# bibtab

bibtype: article
filename: elefunt.bib
label: Matos:1992:CAP
author: Ana C. Matos
title: Convergence and acceleration properties for the vector $ epsilon $-algorithm
journal: j-NUMER-ALGORITHMS
volume: 3
number: 1--4
pages: 313--319
month: dec
monthnumber: 12
year: 1992
CODEN: NUALEG
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
MRclass: 65B99
MRnumber: 93h:65006
bibdate: Fri Nov 6 18:06:29 MST 1998
bibsource: http://www.math.psu.edu/dna/contents/na.html; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1998.11.06 18:06:29 MST
note: Extrapolation and rational approximation (Puerto de la Cruz, 1992).
fjournal: Numerical Algorithms
acknowledgement: ack-nhfb
corpsource: Fac. de Ciencias, Porto Univ., Portugal
journalURL: http://link.springer.com/journal/11075
treatment: T Theoretical or Mathematical
rawauthor: Ana C. Matos
rawnote: Extrapolation and rational approximation (Puerto de la Cruz, 1992).
rawtitle: Convergence and acceleration properties for the vector $ \epsilon $-algorithm
keywords:
acceleration; convergence acceleration; convergence of numerical methods; convergence speed; exactness; extrapolation; extrapolation algorithm; speed of convergence; vector $epsilon $-algorithm; vector sequences

entry:
@Article{Matos:1992:CAP,
  author =       "Ana C. Matos",
  title =        "Convergence and acceleration properties for the vector
                 $ \epsilon $-algorithm",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "3",
  number =       "1--4",
  pages =        "313--319",
  month =        dec,
  year =         "1992",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  MRclass =      "65B99",
  MRnumber =     "93h:65006",
  bibdate =      "Fri Nov 6 18:06:29 MST 1998",
  bibsource =    "http://www.math.psu.edu/dna/contents/na.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Extrapolation and rational approximation (Puerto de la
                 Cruz, 1992).",
  acknowledgement = ack-nhfb,
  classification = "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  conflocation = "Puerto de la Cruz, Spain; 13-17 Jan. 1992",
  conftitle =    "International Mathematical Congress on Extrapolation
                 and Rational Approximation",
  corpsource =   "Fac. de Ciencias, Porto Univ., Portugal",
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "acceleration; convergence acceleration; convergence of
                 numerical methods; convergence speed; exactness;
                 extrapolation; extrapolation algorithm; speed of
                 convergence; vector $\epsilon$-algorithm; vector
                 sequences",
  pubcountry =   "Switzerland",
  treatment =    "T Theoretical or Mathematical",
}


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


bibtype: article
filename: elefunt.bib
label: Mikami:1992:NDO
author: N. Mikami and M. Kobayashi and Y. Yokoyama
title: A New DSP-Oriented Algorithm for Calculation of the Square Root Using a Nonlinear Digital Filter
journal: j-IEEE-TRANS-SIG-PROC
volume: 40
number: 7
pages: 1663--1669
month: jul
monthnumber: 7
year: 1992
CODEN: ITPRED
DOI: https://doi.org/10.1109/78.143438
ISSN: 1053-587X (print), 1941-0476 (electronic) OR 1053587X (print), 19410476 (electronic)
ISSNL: 1053-587X OR 1053587X
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
fjournal: IEEE Transactions on Signal Processing
acknowledgement: ack-nj
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78
rawauthor: N. Mikami and M. Kobayashi and Y. Yokoyama
rawtitle: A New {DSP}-Oriented Algorithm for Calculation of the Square Root Using a Nonlinear Digital Filter
entry:
@Article{Mikami:1992:NDO,
  author =       "N. Mikami and M. Kobayashi and Y. Yokoyama",
  title =        "A New {DSP}-Oriented Algorithm for Calculation of the
                 Square Root Using a Nonlinear Digital Filter",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "40",
  number =       "7",
  pages =        "1663--1669",
  month =        jul,
  year =         "1992",
  CODEN =        "ITPRED",
  DOI =          "https://doi.org/10.1109/78.143438",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  summary =      "A high-speed algorithm for calculating the square root
                 is proposed. This algorithm, which can be regarded as
                 calculation of the step response of a kind of nonlinear
                 IIR filter, requires no divisions. Therefore, it is
                 suitable for a VLSI digital \ldots{}",
}


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


bibtype: article
filename: elefunt.bib
label: Paris:1992:EIA
author: R. B. Paris and A. D. Wood
title: Exponentially-improved asymptotics for the gamma function
journal: j-J-COMPUT-APPL-MATH
volume: 41
number: 1--2
pages: 135--143
day: 20
month: aug
monthnumber: 8
year: 1992
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:20:53 MST 2017
bibtimestamp: 2017.02.25 12:20:53 MST
URL: http://www.sciencedirect.com/science/article/pii/037704279290243Q
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: R. B. Paris and A. D. Wood
rawtitle: Exponentially-improved asymptotics for the gamma function
entry:
@Article{Paris:1992:EIA,
  author =       "R. B. Paris and A. D. Wood",
  title =        "Exponentially-improved asymptotics for the gamma
                 function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "41",
  number =       "1--2",
  pages =        "135--143",
  day =          "20",
  month =        aug,
  year =         "1992",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:20:53 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/037704279290243Q",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Paszkowski:1992:CAC
author: Stefan Paszkowski
title: Convergence acceleration of continued fractions of Poincare's type $1$
journal: j-NUMER-ALGORITHMS
volume: 2
number: 2
pages: 155--170
year: 1992
CODEN: NUALEG
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
MRclass: 65B05 (40A15)
MRnumber: 93c:65006
MRreviewer: A. Bultheel
bibdate: Fri Nov 6 18:06:29 MST 1998
bibsource: http://www.math.psu.edu/dna/contents/na.html; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1998.11.06 18:06:29 MST
fjournal: Numerical Algorithms
acknowledgement: ack-nhfb
corpsource: Instytut Niskich Temp. i Badan Strukturalnych PAN, Wroclaw, Poland
journalURL: http://link.springer.com/journal/11075
treatment: T Theoretical or Mathematical
rawauthor: Stefan Paszkowski
rawtitle: Convergence acceleration of continued fractions of {Poincar{\'e}}'s type $1$
keywords:
asymptotic behaviour; continued fractions; convergence acceleration; convergence of numerical methods; function approximation

entry:
@Article{Paszkowski:1992:CAC,
  author =       "Stefan Paszkowski",
  title =        "Convergence acceleration of continued fractions of
                 {Poincar{\'e}}'s type $1$",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "2",
  number =       "2",
  pages =        "155--170",
  month =        "????",
  year =         "1992",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  MRclass =      "65B05 (40A15)",
  MRnumber =     "93c:65006",
  MRreviewer =   "A. Bultheel",
  bibdate =      "Fri Nov 6 18:06:29 MST 1998",
  bibsource =    "http://www.math.psu.edu/dna/contents/na.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  classification = "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  corpsource =   "Instytut Niskich Temp. i Badan Strukturalnych PAN,
                 Wroclaw, Poland",
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "asymptotic behaviour; continued fractions; convergence
                 acceleration; convergence of numerical methods;
                 function approximation",
  pubcountry =   "Switzerland",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: book
filename: elefunt.bib
label: Prudnikov:1992:IS
author: Anatolij P. Prudnikov and Jurij A. Bryckov and Oleg I. Maricev
title: Integrals and series. More special functions
volume: 3
publisher: Gordon and Breach Science Publishers
address: New York, NY, USA
pages: xx + 618
year: 1992
ISBN: 2-88124-097-6 OR 2881240976
ISBN13: 978-2-88124-097-3 OR 9782881240973
LCCN: QA308 P68 1986
bibdate: Thu Nov 2 15:54:36 MDT 2017
bibsource: fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.11.02 15:54:36 MDT
remark: Translated from the Russian by N. M. Queen.
subject: Mathematics
acknowledgement: ack-nhfb
rawauthor: Anatolij P. Prudnikov and Jurij A. Bry{\v{c}}kov and Oleg I. Mari{\v{c}}ev
rawtitle: Integrals and series. {More} special functions
entry:
@Book{Prudnikov:1992:IS,
  author =       "Anatolij P. Prudnikov and Jurij A. Bry{\v{c}}kov and
                 Oleg I. Mari{\v{c}}ev",
  title =        "Integrals and series. {More} special functions",
  volume =       "3",
  publisher =    "Gordon and Breach Science Publishers",
  address =      "New York, NY, USA",
  pages =        "xx + 618",
  year =         "1992",
  ISBN =         "2-88124-097-6",
  ISBN-13 =      "978-2-88124-097-3",
  LCCN =         "QA308 P68 1986",
  bibdate =      "Thu Nov 2 15:54:36 MDT 2017",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  remark =       "Translated from the Russian by N. M. Queen.",
  seriestableofcontents = "v. 1. Elementary functions \\
                 v. 2. Special functions \\
                 v. 3. More special functions \\
                 v. 4. Direct Laplace transforms \\
                 v. 5. Inverse Laplace transforms",
  subject =      "Mathematics",
}


bibtype: book
filename: elefunt.bib
label: Rockett:1992:CF
author: Andrew Mansfield Rockett and Peter Szusz
title: Continued Fractions
publisher: pub-WORLD-SCI
address: pub-WORLD-SCI:adr
pages: ix + 188
year: 1992
ISBN: 981-02-1047-7 OR 9810210477
ISBN13: 978-981-02-1047-2 OR 9789810210472
LCCN: QA295.R6 1992; QA295 .R6 1992
bibdate: Wed Apr 15 16:49:47 MDT 2009
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; melvyl.cdlib.org:210/CDL90
bibtimestamp: 2009.04.15 16:49:47 MDT
subject: continued fractions; processes, infinite
acknowledgement: ack-nhfb
rawauthor: Andrew Mansfield Rockett and Peter Sz{\"u}sz
rawtitle: Continued Fractions
remark:
From the first line of the Preface: ``The theory of continued fractions does not receive the attention it deserves.''.

TOC:
I. Introduction 1. What is a continued fraction? 2. Regular continued fractions 3. The transformation $ T(x) = 1 / x $ 4. The quantity $ D_k = B_k t - A_k $ 5. Convergents to a number and its reciprocal 6. The ratio $ xi _k = B_k - 1 / B_k $ 7. The golden ratio and the Fibonacci sequence 8. The continued fraction for $ e $ II. The Law of Best Approximation 1. Best approximation 2. The first proof 3. A theorem of Lagrange 4. Ostrowski's algorithm and a second proof. 5. The approximation $ B ||b t|| < K $ 6. The $t$-expansion of a real number III. Periodic Continued Fractions 1. The classical theorems 2. Period lengths 3. Second order linear recurrences IV. Applications 1. Gear ratio problems 2. Pell's equation 3. Fermat's theorem on the sum of two squares 4. Hall's theorem 5. A theorem of Hurwitz 6. The Lagrange and Markov spectra 7. Asymmetric approximation and Segre's theorem 8. Approximation by non-convergents 9. Inhomogeneous approximation 10. Szekeres' empty parallelogram theorem V. Metrical Theory 1. Numbers with bounded partial quotients 2. The Borel--Cantelli lemma 3. Random variables and expectations 4. Chebyshev's inequality and large number laws 5. The Gauss--Kuzmin theorem 6. The distribution of $ xi _n $ 7. Partial quotients are weakly dependent 8. Khintchine's theorem 9. The Khintchine--Levy theorem for $ sqrt [n]B_n $ VI. Applications to Metrical Diophantine Approximation Notes Bibliography Symbols Index

rawTOC:
I. Introduction \\ 1. What is a continued fraction? \\ 2. Regular continued fractions \\ 3. The transformation $ T(x) = \{ 1 / x \} $ \\ 4. The quantity $ D_k = B_k t - A_k $ \\ 5. Convergents to a number and its reciprocal \\ 6. The ratio $ \xi_k = B_{k - 1} / B_k $ \\ 7. The golden ratio and the Fibonacci sequence \\ 8. The continued fraction for $ e $ \\ \\ II. The Law of Best Approximation \\ 1. Best approximation \\ 2. The first proof \\ 3. A theorem of Lagrange \\ 4. Ostrowski's algorithm and a second proof. \\ 5. The approximation $ B ||b t|| < K $ \\ 6. The $t$-expansion of a real number \\ \\ III. Periodic Continued Fractions \\ 1. The classical theorems \\ 2. Period lengths \\ 3. Second order linear recurrences \\ \\ IV. Applications \\ 1. Gear ratio problems \\ 2. Pell's equation \\ 3. Fermat's theorem on the sum of two squares \\ 4. Hall's theorem \\ 5. A theorem of Hurwitz \\ 6. The Lagrange and Markov spectra \\ 7. Asymmetric approximation and S{\`e}gre's theorem \\ 8. Approximation by non-convergents \\ 9. Inhomogeneous approximation \\ 10. Szekeres' empty parallelogram theorem \\ \\ V. Metrical Theory \\ 1. Numbers with bounded partial quotients \\ 2. The Borel--Cantelli lemma \\ 3. Random variables and expectations \\ 4. Chebyshev's inequality and large number laws \\ 5. The Gauss--Kuzmin theorem \\ 6. The distribution of $ \xi_n $ \\ 7. Partial quotients are weakly dependent \\ 8. Khintchine's theorem \\ 9. The Khintchine--L{\'e}vy theorem for $ \sqrt[n]{B_n} $ \\ \\ VI. Applications to Metrical Diophantine Approximation \\ Notes \\ Bibliography \\ Symbols \\ Index

entry:
@Book{Rockett:1992:CF,
  author =       "Andrew Mansfield Rockett and Peter Sz{\"u}sz",
  title =        "Continued Fractions",
  publisher =    pub-WORLD-SCI,
  address =      pub-WORLD-SCI:adr,
  pages =        "ix + 188",
  year =         "1992",
  ISBN =         "981-02-1047-7",
  ISBN-13 =      "978-981-02-1047-2",
  LCCN =         "QA295.R6 1992; QA295 .R6 1992",
  bibdate =      "Wed Apr 15 16:49:47 MDT 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 melvyl.cdlib.org:210/CDL90",
  acknowledgement = ack-nhfb,
  remark =       "From the first line of the Preface: ``The theory of
                 continued fractions does not receive the attention it
                 deserves.''.",
  subject =      "continued fractions; processes, infinite",
  tableofcontents = "I. Introduction \\
                 1. What is a continued fraction? \\
                 2. Regular continued fractions \\
                 3. The transformation $ T(x) = \{ 1 / x \} $ \\
                 4. The quantity $ D_k = B_k t - A_k $ \\
                 5. Convergents to a number and its reciprocal \\
                 6. The ratio $ \xi_k = B_{k - 1} / B_k $ \\
                 7. The golden ratio and the Fibonacci sequence \\
                 8. The continued fraction for $ e $ \\
                 \\
                 II. The Law of Best Approximation \\
                 1. Best approximation \\
                 2. The first proof \\
                 3. A theorem of Lagrange \\
                 4. Ostrowski's algorithm and a second proof. \\
                 5. The approximation $ B ||b t|| < K $ \\
                 6. The $t$-expansion of a real number \\
                 \\
                 III. Periodic Continued Fractions \\
                 1. The classical theorems \\
                 2. Period lengths \\
                 3. Second order linear recurrences \\
                 \\
                 IV. Applications \\
                 1. Gear ratio problems \\
                 2. Pell's equation \\
                 3. Fermat's theorem on the sum of two squares \\
                 4. Hall's theorem \\
                 5. A theorem of Hurwitz \\
                 6. The Lagrange and Markov spectra \\
                 7. Asymmetric approximation and S{\`e}gre's theorem \\
                 8. Approximation by non-convergents \\
                 9. Inhomogeneous approximation \\
                 10. Szekeres' empty parallelogram theorem \\
                 \\
                 V. Metrical Theory \\
                 1. Numbers with bounded partial quotients \\
                 2. The Borel--Cantelli lemma \\
                 3. Random variables and expectations \\
                 4. Chebyshev's inequality and large number laws \\
                 5. The Gauss--Kuzmin theorem \\
                 6. The distribution of $ \xi_n $ \\
                 7. Partial quotients are weakly dependent \\
                 8. Khintchine's theorem \\
                 9. The Khintchine--L{\'e}vy theorem for $ \sqrt[n]{B_n}
                 $ \\
                 \\
                 VI. Applications to Metrical Diophantine Approximation
                 \\
                 Notes \\
                 Bibliography \\
                 Symbols \\
                 Index",
}


bibtype: article
filename: elefunt.bib
label: Salwin:1992:UPE
author: Arthur E. Salwin
title: Using the Proposed Elementary Functions Standard to Build a Strongly Typed Trig Package
journal: j-SIGADA-LETTERS
volume: 12
number: 5
pages: 59--63
month: sep
monthnumber: 9
year: 1992
CODEN: AALEE5
ISSN: 1094-3641 (print), 1557-9476 (electronic) OR 10943641 (print), 15579476 (electronic)
ISSNL: 1094-3641 OR 10943641
bibdate: Sat Aug 9 09:05:46 MDT 2003
bibtimestamp: 2003.08.09 09:05:46 MDT
fjournal: ACM SIGAda Ada Letters
acknowledgement: ack-nhfb
classcodes: C6140D (High level languages)
corpsource: Mitre Corp., McLean, VA, USA
journalURL: http://portal.acm.org/citation.cfm?id=J32
treatment: P Practical
rawauthor: Arthur E. Salwin
rawtitle: Using the Proposed Elementary Functions Standard to Build a Strongly Typed Trig Package
bibsource:
http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/sigada.bib

keywords:
Ada; compiler; elementary functions standard; standards; strong typing; strongly typed trig package; trigonometric functions

entry:
@Article{Salwin:1992:UPE,
  author =       "Arthur E. Salwin",
  title =        "Using the Proposed Elementary Functions Standard to
                 Build a Strongly Typed Trig Package",
  journal =      j-SIGADA-LETTERS,
  volume =       "12",
  number =       "5",
  pages =        "59--63",
  month =        sep # "\slash " # oct,
  year =         "1992",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Sat Aug 9 09:05:46 MDT 2003",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigada.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C6140D (High level languages)",
  corpsource =   "Mitre Corp., McLean, VA, USA",
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "Ada; compiler; elementary functions standard;
                 standards; strong typing; strongly typed trig package;
                 trigonometric functions",
  treatment =    "P Practical",
}


bibtype: article
filename: elefunt.bib
label: Saunders:1992:EFS
author: L. R. Saunders
journal: j-AUST-J-STAT
volume: 34
number: 2
pages: 261--264
month: jun
monthnumber: 6
year: 1992
CODEN: AUJSA3
DOI: https://doi.org/10.1111/j.1467-842X.1992.tb01358.x
ISSN: 0004-9581 OR 00049581
ISSNL: 0004-9581 OR 00049581
bibdate: Fri Jul 15 14:28:59 MDT 2016
bibsource: https://www.math.utah.edu/pub/tex/bib/anzjs.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2016.07.15 14:28:59 MDT
fjournal: Australian Journal of Statistics
acknowledgement: ack-nhfb
journalURL: http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-842X/issues
rawauthor: L. R. Saunders
title:
An Exact Formula for the Symmetrical Incomplete Beta Function Where the Parameter Is an Integer or Half-Integer

rawtitle:
An Exact Formula for the Symmetrical Incomplete Beta Function Where the Parameter Is an Integer or Half-Integer

entry:
@Article{Saunders:1992:EFS,
  author =       "L. R. Saunders",
  title =        "An Exact Formula for the Symmetrical Incomplete Beta
                 Function Where the Parameter Is an Integer or
                 Half-Integer",
  journal =      j-AUST-J-STAT,
  volume =       "34",
  number =       "2",
  pages =        "261--264",
  month =        jun,
  year =         "1992",
  CODEN =        "AUJSA3",
  DOI =          "https://doi.org/10.1111/j.1467-842X.1992.tb01358.x",
  ISSN =         "0004-9581",
  ISSN-L =       "0004-9581",
  bibdate =      "Fri Jul 15 14:28:59 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/anzjs.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Australian Journal of Statistics",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-842X/issues",
}


bibtype: mastersthesis
filename: elefunt.bib
label: Schulte:1992:AHD
author: Michael Joseph Schulte and Function generation
title: Algorithms and hardware designs for parallel elementary function generation
type: Thesis (M.S. in Engin.)
school: University of Texas at Austin
address: Austin, TX, USA
pages: ix + 73
year: 1992
bibdate: Sat Jan 11 10:14:06 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 10:14:06 MST
acknowledgement: ack-nhfb
rawauthor: Michael Joseph Schulte and Function generation
rawtitle: Algorithms and hardware designs for parallel elementary function generation
keywords:
Computer input-output equipment -- Design and construction.; Computer science -- Mathematics.; Numerical analysis.; Parallel processing (Electronic computers)

entry:
@MastersThesis{Schulte:1992:AHD,
  author =       "Michael Joseph Schulte and Function generation",
  title =        "Algorithms and hardware designs for parallel
                 elementary function generation",
  type =         "Thesis ({M.S.} in Engin.)",
  school =       "University of Texas at Austin",
  address =      "Austin, TX, USA",
  pages =        "ix + 73",
  year =         "1992",
  bibdate =      "Sat Jan 11 10:14:06 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer input-output equipment -- Design and
                 construction.; Computer science -- Mathematics.;
                 Numerical analysis.; Parallel processing (Electronic
                 computers)",
  searchkey =    "ti:elementary n1 function",
}


bibtype: article
filename: elefunt.bib
label: Tang:1992:TDI
author: Ping Tak Peter Tang
title: Table-Driven Implementation of the tt Expm1 Function in IEEE Floating-Point Arithmetic
journal: j-TOMS
volume: 18
number: 2
pages: 211--222
month: jun
monthnumber: 6
year: 1992
CODEN: ACMSCU
DOI: https://doi.org/10.1145/146847.146928
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 65D15
MRnumber: 1 167 891
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1996.02.24 15:01:45 MST
note: See independent analysis and accuracy confirmation of this algorithm in cite Kramer:1998:PWC.
URL: http://www.acm.org/pubs/citations/journals/toms/1992-18-2/p211-tang/
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Ping Tak Peter Tang
rawnote: See independent analysis and accuracy confirmation of this algorithm in \cite{Kramer:1998:PWC}.
rawtitle: Table-Driven Implementation of the {{\tt Expm1}} Function in {IEEE} Floating-Point Arithmetic
abstract:
Algorithms and implementation details for the function $ e^x - 1 $ in both single and double precision of IEEE 754 arithmetic are presented here. With a table of moderate size, the implementations need only working-precision arithmetic and are provably accurate to within 0.58 ulp.

subject:
bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic. bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Error analysis. bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.

rawabstract:
Algorithms and implementation details for the function $ e^x - 1 $ in both single and double precision of IEEE 754 arithmetic are presented here. With a table of moderate size, the implementations need only working-precision arithmetic and are provably accurate to within 0.58 ulp.

entry:
@Article{Tang:1992:TDI,
  author =       "Ping Tak Peter Tang",
  title =        "Table-Driven Implementation of the {{\tt Expm1}}
                 Function in {IEEE} Floating-Point Arithmetic",
  journal =      j-TOMS,
  volume =       "18",
  number =       "2",
  pages =        "211--222",
  month =        jun,
  year =         "1992",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/146847.146928",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D15",
  MRnumber =     "1 167 891",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See independent analysis and accuracy confirmation of
                 this algorithm in \cite{Kramer:1998:PWC}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1992-18-2/p211-tang/",
  abstract =     "Algorithms and implementation details for the function
                 $ e^x - 1 $ in both single and double precision of IEEE
                 754 arithmetic are presented here. With a table of
                 moderate size, the implementations need only
                 working-precision arithmetic and are provably accurate
                 to within 0.58 ulp.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Computer arithmetic. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Error analysis. {\bf G.1.0}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Algorithm analysis.",
}


bibtype: article
filename: elefunt.bib
label: Temme:1992:AII
author: N. M. Temme
title: Asymptotic Inversion of Incomplete Gamma Functions
journal: j-MATH-COMPUT
volume: 58
number: 198
pages: 755--764
month: apr
monthnumber: 4
year: 1992
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 33B20
MRnumber: 93a:33003
MRreviewer: F. W. J. Olver
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: N. M. Temme
rawtitle: Asymptotic Inversion of Incomplete Gamma Functions
entry:
@Article{Temme:1992:AII,
  author =       "N. M. Temme",
  title =        "Asymptotic Inversion of Incomplete Gamma Functions",
  journal =      j-MATH-COMPUT,
  volume =       "58",
  number =       "198",
  pages =        "755--764",
  month =        apr,
  year =         "1992",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33B20",
  MRnumber =     "93a:33003",
  MRreviewer =   "F. W. J. Olver",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Wong:1992:DSR
author: W. F. Wong and E. Goto
title: Division and square-rooting using a split multiplier
journal: j-ELECT-LETTERS
volume: 28
number: 18
pages: 1758--1759
day: 27
month: aug
monthnumber: 8
year: 1992
CODEN: ELLEAK
ISSN: 0013-5194 (print), 1350-911X (electronic) OR 00135194 (print), 1350911X (electronic)
ISSNL: 0013-5194 OR 00135194
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
fjournal: Electronics Letters
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220
rawauthor: W. F. Wong and E. Goto
rawtitle: Division and square-rooting using a split multiplier
entry:
@Article{Wong:1992:DSR,
  author =       "W. F. Wong and E. Goto",
  title =        "Division and square-rooting using a split multiplier",
  journal =      j-ELECT-LETTERS,
  volume =       "28",
  number =       "18",
  pages =        "1758--1759",
  day =          "27",
  month =        aug,
  year =         "1992",
  CODEN =        "ELLEAK",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  summary =      "A modification is proposed to the traditional design
                 of a fast floating point multiplication circuit such
                 that instead of just performing A$\times$B where A and
                 B are m bits long, it is also capable of \ldots{}",
}


bibtype: techreport
filename: elefunt.bib
label: Wood:1992:CP
author: David C. Wood
title: The Computation of Polylogarithms
type: Report
institution: University of Kent
address: Canterbury, Kent CT2 7NZ, UK
pages: 1758--1759
year: 1992
bibdate: Fri Jun 30 10:12:54 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2023.06.30 10:12:54 ???
URL: https://www.cs.kent.ac.uk/pubs/1992/110/content.pdf
keywords: polylogarithm
acknowledgement: ack-nhfb
rawauthor: David C. Wood
rawtitle: The Computation of Polylogarithms
abstract:
The polylogarithm function, $ Li _p(z) $, is defined, and a number of algorithms are derived for its computation, valid in different ranges of its real parameter $p$ and complex argument $z$.

remark:
Undated, but its URL suggests the year. The PDF file was created 20-Mar-2014. The latest reference is to a 1992 journal article.

rawabstract:
The polylogarithm function, $ \Li_p(z) $, is defined, and a number of algorithms are derived for its computation, valid in different ranges of its real parameter $p$ and complex argument $z$.

entry:
@TechReport{Wood:1992:CP,
  author =       "David C. Wood",
  title =        "The Computation of Polylogarithms",
  type =         "Report",
  institution =  "University of Kent",
  address =      "Canterbury, Kent CT2 7NZ, UK",
  year =         "1992",
  bibdate =      "Fri Jun 30 10:12:54 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://www.cs.kent.ac.uk/pubs/1992/110/content.pdf",
  abstract =     "The polylogarithm function, $ \Li_p(z) $, is defined,
                 and a number of algorithms are derived for its
                 computation, valid in different ranges of its real
                 parameter $p$ and complex argument $z$.",
  acknowledgement = ack-nhfb,
  keywords =     "polylogarithm",
  remark =       "Undated, but its URL suggests the year. The PDF file
                 was created 20-Mar-2014. The latest reference is to a
                 1992 journal article.",
}


bibtype: inproceedings
filename: elefunt.bib
label: Woods:1992:HPD
author: R. F. Woods and S. E. McQuillan and J. Dowling and J. V. McCanny
booktitle: Proceedings of Fifth Annual IEEE International ASIC Conference and Exhibit, 1992
title: High performance DSP ASIC for multiply, divide and square root
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 209--213
year: 1992
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: R. F. Woods and S. E. McQuillan and J. Dowling and J. V. McCanny
rawbooktitle: Proceedings of Fifth Annual {IEEE} International {ASIC} Conference and Exhibit, 1992
rawtitle: High performance {DSP} {ASIC} for multiply, divide and square root
entry:
@InProceedings{Woods:1992:HPD,
  author =       "R. F. Woods and S. E. McQuillan and J. Dowling and J.
                 V. McCanny",
  booktitle =    "Proceedings of Fifth Annual {IEEE} International
                 {ASIC} Conference and Exhibit, 1992",
  title =        "High performance {DSP} {ASIC} for multiply, divide and
                 square root",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "209--213",
  year =         "1992",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "The design of a high-speed ASIC that combines the
                 operations of multiplication, division and square root
                 is described. The chip is based on a systolic array
                 architecture that uses a redundant number system and
                 allows multiplication, division, and \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Yeyios:1992:TSA
author: A. K. Yeyios
title: On two sequences of algorithms for approximating square roots
journal: j-J-COMPUT-APPL-MATH
volume: 40
number: 1
pages: 63--72
month: jun
monthnumber: 6
year: 1992
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Thu Sep 1 10:15:56 1994
bibtimestamp: 1994.09.01 10:15:56 ???
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nj
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: A. K. Yeyios
rawtitle: On two sequences of algorithms for approximating square roots
entry:
@Article{Yeyios:1992:TSA,
  author =       "A. K. Yeyios",
  title =        "On two sequences of algorithms for approximating
                 square roots",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "40",
  number =       "1",
  pages =        "63--72",
  month =        jun,
  year =         "1992",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Thu Sep 1 10:15:56 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Alzer:1993:SGF
author: Horst Alzer
title: Some gamma function inequalities
journal: j-MATH-COMPUT
volume: 60
number: 201
pages: 337--346
month: jan
monthnumber: 1
year: 1993
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 33B15 (26D20)
MRnumber: 93f:33001
MRreviewer: Aurelio Cannizzo
bibdate: Sat Jan 11 13:29:06 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 13:29:06 MST
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Horst Alzer
rawtitle: Some gamma function inequalities
entry:
@Article{Alzer:1993:SGF,
  author =       "Horst Alzer",
  title =        "Some gamma function inequalities",
  journal =      j-MATH-COMPUT,
  volume =       "60",
  number =       "201",
  pages =        "337--346",
  month =        jan,
  year =         "1993",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33B15 (26D20)",
  MRnumber =     "93f:33001",
  MRreviewer =   "Aurelio Cannizzo",
  bibdate =      "Sat Jan 11 13:29:06 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: periodical
filename: elefunt.bib
label: Anonymous:1993:ITS
author: Anonymous
title: Integral transforms and special functions
publisher: Gordon and Breach Science Publishers
address: Yverdon, Switzerland
pages: 337--346
year: 1993
ISSN: 1065-2469, 1476-8291 OR 10652469, 14768291
ISSNL: 1065-2469 OR 10652469
bibdate: Mon Oct 24 11:37:20 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.10.24 11:37:20 ???
note: Appears with variable frequency from 1993--2001, and six times yearly from 2002--date.
acknowledgement: ack-nhfb
rawauthor: Anonymous
rawnote: Appears with variable frequency from 1993--2001, and six times yearly from 2002--date.
rawtitle: Integral transforms and special functions
entry:
@Periodical{Anonymous:1993:ITS,
  author =       "Anonymous",
  title =        "Integral transforms and special functions",
  publisher =    "Gordon and Breach Science Publishers",
  address =      "Yverdon, Switzerland",
  year =         "1993",
  ISSN =         "1065-2469, 1476-8291",
  ISSN-L =       "1065-2469",
  bibdate =      "Mon Oct 24 11:37:20 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Appears with variable frequency from 1993--2001, and
                 six times yearly from 2002--date.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Arenstorf:1993:SMZ
author: R. F. Arenstorf and L. L. Brewer
journal: j-COMPUT-MATH-APPL
volume: 26
number: 5
pages: 57--69
month: sep
monthnumber: 9
year: 1993
CODEN: CMAPDK
DOI: https://doi.org/10.1016/0898-1221(93)90074-6
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 19:11:16 MST 2017
bibtimestamp: 2017.03.01 19:11:16 MST
URL: http://www.sciencedirect.com/science/article/pii/0898122193900746
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: R. F. Arenstorf and L. L. Brewer
title:
A study of the motion of zeros of the Epstein zeta function associated to $ m^2 + y^2 n^2 $ as $y$ varies from $1$ to $ sqrt 6$

bibsource:
https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

rawtitle:
A study of the motion of zeros of the {Epstein} zeta function associated to $ m^2 + y^2 n^2 $ as $y$ varies from $1$ to $ \sqrt {6}$

entry:
@Article{Arenstorf:1993:SMZ,
  author =       "R. F. Arenstorf and L. L. Brewer",
  title =        "A study of the motion of zeros of the {Epstein} zeta
                 function associated to $ m^2 + y^2 n^2 $ as $y$ varies
                 from $1$ to $ \sqrt {6}$",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "26",
  number =       "5",
  pages =        "57--69",
  month =        sep,
  year =         "1993",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(93)90074-6",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 19:11:16 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122193900746",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: article
filename: elefunt.bib
label: Bailey:1993:AMT
author: D. H. Bailey
title: Algorithm 719: Multiprecision Translation and Execution of FORTRAN Programs
journal: j-TOMS
volume: 19
number: 3
pages: 288--319
month: sep
monthnumber: 9
year: 1993
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Wed Dec 13 18:37:31 1995
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1995.12.13 18:37:31 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
affiliation: NASA Ames Res. Center, Moffett Field, CA, USA
journalURL: https://dl.acm.org/loi/toms
rawauthor: D. H. Bailey
rawtitle: Algorithm 719: Multiprecision Translation and Execution of {FORTRAN} Programs
abstract:
The author describes two Fortran utilities for multiprecision computation. The first is a package of Fortran subroutines that perform a variety of arithmetic operations and transcendental functions on floating point numbers of arbitrarily high precision. This package is in some cases over 200 times faster than that of certain other packages that have been developed for this purpose. The second utility is a translator program, which facilitates the conversion of ordinary Fortran programs to use this package. By means of source directives (special comments) in the original Fortran program, the user declares the precision level and specifies which variables in each subprogram are to be treated as multiprecision. The translator program reads this source program and outputs a program with the appropriate multiprecision subroutine calls. This translator supports multiprecision integer, real, and complex datatypes. The required array space for multiprecision data types is automatically allocated. In the evaluation of computational expressions, all of the usual conventions for operator precedence and mixed mode operations are upheld. Furthermore, most of the Fortran-77 intrinsics, such as ABS, MOD, NINT, COS, EXP are supported and produce true multiprecision values.

keywords:
Algorithm 719; Arithmetic operations; Array space; Complex data types; Computational expressions; Floating point numbers; Fortran programs; Fortran subroutines; Fortran utilities; Fortran-77 intrinsics; Mixed mode operations; Multiprecision computation; Multiprecision data types; Multiprecision subroutine calls; Multiprecision translation; Operator precedence; Source directives; Transcendental functions; Translator program

thesaurus:
Data structures; Digital arithmetic; FORTRAN; Mathematics computing; Program interpreters; Subroutines

rawabstract:
The author describes two Fortran utilities for multiprecision computation. The first is a package of Fortran subroutines that perform a variety of arithmetic operations and transcendental functions on floating point numbers of arbitrarily high precision. This package is in some cases over 200 times faster than that of certain other packages that have been developed for this purpose. The second utility is a translator program, which facilitates the conversion of ordinary Fortran programs to use this package. By means of source directives (special comments) in the original Fortran program, the user declares the precision level and specifies which variables in each subprogram are to be treated as multiprecision. The translator program reads this source program and outputs a program with the appropriate multiprecision subroutine calls. This translator supports multiprecision integer, real, and complex datatypes. The required array space for multiprecision data types is automatically allocated. In the evaluation of computational expressions, all of the usual conventions for operator precedence and mixed mode operations are upheld. Furthermore, most of the Fortran-77 intrinsics, such as ABS, MOD, NINT, COS, EXP are supported and produce true multiprecision values.

entry:
@Article{Bailey:1993:AMT,
  author =       "D. H. Bailey",
  title =        "Algorithm 719: Multiprecision Translation and
                 Execution of {FORTRAN} Programs",
  journal =      j-TOMS,
  volume =       "19",
  number =       "3",
  pages =        "288--319",
  month =        sep,
  year =         "1993",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Dec 13 18:37:31 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "The author describes two Fortran utilities for
                 multiprecision computation. The first is a package of
                 Fortran subroutines that perform a variety of
                 arithmetic operations and transcendental functions on
                 floating point numbers of arbitrarily high precision.
                 This package is in some cases over 200 times faster
                 than that of certain other packages that have been
                 developed for this purpose. The second utility is a
                 translator program, which facilitates the conversion of
                 ordinary Fortran programs to use this package. By means
                 of source directives (special comments) in the original
                 Fortran program, the user declares the precision level
                 and specifies which variables in each subprogram are to
                 be treated as multiprecision. The translator program
                 reads this source program and outputs a program with
                 the appropriate multiprecision subroutine calls. This
                 translator supports multiprecision integer, real, and
                 complex datatypes. The required array space for
                 multiprecision data types is automatically allocated.
                 In the evaluation of computational expressions, all of
                 the usual conventions for operator precedence and mixed
                 mode operations are upheld. Furthermore, most of the
                 Fortran-77 intrinsics, such as ABS, MOD, NINT, COS, EXP
                 are supported and produce true multiprecision values.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "NASA Ames Res. Center, Moffett Field, CA, USA",
  classification = "C5230 (Digital arithmetic methods); C6120 (File
                 organisation); C6140D (High level languages); C6150C
                 (Compilers, interpreters and other processors); C7310
                 (Mathematics)",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Algorithm 719; Arithmetic operations; Array space;
                 Complex data types; Computational expressions; Floating
                 point numbers; Fortran programs; Fortran subroutines;
                 Fortran utilities; Fortran-77 intrinsics; Mixed mode
                 operations; Multiprecision computation; Multiprecision
                 data types; Multiprecision subroutine calls;
                 Multiprecision translation; Operator precedence; Source
                 directives; Transcendental functions; Translator
                 program",
  pubcountry =   "USA",
  thesaurus =    "Data structures; Digital arithmetic; FORTRAN;
                 Mathematics computing; Program interpreters;
                 Subroutines",
}


bibtype: article
filename: elefunt.bib
label: Barrera:1993:IBS
author: Tony Barrera and Pelle Olsson
title: An Integer Based Square Root Algorithm
journal: j-BIT
volume: 33
number: 2
pages: 253--261
month: jun
monthnumber: 6
year: 1993
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01989748
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
MRclass: 68M07
MRnumber: 1 326 017
bibdate: Wed Jan 4 18:52:23 MST 2006
bibtimestamp: 2006.01.04 18:52:23 MST
fjournal: BIT (Nordisk tidskrift for informationsbehandling)
acknowledgement: ack-nhfb
affiliation: AB Consonant, Uppsala, Sweden
journalURL: http://link.springer.com/journal/10543
thesaurus: Digital arithmetic
rawauthor: Tony Barrera and Pelle Olsson
rawtitle: An Integer Based Square Root Algorithm
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=33&issue=2; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://www.mai.liu.se/BIT/contents/bit33.html; http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=33&issue=2&spage=253

abstract:
The authors propose a fast integer based method for computing square roots of floating point numbers. This implies high accuracy and robustness, since no precision will be lost during the computation. Only integer addition and shifts are necessary to obtain the square root. Comparisons made with the modified Newton method indicate that the suggested method is twice as fast for computing floating point square roots. (5 Refs.)

keywords:
Floating point numbers; floating-point arithmetic; Integer based square root algorithm; Modified Newton method; Robustness

rawabstract:
The authors propose a fast integer based method for computing square roots of floating point numbers. This implies high accuracy and robustness, since no precision will be lost during the computation. Only integer addition and shifts are necessary to obtain the square root. Comparisons made with the modified Newton method indicate that the suggested method is twice as fast for computing floating point square roots. (5 Refs.)

entry:
@Article{Barrera:1993:IBS,
  author =       "Tony Barrera and Pelle Olsson",
  title =        "An Integer Based Square Root Algorithm",
  journal =      j-BIT,
  volume =       "33",
  number =       "2",
  pages =        "253--261",
  month =        jun,
  year =         "1993",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01989748",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "68M07",
  MRnumber =     "1 326 017",
  bibdate =      "Wed Jan 4 18:52:23 MST 2006",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=33&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.mai.liu.se/BIT/contents/bit33.html;
                 http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=33&issue=2&spage=253",
  abstract =     "The authors propose a fast integer based method for
                 computing square roots of floating point numbers. This
                 implies high accuracy and robustness, since no
                 precision will be lost during the computation. Only
                 integer addition and shifts are necessary to obtain the
                 square root. Comparisons made with the modified Newton
                 method indicate that the suggested method is twice as
                 fast for computing floating point square roots. (5
                 Refs.)",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "AB Consonant, Uppsala, Sweden",
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "Floating point numbers; floating-point arithmetic;
                 Integer based square root algorithm; Modified Newton
                 method; Robustness",
  pubcountry =   "Denmark",
  thesaurus =    "Digital arithmetic",
  xxpages =      "254--261??",
}


bibtype: incollection
filename: elefunt.bib
label: Bohlender:1993:PAF
author: G. Bohlender and D. Cordes and A. Knofel and U. Kulisch and R. Lohner and W. V. Walter
title: Proposal for accurate floating-point vector arithmetic
crossref: Adams:1993:ACA
pages: 87--102
year: 1993
bibdate: Tue Dec 12 09:27:13 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1995.12.12 09:27:13 MST
acknowledgement: ack-nhfb
affiliation: Inst. fur Angewandte Math., Karlsruhe Univ., Germany
bookpages: x + 612
thesaurus: Digital arithmetic; Mathematics computing; Roundoff errors; Standards
rawauthor: G. Bohlender and D. Cordes and A. Knofel and U. Kulisch and R. Lohner and W. V. Walter
rawtitle: Proposal for accurate floating-point vector arithmetic
abstract:
Many computers provide accurate and reliable scalar arithmetic for floating point numbers. An accurate definition of the four elementary floating-point operations +, -, *, / is given in the IEEE standards for floating-point arithmetic and was well established long before. An increasing number of computers (especially PC's and workstations) feature IEEE arithmetic. In many numerical algorithms, however, compound operations such as the summation of a sequence of numbers or the dot product of two vectors are highly common. A simulation of these compound operations by means of elementary floating-point operations leads to accumulation of rounding errors and may suffer from catastrophic cancellation of leading digits. Existing standards for floating-point arithmetic do not improve this situation. The goal of the proposal is to define vector operations in a manner consistent with the elementary scalar arithmetic operations. The rounding modes and accuracy requirements as well as the data formats of the operands and results of the vector operations described in the proposal are chosen to be fully consistent with the existing scalar floating-point arithmetic.

