers",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  edition =      "Second",
  pages =        "ix + 721",
  year =         "1986",
  ISBN =         "0-486-65241-6 (paperback)",
  ISBN-13 =      "978-0-486-65241-2 (paperback)",
  LCCN =         "QA297 .H28 1986",
  bibdate =      "Fri Aug 20 09:12:08 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  price =        "US\$14.95",
  URL =          "http://www.loc.gov/catdir/description/dover032/86016226.html",
  acknowledgement = ack-nhfb,
  remark =       "Reprint of \cite{Hamming:1973:NMS}.",
  subject =      "numerical analysis; data processing",
}


bibtype: article
filename: fparith.bib
label: Heath:1986:NRD
author: J. Heath
title: A note on ``Realization of digital filters using input-scaled floating-point arithmetic''
journal: j-IEEE-TRANS-ACOUST-SPEECH
volume: 34
number: 4
pages: 995--995
month: aug
monthnumber: 8
year: 1986
CODEN: IETABA
ISSN: 0096-3518 OR 00963518
bibdate: Sat Jul 16 08:40:53 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:53 MDT
note: See cite Heath:1979:RDF.
fjournal: IEEE Transactions on Acoustics, Speech, and Signal Processing
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29
rawauthor: J. Heath
rawnote: See \cite{Heath:1979:RDF}.
rawtitle: A note on {``Realization of digital filters using input-scaled floating-point arithmetic''}
entry:
@Article{Heath:1986:NRD,
  author =       "J. Heath",
  title =        "A note on {``Realization of digital filters using
                 input-scaled floating-point arithmetic''}",
  journal =      j-IEEE-TRANS-ACOUST-SPEECH,
  volume =       "34",
  number =       "4",
  pages =        "995--995",
  month =        aug,
  year =         "1986",
  CODEN =        "IETABA",
  ISSN =         "0096-3518",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Heath:1979:RDF}.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Acoustics, Speech, and Signal
                 Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
  summary =      "In [1] and [2], a theoretical Bode plot with
                 experimental data points is shown. The experimental
                 data points on the Bode plot are not correct \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Henning:1986:KBD
author: D. Henning
journal: Radio Fernsehen Elektronik
volume: 35
number: 11
pages: 731--733
year: 1986
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 ???
keywords: decimal floating-point arithmetic
acknowledgement: ack-nj
rawauthor: D. Henning
title:
Konvertierung binarer in dezimale Gleitkommazahlen fur mess technische Anwendungen toenglish Conversion of Binary [Numbers] to Decimal Floating-Point Numbers for Measurement Applications endtoenglish 

rawtitle:
{Konvertierung bin{\"a}rer in dezimale Gleitkommazahlen f{\"u}r me{\ss}technische Anwendungen} \toenglish {Conversion of Binary [Numbers] to Decimal Floating-Point Numbers for Measurement Applications} \endtoenglish

entry:
@Article{Henning:1986:KBD,
  author =       "D. Henning",
  title =        "{Konvertierung bin{\"a}rer in dezimale
                 Gleitkommazahlen f{\"u}r me{\ss}technische Anwendungen}
                 \toenglish {Conversion of Binary [Numbers] to Decimal
                 Floating-Point Numbers for Measurement Applications}
                 \endtoenglish",
  journal =      "Radio Fernsehen Elektronik",
  volume =       "35",
  number =       "11",
  pages =        "731--733",
  month =        "????",
  year =         "1986",
  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,
  keywords =     "decimal floating-point arithmetic",
}


bibtype: article
filename: fparith.bib
label: Higginbotham:1986:AF
author: T. F. Higginbotham
title: Another factor of $ (10^31 - 1) / 9 $
journal: j-SIGNUM
volume: 21
number: 3
pages: 12--12
month: jul
monthnumber: 7
year: 1986
CODEN: SNEWD6
DOI: https://doi.org/10.1145/1057958.1057960
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Thu Aug 07 18:41:01 2008
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2008.08.07 18:41:01 ???
fjournal: ACM SIGNUM Newsletter
keywords: decimal arithmetic
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/signum
rawauthor: T. F. Higginbotham
rawtitle: Another factor of $ (10^{31} - 1) / 9 $
abstract:
A second factor of $ (10^31 - 1) / 9 $ was found to be 6943319 with the use of an eight spoke wheel [1]. The spokes D(i) were 1, 7, 11, 13, 17, 19, 23, and 29. The possible factors 2, 3, and 5 were tested prior to starting the wheel. The constant multiplier was 30. The possible divisors were of the form $ 30 times K + D(i), K = 0, 1, 2, 3, ldots $. The program was written in COBOL for the Honeywell DPS 8, running under CP-6. The picture clauses were selected such that 31-digit decimal arithmetic was used. Execution time was about forty-five minutes.

remark:
Maple 8 reports in 2 sec on a 1400 MHz Itanium IA-64: ifactor((10^31 - 1)/9) = (57336415063790604359) (6943319) (2791).

rawabstract:
A second factor of $ (10^{31} - 1) / 9 $ was found to be 6943319 with the use of an eight spoke wheel [1]. The spokes D(i) were 1, 7, 11, 13, 17, 19, 23, and 29. The possible factors 2, 3, and 5 were tested prior to starting the wheel. The constant multiplier was 30. The possible divisors were of the form $ 30 \times K + D(i), K = 0, 1, 2, 3, \ldots {} $. The program was written in COBOL for the Honeywell DPS 8, running under CP-6. The picture clauses were selected such that 31-digit decimal arithmetic was used. Execution time was about forty-five minutes.

entry:
@Article{Higginbotham:1986:AF,
  author =       "T. F. Higginbotham",
  title =        "Another factor of $ (10^{31} - 1) / 9 $",
  journal =      j-SIGNUM,
  volume =       "21",
  number =       "3",
  pages =        "12--12",
  month =        jul,
  year =         "1986",
  CODEN =        "SNEWD6",
  DOI =          "https://doi.org/10.1145/1057958.1057960",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Thu Aug 07 18:41:01 2008",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A second factor of $ (10^{31} - 1) / 9 $ was found to
                 be 6943319 with the use of an eight spoke wheel [1].
                 The spokes D(i) were 1, 7, 11, 13, 17, 19, 23, and 29.
                 The possible factors 2, 3, and 5 were tested prior to
                 starting the wheel. The constant multiplier was 30. The
                 possible divisors were of the form $ 30 \times K +
                 D(i), K = 0, 1, 2, 3, \ldots {} $. The program was
                 written in COBOL for the Honeywell DPS 8, running under
                 CP-6. The picture clauses were selected such that
                 31-digit decimal arithmetic was used. Execution time
                 was about forty-five minutes.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "decimal arithmetic",
  remark =       "Maple 8 reports in 2 sec on a 1400 MHz Itanium IA-64:
                 ifactor((10^31 - 1)/9) = (57336415063790604359)
                 (6943319) (2791).",
}


bibtype: article
filename: fparith.bib
label: Hill:1986:DDS
title: Design decisions in SPUR
journal: j-COMPUTER
volume: 19
number: 11
pages: 8--22
month: nov
monthnumber: 11
year: 1986
CODEN: CPTRB4
ISSN: 0018-9162 (print), 1558-0814 (electronic) OR 00189162 (print), 15580814 (electronic)
ISSNL: 0018-9162 OR 00189162
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: Computer
acknowledgement: ack-nhfb
affiliation: University of California, Berkeley
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2
key: C.0.B RISC
reviewer: P. C. Patton
rawtitle: Design decisions in {SPUR}
author:
Mark Hill and Susan Eggers and Jim Larus and George Taylor and Glenn Adams and B. K. Bose and Garth Gibson and Paul Hansen and Jon Keller and Shing Kong and Corinna Lee and Daebum Lee and Joan Pendleton and Scott Ritchie and David Wood and Ben Zorn and Paul Hilfinger and Dave Hodges and Randy Katz and John Ousterhout and Dave Patterson

subject:
C. Computer Systems Organization; C.1 PROCESSOR ARCHITECTURES; C. Computer Systems Organization; C.2 COMPUTER-COMMUNICATION NETWORKS; D. Software; D.4 OPERATING SYSTEMS; C. Computer Systems Organization; C.0 GENERAL; D. Software; D.3 PROGRAMMING LANGUAGES; B. Hardware; B.3 MEMORY STRUCTURES; D. Software; D.3 PROGRAMMING LANGUAGES

rawauthor:
Mark Hill and Susan Eggers and Jim Larus and George Taylor and Glenn Adams and B. K. Bose and Garth Gibson and Paul Hansen and Jon Keller and Shing Kong and Corinna Lee and Daebum Lee and Joan Pendleton and Scott Ritchie and David Wood and Ben Zorn and Paul Hilfinger and Dave Hodges and Randy Katz and John Ousterhout and Dave Patterson

entry:
@Article{Hill:1986:DDS,
  author =       "Mark Hill and Susan Eggers and Jim Larus and George
                 Taylor and Glenn Adams and B. K. Bose and Garth Gibson
                 and Paul Hansen and Jon Keller and Shing Kong and
                 Corinna Lee and Daebum Lee and Joan Pendleton and Scott
                 Ritchie and David Wood and Ben Zorn and Paul Hilfinger
                 and Dave Hodges and Randy Katz and John Ousterhout and
                 Dave Patterson",
  key =          "C.0.B RISC",
  title =        "Design decisions in {SPUR}",
  journal =      j-COMPUTER,
  volume =       "19",
  number =       "11",
  pages =        "8--22",
  month =        nov,
  year =         "1986",
  CODEN =        "CPTRB4",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  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 =  "University of California, Berkeley",
  bibno =        "9486",
  catcode =      "C.1.2; C.2.4; D.4.3; C.0; D.3.0; B.3.2; D.3.2",
  content =      "SPUR (Symbolic Processing Using RISCs) is a
                 multiprocessor workstation under development at the
                 University of California at Berkeley for parallel
                 processing research. Its development is part of a
                 long-term effort to study hardware and software issues
                 in multiprocessing, in general, and parallel processing
                 in LISP, in particular. This paper concentrates on the
                 initial architectural research and development of SPUR.
                 A SPUR processor is a general-purpose RISC processor
                 that provides support for Common LISP and IEEE
                 floating-point. A processor is implemented on a single
                 board with about 200 standard chips and three custom
                 two-micron CMOS chips: the cache controller, the CPU,
                 and the floating-point coprocessor. The chip that
                 manages the cache handles cache access by the CPU,
                 performing address translation, accessing shared memory
                 over the SPUR bus, and maintaining cache consistency.
                 Operating systems researchers are investigating network
                 file systems, network page servers, the effects of
                 large physical memories on virtual memory
                 implementations, and workload distribution. Programming
                 languages researchers ar",
  CRclass =      "C.1.2 Multiple Data Stream Architectures
                 (Multiprocessors); C.1.2 Parallel processors; C.2.4
                 Distributed Systems; D.4.3 File Systems Management; C.0
                 Instruction set design; D.3.0 General; B.3.2 Design
                 Styles; B.3.2 Cache memories; D.3.2 Language
                 Classifications; D.3.2 LIS-11",
  CRnumber =     "8710-0848",
  descriptor =   "Computer Systems Organization, PROCESSOR
                 ARCHITECTURES, Multiple Data Stream Architectures
                 (Multiprocessors), Parallel processors; Computer
                 Systems Organization, COMPUTER-COMMUNICATION NETWORKS,
                 Distributed Systems; Software, OPERATING SYSTEMS, File
                 Systems Management; Computer Systems Organization,
                 GENERAL, Instruction set design; Software, PROGRAMMING
                 LANGUAGES, General; Hardware, MEMORY STRUCTURES, Design
                 Styles, Cache memories; Software, PROGRAMMING
                 LANGUAGES, Language Classifications, LIS-11",
  fjournal =     "Computer",
  genterm =      "DESIGN; HUMAN FACTORS; PERFORMANCE; EXPERIMENTATION",
  guideno =      "1986-03762",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
  journalabbrev = "Computer",
  reviewer =     "P. C. Patton",
  subject =      "C. Computer Systems Organization; C.1 PROCESSOR
                 ARCHITECTURES; C. Computer Systems Organization; C.2
                 COMPUTER-COMMUNICATION NETWORKS; D. Software; D.4
                 OPERATING SYSTEMS; C. Computer Systems Organization;
                 C.0 GENERAL; D. Software; D.3 PROGRAMMING LANGUAGES; B.
                 Hardware; B.3 MEMORY STRUCTURES; D. Software; D.3
                 PROGRAMMING LANGUAGES",
}


bibtype: article
filename: fparith.bib
label: Hongyuan:1986:CSL
author: Wang Hongyuan and S. C. Lee
title: Comments on ``Sign / Logarithm Arithmetic for FFT Implementation''
journal: j-IEEE-TRANS-COMPUT
volume: C-35
number: 5
pages: 482--484
month: may
monthnumber: 5
year: 1986
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1986.1676792
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 9 14:09:48 MDT 2011
bibtimestamp: 2011.07.09 14:09:48 MDT
note: See cite Swartzlander:1983:SLA.
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676792
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Wang Hongyuan and S. C. Lee
rawnote: See \cite{Swartzlander:1983:SLA}.
rawtitle: Comments on {``Sign\slash Logarithm Arithmetic for FFT Implementation''}
entry:
@Article{Hongyuan:1986:CSL,
  author =       "Wang Hongyuan and S. C. Lee",
  title =        "Comments on {``Sign\slash Logarithm Arithmetic for FFT
                 Implementation''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-35",
  number =       "5",
  pages =        "482--484",
  month =        may,
  year =         "1986",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1986.1676792",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 14:09:48 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  note =         "See \cite{Swartzlander:1983:SLA}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676792",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Hull:1986:VPE
author: T. E. Hull and A. Abrham
title: Variable Precision Exponential Function
journal: j-TOMS
volume: 12
number: 2
pages: 79--91
month: jun
monthnumber: 6
year: 1986
CODEN: ACMSCU
DOI: https://doi.org/10.1145/6497.6498
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 65D15 (65D20)
MRnumber: 863 786
bibdate: Sun Sep 04 21:17:51 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.04 21:17:51 ???
URL: http://www.acm.org/pubs/citations/journals/toms/1986-12-2/p79-hull/
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms; decimal floating-point arithmetic; theory; verification
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: T. E. Hull and A. Abrham
rawtitle: Variable Precision Exponential Function
abstract:
The exponential function presented here returns a result which differs from $ e^x $ by less than one unit in the last place, for any representable value of $x$ which is not too close to values for which $ e^x $ would overflow or underflow. (For values of $x$ which are not within this range, an error condition is raised.) It is a ``variable precision'' function in that it returns a $p$-digit approximation for a $p$-digit argument, for any $ p > 0 $ ($p$-digit means $p$-decimal-digit). The program and analysis are valid for all $ p > 0 $, but current implementations place a restriction on $p$. The program is presented in a Pascal-like programming language called Numerical Turing which has special facilities for scientific computing, including precision control, directed roundings, and built-in functions for getting and setting exponents.

subject:
bf G.1.2: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation. bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Verification.

rawabstract:
The exponential function presented here returns a result which differs from $ e^x $ by less than one unit in the last place, for any representable value of $x$ which is not too close to values for which $ e^x $ would overflow or underflow. (For values of $x$ which are not within this range, an error condition is raised.) It is a ``variable precision'' function in that it returns a $p$-digit approximation for a $p$-digit argument, for any $ p > 0 $ ($p$-digit means $p$-decimal-digit). The program and analysis are valid for all $ p > 0 $, but current implementations place a restriction on $p$. The program is presented in a Pascal-like programming language called Numerical Turing which has special facilities for scientific computing, including precision control, directed roundings, and built-in functions for getting and setting exponents.