keywords:
Accuracy requirements; Catastrophic cancellation; Compound operations; Data formats; Dot product; Elementary floating-point operations; Elementary scalar arithmetic operations; Floating point numbers; IEEE arithmetic; IEEE standards; Leading digits; Numerical algorithms; Operands; Rounding errors; Rounding modes; Scalar floating-point arithmetic; Sequence; Standards; Summation; Vector operations

rawabstract:
Many computers provide accurate and reliable scalar arithmetic for floating point numbers. An accurate definition of the four elementary floating-point operations +, -, *, / is given in the IEEE standards for floating-point arithmetic and was well established long before. An increasing number of computers (especially PC's and workstations) feature IEEE arithmetic. In many numerical algorithms, however, compound operations such as the summation of a sequence of numbers or the dot product of two vectors are highly common. A simulation of these compound operations by means of elementary floating-point operations leads to accumulation of rounding errors and may suffer from catastrophic cancellation of leading digits. Existing standards for floating-point arithmetic do not improve this situation. The goal of the proposal is to define vector operations in a manner consistent with the elementary scalar arithmetic operations. The rounding modes and accuracy requirements as well as the data formats of the operands and results of the vector operations described in the proposal are chosen to be fully consistent with the existing scalar floating-point arithmetic.

entry:
@InCollection{Bohlender:1993:PAF,
  author =       "G. Bohlender and D. Cordes and A. Knofel and U.
                 Kulisch and R. Lohner and W. V. Walter",
  title =        "Proposal for accurate floating-point vector
                 arithmetic",
  crossref =     "Adams:1993:ACA",
  bookpages =    "x + 612",
  pages =        "87--102",
  year =         "1993",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Many computers provide accurate and reliable scalar
                 arithmetic for floating point numbers. An accurate
                 definition of the four elementary floating-point
                 operations +, -, *, / is given in the IEEE standards
                 for floating-point arithmetic and was well established
                 long before. An increasing number of computers
                 (especially PC's and workstations) feature IEEE
                 arithmetic. In many numerical algorithms, however,
                 compound operations such as the summation of a sequence
                 of numbers or the dot product of two vectors are highly
                 common. A simulation of these compound operations by
                 means of elementary floating-point operations leads to
                 accumulation of rounding errors and may suffer from
                 catastrophic cancellation of leading digits. Existing
                 standards for floating-point arithmetic do not improve
                 this situation. The goal of the proposal is to define
                 vector operations in a manner consistent with the
                 elementary scalar arithmetic operations. The rounding
                 modes and accuracy requirements as well as the data
                 formats of the operands and results of the vector
                 operations described in the proposal are chosen to be
                 fully consistent with the existing scalar
                 floating-point arithmetic.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. fur Angewandte Math., Karlsruhe Univ., Germany",
  classification = "C5230 (Digital arithmetic methods); C6130 (Data
                 handling techniques); C7310 (Mathematics)",
  keywords =     "Accuracy requirements; Catastrophic cancellation;
                 Compound operations; Data formats; Dot product;
                 Elementary floating-point operations; Elementary scalar
                 arithmetic operations; Floating point numbers; IEEE
                 arithmetic; IEEE standards; Leading digits; Numerical
                 algorithms; Operands; Rounding errors; Rounding modes;
                 Scalar floating-point arithmetic; Sequence; Standards;
                 Summation; Vector operations",
  pubcountry =   "USA",
  thesaurus =    "Digital arithmetic; Mathematics computing; Roundoff
                 errors; Standards",
}


bibtype: article
filename: elefunt.bib
label: Cody:1993:ACP
author: W. J. Cody
title: Algorithm 714: CELEFUNT: a Portable Test Package for Complex Elementary Functions
journal: j-TOMS
volume: 19
number: 1
pages: 1--21
month: mar
monthnumber: 3
year: 1993
CODEN: ACMSCU
DOI: https://doi.org/10.1145/151271.151272
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Sep 20 18:24:35 1994
bibtimestamp: 1994.09.20 18:24:35 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
affiliation: Div. of Math. and Comput. Sci., Argonne Nat. Lab., IL, USA
journalURL: https://dl.acm.org/loi/toms
rawauthor: W. J. Cody
rawtitle: {Algorithm 714}: {CELEFUNT}: a Portable Test Package for Complex Elementary Functions
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib

URL:
http://www.acm.org/pubs/citations/journals/toms/1993-19-1/p1-cody/; http://www.acm.org/pubs/toc/Abstracts/toms/151272.html

abstract:
This paper discusses CELEFUNT, a package of Fortran programs for testing complex elementary functions.

keywords:
algorithms; CABS; CELEFUNT; CEXP; CLOG; Complex elementary functions; Complex power function; CSIN/CCOS; CSQRT; Floating-point elementary functions; Fortran programs; measurement; performance; Portable test package

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

thesaurus:
Conformance testing; Digital arithmetic; FORTRAN; Mathematics computing; Numerical analysis; Program testing; Software packages

rawabstract:
This paper discusses CELEFUNT, a package of Fortran programs for testing complex elementary functions.

entry:
@Article{Cody:1993:ACP,
  author =       "W. J. Cody",
  title =        "{Algorithm 714}: {CELEFUNT}: a Portable Test Package
                 for Complex Elementary Functions",
  journal =      j-TOMS,
  volume =       "19",
  number =       "1",
  pages =        "1--21",
  month =        mar,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/151271.151272",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 20 18:24:35 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-1/p1-cody/;
                 http://www.acm.org/pubs/toc/Abstracts/toms/151272.html",
  abstract =     "This paper discusses CELEFUNT, a package of Fortran
                 programs for testing complex elementary functions.",
  abstract-2 =   "The author discusses CELEFUNT, a package of Fortran
                 programs for testing complex elementary functions.
                 CELEFUNT is a collection of test programs for the
                 complex floating-point elementary functions required by
                 the 1978 ANSI Fortran Standard (CABS), CSQRT, CLOG,
                 CEXP, CSIN/CCOS, and the complex power function.",
  acknowledgement = ack-nhfb,
  affiliation =  "Div. of Math. and Comput. Sci., Argonne Nat. Lab., IL,
                 USA",
  classification = "C4100 (Numerical analysis); C5230 (Digital
                 arithmetic methods); C7310 (Mathematics)",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; CABS; CELEFUNT; CEXP; CLOG; Complex
                 elementary functions; Complex power function;
                 CSIN/CCOS; CSQRT; Floating-point elementary functions;
                 Fortran programs; measurement; performance; Portable
                 test package",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Certification and testing. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Numerical algorithms.",
  thesaurus =    "Conformance testing; Digital arithmetic; FORTRAN;
                 Mathematics computing; Numerical analysis; Program
                 testing; Software packages",
}


bibtype: article
filename: elefunt.bib
label: Cody:1993:ASP
author: W. J. Cody, Jr.
title: Algorithm 715: SPECFUN: a Portable FORTRAN Package of Special Function Routines and Test Drivers
journal: j-TOMS
volume: 19
number: 1
pages: 22--32
month: mar
monthnumber: 3
year: 1993
CODEN: ACMSCU
DOI: https://doi.org/10.1145/151271.151273
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Sep 20 18:24:38 1994
bibtimestamp: 1994.09.20 18:24:38 ???
URL: http://www.acm.org/pubs/toc/Abstracts/0098-3500/151273.html
fjournal: ACM Transactions on Mathematical Software
acknowledgement: ack-nhfb
affiliation: Div. of Math. and Comput. Sci., Argonne Nat. Lab., IL, USA
journalURL: http://portal.acm.org/toc.cfm?idx=J782
thesaurus: FORTRAN; Mathematics computing; Numerical analysis; Software packages; Software portability
rawauthor: W. J. {Cody, Jr.}
abstract:
SPECFUN is a package containing transportable FORTRAN special function programs for real arguments and accompanying test drivers. Components include Bessel functions, exponential integrals, error functions and related functions, and gamma functions and related functions.

keywords:
algorithms; Bessel functions; Error functions; Exponential integrals; Gamma functions; Portable FORTRAN package; Real arguments; SPECFUN; Special function routines; Test drivers

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

rawabstract:
SPECFUN is a package containing transportable FORTRAN special function programs for real arguments and accompanying test drivers. Components include Bessel functions, exponential integrals, error functions and related functions, and gamma functions and related functions.

rawtitle:
Algorithm 715: {SPECFUN}: a Portable {FORTRAN} Package of Special Function Routines and Test Drivers

entry:
@Article{Cody:1993:ASP,
  author =       "W. J. {Cody, Jr.}",
  title =        "Algorithm 715: {SPECFUN}: a Portable {FORTRAN} Package
                 of Special Function Routines and Test Drivers",
  journal =      j-TOMS,
  volume =       "19",
  number =       "1",
  pages =        "22--32",
  month =        mar,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/151271.151273",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 20 18:24:38 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/toc/Abstracts/0098-3500/151273.html",
  abstract =     "SPECFUN is a package containing transportable FORTRAN
                 special function programs for real arguments and
                 accompanying test drivers. Components include Bessel
                 functions, exponential integrals, error functions and
                 related functions, and gamma functions and related
                 functions.",
  acknowledgement = ack-nhfb,
  affiliation =  "Div. of Math. and Comput. Sci., Argonne Nat. Lab., IL,
                 USA",
  classification = "C4100 (Numerical analysis); C7310 (Mathematics)",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://portal.acm.org/toc.cfm?idx=J782",
  keywords =     "algorithms; Bessel functions; Error functions;
                 Exponential integrals; Gamma functions; Portable
                 FORTRAN package; Real arguments; SPECFUN; Special
                 function routines; Test drivers",
  pubcountry =   "USA",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Certification and testing. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Numerical algorithms.",
  thesaurus =    "FORTRAN; Mathematics computing; Numerical analysis;
                 Software packages; Software portability",
}


bibtype: article
filename: elefunt.bib
label: duToit:1993:BFI
author: C. F. du Toit
title: Bessel functions $ J_n(z) $ and $ Y_n(z) $ of integer order and complex argument
journal: j-COMP-PHYS-COMM
volume: 78
number: 1--2
pages: 181--189
month: dec
monthnumber: 12
year: 1993
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(93)90153-4
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Mon Feb 13 21:29:41 MST 2012
bibtimestamp: 2012.02.13 21:29:41 MST
URL: http://www.sciencedirect.com/science/article/pii/0010465593901534
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: C. F. du Toit
rawtitle: {Bessel} functions {$ J_n(z) $} and {$ Y_n(z) $} of integer order and complex argument
bibsource:
https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

abstract:
This paper describes computer subroutines which were developed to compute Bessel functions of the first and second kind ($ J_n(z) $ and $ Y_n(z) $, respectively) for a complex argument $z$ and a range of integer orders. A novel way of determining the starting point of backward recurrence is used, and the algorithm for $ Y_n(z) $ improves on previous algorithms in terms of accuracy and restrictions on the range of orders.

rawabstract:
This paper describes computer subroutines which were developed to compute Bessel functions of the first and second kind ($ J_n(z) $ and $ Y_n(z) $, respectively) for a complex argument $z$ and a range of integer orders. A novel way of determining the starting point of backward recurrence is used, and the algorithm for $ Y_n(z) $ improves on previous algorithms in terms of accuracy and restrictions on the range of orders.

entry:
@Article{duToit:1993:BFI,
  author =       "C. F. du Toit",
  title =        "{Bessel} functions {$ J_n(z) $} and {$ Y_n(z) $} of
                 integer order and complex argument",
  journal =      j-COMP-PHYS-COMM,
  volume =       "78",
  number =       "1--2",
  pages =        "181--189",
  month =        dec,
  year =         "1993",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(93)90153-4",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 21:29:41 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465593901534",
  abstract =     "This paper describes computer subroutines which were
                 developed to compute Bessel functions of the first and
                 second kind ($ J_n(z) $ and $ Y_n(z) $, respectively)
                 for a complex argument $z$ and a range of integer
                 orders. A novel way of determining the starting point
                 of backward recurrence is used, and the algorithm for $
                 Y_n(z) $ improves on previous algorithms in terms of
                 accuracy and restrictions on the range of orders.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: book
filename: elefunt.bib
label: Feinsilver:1993:ASO
author: Philip J. (Philip Joel) Feinsilver and Rene Schott
title: Algebraic Structures and Operator Calculus
volume: 241, 292, 347
publisher: pub-KLUWER
address: pub-KLUWER:adr
year: 1993, 1994, 1996
LCCN: QA432 .F45 1993
bibdate: Sat Oct 30 17:31:34 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; prodorbis.library.yale.edu:7090/voyager
bibtimestamp: 2010.10.30 17:31:34 MDT
series: Mathematics and its applications
subject: Calculus, Operational; Probabilities; Representations of groups
acknowledgement: ack-nhfb
rawauthor: Philip J. (Philip Joel) Feinsilver and Ren{\'e} Schott
rawtitle: Algebraic Structures and Operator Calculus
ISBN:
0-7923-2116-2 (v. 1), 0-7923-2921-X (v. 2), 0-7923-3834-0 (v. 3) OR 0792321162 (v. 1), 079232921X (v. 2), 0792338340 (v. 3)

ISBN13:
978-0-7923-2116-3 (v. 1), 978-0-7923-2921-3 (v. 2), 978-0-7923-3834-5 (v. 3) OR 9780792321163 (v. 1), 9780792329213 (v. 2), 9780792338345 (v. 3)

note:
Volume 1: Representations and probability theory. Volume 2: Special functions and computer science. Volume 3: Representations of Lie groups

rawnote:
Volume 1: Representations and probability theory. Volume 2: Special functions and computer science. Volume 3: Representations of Lie groups

entry:
@Book{Feinsilver:1993:ASO,
  author =       "Philip J. (Philip Joel) Feinsilver and Ren{\'e}
                 Schott",
  title =        "Algebraic Structures and Operator Calculus",
  volume =       "241, 292, 347",
  publisher =    pub-KLUWER,
  address =      pub-KLUWER:adr,
  pages =        "?????",
  year =         "1993, 1994, 1996",
  ISBN =         "0-7923-2116-2 (v. 1), 0-7923-2921-X (v. 2),
                 0-7923-3834-0 (v. 3)",
  ISBN-13 =      "978-0-7923-2116-3 (v. 1), 978-0-7923-2921-3 (v. 2),
                 978-0-7923-3834-5 (v. 3)",
  LCCN =         "QA432 .F45 1993",
  bibdate =      "Sat Oct 30 17:31:34 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 prodorbis.library.yale.edu:7090/voyager",
  note =         "Volume 1: Representations and probability theory.
                 Volume 2: Special functions and computer science.
                 Volume 3: Representations of Lie groups",
  series =       "Mathematics and its applications",
  acknowledgement = ack-nhfb,
  subject =      "Calculus, Operational; Probabilities; Representations
                 of groups",
}


bibtype: article
filename: elefunt.bib
label: Fowkes:1993:HEA
author: R. E. Fowkes
title: Hardware Efficient Algorithms for Trigonometric Functions
journal: j-IEEE-TRANS-COMPUT
volume: 42
number: 2
pages: 235--239
month: feb
monthnumber: 2
year: 1993
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.204796
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 07:58:47 MDT 2011
bibtimestamp: 2011.07.07 07:58:47 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=204796
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: R. E. Fowkes
rawtitle: Hardware Efficient Algorithms for Trigonometric Functions
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib

entry:
@Article{Fowkes:1993:HEA,
  author =       "R. E. Fowkes",
  title =        "Hardware Efficient Algorithms for Trigonometric
                 Functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "42",
  number =       "2",
  pages =        "235--239",
  month =        feb,
  year =         "1993",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.204796",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:58:47 MDT 2011",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=204796",
  acknowledgement = ack-nj # "\slash " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: elefunt.bib
label: Frappier:1993:QFI
author: Clement Frappier and Patrick Olivier
title: A quadrature formula involving zeros of Bessel functions
journal: j-MATH-COMPUT
volume: 60
number: 201
pages: 303--316
month: jan
monthnumber: 1
year: 1993
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 41A55 (65D32)
MRnumber: 93d:41025
MRreviewer: Hans Strauss
bibdate: Tue Mar 25 15:38:13 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.03.25 15:38:13 MST
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
corpsource: Dept. de Math. Appliquees, Montreal, Que., Canada
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Cl{\'e}ment Frappier and Patrick Olivier
rawtitle: A quadrature formula involving zeros of {Bessel} functions
keywords:
Bessel functions; integration; interpolation; poles and; polynomials; quadrature formula; sampling theorem; zeros

classcodes:
B0290F (Interpolation and function approximation); B0290M (Numerical integration and differentiation); C4130 (Interpolation and function approximation); C4160 (Numerical integration and differentiation)

entry:
@Article{Frappier:1993:QFI,
  author =       "Cl{\'e}ment Frappier and Patrick Olivier",
  title =        "A quadrature formula involving zeros of {Bessel}
                 functions",
  journal =      j-MATH-COMPUT,
  volume =       "60",
  number =       "201",
  pages =        "303--316",
  month =        jan,
  year =         "1993",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "41A55 (65D32)",
  MRnumber =     "93d:41025",
  MRreviewer =   "Hans Strauss",
  bibdate =      "Tue Mar 25 15:38:13 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290F (Interpolation and function approximation);
                 B0290M (Numerical integration and differentiation);
                 C4130 (Interpolation and function approximation); C4160
                 (Numerical integration and differentiation)",
  corpsource =   "Dept. de Math. Appliqu{\'e}es, Montreal, Que.,
                 Canada",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel functions; integration; interpolation; poles
                 and; polynomials; quadrature formula; sampling theorem;
                 zeros",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: inproceedings
filename: elefunt.bib
label: Han:1993:CAS
author: Weimin Han and Florian A. Potra
title: Convergence acceleration for some rootfinding methods
crossref: Albrecht:1993:VNT
volume: 9
pages: 67--78
year: 1993
CODEN: COSPDM
ISSN: 0344-8029 OR 03448029
bibdate: Sun Oct 17 11:55:48 MDT 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1999.10.17 11:55:48 MDT
series: j-COMPUTING-SUPPLEMENTUM
keywords: convergence acceleration
acknowledgement: ack-nhfb
rawauthor: Weimin Han and Florian A. Potra
rawtitle: Convergence acceleration for some rootfinding methods
entry:
@InProceedings{Han:1993:CAS,
  author =       "Weimin Han and Florian A. Potra",
  title =        "Convergence acceleration for some rootfinding
                 methods",
  crossref =     "Albrecht:1993:VNT",
  volume =       "9",
  pages =        "67--78",
  year =         "1993",
  CODEN =        "COSPDM",
  ISSN =         "0344-8029",
  bibdate =      "Sun Oct 17 11:55:48 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       j-COMPUTING-SUPPLEMENTUM,
  acknowledgement = ack-nhfb,
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Higginbotham:1993:ISR
author: T. F. Higginbotham
title: The integer square root of $N$ via a binary search
journal: j-SIGCSE
volume: 25
number: 4
pages: 41--45
month: dec
monthnumber: 12
year: 1993
CODEN: SIGSD3
DOI: https://doi.org/10.1145/164205.164229
ISSN: 0097-8418 (print), 2331-3927 (electronic) OR 00978418 (print), 23313927 (electronic)
ISSNL: 0097-8418 OR 00978418
bibdate: Sat Nov 17 18:57:24 MST 2012
bibtimestamp: 2012.11.17 18:57:24 MST
fjournal: SIGCSE Bulletin (ACM Special Interest Group on Computer Science Education)
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J688
rawauthor: T. F. Higginbotham
rawtitle: The integer square root of {$N$} via a binary search
bibsource:
http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/sigcse1990.bib

abstract:
An algorithm is presented which may be used to find the integer square root of N. The method is intended for use on a binary computer, where only addition, subtraction, multiplication, or division by 2 is required. The problem arose when the author was working on factoring large numbers, where the machine, the Honeywell DPS 8, had double precision integer addition and subtraction, and the simulation of multiplication was easy. The actual factoring of the large number was to be Fermat's Method, requiring only addition and subtraction, but the integer square root is required in order to test for termination. The algorithm is implemented in FORTRAN for ease of reading. Students enjoy the unconventional approach to solving this problem. It isn't long before some of them think of other unusual solutions.

rawabstract:
An algorithm is presented which may be used to find the integer square root of N. The method is intended for use on a binary computer, where only addition, subtraction, multiplication, or division by 2 is required. The problem arose when the author was working on factoring large numbers, where the machine, the Honeywell DPS 8, had double precision integer addition and subtraction, and the simulation of multiplication was easy. The actual factoring of the large number was to be Fermat's Method, requiring only addition and subtraction, but the integer square root is required in order to test for termination. The algorithm is implemented in FORTRAN for ease of reading. Students enjoy the unconventional approach to solving this problem. It isn't long before some of them think of other unusual solutions.

entry:
@Article{Higginbotham:1993:ISR,
  author =       "T. F. Higginbotham",
  title =        "The integer square root of {$N$} via a binary search",
  journal =      j-SIGCSE,
  volume =       "25",
  number =       "4",
  pages =        "41--45",
  month =        dec,
  year =         "1993",
  CODEN =        "SIGSD3",
  DOI =          "https://doi.org/10.1145/164205.164229",
  ISSN =         "0097-8418 (print), 2331-3927 (electronic)",
  ISSN-L =       "0097-8418",
  bibdate =      "Sat Nov 17 18:57:24 MST 2012",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigcse1990.bib",
  abstract =     "An algorithm is presented which may be used to find
                 the integer square root of N. The method is intended
                 for use on a binary computer, where only addition,
                 subtraction, multiplication, or division by 2 is
                 required. The problem arose when the author was working
                 on factoring large numbers, where the machine, the
                 Honeywell DPS 8, had double precision integer addition
                 and subtraction, and the simulation of multiplication
                 was easy. The actual factoring of the large number was
                 to be Fermat's Method, requiring only addition and
                 subtraction, but the integer square root is required in
                 order to test for termination. The algorithm is
                 implemented in FORTRAN for ease of reading. Students
                 enjoy the unconventional approach to solving this
                 problem. It isn't long before some of them think of
                 other unusual solutions.",
  acknowledgement = ack-nhfb,
  fjournal =     "SIGCSE Bulletin (ACM Special Interest Group on
                 Computer Science Education)",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J688",
}


bibtype: article
filename: elefunt.bib
label: Hu:1993:BRS
author: Chen-Yi Hu and R. Baker Kearfott and Abdulhamid Awad
title: On Bounding the Range of Some Elementary Functions in FORTRAN 77
journal: j-INTERVAL-COMP
volume: 1993
number: 3
pages: 29--39
year: 1993
ISSN: 0135-4868 OR 01354868
MRclass: 65G10
MRnumber: 1 305 844
bibdate: Wed Dec 4 11:13:33 1996
bibtimestamp: 1996.12.04 11:13:33 ???
fjournal: Interval Computations = Interval'nye vychisleniia
acknowledgement: ack-nhfb
rawauthor: Chen-Yi Hu and R. Baker Kearfott and Abdulhamid Awad
rawtitle: On Bounding the Range of Some Elementary Functions in {FORTRAN} 77
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

note:
Proceedings of the International Conference on Numerical Analysis with Automatic Result Verification (Lafayette, LA, 1993)

rawnote:
Proceedings of the International Conference on Numerical Analysis with Automatic Result Verification (Lafayette, LA, 1993)

entry:
@Article{Hu:1993:BRS,
  author =       "Chen-Yi Hu and R. Baker Kearfott and Abdulhamid Awad",
  title =        "On Bounding the Range of Some Elementary Functions in
                 {FORTRAN} 77",
  journal =      j-INTERVAL-COMP,
  volume =       "1993",
  number =       "3",
  pages =        "29--39",
  year =         "1993",
  ISSN =         "0135-4868",
  MRclass =      "65G10",
  MRnumber =     "1 305 844",
  bibdate =      "Wed Dec 4 11:13:33 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Proceedings of the International Conference on
                 Numerical Analysis with Automatic Result Verification
                 (Lafayette, LA, 1993)",
  acknowledgement = ack-nhfb,
  fjournal =     "Interval Computations = Interval'nye vychisleniia",
}


bibtype: techreport
filename: elefunt.bib
label: Karp:1993:HPD
author: A. H. Karp and P. Markstein
title: High precision division and square root
number: HPL-93-42
institution: Hewlett--Packard Lab.
address: Palo Alto, CA, USA
pages: 20
month: jun
monthnumber: 6
year: 1993
bibdate: Tue Dec 12 09:27:13 MST 1995
bibtimestamp: 1995.12.12 09:27:13 MST
keywords: Division; Floating point hardware; Square root algorithms
acknowledgement: ack-nhfb
thesaurus: Digital arithmetic
rawauthor: A. H. Karp and P. Markstein
rawtitle: High precision division and square root
abstract:
The authors present division and square root algorithms for calculations with more bits than are handled by the floating point hardware. These algorithms avoid the need to multiply two high precision numbers, speeding up the last iteration by as much as a factor of ten.

rawabstract:
The authors present division and square root algorithms for calculations with more bits than are handled by the floating point hardware. These algorithms avoid the need to multiply two high precision numbers, speeding up the last iteration by as much as a factor of ten.

entry:
@TechReport{Karp:1993:HPD,
  author =       "A. H. Karp and P. Markstein",
  title =        "High precision division and square root",
  number =       "HPL-93-42",
  institution =  "Hewlett--Packard Lab.",
  address =      "Palo Alto, CA, USA",
  pages =        "20",
  month =        jun,
  year =         "1993",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The authors present division and square root
                 algorithms for calculations with more bits than are
                 handled by the floating point hardware. These
                 algorithms avoid the need to multiply two high
                 precision numbers, speeding up the last iteration by as
                 much as a factor of ten.",
  acknowledgement = ack-nhfb,
  classification = "C5230 (Digital arithmetic methods)",
  keywords =     "Division; Floating point hardware; Square root
                 algorithms",
  thesaurus =    "Digital arithmetic",
}


bibtype: incollection
filename: elefunt.bib
label: Kramer:1993:MPC
author: Walter Kramer
booktitle: Mathematics in Science and Engineering: Scientific Computing with Automatic Result Verification
title: Multiple-Precision Computations with Result Verification
volume: 189
publisher: Elsevier BV
address: Amsterdam, The Netherlands
pages: 325--356
year: 1993
DOI: https://doi.org/10.1016/s0076-5392(08)62851-9
bibdate: Tue Mar 14 19:20:47 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/agm.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.03.14 19:20:47 ???
acknowledgement: ack-nhfb
rawauthor: Walter Kr{\"a}mer
rawbooktitle: Mathematics in Science and Engineering: Scientific Computing with Automatic Result Verification
rawtitle: Multiple-Precision Computations with Result Verification
keywords:
arithmetic-geometric mean iteration; computation of $ e^pi $; computation of a large number of digits of $pi $; computation of elliptic integrals; computation of guaranteed bounds for the natural logarithm; interval arithmetic; PASCAL-XSC

entry:
@InCollection{Kramer:1993:MPC,
  author =       "Walter Kr{\"a}mer",
  booktitle =    "Mathematics in Science and Engineering: Scientific
                 Computing with Automatic Result Verification",
  title =        "Multiple-Precision Computations with Result
                 Verification",
  volume =       "189",
  publisher =    "Elsevier BV",
  address =      "Amsterdam, The Netherlands",
  pages =        "325--356",
  year =         "1993",
  DOI =          "https://doi.org/10.1016/s0076-5392(08)62851-9",
  bibdate =      "Tue Mar 14 19:20:47 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  keywords =     "arithmetic-geometric mean iteration; computation of $
                 e^\pi $; computation of a large number of digits of
                 $\pi$; computation of elliptic integrals; computation
                 of guaranteed bounds for the natural logarithm;
                 interval arithmetic; PASCAL-XSC",
}


bibtype: article
filename: elefunt.bib
label: Laforgia:1993:AMR
author: Andrea Laforgia and Maria Luisa Mathis
title: Additional monotonicity results for the zeros of Bessel functions
journal: j-J-COMPUT-APPL-MATH
volume: 47
number: 1
pages: 135--139
day: 28
month: jun
monthnumber: 6
year: 1993
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:20:58 MST 2017
bibtimestamp: 2017.02.25 12:20:58 MST
URL: http://www.sciencedirect.com/science/article/pii/037704279390095S
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Andrea Laforgia and Maria Luisa Mathis
rawtitle: Additional monotonicity results for the zeros of {Bessel} functions
entry:
@Article{Laforgia:1993:AMR,
  author =       "Andrea Laforgia and Maria Luisa Mathis",
  title =        "Additional monotonicity results for the zeros of
                 {Bessel} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "47",
  number =       "1",
  pages =        "135--139",
  day =          "28",
  month =        jun,
  year =         "1993",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:20:58 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/037704279390095S",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Lee:1993:DAE
author: Joong-Eon Lee and Oh-Young Kwon and Tack-Don Han
title: Design of an area efficient unit for floating-point division and square root
journal: j-J-KOREA-INFO-SCI-SOCIETY
volume: 20
number: 7
pages: 1060--1071
month: jul
monthnumber: 7
year: 1993
CODEN: HJKHDC
ISSN: 0258-9125 OR 02589125
bibdate: Tue Dec 12 09:27:13 MST 1995
bibtimestamp: 1995.12.12 09:27:13 MST
fjournal: Journal of the Korea Information Science Society = Chongbo Kwahakhoe nonmunji
language: Korean
acknowledgement: ack-nhfb
thesaurus: Adders; Digital arithmetic; Parallel algorithms
rawauthor: Joong-Eon Lee and Oh-Young Kwon and Tack-Don Han
rawtitle: Design of an area efficient unit for floating-point division and square root
abstract:
The authors propose an algorithm for a high performance floating point division and square root unit that uses a parallel multiplier. The basic algorithm used in the design is the continued-product normalization method. In this method, an arbitrary number is constantly multiplied to the divisor and dividend and dividend/divisor ends up with quotient/1 and the desired result attained. However this method requires computation of x*(2-x) and x*(3-x)/2 and this is quite an overhead. Therefore they propose a new algorithm to compute (2-x) and (3-x)/2 by using the modified Booth algorithm. When applied to the continued-product normalization method, this algorithm can maximize the inherent parallelism of the continued-product normalization method, and reduce computation time by effectively applying pipelining, and also achieve area efficient design by eliminating one register and one carry propagate adder needed for computing (2-x) and (3-x)/2. When the designed unit is used with the seed generator which has the accuracy of 2/sup -7/, division can be executed in eight cycles and the square root operation in 13 cycles.

keywords:
Area efficient unit; Continued-product normalization method; Floating-point division; Modified Booth algorithm; Parallel multiplier; Pipelining; Seed generator; Square root

rawabstract:
The authors propose an algorithm for a high performance floating point division and square root unit that uses a parallel multiplier. The basic algorithm used in the design is the continued-product normalization method. In this method, an arbitrary number is constantly multiplied to the divisor and dividend and dividend/divisor ends up with quotient/1 and the desired result attained. However this method requires computation of x*(2-x) and x*(3-x)/2 and this is quite an overhead. Therefore they propose a new algorithm to compute (2-x) and (3-x)/2 by using the modified Booth algorithm. When applied to the continued-product normalization method, this algorithm can maximize the inherent parallelism of the continued-product normalization method, and reduce computation time by effectively applying pipelining, and also achieve area efficient design by eliminating one register and one carry propagate adder needed for computing (2-x) and (3-x)/2. When the designed unit is used with the seed generator which has the accuracy of 2/sup -7/, division can be executed in eight cycles and the square root operation in 13 cycles.

entry:
@Article{Lee:1993:DAE,
  author =       "Joong-Eon Lee and Oh-Young Kwon and Tack-Don Han",
  title =        "Design of an area efficient unit for floating-point
                 division and square root",
  journal =      j-J-KOREA-INFO-SCI-SOCIETY,
  volume =       "20",
  number =       "7",
  pages =        "1060--1071",
  month =        jul,
  year =         "1993",
  CODEN =        "HJKHDC",
  ISSN =         "0258-9125",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The authors propose an algorithm for a high
                 performance floating point division and square root
                 unit that uses a parallel multiplier. The basic
                 algorithm used in the design is the continued-product
                 normalization method. In this method, an arbitrary
                 number is constantly multiplied to the divisor and
                 dividend and dividend/divisor ends up with quotient/1
                 and the desired result attained. However this method
                 requires computation of x*(2-x) and x*(3-x)/2 and this
                 is quite an overhead. Therefore they propose a new
                 algorithm to compute (2-x) and (3-x)/2 by using the
                 modified Booth algorithm. When applied to the
                 continued-product normalization method, this algorithm
                 can maximize the inherent parallelism of the
                 continued-product normalization method, and reduce
                 computation time by effectively applying pipelining,
                 and also achieve area efficient design by eliminating
                 one register and one carry propagate adder needed for
                 computing (2-x) and (3-x)/2. When the designed unit is
                 used with the seed generator which has the accuracy of
                 2/sup -7/, division can be executed in eight cycles and
                 the square root operation in 13 cycles.",
  acknowledgement = ack-nhfb,
  classification = "B1265B (Logic circuits); C4240P (Parallel
                 programming and algorithm theory); C5120 (Logic and
                 switching circuits); C5230 (Digital arithmetic
                 methods)",
  fjournal =     "Journal of the Korea Information Science Society =
                 Chongbo Kwahakhoe nonmunji",
  keywords =     "Area efficient unit; Continued-product normalization
                 method; Floating-point division; Modified Booth
                 algorithm; Parallel multiplier; Pipelining; Seed
                 generator; Square root",
  language =     "Korean",
  pubcountry =   "South Korea",
  thesaurus =    "Adders; Digital arithmetic; Parallel algorithms",
}


bibtype: article
filename: elefunt.bib
label: Li:1993:CAF
author: Y. Li and X. Dong and S. Pan
journal: j-IJQC
volume: 45
number: 1
pages: 3--??
year: 1993
CODEN: IJQCB2
ISSN: 0020-7608 (print), 1097-461X (electronic) OR 00207608 (print), 1097461X (electronic)
ISSNL: 0020-7608 OR 00207608
bibdate: Wed Jan 3 14:24:13 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/ijqc.bib
bibtimestamp: 1996.01.03 14:24:13 MST
fjournal: International Journal of Quantum Chemistry
acknowledgement: ack-nhfb
journalURL: http://www.interscience.wiley.com/jpages/0020-7608/
rawauthor: Y. Li and X. Dong and S. Pan
title:
Computation of Auxiliary Functions in STO Molecular Integrals up to Arbitrary Accuracy. I. Evaluation of Incomplete Gamma Function E$_n$ (X) by Forward Recursion

rawtitle:
Computation of Auxiliary Functions in {STO} Molecular Integrals up to Arbitrary Accuracy. {I}. {Evaluation} of Incomplete Gamma Function {E$_n$ (X)} by Forward Recursion

entry:
@Article{Li:1993:CAF,
  author =       "Y. Li and X. Dong and S. Pan",
  title =        "Computation of Auxiliary Functions in {STO} Molecular
                 Integrals up to Arbitrary Accuracy. {I}. {Evaluation}
                 of Incomplete Gamma Function {E$_n$ (X)} by Forward
                 Recursion",
  journal =      j-IJQC,
  volume =       "45",
  number =       "1",
  pages =        "3--??",
  year =         "1993",
  CODEN =        "IJQCB2",
  ISSN =         "0020-7608 (print), 1097-461X (electronic)",
  ISSN-L =       "0020-7608",
  bibdate =      "Wed Jan 3 14:24:13 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ijqc.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Quantum Chemistry",
  journal-URL =  "http://www.interscience.wiley.com/jpages/0020-7608/",
}


bibtype: techreport
filename: elefunt.bib
label: Litvinov:1993:ACR
author: Grigori L. Litvinov
title: Approximate construction of rational approximations and the effect of error autocorrection
type: Technical report
number: 8
institution: Institute of Mathematics, University of Oslo
address: Oslo, Norway
pages: 3--??
month: may
monthnumber: 5
year: 1993
bibdate: Tue Mar 24 20:51:52 2009
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2009.03.24 20:51:52 ???
note: See cite Litvinov:1994:ACR.
acknowledgement: ack-nhfb
rawauthor: Grigori L. Litvinov
rawnote: See \cite{Litvinov:1994:ACR}.
rawtitle: Approximate construction of rational approximations and the effect of error autocorrection
entry:
@TechReport{Litvinov:1993:ACR,
  author =       "Grigori L. Litvinov",
  title =        "Approximate construction of rational approximations
                 and the effect of error autocorrection",
  type =         "Technical report",
  number =       "8",
  institution =  "Institute of Mathematics, University of Oslo",
  address =      "Oslo, Norway",
  month =        may,
  year =         "1993",
  bibdate =      "Tue Mar 24 20:51:52 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Litvinov:1994:ACR}.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Liu:1993:DSC
author: Hui Min Liu
title: Determination of several classes of elementary functions by functional inequalities. (Chinese)
journal: Hunan Jiaoyu Xueyuan Xuebao (Ziran Kexue)
volume: 11
number: 2
pages: 30--35, 12
year: 1993
ISSN: 1001-6074 OR 10016074
MRclass: 26A09 (39B72)
MRnumber: 94g:26003
MRreviewer: Ling Yau Chan
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
acknowledgement: ack-nhfb
rawauthor: Hui Min Liu
rawtitle: Determination of several classes of elementary functions by functional inequalities. ({Chinese})
entry:
@Article{Liu:1993:DSC,
  author =       "Hui Min Liu",
  title =        "Determination of several classes of elementary
                 functions by functional inequalities. ({Chinese})",
  journal =      "Hunan Jiaoyu Xueyuan Xuebao (Ziran Kexue)",
  volume =       "11",
  number =       "2",
  pages =        "30--35, 12",
  year =         "1993",
  ISSN =         "1001-6074",
  MRclass =      "26A09 (39B72)",
  MRnumber =     "94g:26003",
  MRreviewer =   "Ling Yau Chan",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: elefunt.bib
label: Louie:1993:DRS
author: M. E. Louie and M. D. Ercegovac
booktitle: Proceedings of the IEEE Workshop on FPGAs for Custom Computing Machines, 5--7 April 1993
title: A digit-recurrence square root implementation for field programmable gate arrays
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 178--183
year: 1993
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: M. E. Louie and M. D. Ercegovac
rawbooktitle: Proceedings of the {IEEE} Workshop on {FPGAs} for Custom Computing Machines, 5--7 April 1993
rawtitle: A digit-recurrence square root implementation for field programmable gate arrays
entry:
@InProceedings{Louie:1993:DRS,
  author =       "M. E. Louie and M. D. Ercegovac",
  booktitle =    "Proceedings of the {IEEE} Workshop on {FPGAs} for
                 Custom Computing Machines, 5--7 April 1993",
  title =        "A digit-recurrence square root implementation for
                 field programmable gate arrays",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "178--183",
  year =         "1993",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "Creating efficient arithmetic processors requires a
                 pairing of high speed arithmetic algorithms with
                 optimal mapping strategies for a given technology. The
                 authors propose bit reduction as key to an efficient
                 pairing process for lookup table based \ldots{}",
}


bibtype: inproceedings
filename: elefunt.bib
label: Lozier:1993:ABF
author: Daniel W. Lozier and F. W. J. Olver
title: Airy and Bessel Functions by Parallel Integration of ODEs
crossref: Sincovec:1993:PSS
pages: 530--538
year: 1993
bibdate: Fri Jul 09 06:36:27 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2004.07.09 06:36:27 ???
acknowledgement: ack-nhfb
rawauthor: Daniel W. Lozier and F. W. J. Olver
rawtitle: {Airy} and {Bessel} Functions by Parallel Integration of {ODEs}
entry:
@InProceedings{Lozier:1993:ABF,
  author =       "Daniel W. Lozier and F. W. J. Olver",
  title =        "{Airy} and {Bessel} Functions by Parallel Integration
                 of {ODEs}",
  crossref =     "Sincovec:1993:PSS",
  pages =        "530--538",
  year =         "1993",
  bibdate =      "Fri Jul 09 06:36:27 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: elefunt.bib
label: Mathai:1993:HGS
author: A. M. Mathai
title: A handbook of generalized special functions for statistical and physical sciences
publisher: pub-CLARENDON
address: pub-CLARENDON:adr
pages: xi + 235
year: 1993
ISBN: 0-19-853595-3 OR 0198535953
ISBN13: 978-0-19-853595-9 OR 9780198535959
LCCN: QA351 .M35 1993
bibdate: Sat Oct 30 18:57:40 MDT 2010
bibtimestamp: 2010.10.30 18:57:40 MDT
series: Oxford science publications
subject: Functions, Special; Handbooks, manuals, etc
acknowledgement: ack-nhfb
rawauthor: A. M. Mathai
rawtitle: A handbook of generalized special functions for statistical and physical sciences
bibsource:
http://cat.cisti-icist.nrc-cnrc.gc.ca/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager

URL:
http://www.loc.gov/catdir/enhancements/fy0635/92036065-d.html; http://www.loc.gov/catdir/enhancements/fy0635/92036065-t.html

TOC:
I Mathematical preliminaries 1.1 The gamma function 1 1.2 Bernoulli polynomials 6 1.3 Asymptotic expansions of gamma functions 9 1.4 The psi function 11 1.5 The generalized zeta functions 12 1.6 The beta function 15 1.7 Calculation of residues for gamma functions 16 1.8 The Mellin transform 23 1.9 Density functions 24 1.10 Methods of deriving distributions 49 2 The G-function 2.1 The G-function 60 2.2 Some basic properties of the G-function 69 2.3 The Mellin transform of a G-function 78 2.4 Properties connected with the derivatives of a G-function 94 2.5 Series representations for a G-function 96 2.6 G-functions as multiple integrals or as solutions of integral equations 106 2.7 Differential equation for a G-function 111 2.8 Asymptotic expansions for a G-function 112 3 Elementary special functions and the G-function 3.1 Gamma and related functions: notations and definitions 117 3.2 Hypergeometric functions: notations and special cases 118 3.3 Confluent hypergeometric function and related functions 119 3.4 Exponential integral and related functions 121 3.5 Bessel functions and associated functions 121 3.6 Other special functions 122 3.7 Orthogonal polynomials 124 3.8 Elementary special functions expressed in terms of G-functions 127 3.9 G-functions expressed in terms of elementary special functions 129 3.10 Some integrals involving G-functions 132 3.11 The H-function 140 3.12 Computational aspects of G- and H-functions 144 3.13 Orders of the special functions for small and large values of the argument 145 4 Generalizations to matrix variables 4.1 Scalar functions of a symmetric positive definite matrix 152 4.2 Scalar functions of matrix arguments 158 4.3 Laplace transform 160 4.4 Hypergeometric functions of matrix arguments 171 4.5 Generalized matrix transform or M-transform 177 4.6 Zonal polynomial 194 4.7 Matrix variate Dirichlet distribution 197 4.8 Hypergeometric functions of many scalar variables 205 4.9 Hypergeometric functions of many matrix arguments 215 4.10 G- and H-functions of two variables 217 Bibliography 227 Glossary of symbols 231 Author index 233 Subject index 234

rawTOC:
I Mathematical preliminaries \\ 1.1 The gamma function 1 \\ 1.2 Bernoulli polynomials 6 \\ 1.3 Asymptotic expansions of gamma functions 9 \\ 1.4 The psi function 11 \\ 1.5 The generalized zeta functions 12 \\ 1.6 The beta function 15 \\ 1.7 Calculation of residues for gamma functions 16 \\ 1.8 The Mellin transform 23 \\ 1.9 Density functions 24 \\ 1.10 Methods of deriving distributions 49 \\ 2 The G-function \\ 2.1 The G-function 60 \\ 2.2 Some basic properties of the G-function 69 \\ 2.3 The Mellin transform of a G-function 78 \\ 2.4 Properties connected with the derivatives of a G-function 94 \\ 2.5 Series representations for a G-function 96 \\ 2.6 G-functions as multiple integrals or as solutions of integral equations 106 \\ 2.7 Differential equation for a G-function 111 \\ 2.8 Asymptotic expansions for a G-function 112 \\ 3 Elementary special functions and the G-function \\ 3.1 Gamma and related functions: notations and definitions 117 \\ 3.2 Hypergeometric functions: notations and special cases 118 \\ 3.3 Confluent hypergeometric function and related functions 119 \\ 3.4 Exponential integral and related functions 121 \\ 3.5 Bessel functions and associated functions 121 \\ 3.6 Other special functions 122 \\ 3.7 Orthogonal polynomials 124 \\ 3.8 Elementary special functions expressed in terms of G-functions 127 \\ 3.9 G-functions expressed in terms of elementary special functions 129 \\ 3.10 Some integrals involving G-functions 132 \\ 3.11 The H-function 140 \\ 3.12 Computational aspects of G- and H-functions 144 \\ 3.13 Orders of the special functions for small and large values of the argument 145 \\ 4 Generalizations to matrix variables \\ 4.1 Scalar functions of a symmetric positive definite matrix 152 \\ 4.2 Scalar functions of matrix arguments 158 \\ 4.3 Laplace transform 160 \\ 4.4 Hypergeometric functions of matrix arguments 171 \\ 4.5 Generalized matrix transform or M-transform 177 \\ 4.6 Zonal polynomial 194 \\ 4.7 Matrix variate Dirichlet distribution 197 \\ 4.8 Hypergeometric functions of many scalar variables 205 \\ 4.9 Hypergeometric functions of many matrix arguments 215 \\ 4.10 G- and H-functions of two variables 217 \\ Bibliography 227 \\ Glossary of symbols 231 \\ Author index 233 \\ Subject index 234

entry:
@Book{Mathai:1993:HGS,
  author =       "A. M. Mathai",
  title =        "A handbook of generalized special functions for
                 statistical and physical sciences",
  publisher =    pub-CLARENDON,
  address =      pub-CLARENDON:adr,
  pages =        "xi + 235",
  year =         "1993",
  ISBN =         "0-19-853595-3",
  ISBN-13 =      "978-0-19-853595-9",
  LCCN =         "QA351 .M35 1993",
  bibdate =      "Sat Oct 30 18:57:40 MDT 2010",
  bibsource =    "http://cat.cisti-icist.nrc-cnrc.gc.ca/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Oxford science publications",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0635/92036065-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0635/92036065-t.html",
  acknowledgement = ack-nhfb,
  subject =      "Functions, Special; Handbooks, manuals, etc",
  tableofcontents = "I Mathematical preliminaries \\
                 1.1 The gamma function 1 \\
                 1.2 Bernoulli polynomials 6 \\
                 1.3 Asymptotic expansions of gamma functions 9 \\
                 1.4 The psi function 11 \\
                 1.5 The generalized zeta functions 12 \\
                 1.6 The beta function 15 \\
                 1.7 Calculation of residues for gamma functions 16 \\
                 1.8 The Mellin transform 23 \\
                 1.9 Density functions 24 \\
                 1.10 Methods of deriving distributions 49 \\
                 2 The G-function \\
                 2.1 The G-function 60 \\
                 2.2 Some basic properties of the G-function 69 \\
                 2.3 The Mellin transform of a G-function 78 \\
                 2.4 Properties connected with the derivatives of a
                 G-function 94 \\
                 2.5 Series representations for a G-function 96 \\
                 2.6 G-functions as multiple integrals or as solutions
                 of integral equations 106 \\
                 2.7 Differential equation for a G-function 111 \\
                 2.8 Asymptotic expansions for a G-function 112 \\
                 3 Elementary special functions and the G-function \\
                 3.1 Gamma and related functions: notations and
                 definitions 117 \\
                 3.2 Hypergeometric functions: notations and special
                 cases 118 \\
                 3.3 Confluent hypergeometric function and related
                 functions 119 \\
                 3.4 Exponential integral and related functions 121 \\
                 3.5 Bessel functions and associated functions 121 \\
                 3.6 Other special functions 122 \\
                 3.7 Orthogonal polynomials 124 \\
                 3.8 Elementary special functions expressed in terms of
                 G-functions 127 \\
                 3.9 G-functions expressed in terms of elementary
                 special functions 129 \\
                 3.10 Some integrals involving G-functions 132 \\
                 3.11 The H-function 140 \\
                 3.12 Computational aspects of G- and H-functions 144
                 \\
                 3.13 Orders of the special functions for small and
                 large values of the argument 145 \\
                 4 Generalizations to matrix variables \\
                 4.1 Scalar functions of a symmetric positive definite
                 matrix 152 \\
                 4.2 Scalar functions of matrix arguments 158 \\
                 4.3 Laplace transform 160 \\
                 4.4 Hypergeometric functions of matrix arguments 171
                 \\
                 4.5 Generalized matrix transform or M-transform 177 \\
                 4.6 Zonal polynomial 194 \\
                 4.7 Matrix variate Dirichlet distribution 197 \\
                 4.8 Hypergeometric functions of many scalar variables
                 205 \\
                 4.9 Hypergeometric functions of many matrix arguments
                 215 \\
                 4.10 G- and H-functions of two variables 217 \\
                 Bibliography 227 \\
                 Glossary of symbols 231 \\
                 Author index 233 \\
                 Subject index 234",
}


bibtype: article
filename: elefunt.bib
label: Mazenc:1993:CFU
author: Christophe Mazenc and Xavier Merrheim and Jean-Michel Muller
title: Computing functions $ cos ^-1 $ and $ sin ^-1 $ using Cordic
journal: j-IEEE-TRANS-COMPUT
volume: 42
number: 1
pages: 118--122
month: jan
monthnumber: 1
year: 1993
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.192222
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 07:58:47 MDT 2011
bibtimestamp: 2011.07.07 07:58:47 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=192222
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Christophe Mazenc and Xavier Merrheim and Jean-Michel Muller
rawtitle: Computing functions $ \cos^{-1} $ and $ \sin^{-1} $ using {Cordic}
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib

entry:
@Article{Mazenc:1993:CFU,
  author =       "Christophe Mazenc and Xavier Merrheim and Jean-Michel
                 Muller",
  title =        "Computing functions $ \cos^{-1} $ and $ \sin^{-1} $
                 using {Cordic}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "42",
  number =       "1",
  pages =        "118--122",
  month =        jan,
  year =         "1993",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.192222",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:58:47 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=192222",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: elefunt.bib
label: McQuillan:1993:NAV
author: S. E. McQuillan and J. V. McCanny and R. Hamill
booktitle: Proceedings of the 11th Symposium on Computer Arithmetic, 2 July 1993
title: New algorithms and VLSI architectures for SRT division and square root
crossref: Swartzlander:1993:SCA
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 80--86
year: 1993
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
URL: http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_McQuillan.pdf
keywords: ARITH-11
acknowledgement: ack-sfo
rawauthor: S. E. McQuillan and J. V. McCanny and R. Hamill
rawbooktitle: Proceedings of the 11th Symposium on Computer Arithmetic, 2 July 1993
rawtitle: New algorithms and {VLSI} architectures for {SRT} division and square root
entry:
@InProceedings{McQuillan:1993:NAV,
  author =       "S. E. McQuillan and J. V. McCanny and R. Hamill",
  booktitle =    "Proceedings of the 11th Symposium on Computer
                 Arithmetic, 2 July 1993",
  title =        "New algorithms and {VLSI} architectures for {SRT}
                 division and square root",
  crossref =     "Swartzlander:1993:SCA",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "80--86",
  year =         "1993",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_McQuillan.pdf",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  keywords =     "ARITH-11",
  summary =      "Radix two algorithms for SRT division and
                 square-rooting are developed. For these schemes, the
                 result digits and the residuals are computed
                 concurrently and the computations in adjacent rows are
                 overlapped. Consequently, their performance should
                 \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Montuschi:1993:RIT
author: P. Montuschi and L. Ciminiera
journal: j-IEEE-TRANS-COMPUT
volume: 42
number: 2
pages: 239--246
month: feb
monthnumber: 2
year: 1993
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.204797
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
note: See remark cite Montuschi:1995:RRI.
fjournal: IEEE Transactions on Computers
acknowledgement: ack-sfo
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: P. Montuschi and L. Ciminiera
rawnote: See remark \cite{Montuschi:1995:RRI}.
title:
Reducing iteration time when result digit is zero for radix $2$ SRT division and square root with redundant remainders

rawtitle:
Reducing iteration time when result digit is zero for radix $2$ {SRT} division and square root with redundant remainders

entry:
@Article{Montuschi:1993:RIT,
  author =       "P. Montuschi and L. Ciminiera",
  title =        "Reducing iteration time when result digit is zero for
                 radix $2$ {SRT} division and square root with redundant
                 remainders",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "42",
  number =       "2",
  pages =        "239--246",
  month =        feb,
  year =         "1993",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.204797",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See remark \cite{Montuschi:1995:RRI}.",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "A new architecture is presented for shared radix 2
                 division and square root whose main characteristic is
                 the ability to avoid any addition/subtraction, when the
                 digit 0 has been selected. The solution presented uses
                 a redundant representation of the \ldots{}",
}


bibtype: techreport
filename: elefunt.bib
label: Morris:1993:NLM
author: Alfred H. Morris, Jr.
title: NSWC Library of Mathematics Subroutines
type: Report
number: NSWCDD/TR-92/425
institution: Naval Surface Warfare Center
address: Dahlgren, VA 22448-5000, USA; Silver Spring, MD 20903-5000, USA
pages: 464
month: jan
monthnumber: 1
year: 1993
bibdate: Tue Jun 13 08:47:19 2023
bibtimestamp: 2023.06.13 08:47:19 ???
note: See also earlier edition cite Morris:1990:NLM.
URL: https://ntrl.ntis.gov/NTRL/dashboard/searchResults/titleDetail/ADA261511.xhtml
acknowledgement: ack-nhfb
rawauthor: Alfred H. {Morris, Jr.}
rawnote: See also earlier edition \cite{Morris:1990:NLM}.
rawtitle: {NSWC} Library of Mathematics Subroutines
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fortran2.bib

abstract:
The NSWC library is a library of general purpose Fortran subroutines that provide a basic computational capability for a variety of mathematical activities. Emphasis has been placed on the transportability of the codes. Subroutines are available in the following areas: elementary operations, geometry, special functions, polynomials, vectors, matrices, large dense systems of linear equations, banded matrices, sparse matrices, eigenvalues and eigenvectors, l1 solution of linear equations, least-squares solution of linear equations, optimization, transforms, approximation of functions, curve fitting, surface fitting, manifold fitting, numerical integration, integral equations, ordinary differential equations, partial differential equations, and random number generation.

remark:
[13-Jun-2023] Despite several Web searches, a machine-readable freely downloadable copy of this report, and its associated software, has not yet been located. The entry for the earlier edition [Morris:1993:NLM] has links to a PDF file and the Fortran 90 source code. Another entry [Miller:2004:AMF] has links to some of the source code, without indication of software version dates.

rawabstract:
The NSWC library is a library of general purpose Fortran subroutines that provide a basic computational capability for a variety of mathematical activities. Emphasis has been placed on the transportability of the codes. Subroutines are available in the following areas: elementary operations, geometry, special functions, polynomials, vectors, matrices, large dense systems of linear equations, banded matrices, sparse matrices, eigenvalues and eigenvectors, l1 solution of linear equations, least-squares solution of linear equations, optimization, transforms, approximation of functions, curve fitting, surface fitting, manifold fitting, numerical integration, integral equations, ordinary differential equations, partial differential equations, and random number generation.

entry:
@TechReport{Morris:1993:NLM,
  author =       "Alfred H. {Morris, Jr.}",
  title =        "{NSWC} Library of Mathematics Subroutines",
  type =         "Report",
  number =       "NSWCDD/TR-92/425",
  institution =  "Naval Surface Warfare Center",
  address =      "Dahlgren, VA 22448-5000, USA; Silver Spring, MD
                 20903-5000, USA",
  pages =        "464",
  month =        jan,
  year =         "1993",
  bibdate =      "Tue Jun 13 08:47:19 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran2.bib",
  note =         "See also earlier edition \cite{Morris:1990:NLM}.",
  URL =          "https://ntrl.ntis.gov/NTRL/dashboard/searchResults/titleDetail/ADA261511.xhtml",
  abstract =     "The NSWC library is a library of general purpose
                 Fortran subroutines that provide a basic computational
                 capability for a variety of mathematical activities.
                 Emphasis has been placed on the transportability of the
                 codes. Subroutines are available in the following
                 areas: elementary operations, geometry, special
                 functions, polynomials, vectors, matrices, large dense
                 systems of linear equations, banded matrices, sparse
                 matrices, eigenvalues and eigenvectors, l1 solution of
                 linear equations, least-squares solution of linear
                 equations, optimization, transforms, approximation of
                 functions, curve fitting, surface fitting, manifold
                 fitting, numerical integration, integral equations,
                 ordinary differential equations, partial differential
                 equations, and random number generation.",
  acknowledgement = ack-nhfb,
  remark =       "[13-Jun-2023] Despite several Web searches, a
                 machine-readable freely downloadable copy of this
                 report, and its associated software, has not yet been
                 located. The entry for the earlier edition
                 [Morris:1993:NLM] has links to a PDF file and the
                 Fortran 90 source code. Another entry [Miller:2004:AMF]
                 has links to some of the source code, without
                 indication of software version dates.",
}


bibtype: article
filename: elefunt.bib
label: Muller:1993:NAC
author: Jurgen Muller
title: On numerical analytic continuation and convergence acceleration by summability methods
journal: Analysis
volume: 13
number: 3
pages: 279--291
year: 1993
ISSN: 0174-4747 OR 01744747
MRclass: 40G10 (40A30 41A25 65B10)
MRnumber: 1245757 (94j:40013)
MRreviewer: S. Sridhar
bibdate: Thu Dec 1 17:36:45 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 17:36:45 ???
fjournal: Analysis. International Mathematical Journal of Analysis and its Applications
keywords: convergence acceleration
acknowledgement: ack-nhfb
rawauthor: J{\"u}rgen M{\"u}ller
rawtitle: On numerical analytic continuation and convergence acceleration by summability methods
entry:
@Article{Muller:1993:NAC,
  author =       "J{\"u}rgen M{\"u}ller",
  title =        "On numerical analytic continuation and convergence
                 acceleration by summability methods",
  journal =      "Analysis",
  volume =       "13",
  number =       "3",
  pages =        "279--291",
  year =         "1993",
  ISSN =         "0174-4747",
  MRclass =      "40G10 (40A30 41A25 65B10)",
  MRnumber =     "1245757 (94j:40013)",
  MRreviewer =   "S. Sridhar",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Analysis. International Mathematical Journal of
                 Analysis and its Applications",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Perger:1993:NEG
author: Warren F. Perger and Atul Bhalla and Mark Nardin
title: A numerical evaluator for the generalized hypergeometric series
journal: j-COMP-PHYS-COMM
volume: 77
number: 2
pages: 249--254
month: oct
monthnumber: 10
year: 1993
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(93)90008-Z
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Thu Dec 01 09:22:29 2011
bibtimestamp: 2011.12.01 09:22:29 ???
fjournal: Computer Physics Communications
remark: Uses extended precision complex arithmetic.
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: Warren F. Perger and Atul Bhalla and Mark Nardin
rawtitle: A numerical evaluator for the generalized hypergeometric series
bibsource:
https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Perger:1993:NEG,
  author =       "Warren F. Perger and Atul Bhalla and Mark Nardin",
  title =        "A numerical evaluator for the generalized
                 hypergeometric series",
  journal =      j-COMP-PHYS-COMM,
  volume =       "77",
  number =       "2",
  pages =        "249--254",
  month =        oct,
  year =         "1993",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(93)90008-Z",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Thu Dec 01 09:22:29 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
  remark =       "Uses extended precision complex arithmetic.",
}


bibtype: article
filename: elefunt.bib
label: Petkovic:1993:SII
author: Miodrag S. Petkovic and Carsten Carstensen
title: Some improved inclusion methods for polynomial roots with Weierstrass' corrections
journal: j-COMPUT-MATH-APPL
volume: 25
number: 3
pages: 59--67
month: feb
monthnumber: 2
year: 1993
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 19:11:11 MST 2017
bibtimestamp: 2017.03.01 19:11:11 MST
URL: http://www.sciencedirect.com/science/article/pii/089812219390143J
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: Miodrag S. Petkovi{\'c} and Carsten Carstensen
rawtitle: Some improved inclusion methods for polynomial roots with {Weierstrass}' corrections
bibsource:
https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Petkovic:1993:SII,
  author =       "Miodrag S. Petkovi{\'c} and Carsten Carstensen",
  title =        "Some improved inclusion methods for polynomial roots
                 with {Weierstrass}' corrections",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "25",
  number =       "3",
  pages =        "59--67",
  month =        feb,
  year =         "1993",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 19:11:11 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/089812219390143J",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: book
filename: elefunt.bib
label: Povolotskii:1993:OFR
author: A. I. Povolotskiui and G. A. Sviridyuk
publisher: Chelyabinsk. Gos. Univ.
address: Chelyabinsk, USSR
pages: 92
year: 1993
ISBN: 5-230-17764-0 OR 5230177640
ISBN13: 978-5-230-17764-7 OR 9785230177647
MRclass: 26-01 (00A05)
MRnumber: 94e:26001
MRreviewer: J{\'o}zef Kalinowski
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
language: Russian
acknowledgement: ack-nhfb
rawauthor: A. I. Povolotski{\u\i} and G. A. Sviridyuk
title:
cyr Odnomernyui matematicheskiui analiz elementarnykh funktsiui . (Russian) [One-dimensional mathematical analysis of elementary functions] cyr Nepreryvnye funktsii. Differentsiruemye funktsii. Integriruemye funktsii. [Continuous functions. Differentiable functions. Integrable functions]

rawtitle:
{{\cyr Odnomerny{\u\i} matematicheski{\u\i} analiz {\`e}lementarnykh funktsi{\u\i}}}. ({Russian}) [One-dimensional mathematical analysis of elementary functions] {{\cyr Nepreryvnye funktsii. Differentsiruemye funktsii. Integriruemye funktsii}}. [Continuous functions. Differentiable functions. Integrable functions]

entry:
@Book{Povolotskii:1993:OFR,
  author =       "A. I. Povolotski{\u\i} and G. A. Sviridyuk",
  title =        "{{\cyr Odnomerny{\u\i} matematicheski{\u\i} analiz
                 {\`e}lementarnykh funktsi{\u\i}}}. ({Russian})
                 [One-dimensional mathematical analysis of elementary
                 functions] {{\cyr Nepreryvnye funktsii.
                 Differentsiruemye funktsii. Integriruemye funktsii}}.
                 [Continuous functions. Differentiable functions.
                 Integrable functions]",
  publisher =    "Chelyabinsk. Gos. Univ.",
  address =      "Chelyabinsk, USSR",
  pages =        "92",
  year =         "1993",
  ISBN =         "5-230-17764-0",
  ISBN-13 =      "978-5-230-17764-7",
  MRclass =      "26-01 (00A05)",
  MRnumber =     "94e:26001",
  MRreviewer =   "J{\'o}zef Kalinowski",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}


bibtype: article
filename: elefunt.bib
label: Ratis:1993:CCH
author: Yu. L. Ratis and P. Fernandez de Cordoba
title: A code to calculate (high order) Bessel functions based on the continued fractions method
journal: j-COMP-PHYS-COMM
volume: 76
number: 3
pages: 381--388
month: aug
monthnumber: 8
year: 1993
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(93)90062-H
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Mon Feb 13 21:29:39 MST 2012
bibtimestamp: 2012.02.13 21:29:39 MST
URL: http://www.sciencedirect.com/science/article/pii/001046559390062H
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: Yu. L. Ratis and P. Fern{\'a}ndez de C{\'o}rdoba
rawtitle: A code to calculate (high order) {Bessel} functions based on the continued fractions method
abstract:
We have developed a fast code to calculate Bessel functions of integer and fractional order based on the continued fractions method. This algorithm is specially useful in the case of Bessel functions of high order because it does not require any recalculation using normalization relations.

rawabstract:
We have developed a fast code to calculate Bessel functions of integer and fractional order based on the continued fractions method. This algorithm is specially useful in the case of Bessel functions of high order because it does not require any recalculation using normalization relations.

entry:
@Article{Ratis:1993:CCH,
  author =       "Yu. L. Ratis and P. Fern{\'a}ndez de C{\'o}rdoba",
  title =        "A code to calculate (high order) {Bessel} functions
                 based on the continued fractions method",
  journal =      j-COMP-PHYS-COMM,
  volume =       "76",
  number =       "3",
  pages =        "381--388",
  month =        aug,
  year =         "1993",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(93)90062-H",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 21:29:39 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/001046559390062H",
  abstract =     "We have developed a fast code to calculate Bessel
                 functions of integer and fractional order based on the
                 continued fractions method. This algorithm is specially
                 useful in the case of Bessel functions of high order
                 because it does not require any recalculation using
                 normalization relations.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: book
filename: elefunt.bib
label: Saurer:1993:BSF
author: Josef Saurer
title: Bases of special functions and their domains of convergence
volume: 73
publisher: Akademie Verlag GmbH
address: Berlin, Germany
pages: 158
year: 1993
ISBN: 3-05-501613-0 OR 3055016130
ISBN13: 978-3-05-501613-4 OR 9783055016134
ISSN: 0138-3019 OR 01383019
LCCN: QA351 .S28 1993
bibdate: Sat Oct 30 18:53:24 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.10.30 18:53:24 MDT
series: Mathematical research
remark: Revised version of the author's thesis--Universitat Essen, 1992.
subject: Functions, Special; Analytic functions; Eigenfunction expansions; Convergence; Mathematical physics
acknowledgement: ack-nhfb
rawauthor: Josef Saurer
rawtitle: Bases of special functions and their domains of convergence
TOC:
Introduction 9 1 Foundations of the theory 15 1.1 Holomorphic operator functions in Frechet spaces 15 1.2 Floquet eigenvalue problems (with a regular singular point) 22 1.3 Relationships between differential operators corresponding to Floquet eigenvalue problems for systems of differential equations and scalar differential equations 26 1.4 Biholomorphic images of functions 30 1.5 An expansion theorem 37 2 First order differential systems with a regular singular point 43 2.1 Fundamental properties 44 2.2 Construction of fundamental systems depending holomorphically on parameters 46 2.3 A family of second order differential equations 55 2.4 Differential equations and special functions of mathematical physics 57 2.4.1 Bessel equation, Bessel function 57 2.4.2 Whittaker equation, Whittaker function 58 2.4.3 Hypergeometric equation, hypergeometric function 60 2.4.4 Generalised spherical function 61 3 Floquet eigenvalue problems for first order differential systems with a regular singular point 63 3.1 Construction of biorthogonal canonical systems of eigen- and associated vectors of the operator functions $T$ and $T^*$ 67 3.2 A general expansion theorem 73 3.3 Floquet eigenvalue problems and expansion theorems for a family of second order differential equations 75 4 Domains of convergence of the eigenfunction expansions 83 4.1 The Bessel and Whittaker case 85 4.2 The hypergeometric case 95 4.3 Typical domains of convergence 105 5 Examples of expansions in series of special functions 109 5.1 Expansions in series of Bessel functions 109 5.2 Expansions in series of Whittaker functions 115 5.3 Expansions in series of hypergeometric functions 119 6 First order differential systems for products of vector-valued functions 127 6.1 Products of vectors and sums of matrices of different dimensions 128 6.2 Construction of the first order differential system 132 7 Floquet eigenvalue problems and expansions in series, of m - fold products of special functions 135 7.1 Construction of biorthogonal canonical systems of eigen- and associated vectors of the operator functions $T$ and $T^*$ 142 7.2 Application 145 References 151 Notation index 154 Index 157

rawTOC:
Introduction 9 \\ 1 Foundations of the theory 15 \\ 1.1 Holomorphic operator functions in Frechet spaces 15 \\ 1.2 Floquet eigenvalue problems (with a regular singular point) 22 \\ 1.3 Relationships between differential operators corresponding to Floquet eigenvalue problems for systems of differential equations and scalar differential equations 26 \\ 1.4 Biholomorphic images of functions 30 \\ 1.5 An expansion theorem 37 \\ 2 First order differential systems with a regular singular point 43 \\ 2.1 Fundamental properties 44 \\ 2.2 Construction of fundamental systems depending holomorphically on parameters 46 \\ 2.3 A family of second order differential equations 55 \\ 2.4 Differential equations and special functions of mathematical physics 57 \\ 2.4.1 Bessel equation, Bessel function 57 \\ 2.4.2 Whittaker equation, Whittaker function 58 \\ 2.4.3 Hypergeometric equation, hypergeometric function 60 \\ 2.4.4 Generalised spherical function 61 \\ 3 Floquet eigenvalue problems for first order differential systems with a regular singular point 63 \\ 3.1 Construction of biorthogonal canonical systems of eigen- and associated vectors of the operator functions $T$ and $T^*$ 67 \\ 3.2 A general expansion theorem 73 \\ 3.3 Floquet eigenvalue problems and expansion theorems for a family of second order differential equations 75 \\ 4 Domains of convergence of the eigenfunction expansions 83 \\ 4.1 The Bessel and Whittaker case 85 \\ 4.2 The hypergeometric case 95 \\ 4.3 Typical domains of convergence 105 \\ 5 Examples of expansions in series of special functions 109 \\ 5.1 Expansions in series of Bessel functions 109 \\ 5.2 Expansions in series of Whittaker functions 115 \\ 5.3 Expansions in series of hypergeometric functions 119 \\ 6 First order differential systems for products of vector-valued functions 127 \\ 6.1 Products of vectors and sums of matrices of different dimensions 128 \\ 6.2 Construction of the first order differential system 132 \\ 7 Floquet eigenvalue problems and expansions in series, of m - fold products of special functions 135 \\ 7.1 Construction of biorthogonal canonical systems of eigen- and associated vectors of the operator functions $T$ and $T^*$ 142 \\ 7.2 Application 145 \\ References 151 \\ Notation index 154 \\ Index 157

entry:
@Book{Saurer:1993:BSF,
  author =       "Josef Saurer",
  title =        "Bases of special functions and their domains of
                 convergence",
  volume =       "73",
  publisher =    "Akademie Verlag GmbH",
  address =      "Berlin, Germany",
  pages =        "158",
  year =         "1993",
  ISBN =         "3-05-501613-0",
  ISBN-13 =      "978-3-05-501613-4",
  ISSN =         "0138-3019",
  LCCN =         "QA351 .S28 1993",
  bibdate =      "Sat Oct 30 18:53:24 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Mathematical research",
  acknowledgement = ack-nhfb,
  remark =       "Revised version of the author's
                 thesis--Universit{\"a}t Essen, 1992.",
  subject =      "Functions, Special; Analytic functions; Eigenfunction
                 expansions; Convergence; Mathematical physics",
  tableofcontents = "Introduction 9 \\
                 1 Foundations of the theory 15 \\
                 1.1 Holomorphic operator functions in Frechet spaces 15
                 \\
                 1.2 Floquet eigenvalue problems (with a regular
                 singular point) 22 \\
                 1.3 Relationships between differential operators
                 corresponding to Floquet eigenvalue problems for
                 systems of differential equations and scalar
                 differential equations 26 \\
                 1.4 Biholomorphic images of functions 30 \\
                 1.5 An expansion theorem 37 \\
                 2 First order differential systems with a regular
                 singular point 43 \\
                 2.1 Fundamental properties 44 \\
                 2.2 Construction of fundamental systems depending
                 holomorphically on parameters 46 \\
                 2.3 A family of second order differential equations 55
                 \\
                 2.4 Differential equations and special functions of
                 mathematical physics 57 \\
                 2.4.1 Bessel equation, Bessel function 57 \\
                 2.4.2 Whittaker equation, Whittaker function 58 \\
                 2.4.3 Hypergeometric equation, hypergeometric function
                 60 \\
                 2.4.4 Generalised spherical function 61 \\
                 3 Floquet eigenvalue problems for first order
                 differential systems with a regular singular point 63
                 \\
                 3.1 Construction of biorthogonal canonical systems of
                 eigen- and associated vectors of the operator functions
                 $T$ and $T^*$ 67 \\
                 3.2 A general expansion theorem 73 \\
                 3.3 Floquet eigenvalue problems and expansion theorems
                 for a family of second order differential equations 75
                 \\
                 4 Domains of convergence of the eigenfunction
                 expansions 83 \\
                 4.1 The Bessel and Whittaker case 85 \\
                 4.2 The hypergeometric case 95 \\
                 4.3 Typical domains of convergence 105 \\
                 5 Examples of expansions in series of special functions
                 109 \\
                 5.1 Expansions in series of Bessel functions 109 \\
                 5.2 Expansions in series of Whittaker functions 115 \\
                 5.3 Expansions in series of hypergeometric functions
                 119 \\
                 6 First order differential systems for products of
                 vector-valued functions 127 \\
                 6.1 Products of vectors and sums of matrices of
                 different dimensions 128 \\
                 6.2 Construction of the first order differential system
                 132 \\
                 7 Floquet eigenvalue problems and expansions in series,
                 of m - fold products of special functions 135 \\
                 7.1 Construction of biorthogonal canonical systems of
                 eigen- and associated vectors of the operator functions
                 $T$ and $T^*$ 142 \\
                 7.2 Application 145 \\
                 References 151 \\
                 Notation index 154 \\
                 Index 157",
}


bibtype: inproceedings
filename: elefunt.bib
label: Schulte:1993:ERC
author: M. Schulte and E. Swartzlander
title: Exact rounding of certain elementary functions
crossref: Swartzlander:1993:SCA
pages: 138--145
year: 1993
bibdate: Thu Dec 14 11:25:18 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1995.12.14 11:25:18 MST
URL: http://mesa.ece.wisc.edu/publications/cp_1993-01.pdf
acknowledgement: ack-nhfb
affiliation: Dept. of Electr. and Comput. Eng., Texas Univ., Austin, TX, USA
bookpages: xii + 284
thesaurus: Floating point arithmetic; Function evaluation
rawauthor: M. Schulte and E. Swartzlander
rawtitle: Exact rounding of certain elementary functions
abstract:
An algorithm is described which produces exactly rounded results for the functions of reciprocal, square root, 2/sup x/, and log 2/sup x/. Hardware designs based on this algorithm are presented for floating point numbers with 16- and 24-b significands. These designs use a polynomial approximation in which coefficients are originally selected based on the Chebyshev series approximation and are then adjusted to ensure exactly rounded results for all inputs. To reduce the number of terms in the approximation, the input interval is divided into subintervals of equal size and different coefficients are used for each subinterval. For floating point numbers with 16-b significands, the exactly rounded value of the function can be computed in 51 ns on a 20-mm/sup 2/ chip. For floating point numbers with 24-b significands, the functions can be computed in 80 ns on a 98-mm/sup 2/ chip.

keywords:
Elementary functions; Exact rounding; Floating point numbers; Polynomial approximation; Reciprocal; Rounded results; Square root

rawabstract:
An algorithm is described which produces exactly rounded results for the functions of reciprocal, square root, 2/sup x/, and log 2/sup x/. Hardware designs based on this algorithm are presented for floating point numbers with 16- and 24-b significands. These designs use a polynomial approximation in which coefficients are originally selected based on the Chebyshev series approximation and are then adjusted to ensure exactly rounded results for all inputs. To reduce the number of terms in the approximation, the input interval is divided into subintervals of equal size and different coefficients are used for each subinterval. For floating point numbers with 16-b significands, the exactly rounded value of the function can be computed in 51 ns on a 20-mm/sup 2/ chip. For floating point numbers with 24-b significands, the functions can be computed in 80 ns on a 98-mm/sup 2/ chip.

entry:
@InProceedings{Schulte:1993:ERC,
  author =       "M. Schulte and E. Swartzlander",
  title =        "Exact rounding of certain elementary functions",
  crossref =     "Swartzlander:1993:SCA",
  bookpages =    "xii + 284",
  pages =        "138--145",
  year =         "1993",
  bibdate =      "Thu Dec 14 11:25:18 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1993-01.pdf",
  abstract =     "An algorithm is described which produces exactly
                 rounded results for the functions of reciprocal, square
                 root, 2/sup x/, and log 2/sup x/. Hardware designs
                 based on this algorithm are presented for floating
                 point numbers with 16- and 24-b significands. These
                 designs use a polynomial approximation in which
                 coefficients are originally selected based on the
                 Chebyshev series approximation and are then adjusted to
                 ensure exactly rounded results for all inputs. To
                 reduce the number of terms in the approximation, the
                 input interval is divided into subintervals of equal
                 size and different coefficients are used for each
                 subinterval. For floating point numbers with 16-b
                 significands, the exactly rounded value of the function
                 can be computed in 51 ns on a 20-mm/sup 2/ chip. For
                 floating point numbers with 24-b significands, the
                 functions can be computed in 80 ns on a 98-mm/sup 2/
                 chip.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Electr. and Comput. Eng., Texas Univ.,
                 Austin, TX, USA",
  classification = "C4120 (Functional analysis); C5230 (Digital
                 arithmetic methods)",
  confdate =     "29 June--2 July 1993",
  conflocation = "Windsor, Ont., Canada",
  confsponsor =  "IEEE Comput. Soc.; IEEE Tech. Committee on VLSI;
                 Natural Sci. and Eng. Res.; Council of Canada",
  keywords =     "Elementary functions; Exact rounding; Floating point
                 numbers; Polynomial approximation; Reciprocal; Rounded
                 results; Square root",
  thesaurus =    "Floating point arithmetic; Function evaluation",
}


bibtype: article
filename: elefunt.bib
label: Schulte:1993:PHD
author: Michael J. Schulte and Earl E. Swartzlander, Jr.
title: Parallel hardware designs for correctly rounded elementary functions
journal: j-INTERVAL-COMP
volume: 4
pages: 65--88
year: 1993
ISSN: 0135-4868 OR 01354868
MRclass: 65G10 (65C20)
MRnumber: 1 305 859
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
fjournal: Interval Computations = Interval'nye vychisleniia
acknowledgement: ack-nhfb
rawauthor: Michael J. Schulte and Earl E. {Swartzlander, Jr.}
rawtitle: Parallel hardware designs for correctly rounded elementary functions
note:
Proceedings of the International Conference on Numerical Analysis with Automatic Result Verification (Lafayette, LA, 1993)

entry:
@Article{Schulte:1993:PHD,
  author =       "Michael J. Schulte and Earl E. {Swartzlander, Jr.}",
  title =        "Parallel hardware designs for correctly rounded
                 elementary functions",
  journal =      j-INTERVAL-COMP,
  volume =       "4",
  pages =        "65--88",
  year =         "1993",
  ISSN =         "0135-4868",
  MRclass =      "65G10 (65C20)",
  MRnumber =     "1 305 859",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Proceedings of the International Conference on
                 Numerical Analysis with Automatic Result Verification
                 (Lafayette, LA, 1993)",
  acknowledgement = ack-nhfb,
  fjournal =     "Interval Computations = Interval'nye vychisleniia",
}


bibtype: techreport
filename: elefunt.bib
label: Schwarz:1993:HRAa
author: E. Schwarz
title: High-radix algorithms for high-order arithmetic operations
type: Technical Report
number: CSL-TR-93-559
institution: Computer Systems Laboratory, Stanford University
address: Stanford, CA, USA
pages: 65--88
month: jan
monthnumber: 1
year: 1993
bibdate: Thu Apr 2 08:38:35 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1998.04.02 08:38:35 ???
acknowledgement: ack-sfo
rawauthor: E. Schwarz
rawtitle: High-radix algorithms for high-order arithmetic operations
entry:
@TechReport{Schwarz:1993:HRAa,
  author =       "E. Schwarz",
  title =        "High-radix algorithms for high-order arithmetic
                 operations",
  type =         "Technical Report",
  number =       "CSL-TR-93-559",
  institution =  "Computer Systems Laboratory, Stanford University",
  address =      "Stanford, CA, USA",
  month =        jan,
  year =         "1993",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
}


bibtype: phdthesis
filename: elefunt.bib
label: Schwarz:1993:HRAb
author: Eric Mark Schwarz
title: High-radix algorithms for high-order arithmetic operations
type: Thesis (Ph.D.)
school: Department of Electrical Engineering, Stanford University
address: Stanford, CA, USA
pages: 224
month: apr
monthnumber: 4
year: 1993
bibdate: Mon Jan 07 22:38:06 2008
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2008.01.07 22:38:06 ???
remark: AAT 9317816. ProQuest document ID 746798521.
acknowledgement: ack-nhfb
rawauthor: Eric Mark Schwarz
rawtitle: High-radix algorithms for high-order arithmetic operations
abstract:
Many common algorithms for high-order arithmetic operations require an initial approximation. The Newton--Raphson algorithm starts with an approximation and then quadratically converges on the solution. The initial approximation determines the number of iterations of the algorithm and is typically implemented as a look-up table in the form of a ROM or PLA. A novel method is suggested which describes high-order arithmetic operations with a partial product array. This method applies to the operations of division, reciprocal, square root, natural logarithm, exponential, and trigonometric functions. The partial product array of Boolean elements which describes the operation can be summed on an existing floating-point multiplier. The hardware needed is only the logic gates to create the Boolean elements in the array and a multiplexor, and the latency is that of the multiplier. Thus, by reusing a floating-point multiplier, a high-precision approximation to a high-order arithmetic operation can be implemented with a low marginal cost.par This dissertation describes the implementation and shows a method for deriving partial product arrays to approximate arithmetic operations. Then the proposed method is applied and evaluated for several operations. The proposed method yields a minimum approximation of twelve bits correct for the reciprocal operation and sixteen bits for the square root operation. The proposed method is shown to be as small as 0.05% the size (in gates) of an equivalent precision look-up table and has up to four times the accuracy (in bits) as an equivalent latency polynomial approximation. Also, three new iterative algorithms to increase the precision of the approximations and a theoretical analysis of the partial product array representation are detailed. Thus, high-radix algorithms of many arithmetic operations are possible at low cost.

keywords:
division; elementary functions; exponential; logarithm; PPA (partial product array); reciprocal square root; square root

rawabstract:
Many common algorithms for high-order arithmetic operations require an initial approximation. The Newton--Raphson algorithm starts with an approximation and then quadratically converges on the solution. The initial approximation determines the number of iterations of the algorithm and is typically implemented as a look-up table in the form of a ROM or PLA. A novel method is suggested which describes high-order arithmetic operations with a partial product array. This method applies to the operations of division, reciprocal, square root, natural logarithm, exponential, and trigonometric functions. The partial product array of Boolean elements which describes the operation can be summed on an existing floating-point multiplier. The hardware needed is only the logic gates to create the Boolean elements in the array and a multiplexor, and the latency is that of the multiplier. Thus, by reusing a floating-point multiplier, a high-precision approximation to a high-order arithmetic operation can be implemented with a low marginal cost.\par This dissertation describes the implementation and shows a method for deriving partial product arrays to approximate arithmetic operations. Then the proposed method is applied and evaluated for several operations. The proposed method yields a minimum approximation of twelve bits correct for the reciprocal operation and sixteen bits for the square root operation. The proposed method is shown to be as small as 0.05\% the size (in gates) of an equivalent precision look-up table and has up to four times the accuracy (in bits) as an equivalent latency polynomial approximation. Also, three new iterative algorithms to increase the precision of the approximations and a theoretical analysis of the partial product array representation are detailed. Thus, high-radix algorithms of many arithmetic operations are possible at low cost.