entry:
@Article{Hull:1986:VPE,
  author =       "T. E. Hull and A. Abrham",
  title =        "Variable Precision Exponential Function",
  journal =      j-TOMS,
  volume =       "12",
  number =       "2",
  pages =        "79--91",
  month =        jun,
  year =         "1986",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/6497.6498",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D15 (65D20)",
  MRnumber =     "863 786",
  bibdate =      "Sun Sep 04 21:17:51 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1986-12-2/p79-hull/",
  abstract =     "The exponential function presented here returns a
                 result which differs from $ e^x $ by less than one unit
                 in the last place, for any representable value of $x$
                 which is not too close to values for which $ e^x $
                 would overflow or underflow. (For values of $x$ which
                 are not within this range, an error condition is
                 raised.) It is a ``variable precision'' function in
                 that it returns a $p$-digit approximation for a
                 $p$-digit argument, for any $ p > 0 $ ($p$-digit means
                 $p$-decimal-digit). The program and analysis are valid
                 for all $ p > 0 $, but current implementations place a
                 restriction on $p$. The program is presented in a
                 Pascal-like programming language called Numerical
                 Turing which has special facilities for scientific
                 computing, including precision control, directed
                 roundings, and built-in functions for getting and
                 setting exponents.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; decimal floating-point arithmetic; theory;
                 verification",
  review =       "ACM CR 8702-0091",
  subject =      "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Certification and testing. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Verification.",
}


bibtype: techreport
filename: fparith.bib
label: IBM:1986:IHA
author: IBM Corporation
title: IBM High-Accuracy Arithmetic Subroutine Library (ACRITH)
type: Technical Report
number: GC 33-6163-02, SC 33-6164-02, GX 33-9009-02
institution: pub-IBM
address: pub-IBM:adr
edition: Third
pages: 79--91
year: 1986
bibdate: Thu Jan 21 17:27:09 2016
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2016.01.21 17:27:09 ???
TOC: 1. General Information Manual 2. Program Description and User's Guide 3. Reference Summary
acknowledgement: ack-nhfb
rawauthor: {IBM Corporation}
rawtitle: {IBM High-Accuracy Arithmetic Subroutine Library (ACRITH)}
rawTOC: 1. General Information Manual \\ 2. Program Description and User's Guide \\ 3. Reference Summary
entry:
@TechReport{IBM:1986:IHA,
  author =       "{IBM Corporation}",
  title =        "{IBM High-Accuracy Arithmetic Subroutine Library
                 (ACRITH)}",
  type =         "Technical Report",
  number =       "GC 33-6163-02, SC 33-6164-02, GX 33-9009-02",
  institution =  pub-IBM,
  address =      pub-IBM:adr,
  edition =      "Third",
  year =         "1986",
  bibdate =      "Thu Jan 21 17:27:09 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  tableofcontents = "1. General Information Manual \\
                 2. Program Description and User's Guide \\
                 3. Reference Summary",
}


bibtype: book
filename: fparith.bib
label: IBM:1986:IRP
author: IBM
title: IBM RT Personal Computer Technology, publication SA23-1057
publisher: pub-IBM
address: pub-IBM:adr
pages: 79--91
year: 1986
bibdate: Sat Oct 28 08:16:44 2000
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2000.10.28 08:16:44 ???
acknowledgement: ack-nhfb
rawauthor: {IBM}
rawtitle: {IBM RT} Personal Computer Technology, publication {SA23-1057}
entry:
@Book{IBM:1986:IRP,
  author =       "{IBM}",
  title =        "{IBM RT} Personal Computer Technology, publication
                 {SA23-1057}",
  publisher =    pub-IBM,
  address =      pub-IBM:adr,
  year =         "1986",
  bibdate =      "Sat Oct 28 08:16:44 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Iiguni:1986:REA
author: Y. Iiguni and H. Sakai and H. Tokumaru
booktitle: IEEE International Conference on Acoustics, Speech, and Signal Processing: ICASSP '86
title: Rounding error analysis of the triangular lattice and escalator algorithms
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 2119--2122
year: 1986
bibdate: Sat Jul 16 11:25:04 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:04 MDT
acknowledgement: ack-nhfb
rawauthor: Y. Iiguni and H. Sakai and H. Tokumaru
rawbooktitle: {IEEE} International Conference on Acoustics, Speech, and Signal Processing: {ICASSP '86}
rawtitle: Rounding error analysis of the triangular lattice and escalator algorithms
entry:
@InProceedings{Iiguni:1986:REA,
  author =       "Y. Iiguni and H. Sakai and H. Tokumaru",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing: {ICASSP '86}",
  title =        "Rounding error analysis of the triangular lattice and
                 escalator algorithms",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "2119--2122",
  year =         "1986",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:04 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "In this paper, first, the normalized Triangular
                 Lattice and Escalator algorithms for recursive least
                 squares estimation are presented. Next, roundoff errors
                 of both algorithms in fixed point arithmetic are
                 analyzed and compared. Expressions are \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Jansen:1986:HAA
author: Paul Jansen and Peter Weidner
title: High-Accuracy Arithmetic Software --- Some Tests of the ACRITH Problem-Solving Routines
journal: j-TOMS
volume: 12
number: 1
pages: 62--70
month: mar
monthnumber: 3
year: 1986
CODEN: ACMSCU
DOI: https://doi.org/10.1145/5960.5962
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 65Dxx
MRnumber: 868 096
bibdate: Sat Aug 13 17:26:53 MDT 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.08.13 17:26:53 MDT
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms; floating-point testing
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Paul Jansen and Peter Weidner
rawtitle: High-Accuracy Arithmetic Software --- Some Tests of the {ACRITH} Problem-Solving Routines
URL:
http://doi.acm.org/10.1145/5960.5962; http://www.acm.org/pubs/citations/journals/toms/1986-12-1/p62-jansen/

abstract:
The program package ACRITH (High-Accuracy Arithmetic Subroutine Library) provides FORTRAN subroutines for the solution of several standard mathematical problems. The routines use floating point operations with extended precision and interval arithmetic and are designated especially for the solution of ill-conditioned problems. Test results for most of the routines are presented with emphasis on the practical usability of the package. It turns out that not all routines are of equal high quality and reliability; in the documentation, hints to the implemented numerical algorithms are completely missing, and the error messages are not always concise. Some possible alternatives like symbolic algebra systems or multiple precision packages are mentioned.

subject:
bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, ACRITH. bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. bf I.1.3: Computing Methodologies, ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE. bf D.3.2: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Reliability and robustness.

rawabstract:
The program package ACRITH (High-Accuracy Arithmetic Subroutine Library) provides FORTRAN subroutines for the solution of several standard mathematical problems. The routines use floating point operations with extended precision and interval arithmetic and are designated especially for the solution of ill-conditioned problems. Test results for most of the routines are presented with emphasis on the practical usability of the package. It turns out that not all routines are of equal high quality and reliability; in the documentation, hints to the implemented numerical algorithms are completely missing, and the error messages are not always concise. Some possible alternatives like symbolic algebra systems or multiple precision packages are mentioned.

entry:
@Article{Jansen:1986:HAA,
  author =       "Paul Jansen and Peter Weidner",
  title =        "High-Accuracy Arithmetic Software --- Some Tests of
                 the {ACRITH} Problem-Solving Routines",
  journal =      j-TOMS,
  volume =       "12",
  number =       "1",
  pages =        "62--70",
  month =        mar,
  year =         "1986",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/5960.5962",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65Dxx",
  MRnumber =     "868 096",
  bibdate =      "Sat Aug 13 17:26:53 MDT 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://doi.acm.org/10.1145/5960.5962;
                 http://www.acm.org/pubs/citations/journals/toms/1986-12-1/p62-jansen/",
  abstract =     "The program package ACRITH (High-Accuracy Arithmetic
                 Subroutine Library) provides FORTRAN subroutines for
                 the solution of several standard mathematical problems.
                 The routines use floating point operations with
                 extended precision and interval arithmetic and are
                 designated especially for the solution of
                 ill-conditioned problems. Test results for most of the
                 routines are presented with emphasis on the practical
                 usability of the package. It turns out that not all
                 routines are of equal high quality and reliability; in
                 the documentation, hints to the implemented numerical
                 algorithms are completely missing, and the error
                 messages are not always concise. Some possible
                 alternatives like symbolic algebra systems or multiple
                 precision packages are mentioned.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; floating-point testing",
  review =       "ACM CR 8612-1110",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, ACRITH. {\bf G.1.0}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Numerical
                 algorithms. {\bf I.1.3}: Computing Methodologies,
                 ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
                 {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Reliability and
                 robustness.",
}


bibtype: inproceedings
filename: fparith.bib
label: Johnson:1986:TRH
author: T. Johnson and G. Clark
crossref: IEEE:1986:III
volume: 11
pages: 2623--2626
month: apr
monthnumber: 4
year: 1986
CODEN: ITCOB4
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
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: T. Johnson and G. Clark
title:
Techniques for realization of high-speed recursive digital filters using residue number system arithmetic

rawtitle:
Techniques for realization of high-speed recursive digital filters using residue number system arithmetic

entry:
@InProceedings{Johnson:1986:TRH,
  author =       "T. Johnson and G. Clark",
  title =        "Techniques for realization of high-speed recursive
                 digital filters using residue number system
                 arithmetic",
  crossref =     "IEEE:1986:III",
  volume =       "11",
  pages =        "2623--2626",
  month =        apr,
  year =         "1986",
  CODEN =        "ITCOB4",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  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 =      "Residue-number-arithmetic digital filters offer major
                 cost and speed advantages over binary-arithmetic
                 digital filters but suffer one major drawback. The
                 filter coefficients must remain constant because
                 efficient means of updating by fractional arithmetic in
                 residue number systems involves time consuming
                 overhead. To maintain high speed in the system the
                 choices are to use RNS in the adders and multipliers
                 with scaling done in ROM, to do RNS multiplies and
                 additions and scale as part of CRT conversion at the
                 output, or to apply a new fractional NTT interpretation
                 of multiplier output and use RNS throughout. These
                 methods are discussed in this paper.",
}


bibtype: inproceedings
filename: fparith.bib
label: Kabal:1986:PFP
author: P. Kabal and B. Sayar
booktitle: IEEE International Conference on Acoustics, Speech, and Signal Processing: ICASSP '86
title: Performance of fixed-point FFT's: Rounding and scaling considerations
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 221--224
year: 1986
bibdate: Sat Jul 16 11:25:04 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:04 MDT
acknowledgement: ack-nhfb
rawauthor: P. Kabal and B. Sayar
rawbooktitle: {IEEE} International Conference on Acoustics, Speech, and Signal Processing: {ICASSP '86}
rawtitle: Performance of fixed-point {FFT}'s: Rounding and scaling considerations
entry:
@InProceedings{Kabal:1986:PFP,
  author =       "P. Kabal and B. Sayar",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing: {ICASSP '86}",
  title =        "Performance of fixed-point {FFT}'s: Rounding and
                 scaling considerations",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "221--224",
  year =         "1986",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:04 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "The calculation of the discrete Fourier transform
                 using a fast Fourier transform (FFT) algorithm with
                 fixed-point arithmetic is considered. The input data is
                 scaled to prevent overflow and to maintain accuracy.
                 The implementation uses 16-bit fixed- \ldots{}",
}


bibtype: techreport
filename: fparith.bib
label: Kahan:1986:RAF
author: W. Kahan
title: Rational Arithmetic in Floating-Point
type: Technical Report
number: PAM-343
institution: inst-BERKELEY-CPAM
address: inst-BERKELEY-CPAM:adr
pages: 8
month: sep
monthnumber: 9
year: 1986
bibdate: Sun Dec 18 15:33:08 GMT 1994
bibtimestamp: 1994.12.18 15:33:08 GMT
acknowledgement: ack-nhfb
rawauthor: W. Kahan
rawtitle: Rational Arithmetic in Floating-Point
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@TechReport{Kahan:1986:RAF,
  author =       "W. Kahan",
  title =        "Rational Arithmetic in Floating-Point",
  type =         "Technical Report",
  number =       "PAM-343",
  institution =  inst-BERKELEY-CPAM,
  address =      inst-BERKELEY-CPAM:adr,
  pages =        "8",
  month =        sep,
  year =         "1986",
  bibdate =      "Sun Dec 18 15:33:08 GMT 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: fparith.bib
label: Kreithen:1986:FPC
author: Daniel E. Kreithen
title: Floating point calculation speeds for the image processing workstation
institution: Brown University, Division of Engineering
address: Providence, RI, USA
pages: 23
year: 1986
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: Daniel E. Kreithen
rawtitle: Floating point calculation speeds for the image processing workstation
entry:
@TechReport{Kreithen:1986:FPC,
  author =       "Daniel E. Kreithen",
  title =        "Floating point calculation speeds for the image
                 processing workstation",
  institution =  "Brown University, Division of Engineering",
  address =      "Providence, RI, USA",
  pages =        "23",
  year =         "1986",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Krishnan:1986:CCN
author: R. Krishnan and G. Jullien and W. Miller
booktitle: IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP '86
title: Computation of complex number theoretic transforms using quadratic residue number systems
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 233--236
year: 1986
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 and G. Jullien and W. Miller
rawbooktitle: {IEEE} International Conference on Acoustics, Speech, and Signal Processing, {ICASSP '86}
rawtitle: Computation of complex number theoretic transforms using quadratic residue number systems
entry:
@InProceedings{Krishnan:1986:CCN,
  author =       "R. Krishnan and G. Jullien and W. Miller",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing, {ICASSP '86}",
  title =        "Computation of complex number theoretic transforms
                 using quadratic residue number systems",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "233--236",
  year =         "1986",
  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 =      "Very recently, the Quadratic Residue Number System
                 (QRNS) has been introduced [4,5]. The QRNS is obtained
                 from a mapping of Gaussian integers over a finite ring
                 to a ring of conjugate elements. The conjugate ring has
                 the remarkable property that \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Krishnan:1986:CDS
author: R. Krishnan and G. Jullien and W. Miller
title: Complex digital signal processing using quadratic residue number systems
volume: 34
number: 1
pages: 166--177
month: feb
monthnumber: 2
year: 1986
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
URL: https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=26196
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: R. Krishnan and G. Jullien and W. Miller
rawtitle: Complex digital signal processing using quadratic residue number systems
journal:
Acoustics, Speech, and Signal Processing [see also IEEE Transactions on Signal Processing], IEEE Transactions on

entry:
@Article{Krishnan:1986:CDS,
  author =       "R. Krishnan and G. Jullien and W. Miller",
  title =        "Complex digital signal processing using quadratic
                 residue number systems",
  journal =      "Acoustics, Speech, and Signal Processing [see also
                 IEEE Transactions on Signal Processing], IEEE
                 Transactions on",
  volume =       "34",
  number =       "1",
  pages =        "166--177",
  month =        feb,
  year =         "1986",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=26196",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Recently, the quadratic residue number system (QRNS)
                 has been introduced [6], [7] which allows the
                 multiplication of complex integers with two real
                 multiplications. The restriction is that the number
                 system has either all prime moduli of the form 4K
                 \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Krishnan:1986:ICN
author: R. Krishnan and G. Jullien and W. Miller
title: Implementation of complex number theoretic transforms using quadratic residue number systems
journal: j-IEEE-TRANS-CIRCUITS-SYST
volume: 33
number: 8
pages: 759--766
month: aug
monthnumber: 8
year: 1986
CODEN: ICSYBT
DOI: https://doi.org/10.1049/el:19850252
ISSN: 0098-4094 (print), 1558-1276 (electronic) OR 00984094 (print), 15581276 (electronic)
ISSNL: 0098-4094 OR 00984094
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
URL: https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23583
fjournal: IEEE Transactions on Circuits and Systems
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: R. Krishnan and G. Jullien and W. Miller
rawtitle: Implementation of complex number theoretic transforms using quadratic residue number systems
entry:
@Article{Krishnan:1986:ICN,
  author =       "R. Krishnan and G. Jullien and W. Miller",
  title =        "Implementation of complex number theoretic transforms
                 using quadratic residue number systems",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "33",
  number =       "8",
  pages =        "759--766",
  month =        aug,
  year =         "1986",
  CODEN =        "ICSYBT",
  DOI =          "https://doi.org/10.1049/el:19850252",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23583",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  keywords =     "residue arithmetic; residue number system",
  summary =      "Very recently, the Quadratic Residue Number System
                 (QRNS) has been introduced [6], [7]. The QRNS is
                 obtained from a mapping of Gaussian integers over a
                 finite ring to a ring of conjugate elements. The
                 conjugate ring has the remarkable property that
                 \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Krishnan:1986:MQR
author: R. Krishnan and G. Jullien and W. Miller
title: The modified quadratic residue number system (MQRNS) for complex high-speed signal processing
journal: j-IEEE-TRANS-CIRCUITS-SYST
volume: 33
number: 3
pages: 325--327
month: mar
monthnumber: 3
year: 1986
CODEN: ICSYBT
DOI: https://doi.org/10.1049/el:19850252
ISSN: 0098-4094 (print), 1558-1276 (electronic) OR 00984094 (print), 15581276 (electronic)
ISSNL: 0098-4094 OR 00984094
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
URL: https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23578
fjournal: IEEE Transactions on Circuits and Systems
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: R. Krishnan and G. Jullien and W. Miller
rawtitle: The modified quadratic residue number system ({MQRNS}) for complex high-speed signal processing
entry:
@Article{Krishnan:1986:MQR,
  author =       "R. Krishnan and G. Jullien and W. Miller",
  title =        "The modified quadratic residue number system ({MQRNS})
                 for complex high-speed signal processing",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "33",
  number =       "3",
  pages =        "325--327",
  month =        mar,
  year =         "1986",
  CODEN =        "ICSYBT",
  DOI =          "https://doi.org/10.1049/el:19850252",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23578",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  keywords =     "residue arithmetic; residue number system",
  summary =      "Recently, the Quadratic Residue Number System,(QRNS)
                 has been introduced [5], [6], which allows the
                 multiplication of complex integers with two real
                 multiplications. The restriction is that this special
                 residue number system has all moduli with \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Kulisch:1986:ADC
author: Ulrich W. Kulisch and Willard L. Miranker
title: The Arithmetic of the Digital Computer: a New Approach
journal: j-SIAM-REVIEW
volume: 28
number: 1
pages: 1--40
month: mar
monthnumber: 3
year: 1986
CODEN: SIREAD
DOI: https://doi.org/10.1137/1028001
ISSN: 0036-1445 (print), 1095-7200 (electronic) OR 00361445 (print), 10957200 (electronic)
ISSNL: 0036-1445 OR 00361445
MRclass: 65G10 (68M15)
MRnumber: 87e:65030
MRreviewer: G. Blanch
bibdate: Sat Mar 29 09:54:03 MDT 2014
bibtimestamp: 2014.03.29 09:54:03 MDT
fjournal: SIAM Review
acknowledgement: ack-nhfb
affiliationaddress: Univ of California, Computer Science Dep, Santa Barbara, CA, USA
journalURL: http://epubs.siam.org/sirev
journalabr: SIAM Rev
onlinedate: March 1986
rawauthor: Ulrich W. Kulisch and Willard L. Miranker
rawtitle: The Arithmetic of the Digital Computer: a New Approach
bibsource:
Compendex database; http://epubs.siam.org/toc/siread/28/1; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib

abstract:
A new approach to the arithmetic of the digital computer is surveyed. The methodology for defining and implementing floating-point arithmetic is described. Shortcomings of elementary floating-point arithmetic are revealed through sample problems. The development of automatic computation with emphasis on the user control of errors is reviewed. The limitations of conventional rule-of-thumb procedures for error control in scientific computation are demonstrated by means of examples. Computer arithmetic is extended so that the arithmetic operations in the linear spaces and their interval correspondents which are most commonly used in computation can be performed with maximum accuracy on digital computers. A new fundamental computer operation, the scalar product, is introduced to develop this advanced computer arithmetic.