entry:
@PhdThesis{Schwarz:1993:HRAb,
  author =       "Eric Mark Schwarz",
  title =        "High-radix algorithms for high-order arithmetic
                 operations",
  type =         "Thesis ({Ph.D.})",
  school =       "Department of Electrical Engineering, Stanford
                 University",
  address =      "Stanford, CA, USA",
  pages =        "224",
  month =        apr,
  year =         "1993",
  bibdate =      "Mon Jan 07 22:38:06 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Many common algorithms for high-order arithmetic
                 operations require an initial approximation. The
                 Newton--Raphson algorithm starts with an approximation
                 and then quadratically converges on the solution. The
                 initial approximation determines the number of
                 iterations of the algorithm and is typically
                 implemented as a look-up table in the form of a ROM or
                 PLA. A novel method is suggested which describes
                 high-order arithmetic operations with a partial product
                 array. This method applies to the operations of
                 division, reciprocal, square root, natural logarithm,
                 exponential, and trigonometric functions. The partial
                 product array of Boolean elements which describes the
                 operation can be summed on an existing floating-point
                 multiplier. The hardware needed is only the logic gates
                 to create the Boolean elements in the array and a
                 multiplexor, and the latency is that of the multiplier.
                 Thus, by reusing a floating-point multiplier, a
                 high-precision approximation to a high-order arithmetic
                 operation can be implemented with a low marginal
                 cost.\par

                 This dissertation describes the implementation and
                 shows a method for deriving partial product arrays to
                 approximate arithmetic operations. Then the proposed
                 method is applied and evaluated for several operations.
                 The proposed method yields a minimum approximation of
                 twelve bits correct for the reciprocal operation and
                 sixteen bits for the square root operation. The
                 proposed method is shown to be as small as 0.05\% the
                 size (in gates) of an equivalent precision look-up
                 table and has up to four times the accuracy (in bits)
                 as an equivalent latency polynomial approximation.
                 Also, three new iterative algorithms to increase the
                 precision of the approximations and a theoretical
                 analysis of the partial product array representation
                 are detailed. Thus, high-radix algorithms of many
                 arithmetic operations are possible at low cost.",
  acknowledgement = ack-nhfb,
  keywords =     "division; elementary functions; exponential;
                 logarithm; PPA (partial product array); reciprocal
                 square root; square root",
  remark =       "AAT 9317816. ProQuest document ID 746798521.",
}


bibtype: inproceedings
filename: elefunt.bib
label: Schwarz:1993:HSA
author: E. M. Schwarz and M. J. Flynn
booktitle: Proceedings of the 11th Symposium on Computer Arithmetic, 2 July 1993
title: Hardware starting approximation for the square root operation
crossref: Swartzlander:1993:SCA
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 103--111
year: 1993
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-sfo
rawauthor: E. M. Schwarz and M. J. Flynn
rawbooktitle: Proceedings of the 11th Symposium on Computer Arithmetic, 2 July 1993
rawtitle: Hardware starting approximation for the square root operation
entry:
@InProceedings{Schwarz:1993:HSA,
  author =       "E. M. Schwarz and M. J. Flynn",
  booktitle =    "Proceedings of the 11th Symposium on Computer
                 Arithmetic, 2 July 1993",
  title =        "Hardware starting approximation for the square root
                 operation",
  crossref =     "Swartzlander:1993:SCA",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "103--111",
  year =         "1993",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  summary =      "A method for obtaining high-precision approximations
                 of high-order arithmetic operations is presented. These
                 approximations provide an accurate starting
                 approximation for high-precision iterative algorithms,
                 which translates into few iterations and \ldots{}",
}


bibtype: techreport
filename: elefunt.bib
label: Schwarz:1993:UFM
author: Eric Mark Schwarz and M. J. (Michael J.) Flynn
title: Using a floating-point multiplier's internals for high-radix division and square root
type: Technical report
number: CSL-TR-93-554
institution: Computer Systems Laboratory, Stanford University
address: Stanford, CA, USA
pages: iv + 45
year: 1993
bibdate: Sat Feb 24 15:01:45 MST 1996
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Computer arithmetic.
acknowledgement: ack-nhfb
rawauthor: Eric Mark Schwarz and M. J. (Michael J.) Flynn
rawtitle: Using a floating-point multiplier's internals for high-radix division and square root
remark:
``January 1993.'' Abstract: ``A method for obtaining high-precision approximations of high-order arithmetic operations at low-cost is presented in this study. Specifically, high-precision approximations of the reciprocal (12 bits worst case) and square root (16 bits) operations are obtained using the internal hardware of a floating-point multiplier without the use of look-up tables. The additional combinatorial logic necessary is very small due to the reuse of existing hardware. These low-cost high-precision approximations are used by iterative algorithms to perform the operations of division and square root. The method presented also applies to several other high-order arithmetic operations. Thus, high-radix algorithms for high-order arithmetic operations such as division and square root are possible at low-cost.''

entry:
@TechReport{Schwarz:1993:UFM,
  author =       "Eric Mark Schwarz and M. J. (Michael J.) Flynn",
  title =        "Using a floating-point multiplier's internals for
                 high-radix division and square root",
  type =         "Technical report",
  number =       "CSL-TR-93-554",
  institution =  "Computer Systems Laboratory, Stanford University",
  address =      "Stanford, CA, USA",
  pages =        "iv + 45",
  year =         "1993",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer arithmetic.",
  remark =       "``January 1993.'' Abstract: ``A method for obtaining
                 high-precision approximations of high-order arithmetic
                 operations at low-cost is presented in this study.
                 Specifically, high-precision approximations of the
                 reciprocal (12 bits worst case) and square root (16
                 bits) operations are obtained using the internal
                 hardware of a floating-point multiplier without the use
                 of look-up tables. The additional combinatorial logic
                 necessary is very small due to the reuse of existing
                 hardware. These low-cost high-precision approximations
                 are used by iterative algorithms to perform the
                 operations of division and square root. The method
                 presented also applies to several other high-order
                 arithmetic operations. Thus, high-radix algorithms for
                 high-order arithmetic operations such as division and
                 square root are possible at low-cost.''",
}


bibtype: article
filename: elefunt.bib
label: Sellers:1993:CDC
author: H. Sellers
title: The C$^2$-DIIS Convergence Acceleration Algorithm
journal: j-IJQC
volume: 45
number: 1
pages: 31--??
year: 1993
CODEN: IJQCB2
ISSN: 0020-7608 (print), 1097-461X (electronic) OR 00207608 (print), 1097461X (electronic)
ISSNL: 0020-7608 OR 00207608
bibdate: Wed Jan 3 14:24:13 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1996.01.03 14:24:13 MST
fjournal: International Journal of Quantum Chemistry
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://www.interscience.wiley.com/jpages/0020-7608/
rawauthor: H. Sellers
rawtitle: The {C$^2$-DIIS} Convergence Acceleration Algorithm
entry:
@Article{Sellers:1993:CDC,
  author =       "H. Sellers",
  title =        "The {C$^2$-DIIS} Convergence Acceleration Algorithm",
  journal =      j-IJQC,
  volume =       "45",
  number =       "1",
  pages =        "31--??",
  year =         "1993",
  CODEN =        "IJQCB2",
  ISSN =         "0020-7608 (print), 1097-461X (electronic)",
  ISSN-L =       "0020-7608",
  bibdate =      "Wed Jan 3 14:24:13 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Quantum Chemistry",
  journal-URL =  "http://www.interscience.wiley.com/jpages/0020-7608/",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Shishkov:1993:RDB
author: Dimitcdprime r Shishkov
title: Reduction of domains of basic elementary functions to arbitrary small intervals
journal: Annuaire Univ. Sofia Fac. Math. Inform.
volume: 87
number: 1--2
pages: 3--32 (1999)
year: 1993
ISSN: 0205-0808 OR 02050808
MRclass: 65D20
MRnumber: MR1745336
bibdate: Wed Apr 13 06:46:35 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.04.13 06:46:35 ???
acknowledgement: ack-nhfb
rawauthor: Dimit{\cdprime}r Shishkov
rawtitle: Reduction of domains of basic elementary functions to arbitrary small intervals
fjournal:
Godishnik na Sofiui skiya Universitet ``Sv. Kliment Okhridski''. Fakultet po Matematika i Informatika. Annuaire de l'Universite de Sofia ``St. Kliment Ohridski''. Faculte de Mathematiques et Informatique

entry:
@Article{Shishkov:1993:RDB,
  author =       "Dimit{\cdprime}r Shishkov",
  title =        "Reduction of domains of basic elementary functions to
                 arbitrary small intervals",
  journal =      "Annuaire Univ. Sofia Fac. Math. Inform.",
  volume =       "87",
  number =       "1--2",
  pages =        "3--32 (1999)",
  year =         "1993",
  ISSN =         "0205-0808",
  MRclass =      "65D20",
  MRnumber =     "MR1745336",
  bibdate =      "Wed Apr 13 06:46:35 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Godishnik na Sofi\u\i skiya Universitet ``Sv. Kliment
                 Okhridski''. Fakultet po Matematika i Informatika.
                 Annuaire de l'Universit{\'e} de Sofia ``St. Kliment
                 Ohridski''. Facult{\'e} de Math{\'e}matiques et
                 Informatique",
}


bibtype: article
filename: elefunt.bib
label: Snyder:1993:AFI
author: W. Van Snyder
title: Algorithm 723: Fresnel Integrals
journal: j-TOMS
volume: 19
number: 4
pages: 452--456
month: dec
monthnumber: 12
year: 1993
CODEN: ACMSCU
DOI: https://doi.org/10.1145/168173.168193
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Thu Apr 29 15:24:56 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib
bibtimestamp: 1999.04.29 15:24:56 ???
note: See remarks cite Snyder:1996:RAF,Snyder:2021:CRA.
URL: http://www.acm.org/pubs/citations/journals/toms/1993-19-4/p452-van_snyder/
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms; special functions
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: W. Van Snyder
rawnote: See remarks \cite{Snyder:1996:RAF,Snyder:2021:CRA}.
rawtitle: {Algorithm 723}: {Fresnel} Integrals
abstract:
An implementation of approximations for Fresnel integrals and associated functions is described. The approximations were originally developed by W. J. Cody, but a Fortran implementation using them has not previously been published.

subject:
bf G.1.2: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Rational approximation. bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing.

rawabstract:
An implementation of approximations for Fresnel integrals and associated functions is described. The approximations were originally developed by W. J. Cody, but a Fortran implementation using them has not previously been published.

entry:
@Article{Snyder:1993:AFI,
  author =       "W. Van Snyder",
  title =        "{Algorithm 723}: {Fresnel} Integrals",
  journal =      j-TOMS,
  volume =       "19",
  number =       "4",
  pages =        "452--456",
  month =        dec,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/168173.168193",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Apr 29 15:24:56 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See remarks \cite{Snyder:1996:RAF,Snyder:2021:CRA}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-4/p452-van_snyder/",
  abstract =     "An implementation of approximations for Fresnel
                 integrals and associated functions is described. The
                 approximations were originally developed by W. J. Cody,
                 but a Fortran implementation using them has not
                 previously been published.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; special functions",
  subject =      "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Rational approximation. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Certification and testing.",
}


bibtype: article
filename: elefunt.bib
label: Thompson:1993:CCQ
author: William J. Thompson
title: Cutting Corners: Quick Square Roots and Trig Functions
journal: j-COMPUT-PHYS
volume: 7
number: 1
pages: 18--??
month: jan
monthnumber: 1
year: 1993
CODEN: CPHYE2
DOI: https://doi.org/10.1063/1.4823136
ISSN: 0894-1866 (print), 1558-4208 (electronic) OR 08941866 (print), 15584208 (electronic)
ISSNL: 0894-1866 OR 08941866
bibdate: Wed Apr 10 08:45:39 MDT 2019
bibtimestamp: 2019.04.10 08:45:39 MDT
URL: https://aip.scitation.org/doi/10.1063/1.4823136
fjournal: Computers in Physics
acknowledgement: ack-nhfb
ajournal: Comput. Phys
journalURL: https://aip.scitation.org/journal/cip
rawauthor: William J. Thompson
rawtitle: Cutting Corners: Quick Square Roots and Trig Functions
bibsource:
https://www.math.utah.edu/pub/tex/bib/computphys.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Thompson:1993:CCQ,
  author =       "William J. Thompson",
  title =        "Cutting Corners: Quick Square Roots and Trig
                 Functions",
  journal =      j-COMPUT-PHYS,
  volume =       "7",
  number =       "1",
  pages =        "18--??",
  month =        jan,
  year =         "1993",
  CODEN =        "CPHYE2",
  DOI =          "https://doi.org/10.1063/1.4823136",
  ISSN =         "0894-1866 (print), 1558-4208 (electronic)",
  ISSN-L =       "0894-1866",
  bibdate =      "Wed Apr 10 08:45:39 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computphys.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://aip.scitation.org/doi/10.1063/1.4823136",
  acknowledgement = ack-nhfb,
  ajournal =     "Comput. Phys",
  fjournal =     "Computers in Physics",
  journal-URL =  "https://aip.scitation.org/journal/cip",
}


bibtype: article
filename: elefunt.bib
label: Vedder:1993:IAN
author: John D. Vedder
title: An invertible approximation to the normal distribution function
journal: j-COMPUT-STAT-DATA-ANAL
volume: 16
number: 1
pages: 119--123
month: jun
monthnumber: 6
year: 1993
CODEN: CSDADW
ISSN: 0167-9473 (print), 1872-7352 (electronic) OR 01679473 (print), 18727352 (electronic)
ISSNL: 0167-9473 OR 01679473
bibdate: Fri Feb 6 11:39:39 MST 2015
bibtimestamp: 2015.02.06 11:39:39 MST
URL: http://www.sciencedirect.com/science/article/pii/016794739390248R
fjournal: Computational Statistics & Data Analysis
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01679473
rawauthor: John D. Vedder
rawtitle: An invertible approximation to the normal distribution function
bibsource:
https://www.math.utah.edu/pub/tex/bib/computstatdataanal1990.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Vedder:1993:IAN,
  author =       "John D. Vedder",
  title =        "An invertible approximation to the normal distribution
                 function",
  journal =      j-COMPUT-STAT-DATA-ANAL,
  volume =       "16",
  number =       "1",
  pages =        "119--123",
  month =        jun,
  year =         "1993",
  CODEN =        "CSDADW",
  ISSN =         "0167-9473 (print), 1872-7352 (electronic)",
  ISSN-L =       "0167-9473",
  bibdate =      "Fri Feb 6 11:39:39 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computstatdataanal1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/016794739390248R",
  acknowledgement = ack-nhfb,
  fjournal =     "Computational Statistics \& Data Analysis",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01679473",
}


bibtype: article
filename: elefunt.bib
label: Zaitsev:1993:IMM
author: A. V. Zaitsev
title: Implementation of Miller's method for evaluation of Bessel functions of first kind
journal: j-J-SOV-MATH
volume: 63
number: 5
pages: 558--560
month: feb
monthnumber: 2
year: 1993
CODEN: JSOMAR
DOI: https://doi.org/10.1007/bf01142530
ISSN: 0090-4104 (print), 2376-5798 (electronic) OR 00904104 (print), 23765798 (electronic)
ISSNL: 0090-4104 OR 00904104
bibdate: Wed Mar 1 09:29:38 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.03.01 09:29:38 ???
fjournal: Journal of Soviet Mathematics
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10958
rawauthor: A. V. Zaitsev
rawtitle: Implementation of {Miller}'s method for evaluation of {Bessel} functions of first kind
entry:
@Article{Zaitsev:1993:IMM,
  author =       "A. V. Zaitsev",
  title =        "Implementation of {Miller}'s method for evaluation of
                 {Bessel} functions of first kind",
  journal =      j-J-SOV-MATH,
  volume =       "63",
  number =       "5",
  pages =        "558--560",
  month =        feb,
  year =         "1993",
  CODEN =        "JSOMAR",
  DOI =          "https://doi.org/10.1007/bf01142530",
  ISSN =         "0090-4104 (print), 2376-5798 (electronic)",
  ISSN-L =       "0090-4104",
  bibdate =      "Wed Mar 1 09:29:38 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Soviet Mathematics",
  journal-URL =  "http://link.springer.com/journal/10958",
}


bibtype: article
filename: elefunt.bib
label: Anonymous:1994:C
author: Anonymous
title: Corrigenda
journal: j-TOMS
volume: 20
number: 4
pages: 553--553
month: dec
monthnumber: 12
year: 1994
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Mar 14 16:17:03 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1995.03.14 16:17:03 ???
note: See cite Hull:1994:ICE
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-rfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Anonymous
rawnote: See \cite{Hull:1994:ICE}
rawtitle: Corrigenda
entry:
@Article{Anonymous:1994:C,
  author =       "Anonymous",
  title =        "Corrigenda",
  journal =      j-TOMS,
  volume =       "20",
  number =       "4",
  pages =        "553--553",
  month =        dec,
  year =         "1994",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 14 16:17:03 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Hull:1994:ICE}",
  acknowledgement = ack-rfb # "\slash " # ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Bajard:1994:BNH
author: Jean-Claude Bajard and Sylvanus Kla and Jean-Michel Muller
title: BKM: a new hardware algorithm for complex elementary functions
journal: j-IEEE-TRANS-COMPUT
volume: 43
number: 8
pages: 955--963
year: 1994
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.295857
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
MRclass: 68M07
MRnumber: 1 294 301
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Jean-Claude Bajard and Sylvanus Kla and Jean-Michel Muller
rawtitle: {BKM}: a new hardware algorithm for complex elementary functions
entry:
@Article{Bajard:1994:BNH,
  author =       "Jean-Claude Bajard and Sylvanus Kla and Jean-Michel
                 Muller",
  title =        "{BKM}: a new hardware algorithm for complex elementary
                 functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "43",
  number =       "8",
  pages =        "955--963",
  year =         "1994",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.295857",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  MRclass =      "68M07",
  MRnumber =     "1 294 301",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: elefunt.bib
label: Bender:1994:DAS
author: Carl M. Bender and Stefan Boettcher
title: Determination of $ f(infty ) $ from the asymptotic series for $ f(x) $ about $ x = 0 $
journal: j-J-MATH-PHYS
volume: 35
number: 4
pages: 1914--1921
month: apr
monthnumber: 4
year: 1994
CODEN: JMAPAQ
DOI: https://doi.org/10.1063/1.530577
ISSNL: 0022-2488 OR 00222488
MRclass: 41A60 (41A21 65D15 81Q15)
MRnumber: 95d:41063
bibdate: Tue Nov 1 08:58:10 MDT 2011
bibtimestamp: 2011.11.01 08:58:10 MDT
URL: http://jmp.aip.org/resource/1/jmapaq/v35/i4/p1914_s1
fjournal: Journal of Mathematical Physics
acknowledgement: ack-nhfb
journalURL: http://jmp.aip.org/
rawauthor: Carl M. Bender and Stefan Boettcher
rawtitle: Determination of $ f(\infty) $ from the asymptotic series for $ f(x) $ about $ x = 0 $
bibsource:
http://jmp.aip.org/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys1990.bib

entry:
@Article{Bender:1994:DAS,
  author =       "Carl M. Bender and Stefan Boettcher",
  title =        "Determination of $ f(\infty) $ from the asymptotic
                 series for $ f(x) $ about $ x = 0 $",
  journal =      j-J-MATH-PHYS,
  volume =       "35",
  number =       "4",
  pages =        "1914--1921",
  month =        apr,
  year =         "1994",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.530577",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  MRclass =      "41A60 (41A21 65D15 81Q15)",
  MRnumber =     "95d:41063",
  bibdate =      "Tue Nov 1 08:58:10 MDT 2011",
  bibsource =    "http://jmp.aip.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys1990.bib",
  URL =          "http://jmp.aip.org/resource/1/jmapaq/v35/i4/p1914_s1",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  pagecount =    "8",
}


bibtype: article
filename: elefunt.bib
label: Brown:1994:CAS
author: Barry W. Brown and Lawrence Levy
title: Certification of Algorithm 708: Significant Digit Computation of the Incomplete Beta
journal: j-TOMS
volume: 20
number: 3
pages: 393--397
month: sep
monthnumber: 9
year: 1994
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sat Nov 19 12:53:17 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.11.19 12:53:17 ???
note: See cite DiDonato:1992:ASD.
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms; continued fractions; F-distribution
subject: G.1.2 [Numerical Analysis]: Approximation
acknowledgement: ack-rfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Barry W. Brown and Lawrence Levy
rawnote: See \cite{DiDonato:1992:ASD}.
rawtitle: Certification of {Algorithm 708}: Significant Digit Computation of the Incomplete Beta
URL:
http://doi.acm.org/10.1145/192115.192155; http://www.acm.org/pubs/citations/journals/toms/1994-20-3/p393-brown/

entry:
@Article{Brown:1994:CAS,
  author =       "Barry W. Brown and Lawrence Levy",
  title =        "Certification of {Algorithm 708}: Significant Digit
                 Computation of the Incomplete Beta",
  journal =      j-TOMS,
  volume =       "20",
  number =       "3",
  pages =        "393--397",
  month =        sep,
  year =         "1994",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 19 12:53:17 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{DiDonato:1992:ASD}.",
  URL =          "http://doi.acm.org/10.1145/192115.192155;
                 http://www.acm.org/pubs/citations/journals/toms/1994-20-3/p393-brown/",
  acknowledgement = ack-rfb # "\slash " # ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; continued fractions; F-distribution",
  subject =      "G.1.2 [Numerical Analysis]: Approximation",
}


bibtype: article
filename: elefunt.bib
label: Bruno:1994:AAF
author: Oscar P. Bruno and Fernando Reitich
title: Approximation of analytic functions: a method of enhanced convergence
journal: j-MATH-COMPUT
volume: 63
number: 207
pages: 195--213
month: jul
monthnumber: 7
year: 1994
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 30B10 (41A21 41A25)
MRnumber: 94m:30003
MRreviewer: A. Edrei
bibdate: Tue Mar 25 15:38:13 MST 1997
bibtimestamp: 1997.03.25 15:38:13 MST
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
affiliation: Sch. of Math., Georgia Inst. of Technol., Atlanta, GA, USA
ajournal: Math. Comput.
classcodes: B0290F (Interpolation and function approximation); C4130 (Interpolation and function approximation)
corpsource: Sch. of Math., Georgia Inst. of Technol., Atlanta, GA, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Oscar P. Bruno and Fernando Reitich
rawtitle: Approximation of analytic functions: a method of enhanced convergence
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib

keywords:
analytic functions; approximation; conformal; conformal maps; convergence of numerical methods; convergence rates; enhanced convergence; Euler transform; function approximation; Pade; perturbation methods; perturbation techniques; power; series; series (mathematics); series expansions; Stieltjes-type functions; Taylor expansion; transformations; truncated enhanced

entry:
@Article{Bruno:1994:AAF,
  author =       "Oscar P. Bruno and Fernando Reitich",
  title =        "Approximation of analytic functions: a method of
                 enhanced convergence",
  journal =      j-MATH-COMPUT,
  volume =       "63",
  number =       "207",
  pages =        "195--213",
  month =        jul,
  year =         "1994",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "30B10 (41A21 41A25)",
  MRnumber =     "94m:30003",
  MRreviewer =   "A. Edrei",
  bibdate =      "Tue Mar 25 15:38:13 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Sch. of Math., Georgia Inst. of Technol., Atlanta, GA,
                 USA",
  ajournal =     "Math. Comput.",
  classcodes =   "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  corpsource =   "Sch. of Math., Georgia Inst. of Technol., Atlanta, GA,
                 USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "analytic functions; approximation; conformal;
                 conformal maps; convergence of numerical methods;
                 convergence rates; enhanced convergence; Euler
                 transform; function approximation; Pad{\'e};
                 perturbation methods; perturbation techniques; power;
                 series; series (mathematics); series expansions;
                 Stieltjes-type functions; Taylor expansion;
                 transformations; truncated enhanced",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Carlson:1994:AAS
author: B. C. Carlson and J. L. Gustafson
title: Asymptotic Approximations for Symmetric Elliptic Integrals
journal: j-SIAM-J-MATH-ANA
volume: 25
number: 2
pages: 288--303
month: mar
monthnumber: 3
year: 1994
CODEN: SJMAAH
ISSN: 0036-1410 (print), 1095-7154 (electronic) OR 00361410 (print), 10957154 (electronic)
ISSNL: 0036-1410 OR 00361410
MRclass: 33E05 (41A60)
MRnumber: 95b:33056
MRreviewer: Bruce C. Berndt
bibdate: Sat Dec 5 18:14:13 MST 1998
bibsource: http://epubs.siam.org/sam-bin/dbq/toc/SIMA/25/2; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1998.12.05 18:14:13 MST
URL: http://epubs.siam.org/sam-bin/dbq/article/22847
fjournal: SIAM Journal on Mathematical Analysis
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sima
rawauthor: B. C. Carlson and J. L. Gustafson
rawtitle: Asymptotic Approximations for Symmetric Elliptic Integrals
entry:
@Article{Carlson:1994:AAS,
  author =       "B. C. Carlson and J. L. Gustafson",
  title =        "Asymptotic Approximations for Symmetric Elliptic
                 Integrals",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "25",
  number =       "2",
  pages =        "288--303",
  month =        mar,
  year =         "1994",
  CODEN =        "SJMAAH",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  MRclass =      "33E05 (41A60)",
  MRnumber =     "95b:33056",
  MRreviewer =   "Bruce C. Berndt",
  bibdate =      "Sat Dec 5 18:14:13 MST 1998",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/25/2;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/22847",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Mathematical Analysis",
  journal-URL =  "http://epubs.siam.org/sima",
}


bibtype: article
filename: elefunt.bib
label: Chaudhry:1994:GIG
author: M. Aslam Chaudhry and S. M. Zubair
title: Generalized incomplete gamma functions with applications
journal: j-J-COMPUT-APPL-MATH
volume: 55
number: 1
pages: 99--123
day: 31
month: oct
monthnumber: 10
year: 1994
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:24:33 MST 2017
bibtimestamp: 2017.02.25 12:24:33 MST
URL: http://www.sciencedirect.com/science/article/pii/0377042794901872
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: M. Aslam Chaudhry and S. M. Zubair
rawtitle: Generalized incomplete gamma functions with applications
entry:
@Article{Chaudhry:1994:GIG,
  author =       "M. Aslam Chaudhry and S. M. Zubair",
  title =        "Generalized incomplete gamma functions with
                 applications",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "55",
  number =       "1",
  pages =        "99--123",
  day =          "31",
  month =        oct,
  year =         "1994",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:24:33 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042794901872",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Chen:1994:ABB
author: Yang Chen and Mourad E. H. Ismail and K. A. Muttalib
title: Asymptotics of basic Bessel functions and $q$-Laguerre polynomials
journal: j-J-COMPUT-APPL-MATH
volume: 54
number: 3
pages: 263--272
day: 20
month: oct
monthnumber: 10
year: 1994
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:24:33 MST 2017
bibtimestamp: 2017.02.25 12:24:33 MST
URL: http://www.sciencedirect.com/science/article/pii/037704279200128V
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Yang Chen and Mourad E. H. Ismail and K. A. Muttalib
rawtitle: Asymptotics of basic {Bessel} functions and $q$-{Laguerre} polynomials
entry:
@Article{Chen:1994:ABB,
  author =       "Yang Chen and Mourad E. H. Ismail and K. A. Muttalib",
  title =        "Asymptotics of basic {Bessel} functions and
                 $q$-{Laguerre} polynomials",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "54",
  number =       "3",
  pages =        "263--272",
  day =          "20",
  month =        oct,
  year =         "1994",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:24:33 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/037704279200128V",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: inproceedings
filename: elefunt.bib
label: Chen:1994:EDU
author: Sau-Gee Chen and Chieh-Chih Li
title: Efficient designs of unified $2$'s complement division and square root algorithm and architecture
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 943--947
year: 1994
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: Sau-Gee Chen and Chieh-Chih Li
rawtitle: Efficient designs of unified $2$'s complement division and square root algorithm and architecture
booktitle:
Proceedings of TENCON '94. IEEE Region 10's Ninth Annual International Conference. Theme: `Frontiers of Computer Technology'

rawbooktitle:
{Proceedings of TENCON '94. IEEE Region 10's Ninth Annual International Conference. Theme: `Frontiers of Computer Technology'}

entry:
@InProceedings{Chen:1994:EDU,
  author =       "Sau-Gee Chen and Chieh-Chih Li",
  booktitle =    "{Proceedings of TENCON '94. IEEE Region 10's Ninth
                 Annual International Conference. Theme: `Frontiers of
                 Computer Technology'}",
  title =        "Efficient designs of unified $2$'s complement division
                 and square root algorithm and architecture",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "943--947",
  year =         "1994",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "Efficient unified 2's complement division and square
                 root algorithm, and their architectures are proposed in
                 this work. The designs are high speed, small area and
                 high compatibility. The architectures provide bit level
                 pipelined operation, as well \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Cortadella:1994:HRD
author: J. Cortadella and T. Lang
title: High-Radix Division and Square-Root with Speculation
journal: j-IEEE-TRANS-COMPUT
volume: 43
number: 8
pages: 919--931
month: aug
monthnumber: 8
year: 1994
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.295854
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; OCLC Proceedings database
bibtimestamp: 2005.07.16 15:28:13 MDT
fjournal: IEEE Transactions on Computers
remark: Selected revised and extended papers from ARITH'11 cite Swartzlander:1993:SCA.
acknowledgement: ack-sfo
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: J. Cortadella and T. Lang
rawtitle: High-Radix Division and Square-Root with Speculation
entry:
@Article{Cortadella:1994:HRD,
  author =       "J. Cortadella and T. Lang",
  title =        "High-Radix Division and Square-Root with Speculation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "43",
  number =       "8",
  pages =        "919--931",
  month =        aug,
  year =         "1994",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.295854",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  remark =       "Selected revised and extended papers from ARITH'11
                 \cite{Swartzlander:1993:SCA}.",
  summary =      "The speed of high-radix digit-recurrence dividers and
                 square-root units is mainly determined by the
                 complexity of the result-digit selection. We present a
                 scheme in which a simpler function speculates the
                 result digit, and, when this speculation is \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Damnjanovic:1994:EFL
author: Zlatan Damnjanovic
title: Elementary functions and loop programs
journal: j-NOTRE-DAME-J-FORM-LOG
volume: 35
number: 4
pages: 496--522
year: 1994
CODEN: NDJFAM
ISSN: 0029-4527 (print), 1939-0726 (electronic) OR 00294527 (print), 19390726 (electronic)
ISSNL: 0029-4527 OR 00294527
MRclass: 03D20 (68Q15)
MRnumber: 96i:03036
MRreviewer: John P. Helm
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
fjournal: Notre Dame journal of formal logic
acknowledgement: ack-nhfb
journalURL: http://projecteuclid.org/all/euclid.ndjfl
rawauthor: Zlatan Damnjanovic
rawtitle: Elementary functions and loop programs
entry:
@Article{Damnjanovic:1994:EFL,
  author =       "Zlatan Damnjanovic",
  title =        "Elementary functions and loop programs",
  journal =      j-NOTRE-DAME-J-FORM-LOG,
  volume =       "35",
  number =       "4",
  pages =        "496--522",
  year =         "1994",
  CODEN =        "NDJFAM",
  ISSN =         "0029-4527 (print), 1939-0726 (electronic)",
  ISSN-L =       "0029-4527",
  MRclass =      "03D20 (68Q15)",
  MRnumber =     "96i:03036",
  MRreviewer =   "John P. Helm",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Notre Dame journal of formal logic",
  journal-URL =  "http://projecteuclid.org/all/euclid.ndjfl",
}


bibtype: article
filename: elefunt.bib
label: Das:1994:ATE
author: Mrinal Kanti Das
title: Analysis of two elementary functions
journal: j-INT-J-MATH-EDU-SCI-TECH
volume: 25
number: 1
pages: 17--24
year: 1994
CODEN: IJMEBM
ISSN: 0020-739X (print), 1464-5211 (electronic) OR 0020739X (print), 14645211 (electronic)
ISSNL: 0020-739X OR 0020739X
MRclass: 26-01 (33B10)
MRnumber: 1 257 731
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
fjournal: International Journal of Mathematical Education in Science and Technology
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/tmes20
rawauthor: Mrinal Kanti Das
rawtitle: Analysis of two elementary functions
entry:
@Article{Das:1994:ATE,
  author =       "Mrinal Kanti Das",
  title =        "Analysis of two elementary functions",
  journal =      j-INT-J-MATH-EDU-SCI-TECH,
  volume =       "25",
  number =       "1",
  pages =        "17--24",
  year =         "1994",
  CODEN =        "IJMEBM",
  ISSN =         "0020-739X (print), 1464-5211 (electronic)",
  ISSN-L =       "0020-739X",
  MRclass =      "26-01 (33B10)",
  MRnumber =     "1 257 731",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Mathematical Education in
                 Science and Technology",
  journal-URL =  "http://www.tandfonline.com/loi/tmes20",
}


bibtype: techreport
filename: elefunt.bib
label: Dunham:1994:PMAa
author: Charles B. Dunham
title: Provably Monotone Approximations, IV
type: Technical report
number: TR-417
institution: Department of Computer Science, University of Western Ontario
address: London, Ontario, Canada
pages: 17--24
day: 8
month: mar
monthnumber: 3
year: 1994
bibdate: Tue Apr 12 11:26:47 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.04.12 11:26:47 ???
URL: http://www.csd.uwo.ca/tech-reports/
acknowledgement: ack-nhfb
rawauthor: Charles B. Dunham
rawtitle: Provably Monotone Approximations, {IV}
entry:
@TechReport{Dunham:1994:PMAa,
  author =       "Charles B. Dunham",
  title =        "Provably Monotone Approximations, {IV}",
  type =         "Technical report",
  number =       "TR-417",
  institution =  "Department of Computer Science, University of Western
                 Ontario",
  address =      "London, Ontario, Canada",
  day =          "8",
  month =        mar,
  year =         "1994",
  bibdate =      "Tue Apr 12 11:26:47 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.csd.uwo.ca/tech-reports/",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: elefunt.bib
label: Dunham:1994:PMAb
author: Charles B. Dunham
title: Provably Monotone Approximations, IV, Revised
type: Technical report
number: TR-422
institution: Department of Computer Science, University of Western Ontario
address: London, Ontario, Canada
pages: 17--24
day: 4
month: apr
monthnumber: 4
year: 1994
bibdate: Tue Apr 12 11:26:47 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.04.12 11:26:47 ???
URL: http://www.csd.uwo.ca/tech-reports/
acknowledgement: ack-nhfb
rawauthor: Charles B. Dunham
rawtitle: Provably Monotone Approximations, {IV}, Revised
entry:
@TechReport{Dunham:1994:PMAb,
  author =       "Charles B. Dunham",
  title =        "Provably Monotone Approximations, {IV}, Revised",
  type =         "Technical report",
  number =       "TR-422",
  institution =  "Department of Computer Science, University of Western
                 Ontario",
  address =      "London, Ontario, Canada",
  day =          "4",
  month =        apr,
  year =         "1994",
  bibdate =      "Tue Apr 12 11:26:47 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.csd.uwo.ca/tech-reports/",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Dunkl:1994:AHI
author: Charles F. Dunkl and Donald E. Ramirez
title: Algorithm 736: Hyperelliptic Integrals and the Surface Measure of Ellipsoids
journal: j-TOMS
volume: 20
number: 4
pages: 427--435
month: dec
monthnumber: 12
year: 1994
CODEN: ACMSCU
DOI: https://doi.org/10.1145/198429.198431
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 65D30
MRnumber: 1 368 025
bibdate: Tue Mar 14 16:16:51 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1995.03.14 16:16:51 ???
URL: http://www.acm.org/pubs/citations/journals/toms/1994-20-4/p427-dunkl/
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-rfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Charles F. Dunkl and Donald E. Ramirez
rawtitle: {Algorithm 736}: Hyperelliptic Integrals and the Surface Measure of Ellipsoids
keywords:
elliptic integral; expected radius; Lauricella's hypergeometric function; optimal designs; surface measure

subject:
G.1.4 [Numerical Analysis]: Quadrature and Numerical Differentiation -- multiple quadrature; G.3 [Mathematics of Computing]: Probability and Statistics

entry:
@Article{Dunkl:1994:AHI,
  author =       "Charles F. Dunkl and Donald E. Ramirez",
  title =        "{Algorithm 736}: Hyperelliptic Integrals and the
                 Surface Measure of Ellipsoids",
  journal =      j-TOMS,
  volume =       "20",
  number =       "4",
  pages =        "427--435",
  month =        dec,
  year =         "1994",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/198429.198431",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D30",
  MRnumber =     "1 368 025",
  bibdate =      "Tue Mar 14 16:16:51 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1994-20-4/p427-dunkl/",
  acknowledgement = ack-rfb # "\slash " # ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "elliptic integral; expected radius; Lauricella's
                 hypergeometric function; optimal designs; surface
                 measure",
  subject =      "G.1.4 [Numerical Analysis]: Quadrature and Numerical
                 Differentiation -- multiple quadrature; G.3
                 [Mathematics of Computing]: Probability and
                 Statistics",
}


bibtype: article
filename: elefunt.bib
label: Dunkl:1994:CHI
author: Charles F. Dunkl and Donald E. Ramirez
title: Computing Hyperelliptic Integrals for Surface Measure of Ellipsoids
journal: j-TOMS
volume: 20
number: 4
pages: 413--426
month: dec
monthnumber: 12
year: 1994
CODEN: ACMSCU
DOI: https://doi.org/10.1145/198429.198430
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 65D30
MRnumber: 1 368 024
bibdate: Tue Mar 14 16:16:49 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1995.03.14 16:16:49 ???
URL: http://www.acm.org/pubs/citations/journals/toms/1994-20-4/p413-dunkl/
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-rfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Charles F. Dunkl and Donald E. Ramirez
rawtitle: Computing Hyperelliptic Integrals for Surface Measure of Ellipsoids
keywords:
elliptic integral; expected radius; Lauricella's hypergeometric function; optimal designs; surface measure

subject:
G.1.4 [Numerical Analysis]: Quadrature and Numerical Differentiation -- multiple quadrature; G.3 [Mathematics of Computing]: Probability and Statistics

entry:
@Article{Dunkl:1994:CHI,
  author =       "Charles F. Dunkl and Donald E. Ramirez",
  title =        "Computing Hyperelliptic Integrals for Surface Measure
                 of Ellipsoids",
  journal =      j-TOMS,
  volume =       "20",
  number =       "4",
  pages =        "413--426",
  month =        dec,
  year =         "1994",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/198429.198430",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D30",
  MRnumber =     "1 368 024",
  bibdate =      "Tue Mar 14 16:16:49 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1994-20-4/p413-dunkl/",
  acknowledgement = ack-rfb # "\slash " # ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "elliptic integral; expected radius; Lauricella's
                 hypergeometric function; optimal designs; surface
                 measure",
  subject =      "G.1.4 [Numerical Analysis]: Quadrature and Numerical
                 Differentiation -- multiple quadrature; G.3
                 [Mathematics of Computing]: Probability and
                 Statistics",
}


bibtype: book
filename: elefunt.bib
label: Ercegovac:1994:DSR
author: Milos D. (Dragutin) Ercegovac and Tomas Lang
title: Division and Square Root: Digit-recurrence Algorithms and Implementations
publisher: pub-KLUWER
address: pub-KLUWER:adr
pages: x + 230
year: 1994
ISBN: 0-7923-9438-0 OR 0792394380
ISBN13: 978-0-7923-9438-9 OR 9780792394389
LCCN: QA76.9.C62 E73 1994
bibdate: Fri Mar 27 09:46:24 1998
bibtimestamp: 1998.03.27 09:46:24 ???
acknowledgement: ack-nhfb
rawauthor: Milo{\v{s}} D. (Dragutin) Ercegovac and Tomas Lang
rawtitle: Division and Square Root: Digit-recurrence Algorithms and Implementations
TOC:
Preface / 1 1. General Comments / 5 2. Division by Digit Recurrence / 5 3. Theory of Digit-Recurrence Division / 19 4. Division With Scaling and Prediction /65 5. Higher Radix Division / 91 6. On-The-Fly Conversion and Round / 121 7. Square Root by Digit Recurrence / 135 8. Implementations of Square Root / 153 A: Restoring and Non-Restoring Division / 182 B: Evaluation of Some Implementations / 182 Bibliography / 207 Index / 227

rawTOC:
Preface / 1 \\ 1. General Comments / 5 \\ 2. Division by Digit Recurrence / 5 \\ 3. Theory of Digit-Recurrence Division / 19 \\ 4. Division With Scaling and Prediction /65 \\ 5. Higher Radix Division / 91 \\ 6. On-The-Fly Conversion and Round / 121 \\ 7. Square Root by Digit Recurrence / 135 \\ 8. Implementations of Square Root / 153 \\ A: Restoring and Non-Restoring Division / 182 \\ B: Evaluation of Some Implementations / 182 \\ Bibliography / 207 \\ Index / 227

entry:
@Book{Ercegovac:1994:DSR,
  author =       "Milo{\v{s}} D. (Dragutin) Ercegovac and Tomas Lang",
  title =        "Division and Square Root: Digit-recurrence Algorithms
                 and Implementations",
  publisher =    pub-KLUWER,
  address =      pub-KLUWER:adr,
  pages =        "x + 230",
  year =         "1994",
  ISBN =         "0-7923-9438-0",
  ISBN-13 =      "978-0-7923-9438-9",
  LCCN =         "QA76.9.C62 E73 1994",
  bibdate =      "Fri Mar 27 09:46:24 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  tableofcontents = "Preface / 1 \\
                 1. General Comments / 5 \\
                 2. Division by Digit Recurrence / 5 \\
                 3. Theory of Digit-Recurrence Division / 19 \\
                 4. Division With Scaling and Prediction /65 \\
                 5. Higher Radix Division / 91 \\
                 6. On-The-Fly Conversion and Round / 121 \\
                 7. Square Root by Digit Recurrence / 135 \\
                 8. Implementations of Square Root / 153 \\
                 A: Restoring and Non-Restoring Division / 182 \\
                 B: Evaluation of Some Implementations / 182 \\
                 Bibliography / 207 \\
                 Index / 227",
}


bibtype: article
filename: elefunt.bib
label: Everitt:1994:GBF
author: W. N. Everitt and C. Markett
title: On a generalization of Bessel functions satisfying higher-order differential equations
journal: j-J-COMPUT-APPL-MATH
volume: 54
number: 3
pages: 325--349
day: 20
month: oct
monthnumber: 10
year: 1994
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:24:33 MST 2017
bibtimestamp: 2017.02.25 12:24:33 MST
URL: http://www.sciencedirect.com/science/article/pii/0377042794902550
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: W. N. Everitt and C. Markett
rawtitle: On a generalization of {Bessel} functions satisfying higher-order differential equations
entry:
@Article{Everitt:1994:GBF,
  author =       "W. N. Everitt and C. Markett",
  title =        "On a generalization of {Bessel} functions satisfying
                 higher-order differential equations",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "54",
  number =       "3",
  pages =        "325--349",
  day =          "20",
  month =        oct,
  year =         "1994",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:24:33 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042794902550",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Fukushima:1994:NCI
author: Toshio Fukushima and Hideharu Ishizaki
title: Numerical computation of incomplete elliptic integrals of a general form
journal: j-CELEST-MECH-DYN-ASTR
volume: 59
number: 3
pages: 237--251
month: jul
monthnumber: 7
year: 1994
CODEN: CLMCAV
DOI: https://doi.org/10.1007/BF00692874
ISSN: 0923-2958 (print), 1572-9478 (electronic) OR 09232958 (print), 15729478 (electronic)
ISSNL: 0923-2958 OR 09232958
MRclass: 33E05 65R20 65D32 (33E30 70-08 70E15)
MRnumber: 1285916 (95c:65041)
bibdate: Wed Oct 20 21:26:45 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.20 21:26:45 ???
URL: http://www.springerlink.com/content/0923-2958/
fjournal: Celestial Mechanics & Dynamical Astronomy. An International Journal of Space Dynamics
keywords: Incomplete elliptic integrals; numerical computation
ZMnumber: Zbl 0818.33013
acknowledgement: ack-nhfb
rawauthor: Toshio Fukushima and Hideharu Ishizaki
rawtitle: Numerical computation of incomplete elliptic integrals of a general form
abstract:
We present an algorithm to compute the incomplete elliptic integral of a general form. The algorithm efficiently evaluates some linear combinations of incomplete elliptic integrals of all kinds to a high precision. Some numerical examples are given as illustrations. This enables us to numerically calculate the values and the partial derivatives of incomplete elliptic integrals of all kinds, which are essential when dealing with many problems in celestial mechanics, including the analytic solution of the torque-free rotational motion of a rigid body around its barycenter.