keywords:
accurate floating-point summation; computer arithmetic; computer metatheory; computer programming languages; computers, digital; floating-point arithmetic

rawabstract:
A new approach to the arithmetic of the digital computer is surveyed. The methodology for defining and implementing floating-point arithmetic is described. Shortcomings of elementary floating-point arithmetic are revealed through sample problems. The development of automatic computation with emphasis on the user control of errors is reviewed. The limitations of conventional rule-of-thumb procedures for error control in scientific computation are demonstrated by means of examples. Computer arithmetic is extended so that the arithmetic operations in the linear spaces and their interval correspondents which are most commonly used in computation can be performed with maximum accuracy on digital computers. A new fundamental computer operation, the scalar product, is introduced to develop this advanced computer arithmetic.

entry:
@Article{Kulisch:1986:ADC,
  author =       "Ulrich W. Kulisch and Willard L. Miranker",
  title =        "The Arithmetic of the Digital Computer: a New
                 Approach",
  journal =      j-SIAM-REVIEW,
  volume =       "28",
  number =       "1",
  pages =        "1--40",
  month =        mar,
  year =         "1986",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1028001",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  MRclass =      "65G10 (68M15)",
  MRnumber =     "87e:65030",
  MRreviewer =   "G. Blanch",
  bibdate =      "Sat Mar 29 09:54:03 MDT 2014",
  bibsource =    "Compendex database;
                 http://epubs.siam.org/toc/siread/28/1;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  abstract =     "A new approach to the arithmetic of the digital
                 computer is surveyed. The methodology for defining and
                 implementing floating-point arithmetic is described.
                 Shortcomings of elementary floating-point arithmetic
                 are revealed through sample problems. The development
                 of automatic computation with emphasis on the user
                 control of errors is reviewed. The limitations of
                 conventional rule-of-thumb procedures for error control
                 in scientific computation are demonstrated by means of
                 examples. Computer arithmetic is extended so that the
                 arithmetic operations in the linear spaces and their
                 interval correspondents which are most commonly used in
                 computation can be performed with maximum accuracy on
                 digital computers. A new fundamental computer
                 operation, the scalar product, is introduced to develop
                 this advanced computer arithmetic.",
  acknowledgement = ack-nhfb,
  affiliationaddress = "Univ of California, Computer Science Dep, Santa
                 Barbara, CA, USA",
  classification = "723",
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  journalabr =   "SIAM Rev",
  keywords =     "accurate floating-point summation; computer
                 arithmetic; computer metatheory; computer programming
                 languages; computers, digital; floating-point
                 arithmetic",
  onlinedate =   "March 1986",
  referred =     "[Layn91a].",
}


bibtype: misc
filename: fparith.bib
label: Kulisch:1986:CGS
author: Ulrich Kulisch
title: Circuitry for generating scalar products and sums of floating point numbers with maximum accuracy
pages: 1--40
day: 11
month: nov
monthnumber: 11
year: 1986
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/4622650/fulltext.html
acknowledgement: ack-nhfb
howpublished: US Patent 4622650
rawauthor: Ulrich Kulisch
rawtitle: Circuitry for generating scalar products and sums of floating point numbers with maximum accuracy
abstract:
Circuitry for generating scalar products and sums of floating point numbers with maximum accuracy and circuitry and a method for electronic computers by which scalar products of floating point numbers of the type pi, qi, ES(b,l,e1,e2) are summed with full precision in a fixed point representation by means of a summing unit (ALU) and one or more accumulator registers (ARC1, ARC2) with cells (Ai, j) for storing of codes of a base b having a length (2l + 2 e1 + 2e2) for fixed point representation and certain overflow positions. By control means (SHR, E, Contr) the mantissas of products are delivered depending on the value of the respective exponents into the summing unit (ALU). By control means (RD, Contro), rounding operations demanded by the higher level computer are performed, and a rounded floating point number and overflow (OF) and underflow (UF) criteria are delivered. Parallel, serial and word organized summing units (ALU) and accumulator registers (ACR) are usable and in another embodiment, the multiplication of the factors (pi, qi) is performed using a table of multiples store.

rawabstract:
Circuitry for generating scalar products and sums of floating point numbers with maximum accuracy and circuitry and a method for electronic computers by which scalar products of floating point numbers of the type pi, qi, ES(b,l,e1,e2) are summed with full precision in a fixed point representation by means of a summing unit (ALU) and one or more accumulator registers (ARC1, ARC2) with cells (Ai, j) for storing of codes of a base b having a length (2l + 2 e1 + 2e2) for fixed point representation and certain overflow positions. By control means (SHR, E, Contr) the mantissas of products are delivered depending on the value of the respective exponents into the summing unit (ALU). By control means (RD, Contro), rounding operations demanded by the higher level computer are performed, and a rounded floating point number and overflow (OF) and underflow (UF) criteria are delivered. Parallel, serial and word organized summing units (ALU) and accumulator registers (ACR) are usable and in another embodiment, the multiplication of the factors (pi, qi) is performed using a table of multiples store.

entry:
@Misc{Kulisch:1986:CGS,
  author =       "Ulrich Kulisch",
  title =        "Circuitry for generating scalar products and sums of
                 floating point numbers with maximum accuracy",
  howpublished = "US Patent 4622650",
  day =          "11",
  month =        nov,
  year =         "1986",
  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/4622650/fulltext.html",
  abstract =     "Circuitry for generating scalar products and sums of
                 floating point numbers with maximum accuracy and
                 circuitry and a method for electronic computers by
                 which scalar products of floating point numbers of the
                 type pi, qi, ES(b,l,e1,e2) are summed with full
                 precision in a fixed point representation by means of a
                 summing unit (ALU) and one or more accumulator
                 registers (ARC1, ARC2) with cells (Ai, j) for storing
                 of codes of a base b having a length (2l + 2 e1 + 2e2)
                 for fixed point representation and certain overflow
                 positions. By control means (SHR, E, Contr) the
                 mantissas of products are delivered depending on the
                 value of the respective exponents into the summing unit
                 (ALU). By control means (RD, Contro), rounding
                 operations demanded by the higher level computer are
                 performed, and a rounded floating point number and
                 overflow (OF) and underflow (UF) criteria are
                 delivered. Parallel, serial and word organized summing
                 units (ALU) and accumulator registers (ACR) are usable
                 and in another embodiment, the multiplication of the
                 factors (pi, qi) is performed using a table of
                 multiples store.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Lorang:1986:SD
author: O. Lorang
title: Schnelle Division toenglish Fast Division endtoenglish
journal: j-ELECTRONIK
volume: 22
pages: 167--168
year: 1986
CODEN: EKRKAR
ISSN: 0013-5658 OR 00135658
bibdate: Fri Sep 16 16:30:40 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.16 16:30:40 ???
fjournal: Elektronik
acknowledgement: ack-nj
rawauthor: O. Lorang
rawtitle: {Schnelle Division} \toenglish {Fast Division} \endtoenglish
entry:
@Article{Lorang:1986:SD,
  author =       "O. Lorang",
  title =        "{Schnelle Division} \toenglish {Fast Division}
                 \endtoenglish",
  journal =      j-ELECTRONIK,
  volume =       "22",
  pages =        "167--168",
  year =         "1986",
  CODEN =        "EKRKAR",
  ISSN =         "0013-5658",
  bibdate =      "Fri Sep 16 16:30:40 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 =     "Elektronik",
}


bibtype: article
filename: fparith.bib
label: MacIntyre:1986:UOS
author: Ferren MacIntyre and Thomas Dowling
title: User-oriented suggestions for floating-point and complex-arithmetic Forth standard extensions
journal: j-J-FORTH-APPL-RES
volume: 3
number: 4
pages: 65--84
year: 1986
CODEN: JFAREL
ISSN: 0738-2022 OR 07382022
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: Journal of FORTH Application and Research
acknowledgement: ack-nhfb
rawauthor: Ferren MacIntyre and Thomas Dowling
rawtitle: User-oriented suggestions for floating-point and complex-arithmetic {Forth} standard extensions
subject:
D. Software; D.3 PROGRAMMING LANGUAGES; D. Software; D.3 PROGRAMMING LANGUAGES; H. Information Systems; H.1 MODELS AND PRINCIPLES; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS

entry:
@Article{MacIntyre:1986:UOS,
  author =       "Ferren MacIntyre and Thomas Dowling",
  title =        "User-oriented suggestions for floating-point and
                 complex-arithmetic {Forth} standard extensions",
  journal =      j-J-FORTH-APPL-RES,
  volume =       "3",
  number =       "4",
  pages =        "65--84",
  year =         "1986",
  CODEN =        "JFAREL",
  ISSN =         "0738-2022",
  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 =        "11736",
  catcode =      "D.3.2; D.3.0; H.1.2; G.1.0",
  CRclass =      "D.3.2 Language Classifications; D.3.2 FORTH; D.3.0
                 General; D.3.0 Standards; H.1.2 User/Machine Systems;
                 H.1.2 Human factors; G.1.0 General; G.1.0 Computer
                 arithmetic",
  descriptor =   "Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTH; Software, PROGRAMMING
                 LANGUAGES, General, Standards; Information Systems,
                 MODELS AND PRINCIPLES, User/Machine Systems, Human
                 factors; Mathematics of Computing, NUMERICAL ANALYSIS,
                 General, Computer arithmetic",
  fjournal =     "Journal of FORTH Application and Research",
  genterm =      "LANGUAGES; THEORY; HUMAN FACTORS; STANDARDIZATION",
  guideno =      "1986-08466",
  journalabbrev = "J. FORTH Appl. Res.",
  subject =      "D. Software; D.3 PROGRAMMING LANGUAGES; D. Software;
                 D.3 PROGRAMMING LANGUAGES; H. Information Systems; H.1
                 MODELS AND PRINCIPLES; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS",
}


bibtype: article
filename: fparith.bib
label: Marrin:1986:MBF
author: K. Marrin
title: Microprocessor brings floating-point capability to 32-bit market
journal: j-COMP-DESIGN
volume: 25
number: 9
pages: 31--38
day: 1
month: may
monthnumber: 5
year: 1986
CODEN: CMPDAM
ISSN: 0010-4566 OR 00104566
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: Computer Design
subject: B. Hardware; B.7 INTEGRATED CIRCUITS
acknowledgement: ack-nhfb
rawauthor: K. Marrin
rawtitle: Microprocessor brings floating-point capability to 32-bit market
entry:
@Article{Marrin:1986:MBF,
  author =       "K. Marrin",
  title =        "Microprocessor brings floating-point capability to
                 32-bit market",
  journal =      j-COMP-DESIGN,
  volume =       "25",
  number =       "9",
  pages =        "31--38",
  day =          "1",
  month =        may,
  year =         "1986",
  CODEN =        "CMPDAM",
  ISSN =         "0010-4566",
  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 =        "20530",
  catcode =      "B.7.1",
  CRclass =      "B.7.1 Types and Design Styles; B.7.1 Advanced
                 technologies",
  descriptor =   "Hardware, INTEGRATED CIRCUITS, Types and Design
                 Styles, Advanced technologies",
  fjournal =     "Computer Design",
  genterm =      "DESIGN",
  guideno =      "1986-03960",
  journalabbrev = "Comput. Des.",
  subject =      "B. Hardware; B.7 INTEGRATED CIRCUITS",
}


bibtype: article
filename: fparith.bib
label: Marrin:1986:PBT
author: K. Marrin
title: Plug-in boards transform PCs into floating-point workstations
journal: j-COMP-DESIGN
volume: 25
number: 4
pages: 31--34
day: 15
month: feb
monthnumber: 2
year: 1986
CODEN: CMPDAM
ISSN: 0010-4566 OR 00104566
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: Computer Design
acknowledgement: ack-nhfb
rawauthor: K. Marrin
rawtitle: Plug-in boards transform {PCs} into floating-point workstations
subject:
K. Computing Milieux; K.8 PERSONAL COMPUTING; C. Computer Systems Organization; C.1 PROCESSOR ARCHITECTURES; C. Computer Systems Organization; C.4 PERFORMANCE OF SYSTEMS

entry:
@Article{Marrin:1986:PBT,
  author =       "K. Marrin",
  title =        "Plug-in boards transform {PCs} into floating-point
                 workstations",
  journal =      j-COMP-DESIGN,
  volume =       "25",
  number =       "4",
  pages =        "31--34",
  day =          "15",
  month =        feb,
  year =         "1986",
  CODEN =        "CMPDAM",
  ISSN =         "0010-4566",
  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 =        "19192",
  catcode =      "K.8; C.1.2; C.4",
  CRclass =      "C.1.2 Multiple Data Stream Architectures
                 (Multiprocessors); C.1.2 Array and vector processors",
  descriptor =   "Computing Milieux, PERSONAL COMPUTING; Computer
                 Systems Organization, PROCESSOR ARCHITECTURES, Multiple
                 Data Stream Architectures (Multiprocessors), Array and
                 vector processors; Computer Systems Organization,
                 PERFORMANCE OF SYSTEMS",
  fjournal =     "Computer Design",
  genterm =      "DESIGN; PERFORMANCE; MEASUREMENT",
  guideno =      "1986-03913",
  journalabbrev = "Comput. Des.",
  subject =      "K. Computing Milieux; K.8 PERSONAL COMPUTING; C.
                 Computer Systems Organization; C.1 PROCESSOR
                 ARCHITECTURES; C. Computer Systems Organization; C.4
                 PERFORMANCE OF SYSTEMS",
}


bibtype: inproceedings
filename: fparith.bib
label: Melear:1986:HSM
author: C. Melear and D. Tietjen
title: High Speed Math Using a Floating Point Coprocessor
crossref: Mini-Micro:1986:EMM
pages: 14/3/1--8
year: 1986
bibdate: Wed Sep 7 22:31:45 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 22:31:45 ???
acknowledgement: ack-nj
rawauthor: C. Melear and D. Tietjen
rawtitle: High Speed Math Using a Floating Point Coprocessor
entry:
@InProceedings{Melear:1986:HSM,
  author =       "C. Melear and D. Tietjen",
  title =        "High Speed Math Using a Floating Point Coprocessor",
  crossref =     "Mini-Micro:1986:EMM",
  pages =        "14/3/1--8",
  year =         "1986",
  bibdate =      "Wed Sep 7 22:31:45 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: Moore:1986:PFS
author: Brian A. Moore
title: A pipelined floating-point systolic array arithmetic processor
type: Thesis (M.S.)
school: Brigham Young University. Department of Electrical Engineering
address: Provo, UT, USA
pages: vi + 58
year: 1986
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 arithmetic and logic units.; Computers, Pipeline.
acknowledgement: ack-nhfb
rawauthor: Brian A. Moore
rawtitle: A pipelined floating-point systolic array arithmetic processor
entry:
@MastersThesis{Moore:1986:PFS,
  author =       "Brian A. Moore",
  title =        "A pipelined floating-point systolic array arithmetic
                 processor",
  type =         "Thesis ({M.S.})",
  school =       "Brigham Young University. Department of Electrical
                 Engineering",
  address =      "Provo, UT, USA",
  pages =        "vi + 58",
  year =         "1986",
  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 arithmetic and logic
                 units.; Computers, Pipeline.",
}


bibtype: article
filename: fparith.bib
label: Moshier:1986:CA
author: S. L. Moshier
title: Computer Approximations
journal: j-BYTE
volume: 11
number: 4
pages: 161--178
month: apr
monthnumber: 4
year: 1986
CODEN: BYTEDJ
ISSN: 0360-5280 (print), 1082-7838 (electronic) OR 03605280 (print), 10827838 (electronic)
ISSNL: 0360-5280 OR 03605280
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: BYTE Magazine
acknowledgement: ack-nj
rawauthor: S. L. Moshier
rawtitle: Computer Approximations
entry:
@Article{Moshier:1986:CA,
  author =       "S. L. Moshier",
  title =        "Computer Approximations",
  journal =      j-BYTE,
  volume =       "11",
  number =       "4",
  pages =        "161--178",
  month =        apr,
  year =         "1986",
  CODEN =        "BYTEDJ",
  ISSN =         "0360-5280 (print), 1082-7838 (electronic)",
  ISSN-L =       "0360-5280",
  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 =     "BYTE Magazine",
}


bibtype: article
filename: fparith.bib
label: Ngai:1986:RAT
author: Tin-Fook Ngai and Mary Jane Irwin and Shishpal Rawat
title: Regular, Area-Time Efficient Carry-Lookahead Adders
journal: j-J-PAR-DIST-COMP
volume: 3
number: 1
pages: 92--105
month: mar
monthnumber: 3
year: 1986
CODEN: JPDCER
ISSN: 0743-7315 (print), 1096-0848 (electronic) OR 07437315 (print), 10960848 (electronic)
ISSNL: 0743-7315 OR 07437315
bibdate: Mon Apr 14 07:47:57 1997
bibsource: Compendex database; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.04.14 07:47:57 ???
fjournal: Journal of Parallel and Distributed Computing
acknowledgement: ack-nhfb
affiliationaddress: Stanford Univ, Stanford, CA, USA
corpsource: Department of Electr. Eng., Stanford University, CA, USA
journalURL: http://www.sciencedirect.com/science/journal/07437315
journalabr: J Parallel Distrib Comput
treatment: P Practical
rawauthor: Tin-Fook Ngai and Mary Jane Irwin and Shishpal Rawat
rawtitle: Regular, Area-Time Efficient Carry-Lookahead Adders
keywords:
adders; Adders; area-time efficiency; carry chain computation; carry logic; carry-lookahead adders; carry-lookahead adders (cla); computers; digital arithmetic; fast binary addition; integrated circuits, VLSI --- Electric Wiring; interconnection wire length; log n; log N stage design; maximum; regularity; stage design; VLSI

entry:
@Article{Ngai:1986:RAT,
  author =       "Tin-Fook Ngai and Mary Jane Irwin and Shishpal Rawat",
  title =        "Regular, Area-Time Efficient Carry-Lookahead Adders",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "3",
  number =       "1",
  pages =        "92--105",
  month =        mar,
  year =         "1986",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Mon Apr 14 07:47:57 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliationaddress = "Stanford Univ, Stanford, CA, USA",
  classification = "723; 921; C5230 (Digital arithmetic methods)",
  corpsource =   "Department of Electr. Eng., Stanford University, CA,
                 USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "adders; Adders; area-time efficiency; carry chain
                 computation; carry logic; carry-lookahead adders;
                 carry-lookahead adders (cla); computers; digital
                 arithmetic; fast binary addition; integrated circuits,
                 VLSI --- Electric Wiring; interconnection wire length;
                 log n; log N stage design; maximum; regularity; stage
                 design; VLSI",
  treatment =    "P Practical",
}


bibtype: article
filename: fparith.bib
label: Nowak:1986:HBU
author: M. Nowak
title: Hex-BCD-Umwandlung toenglish Hexadecimal-BCD Conversion endtoenglish
journal: j-MC
volume: 10
pages: 68
year: 1986
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: M. Nowak
rawtitle: {Hex-BCD-Um\-wand\-lung} \toenglish {Hexadecimal-BCD Conversion} \endtoenglish
entry:
@Article{Nowak:1986:HBU,
  author =       "M. Nowak",
  title =        "{Hex-BCD-Um\-wand\-lung} \toenglish {Hexadecimal-BCD
                 Conversion} \endtoenglish",
  journal =      j-MC,
  volume =       "10",
  pages =        "68",
  year =         "1986",
  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: phdthesis
filename: fparith.bib
label: Paez-Monzon:1986:ERC
author: Gerard Paez-Monzon
type: Doctorat d'Etat
school: Sciences Appliquees, Universite Paris 6
address: Paris, France
pages: 229
year: 1986
bibdate: Thu May 09 09:55:31 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.09 09:55:31 ???
note: Sous la direction de Gerard Noguez.
language: French
acknowledgement: ack-nhfb
rawauthor: Gerard Paez-Monzon
rawnote: Sous la direction de Gerard Noguez.
title:
Etude et Realisation d'un Co-processeur Arithmetique en Virgule Flottante. (French) [Study and Implementation of a Floating-Point Coprocessor]

abstract:
Le premier chapitre d'introduction decrit l'etat de l'art dans le domaine des algorithmes-cables elementaires utilises dans l'arithmetique flottante. Nous y presentons une classification architecturale des coprocesseurs arithmetiques en virgule flottante. A partir d'une comparaison de trois standards de virgule flottante orientes vers les systemes bases sur microprocesseurs: IEEE-P754, VAX-DEC, et Hewlett--Packard, le deuxieme chapitre explique le choix de l'architecture externe de coprocesseur. Le troisieme chapitre presente l'architecture interne microprogrammee et l'organisation du coprocesseur developpe dans l'etude, nommee FPU-IP6. Dans le quatrieme chapitre, nous proposons une nouvelle methode pour le developpement des microprogrammes. La cle de la methode est la visualisation de la separation des phases de planification et d'implantation. Le cinquieme chapitre presente les microprogrammes developpes pour notre coprocesseur. Nous analysons les differents micro-algorithmes selon le type d'instruction (E/S, arith, etc) et la precision (simple, double). L'organisation de l'espace de la micromemoire est presentee. Le sixieme chapitre decrit l'etude realisee pour l'integration du coprocesseur dans le compilateur C et le systeme UNIX de la machine SM90.

rawabstract:
Le premier chapitre d'introduction d{\'e}crit l'{\'e}tat de l'art dans le domaine des algorithmes-cabl{\'e}s {\'e}l{\'e}mentaires utilis{\'e}s dans l'arithm{\'e}tique flottante. Nous y pr{\'e}sentons une classification architecturale des coprocesseurs arithm{\'e}tiques en virgule flottante. {\`A} partir d'une comparaison de trois standards de virgule flottante orient{\'e}s vers les syst{\`e}mes bases sur microprocesseurs: IEEE-P754, VAX-DEC, et Hewlett--Packard, le deuxi{\`e}me chapitre explique le choix de l'architecture externe de coprocesseur. Le troisi{\`e}me chapitre pr{\'e}sente l'architecture interne microprogramm{\'e}e et l'organisation du coprocesseur d{\'e}velopp{\'e} dans l'{\'e}tude, nomm{\'e}e FPU-IP6. Dans le quatri{\`e}me chapitre, nous proposons une nouvelle m{\'e}thode pour le d{\'e}veloppement des microprogrammes. La cle de la m{\'e}thode est la visualisation de la s{\'e}paration des phases de planification et d'implantation. Le cinqui{\`e}me chapitre pr{\'e}sente les microprogrammes d{\'e}velopp{\'e}s pour notre coprocesseur. Nous analysons les diff{\'e}rents micro-algorithmes selon le type d'instruction (E/S, arith, etc) et la pr{\'e}cision (simple, double). L'organisation de l'espace de la microm{\'e}moire est present{\'e}e. Le sixi{\`e}me chapitre d{\'e}crit l'{\'e}tude realis{\'e}e pour l'int{\'e}gration du coprocesseur dans le compilateur C et le syst{\`e}me UNIX de la machine SM90.

rawtitle:
{{\'E}}tude et {R}{\'e}alisation d'un Co-processeur Arithm{\'e}tique en Virgule Flottante. ({French}) [{Study} and Implementation of a Floating-Point Coprocessor]

entry:
@PhdThesis{Paez-Monzon:1986:ERC,
  author =       "Gerard Paez-Monzon",
  title =        "{{\'E}}tude et {R}{\'e}alisation d'un Co-processeur
                 Arithm{\'e}tique en Virgule Flottante. ({French})
                 [{Study} and Implementation of a Floating-Point
                 Coprocessor]",
  type =         "Doctorat d'{\'E}tat",
  school =       "Sciences Appliqu{\'e}es, Universit{\'e} Paris 6",
  address =      "Paris, France",
  pages =        "229",
  year =         "1986",
  bibdate =      "Thu May 09 09:55:31 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Sous la direction de Gerard Noguez.",
  abstract =     "Le premier chapitre d'introduction d{\'e}crit
                 l'{\'e}tat de l'art dans le domaine des
                 algorithmes-cabl{\'e}s {\'e}l{\'e}mentaires
                 utilis{\'e}s dans l'arithm{\'e}tique flottante. Nous y
                 pr{\'e}sentons une classification architecturale des
                 coprocesseurs arithm{\'e}tiques en virgule flottante.
                 {\`A} partir d'une comparaison de trois standards de
                 virgule flottante orient{\'e}s vers les syst{\`e}mes
                 bases sur microprocesseurs: IEEE-P754, VAX-DEC, et
                 Hewlett--Packard, le deuxi{\`e}me chapitre explique le
                 choix de l'architecture externe de coprocesseur. Le
                 troisi{\`e}me chapitre pr{\'e}sente l'architecture
                 interne microprogramm{\'e}e et l'organisation du
                 coprocesseur d{\'e}velopp{\'e} dans l'{\'e}tude,
                 nomm{\'e}e FPU-IP6. Dans le quatri{\`e}me chapitre,
                 nous proposons une nouvelle m{\'e}thode pour le
                 d{\'e}veloppement des microprogrammes. La cle de la
                 m{\'e}thode est la visualisation de la s{\'e}paration
                 des phases de planification et d'implantation. Le
                 cinqui{\`e}me chapitre pr{\'e}sente les microprogrammes
                 d{\'e}velopp{\'e}s pour notre coprocesseur. Nous
                 analysons les diff{\'e}rents micro-algorithmes selon le
                 type d'instruction (E/S, arith, etc) et la
                 pr{\'e}cision (simple, double). L'organisation de
                 l'espace de la microm{\'e}moire est present{\'e}e. Le
                 sixi{\`e}me chapitre d{\'e}crit l'{\'e}tude
                 realis{\'e}e pour l'int{\'e}gration du coprocesseur
                 dans le compilateur C et le syst{\`e}me UNIX de la
                 machine SM90.",
  acknowledgement = ack-nhfb,
  language =     "French",
}


bibtype: article
filename: fparith.bib
label: Payne:1986:PTF
author: Mary H. Payne
title: Proposal for the transfer of floating point data
journal: j-SIGNUM
volume: 21
number: 3
pages: 25--26
month: jul
monthnumber: 7
year: 1986
CODEN: SNEWD6
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Mon Apr 25 11:24:15 MDT 2005
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.04.25 11:24:15 MDT
fjournal: ACM SIGNUM Newsletter
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/signum
rawauthor: Mary H. Payne
rawtitle: Proposal for the transfer of floating point data
entry:
@Article{Payne:1986:PTF,
  author =       "Mary H. Payne",
  title =        "Proposal for the transfer of floating point data",
  journal =      j-SIGNUM,
  volume =       "21",
  number =       "3",
  pages =        "25--26",
  month =        jul,
  year =         "1986",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Mon Apr 25 11:24:15 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
}


bibtype: article
filename: fparith.bib
label: Petkovic:1986:SIS
author: M. S. Petkovic and L. V. Stefanovic
title: On some improvements of square root iteration for polynomial complex zeros
journal: j-J-COMPUT-APPL-MATH
volume: 15
number: 1
pages: 13--25
month: may
monthnumber: 5
year: 1986
CODEN: JCAMDI
DOI: https://doi.org/10.1016/0377-0427(86)90235-9
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 11:59:55 MST 2017
bibtimestamp: 2017.02.25 11:59:55 MST
URL: http://www.sciencedirect.com/science/article/pii/0377042786902359
fjournal: Journal of Computational and Applied Mathematics
keywords: polynomial root finding
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: M. S. Petkovi{\'c} and L. V. Stefanovi{\'c}
rawtitle: On some improvements of square root iteration for polynomial complex zeros
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib

entry:
@Article{Petkovic:1986:SIS,
  author =       "M. S. Petkovi{\'c} and L. V. Stefanovi{\'c}",
  title =        "On some improvements of square root iteration for
                 polynomial complex zeros",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "15",
  number =       "1",
  pages =        "13--25",
  month =        may,
  year =         "1986",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/0377-0427(86)90235-9",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 11:59:55 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042786902359",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  keywords =     "polynomial root finding",
}


bibtype: article
filename: fparith.bib
label: Pfenninger:1986:SQA
author: E. Pfenninger
title: Schneller Quadratwurzel-Algorithmus toenglish Fast Square-Root Algorithms endtoenglish
journal: j-ELECTRONIK
volume: 22
pages: 179--180
year: 1986
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: E. Pfenninger
rawtitle: {Schneller Quadratwurzel-Algorithmus} \toenglish {Fast Square-Root Algorithms} \endtoenglish
entry:
@Article{Pfenninger:1986:SQA,
  author =       "E. Pfenninger",
  title =        "{Schneller Quadratwurzel-Algorithmus} \toenglish {Fast
                 Square-Root Algorithms} \endtoenglish",
  journal =      j-ELECTRONIK,
  volume =       "22",
  pages =        "179--180",
  year =         "1986",
  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: Porter:1986:FPM
author: K. Porter and J. Kath
title: Floating-point methods combine to boost performance
journal: j-COMP-DESIGN
volume: 25
number: 3
pages: 75--80
month: feb
monthnumber: 2
year: 1986
CODEN: CMPDAM
ISSN: 0010-4566 OR 00104566
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: Computer Design
acknowledgement: ack-nhfb
rawauthor: K. Porter and J. Kath
rawtitle: Floating-point methods combine to boost performance
subject:
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; K. Computing Milieux; K.1 THE COMPUTER INDUSTRY

entry:
@Article{Porter:1986:FPM,
  author =       "K. Porter and J. Kath",
  title =        "Floating-point methods combine to boost performance",
  journal =      j-COMP-DESIGN,
  volume =       "25",
  number =       "3",
  pages =        "75--80",
  month =        feb,
  year =         "1986",
  CODEN =        "CMPDAM",
  ISSN =         "0010-4566",
  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 =        "18468",
  catcode =      "G.1.0; K.1",
  CRclass =      "G.1.0 General; G.1.0 Computer arithmetic; K.1
                 Standards",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Computer arithmetic; Computing Milieux, THE COMPUTER
                 INDUSTRY, Standards",
  fjournal =     "Computer Design",
  genterm =      "DESIGN; THEORY; ALGORITHMS; PERFORMANCE;
                 STANDARDIZATION",
  guideno =      "1986-03910",
  journalabbrev = "Comput. Des.",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 K. Computing Milieux; K.1 THE COMPUTER INDUSTRY",
}


bibtype: article
filename: fparith.bib
label: Quong:1986:FPI
author: D. Quong
title: Floating-point $ mu P $ implements high-speed math functions
journal: j-EDN
volume: 31
number: 3
pages: 143--150
month: feb
monthnumber: 2
year: 1986
CODEN: EDNSBH
ISSN: 0012-7515, 0364-6637 OR 00127515, 03646637
bibdate: Wed Sep 7 22:31:45 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 22:31:45 ???
fjournal: EDN
acknowledgement: ack-nj
rawauthor: D. Quong
rawtitle: Floating-point $ \mu {P} $ implements high-speed math functions
entry:
@Article{Quong:1986:FPI,
  author =       "D. Quong",
  title =        "Floating-point $ \mu {P} $ implements high-speed math
                 functions",
  journal =      j-EDN,
  volume =       "31",
  number =       "3",
  pages =        "143--150",
  month =        feb,
  year =         "1986",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  bibdate =      "Wed Sep 7 22:31:45 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 =     "EDN",
}


bibtype: article
filename: fparith.bib
label: Ramnarayan:1986:LCL
author: R. Ramnarayan and F. Taylor
title: Limit cycles in large moduli residue number system digital filters
journal: j-IEEE-TRANS-CIRCUITS-SYST
volume: 33
number: 9
pages: 912--915
month: sep
monthnumber: 9
year: 1986
CODEN: ICSYBT
DOI: https://doi.org/10.1049/el:19850252
ISSN: 0098-4094 (print), 1558-1276 (electronic) OR 00984094 (print), 15581276 (electronic)
ISSNL: 0098-4094 OR 00984094
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
URL: https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23584
fjournal: IEEE Transactions on Circuits and Systems
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: R. Ramnarayan and F. Taylor
rawtitle: Limit cycles in large moduli residue number system digital filters
entry:
@Article{Ramnarayan:1986:LCL,
  author =       "R. Ramnarayan and F. Taylor",
  title =        "Limit cycles in large moduli residue number system
                 digital filters",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "33",
  number =       "9",
  pages =        "912--915",
  month =        sep,
  year =         "1986",
  CODEN =        "ICSYBT",
  DOI =          "https://doi.org/10.1049/el:19850252",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23584",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  keywords =     "residue arithmetic; residue number system",
}