rawabstract:
We present an algorithm to compute the incomplete elliptic integral of a general form. The algorithm efficiently evaluates some linear combinations of incomplete elliptic integrals of all kinds to a high precision. Some numerical examples are given as illustrations. This enables us to numerically calculate the values and the partial derivatives of incomplete elliptic integrals of all kinds, which are essential when dealing with many problems in celestial mechanics, including the analytic solution of the torque-free rotational motion of a rigid body around its barycenter.

entry:
@Article{Fukushima:1994:NCI,
  author =       "Toshio Fukushima and Hideharu Ishizaki",
  title =        "Numerical computation of incomplete elliptic integrals
                 of a general form",
  journal =      j-CELEST-MECH-DYN-ASTR,
  volume =       "59",
  number =       "3",
  pages =        "237--251",
  month =        jul,
  year =         "1994",
  CODEN =        "CLMCAV",
  DOI =          "https://doi.org/10.1007/BF00692874",
  ISSN =         "0923-2958 (print), 1572-9478 (electronic)",
  ISSN-L =       "0923-2958",
  MRclass =      "33E05 65R20 65D32 (33E30 70-08 70E15)",
  MRnumber =     "1285916 (95c:65041)",
  bibdate =      "Wed Oct 20 21:26:45 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/content/0923-2958/",
  ZMnumber =     "Zbl 0818.33013",
  abstract =     "We present an algorithm to compute the incomplete
                 elliptic integral of a general form. The algorithm
                 efficiently evaluates some linear combinations of
                 incomplete elliptic integrals of all kinds to a high
                 precision. Some numerical examples are given as
                 illustrations. This enables us to numerically calculate
                 the values and the partial derivatives of incomplete
                 elliptic integrals of all kinds, which are essential
                 when dealing with many problems in celestial mechanics,
                 including the analytic solution of the torque-free
                 rotational motion of a rigid body around its
                 barycenter.",
  acknowledgement = ack-nhfb,
  fjournal =     "Celestial Mechanics \& Dynamical Astronomy. An
                 International Journal of Space Dynamics",
  keywords =     "Incomplete elliptic integrals; numerical computation",
}


bibtype: article
filename: elefunt.bib
label: Hahn:1994:UDF
author: H. Hahn and D. Timmermann and B. J. Hosticka and B. Rix
journal: j-IEEE-TRANS-COMPUT
volume: 43
number: 11
pages: 1339--1344
month: nov
monthnumber: 11
year: 1994
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.324568
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 07:13:58 MDT 2011
bibtimestamp: 2011.07.07 07:13:58 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=324568
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: H. Hahn and D. Timmermann and B. J. Hosticka and B. Rix
title:
A unified and division-free CORDIC argument reduction method with unlimited convergence domain including inverse hyperbolic functions

bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib

rawtitle:
A unified and division-free {CORDIC} argument reduction method with unlimited convergence domain including inverse hyperbolic functions

entry:
@Article{Hahn:1994:UDF,
  author =       "H. Hahn and D. Timmermann and B. J. Hosticka and B.
                 Rix",
  title =        "A unified and division-free {CORDIC} argument
                 reduction method with unlimited convergence domain
                 including inverse hyperbolic functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "43",
  number =       "11",
  pages =        "1339--1344",
  month =        nov,
  year =         "1994",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.324568",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:13:58 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=324568",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: elefunt.bib
label: Homeier:1994:NCA
author: Herbert H. H. Homeier
editor: Ralf Gruber and Marco Tomassini
title: Nonlinear convergence acceleration for orthogonal series
publisher: European Physical Society, Boite Postale 69, CH-1213 Petit-Lancy, Geneva, Switzerland
address: Lugano
pages: 47--50
year: 1994
ISBN: 2-88270-011-3 OR 2882700113
ISBN13: 978-2-88270-011-7 OR 9782882700117
URL: http://www.chemie.uni-regensburg.de/pub/preprint/preprint.html#TCNA942
keywords: convergence acceleration
rawauthor: Herbert H. H. Homeier
raweditor: Ralf Gruber and Marco Tomassini
rawtitle: Nonlinear convergence acceleration for orthogonal series
booktitle:
Proceedings of the 6th Joint EPS-APS International Conference on Physics Computing, Physics Computing '94

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/h/homeier-herbert-h-h.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

rawbooktitle:
Proceedings of the 6th {Joint EPS-APS International Conference} on {Physics Computing, Physics Computing} '94

entry:
@InProceedings{Homeier:1994:NCA,
  author =       "Herbert H. H. Homeier",
  editor =       "Ralf Gruber and Marco Tomassini",
  booktitle =    "Proceedings of the 6th {Joint EPS-APS International
                 Conference} on {Physics Computing, Physics Computing}
                 '94",
  title =        "Nonlinear convergence acceleration for orthogonal
                 series",
  publisher =    "European Physical Society, Boite Postale 69, CH-1213
                 Petit-Lancy, Geneva, Switzerland",
  address =      "Lugano",
  pages =        "47--50",
  year =         "1994",
  ISBN =         "2-88270-011-3",
  ISBN-13 =      "978-2-88270-011-7",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/homeier-herbert-h-h.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.chemie.uni-regensburg.de/pub/preprint/preprint.html#TCNA942",
  keywords =     "convergence acceleration",
  tech =         "Technical Report TC-NA-94-2, Institut f{\"u}r
                 {Physikalische} und {Theoretische Chemie,
                 Universit{\"a}t Regensburg, D-93040 Regensburg}, 1994",
}


bibtype: article
filename: elefunt.bib
label: Hull:1994:ICE
author: T. E. Hull and Thomas F. Fairgrieve and Ping Tak Peter Tang
title: Implementing Complex Elementary Functions Using Exception Handling
journal: j-TOMS
volume: 20
number: 2
pages: 215--244
month: jun
monthnumber: 6
year: 1994
CODEN: ACMSCU
DOI: https://doi.org/10.1145/178365.178404
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Mar 21 15:10:29 1995
bibtimestamp: 1995.03.21 15:10:29 ???
URL: http://www.acm.org/pubs/citations/journals/toms/1994-20-2/p215-hull/
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms; complex elementary functions; design; implementation
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: T. E. Hull and Thomas F. Fairgrieve and Ping Tak Peter Tang
rawtitle: Implementing Complex Elementary Functions Using Exception Handling
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/toms.bib

note:
See correction cite Anonymous:1994:C, and improved analysis, tightened bounds, and exhibition of worst cases for complex square roots cite Jeannerod:2017:REC.

abstract:
Algorithms are developed for reliable and accurate evaluations of the complex elementary functions required in Fortran 77 and Fortran 90, namely cabs, csqrt, cexp, clog, csin, and ccos. The algorithms are presented in a pseudocode that has a convenient exception-handling facility. A tight error bound is derived for each algorithm. Corresponding Fortran programs for an IEEE environment have also been developed to illustrate the practicality of the algorithms, and these programs have been tested very carefully to help confirm the correctness of the algorithms and their error bounds. The results are of these tests are included in the paper, but the Fortran programs are not; the programs are available from Fairgrieve, (tff@cs.toronto.edu).

subject:
G.1.0 [Numerical Analysis]: General--error analysis; numerical algorithms; G.1.2 [Numerical Analysis]: Approximation--elementary function approximation; G.4 [Mathematics of Computing]: Mathematical Software--algorithm analysis; reliability and robustness; verification

rawabstract:
Algorithms are developed for reliable and accurate evaluations of the complex elementary functions required in Fortran 77 and Fortran 90, namely cabs, csqrt, cexp, clog, csin, and ccos. The algorithms are presented in a pseudocode that has a convenient exception-handling facility. A tight error bound is derived for each algorithm. Corresponding Fortran programs for an IEEE environment have also been developed to illustrate the practicality of the algorithms, and these programs have been tested very carefully to help confirm the correctness of the algorithms and their error bounds. The results are of these tests are included in the paper, but the Fortran programs are not; the programs are available from Fairgrieve, (tff@cs.toronto.edu).

rawnote:
See correction \cite{Anonymous:1994:C}, and improved analysis, tightened bounds, and exhibition of worst cases for complex square roots \cite{Jeannerod:2017:REC}.

entry:
@Article{Hull:1994:ICE,
  author =       "T. E. Hull and Thomas F. Fairgrieve and Ping Tak Peter
                 Tang",
  title =        "Implementing Complex Elementary Functions Using
                 Exception Handling",
  journal =      j-TOMS,
  volume =       "20",
  number =       "2",
  pages =        "215--244",
  month =        jun,
  year =         "1994",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/178365.178404",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 21 15:10:29 1995",
  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/toms.bib",
  note =         "See correction \cite{Anonymous:1994:C}, and improved
                 analysis, tightened bounds, and exhibition of worst
                 cases for complex square roots
                 \cite{Jeannerod:2017:REC}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1994-20-2/p215-hull/",
  abstract =     "Algorithms are developed for reliable and accurate
                 evaluations of the complex elementary functions
                 required in Fortran 77 and Fortran 90, namely cabs,
                 csqrt, cexp, clog, csin, and ccos. The algorithms are
                 presented in a pseudocode that has a convenient
                 exception-handling facility. A tight error bound is
                 derived for each algorithm. Corresponding Fortran
                 programs for an IEEE environment have also been
                 developed to illustrate the practicality of the
                 algorithms, and these programs have been tested very
                 carefully to help confirm the correctness of the
                 algorithms and their error bounds. The results are of
                 these tests are included in the paper, but the Fortran
                 programs are not; the programs are available from
                 Fairgrieve, (tff@cs.toronto.edu).",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; complex elementary functions; design;
                 implementation",
  subject =      "G.1.0 [Numerical Analysis]: General--error analysis;
                 numerical algorithms; G.1.2 [Numerical Analysis]:
                 Approximation--elementary function approximation; G.4
                 [Mathematics of Computing]: Mathematical
                 Software--algorithm analysis; reliability and
                 robustness; verification",
}


bibtype: article
filename: elefunt.bib
label: Iserles:1994:CAD
author: A. Iserles
title: Convergence acceleration as a dynamical system
journal: j-APPL-NUM-MATH
volume: 15
number: 2
pages: 101--121
day: 13
month: sep
monthnumber: 9
year: 1994
CODEN: ANMAEL
ISSN: 0168-9274 (print), 1873-5460 (electronic) OR 01689274 (print), 18735460 (electronic)
ISSNL: 0168-9274 OR 01689274
MRclass: 58F23 (30D05 58F08 65D99 65H99)
MRnumber: 95i:58155
MRreviewer: Peter M. Makienko
bibdate: Wed Jul 28 14:35:48 MDT 1999
bibtimestamp: 1999.07.28 14:35:48 MDT
note: Innovative methods in numerical analysis (Bressanone, 1992).
fjournal: Applied Numerical Mathematics: Transactions of IMACS
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01689274/
rawauthor: A. Iserles
rawnote: Innovative methods in numerical analysis (Bressanone, 1992).
rawtitle: Convergence acceleration as a dynamical system
bibsource:
http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_free/browse/browse.cgi?year=1994&volume=15&issue=2; https://www.math.utah.edu/pub/tex/bib/applnummath.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

URL:
http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_sub/browse/browse.cgi?year=1994&volume=15&issue=2&aid=496

entry:
@Article{Iserles:1994:CAD,
  author =       "A. Iserles",
  title =        "Convergence acceleration as a dynamical system",
  journal =      j-APPL-NUM-MATH,
  volume =       "15",
  number =       "2",
  pages =        "101--121",
  day =          "13",
  month =        sep,
  year =         "1994",
  CODEN =        "ANMAEL",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  MRclass =      "58F23 (30D05 58F08 65D99 65H99)",
  MRnumber =     "95i:58155",
  MRreviewer =   "Peter M. Makienko",
  bibdate =      "Wed Jul 28 14:35:48 MDT 1999",
  bibsource =    "http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_free/browse/browse.cgi?year=1994&volume=15&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Innovative methods in numerical analysis (Bressanone,
                 1992).",
  URL =          "http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_sub/browse/browse.cgi?year=1994&volume=15&issue=2&aid=496",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274/",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Jablonski:1994:NES
author: Aleksander Jablonski
title: Numerical Evaluation of Spherical Bessel Functions of the First Kind
journal: j-J-COMPUT-PHYS
volume: 111
number: 2
pages: 256--259
month: apr
monthnumber: 4
year: 1994
CODEN: JCTPAH
DOI: https://doi.org/10.1006/jcph.1994.1060
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Mon Jan 2 07:54:54 MST 2012
bibtimestamp: 2012.01.02 07:54:54 MST
URL: http://www.sciencedirect.com/science/article/pii/S0021999184710606
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: Aleksander Jablonski
rawtitle: Numerical Evaluation of Spherical {Bessel} Functions of the First Kind
abstract:
Calculations of cross sections for elastic scattering of electrons require frequent evaluations of the spherical Bessel functions, $ j_l(x) $ and $ n_l(x) $, in a wide range of the argument $x$ and the order $l$. It turns out that the usual algorithms providing the values of the spherical Bessel function of the first kind, $ j_l(x) $, have a rather limited range of stability. It is shown that there is no algorithm implementing a single method which can be used in calculations associated with the theory of elastic scattering of electrons. An attempt is made to select different areas of stability from different algorithms in order to create a relatively fast and universal algorithm.

rawabstract:
Calculations of cross sections for elastic scattering of electrons require frequent evaluations of the spherical Bessel functions, $ j_l(x) $ and $ n_l(x) $, in a wide range of the argument $x$ and the order $l$. It turns out that the usual algorithms providing the values of the spherical Bessel function of the first kind, $ j_l(x) $, have a rather limited range of stability. It is shown that there is no algorithm implementing a single method which can be used in calculations associated with the theory of elastic scattering of electrons. An attempt is made to select different areas of stability from different algorithms in order to create a relatively fast and universal algorithm.

entry:
@Article{Jablonski:1994:NES,
  author =       "Aleksander Jablonski",
  title =        "Numerical Evaluation of Spherical {Bessel} Functions
                 of the First Kind",
  journal =      j-J-COMPUT-PHYS,
  volume =       "111",
  number =       "2",
  pages =        "256--259",
  month =        apr,
  year =         "1994",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1006/jcph.1994.1060",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Mon Jan 2 07:54:54 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0021999184710606",
  abstract =     "Calculations of cross sections for elastic scattering
                 of electrons require frequent evaluations of the
                 spherical Bessel functions, $ j_l(x) $ and $ n_l(x) $,
                 in a wide range of the argument $x$ and the order $l$.
                 It turns out that the usual algorithms providing the
                 values of the spherical Bessel function of the first
                 kind, $ j_l(x) $, have a rather limited range of
                 stability. It is shown that there is no algorithm
                 implementing a single method which can be used in
                 calculations associated with the theory of elastic
                 scattering of electrons. An attempt is made to select
                 different areas of stability from different algorithms
                 in order to create a relatively fast and universal
                 algorithm.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}


bibtype: inproceedings
filename: elefunt.bib
label: Jain:1994:SRR
author: V. K. Jain and Lei Lin
title: Square-root, reciprocal, sine / cosine, arctangent cell for signal and image processing
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: II/521--II/524
year: 1994
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: V. K. Jain and Lei Lin
rawtitle: Square-root, reciprocal, sine\slash cosine, arctangent cell for signal and image processing
booktitle:
IEEE International Conference on Acoustics, Speech, and Signal Processing: ICASSP-94, 19--22 April 1994

rawbooktitle:
{IEEE} International Conference on Acoustics, Speech, and Signal Processing: {ICASSP-94, 19--22} April 1994

entry:
@InProceedings{Jain:1994:SRR,
  author =       "V. K. Jain and Lei Lin",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing: {ICASSP-94, 19--22} April 1994",
  title =        "Square-root, reciprocal, sine\slash cosine, arctangent
                 cell for signal and image processing",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "II/521--II/524",
  year =         "1994",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "This paper discusses an efficient interpolation method
                 for nonlinear function generation. Based on this, a 24
                 bit VLSI cell, capable of computing the (1) square
                 root, (2) reciprocal, (3) sine/cosine, and (4)
                 arctangent functions, is presented for \ldots{}",
}


bibtype: misc
filename: elefunt.bib
label: Karp:1994:FPA
author: Alan H. Karp and Peter Markstein and Dennis Brzezinski
pages: II/521--II/524
day: 23
month: aug
monthnumber: 8
year: 1994
bibdate: Thu Oct 17 10:20:52 2019
bibtimestamp: 2019.10.17 10:20:52 ???
URL: http://patft.uspto.gov/netahtml/PTO/search-bool.html; https://patents.google.com/patent/US5341321A
acknowledgement: ack-nhfb
howpublished: US Patent 5,341,321
rawauthor: Alan H. Karp and Peter Markstein and Dennis Brzezinski
title:
Floating point arithmetic unit using modified Newton--Raphson technique for division and square root

note:
Patent filed 5 May 1993, granted to Hewlett-Packard Company on 23 August 1994. Patent expired 5-May-2013. See criticism in cite Zimmermann:2005:XXX.

abstract:
A floating point processing system which uses a multiplier unit and an adder unit to perform floating point division and square root operations using both a conventional and a modified form of the Newton--Raphson method. The modified form of the Newton--Raphson method is used in place of the final iteration of the conventional Newton--Raphson so as to compute high precision approximated results with a substantial improvement in speed. The invention computes approximated results faster and simplifies hardware requirements because no multiplications of numbers of the precision of the result are required.

rawabstract:
A floating point processing system which uses a multiplier unit and an adder unit to perform floating point division and square root operations using both a conventional and a modified form of the Newton--Raphson method. The modified form of the Newton--Raphson method is used in place of the final iteration of the conventional Newton--Raphson so as to compute high precision approximated results with a substantial improvement in speed. The invention computes approximated results faster and simplifies hardware requirements because no multiplications of numbers of the precision of the result are required.

rawnote:
Patent filed 5 May 1993, granted to Hewlett-Packard Company on 23 August 1994. Patent expired 5-May-2013. See criticism in \cite{Zimmermann:2005:XXX}.

rawtitle:
Floating point arithmetic unit using modified {Newton--Raphson} technique for division and square root

entry:
@Misc{Karp:1994:FPA,
  author =       "Alan H. Karp and Peter Markstein and Dennis
                 Brzezinski",
  title =        "Floating point arithmetic unit using modified
                 {Newton--Raphson} technique for division and square
                 root",
  howpublished = "US Patent 5,341,321",
  day =          "23",
  month =        aug,
  year =         "1994",
  bibdate =      "Thu Oct 17 10:20:52 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Patent filed 5 May 1993, granted to Hewlett-Packard
                 Company on 23 August 1994. Patent expired 5-May-2013.
                 See criticism in \cite{Zimmermann:2005:XXX}.",
  URL =          "http://patft.uspto.gov/netahtml/PTO/search-bool.html;
                 https://patents.google.com/patent/US5341321A",
  abstract =     "A floating point processing system which uses a
                 multiplier unit and an adder unit to perform floating
                 point division and square root operations using both a
                 conventional and a modified form of the Newton--Raphson
                 method. The modified form of the Newton--Raphson method
                 is used in place of the final iteration of the
                 conventional Newton--Raphson so as to compute high
                 precision approximated results with a substantial
                 improvement in speed. The invention computes
                 approximated results faster and simplifies hardware
                 requirements because no multiplications of numbers of
                 the precision of the result are required.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Kearfott:1994:AIP
author: R. B. Kearfott and M. Dawande and K. Du and C. Hu
title: Algorithm 737: INTLIB: a Portable Fortran-77 Elementary Function Library
journal: j-TOMS
volume: 20
number: 4
pages: 447--459
month: dec
monthnumber: 12
year: 1994
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sat May 20 15:54:18 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1995.05.20 15:54:18 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: BLAS; Fortran 77; Fortran 90; interval arithmetic; operator overloading; standard functions
acknowledgement: ack-rfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: R. B. Kearfott and M. Dawande and K. Du and C. Hu
rawtitle: Algorithm 737: {INTLIB}: a Portable {Fortran}-77 Elementary Function Library
subject:
D.2.2 [Software Engineering]: Tools and Techniques -- software libraries; D.2.7 [Software Engineering]: Distribution and Maintenance -- documentation; portability; G.1.0 [Numerical Analysis]: General -- computer arithmetic; G.1.2 [Numerical Analysis]: Approximation -- elementary function approximation

entry:
@Article{Kearfott:1994:AIP,
  author =       "R. B. Kearfott and M. Dawande and K. Du and C. Hu",
  title =        "Algorithm 737: {INTLIB}: a Portable {Fortran}-77
                 Elementary Function Library",
  journal =      j-TOMS,
  volume =       "20",
  number =       "4",
  pages =        "447--459",
  month =        dec,
  year =         "1994",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat May 20 15:54:18 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  accepted =     "December 1993",
  acknowledgement = ack-rfb # "\slash " # ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "BLAS; Fortran 77; Fortran 90; interval arithmetic;
                 operator overloading; standard functions",
  subject =      "D.2.2 [Software Engineering]: Tools and Techniques --
                 software libraries; D.2.7 [Software Engineering]:
                 Distribution and Maintenance -- documentation;
                 portability; G.1.0 [Numerical Analysis]: General --
                 computer arithmetic; G.1.2 [Numerical Analysis]:
                 Approximation -- elementary function approximation",
}


bibtype: article
filename: elefunt.bib
label: Khajah:1994:UHP
author: H. G. Khajah and E. L. Ortiz
title: Ultra-high precision computations
journal: j-COMPUT-MATH-APPL
volume: 27
number: 7
pages: 41--57
month: apr
monthnumber: 4
year: 1994
CODEN: CMAPDK
DOI: https://doi.org/10.1016/0898-1221(94)90148-1
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Mon Jun 13 22:03:39 2011
bibtimestamp: 2011.06.13 22:03:39 ???
URL: http://www.sciencedirect.com/science/article/pii/0898122194901481
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
affiliation: Dept. of Math., Imperial Coll. of Sci., Technol. and Med., London, UK
journalURL: http://www.sciencedirect.com/science/journal/08981221
thesaurus: FORTRAN; Mathematics computing
rawauthor: H. G. Khajah and E. L. Ortiz
rawtitle: Ultra-high precision computations
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

abstract:
We describe a machine independent Fortran subroutine which performs the four basic arithmetic operations with a degree of accuracy prescribed by the user. Tables of Chebyshev expansions of orders 48 and 50 for some basic mathematical functions are obtained as a result of applying this subroutine in conjunction with the recursive formulation of the Tau Method. A recently devised technique for the sharp determination of upper and lower error bounds for Tau Method approximations enables us to find the degree $n$ required to achieve a prescribed accuracy $ epsilon $ over a given interval $ [a, b] $. A number of practical illustrations are given.

keywords:
$cos (pi x)$; $erf (x) / x$; $exp (-x^2)$; $exp (x)$; $sin (pi x)$; $x exp (x^2) erfc(x)$; $z exp (z) Ei (-z)$; Arithmetic operations; Chebyshev expansions; Lower error bounds; Machine independent Fortran subroutine; Mathematical functions; Tau method; Upper error bounds

rawabstract:
We describe a machine independent Fortran subroutine which performs the four basic arithmetic operations with a degree of accuracy prescribed by the user. Tables of Chebyshev expansions of orders 48 and 50 for some basic mathematical functions are obtained as a result of applying this subroutine in conjunction with the recursive formulation of the Tau Method. A recently devised technique for the sharp determination of upper and lower error bounds for Tau Method approximations enables us to find the degree $n$ required to achieve a prescribed accuracy $ \epsilon $ over a given interval $ [a, b] $. A number of practical illustrations are given.

entry:
@Article{Khajah:1994:UHP,
  author =       "H. G. Khajah and E. L. Ortiz",
  title =        "Ultra-high precision computations",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "27",
  number =       "7",
  pages =        "41--57",
  month =        apr,
  year =         "1994",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(94)90148-1",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Mon Jun 13 22:03:39 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122194901481",
  abstract =     "We describe a machine independent Fortran subroutine
                 which performs the four basic arithmetic operations
                 with a degree of accuracy prescribed by the user.
                 Tables of Chebyshev expansions of orders 48 and 50 for
                 some basic mathematical functions are obtained as a
                 result of applying this subroutine in conjunction with
                 the recursive formulation of the Tau Method. A recently
                 devised technique for the sharp determination of upper
                 and lower error bounds for Tau Method approximations
                 enables us to find the degree $n$ required to achieve a
                 prescribed accuracy $ \epsilon $ over a given interval
                 $ [a, b] $. A number of practical illustrations are
                 given.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math., Imperial Coll. of Sci., Technol. and
                 Med., London, UK",
  classification = "C6140D (High level languages); C7310 (Mathematics)",
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  keywords =     "$\cos(\pi x)$; $\erf(x) / x$; $\exp(-x^2)$; $\exp(x)$;
                 $\sin(\pi x)$; $x \exp(x^2) erfc(x)$; $z \exp(z)
                 \Ei(-z)$; Arithmetic operations; Chebyshev expansions;
                 Lower error bounds; Machine independent Fortran
                 subroutine; Mathematical functions; Tau method; Upper
                 error bounds",
  pubcountry =   "UK",
  thesaurus =    "FORTRAN; Mathematics computing",
}


bibtype: article
filename: elefunt.bib
label: Lewanowicz:1994:SAS
author: Stanislaw Lewanowicz
title: A simple approach to the summation of certain slowly convergent series
journal: j-MATH-COMPUT
volume: 63
number: 208
pages: 741--745
month: oct
monthnumber: 10
year: 1994
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65B10
MRnumber: 95a:65010
MRreviewer: Thomas A. Atchison
bibdate: Sat Jan 11 13:29:06 MST 1997
bibtimestamp: 1997.01.11 13:29:06 MST
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Stanis{\l}aw Lewanowicz
rawtitle: A simple approach to the summation of certain slowly convergent series
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib

entry:
@Article{Lewanowicz:1994:SAS,
  author =       "Stanis{\l}aw Lewanowicz",
  title =        "A simple approach to the summation of certain slowly
                 convergent series",
  journal =      j-MATH-COMPUT,
  volume =       "63",
  number =       "208",
  pages =        "741--745",
  month =        oct,
  year =         "1994",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65B10",
  MRnumber =     "95a:65010",
  MRreviewer =   "Thomas A. Atchison",
  bibdate =      "Sat Jan 11 13:29:06 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Litvinov:1994:ACR
author: Grigori L. Litvinov
title: Approximate construction of rational approximations and the effect of error autocorrection
journal: j-RUSS-J-MATH-PHYS
volume: 1
number: 3
pages: 313--352
year: 1994
CODEN: RJMPEL
ISSN: 1061-9208 (print), 1555-6638 (electronic) OR 10619208 (print), 15556638 (electronic)
ISSNL: 1061-9208 OR 10619208
bibdate: Tue Mar 24 20:54:11 2009
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2009.03.24 20:54:11 ???
URL: http://arxiv.org/abs/math/0101042
fjournal: Russian Journal of Mathematical Physics
acknowledgement: ack-nhfb
rawauthor: Grigori L. Litvinov
rawtitle: Approximate construction of rational approximations and the effect of error autocorrection
abstract:
Several construction methods for rational approximations to functions of one real variable are described in the present paper; the computational results that characterize the comparative accuracy of these methods are presented; an effect of error autocorrection is considered. This effect occurs in efficient methods of rational approximation (e.g., Pade approximations, linear and nonlinear Pade Chebyshev approximations) where very significant errors in the coefficients do not affect the accuracy of the approximation. The matter of import is that the errors in the numerator and the denominator of a fractional rational approximant compensate each other. This effect is related to the fact that the errors in the coefficients of a rational approximant are not distributed in an arbitrary way but form the coefficients of a new approximant to the approximated function. Understanding of the error autocorrection mechanism allows to decrease this error by varying the approximation procedure depending on the form of the approximant. Some applications are described in the paper. In particular, a method of implementation of basic calculations on decimal computers that uses the technique of rational approximations is described in the Appendix.par To a considerable extent the paper is a survey and the exposition is as elementary as possible.

rawabstract:
Several construction methods for rational approximations to functions of one real variable are described in the present paper; the computational results that characterize the comparative accuracy of these methods are presented; an effect of error autocorrection is considered. This effect occurs in efficient methods of rational approximation (e.g., Pad{\'e} approximations, linear and nonlinear Pad{\'e} Chebyshev approximations) where very significant errors in the coefficients do not affect the accuracy of the approximation. The matter of import is that the errors in the numerator and the denominator of a fractional rational approximant compensate each other. This effect is related to the fact that the errors in the coefficients of a rational approximant are not distributed in an arbitrary way but form the coefficients of a new approximant to the approximated function. Understanding of the error autocorrection mechanism allows to decrease this error by varying the approximation procedure depending on the form of the approximant. Some applications are described in the paper. In particular, a method of implementation of basic calculations on decimal computers that uses the technique of rational approximations is described in the Appendix.\par To a considerable extent the paper is a survey and the exposition is as elementary as possible.

entry:
@Article{Litvinov:1994:ACR,
  author =       "Grigori L. Litvinov",
  title =        "Approximate construction of rational approximations
                 and the effect of error autocorrection",
  journal =      j-RUSS-J-MATH-PHYS,
  volume =       "1",
  number =       "3",
  pages =        "313--352",
  month =        "????",
  year =         "1994",
  CODEN =        "RJMPEL",
  ISSN =         "1061-9208 (print), 1555-6638 (electronic)",
  ISSN-L =       "1061-9208",
  bibdate =      "Tue Mar 24 20:54:11 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://arxiv.org/abs/math/0101042",
  abstract =     "Several construction methods for rational
                 approximations to functions of one real variable are
                 described in the present paper; the computational
                 results that characterize the comparative accuracy of
                 these methods are presented; an effect of error
                 autocorrection is considered. This effect occurs in
                 efficient methods of rational approximation (e.g.,
                 Pad{\'e} approximations, linear and nonlinear Pad{\'e}
                 Chebyshev approximations) where very significant errors
                 in the coefficients do not affect the accuracy of the
                 approximation. The matter of import is that the errors
                 in the numerator and the denominator of a fractional
                 rational approximant compensate each other. This effect
                 is related to the fact that the errors in the
                 coefficients of a rational approximant are not
                 distributed in an arbitrary way but form the
                 coefficients of a new approximant to the approximated
                 function. Understanding of the error autocorrection
                 mechanism allows to decrease this error by varying the
                 approximation procedure depending on the form of the
                 approximant. Some applications are described in the
                 paper. In particular, a method of implementation of
                 basic calculations on decimal computers that uses the
                 technique of rational approximations is described in
                 the Appendix.\par

                 To a considerable extent the paper is a survey and the
                 exposition is as elementary as possible.",
  acknowledgement = ack-nhfb,
  fjournal =     "Russian Journal of Mathematical Physics",
}


bibtype: techreport
filename: elefunt.bib
label: Lozier:1994:NESa
author: D. W. Lozier and F. W. J. Olver
title: Numerical evaluation of special functions
type: Report
number: NISTIR 5383
institution: Computing and Applied Mathematics Laboratory, U. S. Department of Commerce
address: Washington, DC, USA
pages: 47
month: mar
monthnumber: 3
year: 1994
MRclass: 65D20 (33-00)
bibdate: Thu Nov 16 07:52:34 2023
bibtimestamp: 2023.11.16 07:52:34 ???
URL: https://math.nist.gov/~DLozier/publications/nistir5383.pdf
acknowledgement: ack-nhfb
authordates: Frank William John Olver (15 December 1924--23 April 2013)
rawauthor: D. W. Lozier and F. W. J. Olver
rawtitle: Numerical evaluation of special functions
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

abstract:
Higher transcendental functions continue to play varied and important roles in investigations by engineers, mathematicians, scientists and statisticians. The purpose of this paper is to assist in locating useful approximations and software for the numerical generation of these functions, and to offer some suggestions for future developments in this field.

TOC:
1. Introduction / 3 2. Mathematical Developments / 5 3. Packages, Libraries and Systems / 6 3.1. Software Packages / 6 3.2. Intermediate Libraries / 8 3.3. Comprehensive Libraries / 8 3.4. Interactive Systems / 12 4. Functions of One Variable / 15 4.1. Airy Functions / 15 4.2. Error Functions, Dawson's Integral, Fresnel Integrals, Goodwin--Staton Integral / 15 4.3. Exponential Integrals, Logarithmic Integral, Sine and Cosine Integrals / 16 4.4. Gamma, Psi, and Polygamma Functions / 16 4.5. Landau Density and Distribution Functions / 16 4.6. Polylogarithms, Clausen Integral / 16 4.7. Zeta Function / 17 4.8. Additional Functions of One Variable / 17 5. Functions of Two or More Variables / 17 5.1. Bessel Functions / 17 5.2. Coulomb Wave Functions / 18 5.3. Elliptic Integrals and Functions / 18 5.4. Fermi--Dirac, Bose--Einstein, and Debye Integrals / 19 5.5. Hypergeometric and Concuent Hypergeometric Functions / 19 5.6. Incomplete Bessel Functions, Incomplete Beta Function / 19 5.7. Incomplete Gamma Functions, Generalized Exponential Integrals / 20 5.8. Legendre Functions and Associated Legendre Functions / 20 5.9. Mathieu, Lame, and Spheroidal Wave Functions / 20 5.10. Orthogonal Polynomials / 21 5.11. Polylogarithms (Generalized) / 21 5.12. Struve and Anger--Weber Functions / 21 5.13. Weber Parabolic Cylinder Functions / 21 5.14. Zeta Function (Generalized) / 21 5.15. Additional Functions of Two or More Variables / 21 6. Testing and Library Construction / 22 7. Future Trends / 22 Acknowledgments / 23 A Note on the Reference Acronyms / 23 References / 23--47

rawabstract:
Higher transcendental functions continue to play varied and important roles in investigations by engineers, mathematicians, scientists and statisticians. The purpose of this paper is to assist in locating useful approximations and software for the numerical generation of these functions, and to offer some suggestions for future developments in this field.

rawTOC:
1. Introduction / 3 \\ 2. Mathematical Developments / 5 \\ 3. Packages, Libraries and Systems / 6 \\ 3.1. Software Packages / 6 \\ 3.2. Intermediate Libraries / 8 \\ 3.3. Comprehensive Libraries / 8 \\ 3.4. Interactive Systems / 12 \\ 4. Functions of One Variable / 15 \\ 4.1. Airy Functions / 15 \\ 4.2. Error Functions, Dawson's Integral, Fresnel Integrals, Goodwin--Staton Integral / 15 \\ 4.3. Exponential Integrals, Logarithmic Integral, Sine and Cosine Integrals / 16 \\ 4.4. Gamma, Psi, and Polygamma Functions / 16 \\ 4.5. Landau Density and Distribution Functions / 16 \\ 4.6. Polylogarithms, Clausen Integral / 16 \\ 4.7. Zeta Function / 17 \\ 4.8. Additional Functions of One Variable / 17 \\ 5. Functions of Two or More Variables / 17 \\ 5.1. Bessel Functions / 17 \\ 5.2. Coulomb Wave Functions / 18 \\ 5.3. Elliptic Integrals and Functions / 18 \\ 5.4. Fermi--Dirac, Bose--Einstein, and Debye Integrals / 19 \\ 5.5. Hypergeometric and Concuent Hypergeometric Functions / 19 \\ 5.6. Incomplete Bessel Functions, Incomplete Beta Function / 19 \\ 5.7. Incomplete Gamma Functions, Generalized Exponential Integrals / 20 \\ 5.8. Legendre Functions and Associated Legendre Functions / 20 \\ 5.9. Mathieu, Lam{\'e}, and Spheroidal Wave Functions / 20 \\ 5.10. Orthogonal Polynomials / 21 \\ 5.11. Polylogarithms (Generalized) / 21 \\ 5.12. Struve and Anger--Weber Functions / 21 \\ 5.13. Weber Parabolic Cylinder Functions / 21 \\ 5.14. Zeta Function (Generalized) / 21 \\ 5.15. Additional Functions of Two or More Variables / 21 \\ 6. Testing and Library Construction / 22 \\ 7. Future Trends / 22 \\ Acknowledgments / 23 \\ A Note on the Reference Acronyms / 23 \\ References / 23--47

entry:
@TechReport{Lozier:1994:NESa,
  author =       "D. W. Lozier and F. W. J. Olver",
  title =        "Numerical evaluation of special functions",
  type =         "Report",
  number =       "NISTIR 5383",
  institution =  "Computing and Applied Mathematics Laboratory, U. S.
                 Department of Commerce",
  address =      "Washington, DC, USA",
  pages =        "47",
  month =        mar,
  year =         "1994",
  MRclass =      "65D20 (33-00)",
  bibdate =      "Thu Nov 16 07:52:34 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://math.nist.gov/~DLozier/publications/nistir5383.pdf",
  abstract =     "Higher transcendental functions continue to play
                 varied and important roles in investigations by
                 engineers, mathematicians, scientists and
                 statisticians. The purpose of this paper is to assist
                 in locating useful approximations and software for the
                 numerical generation of these functions, and to offer
                 some suggestions for future developments in this
                 field.",
  acknowledgement = ack-nhfb,
  author-dates = "Frank William John Olver (15 December 1924--23 April
                 2013)",
  tableofcontents = "1. Introduction / 3 \\
                 2. Mathematical Developments / 5 \\
                 3. Packages, Libraries and Systems / 6 \\
                 3.1. Software Packages / 6 \\
                 3.2. Intermediate Libraries / 8 \\
                 3.3. Comprehensive Libraries / 8 \\
                 3.4. Interactive Systems / 12 \\
                 4. Functions of One Variable / 15 \\
                 4.1. Airy Functions / 15 \\
                 4.2. Error Functions, Dawson's Integral, Fresnel
                 Integrals, Goodwin--Staton Integral / 15 \\
                 4.3. Exponential Integrals, Logarithmic Integral, Sine
                 and Cosine Integrals / 16 \\
                 4.4. Gamma, Psi, and Polygamma Functions / 16 \\
                 4.5. Landau Density and Distribution Functions / 16 \\
                 4.6. Polylogarithms, Clausen Integral / 16 \\
                 4.7. Zeta Function / 17 \\
                 4.8. Additional Functions of One Variable / 17 \\
                 5. Functions of Two or More Variables / 17 \\
                 5.1. Bessel Functions / 17 \\
                 5.2. Coulomb Wave Functions / 18 \\
                 5.3. Elliptic Integrals and Functions / 18 \\
                 5.4. Fermi--Dirac, Bose--Einstein, and Debye Integrals
                 / 19 \\
                 5.5. Hypergeometric and Concuent Hypergeometric
                 Functions / 19 \\
                 5.6. Incomplete Bessel Functions, Incomplete Beta
                 Function / 19 \\
                 5.7. Incomplete Gamma Functions, Generalized
                 Exponential Integrals / 20 \\
                 5.8. Legendre Functions and Associated Legendre
                 Functions / 20 \\
                 5.9. Mathieu, Lam{\'e}, and Spheroidal Wave Functions /
                 20 \\
                 5.10. Orthogonal Polynomials / 21 \\
                 5.11. Polylogarithms (Generalized) / 21 \\
                 5.12. Struve and Anger--Weber Functions / 21 \\
                 5.13. Weber Parabolic Cylinder Functions / 21 \\
                 5.14. Zeta Function (Generalized) / 21 \\
                 5.15. Additional Functions of Two or More Variables /
                 21 \\
                 6. Testing and Library Construction / 22 \\
                 7. Future Trends / 22 \\
                 Acknowledgments / 23 \\
                 A Note on the Reference Acronyms / 23 \\
                 References / 23--47",
}


bibtype: inproceedings
filename: elefunt.bib
label: Lozier:1994:NESb
author: D. W. Lozier and F. W. J. Olver
title: Numerical evaluation of special functions
crossref: Gautschi:1994:MCH
volume: 48
pages: 79--125
year: 1994
DOI: https://doi.org/10.1090/psapm/048/1314844
MRclass: 65D20 (30-04 33-04 41-04)
MRnumber: 95m:65036 (1314844)
MRreviewer: John P. Coleman
bibdate: Fri Jul 9 05:44:10 2004
bibtimestamp: 2004.07.09 05:44:10 ???
series: Proc. Sympos. Appl. Math.
URL: http://math.nist.gov/mcsd/Reports/2001/nesf/
acknowledgement: ack-nhfb
authordates: Frank William John Olver (15 December 1924--23 April 2013)
rawauthor: D. W. Lozier and F. W. J. Olver
rawtitle: Numerical evaluation of special functions
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib

abstract:
Higher transcendental functions continue to play varied and important roles in investigations by engineers, mathematicians, scientists, and statisticians. The purpose of this paper is to assist in locating useful approximations and software for the numerical generation of these functions, and to offer some suggestions for future developments in the field.

remark:
The references list contains about 400 entries which should ultimately be incorporated in this BibTeX bibliography collection.

rawabstract:
Higher transcendental functions continue to play varied and important roles in investigations by engineers, mathematicians, scientists, and statisticians. The purpose of this paper is to assist in locating useful approximations and software for the numerical generation of these functions, and to offer some suggestions for future developments in the field.

entry:
@InProceedings{Lozier:1994:NESb,
  author =       "D. W. Lozier and F. W. J. Olver",
  title =        "Numerical evaluation of special functions",
  crossref =     "Gautschi:1994:MCH",
  volume =       "48",
  pages =        "79--125",
  year =         "1994",
  DOI =          "https://doi.org/10.1090/psapm/048/1314844",
  MRclass =      "65D20 (30-04 33-04 41-04)",
  MRnumber =     "95m:65036 (1314844)",
  MRreviewer =   "John P. Coleman",
  bibdate =      "Fri Jul 9 05:44:10 2004",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
  series =       "Proc. Sympos. Appl. Math.",
  URL =          "http://math.nist.gov/mcsd/Reports/2001/nesf/",
  abstract =     "Higher transcendental functions continue to play
                 varied and important roles in investigations by
                 engineers, mathematicians, scientists, and
                 statisticians. The purpose of this paper is to assist
                 in locating useful approximations and software for the
                 numerical generation of these functions, and to offer
                 some suggestions for future developments in the
                 field.",
  acknowledgement = ack-nhfb,
  author-dates = "Frank William John Olver (15 December 1924--23 April
                 2013)",
  remark =       "The references list contains about 400 entries which
                 should ultimately be incorporated in this BibTeX
                 bibliography collection.",
}


bibtype: techreport
filename: elefunt.bib
label: Lozier:1994:SNS
author: Daniel W. Lozier
title: Software Needs in Special Functions
type: Technical Report
number: NISTIR 5490
institution: pub-NIST
address: pub-NIST:adr
pages: 16
month: aug
monthnumber: 8
year: 1994
bibdate: Fri Jul 09 05:47:26 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2004.07.09 05:47:26 ???
note: Published in cite Lozier:1996:SNS.
URL: http://math.nist.gov/acmd/Staff/DLozier/publications/nistir5490.ps
acknowledgement: ack-nhfb
rawauthor: Daniel W. Lozier
rawnote: Published in \cite{Lozier:1996:SNS}.
rawtitle: Software Needs in Special Functions
entry:
@TechReport{Lozier:1994:SNS,
  author =       "Daniel W. Lozier",
  title =        "Software Needs in Special Functions",
  type =         "Technical Report",
  number =       "NISTIR 5490",
  institution =  pub-NIST,
  address =      pub-NIST:adr,
  pages =        "16",
  month =        aug,
  year =         "1994",
  bibdate =      "Fri Jul 09 05:47:26 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Published in \cite{Lozier:1996:SNS}.",
  URL =          "http://math.nist.gov/acmd/Staff/DLozier/publications/nistir5490.ps",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: MacLeod:1994:CIA
author: Allan J. MacLeod
title: Computation of inhomogeneous Airy functions
journal: j-J-COMPUT-APPL-MATH
volume: 53
number: 1
pages: 109--116
day: 29
month: jul
monthnumber: 7
year: 1994
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:24:31 MST 2017
bibtimestamp: 2017.02.25 12:24:31 MST
URL: http://www.sciencedirect.com/science/article/pii/0377042794901961
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Allan J. MacLeod
rawtitle: Computation of inhomogeneous {Airy} functions
entry:
@Article{MacLeod:1994:CIA,
  author =       "Allan J. MacLeod",
  title =        "Computation of inhomogeneous {Airy} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "53",
  number =       "1",
  pages =        "109--116",
  day =          "29",
  month =        jul,
  year =         "1994",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:24:31 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042794901961",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: MacLeod:1994:TBT
author: Allan J. MacLeod
title: Table-based tests for Bessel function software
journal: j-ADV-COMPUT-MATH
volume: 2
number: 2
pages: 251--260
month: mar
monthnumber: 3
year: 1994
CODEN: ACMHEX
DOI: https://doi.org/10.1007/BF02521111
ISSN: 1019-7168 (print), 1572-9044 (electronic) OR 10197168 (print), 15729044 (electronic)
ISSNL: 1019-7168 OR 10197168
MRclass: 65-04 (33-04 33C10 65D20)
MRnumber: 1269384
bibdate: Sat Feb 3 18:21:41 MST 2018
bibtimestamp: 2018.02.03 18:21:41 MST
URL: http://link.springer.com/article/10.1007/BF02521111
fjournal: Advances in Computational Mathematics
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10444
rawauthor: Allan J. MacLeod
rawtitle: Table-based tests for {Bessel} function software
bibsource:
https://www.math.utah.edu/pub/tex/bib/advcomputmath.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{MacLeod:1994:TBT,
  author =       "Allan J. MacLeod",
  title =        "Table-based tests for {Bessel} function software",
  journal =      j-ADV-COMPUT-MATH,
  volume =       "2",
  number =       "2",
  pages =        "251--260",
  month =        mar,
  year =         "1994",
  CODEN =        "ACMHEX",
  DOI =          "https://doi.org/10.1007/BF02521111",
  ISSN =         "1019-7168 (print), 1572-9044 (electronic)",
  ISSN-L =       "1019-7168",
  MRclass =      "65-04 (33-04 33C10 65D20)",
  MRnumber =     "1269384",
  bibdate =      "Sat Feb 3 18:21:41 MST 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/advcomputmath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://link.springer.com/article/10.1007/BF02521111",
  acknowledgement = ack-nhfb,
  fjournal =     "Advances in Computational Mathematics",
  journal-URL =  "http://link.springer.com/journal/10444",
}


bibtype: inproceedings
filename: elefunt.bib
label: Magnus:1994:ASA
author: Alphonse P. Magnus
crossref: Cuyt:1994:NNM
pages: 173--185
year: 1994
bibdate: Mon Nov 24 21:30:41 2008
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2008.11.24 21:30:41 ???
ZMnumber: 809.41015
acknowledgement: ack-nhfb
rawauthor: Alphonse P. Magnus
title:
Asymptotics and super asymptotics of best rational approximation error norms for the exponential function (the `$ 1 / 9 $' problem) by the Caratheodory--Fejer method

rawtitle:
Asymptotics and super asymptotics of best rational approximation error norms for the exponential function (the `$ 1 / 9 $' problem) by the {Carath{\'e}odory--Fej{\'e}r} method

entry:
@InProceedings{Magnus:1994:ASA,
  author =       "Alphonse P. Magnus",
  title =        "Asymptotics and super asymptotics of best rational
                 approximation error norms for the exponential function
                 (the `$ 1 / 9 $' problem) by the
                 {Carath{\'e}odory--Fej{\'e}r} method",
  crossref =     "Cuyt:1994:NNM",
  pages =        "173--185",
  year =         "1994",
  bibdate =      "Mon Nov 24 21:30:41 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  ZMnumber =     "809.41015",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Marsaglia:1994:REI
author: George Marsaglia and Arif Zaman and John C. W. Marsaglia
title: Rapid evaluation of the inverse of the normal distribution function
journal: j-STAT-PROB-LETT
volume: 19
number: 4
pages: 259--266
day: 15
month: mar
monthnumber: 3
year: 1994
CODEN: SPLTDC
DOI: https://doi.org/10.1016/0167-7152(94)90174-0
ISSN: 0167-7152 (print), 1879-2103 (electronic) OR 01677152 (print), 18792103 (electronic)
ISSNL: 0167-7152 OR 01677152
MRclass: 65U05
MRnumber: 1 278 658
bibdate: Thu Dec 22 07:42:24 2011
bibtimestamp: 2011.12.22 07:42:24 ???
fjournal: Statistics & Probability Letters
ZMnumber: 0798.65132
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01677152
rawauthor: George Marsaglia and Arif Zaman and John C. W. Marsaglia
rawtitle: Rapid evaluation of the inverse of the normal distribution function
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; MathSciNet database

abstract:
This is an interesting article with direct application in generating normal random variable by computer programs. The suggested applications are related to Monte Carlo simulation based on massively parallel systems or supercomputers. The idea is to replace larger programs with complicated computations and with difficulties in accuracy controlling by simpler arithmetic programs that use tabled constants. These seem to be the normal evolution since memory becomes cheaper and cheaper.par The authors compute the inverse of the cPhi function $$ c P h i(x) = (2 / pi )^1 / 2 int ^infty _x exp ( - t^2 / 2) d t = u, $$ using a uniform random variable as input and the truncated Taylor series development of it. In order to increase the speed the coefficients of the truncated Taylor series $$ x(u_0 + h) = x(u_0) + x'(u_0) cdot h + 1 over 2 x''(u_0) cdot h^2 + 1 over 6 x'''(u_0) cdot h^3, $$ are predetermined for 1024 points. And here comes another bright idea: the 1024 points are chosen based on the representation of the uniform random variable in modern computers as floating point variable of the form: $ u = 2^-k ((1 / 2) + (j / 64)) + 2^-k cdot (m / 2^24) $ with $ 0 le k & l t; 32 $, $ 0 le j & l t; 32 $ and $ 0 le m & l t; 2^18 $ and considering 32 bit representation.par With this assumptions and the truncation to the third power of $h$ of the Taylor series, the authors show that the error does not exceed the limit of single precision accuracy. Furthermore the calculations are speeded up based on reducing multiplications. A number of FORTRAN programs are also presented in order to evaluate the complementary normal distribution function cPhi (several versions) with great accuracy, create the constant tables, and generate the normal distribution variable. These simple programs give the user the possibility to completely control the accuracy.

keywords:
cPhi function; FORTRAN programs; massive parallel systems; Monte Carlo simulation; normal distribution function; normal random variable; supercomputers; truncated Taylor series

ZMclass:
*65C99 Numerical simulation 65C05 Monte Carlo methods 60-04 Machine computation, programs (probability theory) 60E05 General theory of probability distributions 62E17 Approximations to statistical distributions (nonasymptotic)

rawabstract:
This is an interesting article with direct application in generating normal random variable by computer programs. The suggested applications are related to Monte Carlo simulation based on massively parallel systems or supercomputers. The idea is to replace larger programs with complicated computations and with difficulties in accuracy controlling by simpler arithmetic programs that use tabled constants. These seem to be the normal evolution since memory becomes cheaper and cheaper.\par The authors compute the inverse of the cPhi function $$ c P h i(x) = (2 / \pi)^{1 / 2} \int^\infty_x \exp ( - t^2 / 2) d t = u, $$ using a uniform random variable as input and the truncated Taylor series development of it. In order to increase the speed the coefficients of the truncated Taylor series $$ x(u_0 + h) = x(u_0) + x'(u_0) \cdot h + {1 \over 2} x''(u_0) \cdot h^2 + {1 \over 6} x'''(u_0) \cdot h^3, $$ are predetermined for 1024 points. And here comes another bright idea: the 1024 points are chosen based on the representation of the uniform random variable in modern computers as floating point variable of the form: $ u = 2^{-k} ((1 / 2) + (j / 64)) + 2^{-k} \cdot (m / 2^{24}) $ with $ 0 \le k & l t; 32 $, $ 0 \le j & l t; 32 $ and $ 0 \le m & l t; 2^{18} $ and considering 32 bit representation.\par With this assumptions and the truncation to the third power of $h$ of the Taylor series, the authors show that the error does not exceed the limit of single precision accuracy. Furthermore the calculations are speeded up based on reducing multiplications. A number of FORTRAN programs are also presented in order to evaluate the complementary normal distribution function cPhi (several versions) with great accuracy, create the constant tables, and generate the normal distribution variable. These simple programs give the user the possibility to completely control the accuracy.

entry:
@Article{Marsaglia:1994:REI,
  author =       "George Marsaglia and Arif Zaman and John C. W.
                 Marsaglia",
  title =        "Rapid evaluation of the inverse of the normal
                 distribution function",
  journal =      j-STAT-PROB-LETT,
  volume =       "19",
  number =       "4",
  pages =        "259--266",
  day =          "15",
  month =        mar,
  year =         "1994",
  CODEN =        "SPLTDC",
  DOI =          "https://doi.org/10.1016/0167-7152(94)90174-0",
  ISSN =         "0167-7152 (print), 1879-2103 (electronic)",
  ISSN-L =       "0167-7152",
  MRclass =      "65U05",
  MRnumber =     "1 278 658",
  bibdate =      "Thu Dec 22 07:42:24 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 MathSciNet database",
  ZMnumber =     "0798.65132",
  abstract =     "This is an interesting article with direct application
                 in generating normal random variable by computer
                 programs. The suggested applications are related to
                 Monte Carlo simulation based on massively parallel
                 systems or supercomputers. The idea is to replace
                 larger programs with complicated computations and with
                 difficulties in accuracy controlling by simpler
                 arithmetic programs that use tabled constants. These
                 seem to be the normal evolution since memory becomes
                 cheaper and cheaper.\par

                 The authors compute the inverse of the cPhi function $$
                 c P h i(x) = (2 / \pi)^{1 / 2} \int^\infty_x \exp ( -
                 t^2 / 2) d t = u, $$ using a uniform random variable as
                 input and the truncated Taylor series development of
                 it. In order to increase the speed the coefficients of
                 the truncated Taylor series $$ x(u_0 + h) = x(u_0) +
                 x'(u_0) \cdot h + {1 \over 2} x''(u_0) \cdot h^2 + {1
                 \over 6} x'''(u_0) \cdot h^3, $$ are predetermined for
                 1024 points. And here comes another bright idea: the
                 1024 points are chosen based on the representation of
                 the uniform random variable in modern computers as
                 floating point variable of the form: $ u = 2^{-k} ((1 /
                 2) + (j / 64)) + 2^{-k} \cdot (m / 2^{24}) $ with $ 0
                 \le k & l t; 32 $, $ 0 \le j & l t; 32 $ and $ 0 \le m
                 & l t; 2^{18} $ and considering 32 bit
                 representation.\par

                 With this assumptions and the truncation to the third
                 power of $h$ of the Taylor series, the authors show
                 that the error does not exceed the limit of single
                 precision accuracy. Furthermore the calculations are
                 speeded up based on reducing multiplications. A number
                 of FORTRAN programs are also presented in order to
                 evaluate the complementary normal distribution function
                 cPhi (several versions) with great accuracy, create the
                 constant tables, and generate the normal distribution
                 variable. These simple programs give the user the
                 possibility to completely control the accuracy.",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistics \& Probability Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01677152",
  keywords =     "cPhi function; FORTRAN programs; massive parallel
                 systems; Monte Carlo simulation; normal distribution
                 function; normal random variable; supercomputers;
                 truncated Taylor series",
  ZMclass =      "*65C99 Numerical simulation 65C05 Monte Carlo methods
                 60-04 Machine computation, programs (probability
                 theory) 60E05 General theory of probability
                 distributions 62E17 Approximations to statistical
                 distributions (nonasymptotic)",
  ZMreviewer =   "A. Pasculescu (Bucuresti)",
}


bibtype: article
filename: elefunt.bib
label: Merrheim:1994:CEF
author: X. Merrheim
title: The computation of elementary functions in radix $ 2^p $
journal: j-COMPUTING
volume: 53
number: 3--4
pages: 219--232
year: 1994
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
MRclass: 68M07
MRnumber: 95j:68028
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
fjournal: Computing
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/607
rawauthor: X. Merrheim
rawtitle: The computation of elementary functions in radix $ 2^p $
note:
International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (Vienna, 1993).

rawnote:
International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (Vienna, 1993).

entry:
@Article{Merrheim:1994:CEF,
  author =       "X. Merrheim",
  title =        "The computation of elementary functions in radix $ 2^p
                 $",
  journal =      j-COMPUTING,
  volume =       "53",
  number =       "3--4",
  pages =        "219--232",
  year =         "1994",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "68M07",
  MRnumber =     "95j:68028",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "International Symposium on Scientific Computing,
                 Computer Arithmetic and Validated Numerics (Vienna,
                 1993).",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
}


bibtype: article
filename: elefunt.bib
label: Narayanaswami:1994:AE
author: Chandrasekhar Narayanaswami and William Luken
title: Approximating $ x^n $ efficiently
journal: j-INFO-PROC-LETT
volume: 50
number: 4
pages: 205--210
day: 25
month: may
monthnumber: 5
year: 1994
CODEN: IFPLAT
ISSN: 0020-0190 (print), 1872-6119 (electronic) OR 00200190 (print), 18726119 (electronic)
ISSNL: 0020-0190 OR 00200190
MRclass: 65D20 (41-04 65B99)
MRnumber: 95b:65031
bibdate: Wed Nov 11 12:16:26 MST 1998
bibtimestamp: 1998.11.11 12:16:26 MST
fjournal: Information Processing Letters
acknowledgement: ack-nhfb
affiliation: IBM Advanced Workstations and Systems Div
affiliationaddress: Austin, TX, USA
corpsource: IBM Adv. Workstations and Syst. Div., Austin, TX, USA
journalURL: http://www.sciencedirect.com/science/journal/00200190
journalabr: Inf Process Lett
treatment: T Theoretical or Mathematical
rawauthor: Chandrasekhar Narayanaswami and William Luken
rawtitle: Approximating $ x^n $ efficiently
bibsource:
Compendex database; http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

keywords:
$x^n$ approximation; approximation theory; Approximation theory; Color computer graphics; Computational complexity; Computational methods; computer graphics; elementary functions; floating-point arithmetic; Function evaluation; graphics modeling; Image quality; Light intensity computation; look-up tables; performance requirements; Polynomial evaluation; Polynomials; polynomials; power function; scientific applications; Semiconducting silicon; Table lookup

entry:
@Article{Narayanaswami:1994:AE,
  author =       "Chandrasekhar Narayanaswami and William Luken",
  title =        "Approximating $ x^n $ efficiently",
  journal =      j-INFO-PROC-LETT,
  volume =       "50",
  number =       "4",
  pages =        "205--210",
  day =          "25",
  month =        may,
  year =         "1994",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  MRclass =      "65D20 (41-04 65B99)",
  MRnumber =     "95b:65031",
  bibdate =      "Wed Nov 11 12:16:26 MST 1998",
  bibsource =    "Compendex database;
                 http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM Advanced Workstations and Systems Div",
  affiliationaddress = "Austin, TX, USA",
  classification = "721.1; 723.2; 723.5; 741.2; 921.1; 921.6; B0290F
                 (Interpolation and function approximation); C4130
                 (Interpolation and function approximation); C6130B
                 (Graphics techniques)",
  corpsource =   "IBM Adv. Workstations and Syst. Div., Austin, TX,
                 USA",
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
  journalabr =   "Inf Process Lett",
  keywords =     "$x^n$ approximation; approximation theory;
                 Approximation theory; Color computer graphics;
                 Computational complexity; Computational methods;
                 computer graphics; elementary functions; floating-point
                 arithmetic; Function evaluation; graphics modeling;
                 Image quality; Light intensity computation; look-up
                 tables; performance requirements; Polynomial
                 evaluation; Polynomials; polynomials; power function;
                 scientific applications; Semiconducting silicon; Table
                 lookup",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Nishioka:1994:EFB
author: Keiji Nishioka
title: Elementary functions based on elliptic curves
journal: j-TOKYO-J-MATH
volume: 17
number: 2
pages: 439--446
year: 1994
ISSN: 0387-3870 OR 03873870
MRclass: 12H05
MRnumber: 96b:12011
MRreviewer: Alexandru Buium
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
fjournal: Tokyo journal of mathematics
acknowledgement: ack-nhfb
rawauthor: Keiji Nishioka
rawtitle: Elementary functions based on elliptic curves
entry:
@Article{Nishioka:1994:EFB,
  author =       "Keiji Nishioka",
  title =        "Elementary functions based on elliptic curves",
  journal =      j-TOKYO-J-MATH,
  volume =       "17",
  number =       "2",
  pages =        "439--446",
  year =         "1994",
  ISSN =         "0387-3870",
  MRclass =      "12H05",
  MRnumber =     "96b:12011",
  MRreviewer =   "Alexandru Buium",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Tokyo journal of mathematics",
}


bibtype: article
filename: elefunt.bib
label: Ohta:1994:INP
author: Shigemi Ohta and Eiichi Goto and Weng Fai Wong and Nobuaki Yoshida
title: Improvement and new proposal on fast evaluation of elementary functions. (Japanese)
journal: j-TRANS-INFO-PROCESSING-SOC-JAPAN
volume: 35
number: 5
pages: 926--933
month: may
monthnumber: 5
year: 1994
CODEN: JSGRD5
ISSN: 0387-5806 OR 03875806
ISSNL: 0387-5806 OR 03875806
MRclass: 65D20
MRnumber: 95f:65045
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
fjournal: Transactions of the Information Processing Society of Japan
language: Japanese
acknowledgement: ack-nhfb
affiliation: RIKEN, Inst. of Phys. and Chem. Res., Saitama, Japan
thesaurus: Digital arithmetic; Function evaluation; Random number generation; Table lookup
rawauthor: Shigemi Ohta and Eiichi Goto and Weng Fai Wong and Nobuaki Yoshida
rawtitle: Improvement and new proposal on fast evaluation of elementary functions. ({Japanese})
abstract:
Wong, Gore, and Yoshida (ibid., vol. 34, no. 7, pp. 1570-1579, 1993) introduced fast methods for numerical evaluation of elementary functions based on table lookup. They are called ATA (add/table-lookup/add) and ATA-M (add/table-lookup/add and multiply) methods for single- and double-precision calculations respectively. In this paper, an improvement to these methods that shrinks the size of the table by a factor of about 3/16 is presented. Another method called the `split parallel multiplication method', which is characterized by simpler table lookup than ATA-M and by split and parallel use of double-precision floating point circuitry, is also introduced, These new methods fit on to integrated circuits of a size comparable with commercially available floating-point accelerators. Methods for accelerating double-precision division, generating uniform pseudo-random numbers in double-precision, and accelerating the multiplication of single-precision complex numbers using the same circuitry are proposed.

keywords:
Add/table-lookup/add method; Add/table-lookup/add/multiply method; ATA method; ATA-M method; Double-precision calculations; Double-precision division; Double-precision floating point circuitry; Elementary functions evaluation; Floating-point accelerators; Integrated circuits; Numerical evaluation; Single-precision calculations; Single-precision complex number multiplication; Split parallel multiplication method; Table size; Uniform pseudo-random number generation

rawabstract:
Wong, Gore, and Yoshida (ibid., vol. 34, no. 7, pp. 1570-1579, 1993) introduced fast methods for numerical evaluation of elementary functions based on table lookup. They are called ATA (add/table-lookup/add) and ATA-M (add/table-lookup/add and multiply) methods for single- and double-precision calculations respectively. In this paper, an improvement to these methods that shrinks the size of the table by a factor of about 3/16 is presented. Another method called the `split parallel multiplication method', which is characterized by simpler table lookup than ATA-M and by split and parallel use of double-precision floating point circuitry, is also introduced, These new methods fit on to integrated circuits of a size comparable with commercially available floating-point accelerators. Methods for accelerating double-precision division, generating uniform pseudo-random numbers in double-precision, and accelerating the multiplication of single-precision complex numbers using the same circuitry are proposed.

entry:
@Article{Ohta:1994:INP,
  author =       "Shigemi Ohta and Eiichi Goto and Weng Fai Wong and
                 Nobuaki Yoshida",
  title =        "Improvement and new proposal on fast evaluation of
                 elementary functions. ({Japanese})",
  journal =      j-TRANS-INFO-PROCESSING-SOC-JAPAN,
  volume =       "35",
  number =       "5",
  pages =        "926--933",
  month =        may,
  year =         "1994",
  CODEN =        "JSGRD5",
  ISSN =         "0387-5806",
  ISSN-L =       "0387-5806",
  MRclass =      "65D20",
  MRnumber =     "95f:65045",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Wong, Gore, and Yoshida (ibid., vol. 34, no. 7, pp.
                 1570-1579, 1993) introduced fast methods for numerical
                 evaluation of elementary functions based on table
                 lookup. They are called ATA (add/table-lookup/add) and
                 ATA-M (add/table-lookup/add and multiply) methods for
                 single- and double-precision calculations respectively.
                 In this paper, an improvement to these methods that
                 shrinks the size of the table by a factor of about 3/16
                 is presented. Another method called the `split parallel
                 multiplication method', which is characterized by
                 simpler table lookup than ATA-M and by split and
                 parallel use of double-precision floating point
                 circuitry, is also introduced, These new methods fit on
                 to integrated circuits of a size comparable with
                 commercially available floating-point accelerators.
                 Methods for accelerating double-precision division,
                 generating uniform pseudo-random numbers in
                 double-precision, and accelerating the multiplication
                 of single-precision complex numbers using the same
                 circuitry are proposed.",
  acknowledgement = ack-nhfb,
  affiliation =  "RIKEN, Inst. of Phys. and Chem. Res., Saitama, Japan",
  classification = "C4120 (Functional analysis); C5230 (Digital
                 arithmetic methods); C6130 (Data handling techniques)",
  fjournal =     "Transactions of the Information Processing Society of
                 Japan",
  keywords =     "Add/table-lookup/add method;
                 Add/table-lookup/add/multiply method; ATA method; ATA-M
                 method; Double-precision calculations; Double-precision
                 division; Double-precision floating point circuitry;
                 Elementary functions evaluation; Floating-point
                 accelerators; Integrated circuits; Numerical
                 evaluation; Single-precision calculations;
                 Single-precision complex number multiplication; Split
                 parallel multiplication method; Table size; Uniform
                 pseudo-random number generation",
  language =     "Japanese",
  pubcountry =   "Japan",
  thesaurus =    "Digital arithmetic; Function evaluation; Random number
                 generation; Table lookup",
}


bibtype: inproceedings
filename: elefunt.bib
label: Olver:1994:GEI
author: F. W. J. Olver
title: The generalized exponential integral
crossref: Zahar:1994:ACF
pages: 497--510
year: 1994
MRclass: 33B20 (34E05 41A60)
MRnumber: 1333639
MRreviewer: Richard B. Paris
bibdate: Sat Feb 18 15:02:52 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.02.18 15:02:52 ???
series: International Series of Numerical Mathematics
acknowledgement: ack-nhfb
rawauthor: F. W. J. Olver
rawtitle: The generalized exponential integral
entry:
@InProceedings{Olver:1994:GEI,
  author =       "F. W. J. Olver",
  title =        "The generalized exponential integral",
  crossref =     "Zahar:1994:ACF",
  pages =        "497--510",
  year =         "1994",
  MRclass =      "33B20 (34E05 41A60)",
  MRnumber =     "1333639",
  MRreviewer =   "Richard B. Paris",
  bibdate =      "Sat Feb 18 15:02:52 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "International Series of Numerical Mathematics",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Osada:1994:CAM
author: Naoki Osada
title: Convergence acceleration methods
journal: Surikaisekikenkyusho Kokyuroku
volume: 880
pages: 28--43
year: 1994
MRclass: 65B05
MRnumber: 1366233
bibdate: Thu Dec 1 17:36:45 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 17:36:45 ???
note: The state of the art of scientific computing and its prospects (Japanese) (Kyoto, 1993)
fjournal: Surikaisekikenkyusho Kokyuroku
keywords: convergence acceleration
acknowledgement: ack-nhfb
rawauthor: Naoki Osada
rawnote: The state of the art of scientific computing and its prospects (Japanese) (Kyoto, 1993)
rawtitle: Convergence acceleration methods
entry:
@Article{Osada:1994:CAM,
  author =       "Naoki Osada",
  title =        "Convergence acceleration methods",
  journal =      "S{\=u}rikaisekikenky{\=u}sho K{\=o}ky{\=u}roku",
  volume =       "880",
  number =       "??",
  pages =        "28--43",
  month =        "????",
  year =         "1994",
  MRclass =      "65B05",
  MRnumber =     "1366233",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "The state of the art of scientific computing and its
                 prospects (Japanese) (Kyoto, 1993)",
  acknowledgement = ack-nhfb,
  fjournal =     "S{\=u}rikaisekikenky{\=u}sho K{\=o}ky{\=u}roku",
  keywords =     "convergence acceleration",
}


bibtype: inproceedings
filename: elefunt.bib
label: Rappoport:1994:TMC
author: Juri M. Rappoport
title: The Tau-Method and the Computation of the Bessel Functions of the Complex Order
crossref: Brown:1994:PCL
pages: 353--355
year: 1994
bibdate: Sat Jun 11 17:22:09 2011
bibtimestamp: 2011.06.11 17:22:09 ???
acknowledgement: ack-nhfb
rawauthor: Juri M. Rappoport
rawtitle: The {Tau-Method} and the Computation of the {Bessel} Functions of the Complex Order
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; MathSciNet database

entry:
@InProceedings{Rappoport:1994:TMC,
  author =       "Juri M. Rappoport",
  title =        "The {Tau-Method} and the Computation of the {Bessel}
                 Functions of the Complex Order",
  crossref =     "Brown:1994:PCL",
  pages =        "353--355",
  year =         "1994",
  bibdate =      "Sat Jun 11 17:22:09 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 MathSciNet database",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Schulte:1994:HDE
author: M. J. Schulte and E. E. Swartzlander, Jr.
title: Hardware Design for Exactly Rounded Elementary Functions
journal: j-IEEE-TRANS-COMPUT
volume: 43
number: 8
pages: 964--973
month: aug
monthnumber: 8
year: 1994
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.295858
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Dec 12 09:29:07 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1995.12.12 09:29:07 MST
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
affiliation: Dept. of Electr. and Comput. Eng., Texas Univ., Austin, TX, USA
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: M. J. Schulte and E. E. {Swartzlander, Jr.}
rawtitle: Hardware Design for Exactly Rounded Elementary Functions
abstract:
This paper presents hardware designs that produce exactly rounded results for the functions of reciprocal, square-root, 2/sup x/, and log/sub 2/(x). These designs use polynomial approximation in which the terms in the approximation are generated in parallel, and then summed by using a multi-operand adder. To reduce the number of terms in the approximation, the input interval is partitioned into subintervals of equal size, and different coefficients are used for each subinterval. The coefficients used in the approximation are initially determined based on the Chebyshev series approximation. They are then adjusted to obtain exactly rounded results for all inputs. Hardware designs are presented, and delay and area comparisons are made based on the degree of the approximating polynomial and the accuracy of the final result. For single-precision floating point numbers, a design that produces exactly rounded results for all four functions has an estimated delay of 80 ns and a total chip area of 98 mm/sup 2/ in a 1.0-micron CMOS technology. Allowing the results to have a maximum error of one unit in the last place reduces the computational delay by 5% to 30% and the area requirements by 33% to 77%.

keywords:
1 Micron; 1.0-Micron CMOS technology; Argument reduction; Chebyshev series approximation; Chip area; Computational delay; Computer arithmetic; Exact rounding; Exactly rounded elementary functions; Hardware designs; Multi-operand adder; Parallel multiplier; Polynomial approximation; Reciprocal; Single-precision floating point numbers; Special-purpose hardware; Square-root

thesaurus:
Approximation theory; Chebyshev approximation; CMOS integrated circuits; Digital arithmetic; Multiplying circuits; Polynomials; Summing circuits

rawabstract:
This paper presents hardware designs that produce exactly rounded results for the functions of reciprocal, square-root, 2/sup x/, and log/sub 2/(x). These designs use polynomial approximation in which the terms in the approximation are generated in parallel, and then summed by using a multi-operand adder. To reduce the number of terms in the approximation, the input interval is partitioned into subintervals of equal size, and different coefficients are used for each subinterval. The coefficients used in the approximation are initially determined based on the Chebyshev series approximation. They are then adjusted to obtain exactly rounded results for all inputs. Hardware designs are presented, and delay and area comparisons are made based on the degree of the approximating polynomial and the accuracy of the final result. For single-precision floating point numbers, a design that produces exactly rounded results for all four functions has an estimated delay of 80 ns and a total chip area of 98 mm/sup 2/ in a 1.0-micron CMOS technology. Allowing the results to have a maximum error of one unit in the last place reduces the computational delay by 5\% to 30\% and the area requirements by 33\% to 77\%.

entry:
@Article{Schulte:1994:HDE,
  author =       "M. J. Schulte and E. E. {Swartzlander, Jr.}",
  title =        "Hardware Design for Exactly Rounded Elementary
                 Functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "43",
  number =       "8",
  pages =        "964--973",
  month =        aug,
  year =         "1994",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.295858",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Dec 12 09:29:07 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "This paper presents hardware designs that produce
                 exactly rounded results for the functions of
                 reciprocal, square-root, 2/sup x/, and log/sub 2/(x).
                 These designs use polynomial approximation in which the
                 terms in the approximation are generated in parallel,
                 and then summed by using a multi-operand adder. To
                 reduce the number of terms in the approximation, the
                 input interval is partitioned into subintervals of
                 equal size, and different coefficients are used for
                 each subinterval. The coefficients used in the
                 approximation are initially determined based on the
                 Chebyshev series approximation. They are then adjusted
                 to obtain exactly rounded results for all inputs.
                 Hardware designs are presented, and delay and area
                 comparisons are made based on the degree of the
                 approximating polynomial and the accuracy of the final
                 result. For single-precision floating point numbers, a
                 design that produces exactly rounded results for all
                 four functions has an estimated delay of 80 ns and a
                 total chip area of 98 mm/sup 2/ in a 1.0-micron CMOS
                 technology. Allowing the results to have a maximum
                 error of one unit in the last place reduces the
                 computational delay by 5\% to 30\% and the area
                 requirements by 33\% to 77\%.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "Dept. of Electr. and Comput. Eng., Texas Univ.,
                 Austin, TX, USA",
  ajournal =     "IEEE Trans. Comput.",
  classification = "B0290F (Interpolation and function approximation);
                 B1265B (Logic circuits); B2570D (CMOS integrated
                 circuits); C4130 (Interpolation and function
                 approximation); C5120 (Logic and switching circuits);
                 C5230 (Digital arithmetic methods)",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "1 Micron; 1.0-Micron CMOS technology; Argument
                 reduction; Chebyshev series approximation; Chip area;
                 Computational delay; Computer arithmetic; Exact
                 rounding; Exactly rounded elementary functions;
                 Hardware designs; Multi-operand adder; Parallel
                 multiplier; Polynomial approximation; Reciprocal;
                 Single-precision floating point numbers;
                 Special-purpose hardware; Square-root",
  numericalindex = "Size 1.0E-06 m",
  pubcountry =   "USA",
  thesaurus =    "Approximation theory; Chebyshev approximation; CMOS
                 integrated circuits; Digital arithmetic; Multiplying
                 circuits; Polynomials; Summing circuits",
}


bibtype: inproceedings
filename: elefunt.bib
label: Skaf:1994:LHI
author: Ali Skaf and Jean-Michel Muller and Alain Guyot
editor: Anonymous
title: On-Line Hardware Implementation for Complex Exponential and Logarithm
publisher: Editions Frontieres
address: B. P. 33. 91192 Gif-sur-Yvette Cedex, France
pages: 252--255
year: 1994
ISBN: 2-86332-160-9 OR 2863321609
ISBN13: 978-2-86332-160-7 OR 9782863321607
bibdate: Fri Sep 29 10:32:36 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2023.09.29 10:32:36 ???
acknowledgement: ack-nhfb
rawauthor: Ali Skaf and Jean-Michel Muller and Alain Guyot
raweditor: Anonymous
rawtitle: On-Line Hardware Implementation for Complex Exponential and Logarithm
booktitle:
ESSCIRC '94: Twentieth European Solid-State Circuits Conference. Ulm, Germany. September 20--22, 1994

rawbooktitle:
{ESSCIRC '94: Twentieth European Solid-State Circuits Conference. Ulm, Germany. September 20--22, 1994}

entry:
@InProceedings{Skaf:1994:LHI,
  author =       "Ali Skaf and Jean-Michel Muller and Alain Guyot",
  editor =       "Anonymous",
  booktitle =    "{ESSCIRC '94: Twentieth European Solid-State Circuits
                 Conference. Ulm, Germany. September 20--22, 1994}",
  title =        "On-Line Hardware Implementation for Complex
                 Exponential and Logarithm",
  publisher =    "{\'E}ditions Fronti{\`e}res",
  address =      "B. P. 33. 91192 Gif-sur-Yvette Cedex, France",
  pages =        "252--255",
  year =         "1994",
  ISBN =         "2-86332-160-9",
  ISBN-13 =      "978-2-86332-160-7",
  bibdate =      "Fri Sep 29 10:32:36 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Sorenson:1994:TFG
author: J. Sorenson
title: Two Fast GCD Algorithms
journal: j-J-ALG
volume: 16
number: 1
pages: 110--144
month: jan
monthnumber: 1
year: 1994
CODEN: JOALDV
DOI: https://doi.org/10.1006/jagm.1994.1006
ISSN: 0196-6774 (print), 1090-2678 (electronic) OR 01966774 (print), 10902678 (electronic)
ISSNL: 0196-6774 OR 01966774
bibdate: Tue Dec 11 09:15:38 MST 2012
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jalg.bib
bibtimestamp: 2012.12.11 09:15:38 MST
URL: http://www.sciencedirect.com/science/article/pii/S0196677484710066
fjournal: Journal of Algorithms
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01966774
rawauthor: J. Sorenson
rawtitle: Two Fast {GCD} Algorithms
entry:
@Article{Sorenson:1994:TFG,
  author =       "J. Sorenson",
  title =        "Two Fast {GCD} Algorithms",
  journal =      j-J-ALG,
  volume =       "16",
  number =       "1",
  pages =        "110--144",
  month =        jan,
  year =         "1994",
  CODEN =        "JOALDV",
  DOI =          "https://doi.org/10.1006/jagm.1994.1006",
  ISSN =         "0196-6774 (print), 1090-2678 (electronic)",
  ISSN-L =       "0196-6774",
  bibdate =      "Tue Dec 11 09:15:38 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jalg.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0196677484710066",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Algorithms",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01966774",
}


bibtype: article
filename: elefunt.bib
label: Spouge:1994:CGD
author: John L. Spouge
title: Computation of the Gamma, Digamma, and Trigamma Functions
journal: j-SIAM-J-NUMER-ANAL
volume: 31
number: 3
pages: 931--944
month: jun
monthnumber: 6
year: 1994
CODEN: SJNAAM
ISSN: 0036-1429 (print), 1095-7170 (electronic) OR 00361429 (print), 10957170 (electronic)
ISSNL: 0036-1429 OR 00361429
MRclass: 33B15 (30E10 33-04 40-04 65D20)
MRnumber: 95g:33002
MRreviewer: E. Kaucher
bibdate: Mon Jan 20 15:27:00 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.20 15:27:00 MST
fjournal: SIAM Journal on Numerical Analysis
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sinum
rawauthor: John L. Spouge
rawtitle: Computation of the Gamma, Digamma, and Trigamma Functions
entry:
@Article{Spouge:1994:CGD,
  author =       "John L. Spouge",
  title =        "Computation of the Gamma, Digamma, and Trigamma
                 Functions",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "31",
  number =       "3",
  pages =        "931--944",
  month =        jun,
  year =         "1994",
  CODEN =        "SJNAAM",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  MRclass =      "33B15 (30E10 33-04 40-04 65D20)",
  MRnumber =     "95g:33002",
  MRreviewer =   "E. Kaucher",
  bibdate =      "Mon Jan 20 15:27:00 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
}


bibtype: inproceedings
filename: elefunt.bib
label: Temme:1994:CAI
author: N. M. Temme
title: Computational aspects of incomplete gamma functions with large complex parameters
crossref: Zahar:1994:ACF
pages: 551--562
year: 1994
bibdate: Sat Feb 18 15:02:52 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.02.18 15:02:52 ???
series: International Series of Numerical Mathematics
acknowledgement: ack-nhfb
rawauthor: N. M. Temme
rawtitle: Computational aspects of incomplete gamma functions with large complex parameters
entry:
@InProceedings{Temme:1994:CAI,
  author =       "N. M. Temme",
  title =        "Computational aspects of incomplete gamma functions
                 with large complex parameters",
  crossref =     "Zahar:1994:ACF",
  pages =        "551--562",
  year =         "1994",
  bibdate =      "Sat Feb 18 15:02:52 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "International Series of Numerical Mathematics",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Temme:1994:SAI
author: N. M. Temme
title: A Set of Algorithms for the Incomplete Gamma Functions
journal: j-PROBAB-ENGRG-INFORM-SCI
volume: 8
number: 2
pages: 291--307
month: apr
monthnumber: 4
year: 1994
DOI: https://doi.org/10.1017/S0269964800003417
ISSN: 0269-9648 (print), 1469-8951 (electronic) OR 02699648 (print), 14698951 (electronic)
ISSNL: 0269-9648 OR 02699648
bibdate: Thu Aug 24 08:18:58 MDT 2017
bibtimestamp: 2017.08.24 08:18:58 MDT
URL: https://www.cambridge.org/core/product/F5677268895A0805A0BDF31E4B20A106
fjournal: Probability in the Engineering and Informational Sciences
acknowledgement: ack-nhfb
ajournal: Probab. Engrg. Inform. Sci.
journalURL: http://www.journals.cambridge.org/jid_PES
onlinedate: 01 July 2009
rawauthor: N. M. Temme
rawtitle: A Set of Algorithms for the Incomplete Gamma Functions
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/probab-engrg-inform-sci.bib

entry:
@Article{Temme:1994:SAI,
  author =       "N. M. Temme",
  title =        "A Set of Algorithms for the Incomplete Gamma
                 Functions",
  journal =      j-PROBAB-ENGRG-INFORM-SCI,
  volume =       "8",
  number =       "2",
  pages =        "291--307",
  month =        apr,
  year =         "1994",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1017/S0269964800003417",
  ISSN =         "0269-9648 (print), 1469-8951 (electronic)",
  ISSN-L =       "0269-9648",
  bibdate =      "Thu Aug 24 08:18:58 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/probab-engrg-inform-sci.bib",
  URL =          "https://www.cambridge.org/core/product/F5677268895A0805A0BDF31E4B20A106",
  acknowledgement = ack-nhfb,
  ajournal =     "Probab. Engrg. Inform. Sci.",
  fjournal =     "Probability in the Engineering and Informational
                 Sciences",
  journal-URL =  "http://www.journals.cambridge.org/jid_PES",
  onlinedate =   "01 July 2009",
}


bibtype: article
filename: elefunt.bib
label: Timmermann:1994:CFV
author: D. Timmermann and B. Rix and H. Hahn and B. J. Hosticka
title: A CMOS floating-point vector-arithmetic unit
journal: j-IEEE-J-SOLID-STATE-CIRCUITS
volume: 29
number: 5
pages: 634--639
month: may
monthnumber: 5
year: 1994
CODEN: IJSCBC
DOI: https://doi.org/10.1109/4.284719
ISSN: 0018-9200 (print), 1558-173X (electronic) OR 00189200 (print), 1558173X (electronic)
ISSNL: 0018-9200 OR 00189200
bibdate: Tue Dec 12 09:29:07 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1995.12.12 09:29:07 MST
fjournal: IEEE Journal of Solid-State Circuits
acknowledgement: ack-nhfb
affiliation: Fraunhofer Inst. of Microelectron. Circuits and Syst., Duisburg, Germany
rawauthor: D. Timmermann and B. Rix and H. Hahn and B. J. Hosticka
rawtitle: A {CMOS} floating-point vector-arithmetic unit
abstract:
This work describes a floating-point arithmetic unit based on the CORDIC algorithm. The unit computes a full set of high level arithmetic and elementary functions: multiplication, division, (co)sine, hyperbolic (co)sine, square root, natural logarithm, inverse (hyperbolic) tangent, vector norm, and phase. The chip has been integrated in 1.6 mu m double-metal n-well CMOS technology and achieves a normalized peak performance of 220 MFLOPS.