bibtype: article
filename: fparith.bib
label: Rhyne:1986:SBS
author: T. Rhyne and N. R. Strader II
title: A Signed Bit-Sequential Multiplier
journal: j-IEEE-TRANS-COMPUT
volume: C-35
number: 10
pages: 896--901
month: oct
monthnumber: 10
year: 1986
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1986.1676680
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 9 14:09:51 MDT 2011
bibtimestamp: 2011.07.09 14:09:51 MDT
note: See comments cite Smith:1989:CSB.
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676680
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: T. Rhyne and N. R. {Strader II}
rawnote: See comments \cite{Smith:1989:CSB}.
rawtitle: A Signed Bit-Sequential Multiplier
entry:
@Article{Rhyne:1986:SBS,
  author =       "T. Rhyne and N. R. {Strader II}",
  title =        "A Signed Bit-Sequential Multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-35",
  number =       "10",
  pages =        "896--901",
  month =        oct,
  year =         "1986",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1986.1676680",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 14:09:51 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  note =         "See comments \cite{Smith:1989:CSB}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676680",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: techreport
filename: fparith.bib
label: Robertson:1986:NQD
author: James Evans Robertson
title: Normalization and quotient digit selection for a variable precision arithmetic unit
type: Report
number: UIUCDCS-R-86-1229
institution: Department of Computer Science, University of Illinois at Urbana-Champaign
address: Urbana, IL, USA
pages: 14
year: 1986
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: ``April 1986.''--Cover. ``UILU-ENG-86-1723.''--Cover. Bibliography: p. 13.
acknowledgement: ack-nhfb
rawauthor: James Evans Robertson
rawtitle: Normalization and quotient digit selection for a variable precision arithmetic unit
entry:
@TechReport{Robertson:1986:NQD,
  author =       "James Evans Robertson",
  title =        "Normalization and quotient digit selection for a
                 variable precision arithmetic unit",
  type =         "Report",
  number =       "UIUCDCS-R-86-1229",
  institution =  "Department of Computer Science, University of Illinois
                 at Urbana-Champaign",
  address =      "Urbana, IL, USA",
  pages =        "14",
  year =         "1986",
  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 =       "``April 1986.''--Cover. ``UILU-ENG-86-1723.''--Cover.
                 Bibliography: p. 13.",
}


bibtype: article
filename: fparith.bib
label: Rump:1986:SER
author: Siegfried M. Rump
title: Sichere Ergebnisse auf Rechenanlagen toenglish Safe Results from Computers endtoenglish
journal: j-INFORMATIK-SPEKTRUM
volume: 9
number: 3
pages: 174--183
month: jun
monthnumber: 6
year: 1986
CODEN: INSKDW
ISSN: 0170-6012 (print), 1432-122X (electronic) OR 01706012 (print), 1432122X (electronic)
ISSNL: 0170-6012 OR 01706012
bibdate: Fri Sep 16 16:30:39 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 16:30:39 ???
fjournal: Informatik Spektrum
acknowledgement: ack-nj
journalURL: http://link.springer.com/journal/287
rawauthor: Siegfried M. Rump
rawtitle: {Sichere Ergebnisse auf Rechenanlagen} \toenglish {Safe Results from Computers} \endtoenglish
entry:
@Article{Rump:1986:SER,
  author =       "Siegfried M. Rump",
  title =        "{Sichere Ergebnisse auf Rechenanlagen} \toenglish
                 {Safe Results from Computers} \endtoenglish",
  journal =      j-INFORMATIK-SPEKTRUM,
  volume =       "9",
  number =       "3",
  pages =        "174--183",
  month =        jun,
  year =         "1986",
  CODEN =        "INSKDW",
  ISSN =         "0170-6012 (print), 1432-122X (electronic)",
  ISSN-L =       "0170-6012",
  bibdate =      "Fri Sep 16 16:30:39 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 =     "Informatik Spektrum",
  journal-URL =  "http://link.springer.com/journal/287",
}


bibtype: article
filename: fparith.bib
label: Schatte:1986:ALD
author: Peter Schatte
title: On the asymptotic logarithmic distribution of the floating-point mantissas of sums
journal: j-MATH-NACHR
volume: 127
pages: 7--20
year: 1986
CODEN: MTMNAQ
ISSN: 0025-584X OR 0025584X
MRclass: 60F05
MRnumber: 87m:60059
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: Mathematische Nachrichten
acknowledgement: ack-nhfb
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616
reviewer: A. Fuchs
rawauthor: Peter Schatte
rawtitle: On the asymptotic logarithmic distribution of the floating-point mantissas of sums
entry:
@Article{Schatte:1986:ALD,
  author =       "Peter Schatte",
  title =        "On the asymptotic logarithmic distribution of the
                 floating-point mantissas of sums",
  journal =      j-MATH-NACHR,
  volume =       "127",
  pages =        "7--20",
  year =         "1986",
  CODEN =        "MTMNAQ",
  ISSN =         "0025-584X",
  MRclass =      "60F05",
  MRnumber =     "87m:60059",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematische Nachrichten",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616",
  reviewer =     "A. Fuchs",
}


bibtype: techreport
filename: fparith.bib
label: Schmickley:1986:CCP
author: Ronald D. Schmickley and David H. Bailey
title: A comparison of the Cray-2 performance before and after the installation of memory psudo-banking
type: NASA contractor report
number: NASA CR-177462
address: Moffett Field, CA, USA
year: 1986
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: Ronald D. Schmickley and David H. Bailey
rawtitle: A comparison of the {Cray-2} performance before and after the installation of memory psudo-banking
institution:
National Aeronautics and Space Administration, Ames Research Center; National Technical Information Service, distributor

keywords:
Accounting.; Computer systems performance.; Cray computers.; Floating point arithmetic.; Memory (Computers); Response time (Computers)

remark:
Distributed to depository libraries in microfiche. Microfiche. [Washington, D.C.: National Aeronautics and Space Administration, 1988] 1 microfiche.

entry:
@TechReport{Schmickley:1986:CCP,
  author =       "Ronald D. Schmickley and David H. Bailey",
  title =        "A comparison of the {Cray-2} performance before and
                 after the installation of memory psudo-banking",
  type =         "{NASA} contractor report",
  number =       "NASA CR-177462",
  institution =  "National Aeronautics and Space Administration, Ames
                 Research Center; National Technical Information
                 Service, distributor",
  address =      "Moffett Field, CA, USA",
  pages =        "????",
  year =         "1986",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  govtdocnumber = "NAS 1.26:177462 0830-H-14 (MF)",
  keywords =     "Accounting.; Computer systems performance.; Cray
                 computers.; Floating point arithmetic.; Memory
                 (Computers); Response time (Computers)",
  remark =       "Distributed to depository libraries in microfiche.
                 Microfiche. [Washington, D.C.: National Aeronautics and
                 Space Administration, 1988] 1 microfiche.",
}


bibtype: article
filename: fparith.bib
label: Semba:1986:ADL
author: I. Semba
title: An Algorithm for Division of Large Integers
journal: j-INFO-PROC
volume: 9
number: 3
pages: 145--147
year: 1986
bibdate: Thu Sep 1 10:15:09 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:15:09 ???
acknowledgement: ack-nj
rawauthor: I. Semba
rawtitle: An Algorithm for Division of Large Integers
entry:
@Article{Semba:1986:ADL,
  author =       "I. Semba",
  title =        "An Algorithm for Division of Large Integers",
  journal =      j-INFO-PROC,
  volume =       "9",
  number =       "3",
  pages =        "145--147",
  month =        "????",
  year =         "1986",
  bibdate =      "Thu Sep 1 10:15:09 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: mastersthesis
filename: fparith.bib
label: Shukla:1986:IMN
author: Pankaj N. Shukla
type: Thesis (M.S.)
school: Michigan Technological University
address: 1400 Townsend Drive, Houghton, MI 49931-1295, USA
pages: vii + 166
year: 1986
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: Pankaj N. Shukla
title:
An implementation on a MC68000 / NS32081 microcomputer of binary floating-point arithmetic based on the IEEE 754 standard

keywords:
Michigan Technological University. --- Theses (M.S.).; MTU Electrical Engineering. --- Thesis (M.S.).

rawtitle:
An implementation on a {MC68000\slash NS32081} microcomputer of binary floating-point arithmetic based on the {IEEE 754} standard

entry:
@MastersThesis{Shukla:1986:IMN,
  author =       "Pankaj N. Shukla",
  title =        "An implementation on a {MC68000\slash NS32081}
                 microcomputer of binary floating-point arithmetic based
                 on the {IEEE 754} standard",
  type =         "Thesis ({M.S.})",
  school =       "Michigan Technological University",
  address =      "1400 Townsend Drive, Houghton, MI 49931-1295, USA",
  pages =        "vii + 166",
  year =         "1986",
  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 Electrical Engineering. --- Thesis
                 ({M.S.}).",
}


bibtype: inproceedings
filename: fparith.bib
label: Simcoe:1986:MFP
author: R. J. Simcoe and A. Fisher and B. M. Leary and W. R. Bidermann and W. R. Wheeler
title: The MicroVAX 78132 Floating Point Chip
crossref: IEEE:1986:PII
pages: 420--425
year: 1986
bibdate: Wed Sep 07 23:14:42 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.07 23:14:42 ???
acknowledgement: ack-nj
rawauthor: R. J. Simcoe and A. Fisher and B. M. Leary and W. R. Bidermann and W. R. Wheeler
rawtitle: The {MicroVAX} 78132 Floating Point Chip
entry:
@InProceedings{Simcoe:1986:MFP,
  author =       "R. J. Simcoe and A. Fisher and B. M. Leary and W. R.
                 Bidermann and W. R. Wheeler",
  title =        "The {MicroVAX} 78132 Floating Point Chip",
  crossref =     "IEEE:1986:PII",
  pages =        "420--425",
  year =         "1986",
  bibdate =      "Wed Sep 07 23:14:42 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: book
filename: fparith.bib
label: Soderstrand:1986:RNS
editor: Michael A. Soderstrand and W. K. Jenkins and G. A. Graham and F. J. Taylor
title: Residue number system arithmetic: modern applications in digital signal processing
publisher: pub-IEEE
address: pub-IEEE:adr
pages: vii + 418
year: 1986
ISBN: 0-87942-205-X OR 087942205X
ISBN13: 978-0-87942-205-9 OR 9780879422059
LCCN: QA247.35 .R45 1986
bibdate: Wed Nov 14 14:28:02 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2007.11.14 14:28:02 MST
series: IEEE Press selected reprint series
subject: modular arithmetic; signal processing; digital techniques; computer programming
acknowledgement: ack-nhfb
raweditor: Michael A. Soderstrand and W. K. Jenkins and G. A. Graham and F. J. Taylor
rawtitle: Residue number system arithmetic: modern applications in digital signal processing
entry:
@Book{Soderstrand:1986:RNS,
  editor =       "Michael A. Soderstrand and W. K. Jenkins and G. A.
                 Graham and F. J. Taylor",
  title =        "Residue number system arithmetic: modern applications
                 in digital signal processing",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "vii + 418",
  year =         "1986",
  ISBN =         "0-87942-205-X",
  ISBN-13 =      "978-0-87942-205-9",
  LCCN =         "QA247.35 .R45 1986",
  bibdate =      "Wed Nov 14 14:28:02 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "IEEE Press selected reprint series",
  acknowledgement = ack-nhfb,
  subject =      "modular arithmetic; signal processing; digital
                 techniques; computer programming",
}


bibtype: article
filename: fparith.bib
label: Soderstrand:1986:VIM
author: M. Soderstrand and R. Escott
journal: j-IEEE-TRANS-CIRCUITS-SYST
volume: 33
number: 1
pages: 5--25
month: jan
monthnumber: 1
year: 1986
CODEN: ICSYBT
DOI: https://doi.org/10.1049/el:19850252
ISSN: 0098-4094 (print), 1558-1276 (electronic) OR 00984094 (print), 15581276 (electronic)
ISSNL: 0098-4094 OR 00984094
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
URL: https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23573
fjournal: IEEE Transactions on Circuits and Systems
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: M. Soderstrand and R. Escott
title:
VLSI implementation in multiple-valued logic of an FIR digital filter using residue number system arithmetic

rawtitle:
{VLSI} implementation in multiple-valued logic of an {FIR} digital filter using residue number system arithmetic

entry:
@Article{Soderstrand:1986:VIM,
  author =       "M. Soderstrand and R. Escott",
  title =        "{VLSI} implementation in multiple-valued logic of an
                 {FIR} digital filter using residue number system
                 arithmetic",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "33",
  number =       "1",
  pages =        "5--25",
  month =        jan,
  year =         "1986",
  CODEN =        "ICSYBT",
  DOI =          "https://doi.org/10.1049/el:19850252",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23573",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  keywords =     "residue arithmetic; residue number system",
  summary =      "Computer simulations using SPICE establish the
                 feasibility of implementing a highly pipelined
                 high-speed FIR digital filter using Multiple-Valued
                 Logic (MVL) Read-Only Memories (ROM's) to implement
                 Residue Number System (RNS) Arithmetic in VLSI
                 \ldots{}",
}


bibtype: techreport
filename: fparith.bib
label: Spafford:1986:RASa
author: E. H. Spafford and J. C. Flaspohler
title: A Report on the Accuracy of Some Floating-Point Math Functions on Selected Computers
type: Technical Report
number: GIT-SERC-86/02, GIT-ICS-85/06
institution: Georgia Institute of Technology
year: 1986
bibdate: Mon Sep 12 23:54:04 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.12 23:54:04 ???
acknowledgement: ack-nj
rawauthor: E. H. Spafford and J. C. Flaspohler
rawtitle: A Report on the Accuracy of Some Floating-Point Math Functions on Selected Computers
entry:
@TechReport{Spafford:1986:RASa,
  author =       "E. H. Spafford and J. C. Flaspohler",
  title =        "A Report on the Accuracy of Some Floating-Point Math
                 Functions on Selected Computers",
  type =         "Technical Report",
  number =       "GIT-SERC-86/02, GIT-ICS-85/06",
  institution =  "Georgia Institute of Technology",
  pages =        "??",
  year =         "1986",
  bibdate =      "Mon Sep 12 23:54:04 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: Spafford:1986:RASb
author: Eugene H. Spafford and John C. Flaspohler
title: A Report on the Accuracy of Some Floating Point Math Functions on Selected Computers
journal: j-LOGIN
volume: 11
number: 2
pages: 31--56
month: mar
monthnumber: 3
year: 1986
CODEN: LOGNEM
ISSN: 1044-6397 (print), 2169-9364 (electronic) OR 10446397 (print), 21699364 (electronic)
bibdate: Tue Feb 20 15:42:13 MST 1996
bibsource: ftp://ftp.uu.net/library/bibliography; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.20 15:42:13 MST
fjournal: ;login: the USENIX Association newsletter
acknowledgement: ack-nhfb
affiliation: Georgia Institute of Technology
rawauthor: Eugene H. Spafford and John C. Flaspohler
rawtitle: A Report on the Accuracy of Some Floating Point Math Functions on Selected Computers
entry:
@Article{Spafford:1986:RASb,
  author =       "Eugene H. Spafford and John C. Flaspohler",
  title =        "A Report on the Accuracy of Some Floating Point Math
                 Functions on Selected Computers",
  journal =      j-LOGIN,
  volume =       "11",
  number =       "2",
  pages =        "31--56",
  month =        mar # "\slash " # apr,
  year =         "1986",
  CODEN =        "LOGNEM",
  ISSN =         "1044-6397 (print), 2169-9364 (electronic)",
  bibdate =      "Tue Feb 20 15:42:13 MST 1996",
  bibsource =    "ftp://ftp.uu.net/library/bibliography;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Georgia Institute of Technology",
  fjournal =     ";login: the USENIX Association newsletter",
}


bibtype: article
filename: fparith.bib
label: Stewart:1986:CNC
author: G. W. Stewart
title: Corrigendum: ``A Note on Complex Division''
journal: j-TOMS
volume: 12
number: 3
pages: 285
month: sep
monthnumber: 9
year: 1986
CODEN: ACMSCU
DOI: https://doi.org/10.1145/7921.356182
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sun Sep 04 21:20:12 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.04 21:20:12 ???
note: See cite Stewart:1985:NCD.
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: G. W. Stewart
rawnote: See \cite{Stewart:1985:NCD}.
rawtitle: Corrigendum: ``{A} Note on Complex Division''
entry:
@Article{Stewart:1986:CNC,
  author =       "G. W. Stewart",
  title =        "Corrigendum: ``{A} Note on Complex Division''",
  journal =      j-TOMS,
  volume =       "12",
  number =       "3",
  pages =        "285",
  month =        sep,
  year =         "1986",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/7921.356182",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 21:20:12 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Stewart:1985:NCD}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: inproceedings
filename: fparith.bib
label: Strobach:1986:NFL
author: P. Strobach
booktitle: IEEE International Conference on Acoustics, Speech, and Signal Processing: ICASSP '86
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 573--576
year: 1986
bibdate: Sat Jul 16 11:25:04 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:04 MDT
acknowledgement: ack-nhfb
rawauthor: P. Strobach
rawbooktitle: {IEEE} International Conference on Acoustics, Speech, and Signal Processing: {ICASSP '86}
title:
New forms of least squares lattice algorithms and a comparison of their round-off error characteristics

rawtitle:
New forms of least squares lattice algorithms and a comparison of their round-off error characteristics

entry:
@InProceedings{Strobach:1986:NFL,
  author =       "P. Strobach",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing: {ICASSP '86}",
  title =        "New forms of least squares lattice algorithms and a
                 comparison of their round-off error characteristics",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "573--576",
  year =         "1986",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:04 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Two versions of the most recently introduced ``pure
                 order recursive'' LS lattice algorithm are discussed in
                 this paper. An analysis of the round-off error
                 characteristics of the new order recursive lattice
                 method is performed and a comparison is made \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Stummel:1986:SOP
author: F. Stummel
journal: j-COMPUTING
volume: 37
number: 2
pages: 103--124
year: 1986
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
MRclass: 65F05 (65G05)
MRnumber: 88b:65047
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: Alfonso Laratta
rawauthor: F. Stummel
title:
Strict optimal a posteriori error and residual bounds for Gaussian elimination in floating-point arithmetic