keywords:
1.6 Micron; 220 MFLOPS; CORDIC algorithm; Cosine; Division; Double-metal n-well CMOS technology; Floating-point vector-arithmetic unit; Hyperbolic sine; Inverse tangent; Multiplication; Natural logarithm; Phase; Sine; Square root; Vector norm

thesaurus:
CMOS integrated circuits; Digital arithmetic; Integrated logic circuits; Parallel architectures; Pipeline processing; Vector processor systems

rawabstract:
This work describes a floating-point arithmetic unit based on the CORDIC algorithm. The unit computes a full set of high level arithmetic and elementary functions: multiplication, division, (co)sine, hyperbolic (co)sine, square root, natural logarithm, inverse (hyperbolic) tangent, vector norm, and phase. The chip has been integrated in 1.6 mu m double-metal n-well CMOS technology and achieves a normalized peak performance of 220 MFLOPS.

entry:
@Article{Timmermann:1994:CFV,
  author =       "D. Timmermann and B. Rix and H. Hahn and B. J.
                 Hosticka",
  title =        "A {CMOS} floating-point vector-arithmetic unit",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "29",
  number =       "5",
  pages =        "634--639",
  month =        may,
  year =         "1994",
  CODEN =        "IJSCBC",
  DOI =          "https://doi.org/10.1109/4.284719",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Tue Dec 12 09:29:07 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "This work describes a floating-point arithmetic unit
                 based on the CORDIC algorithm. The unit computes a full
                 set of high level arithmetic and elementary functions:
                 multiplication, division, (co)sine, hyperbolic
                 (co)sine, square root, natural logarithm, inverse
                 (hyperbolic) tangent, vector norm, and phase. The chip
                 has been integrated in 1.6 mu m double-metal n-well
                 CMOS technology and achieves a normalized peak
                 performance of 220 MFLOPS.",
  acknowledgement = ack-nhfb,
  affiliation =  "Fraunhofer Inst. of Microelectron. Circuits and Syst.,
                 Duisburg, Germany",
  classification = "B1265B (Logic circuits); B2570D (CMOS integrated
                 circuits); C5120 (Logic and switching circuits); C5220P
                 (Parallel architecture); C5230 (Digital arithmetic
                 methods)",
  fjournal =     "IEEE Journal of Solid-State Circuits",
  keywords =     "1.6 Micron; 220 MFLOPS; CORDIC algorithm; Cosine;
                 Division; Double-metal n-well CMOS technology;
                 Floating-point vector-arithmetic unit; Hyperbolic sine;
                 Inverse tangent; Multiplication; Natural logarithm;
                 Phase; Sine; Square root; Vector norm",
  numericalindex = "Size 1.6E-06 m; Computer speed 2.2E+08 FLOPS",
  pubcountry =   "USA",
  thesaurus =    "CMOS integrated circuits; Digital arithmetic;
                 Integrated logic circuits; Parallel architectures;
                 Pipeline processing; Vector processor systems",
}


bibtype: article
filename: elefunt.bib
label: Turner:1994:SRM
author: Stephen M. Turner
title: Square roots mod $p$
journal: j-AMER-MATH-MONTHLY
volume: 101
number: 5
pages: 443--449
month: may
monthnumber: 5
year: 1994
CODEN: AMMYAE
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
MRclass: 11A07
MRnumber: 95c:11004
MRreviewer: David Lee Hilliker
bibdate: Wed Dec 3 17:17:33 MST 1997
bibtimestamp: 1997.12.03 17:17:33 MST
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
journalURL: https://www.jstor.org/journals/00029890.htm
rawauthor: Stephen M. Turner
rawtitle: Square roots mod $p$
entry:
@Article{Turner:1994:SRM,
  author =       "Stephen M. Turner",
  title =        "Square roots mod $p$",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "101",
  number =       "5",
  pages =        "443--449",
  month =        may,
  year =         "1994",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "11A07",
  MRnumber =     "95c:11004",
  MRreviewer =   "David Lee Hilliker",
  bibdate =      "Wed Dec 3 17:17:33 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}


bibtype: book
filename: elefunt.bib
label: Watanabe:1994:MSP
author: T. (Tsutomu) Watanabe and Makoto Natori and Tsutomu Oguni
title: Mathematical Software for the P.C. and Work Stations: a Collection of Fortran 77 Programs
publisher: pub-NORTH-HOLLAND
address: pub-NORTH-HOLLAND:adr
pages: xiv + 387
month: jun
monthnumber: 6
year: 1994
ISBN: 0-444-82000-0 OR 0444820000
ISBN13: 978-0-444-82000-6 OR 9780444820006
LCCN: QA 76.73 F25 F6813 1994
bibdate: Sun Sep 28 10:42:07 MDT 1997
bibtimestamp: 1997.09.28 10:42:07 MDT
note: Translation of: FORTRAN 77 ni yoru suchi keisan sofutowea.
URL: http://www.cbooks.com/sqlnut/SP/search/gtsumt?source=&isbn=0444820000
acknowledgement: ack-nhfb
rawauthor: T. (Tsutomu) Watanabe and Makoto Natori and Tsutomu Oguni
rawnote: Translation of: FORTRAN 77 ni yoru suchi keisan sofutowea.
rawtitle: Mathematical Software for the {P.C.} and Work Stations: a Collection of {Fortran 77} Programs
bibsource:
http://www.amazon.com/exec/obidos/ISBN=0444820000/wholesaleproductA/; http://www.cbooks.com/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

keywords:
Fortran 77 (computer program language); Numerical analysis --- Use of --- Computers; Fortran 77 (Computer program language)

entry:
@Book{Watanabe:1994:MSP,
  author =       "T. (Tsutomu) Watanabe and Makoto Natori and Tsutomu
                 Oguni",
  title =        "Mathematical Software for the {P.C.} and Work
                 Stations: a Collection of {Fortran 77} Programs",
  publisher =    pub-NORTH-HOLLAND,
  address =      pub-NORTH-HOLLAND:adr,
  pages =        "xiv + 387",
  month =        jun,
  year =         "1994",
  ISBN =         "0-444-82000-0",
  ISBN-13 =      "978-0-444-82000-6",
  LCCN =         "QA 76.73 F25 F6813 1994",
  bibdate =      "Sun Sep 28 10:42:07 MDT 1997",
  bibsource =    "http://www.amazon.com/exec/obidos/ISBN=0444820000/wholesaleproductA/;
                 http://www.cbooks.com/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Translation of: FORTRAN 77 ni yoru suchi keisan
                 sofutowea.",
  price =        "US\$178.50",
  URL =          "http://www.cbooks.com/sqlnut/SP/search/gtsumt?source=&isbn=0444820000",
  acknowledgement = ack-nhfb,
  alttitle =     "{Fortran 77} ni yoru suchi keisan sofutowea.
                 English.",
  keywords =     "Fortran 77 (computer program language); Numerical
                 analysis --- Use of --- Computers; {Fortran 77}
                 (Computer program language)",
}


bibtype: inproceedings
filename: elefunt.bib
label: Wong:1994:FEE
author: W. F. Wong and E. Goto
title: Fast evaluation of the elementary functions in double precision
crossref: Mudge:1994:PTS
pages: 349--358
year: 1994
bibdate: Tue Dec 12 09:29:07 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1995.12.12 09:29:07 MST
acknowledgement: ack-nhfb
affiliation: Dept. of Inf. Syst. and Comput. Sci., Nat. Univ. of Singapore, Singapore
bookpages: xi + 621
thesaurus: Digital arithmetic; Polynomials; Table lookup
rawauthor: W. F. Wong and E. Goto
rawtitle: Fast evaluation of the elementary functions in double precision
abstract:
One of the most spectacular development in computer technology is the growth in memory density and speed. It is with this development in mind that we intend to tackle the old problem of computing the elementary functions. Since the dawn of computing, the fast and accurate computation of the elementary functions has been a constant concern of numerical computing. It now seems possible to use tables of sizes in the range of megabits to aid in such computation. To this end, in this paper, we propose a method called ATA-M (Add-Table Lookup-Add with Multiplication) for evaluating polynomials with the aid of tables. When applied to the elementary functions, we obtained a set of algorithms which computes the reciprocal, square root, exponential, sine, cosine, logarithm, are tangent and the hyperbolic functions in about 3 to 4 double precision floating point multiplication time and utilizing about 2 Mbyte of tables.

keywords:
Add-Table Lookup-Add with Multiplication; ATA-M; Double precision; Elementary functions; Floating point multiplication time; Hyperbolic functions; Memory density; Memory speed; Numerical computing; Polynomials

rawabstract:
One of the most spectacular development in computer technology is the growth in memory density and speed. It is with this development in mind that we intend to tackle the old problem of computing the elementary functions. Since the dawn of computing, the fast and accurate computation of the elementary functions has been a constant concern of numerical computing. It now seems possible to use tables of sizes in the range of megabits to aid in such computation. To this end, in this paper, we propose a method called ATA-M (Add-Table Lookup-Add with Multiplication) for evaluating polynomials with the aid of tables. When applied to the elementary functions, we obtained a set of algorithms which computes the reciprocal, square root, exponential, sine, cosine, logarithm, are tangent and the hyperbolic functions in about 3 to 4 double precision floating point multiplication time and utilizing about 2 Mbyte of tables.

entry:
@InProceedings{Wong:1994:FEE,
  author =       "W. F. Wong and E. Goto",
  title =        "Fast evaluation of the elementary functions in double
                 precision",
  crossref =     "Mudge:1994:PTS",
  bookpages =    "xi + 621",
  pages =        "349--358",
  year =         "1994",
  bibdate =      "Tue Dec 12 09:29:07 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "One of the most spectacular development in computer
                 technology is the growth in memory density and speed.
                 It is with this development in mind that we intend to
                 tackle the old problem of computing the elementary
                 functions. Since the dawn of computing, the fast and
                 accurate computation of the elementary functions has
                 been a constant concern of numerical computing. It now
                 seems possible to use tables of sizes in the range of
                 megabits to aid in such computation. To this end, in
                 this paper, we propose a method called ATA-M (Add-Table
                 Lookup-Add with Multiplication) for evaluating
                 polynomials with the aid of tables. When applied to the
                 elementary functions, we obtained a set of algorithms
                 which computes the reciprocal, square root,
                 exponential, sine, cosine, logarithm, are tangent and
                 the hyperbolic functions in about 3 to 4 double
                 precision floating point multiplication time and
                 utilizing about 2 Mbyte of tables.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Inf. Syst. and Comput. Sci., Nat. Univ. of
                 Singapore, Singapore",
  classification = "C4130 (Interpolation and function approximation);
                 C5230 (Digital arithmetic methods)",
  confdate =     "4-7 Jan. 1994",
  conflocation = "Wailea, HI, USA",
  confsponsor =  "IEEE; ACM; Univ. Hawaii; Univ. Hawaii Coll. Bus.
                 Admin",
  keywords =     "Add-Table Lookup-Add with Multiplication; ATA-M;
                 Double precision; Elementary functions; Floating point
                 multiplication time; Hyperbolic functions; Memory
                 density; Memory speed; Numerical computing;
                 Polynomials",
  pubcountry =   "USA",
  thesaurus =    "Digital arithmetic; Polynomials; Table lookup",
}


bibtype: article
filename: elefunt.bib
label: Wong:1994:FHB
author: W. F. Wong and E. Goto
title: Fast Hardware-Based Algorithms for Elementary Function Computations Using Rectangular Multipliers
journal: j-IEEE-TRANS-COMPUT
volume: 43
number: 3
pages: 278--294
month: mar
monthnumber: 3
year: 1994
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.272429
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 07:13:54 MDT 2011
bibtimestamp: 2011.07.07 07:13:54 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=272429
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nj
affiliation: Dept. of Inf. Syst. and Comput. Sci., Nat. Univ. of Singapore, Singapore
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
thesaurus: Digital arithmetic; Error analysis
rawauthor: W. F. Wong and E. Goto
rawtitle: Fast Hardware-Based Algorithms for Elementary Function Computations Using Rectangular Multipliers
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; 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/ieeetranscomput1990.bib

abstract:
As the name suggests, elementary functions play a vital role in scientific computations. Yet due to their inherent nature, they are a considerable computing task by themselves. Not surprisingly, since the dawn of computing, the goal of speeding up elementary function computation has been pursued. This paper describes new hardware based algorithms for the computation of the common elementary functions, namely division, logarithm, reciprocal square root, arc tangent, sine and cosine. These algorithms exploit microscopic parallelism using specialized hardware with heavy use of truncation based on detailed accuracy analysis. The contribution of this work lies in the fact that these algorithms are very fast and yet are accurate. If we let the time to perform an IEEE Standard 754 double precision floating point multiplication be $ tau _times $, our algorithms to achieve roughly $ 3.68 tau _times $, $ 4.56 tau _times $, $ 5.25 tau _times $, $ 3.69 tau _times $, $ 7.06 tau _times $, and $ 6.5 tau _times $, for division, logarithm, square root, exponential, are tangent and complex exponential (sine and cosine) respectively. The trade-off is the need for tables and some specialized hardware. The total amount of tables required, however, is less than 128 Kbytes. We discuss the hardware, algorithmic and accuracy aspects of these algorithms.

keywords:
Arc tangent; Common elementary functions; Cosine; Elementary function computations; Floating point multiplication; Hardware-based algorithms; Microscopic parallelism; Reciprocal square root; Rectangular multipliers; Scientific computations; Sine

rawabstract:
As the name suggests, elementary functions play a vital role in scientific computations. Yet due to their inherent nature, they are a considerable computing task by themselves. Not surprisingly, since the dawn of computing, the goal of speeding up elementary function computation has been pursued. This paper describes new hardware based algorithms for the computation of the common elementary functions, namely division, logarithm, reciprocal square root, arc tangent, sine and cosine. These algorithms exploit microscopic parallelism using specialized hardware with heavy use of truncation based on detailed accuracy analysis. The contribution of this work lies in the fact that these algorithms are very fast and yet are accurate. If we let the time to perform an IEEE Standard 754 double precision floating point multiplication be $ \tau_\times $, our algorithms to achieve roughly $ 3.68 \tau_\times $, $ 4.56 \tau_\times $, $ 5.25 \tau_\times $, $ 3.69 \tau_\times $, $ 7.06 \tau_\times $, and $ 6.5 \tau_\times $, for division, logarithm, square root, exponential, are tangent and complex exponential (sine and cosine) respectively. The trade-off is the need for tables and some specialized hardware. The total amount of tables required, however, is less than 128 Kbytes. We discuss the hardware, algorithmic and accuracy aspects of these algorithms.

entry:
@Article{Wong:1994:FHB,
  author =       "W. F. Wong and E. Goto",
  title =        "Fast Hardware-Based Algorithms for Elementary Function
                 Computations Using Rectangular Multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "43",
  number =       "3",
  pages =        "278--294",
  month =        mar,
  year =         "1994",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.272429",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:13:54 MDT 2011",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 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/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=272429",
  abstract =     "As the name suggests, elementary functions play a
                 vital role in scientific computations. Yet due to their
                 inherent nature, they are a considerable computing task
                 by themselves. Not surprisingly, since the dawn of
                 computing, the goal of speeding up elementary function
                 computation has been pursued. This paper describes new
                 hardware based algorithms for the computation of the
                 common elementary functions, namely division,
                 logarithm, reciprocal square root, arc tangent, sine
                 and cosine. These algorithms exploit microscopic
                 parallelism using specialized hardware with heavy use
                 of truncation based on detailed accuracy analysis. The
                 contribution of this work lies in the fact that these
                 algorithms are very fast and yet are accurate. If we
                 let the time to perform an IEEE Standard 754 double
                 precision floating point multiplication be $
                 \tau_\times $, our algorithms to achieve roughly $ 3.68
                 \tau_\times $, $ 4.56 \tau_\times $, $ 5.25 \tau_\times
                 $, $ 3.69 \tau_\times $, $ 7.06 \tau_\times $, and $
                 6.5 \tau_\times $, for division, logarithm, square
                 root, exponential, are tangent and complex exponential
                 (sine and cosine) respectively. The trade-off is the
                 need for tables and some specialized hardware. The
                 total amount of tables required, however, is less than
                 128 Kbytes. We discuss the hardware, algorithmic and
                 accuracy aspects of these algorithms.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  affiliation =  "Dept. of Inf. Syst. and Comput. Sci., Nat. Univ. of
                 Singapore, Singapore",
  ajournal =     "IEEE Trans. Comput.",
  classification = "C4110 (Error analysis in numerical methods); C5230
                 (Digital arithmetic methods)",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Arc tangent; Common elementary functions; Cosine;
                 Elementary function computations; Floating point
                 multiplication; Hardware-based algorithms; Microscopic
                 parallelism; Reciprocal square root; Rectangular
                 multipliers; Scientific computations; Sine",
  pubcountry =   "USA",
  thesaurus =    "Digital arithmetic; Error analysis",
}


bibtype: article
filename: elefunt.bib
label: Xu:1994:VPC
author: Guo Liang Xu and Jia Kai Li
title: Variable precision computation of elementary functions. (Chinese)
journal: j-J-NUMER-METHODS-COMPUT-APPL
volume: 15
number: 3
pages: 161--171
year: 1994
ISSN: 1000-3266 OR 10003266
MRclass: 65D20 (65Y20)
MRnumber: MR1357336 (96i:65013)
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
fjournal: Journal on Numerical Methods and Computer Applications. Shuzhi Jisuan yu Jisuanji Yingyong
acknowledgement: ack-nhfb
rawauthor: Guo Liang Xu and Jia Kai Li
rawtitle: Variable precision computation of elementary functions. ({Chinese})
entry:
@Article{Xu:1994:VPC,
  author =       "Guo Liang Xu and Jia Kai Li",
  title =        "Variable precision computation of elementary
                 functions. ({Chinese})",
  journal =      j-J-NUMER-METHODS-COMPUT-APPL,
  volume =       "15",
  number =       "3",
  pages =        "161--171",
  year =         "1994",
  ISSN =         "1000-3266",
  MRclass =      "65D20 (65Y20)",
  MRnumber =     "MR1357336 (96i:65013)",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal on Numerical Methods and Computer
                 Applications. Shuzhi Jisuan yu Jisuanji Yingyong",
}


bibtype: article
filename: elefunt.bib
label: Abad:1995:CRC
author: Julio Abad and Javier Sesma
title: Computation of the Regular Confluent Hypergeometric Function
journal: j-MATHEMATICA-J
volume: 5
number: 4
pages: ??--??
month: Fall
year: 1995
ISSN: 1047-5974 (print), 1097-1610 (electronic) OR 10475974 (print), 10971610 (electronic)
ISSNL: 1047-5974 OR 10475974
bibdate: Sat Nov 6 13:34:06 MDT 2010
bibsource: http://www.mathematica-journal.com/issue/v5i4/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.11.06 13:34:06 MDT
URL: http://www.mathematica-journal.com/issue/v5i4/article/abad/index.html
fjournal: Mathematica Journal
acknowledgement: ack-nhfb
journalURL: http://www.mathematica-journal.com/
rawauthor: Julio Abad and Javier Sesma
rawtitle: Computation of the Regular Confluent Hypergeometric Function
entry:
@Article{Abad:1995:CRC,
  author =       "Julio Abad and Javier Sesma",
  title =        "Computation of the Regular Confluent Hypergeometric
                 Function",
  journal =      j-MATHEMATICA-J,
  volume =       "5",
  number =       "4",
  pages =        "??--??",
  month =        "Fall",
  year =         "1995",
  CODEN =        "????",
  ISSN =         "1047-5974 (print), 1097-1610 (electronic)",
  ISSN-L =       "1047-5974",
  bibdate =      "Sat Nov 6 13:34:06 MDT 2010",
  bibsource =    "http://www.mathematica-journal.com/issue/v5i4/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.mathematica-journal.com/issue/v5i4/article/abad/index.html",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematica Journal",
  journal-URL =  "http://www.mathematica-journal.com/",
}


bibtype: article
filename: elefunt.bib
label: Amos:1995:RAP
author: D. E. Amos
journal: j-TOMS
volume: 21
number: 4
pages: 388--393
month: dec
monthnumber: 12
year: 1995
CODEN: ACMSCU
DOI: https://doi.org/10.1145/212066.212078
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Mar 09 10:24:54 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib
bibtimestamp: 1999.03.09 10:24:54 ???
note: See cite Amos:1986:APP,Amos:1990:RPP,Kodama:2007:RA.
URL: http://www.acm.org/pubs/citations/journals/toms/1995-21-4/p388-amos/
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-rfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: D. E. Amos
rawnote: See \cite{Amos:1986:APP,Amos:1990:RPP,Kodama:2007:RA}.
title:
A Remark on Algorithm 644: a Portable Package for Bessel Functions of a Complex Argument and Nonnegative Order

keywords:
complex Airy Functions; complex Bessel functions; derivatives of Airy functions; H, I, J, K, and Y Bessel functions; log gamma function

subject:
G.1.0 [Numerical Analysis]: General -- numerical algorithms; G.1.m [Numerical Analysis]: Miscellaneous; G.m [Mathematics of Computing]: Miscellaneous

rawtitle:
A Remark on {Algorithm 644}: a Portable Package for {Bessel} Functions of a Complex Argument and Nonnegative Order

entry:
@Article{Amos:1995:RAP,
  author =       "D. E. Amos",
  title =        "A Remark on {Algorithm 644}: a Portable Package for
                 {Bessel} Functions of a Complex Argument and
                 Nonnegative Order",
  journal =      j-TOMS,
  volume =       "21",
  number =       "4",
  pages =        "388--393",
  month =        dec,
  year =         "1995",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/212066.212078",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 09 10:24:54 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See
                 \cite{Amos:1986:APP,Amos:1990:RPP,Kodama:2007:RA}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1995-21-4/p388-amos/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "complex Airy Functions; complex Bessel functions;
                 derivatives of Airy functions; H, I, J, K, and Y Bessel
                 functions; log gamma function",
  subject =      "G.1.0 [Numerical Analysis]: General -- numerical
                 algorithms; G.1.m [Numerical Analysis]: Miscellaneous;
                 G.m [Mathematics of Computing]: Miscellaneous",
}


bibtype: article
filename: elefunt.bib
label: Bagby:1995:CNP
author: Richard J. Bagby
title: Calculating normal probabilities
journal: j-AMER-MATH-MONTHLY
volume: 102
number: 1
pages: 46--48
month: jan
monthnumber: 1
year: 1995
CODEN: AMMYAE
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
MRclass: 65D20
MRnumber: 96f:65021
bibdate: Wed Dec 3 17:17:33 MST 1997
bibtimestamp: 1997.12.03 17:17:33 MST
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
journalURL: https://www.jstor.org/journals/00029890.htm
rawauthor: Richard J. Bagby
rawtitle: Calculating normal probabilities
bibsource:
http://www.jstor.org/journals/00029890.htm; https://www.math.utah.edu/pub/tex/bib/amermathmonthly1990.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Bagby:1995:CNP,
  author =       "Richard J. Bagby",
  title =        "Calculating normal probabilities",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "102",
  number =       "1",
  pages =        "46--48",
  month =        jan,
  year =         "1995",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "65D20",
  MRnumber =     "96f:65021",
  bibdate =      "Wed Dec 3 17:17:33 MST 1997",
  bibsource =    "http://www.jstor.org/journals/00029890.htm;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}


bibtype: article
filename: elefunt.bib
label: Baratchart:1995:RIE
author: L. Baratchart and E. B. Saff and F. Wielonsky
title: Rational interpolation of the exponential function
journal: j-CAN-J-MATH
volume: 47
pages: 1121--1147
year: 1995
CODEN: CJMAAB
DOI: https://doi.org/10.4153/CJM-1995-058-6
ISSN: 0008-414X (print), 1496-4279 (electronic) OR 0008414X (print), 14964279 (electronic)
ISSNL: 0008-414X OR 0008414X
bibdate: Sat Sep 10 15:39:05 MDT 2011
bibtimestamp: 2011.09.10 15:39:05 MDT
fjournal: Canadian Journal of Mathematics = Journal canadien de mathematiques
acknowledgement: ack-nhfb
journalURL: http://cms.math.ca/cjm/
rawauthor: L. Baratchart and E. B. Saff and F. Wielonsky
rawtitle: Rational interpolation of the exponential function
bibsource:
http://cms.math.ca/cjm/v47/; https://www.math.utah.edu/pub/tex/bib/canjmath1990.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Baratchart:1995:RIE,
  author =       "L. Baratchart and E. B. Saff and F. Wielonsky",
  title =        "Rational interpolation of the exponential function",
  journal =      j-CAN-J-MATH,
  volume =       "47",
  number =       "??",
  pages =        "1121--1147",
  month =        "????",
  year =         "1995",
  CODEN =        "CJMAAB",
  DOI =          "https://doi.org/10.4153/CJM-1995-058-6",
  ISSN =         "0008-414X (print), 1496-4279 (electronic)",
  ISSN-L =       "0008-414X",
  bibdate =      "Sat Sep 10 15:39:05 MDT 2011",
  bibsource =    "http://cms.math.ca/cjm/v47/;
                 https://www.math.utah.edu/pub/tex/bib/canjmath1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Canadian Journal of Mathematics = Journal canadien de
                 math{\'e}matiques",
  journal-URL =  "http://cms.math.ca/cjm/",
}


bibtype: techreport
filename: elefunt.bib
label: Borwein:1995:EARa
author: Peter Borwein
title: An Efficient Algorithm for the Riemann Zeta Function
type: Report
institution: Department of Mathematics & Statistics, Simon Fraser University
address: Burnaby, BC V5A 1S6, Canada
pages: 9
day: 20
month: jan
monthnumber: 1
year: 1995
bibdate: Thu Sep 01 18:09:22 2022
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2022.09.01 18:09:22 ???
URL: http://docserver.carma.newcastle.edu.au/107
acknowledgement: ack-nhfb
authordates: 10 May 1953--23 August 2020
rawauthor: Peter Borwein
rawtitle: An Efficient Algorithm for the {Riemann} Zeta Function
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
A very simple class of algorithms for the computation of the Riemann-zeta function to arbitrary precision in arbitrary domains is proposed. These algorithms out perform the standard methods based on Euler--Maclaurin summation, are easier to implement and are easier to analyse.

rawabstract:
A very simple class of algorithms for the computation of the Riemann-zeta function to arbitrary precision in arbitrary domains is proposed. These algorithms out perform the standard methods based on Euler--Maclaurin summation, are easier to implement and are easier to analyse.

entry:
@TechReport{Borwein:1995:EARa,
  author =       "Peter Borwein",
  title =        "An Efficient Algorithm for the {Riemann} Zeta
                 Function",
  type =         "Report",
  institution =  "Department of Mathematics \& Statistics, Simon Fraser
                 University",
  address =      "Burnaby, BC V5A 1S6, Canada",
  pages =        "9",
  day =          "20",
  month =        jan,
  year =         "1995",
  bibdate =      "Thu Sep 01 18:09:22 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/107",
  abstract =     "A very simple class of algorithms for the computation
                 of the Riemann-zeta function to arbitrary precision in
                 arbitrary domains is proposed. These algorithms out
                 perform the standard methods based on Euler--Maclaurin
                 summation, are easier to implement and are easier to
                 analyse.",
  acknowledgement = ack-nhfb,
  author-dates = "10 May 1953--23 August 2020",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: inproceedings
filename: elefunt.bib
label: Borwein:1995:EARb
author: P. Borwein
booktitle: CMS Conference Proceedings
title: An efficient algorithm for the Riemann zeta function
volume: 27
publisher: Canadian Mathematical Society
address: 616 Cooper Street, Ottawa, ON, K1R 5J2, Canada
pages: 29--34
month: jan
monthnumber: 1
year: 1995
bibdate: Wed Jun 28 08:27:14 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2023.06.28 08:27:14 ???
URL: https://web.archive.org/web/20140602151514/http://www.cecm.sfu.ca/personal/pborwein/PAPERS/P155.pdf
acknowledgement: ack-nhfb
rawauthor: P. Borwein
rawbooktitle: {CMS} Conference Proceedings
rawtitle: An efficient algorithm for the {Riemann} zeta function
entry:
@InProceedings{Borwein:1995:EARb,
  author =       "P. Borwein",
  editor =       "????",
  booktitle =    "{CMS} Conference Proceedings",
  title =        "An efficient algorithm for the {Riemann} zeta
                 function",
  volume =       "27",
  publisher =    "Canadian Mathematical Society",
  address =      "616 Cooper Street, Ottawa, ON, K1R 5J2, Canada",
  pages =        "29--34",
  month =        jan,
  year =         "1995",
  bibdate =      "Wed Jun 28 08:27:14 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://web.archive.org/web/20140602151514/http://www.cecm.sfu.ca/personal/pborwein/PAPERS/P155.pdf",
  acknowledgement = ack-nhfb,
  xxURL =        "http://www.cecm.sfu.ca/personal/pborwein/PAPERS/P155.pdf",
}


bibtype: article
filename: elefunt.bib
label: Carlson:1995:NCR
author: B. C. Carlson
title: Numerical computation of real or complex elliptic integrals
journal: j-NUMER-ALGORITHMS
volume: 10
number: 1--2
pages: 13--26
month: jul
monthnumber: 7
year: 1995
CODEN: NUALEG
DOI: https://doi.org/10.1007/BF02198293
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
MRclass: 33Exx (33-04 65D20)
MRnumber: 1 345 407
bibdate: Fri Nov 6 18:06:29 MST 1998
bibsource: http://www.math.psu.edu/dna/contents/na.html; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1998.11.06 18:06:29 MST
note: Special functions (Torino, 1993)
fjournal: Numerical Algorithms
acknowledgement: ack-nhfb
corpsource: Ames Lab., Iowa State Univ., Ames, IA, USA
journalURL: http://link.springer.com/journal/11075
treatment: T Theoretical or Mathematical
rawauthor: B. C. Carlson
rawnote: Special functions (Torino, 1993)
rawtitle: Numerical computation of real or complex elliptic integrals
abstract:
Algorithms for numerical computation of symmetric elliptic integrals of all three kinds are improved in several ways and extended to complex values of the variables (with some restrictions in the case of the integral of the third kind). Numerical check values, consistency checks, and relations to Legendre's integrals and Bulirsch's integrals are included.

keywords:
Bulirsch's integrals; complex elliptic integrals; complex values; consistency checks; elliptic equations; integral equations; Legendre's integrals; numerical analysis; numerical check values; numerical computation algorithms; real elliptic integrals

rawabstract:
Algorithms for numerical computation of symmetric elliptic integrals of all three kinds are improved in several ways and extended to complex values of the variables (with some restrictions in the case of the integral of the third kind). Numerical check values, consistency checks, and relations to Legendre's integrals and Bulirsch's integrals are included.

entry:
@Article{Carlson:1995:NCR,
  author =       "B. C. Carlson",
  title =        "Numerical computation of real or complex elliptic
                 integrals",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "10",
  number =       "1--2",
  pages =        "13--26",
  month =        jul,
  year =         "1995",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/BF02198293",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  MRclass =      "33Exx (33-04 65D20)",
  MRnumber =     "1 345 407",
  bibdate =      "Fri Nov 6 18:06:29 MST 1998",
  bibsource =    "http://www.math.psu.edu/dna/contents/na.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Special functions (Torino, 1993)",
  abstract =     "Algorithms for numerical computation of symmetric
                 elliptic integrals of all three kinds are improved in
                 several ways and extended to complex values of the
                 variables (with some restrictions in the case of the
                 integral of the third kind). Numerical check values,
                 consistency checks, and relations to Legendre's
                 integrals and Bulirsch's integrals are included.",
  acknowledgement = ack-nhfb,
  classification = "B0290R (Integral equations); C4180 (Integral
                 equations)",
  conflocation = "Torino, Italy; 14-15 Oct. 1993",
  conftitle =    "International Joint Symposium on Special Functions and
                 Artificial Intelligence",
  corpsource =   "Ames Lab., Iowa State Univ., Ames, IA, USA",
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "Bulirsch's integrals; complex elliptic integrals;
                 complex values; consistency checks; elliptic equations;
                 integral equations; Legendre's integrals; numerical
                 analysis; numerical check values; numerical computation
                 algorithms; real elliptic integrals",
  pubcountry =   "Switzerland",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Chaudhry:1995:DGI
author: M. Aslam Chaudhry and S. M. Zubair
journal: j-J-COMPUT-APPL-MATH
volume: 59
number: 3
pages: 253--284
day: 30
month: may
monthnumber: 5
year: 1995
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:24:37 MST 2017
bibtimestamp: 2017.02.25 12:24:37 MST
URL: http://www.sciencedirect.com/science/article/pii/037704279400026W
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: M. Aslam Chaudhry and S. M. Zubair
title:
On the decomposition of generalized incomplete gamma functions with applications to Fourier transforms

rawtitle:
On the decomposition of generalized incomplete gamma functions with applications to {Fourier} transforms

entry:
@Article{Chaudhry:1995:DGI,
  author =       "M. Aslam Chaudhry and S. M. Zubair",
  title =        "On the decomposition of generalized incomplete gamma
                 functions with applications to {Fourier} transforms",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "59",
  number =       "3",
  pages =        "253--284",
  day =          "30",
  month =        may,
  year =         "1995",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:24:37 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/037704279400026W",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: inproceedings
filename: elefunt.bib
label: Chen:1995:UCA
author: San-Gee Chen and Chieh-Chih Li
booktitle: IEEE Signal Processing Society Workshop on VLSI Signal Processing, VIII, 1995
title: A unified cellular array for multiplication, division and square root
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 533--541
year: 1995
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: San-Gee Chen and Chieh-Chih Li
rawbooktitle: {IEEE} Signal Processing Society Workshop on {VLSI} Signal Processing, {VIII, 1995}
rawtitle: A unified cellular array for multiplication, division and square root
entry:
@InProceedings{Chen:1995:UCA,
  author =       "San-Gee Chen and Chieh-Chih Li",
  booktitle =    "{IEEE} Signal Processing Society Workshop on {VLSI}
                 Signal Processing, {VIII, 1995}",
  title =        "A unified cellular array for multiplication, division
                 and square root",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "533--541",
  year =         "1995",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "A unified fast, small-area processor capable of
                 executing multiplication, division and square-root
                 operations, all starting from MSD is proposed. Unlike
                 the existing designs which require both addition and
                 subtraction operations, and complicated \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Das:1995:IFC
author: D. Das and K. Mukhopadhyaya and B. P. Sinha
title: Implementation of four common functions on an LNS co-processor
journal: j-IEEE-TRANS-COMPUT
volume: 44
number: 1
pages: 155--161
month: jan
monthnumber: 1
year: 1995
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.367997
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 16 16:14:38 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 16:14:38 MDT
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: D. Das and K. Mukhopadhyaya and B. P. Sinha
rawtitle: Implementation of four common functions on an {LNS} co-processor
entry:
@Article{Das:1995:IFC,
  author =       "D. Das and K. Mukhopadhyaya and B. P. Sinha",
  title =        "Implementation of four common functions on an {LNS}
                 co-processor",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "44",
  number =       "1",
  pages =        "155--161",
  month =        jan,
  year =         "1995",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.367997",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 16:14:38 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "We propose a scheme for evaluating four commonly used
                 functions namely, (1) inverse trigonometric functions,
                 (2) trigonometric functions, (3) the exponential
                 function, and (4) the logarithmic function with the
                 help of a logarithmic number system (\ldots{}).",
}


bibtype: article
filename: elefunt.bib
label: Daumas:1995:MRR
author: Marc Daumas and Christophe Mazenc and Xavier Merrheim and Jean-Michel Muller
journal: j-J-UCS
volume: 1
number: 3
pages: 162--175 (electronic)
year: 1995
ISSN: 0948-6968 OR 09486968
ISSNL: 0948-6968 OR 09486968
MRclass: 68M07 (68Q20)
MRnumber: 1 390 003
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
fjournal: J.UCS: Journal of Universal Computer Science
acknowledgement: ack-nhfb
journalURL: http://www.jucs.org/jucs
rawauthor: Marc Daumas and Christophe Mazenc and Xavier Merrheim and Jean-Michel Muller
title:
Modular range reduction: a new algorithm for fast and accurate computation of the elementary functions

rawtitle:
Modular range reduction: a new algorithm for fast and accurate computation of the elementary functions

entry:
@Article{Daumas:1995:MRR,
  author =       "Marc Daumas and Christophe Mazenc and Xavier Merrheim
                 and Jean-Michel Muller",
  title =        "Modular range reduction: a new algorithm for fast and
                 accurate computation of the elementary functions",
  journal =      j-J-UCS,
  volume =       "1",
  number =       "3",
  pages =        "162--175 (electronic)",
  year =         "1995",
  CODEN =        "????",
  ISSN =         "0948-6968",
  ISSN-L =       "0948-6968",
  MRclass =      "68M07 (68Q20)",
  MRnumber =     "1 390 003",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "J.UCS: Journal of Universal Computer Science",
  journal-URL =  "http://www.jucs.org/jucs",
}


bibtype: article
filename: elefunt.bib
label: Doman:1995:SAP
author: B. G. S. Doman and C. J. Pursglove and W. M. Coen
title: A Set of Ada Packages for High Precision Calculations
journal: j-TOMS
volume: 21
number: 4
pages: 416--431
month: dec
monthnumber: 12
year: 1995
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Nov 14 09:57:55 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1995.11.14 09:57:55 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-rfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: B. G. S. Doman and C. J. Pursglove and W. M. Coen
rawtitle: A Set of {Ada} Packages for High Precision Calculations
keywords:
accuracy; Ada; arithmetic elementary-function evaluation; floating-point; multiple-precision portable software

subject:
G.1.0 [Numerical Analysis]: General -- computer arithmetic; G.1.2 [Numerical Analysis]: Approximation -- elementary function approximation; G.4 [Mathematics of Computing]: Mathematical Software -- algorithm analysis; efficiency; portability

entry:
@Article{Doman:1995:SAP,
  author =       "B. G. S. Doman and C. J. Pursglove and W. M. Coen",
  title =        "A Set of {Ada} Packages for High Precision
                 Calculations",
  journal =      j-TOMS,
  volume =       "21",
  number =       "4",
  pages =        "416--431",
  month =        dec,
  year =         "1995",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Nov 14 09:57:55 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-rfb # "\slash " # ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "accuracy; Ada; arithmetic elementary-function
                 evaluation; floating-point; multiple-precision portable
                 software",
  subject =      "G.1.0 [Numerical Analysis]: General -- computer
                 arithmetic; G.1.2 [Numerical Analysis]: Approximation
                 -- elementary function approximation; G.4 [Mathematics
                 of Computing]: Mathematical Software -- algorithm
                 analysis; efficiency; portability",
}


bibtype: article
filename: elefunt.bib
label: Driver:1995:NQH
author: Kathy Driver
title: Nondiagonal quadratic Hermite--Pade approximation to the exponential function
journal: j-J-COMPUT-APPL-MATH
volume: 65
number: 1--3
pages: 125--134
day: 29
month: dec
monthnumber: 12
year: 1995
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 13:02:25 MST 2017
bibtimestamp: 2017.02.25 13:02:25 MST
URL: http://www.sciencedirect.com/science/article/pii/0377042795001069
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Kathy Driver
rawtitle: Nondiagonal quadratic {Hermite--Pad{\'e}} approximation to the exponential function
entry:
@Article{Driver:1995:NQH,
  author =       "Kathy Driver",
  title =        "Nondiagonal quadratic {Hermite--Pad{\'e}}
                 approximation to the exponential function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "65",
  number =       "1--3",
  pages =        "125--134",
  day =          "29",
  month =        dec,
  year =         "1995",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:02:25 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042795001069",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Goano:1995:ACC
author: Michele Goano
title: Algorithm 745: Computation of the Complete and Incomplete Fermi--Dirac Integral
journal: j-TOMS
volume: 21
number: 3
pages: 221--232
month: sep
monthnumber: 9
year: 1995
CODEN: ACMSCU
DOI: https://doi.org/10.1145/210089.210090
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Mar 09 10:19:43 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1999.03.09 10:19:43 ???
note: See remark cite Goano:1997:RA7
URL: http://www.acm.org/pubs/citations/journals/toms/1995-21-3/p221-goano/
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-rfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Michele Goano
rawnote: See remark \cite{Goano:1997:RA7}
rawtitle: {Algorithm 745}: Computation of the Complete and Incomplete {Fermi--Dirac} Integral
keywords:
asymptotic expansions; confluent hypergeometric functions; convergence acceleration; e[k] transforms; epsilon algorithm; Euler transformation; Fermi--Dirac integral; incomplete Fermi--Dirac integral; incomplete gamma function; Levin's u transform; Riemann's zeta function

subject:
G.1.2 [Mathematics of Computing]: Approximation; G.4 [Mathematics of Computing]: Mathematical Software; J.2 [Computer Applications]: Physical Sciences and Engineering

entry:
@Article{Goano:1995:ACC,
  author =       "Michele Goano",
  title =        "{Algorithm 745}: Computation of the Complete and
                 Incomplete {Fermi--Dirac} Integral",
  journal =      j-TOMS,
  volume =       "21",
  number =       "3",
  pages =        "221--232",
  month =        sep,
  year =         "1995",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/210089.210090",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 09 10:19:43 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See remark \cite{Goano:1997:RA7}",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1995-21-3/p221-goano/",
  acknowledgement = ack-rfb # "\slash " # ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "asymptotic expansions; confluent hypergeometric
                 functions; convergence acceleration; e[k] transforms;
                 epsilon algorithm; Euler transformation; Fermi--Dirac
                 integral; incomplete Fermi--Dirac integral; incomplete
                 gamma function; Levin's u transform; Riemann's zeta
                 function",
  subject =      "G.1.2 [Mathematics of Computing]: Approximation; G.4
                 [Mathematics of Computing]: Mathematical Software; J.2
                 [Computer Applications]: Physical Sciences and
                 Engineering",
}


bibtype: article
filename: elefunt.bib
label: Hobson:1995:EMR
author: R. F. Hobson and M. W. Fraser
title: An efficient maximum-redundancy radix-$8$ SRT division and square-root method
journal: j-IEEE-J-SOLID-STATE-CIRCUITS
volume: 30
number: 1
pages: 29--38
month: jan
monthnumber: 1
year: 1995
CODEN: IJSCBC
DOI: https://doi.org/10.1109/4.350197
ISSN: 0018-9200 (print), 1558-173X (electronic) OR 00189200 (print), 1558173X (electronic)
ISSNL: 0018-9200 OR 00189200
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
fjournal: IEEE Journal of Solid-State Circuits
acknowledgement: ack-nhfb
affiliation: Sch. of Comput. Sci., Simon Fraser Univ., Burnaby, BC, Canada
rawauthor: R. F. Hobson and M. W. Fraser
rawtitle: An efficient maximum-redundancy radix-$8$ {SRT} division and square-root method
abstract:
A new approach to integrating hardware multiplication, division, and square-root is presented. We use a fully integrated control path which simultaneously reduces part of the redundant partial-remainder and performs a truncated multiplication of the next quotient or square-root digit by the divisor or square-root value. A separate (parallel) full precision iterative multiplier is used for partial remainder production. Strategic details of a radix-8 implementation are discussed. It is shown that a maximally redundant digit set is a viable choice for high performance in this case.