rawtitle:
Strict optimal a posteriori error and residual bounds for {Gaussian} elimination in floating-point arithmetic

entry:
@Article{Stummel:1986:SOP,
  author =       "F. Stummel",
  title =        "Strict optimal a posteriori error and residual bounds
                 for {Gaussian} elimination in floating-point
                 arithmetic",
  journal =      j-COMPUTING,
  volume =       "37",
  number =       "2",
  pages =        "103--124",
  year =         "1986",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65F05 (65G05)",
  MRnumber =     "88b:65047",
  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 =     "Alfonso Laratta",
}


bibtype: manual
filename: fparith.bib
label: Sun:1986:FPG
title: Floating-point programmer's guide for the Sun workstation
publisher: Sun Microsystems, Inc.
address: Mountain View, CA, USA
edition: Revision A of 19 September 1986.
pages: various
year: 1986
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 and logic units.; Floating-point arithmetic.
remark: ``Part Number 800-1552-10.''
acknowledgement: ack-nhfb
rawtitle: Floating-point programmer's guide for the {Sun} workstation
entry:
@Manual{Sun:1986:FPG,
  title =        "Floating-point programmer's guide for the {Sun}
                 workstation",
  publisher =    "Sun Microsystems, Inc.",
  address =      "Mountain View, CA, USA",
  edition =      "Revision {A} of 19 {September} 1986.",
  pages =        "various",
  year =         "1986",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer arithmetic and logic units.; Floating-point
                 arithmetic.",
  remark =       "``Part Number 800-1552-10.''",
}


bibtype: article
filename: fparith.bib
label: Thun:1986:RNS
author: R. Thun
title: On residue number system decoding
volume: 34
number: 5
pages: 1346--1347
month: oct
monthnumber: 10
year: 1986
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
URL: https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=26200
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: R. Thun
rawtitle: On residue number system decoding
journal:
Acoustics, Speech, and Signal Processing [see also IEEE Transactions on Signal Processing], IEEE Transactions on

entry:
@Article{Thun:1986:RNS,
  author =       "R. Thun",
  title =        "On residue number system decoding",
  journal =      "Acoustics, Speech, and Signal Processing [see also
                 IEEE Transactions on Signal Processing], IEEE
                 Transactions on",
  volume =       "34",
  number =       "5",
  pages =        "1346--1347",
  month =        oct,
  year =         "1986",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=26200",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "The use of a residue number system (RNS) in digital
                 systems and especially filter designs is facilitated by
                 efficient algorithms for the conversion from RNS to
                 binary numbers. The conversion is generally based on
                 the Chinese remainder theorem or the \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Troutman:1986:DSF
author: W. W. Troutman and P. W. Diodato and A. K. Goksel and Mean-Sea Tsay and R. H. Krambeck
title: Design of a Standard Floating-Point Chip
journal: j-IEEE-J-SOLID-STATE-CIRCUITS
volume: 21
number: 3
pages: 396--399
month: jun
monthnumber: 6
year: 1986
CODEN: IJSCBC
ISSN: 0018-9200 (print), 1558-173X (electronic) OR 00189200 (print), 1558173X (electronic)
ISSNL: 0018-9200 OR 00189200
bibdate: Sat Jul 16 08:40:53 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:53 MDT
fjournal: IEEE Journal of Solid-State Circuits
acknowledgement: ack-nhfb
rawauthor: W. W. Troutman and P. W. Diodato and A. K. Goksel and Mean-Sea Tsay and R. H. Krambeck
rawtitle: Design of a Standard Floating-Point Chip
entry:
@Article{Troutman:1986:DSF,
  author =       "W. W. Troutman and P. W. Diodato and A. K. Goksel and
                 Mean-Sea Tsay and R. H. Krambeck",
  title =        "Design of a Standard Floating-Point Chip",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "21",
  number =       "3",
  pages =        "396--399",
  month =        jun,
  year =         "1986",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  summary =      "Some aspects of design of a VLSI floating-point chip,
                 which provides the WE{\reg}32100 microprocessor with
                 math acceleration capabilities, are described. The chip
                 is implemented in 1.75-$\mu$m twin-tub CMOS II
                 technology [2] and contains \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Truong:1986:TCD
author: T. K. Truong and J. J. Chang and I. S. Hsu and D. Y. Pei and I. S. Reed
journal: j-IEEE-TRANS-COMPUT
volume: C-35
number: 11
pages: 1008--1012
month: nov
monthnumber: 11
year: 1986
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1986.1676704
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 9 14:09:53 MDT 2011
bibtimestamp: 2011.07.09 14:09:53 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676704
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: T. K. Truong and J. J. Chang and I. S. Hsu and D. Y. Pei and I. S. Reed
title:
Techniques for Computing the Discrete Fourier Transform Using the Quadratic Residue Fermat Number Systems

rawtitle:
Techniques for Computing the Discrete {Fourier} Transform Using the Quadratic Residue {Fermat} Number Systems

entry:
@Article{Truong:1986:TCD,
  author =       "T. K. Truong and J. J. Chang and I. S. Hsu and D. Y.
                 Pei and I. S. Reed",
  title =        "Techniques for Computing the Discrete {Fourier}
                 Transform Using the Quadratic Residue {Fermat} Number
                 Systems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-35",
  number =       "11",
  pages =        "1008--1012",
  month =        nov,
  year =         "1986",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1986.1676704",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 14:09:53 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676704",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Twaddell:1986:HPM
author: W. Twaddell
title: Higher performance marks floating-point chips
journal: j-COMP-DESIGN
volume: 25
number: 8
pages: 24--30
day: 15
month: apr
monthnumber: 4
year: 1986
CODEN: CMPDAM
ISSN: 0010-4566 OR 00104566
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: Computer Design
subject: B. Hardware; B.7 INTEGRATED CIRCUITS; C. Computer Systems Organization; C.4 PERFORMANCE OF SYSTEMS
acknowledgement: ack-nhfb
rawauthor: W. Twaddell
rawtitle: Higher performance marks floating-point chips
entry:
@Article{Twaddell:1986:HPM,
  author =       "W. Twaddell",
  title =        "Higher performance marks floating-point chips",
  journal =      j-COMP-DESIGN,
  volume =       "25",
  number =       "8",
  pages =        "24--30",
  day =          "15",
  month =        apr,
  year =         "1986",
  CODEN =        "CMPDAM",
  ISSN =         "0010-4566",
  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 =        "19171",
  catcode =      "B.7.1; C.4",
  CRclass =      "B.7.1 Types and Design Styles; B.7.1 Advanced
                 technologies",
  descriptor =   "Hardware, INTEGRATED CIRCUITS, Types and Design
                 Styles, Advanced technologies; Computer Systems
                 Organization, PERFORMANCE OF SYSTEMS",
  fjournal =     "Computer Design",
  genterm =      "DESIGN; PERFORMANCE",
  guideno =      "1986-03952",
  journalabbrev = "Comput. Des.",
  subject =      "B. Hardware; B.7 INTEGRATED CIRCUITS; C. Computer
                 Systems Organization; C.4 PERFORMANCE OF SYSTEMS",
}


bibtype: inproceedings
filename: fparith.bib
label: Vaccaro:1986:SDF
author: J. Vaccaro and B. Johnson and C. Nowacki
booktitle: IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP '86
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1157--1160
month: aug
monthnumber: 8
year: 1986
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: J. Vaccaro and B. Johnson and C. Nowacki
rawbooktitle: {IEEE} International Conference on Acoustics, Speech, and Signal Processing, {ICASSP '86}
title:
A systolic discrete Fourier transform using residue number systems over the ring of Gaussian integers

rawtitle:
A systolic discrete {Fourier} transform using residue number systems over the ring of {Gaussian} integers

entry:
@InProceedings{Vaccaro:1986:SDF,
  author =       "J. Vaccaro and B. Johnson and C. Nowacki",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing, {ICASSP '86}",
  title =        "A systolic discrete {Fourier} transform using residue
                 number systems over the ring of {Gaussian} integers",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1157--1160",
  month =        aug,
  year =         "1986",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A VLSI implementation of a bit-serial systolic
                 architecture for a DFT processor has been developed
                 which performs residue number system (RNS) processing
                 over the ring of Gaussian integers. An architecture for
                 a 128-point DFT using the chirp z-transform algorithm
                 is described, and its use in an R2FFT architecture to
                 obtain a 16,384-point transform is illustrated. Based
                 on three custom-designed chips, the processor is
                 capable of transforming data at a continuous 2 MHz
                 rate. The use of RNS techniques and systolic arrays
                 provides two dimensions of parallelism, resulting in
                 hardware of low complexity and high speed. The overall
                 system has great flexibility in dynamic range, and can
                 be used in many signal processing applications.",
}


bibtype: mastersthesis
filename: fparith.bib
label: Verma:1986:DEF
author: Deepak Verma
title: Design of an efficient floating point vector coprocessor of an advanced microcomputer system
type: Thesis (M.S.)
school: Department of Computer Engineering and Science, Case Western Reserve University
address: Cleveland, OH 44106, USA
pages: viii + 121
year: 1986
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: Deepak Verma
rawtitle: Design of an efficient floating point vector coprocessor of an advanced microcomputer system
entry:
@MastersThesis{Verma:1986:DEF,
  author =       "Deepak Verma",
  title =        "Design of an efficient floating point vector
                 coprocessor of an advanced microcomputer system",
  type =         "Thesis ({M.S.})",
  school =       "Department of Computer Engineering and Science, Case
                 Western Reserve University",
  address =      "Cleveland, OH 44106, USA",
  pages =        "viii + 121",
  year =         "1986",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Waterhouse:1986:TMW
author: William C. Waterhouse
title: The Teaching of Mathematics: Why Square Roots are Irrational
journal: j-AMER-MATH-MONTHLY
volume: 93
number: 3
pages: 213--214
month: mar
monthnumber: 3
year: 1986
CODEN: AMMYAE
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
bibdate: Mon Jun 28 12:38:15 MDT 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database
bibtimestamp: 1999.06.28 12:38:15 MDT
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
journalURL: https://www.jstor.org/journals/00029890.htm
rawauthor: William C. Waterhouse
rawtitle: The Teaching of Mathematics: Why Square Roots are Irrational
entry:
@Article{Waterhouse:1986:TMW,
  author =       "William C. Waterhouse",
  title =        "The Teaching of Mathematics: Why Square Roots are
                 Irrational",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "93",
  number =       "3",
  pages =        "213--214",
  month =        mar,
  year =         "1986",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jun 28 12:38:15 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}


bibtype: techreport
filename: fparith.bib
label: Weitek:1986:WSW
author: Weitek Corporation
title: WTL 1164 / WTL 1165 64-bit IEEE Floating-Point Multiplier / Divider and ALU
institution: pub-WEITEK
address: pub-WEITEK:adr
pages: 213--214
month: jul
monthnumber: 7
year: 1986
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: {Weitek Corporation}
rawtitle: {WTL} 1164\slash {WTL} 1165 64-bit {IEEE} Float\-ing-Point Multiplier\slash Divider and {ALU}
entry:
@TechReport{Weitek:1986:WSW,
  author =       "{Weitek Corporation}",
  title =        "{WTL} 1164\slash {WTL} 1165 64-bit {IEEE}
                 Float\-ing-Point Multiplier\slash Divider and {ALU}",
  institution =  pub-WEITEK,
  address =      pub-WEITEK:adr,
  month =        jul,
  year =         "1986",
  bibdate =      "Thu Nov 8 14:50:32 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: techreport
filename: fparith.bib
label: Wichmann:1986:FPI
author: Brian A. Wichmann
title: Floating point interval arithmetic for validation
institution: National Physical Laboratory, Division of Information Technology and Computing
address: Teddington Middlesex
pages: i + 12
year: 1986
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: NPL report; DITC 76/86
keywords: Algorithms.; Floating-point arithmetic.
acknowledgement: ack-nhfb
rawauthor: Brian A. Wichmann
rawtitle: Floating point interval arithmetic for validation
entry:
@TechReport{Wichmann:1986:FPI,
  author =       "Brian A. Wichmann",
  title =        "Floating point interval arithmetic for validation",
  institution =  "National Physical Laboratory, Division of Information
                 Technology and Computing",
  address =      "Teddington Middlesex",
  pages =        "i + 12",
  year =         "1986",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "NPL report; DITC 76/86",
  acknowledgement = ack-nhfb,
  keywords =     "Algorithms.; Floating-point arithmetic.",
}


bibtype: article
filename: fparith.bib
label: Wollenberg:1986:SRD
author: R. Wollenberg and R. Milnikel
journal: j-ELECTRONIK
volume: 6
pages: 79--82
year: 1986
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. Wollenberg and R. Milnikel
title:
Schnelles Radizierverfahren durch Tabellenzugriff toenglish Fast Square-rooting Method by Means of Table Lookup endtoenglish 

rawtitle:
{Schnelles Radizierverfahren durch Tabellenzugriff} \toenglish {Fast Square-rooting Method by Means of Table Lookup} \endtoenglish

entry:
@Article{Wollenberg:1986:SRD,
  author =       "R. Wollenberg and R. Milnikel",
  title =        "{Schnelles Radizierverfahren durch Tabellenzugriff}
                 \toenglish {Fast Square-rooting Method by Means of
                 Table Lookup} \endtoenglish",
  journal =      j-ELECTRONIK,
  volume =       "6",
  pages =        "79--82",
  year =         "1986",
  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: Agarwal:1987:CNS
journal: j-IBM-JRD
volume: 31
number: 2
pages: 274--274
month: mar
monthnumber: 3
year: 1987
CODEN: IBMJAE
DOI: https://doi.org/10.1147/rd.312.0274
ISSN: 0018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)
ISSNL: 0018-8646 OR 00188646
MRclass: 76W05
MRnumber: MR894626
bibdate: Mon Feb 12 08:07:08 2001
bibtimestamp: 2001.02.12 08:07:08 ???
note: See cite Agarwal:1986:NSV.
fjournal: IBM Journal of Research and Development
acknowledgement: ack-nhfb
ajournal: IBM J. Res. Develop.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520
rawnote: See \cite{Agarwal:1986:NSV}.
author:
Ramesh C. Agarwal and James W. Cooley and Fred G. Gustavson and James B. Shearer and Gordon Slishman and Bryant Tuckerman

title:
Clarification: ``New scalar and vector elementary functions for the IBM System / 370'' [IBM J. Res. Develop. bf 30 (1986), no. 2, 126--144]

bibsource:
http://www.research.ibm.com/journal/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib

rawtitle:
Clarification: {``New scalar and vector elementary functions for the IBM System\slash 370''} [{IBM J. Res. Develop. {\bf 30} (1986), no. 2, 126--144}]

entry:
@Article{Agarwal:1987:CNS,
  author =       "Ramesh C. Agarwal and James W. Cooley and Fred G.
                 Gustavson and James B. Shearer and Gordon Slishman and
                 Bryant Tuckerman",
  title =        "Clarification: {``New scalar and vector elementary
                 functions for the IBM System\slash 370''} [{IBM J. Res.
                 Develop. {\bf 30} (1986), no. 2, 126--144}]",
  journal =      j-IBM-JRD,
  volume =       "31",
  number =       "2",
  pages =        "274--274",
  month =        mar,
  year =         "1987",
  CODEN =        "IBMJAE",
  DOI =          "https://doi.org/10.1147/rd.312.0274",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  MRclass =      "76W05",
  MRnumber =     "MR894626",
  bibdate =      "Mon Feb 12 08:07:08 2001",
  bibsource =    "http://www.research.ibm.com/journal/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib",
  note =         "See \cite{Agarwal:1986:NSV}.",
  acknowledgement = ack-nhfb,
  ajournal =     "IBM J. Res. Develop.",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}


bibtype: inproceedings
filename: fparith.bib
label: Agrawal:1987:CEF
author: J. C. Agrawal and P. S. Sehdev
title: Comparison and Evaluation of Floating Point Representations in IBM / 370 and VAX-11 / 780
crossref: Zunde:1987:EFI
pages: 353--369
year: 1987
bibdate: Wed Sep 14 20:23:44 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.14 20:23:44 ???
acknowledgement: ack-nj
rawauthor: J. C. Agrawal and P. S. Sehdev
rawtitle:
Comparison and Evaluation of Floating Point Representations in {IBM\slash 370} and {VAX-11\slash 780}

entry:
@InProceedings{Agrawal:1987:CEF,
  author =       "J. C. Agrawal and P. S. Sehdev",
  title =        "Comparison and Evaluation of Floating Point
                 Representations in {IBM\slash 370} and {VAX-11\slash
                 780}",
  crossref =     "Zunde:1987:EFI",
  pages =        "353--369",
  year =         "1987",
  bibdate =      "Wed Sep 14 20:23:44 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: Ahmad:1987:IDA
author: M. Ahmad
title: Implementable Decimal Arithmetic Algorithms for Micro / Minicomputers
journal: j-MICROPROC-MICROPROG
volume: 19
number: 2
pages: 119--128
month: feb
monthnumber: 2
year: 1987
CODEN: MMICDT
ISSN: 0165-6074 (print), 1878-7061 (electronic) OR 01656074 (print), 18787061 (electronic)
ISSNL: 0165-6074 OR 01656074
bibdate: Thu Sep 1 10:16:11 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:16:11 ???
fjournal: Microprocessing and Microprogramming
keywords: decimal floating-point arithmetic
acknowledgement: ack-nj
journalURL: https://www.sciencedirect.com/journal/microprocessing-and-microprogramming/issues
rawauthor: M. Ahmad
rawtitle: Implementable Decimal Arithmetic Algorithms for Micro\slash Minicomputers
entry:
@Article{Ahmad:1987:IDA,
  author =       "M. Ahmad",
  title =        "Implementable Decimal Arithmetic Algorithms for
                 Micro\slash Minicomputers",
  journal =      j-MICROPROC-MICROPROG,
  volume =       "19",
  number =       "2",
  pages =        "119--128",
  month =        feb,
  year =         "1987",
  CODEN =        "MMICDT",
  ISSN =         "0165-6074 (print), 1878-7061 (electronic)",
  ISSN-L =       "0165-6074",
  bibdate =      "Thu Sep 1 10:16:11 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Microprocessing and Microprogramming",
  journal-URL =  "https://www.sciencedirect.com/journal/microprocessing-and-microprogramming/issues",
  keywords =     "decimal floating-point arithmetic",
}


bibtype: article
filename: fparith.bib
label: Anonymous:1987:BRCe
author: Anonymous
journal: j-MATH-COMPUT-SIMUL
volume: 29
number: 5
pages: 448--449
month: oct
monthnumber: 10
year: 1987
CODEN: MCSIDR
DOI: https://doi.org/10.1016/0378-4754(87)90086-3
ISSN: 0378-4754 (print), 1872-7166 (electronic) OR 03784754 (print), 18727166 (electronic)
ISSNL: 0378-4754 OR 03784754
bibdate: Mon Aug 18 16:03:53 MDT 2025
bibtimestamp: 2025.08.18 16:03:53 MDT
URL: https://www.sciencedirect.com/science/article/pii/0378475487900863
fjournal: Mathematics and Computers in Simulation
acknowledgement: ack-nhfb
ajournal: Math. Comput. Simul.
journalURL: https://www.sciencedirect.com/science/journal/03784754
rawauthor: Anonymous
title:
Book Review: booktitle Computer arithmetic --- scientific computation and programming languages: E. Kaucher, U. Kulisch and Ch. Ullrich (Eds): B. G. Teubner, Stuttgart, 1987, 456 pages, DM 28.00, ISBN 3-519- 02448-9

bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/mathcomputsimul1980.bib

rawtitle:
Book Review: {{\booktitle{Computer arithmetic --- scientific computation and programming languages}}: E. Kaucher, U. Kulisch and Ch. Ullrich (Eds): B. G. Teubner, Stuttgart, 1987, 456 pages, DM 28.00, ISBN 3-519- 02448-9}

entry:
@Article{Anonymous:1987:BRCe,
  author =       "Anonymous",
  title =        "Book Review: {{\booktitle{Computer arithmetic ---
                 scientific computation and programming languages}}: E.
                 Kaucher, U. Kulisch and Ch. Ullrich (Eds): B. G.
                 Teubner, Stuttgart, 1987, 456 pages, DM 28.00, ISBN
                 3-519- 02448-9}",
  journal =      j-MATH-COMPUT-SIMUL,
  volume =       "29",
  number =       "5",
  pages =        "448--449",
  month =        oct,
  year =         "1987",
  CODEN =        "MCSIDR",
  DOI =          "https://doi.org/10.1016/0378-4754(87)90086-3",
  ISSN =         "0378-4754 (print), 1872-7166 (electronic)",
  ISSN-L =       "0378-4754",
  bibdate =      "Mon Aug 18 16:03:53 MDT 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomputsimul1980.bib",
  URL =          "https://www.sciencedirect.com/science/article/pii/0378475487900863",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput. Simul.",
  fjournal =     "Mathematics and Computers in Simulation",
  journal-URL =  "https://www.sciencedirect.com/science/journal/03784754",
}


bibtype: article
filename: fparith.bib
label: Anonymous:1987:MAU
author: Anonymous
title: Multiply-Addition --- An Ultra High Performance Dataflow
journal: j-IBM-TDB
volume: 30
number: 3
pages: 982--987
month: aug
monthnumber: 8
year: 1987
CODEN: IBMTAA
ISSN: 0018-8689 OR 00188689
bibdate: Thu Oct 17 12:06:22 2019
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2019.10.17 12:06:22 ???
fjournal: IBM Technical Disclosure Bulletin
keywords: FMA; fused multiply-add
acknowledgement: ack-nhfb
rawauthor: Anonymous
rawtitle: Multiply-Addition --- An Ultra High Performance Dataflow
remark:
Author(s) unknown; I cannot find an online copy of this paper. This may be the first publication on the fused multiply-add operation, first implemented in hardware in early 1990 on the IBM POWER CPU, and standardized in IEEE 754-2008.

entry:
@Article{Anonymous:1987:MAU,
  author =       "Anonymous",
  title =        "Multiply-Addition --- An Ultra High Performance
                 Dataflow",
  journal =      j-IBM-TDB,
  volume =       "30",
  number =       "3",
  pages =        "982--987",
  month =        aug,
  year =         "1987",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Thu Oct 17 12:06:22 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Technical Disclosure Bulletin",
  keywords =     "FMA; fused multiply-add",
  remark =       "Author(s) unknown; I cannot find an online copy of
                 this paper. This may be the first publication on the
                 fused multiply-add operation, first implemented in
                 hardware in early 1990 on the IBM POWER CPU, and
                 standardized in IEEE 754-2008.",
}


bibtype: book
filename: fparith.bib
label: ANSI:1987:AIS
author: ANSI / IEEE
publisher: pub-IEEE-STD
address: pub-IEEE-STD:adr
pages: v + 14
day: 5
month: oct
monthnumber: 10
year: 1987
ISBN: 0-7381-1167-8 OR 0738111678
ISBN13: 978-0-7381-1167-4 OR 9780738111674
bibdate: Thu Mar 02 09:40:18 2006
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2006.03.02 09:40:18 ???
note: Revised 1994. INSPEC Accession Number: 3095617.
acknowledgement: ack-nhfb
rawauthor: {ANSI\slash IEEE}
rawnote: Revised 1994. INSPEC Accession Number: 3095617.
title:
ANSI / IEEE Std 854-1987: An American National Standard: IEEE Standard for Radix-Independent Floating-Point Arithmetic

URL:
http://ieeexplore.ieee.org/xpl/standardstoc.jsp?isnumber=1121&isYear=1987; https://ieeexplore.ieee.org/iel1/2502/1121/00027840.pdf

rawtitle:
{ANSI\slash IEEE Std 854-1987: An American National Standard: IEEE Standard for Radix-Independent Floating-Point Arithmetic}

entry:
@Book{ANSI:1987:AIS,
  author =       "{ANSI\slash IEEE}",
  title =        "{ANSI\slash IEEE Std 854-1987: An American National
                 Standard: IEEE Standard for Radix-Independent
                 Floating-Point Arithmetic}",
  publisher =    pub-IEEE-STD,
  address =      pub-IEEE-STD:adr,
  pages =        "v + 14",
  day =          "5",
  month =        oct,
  year =         "1987",
  ISBN =         "0-7381-1167-8",
  ISBN-13 =      "978-0-7381-1167-4",
  bibdate =      "Thu Mar 02 09:40:18 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Revised 1994. INSPEC Accession Number: 3095617.",
  price =        "US\$44.00",
  URL =          "http://ieeexplore.ieee.org/xpl/standardstoc.jsp?isnumber=1121&isYear=1987;
                 https://ieeexplore.ieee.org/iel1/2502/1121/00027840.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Ardalan:1987:FPR
author: S. Ardalan and S. Alexander
journal: j-IEEE-TRANS-ACOUST-SPEECH
volume: 35
number: 6
pages: 770--783
month: jun
monthnumber: 6
year: 1987
CODEN: IETABA
ISSN: 0096-3518 OR 00963518
bibdate: Sat Jul 16 11:25:06 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:06 MDT
fjournal: IEEE Transactions on Acoustics, Speech, and Signal Processing
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29
rawauthor: S. Ardalan and S. Alexander
title:
Fixed-point roundoff error analysis of the exponentially windowed RLS algorithm for time-varying systems

rawtitle:
Fixed-point roundoff error analysis of the exponentially windowed {RLS} algorithm for time-varying systems

entry:
@Article{Ardalan:1987:FPR,
  author =       "S. Ardalan and S. Alexander",
  title =        "Fixed-point roundoff error analysis of the
                 exponentially windowed {RLS} algorithm for time-varying
                 systems",
  journal =      j-IEEE-TRANS-ACOUST-SPEECH,
  volume =       "35",
  number =       "6",
  pages =        "770--783",
  month =        jun,
  year =         "1987",
  CODEN =        "IETABA",
  ISSN =         "0096-3518",
  bibdate =      "Sat Jul 16 11:25:06 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Acoustics, Speech, and Signal
                 Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
  summary =      "A fixed-point roundoff error analysis of the
                 exponentially windowed RLS algorithm is presented. It
                 is shown that a tradeoff exists in the choice of the
                 forgetting factor {\lambda}. In order to reduce the
                 sensitivity of the algorithm to additive noise, {\&}
                 \ldots{}",
}


bibtype: mastersthesis
filename: fparith.bib
label: Azmi:1987:FPS
author: Aqil M. Azmi
title: A floating point system with variable-length exponent
type: Thesis (M.S.)
school: University of Colorado
address: Boulder, CO, USA
pages: viii + 73
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 arithmetic.; Floating-point arithmetic.
acknowledgement: ack-nhfb
rawauthor: Aqil M. Azmi
rawtitle: A floating point system with variable-length exponent
entry:
@MastersThesis{Azmi:1987:FPS,
  author =       "Aqil M. Azmi",
  title =        "A floating point system with variable-length
                 exponent",
  type =         "Thesis ({M.S.})",
  school =       "University of Colorado",
  address =      "Boulder, CO, USA",
  pages =        "viii + 73",
  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 arithmetic.; Floating-point arithmetic.",
}


bibtype: inproceedings
filename: fparith.bib
label: Balsara:1987:SSS
author: Paras T. Balsara and Robert M. Owens
title: Systolic and Semi-Systolic Digit Serial Multipliers
crossref: Irwin:1987:PSC
pages: 169--173
year: 1987
DOI: https://doi.org/10.1109/ARITH.1987.6158682
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_Balsara_Owens.pdf
keywords: ARITH-8
acknowledgement: ack-nhfb
rawauthor: Paras T. Balsara and Robert M. Owens
rawtitle: Systolic and Semi-Systolic Digit Serial Multipliers
abstract:
Digit serial data transmission can be used to an advantage in the design of special purpose processors where communication issues dominate and where digit pipelining can be used to maintain high data rates. VLSI signal processing is one such problem domain. We propose designs of systolic and semi-systolic digit serial multipliers. These multipliers are programmable i.e., one operand is pre-stored in the multiplier and the other operand is fed in a digit serial fashion.. The VLSI implementation of the systolic multiplier is also given. This systolic multiplier is used in our VLSI signal processing system.

rawabstract:
Digit serial data transmission can be used to an advantage in the design of special purpose processors where communication issues dominate and where digit pipelining can be used to maintain high data rates. VLSI signal processing is one such problem domain. We propose designs of systolic and semi-systolic digit serial multipliers. These multipliers are programmable i.e., one operand is pre-stored in the multiplier and the other operand is fed in a digit serial fashion.. The VLSI implementation of the systolic multiplier is also given. This systolic multiplier is used in our VLSI signal processing system.

entry:
@InProceedings{Balsara:1987:SSS,
  author =       "Paras T. Balsara and Robert M. Owens",
  title =        "Systolic and Semi-Systolic Digit Serial Multipliers",
  crossref =     "Irwin:1987:PSC",
  pages =        "169--173",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158682",
  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_Balsara_Owens.pdf",
  abstract =     "Digit serial data transmission can be used to an
                 advantage in the design of special purpose processors
                 where communication issues dominate and where digit
                 pipelining can be used to maintain high data rates.
                 VLSI signal processing is one such problem domain. We
                 propose designs of systolic and semi-systolic digit
                 serial multipliers. These multipliers are programmable
                 i.e., one operand is pre-stored in the multiplier and
                 the other operand is fed in a digit serial fashion..
                 The VLSI implementation of the systolic multiplier is
                 also given. This systolic multiplier is used in our
                 VLSI signal processing system.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}


bibtype: mastersthesis
filename: fparith.bib
label: Baranyk:1987:EBP
author: Michael L. Baranyk
title: Extensions beyond the proposed IEEE standard number 754 for binary floating point arithmetic
type: Thesis (M.S.)
school: Marquette University
address: Milwaukee, WI, USA
pages: various
year: 1987
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
acknowledgement: ack-nhfb
rawauthor: Michael L. Baranyk
rawtitle: Extensions beyond the proposed {IEEE} standard number 754 for binary floating point arithmetic
keywords:
Binary system (Mathematics); Floating-point arithmetic.; Institute of Electrical and Electronics Engineers. --- IEEE; standard 754.

entry:
@MastersThesis{Baranyk:1987:EBP,
  author =       "Michael L. Baranyk",
  title =        "Extensions beyond the proposed {IEEE} standard number
                 754 for binary floating point arithmetic",
  type =         "Thesis ({M.S.})",
  school =       "Marquette University",
  address =      "Milwaukee, WI, USA",
  pages =        "various",
  year =         "1987",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Binary system (Mathematics); Floating-point
                 arithmetic.; Institute of Electrical and Electronics
                 Engineers. --- IEEE; standard 754.",
}


bibtype: inproceedings
filename: fparith.bib
label: Barrett:1987:FAR
author: Geoff Barrett
title: A formal approach to rounding
crossref: Irwin:1987:PSC
pages: 247--254
year: 1987
DOI: https://doi.org/10.1109/ARITH.1987.6158683
bibdate: Wed Nov 24 12:49:55 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.24 12:49:55 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Barrett.pdf
keywords: ARITH-8
acknowledgement: ack-nhfb
rawauthor: Geoff Barrett
rawtitle: A formal approach to rounding
abstract:
This paper presents a formal description of rounding, as specified in the IEEE Standard, and an algorithm to perform the task along with its proof of correctness.

rawabstract:
This paper presents a formal description of rounding, as specified in the IEEE Standard, and an algorithm to perform the task along with its proof of correctness.

entry:
@InProceedings{Barrett:1987:FAR,
  author =       "Geoff Barrett",
  title =        "A formal approach to rounding",
  crossref =     "Irwin:1987:PSC",
  pages =        "247--254",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158683",
  bibdate =      "Wed Nov 24 12:49:55 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Barrett.pdf",
  abstract =     "This paper presents a formal description of rounding,
                 as specified in the IEEE Standard, and an algorithm to
                 perform the task along with its proof of correctness.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}


bibtype: techreport
filename: fparith.bib
label: Barrett:1987:FMA
author: Geoff Barrett
title: Formal methods applied to a floating point number system
type: Technical monograph
number: PRG 58
institution: Oxford University Computing Laboratory
address: Oxford, England
pages: 47
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: Binary system (Mathematics).; Floating-point arithmetic.; Formal languages.
acknowledgement: ack-nhfb
rawauthor: Geoff Barrett
rawtitle: Formal methods applied to a floating point number system
entry:
@TechReport{Barrett:1987:FMA,
  author =       "Geoff Barrett",
  title =        "Formal methods applied to a floating point number
                 system",
  type =         "Technical monograph",
  number =       "PRG 58",
  institution =  "Oxford University Computing Laboratory",
  address =      "Oxford, England",
  pages =        "47",
  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 =     "Binary system (Mathematics).; Floating-point
                 arithmetic.; Formal languages.",
}


bibtype: article
filename: fparith.bib
label: Boettner:1987:QA
author: H. Bottner
title: Quadratwurzel-Algorithmus toenglish Square-Root Algorithms endtoenglish
journal: j-MC
volume: 5
pages: 58
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: H. B{\"o}ttner
rawtitle: {Quadratwurzel-Algorithmus} \toenglish {Square-Root Algorithms} \endtoenglish
entry:
@Article{Boettner:1987:QA,
  author =       "H. B{\"o}ttner",
  title =        "{Quadratwurzel-Algorithmus} \toenglish {Square-Root
                 Algorithms} \endtoenglish",
  journal =      j-MC,
  volume =       "5",
  pages =        "58",
  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: incollection
filename: fparith.bib
label: Bohlender:1987:DFP
author: G. Bohlender and T. Teufel
title: A Decimal Floating-Point Processor for Optimal Arithmetic
crossref: Kaucher:1987:CAS
pages: 31--58
year: 1987
bibdate: Fri Nov 28 11:46:56 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 11:46:56 ???
keywords: decimal floating-point arithmetic
acknowledgement: ack-nhfb
rawauthor: G. Bohlender and T. Teufel
rawtitle: A Decimal Floating-Point Processor for Optimal Arithmetic
entry:
@InCollection{Bohlender:1987:DFP,
  author =       "G. Bohlender and T. Teufel",
  title =        "A Decimal Floating-Point Processor for Optimal
                 Arithmetic",
  crossref =     "Kaucher:1987:CAS",
  pages =        "31--58",
  year =         "1987",
  bibdate =      "Fri Nov 28 11:46:56 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}


bibtype: article
filename: fparith.bib
label: Boisvert:1987:AAH
author: Ronald F. Boisvert
title: Algorithm 651: Algorithm HFFT --- High-Order Fast-Direct Solution of the Helmholtz Equation
journal: j-TOMS
volume: 13
number: 3
pages: 235--249
month: sep
monthnumber: 9
year: 1987
CODEN: ACMSCU
DOI: https://doi.org/10.1145/29380.214342
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 65V05
MRnumber: 918 578
bibdate: Sun Sep 4 21:40:33 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.04 21:40:33 ???
note: See also cite Johnson:1987:CES.
URL: http://www.acm.org/pubs/citations/journals/toms/1987-13-3/p235-boisvert/
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms; theory; verification
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Ronald F. Boisvert
rawnote: See also \cite{Johnson:1987:CES}.
abstract:
HFFT is a software package for solving the Helmholtz equation on bounded two- and three-dimensional rectangular domains with Dirichlet, Neumann, or periodic boundary conditions. The software is the result of combining new fourth-order accurate compact finite difference (HODIE) discretizations and a fast-direct solution technique (the Fourier method). In this paper we briefly describe the user interface to HFFT and present an example of its usage and several details of its implementation.

subject:
bf G.1.8: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Elliptic equations. bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.

rawabstract:
HFFT is a software package for solving the Helmholtz equation on bounded two- and three-dimensional rectangular domains with Dirichlet, Neumann, or periodic boundary conditions. The software is the result of combining new fourth-order accurate compact finite difference (HODIE) discretizations and a fast-direct solution technique (the Fourier method). In this paper we briefly describe the user interface to HFFT and present an example of its usage and several details of its implementation.

rawtitle:
{Algorithm 651}: Algorithm {HFFT}\emdash High-Order Fast-Direct Solution of the {Helmholtz} Equation

entry:
@Article{Boisvert:1987:AAH,
  author =       "Ronald F. Boisvert",
  title =        "{Algorithm 651}: Algorithm {HFFT}\emdash High-Order
                 Fast-Direct Solution of the {Helmholtz} Equation",
  journal =      j-TOMS,
  volume =       "13",
  number =       "3",
  pages =        "235--249",
  month =        sep,
  year =         "1987",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/29380.214342",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65V05",
  MRnumber =     "918 578",
  bibdate =      "Sun Sep 4 21:40:33 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See also \cite{Johnson:1987:CES}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1987-13-3/p235-boisvert/",
  abstract =     "HFFT is a software package for solving the Helmholtz
                 equation on bounded two- and three-dimensional
                 rectangular domains with Dirichlet, Neumann, or
                 periodic boundary conditions. The software is the
                 result of combining new fourth-order accurate compact
                 finite difference (HODIE) discretizations and a
                 fast-direct solution technique (the Fourier method). In
                 this paper we briefly describe the user interface to
                 HFFT and present an example of its usage and several
                 details of its implementation.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory; verification",
  subject =      "{\bf G.1.8}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Partial Differential Equations, Elliptic
                 equations. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Algorithm analysis.",
}


bibtype: article
filename: fparith.bib
label: Bose:1987:DAR
author: B. Bose
title: $2$-dimensional arithmetic residue check codes
journal: j-COMPUT-MATH-APPL
volume: 13
number: 5--6
pages: 547--554
year: 1987
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 19:01:00 MST 2017
bibtimestamp: 2017.03.01 19:01:00 MST
URL: http://www.sciencedirect.com/science/article/pii/0898122187900824
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: B. Bose
rawtitle: $2$-dimensional arithmetic residue check codes
entry:
@Article{Bose:1987:DAR,
  author =       "B. Bose",
  title =        "$2$-dimensional arithmetic residue check codes",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "13",
  number =       "5--6",
  pages =        "547--554",
  month =        "????",
  year =         "1987",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 19:01:00 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122187900824",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: inproceedings
filename: fparith.bib
label: Bose:1987:FMD
author: B. K. Bose and L. Pei and G. S. Taylor and D. A. Patterson
title: Fast Multiply and Divide for a VLSI Floating-Point Unit
crossref: Irwin:1987:PSC
pages: 87--93
year: 1987
DOI: https://doi.org/10.1109/ARITH.1987.6158684
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_Bose_Pei_Taylor_Patterson.pdf
keywords: ARITH-8
acknowledgement: ack-nhfb
rawauthor: B. K. Bose and L. Pei and G. S. Taylor and D. A. Patterson
rawtitle: Fast Multiply and Divide for a {VLSI} Floating-Point Unit
abstract:
This paper presents the design of a fast and area-efficient multiply-divide unit used in building a VLSI floating-point processor (FPU), conforming to the IEEE standard 754. Details of the algorithms, implementation techniques and design tradeoffs are presented. The multiplier and divider are implemented in 2 micron CMOS technology with two layers of metal, and occupy 23 square mm (23% of the entire FPU). We expect to perform extended-precision multiplication and division in 1.1 and 2.8 microseconds, respectively.

rawabstract:
This paper presents the design of a fast and area-efficient multiply-divide unit used in building a VLSI floating-point processor (FPU), conforming to the IEEE standard 754. Details of the algorithms, implementation techniques and design tradeoffs are presented. The multiplier and divider are implemented in 2 micron CMOS technology with two layers of metal, and occupy 23 square mm (23\% of the entire FPU). We expect to perform extended-precision multiplication and division in 1.1 and 2.8 microseconds, respectively.

entry:
@InProceedings{Bose:1987:FMD,
  author =       "B. K. Bose and L. Pei and G. S. Taylor and D. A.
                 Patterson",
  title =        "Fast Multiply and Divide for a {VLSI} Floating-Point
                 Unit",
  crossref =     "Irwin:1987:PSC",
  pages =        "87--93",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158684",
  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_Bose_Pei_Taylor_Patterson.pdf",
  abstract =     "This paper presents the design of a fast and
                 area-efficient multiply-divide unit used in building a
                 VLSI floating-point processor (FPU), conforming to the
                 IEEE standard 754. Details of the algorithms,
                 implementation techniques and design tradeoffs are
                 presented. The multiplier and divider are implemented
                 in 2 micron CMOS technology with two layers of metal,
                 and occupy 23 square mm (23\% of the entire FPU). We
                 expect to perform extended-precision multiplication and
                 division in 1.1 and 2.8 microseconds, respectively.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}


bibtype: phdthesis
filename: fparith.bib
label: Braune:1987:HSF
author: K. Braune
type: Dissertation
school: Universitat Karlsruhe
address: Karlsruhe, Germany
year: 1987
bibdate: Fri Sep 16 16:30:40 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.16 16:30:40 ???
acknowledgement: ack-nj
rawauthor: K. Braune
title:
Hochgenaue Standardfunktionen fur reelle und komplexe Punkte und Intervalle in beliebigen Gleitpunktrastern toenglish High-Accuracy Elementary Functions for Real and Complex Points and Intervals in Arbitrary Floating-Point Systems endtoenglish 

rawtitle:
{Hochgenaue Standardfunktionen f{\"u}r reelle und komplexe Punkte und Intervalle in beliebigen Gleitpunktrastern} \toenglish {High-Accuracy Elementary Functions for Real and Complex Points and Intervals in Arbitrary Floating-Point Systems} \endtoenglish

entry:
@PhdThesis{Braune:1987:HSF,
  author =       "K. Braune",
  title =        "{Hochgenaue Standardfunktionen f{\"u}r reelle und
                 komplexe Punkte und Intervalle in beliebigen
                 Gleitpunktrastern} \toenglish {High-Accuracy Elementary
                 Functions for Real and Complex Points and Intervals in
                 Arbitrary Floating-Point Systems} \endtoenglish",
  type =         "Dissertation",
  school =       "Universit{\"a}t Karlsruhe",
  address =      "Karlsruhe, Germany",
  pages =        "??",
  year =         "1987",
  bibdate =      "Fri Sep 16 16:30:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: incollection
filename: fparith.bib
label: Breuer:1987:NMR
author: P. T. Breuer
title: A New Method for Real Rational Uniform Approximation
crossref: Mason:1987:AAB
pages: 265--284
year: 1987
bibdate: Thu Sep 01 12:25:00 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 12:25:00 ???
acknowledgement: ack-nj
rawauthor: P. T. Breuer
rawtitle: A New Method for Real Rational Uniform Approximation
entry:
@InCollection{Breuer:1987:NMR,
  author =       "P. T. Breuer",
  title =        "A New Method for Real Rational Uniform Approximation",
  crossref =     "Mason:1987:AAB",
  pages =        "265--284",
  year =         "1987",
  bibdate =      "Thu Sep 01 12:25:00 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: inproceedings
filename: fparith.bib
label: Carter:1987:SAT
author: Tony M. Carter
title: Structured Arithmetic Tiling of Integrated Circuits
crossref: Irwin:1987:PSC
pages: 41--48
year: 1987
DOI: https://doi.org/10.1109/ARITH.1987.6158685
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_Carter.pdf
keywords: ARITH-8
acknowledgement: ack-nhfb
rawauthor: Tony M. Carter
rawtitle: Structured Arithmetic Tiling of Integrated Circuits
abstract:
Robertson's Theory of Decomposition and Structured Tiling (an IC design technique) are combined in a structured arithmetic circuit design method. This method, extended by a set of inverse operators and a set of multiply operators, is used with computer-aided design tools to automate the design of arithmetic circuits.

rawabstract:
Robertson's Theory of Decomposition and Structured Tiling (an IC design technique) are combined in a structured arithmetic circuit design method. This method, extended by a set of inverse operators and a set of multiply operators, is used with computer-aided design tools to automate the design of arithmetic circuits.

entry:
@InProceedings{Carter:1987:SAT,
  author =       "Tony M. Carter",
  title =        "Structured Arithmetic Tiling of Integrated Circuits",
  crossref =     "Irwin:1987:PSC",
  pages =        "41--48",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158685",
  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_Carter.pdf",
  abstract =     "Robertson's Theory of Decomposition and Structured
                 Tiling (an IC design technique) are combined in a
                 structured arithmetic circuit design method. This
                 method, extended by a set of inverse operators and a
                 set of multiply operators, is used with computer-aided
                 design tools to automate the design of arithmetic
                 circuits.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}


bibtype: inproceedings
filename: fparith.bib
label: Cavallaro:1987:CAS
author: Joseph R. Cavallaro and Franklin T. Luk
title: CORDIC Arithmetic for an SVD Processor
crossref: Irwin:1987:PSC
pages: 113--120
year: 1987
DOI: https://doi.org/10.1109/ARITH.1987.6158686
bibdate: Fri Nov 16 21:39:46 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.16 21:39:46 ???
URL: http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Cavallaro_Luk.pdf
keywords: ARITH-8
acknowledgement: ack-nhfb
rawauthor: Joseph R. Cavallaro and Franklin T. Luk
rawtitle: {CORDIC} Arithmetic for an {SVD} Processor
abstract:
Arithmetic issues in the calculation of the Singular Value Decomposition (SVD) are discussed. Traditional algorithms using hardware division and square root are replaced with the special purpose CORDIC algorithms for computing vector rotations and inverse tangents. The CORDIC $ 2 times 2 $ SVD processor can be twice as fast as one assembled from traditional hardware units. A prototype VISI implementation of a CORDIC SVD processor array is planned for use in real-time signal processing applications.

rawabstract:
Arithmetic issues in the calculation of the Singular Value Decomposition (SVD) are discussed. Traditional algorithms using hardware division and square root are replaced with the special purpose CORDIC algorithms for computing vector rotations and inverse tangents. The CORDIC $ 2 \times 2 $ SVD processor can be twice as fast as one assembled from traditional hardware units. A prototype VISI implementation of a CORDIC SVD processor array is planned for use in real-time signal processing applications.

entry:
@InProceedings{Cavallaro:1987:CAS,
  author =       "Joseph R. Cavallaro and Franklin T. Luk",
  title =        "{CORDIC} Arithmetic for an {SVD} Processor",
  crossref =     "Irwin:1987:PSC",
  pages =        "113--120",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158686",
  bibdate =      "Fri Nov 16 21:39:46 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Cavallaro_Luk.pdf",
  abstract =     "Arithmetic issues in the calculation of the Singular
                 Value Decomposition (SVD) are discussed. Traditional
                 algorithms using hardware division and square root are
                 replaced with the special purpose CORDIC algorithms for
                 computing vector rotations and inverse tangents. The
                 CORDIC $ 2 \times 2 $ SVD processor can be twice as
                 fast as one assembled from traditional hardware units.
                 A prototype VISI implementation of a CORDIC SVD
                 processor array is planned for use in real-time signal
                 processing applications.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}


bibtype: article
filename: fparith.bib
label: Chandra:1987:ACR
author: D. V. Chandra
journal: j-IEEE-TRANS-ACOUST-SPEECH
volume: 35
number: 11
pages: 1633--1636
month: nov
monthnumber: 11
year: 1987
CODEN: IETABA
ISSN: 0096-3518 OR 00963518
bibdate: Sat Jul 16 11:25:06 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:06 MDT
fjournal: IEEE Transactions on Acoustics, Speech, and Signal Processing
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29
rawauthor: D. V. Chandra
title:
Accumulation of coefficient roundoff error in fast Fourier transforms implemented with logarithmic number system

rawtitle:
Accumulation of coefficient roundoff error in fast {Fourier} transforms implemented with logarithmic number system

entry:
@Article{Chandra:1987:ACR,
  author =       "D. V. Chandra",
  title =        "Accumulation of coefficient roundoff error in fast
                 {Fourier} transforms implemented with logarithmic
                 number system",
  journal =      j-IEEE-TRANS-ACOUST-SPEECH,
  volume =       "35",
  number =       "11",
  pages =        "1633--1636",
  month =        nov,
  year =         "1987",
  CODEN =        "IETABA",
  ISSN =         "0096-3518",
  bibdate =      "Sat Jul 16 11:25:06 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Acoustics, Speech, and Signal
                 Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
  summary =      "When a fast Fourier transform (FFT) is implemented on
                 a digital computer or with special-purpose hardware,
                 quantization errors will arise due to finite word
                 lengths in the digital system. This correspondence
                 presents an analysis of error \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Chen:1987:MFP
author: Chang-Fuu Chen
title: A modified floating-point code for voice coding and its applications
journal: j-J-CHINESE-INST-ENG
volume: 10
number: 4
pages: 421--427
month: jul
monthnumber: 7
year: 1987
CODEN: CKCKDZ
ISSN: 0253-3839 OR 02533839
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: Journal of the Chinese Institute of Engineers = Chung-kuo kung ch'eng hsueh kan
acknowledgement: ack-nhfb
affiliation: Tatung Institute of Technology, Taipei, Taiwan
rawauthor: Chang-Fuu Chen
rawtitle: A modified floating-point code for voice coding and its applications
subject:
E. Data; E.4 CODING AND INFORMATION THEORY; I. Computing Methodologies; I.2 ARTIFICIAL INTELLIGENCE; I. Computing Methodologies; I.2 ARTIFICIAL INTELLIGENCE; I. Computing Methodologies; I.5 PATTERN RECOGNITION

entry:
@Article{Chen:1987:MFP,
  author =       "Chang-Fuu Chen",
  title =        "A modified floating-point code for voice coding and
                 its applications",
  journal =      j-J-CHINESE-INST-ENG,
  volume =       "10",
  number =       "4",
  pages =        "421--427",
  month =        jul,
  year =         "1987",
  CODEN =        "CKCKDZ",
  ISSN =         "0253-3839",
  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 =  "Tatung Institute of Technology, Taipei, Taiwan",
  bibno =        "43559",
  catcode =      "E.4; I.2.7; I.2.10; I.5.4",
  CRclass =      "E.4 Data compaction and compression; I.2.7 Natural
                 Language Processing; I.2.7 Speech recognition and
                 understanding; I.2.10 Vision and Scene Understanding;
                 I.2.10 Modeling and recovery of physical attributes;
                 I.5.4 Applications; I.5.4 Signal processing",
  descriptor =   "Data, CODING AND INFORMATION THEORY, Data compaction
                 and compression; Computing Methodologies, ARTIFICIAL
                 INTELLIGENCE, Natural Language Processing, Speech
                 recognition and understanding; Computing Methodologies,
                 ARTIFICIAL INTELLIGENCE, Vision and Scene
                 Understanding, Modeling and recovery of physical
                 attributes; Computing Methodologies, PATTERN
                 RECOGNITION, Applications, Signal processing",
  fjournal =     "Journal of the Chinese Institute of Engineers =
                 Chung-kuo kung ch'eng hsueh kan",
  genterm =      "THEORY; ALGORITHMS; HUMAN FACTORS; DESIGN",
  guideno =      "1988-11733",
  journalabbrev = "J. Chin. Inst. Eng.",
  subject =      "E. Data; E.4 CODING AND INFORMATION THEORY; I.
                 Computing Methodologies; I.2 ARTIFICIAL INTELLIGENCE;
                 I. Computing Methodologies; I.2 ARTIFICIAL
                 INTELLIGENCE; I. Computing Methodologies; I.5 PATTERN
                 RECOGNITION",
}