keywords:
1.2 Mum; CMOS adder cell; CMOS divider; Division; IEEE floating point algorithm; Integrated control path; Maximally redundant digit set; Maximum-redundancy radix-8 SRT algorithm; Multiplication; Parallel iterative multiplier; Partial remainder production; Redundant partial-remainder; Square-root method; Table lookup

thesaurus:
Adders; CMOS digital integrated circuits; Digital arithmetic; Dividing circuits; Floating point arithmetic; Multiplying circuits

rawabstract:
A new approach to integrating hardware multiplication, division, and square-root is presented. We use a fully integrated control path which simultaneously reduces part of the redundant partial-remainder and performs a truncated multiplication of the next quotient or square-root digit by the divisor or square-root value. A separate (parallel) full precision iterative multiplier is used for partial remainder production. Strategic details of a radix-8 implementation are discussed. It is shown that a maximally redundant digit set is a viable choice for high performance in this case.

entry:
@Article{Hobson:1995:EMR,
  author =       "R. F. Hobson and M. W. Fraser",
  title =        "An efficient maximum-redundancy radix-$8$ {SRT}
                 division and square-root method",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "30",
  number =       "1",
  pages =        "29--38",
  month =        jan,
  year =         "1995",
  CODEN =        "IJSCBC",
  DOI =          "https://doi.org/10.1109/4.350197",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "A new approach to integrating hardware multiplication,
                 division, and square-root is presented. We use a fully
                 integrated control path which simultaneously reduces
                 part of the redundant partial-remainder and performs a
                 truncated multiplication of the next quotient or
                 square-root digit by the divisor or square-root value.
                 A separate (parallel) full precision iterative
                 multiplier is used for partial remainder production.
                 Strategic details of a radix-8 implementation are
                 discussed. It is shown that a maximally redundant digit
                 set is a viable choice for high performance in this
                 case.",
  acknowledgement = ack-nhfb,
  affiliation =  "Sch. of Comput. Sci., Simon Fraser Univ., Burnaby, BC,
                 Canada",
  classification = "B1265B (Logic circuits); B2570D (CMOS integrated
                 circuits); C5230 (Digital arithmetic methods)",
  fjournal =     "IEEE Journal of Solid-State Circuits",
  keywords =     "1.2 Mum; CMOS adder cell; CMOS divider; Division; IEEE
                 floating point algorithm; Integrated control path;
                 Maximally redundant digit set; Maximum-redundancy
                 radix-8 SRT algorithm; Multiplication; Parallel
                 iterative multiplier; Partial remainder production;
                 Redundant partial-remainder; Square-root method; Table
                 lookup",
  numericalindex = "Size 1.2E-06 m",
  pubcountry =   "USA",
  summary =      "A new approach to integrating hardware multiplication,
                 division, and square-root is presented. We use a fully
                 integrated control path which simultaneously reduces
                 part of the redundant partial-remainder and performs a
                 truncated multiplication of the \ldots{}",
  thesaurus =    "Adders; CMOS digital integrated circuits; Digital
                 arithmetic; Dividing circuits; Floating point
                 arithmetic; Multiplying circuits",
}


bibtype: inproceedings
filename: elefunt.bib
label: Ito:1995:EIA
author: M. Ito and N. Takagi and S. Yajima
booktitle: Proceedings of the 12th Symposium on Computer Arithmetic, 19--21 July 1995
title: Efficient Initial Approximation and Fast Converging Methods for Division and Square Root
crossref: Knowles:1995:PSC
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 2--9
month: jul
monthnumber: 7
year: 1995
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; OCLC Proceedings database
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-sfo
rawauthor: M. Ito and N. Takagi and S. Yajima
rawbooktitle: Proceedings of the 12th Symposium on Computer Arithmetic, 19--21 July 1995
rawtitle: Efficient Initial Approximation and Fast Converging Methods for Division and Square Root
entry:
@InProceedings{Ito:1995:EIA,
  author =       "M. Ito and N. Takagi and S. Yajima",
  booktitle =    "Proceedings of the 12th Symposium on Computer
                 Arithmetic, 19--21 July 1995",
  title =        "Efficient Initial Approximation and Fast Converging
                 Methods for Division and Square Root",
  crossref =     "Knowles:1995:PSC",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "2--9",
  month =        jul,
  year =         "1995",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  summary =      "Efficient initial approximations and fast converging
                 algorithms are important to achieve the desired
                 precision faster at lower hardware cost in
                 multiplicative division and square root. In this paper,
                 a new initial approximation method for division,
                 \ldots{}",
}


bibtype: book
filename: elefunt.bib
label: Jeffrey:1995:HMF
author: Alan Jeffrey
title: Handbook of Mathematical Formulas and Integrals
publisher: pub-ACADEMIC
address: pub-ACADEMIC:adr
pages: xxiv + 410
year: 1995
LCCN: QA47 .J38 1995
bibdate: Wed Jun 12 14:33:38 MDT 2024
bibsource: fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2024.06.12 14:33:38 MDT
URL: http://www.sciencedirect.com/science/book/9780123825803
subject: Mathematics; Tables; Formulae; Mathematiques; Formules; formulas (algorithms); Mathematics.
acknowledgement: ack-nhfb
rawauthor: Alan Jeffrey
rawtitle: Handbook of Mathematical Formulas and Integrals
ISBN:
0-08-052301-3, 0-12-382580-6 (e-book), 1-4832-9514-1 (e-book) OR 0080523013, 0123825806 (ebook), 1483295141 (ebook)

ISBN13:
978-0-08-052301-9, 978-0-12-382580-3 (e-book), 978-1-4832-9514-5 (e-book) OR 9780080523019, 9780123825803 (ebook), 9781483295145 (ebook)

abstract:
If there is a formula to solve a given problem in mathematics, you will find it in Alan Jeffrey's booktitle Handbook of Mathematical Formulas and Integrals. Thanks to its unique thumb-tab indexing feature, answers are easy to find based upon the type of problem they solve. The Handbook covers important formulas, functions, relations, and methods from algebra, trigonometric and exponential functions, combinatorics, probability, matrix theory, calculus and vector calculus, both ordinary and partial differential equations, Fourier series, orthogonal polynomials, and Laplace transforms. Based on Gradshteyn and Ryzhik's Table of Integrals, Series, and Products, Fifth Edition (edited by Jeffrey), but far more accessible and written with particular attention to the needs of students and practicing scientists and engineers, this book is an essential resource. Affordable and authoritative, it is the first place to look for help and a rewarding place to browse.

TOC:
0: Quick Reference List of Frequently Used Data 0.1: Useful Identities / 1 0.2: Complex Relationships / 2 0.3: Constants / 2 0.4: Derivatives of Elementary Functions / 3 0.5: Rules of Differentiation and Integration / 3 0.6: Standard Integrals / 4 0.7: Standard Series / 11 0.8: Geometry / 13 1: Numerical, Algebraic, and Analytical Results for Series and Calculus 1.1: Algebraic Results Involving Real and Complex Numbers / 25 1.2: Finite Sums / 29 1.3: Bernoulli and Euler Numbers and Polynomials 37 1.4: Determinants / 47 1.5: Matrices / 55 1.6: Permutations and Combinations / 62 1.7: Partial Fraction Decomposition / 63 1.8: Convergence of Series / 66 1.9: Infinite Products / 71 1.10: Functional Series / 73 1.11: Power Series / 74 1.12: Taylor Series / 79 1.13: Fourier Series / 81 1.14: Asymptotic Expansions / 85 1.15: Basic Results from the Calculus / 86 2: Functions and Identities 2.1: Complex Numbers and Trigonometric and Hyperbolic Functions / 101 2.2: Logarithms and Exponentials / 112 2.3: The Exponential Function / 114 2.4: Trigonometric Identities / 115 2.5: Hyperbolic Identities / 121 2.6: The Logarithm / 126 2.7: Inverse Trigonometric and Hyperbolic Functions / 128 2.8: Series Representations of Trigonometric and Hyperbolic Functions / 133 2.9: Useful Limiting Values and Inequalities Involving Elementary Functions / 136 3: Derivatives of Elementary Functions 3.1: Derivatives of Algebraic, Logarithmic, and Exponential Functions / 139 3.2: Derivatives of Trigonometric Functions / 140 3.3: Derivatives of Inverse Trigonometric Functions / 140 3.4: Derivatives of Hyperbolic Functions / 141 3.5: Derivatives of Inverse Hyperbolic Functions 142 4: Indefinite Integrals of Algebraic Functions 4.1: Algebraic and Transcendental Functions / 145 4.2: Indefinite Integrals of Rational Functions 146 4.3: Nonrational Algebraic Functions / 158 5: Indefinite Integrals of Exponential Functions 5.1: Basic Results / 167 6: Indefinite Integrals of Logarithmic Functions 6.1: Combinations of Logarithms and Polynomials 173 7: Indefinite Integrals of Hyperbolic Functions 7.1: Basic Results / 179 7.2: Integrands Involving Powers of sinh(bx) or cosh(bx) / 180 7.3: Integrands Involving (a [plus or minus] bx)[superscript m] sinh(cx) or (a + bx)[superscript m] cosh(cx) / 181 7.4: Integrands Involving x[superscript m] sinh[superscript n] x or x[superscript m] cosh[superscript n] x / 183 7.5: Integrands Involving x[superscript m] sinh[superscript -n] x or x[superscript m] cosh[superscript -n] x / 183 7.6: Integrands Involving (1 [plus or minus] cosh x)[superscript -m] / 185 7.7: Integrands Involving sinh(ax)cosh[superscript -n] x or cosh(ax)sinh[superscript -n] x / 185 7.8: Integrands Involving sinh(ax + b) and cosh(cx + d) / 186 7.9: Integrands Involving tanh kx and coth kx 188 7.10: Integrands Involving (a + bx)[superscript m] sinh kx or (a + bx)[superscript m] cosh kx / 189 8: Indefinite Integrals Involving Inverse Hyperbolic Functions 8.1: Basic Results / 191 8.2: Integrands Involving x[superscript -n] arcsinh(x/a) or x[superscript -n] arccosh(x/a) 193 8.3: Integrands Involving x[superscript n] arctanh(x/a) or x[superscript n] arccoth(x/a) 194 8.4: Integrands Involving x[superscript -n] arctanh(x/a) or x[superscript -n] arccoth(x/a) / 195 9: Indefinite Integrals of Trigonometric Functions 9.1: Basic Results / 197 9.2: Integrands Involving Powers of x and Powers of sin x or cos x / 197 9.3: Integrands Involving tan x and/or cot x 205 9.4: Integrands Involving sin x and cos x / 207 9.5: Integrands Involving Sines and Cosines with Linear Arguments and Powers of x / 211 10: Indefinite Integrals of Inverse Trigonometric Functions 10.1: Integrands Involving Powers of x and Powers of Inverse Trigonometric Functions / 215 11: The Gamma, Beta, Pi, and Psi Functions 11.1: The Euler Integral and Limit and Infinite Product Representations for [Gamma] (x) / 221 12: Elliptic Integrals and Functions 12.1: Elliptic Integrals / 229 12.2: Jacobian Elliptic Functions / 235 12.3: Derivatives and Integrals / 237 12.4: Inverse Jacobian Elliptic Functions / 237 13: Probability Integrals and the Error Function 13.1: Normal Distribution / 239 13.2: The Error Function / 242 14: Fresnel Integrals, Sine and Cosine Integrals 14.1: Definitions, Series Representations, and Values at Infinity / 245 14.2: Definitions, Series Representations, and Values at Infinity / 247 15: Definite Integrals 15.1: Integrands Involving Powers of x / 249 15.2: Integrands Involving Trigonometric Functions 251 15.3: Integrands Involving the Exponential Function / 254 15.4: Integrands Involving the Hyperbolic Function 256 15.5: Integrands Involving the Logarithmic Function / 256 16: Different Forms of Fourier Series 16.1: Fourier Series for f(x) on -[pi] [less than or equal] x [less than or equal] [pi] / 257 16.2: Fourier Series for f(x) on -L [less than or equal] x [less than or equal] L / 258 16.3: Fourier Series for f(x) on a [less than or equal] x [less than or equal] b / 258 16.4: Half-Range Fourier Cosine Series for f(x) on 0 [less than or equal] x [less than or equal] [pi] 259 16.5: Half-Range Fourier Cosine Series for f(x) on 0 [less than or equal] x [less than or equal] L 259 16.6: Half-Range Fourier Sine Series for f(x) on 0 [less than or equal] x [less than or equal] [pi] 260 16.7: Half-Range Fourier Sine Series for f(x) on 0 [less than or equal] x [less than or equal] L 260 16.8: Complex (Exponential) Fourier Series for f(x) on -[pi] [less than or equal] x [less than or equal] [pi] / 260 16.9: Complex (Exponential) Fourier Series for f(x) on -L [less than or equal] x [less than or equal] L 261 16.10: Representative Examples of Fourier Series 261 16.11: Fourier Series and Discontinuous Functions 265 17: Bessel Functions 17.1: Bessel's Differential Equation / 269 17.2: Series Expansions for J[subscript v](x) and Y[subscript v](x) / 270 17.3: Bessel Functions of Fractional Order / 272 17.4: Asymptotic Representations for Bessel Functions / 273 17.5: Zeros of Bessel Functions / 273 17.6: Bessel's Modified Equation / 274 17.7: Series Expansions for I[subscript v](x) and K[subscript v](x) / 276 17.8: Modified Bessel Functions of Fractional Order / 277 17.9: Asymptotic Representations of Modified Bessel Functions / 278 17.10: Relationships between Bessel Functions 278 17.11: Integral Representations of J[subscript n](x), I[subscript n](x), and K[subscript n](x) / 281 17.12: Indefinite Integrals of Bessel Functions 281 17.13: Definite Integrals Involving Bessel Functions / 282 17.14: Spherical Bessel Functions / 283 18: Orthogonal Polynomials 18.2: Legendre Polynomials P[subscript n](x) 286 18.3: Chebyshev Polynomials T[subscript n](x) and U[subscript n](x) / 290 18.4: Laguerre Polynomials L[subscript n](x) 294 18.5: Hermite Polynomials H[subscript n](x) / 296 19: Laplace Transformation 20: Fourier Transforms 21: Numerical Integration 21.1: Classical Methods / 315 22: Solutions of Standard Ordinary Differential Equations 22.2: Separation of Variables / 323 22.3: Linear First-Order Equations / 323 22.4: Bernoulli's Equation / 324 22.5: Exact Equations / 325 22.6: Homogeneous Equations / 325 22.7: Linear Differential Equations / 326 22.8: Constant Coefficient Linear Differential Equations Homogeneous Case / 327 22.9: Linear Homogeneous Second-Order Equation 330 22.10: Constant Coefficient Linear Differential Equations Inhomogeneous Case / 331 22.11: Linear Inhomogeneous Second-Order Equation 333 22.12: Determination of Particular Integrals by the Method of Undetermined Coefficients / 334 22.13: The Cauchy-Euler Equation / 336 22.14: Legendre's Equation / 337 22.15: Bessel's Equations / 337 22.16: Power Series and Frobenius Methods / 339 22.17: The Hypergeometric Equation / 344 22.18: Numerical Methods / 345 23: Vector Analysis 23.1: Scalars and Vectors / 353 23.2: Scalar Products / 358 23.3: Vector Products / 359 23.4: Triple Products / 360 23.5: Products of Four Vectors / 361 23.6: Derivatives of Vector Functions of a Scalar t / 361 23.7: Derivatives of Vector Functions of Several Scalar Variables / 362 23.8: Integrals of Vector Functions of a Scalar Variable t / 363 23.9: Line Integrals / 364 23.10: Vector Integral Theorems / 366 23.11: A Vector Rate of Change Theorem / 368 23.12: Useful Vector Identities and Results / 368 24: Systems of Orthogonal Coordinates 24.1: Curvilinear Coordinates / 369 24.2: Vector Operators in Orthogonal Coordinates 371 24.3: Systems of Orthogonal Coordinates / 371 25: Partial Differential Equations and Special Functions 25.1: Fundamental Ideas / 381 25.2: Method of Separation of Variables / 385 25.3: The Sturm--Liouville Problem and Special Functions / 387 25.4: A First-Order System and the Wave Equation 390 25.5: Conservation Equations (Laws) / 391 25.6: The Method of Characteristics / 392 25.7: Discontinuous Solutions (Shocks) / 396 25.8: Similarity Solutions / 398 25.9: Burgers's Equation, the KdV Equation, and the KdVB Equation / 400 26: The z-Transform 26.1: The z-Transform and Transform Pairs / 403 27: Numerical Approximation 27.2: Economization of Series / 411 27.3: Pade Approximation / 413 27.4: Finite Difference Approximations to Ordinary and Partial Derivatives / 415

rawabstract:
If there is a formula to solve a given problem in mathematics, you will find it in Alan Jeffrey's \booktitle{Handbook of Mathematical Formulas and Integrals}. Thanks to its unique thumb-tab indexing feature, answers are easy to find based upon the type of problem they solve. The Handbook covers important formulas, functions, relations, and methods from algebra, trigonometric and exponential functions, combinatorics, probability, matrix theory, calculus and vector calculus, both ordinary and partial differential equations, Fourier series, orthogonal polynomials, and Laplace transforms. Based on Gradshteyn and Ryzhik's Table of Integrals, Series, and Products, Fifth Edition (edited by Jeffrey), but far more accessible and written with particular attention to the needs of students and practicing scientists and engineers, this book is an essential resource. Affordable and authoritative, it is the first place to look for help and a rewarding place to browse.

rawTOC:
0: Quick Reference List of Frequently Used Data \\ 0.1: Useful Identities / 1 \\ 0.2: Complex Relationships / 2 \\ 0.3: Constants / 2 \\ 0.4: Derivatives of Elementary Functions / 3 \\ 0.5: Rules of Differentiation and Integration / 3 \\ 0.6: Standard Integrals / 4 \\ 0.7: Standard Series / 11 \\ 0.8: Geometry / 13 \\ 1: Numerical, Algebraic, and Analytical Results for Series and Calculus \\ 1.1: Algebraic Results Involving Real and Complex Numbers / 25 \\ 1.2: Finite Sums / 29 \\ 1.3: Bernoulli and Euler Numbers and Polynomials 37 \\ 1.4: Determinants / 47 \\ 1.5: Matrices / 55 \\ 1.6: Permutations and Combinations / 62 \\ 1.7: Partial Fraction Decomposition / 63 \\ 1.8: Convergence of Series / 66 \\ 1.9: Infinite Products / 71 \\ 1.10: Functional Series / 73 \\ 1.11: Power Series / 74 \\ 1.12: Taylor Series / 79 \\ 1.13: Fourier Series / 81 \\ 1.14: Asymptotic Expansions / 85 \\ 1.15: Basic Results from the Calculus / 86 \\ 2: Functions and Identities \\ 2.1: Complex Numbers and Trigonometric and Hyperbolic Functions / 101 \\ 2.2: Logarithms and Exponentials / 112 \\ 2.3: The Exponential Function / 114 \\ 2.4: Trigonometric Identities / 115 \\ 2.5: Hyperbolic Identities / 121 \\ 2.6: The Logarithm / 126 \\ 2.7: Inverse Trigonometric and Hyperbolic Functions / 128 \\ 2.8: Series Representations of Trigonometric and Hyperbolic Functions / 133 \\ 2.9: Useful Limiting Values and Inequalities Involving Elementary Functions / 136 \\ 3: Derivatives of Elementary Functions \\ 3.1: Derivatives of Algebraic, Logarithmic, and Exponential Functions / 139 \\ 3.2: Derivatives of Trigonometric Functions / 140 \\ 3.3: Derivatives of Inverse Trigonometric Functions / 140 \\ 3.4: Derivatives of Hyperbolic Functions / 141 \\ 3.5: Derivatives of Inverse Hyperbolic Functions 142 \\ 4: Indefinite Integrals of Algebraic Functions \\ 4.1: Algebraic and Transcendental Functions / 145 \\ 4.2: Indefinite Integrals of Rational Functions 146 \\ 4.3: Nonrational Algebraic Functions / 158 \\ 5: Indefinite Integrals of Exponential Functions \\ 5.1: Basic Results / 167 \\ 6: Indefinite Integrals of Logarithmic Functions \\ 6.1: Combinations of Logarithms and Polynomials 173 \\ 7: Indefinite Integrals of Hyperbolic Functions \\ 7.1: Basic Results / 179 \\ 7.2: Integrands Involving Powers of sinh(bx) or cosh(bx) / 180 \\ 7.3: Integrands Involving (a [plus or minus] bx)[superscript m] sinh(cx) or (a + bx)[superscript m] cosh(cx) / 181 \\ 7.4: Integrands Involving x[superscript m] sinh[superscript n] x or x[superscript m] cosh[superscript n] x / 183 \\ 7.5: Integrands Involving x[superscript m] sinh[superscript -n] x or x[superscript m] cosh[superscript -n] x / 183 \\ 7.6: Integrands Involving (1 [plus or minus] cosh x)[superscript -m] / 185 \\ 7.7: Integrands Involving sinh(ax)cosh[superscript -n] x or cosh(ax)sinh[superscript -n] x / 185 \\ 7.8: Integrands Involving sinh(ax + b) and cosh(cx + d) / 186 \\ 7.9: Integrands Involving tanh kx and coth kx 188 \\ 7.10: Integrands Involving (a + bx)[superscript m] sinh kx or (a + bx)[superscript m] cosh kx / 189 \\ 8: Indefinite Integrals Involving Inverse Hyperbolic Functions \\ 8.1: Basic Results / 191 \\ 8.2: Integrands Involving x[superscript -n] arcsinh(x/a) or x[superscript -n] arccosh(x/a) 193 \\ 8.3: Integrands Involving x[superscript n] arctanh(x/a) or x[superscript n] arccoth(x/a) 194 \\ 8.4: Integrands Involving x[superscript -n] arctanh(x/a) or x[superscript -n] arccoth(x/a) / 195 \\ 9: Indefinite Integrals of Trigonometric Functions \\ 9.1: Basic Results / 197 \\ 9.2: Integrands Involving Powers of x and Powers of sin x or cos x / 197 \\ 9.3: Integrands Involving tan x and/or cot x 205 \\ 9.4: Integrands Involving sin x and cos x / 207 \\ 9.5: Integrands Involving Sines and Cosines with Linear Arguments and Powers of x / 211 \\ 10: Indefinite Integrals of Inverse Trigonometric Functions \\ 10.1: Integrands Involving Powers of x and Powers of Inverse Trigonometric Functions / 215 \\ 11: The Gamma, Beta, Pi, and Psi Functions \\ 11.1: The Euler Integral and Limit and Infinite Product Representations for [Gamma] (x) / 221 \\ 12: Elliptic Integrals and Functions \\ 12.1: Elliptic Integrals / 229 \\ 12.2: Jacobian Elliptic Functions / 235 \\ 12.3: Derivatives and Integrals / 237 \\ 12.4: Inverse Jacobian Elliptic Functions / 237 \\ 13: Probability Integrals and the Error Function \\ 13.1: Normal Distribution / 239 \\ 13.2: The Error Function / 242 \\ 14: Fresnel Integrals, Sine and Cosine Integrals \\ 14.1: Definitions, Series Representations, and Values at Infinity / 245 \\ 14.2: Definitions, Series Representations, and Values at Infinity / 247 \\ 15: Definite Integrals \\ 15.1: Integrands Involving Powers of x / 249 \\ 15.2: Integrands Involving Trigonometric Functions 251 \\ 15.3: Integrands Involving the Exponential Function / 254 \\ 15.4: Integrands Involving the Hyperbolic Function 256 \\ 15.5: Integrands Involving the Logarithmic Function / 256 \\ 16: Different Forms of Fourier Series \\ 16.1: Fourier Series for f(x) on -[pi] [less than or equal] x [less than or equal] [pi] / 257 \\ 16.2: Fourier Series for f(x) on -L [less than or equal] x [less than or equal] L / 258 \\ 16.3: Fourier Series for f(x) on a [less than or equal] x [less than or equal] b / 258 \\ 16.4: Half-Range Fourier Cosine Series for f(x) on 0 [less than or equal] x [less than or equal] [pi] 259 \\ 16.5: Half-Range Fourier Cosine Series for f(x) on 0 [less than or equal] x [less than or equal] L 259 \\ 16.6: Half-Range Fourier Sine Series for f(x) on 0 [less than or equal] x [less than or equal] [pi] 260 \\ 16.7: Half-Range Fourier Sine Series for f(x) on 0 [less than or equal] x [less than or equal] L 260 \\ 16.8: Complex (Exponential) Fourier Series for f(x) on -[pi] [less than or equal] x [less than or equal] [pi] / 260 \\ 16.9: Complex (Exponential) Fourier Series for f(x) on -L [less than or equal] x [less than or equal] L 261 \\ 16.10: Representative Examples of Fourier Series 261 \\ 16.11: Fourier Series and Discontinuous Functions 265 \\ 17: Bessel Functions \\ 17.1: Bessel's Differential Equation / 269 \\ 17.2: Series Expansions for J[subscript v](x) and Y[subscript v](x) / 270 \\ 17.3: Bessel Functions of Fractional Order / 272 \\ 17.4: Asymptotic Representations for Bessel Functions / 273 \\ 17.5: Zeros of Bessel Functions / 273 \\ 17.6: Bessel's Modified Equation / 274 \\ 17.7: Series Expansions for I[subscript v](x) and K[subscript v](x) / 276 \\ 17.8: Modified Bessel Functions of Fractional Order / 277 \\ 17.9: Asymptotic Representations of Modified Bessel Functions / 278 \\ 17.10: Relationships between Bessel Functions 278 \\ 17.11: Integral Representations of J[subscript n](x), I[subscript n](x), and K[subscript n](x) / 281 \\ 17.12: Indefinite Integrals of Bessel Functions 281 \\ 17.13: Definite Integrals Involving Bessel Functions / 282 \\ 17.14: Spherical Bessel Functions / 283 \\ 18: Orthogonal Polynomials \\ 18.2: Legendre Polynomials P[subscript n](x) 286 \\ 18.3: Chebyshev Polynomials T[subscript n](x) and U[subscript n](x) / 290 \\ 18.4: Laguerre Polynomials L[subscript n](x) 294 \\ 18.5: Hermite Polynomials H[subscript n](x) / 296 \\ 19: Laplace Transformation \\ 20: Fourier Transforms \\ 21: Numerical Integration \\ 21.1: Classical Methods / 315 \\ 22: Solutions of Standard Ordinary Differential Equations \\ 22.2: Separation of Variables / 323 \\ 22.3: Linear First-Order Equations / 323 \\ 22.4: Bernoulli's Equation / 324 \\ 22.5: Exact Equations / 325 \\ 22.6: Homogeneous Equations / 325 \\ 22.7: Linear Differential Equations / 326 \\ 22.8: Constant Coefficient Linear Differential Equations \\ Homogeneous Case / 327 \\ 22.9: Linear Homogeneous Second-Order Equation 330 \\ 22.10: Constant Coefficient Linear Differential Equations \\ Inhomogeneous Case / 331 \\ 22.11: Linear Inhomogeneous Second-Order Equation 333 \\ 22.12: Determination of Particular Integrals by the Method of Undetermined Coefficients / 334 \\ 22.13: The Cauchy-Euler Equation / 336 \\ 22.14: Legendre's Equation / 337 \\ 22.15: Bessel's Equations / 337 \\ 22.16: Power Series and Frobenius Methods / 339 \\ 22.17: The Hypergeometric Equation / 344 \\ 22.18: Numerical Methods / 345 \\ 23: Vector Analysis \\ 23.1: Scalars and Vectors / 353 \\ 23.2: Scalar Products / 358 \\ 23.3: Vector Products / 359 \\ 23.4: Triple Products / 360 \\ 23.5: Products of Four Vectors / 361 \\ 23.6: Derivatives of Vector Functions of a Scalar t / 361 \\ 23.7: Derivatives of Vector Functions of Several Scalar Variables / 362 \\ 23.8: Integrals of Vector Functions of a Scalar Variable t / 363 \\ 23.9: Line Integrals / 364 \\ 23.10: Vector Integral Theorems / 366 \\ 23.11: A Vector Rate of Change Theorem / 368 \\ 23.12: Useful Vector Identities and Results / 368 \\ 24: Systems of Orthogonal Coordinates \\ 24.1: Curvilinear Coordinates / 369 \\ 24.2: Vector Operators in Orthogonal Coordinates 371 \\ 24.3: Systems of Orthogonal Coordinates / 371 \\ 25: Partial Differential Equations and Special Functions \\ 25.1: Fundamental Ideas / 381 \\ 25.2: Method of Separation of Variables / 385 \\ 25.3: The Sturm--Liouville Problem and Special Functions / 387 \\ 25.4: A First-Order System and the Wave Equation 390 \\ 25.5: Conservation Equations (Laws) / 391 \\ 25.6: The Method of Characteristics / 392 \\ 25.7: Discontinuous Solutions (Shocks) / 396 \\ 25.8: Similarity Solutions / 398 \\ 25.9: Burgers's Equation, the KdV Equation, and the KdVB Equation / 400 \\ 26: The z-Transform \\ 26.1: The z-Transform and Transform Pairs / 403 \\ 27: Numerical Approximation \\ 27.2: Economization of Series / 411 \\ 27.3: Pade Approximation / 413 \\ 27.4: Finite Difference Approximations to Ordinary and Partial Derivatives / 415

entry:
@Book{Jeffrey:1995:HMF,
  author =       "Alan Jeffrey",
  title =        "Handbook of Mathematical Formulas and Integrals",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xxiv + 410",
  year =         "1995",
  ISBN =         "0-08-052301-3, 0-12-382580-6 (e-book), 1-4832-9514-1
                 (e-book)",
  ISBN-13 =      "978-0-08-052301-9, 978-0-12-382580-3 (e-book),
                 978-1-4832-9514-5 (e-book)",
  LCCN =         "QA47 .J38 1995",
  bibdate =      "Wed Jun 12 14:33:38 MDT 2024",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/book/9780123825803",
  abstract =     "If there is a formula to solve a given problem in
                 mathematics, you will find it in Alan Jeffrey's
                 \booktitle{Handbook of Mathematical Formulas and
                 Integrals}. Thanks to its unique thumb-tab indexing
                 feature, answers are easy to find based upon the type
                 of problem they solve. The Handbook covers important
                 formulas, functions, relations, and methods from
                 algebra, trigonometric and exponential functions,
                 combinatorics, probability, matrix theory, calculus and
                 vector calculus, both ordinary and partial differential
                 equations, Fourier series, orthogonal polynomials, and
                 Laplace transforms. Based on Gradshteyn and Ryzhik's
                 Table of Integrals, Series, and Products, Fifth Edition
                 (edited by Jeffrey), but far more accessible and
                 written with particular attention to the needs of
                 students and practicing scientists and engineers, this
                 book is an essential resource. Affordable and
                 authoritative, it is the first place to look for help
                 and a rewarding place to browse.",
  acknowledgement = ack-nhfb,
  subject =      "Mathematics; Tables; Formulae; Math{\'e}matiques;
                 Formules; formulas (algorithms); Mathematics.",
  tableofcontents = "0: Quick Reference List of Frequently Used Data \\
                 0.1: Useful Identities / 1 \\
                 0.2: Complex Relationships / 2 \\
                 0.3: Constants / 2 \\
                 0.4: Derivatives of Elementary Functions / 3 \\
                 0.5: Rules of Differentiation and Integration / 3 \\
                 0.6: Standard Integrals / 4 \\
                 0.7: Standard Series / 11 \\
                 0.8: Geometry / 13 \\
                 1: Numerical, Algebraic, and Analytical Results for
                 Series and Calculus \\
                 1.1: Algebraic Results Involving Real and Complex
                 Numbers / 25 \\
                 1.2: Finite Sums / 29 \\
                 1.3: Bernoulli and Euler Numbers and Polynomials 37 \\
                 1.4: Determinants / 47 \\
                 1.5: Matrices / 55 \\
                 1.6: Permutations and Combinations / 62 \\
                 1.7: Partial Fraction Decomposition / 63 \\
                 1.8: Convergence of Series / 66 \\
                 1.9: Infinite Products / 71 \\
                 1.10: Functional Series / 73 \\
                 1.11: Power Series / 74 \\
                 1.12: Taylor Series / 79 \\
                 1.13: Fourier Series / 81 \\
                 1.14: Asymptotic Expansions / 85 \\
                 1.15: Basic Results from the Calculus / 86 \\
                 2: Functions and Identities \\
                 2.1: Complex Numbers and Trigonometric and Hyperbolic
                 Functions / 101 \\
                 2.2: Logarithms and Exponentials / 112 \\
                 2.3: The Exponential Function / 114 \\
                 2.4: Trigonometric Identities / 115 \\
                 2.5: Hyperbolic Identities / 121 \\
                 2.6: The Logarithm / 126 \\
                 2.7: Inverse Trigonometric and Hyperbolic Functions /
                 128 \\
                 2.8: Series Representations of Trigonometric and
                 Hyperbolic Functions / 133 \\
                 2.9: Useful Limiting Values and Inequalities Involving
                 Elementary Functions / 136 \\
                 3: Derivatives of Elementary Functions \\
                 3.1: Derivatives of Algebraic, Logarithmic, and
                 Exponential Functions / 139 \\
                 3.2: Derivatives of Trigonometric Functions / 140 \\
                 3.3: Derivatives of Inverse Trigonometric Functions /
                 140 \\
                 3.4: Derivatives of Hyperbolic Functions / 141 \\
                 3.5: Derivatives of Inverse Hyperbolic Functions 142
                 \\
                 4: Indefinite Integrals of Algebraic Functions \\
                 4.1: Algebraic and Transcendental Functions / 145 \\
                 4.2: Indefinite Integrals of Rational Functions 146 \\
                 4.3: Nonrational Algebraic Functions / 158 \\
                 5: Indefinite Integrals of Exponential Functions \\
                 5.1: Basic Results / 167 \\
                 6: Indefinite Integrals of Logarithmic Functions \\
                 6.1: Combinations of Logarithms and Polynomials 173 \\
                 7: Indefinite Integrals of Hyperbolic Functions \\
                 7.1: Basic Results / 179 \\
                 7.2: Integrands Involving Powers of sinh(bx) or
                 cosh(bx) / 180 \\
                 7.3: Integrands Involving (a [plus or minus]
                 bx)[superscript m] sinh(cx) or (a + bx)[superscript m]
                 cosh(cx) / 181 \\
                 7.4: Integrands Involving x[superscript m]
                 sinh[superscript n] x or x[superscript m]
                 cosh[superscript n] x / 183 \\
                 7.5: Integrands Involving x[superscript m]
                 sinh[superscript -n] x or x[superscript m]
                 cosh[superscript -n] x / 183 \\
                 7.6: Integrands Involving (1 [plus or minus] cosh
                 x)[superscript -m] / 185 \\
                 7.7: Integrands Involving sinh(ax)cosh[superscript -n]
                 x or cosh(ax)sinh[superscript -n] x / 185 \\
                 7.8: Integrands Involving sinh(ax + b) and cosh(cx + d)
                 / 186 \\
                 7.9: Integrands Involving tanh kx and coth kx 188 \\
                 7.10: Integrands Involving (a + bx)[superscript m] sinh
                 kx or (a + bx)[superscript m] cosh kx / 189 \\
                 8: Indefinite Integrals Involving Inverse Hyperbolic
                 Functions \\
                 8.1: Basic Results / 191 \\
                 8.2: Integrands Involving x[superscript -n]
                 arcsinh(x/a) or x[superscript -n] arccosh(x/a) 193 \\
                 8.3: Integrands Involving x[superscript n] arctanh(x/a)
                 or x[superscript n] arccoth(x/a) 194 \\
                 8.4: Integrands Involving x[superscript -n]
                 arctanh(x/a) or x[superscript -n] arccoth(x/a) / 195
                 \\
                 9: Indefinite Integrals of Trigonometric Functions \\
                 9.1: Basic Results / 197 \\
                 9.2: Integrands Involving Powers of x and Powers of sin
                 x or cos x / 197 \\
                 9.3: Integrands Involving tan x and/or cot x 205 \\
                 9.4: Integrands Involving sin x and cos x / 207 \\
                 9.5: Integrands Involving Sines and Cosines with Linear
                 Arguments and Powers of x / 211 \\
                 10: Indefinite Integrals of Inverse Trigonometric
                 Functions \\
                 10.1: Integrands Involving Powers of x and Powers of
                 Inverse Trigonometric Functions / 215 \\
                 11: The Gamma, Beta, Pi, and Psi Functions \\
                 11.1: The Euler Integral and Limit and Infinite Product
                 Representations for [Gamma] (x) / 221 \\
                 12: Elliptic Integrals and Functions \\
                 12.1: Elliptic Integrals / 229 \\
                 12.2: Jacobian Elliptic Functions / 235 \\
                 12.3: Derivatives and Integrals / 237 \\
                 12.4: Inverse Jacobian Elliptic Functions / 237 \\
                 13: Probability Integrals and the Error Function \\
                 13.1: Normal Distribution / 239 \\
                 13.2: The Error Function / 242 \\
                 14: Fresnel Integrals, Sine and Cosine Integrals \\
                 14.1: Definitions, Series Representations, and Values
                 at Infinity / 245 \\
                 14.2: Definitions, Series Representations, and Values
                 at Infinity / 247 \\
                 15: Definite Integrals \\
                 15.1: Integrands Involving Powers of x / 249 \\
                 15.2: Integrands Involving Trigonometric Functions 251
                 \\
                 15.3: Integrands Involving the Exponential Function /
                 254 \\
                 15.4: Integrands Involving the Hyperbolic Function 256
                 \\
                 15.5: Integrands Involving the Logarithmic Function /
                 256 \\
                 16: Different Forms of Fourier Series \\
                 16.1: Fourier Series for f(x) on -[pi] [less than or
                 equal] x [less than or equal] [pi] / 257 \\
                 16.2: Fourier Series for f(x) on -L [less than or
                 equal] x [less than or equal] L / 258 \\
                 16.3: Fourier Series for f(x) on a [less than or equal]
                 x [less than or equal] b / 258 \\
                 16.4: Half-Range Fourier Cosine Series for f(x) on 0
                 [less than or equal] x [less than or equal] [pi] 259
                 \\
                 16.5: Half-Range Fourier Cosine Series for f(x) on 0
                 [less than or equal] x [less than or equal] L 259 \\
                 16.6: Half-Range Fourier Sine Series for f(x) on 0
                 [less than or equal] x [less than or equal] [pi] 260
                 \\
                 16.7: Half-Range Fourier Sine Series for f(x) on 0
                 [less than or equal] x [less than or equal] L 260 \\
                 16.8: Complex (Exponential) Fourier Series for f(x) on
                 -[pi] [less than or equal] x [less than or equal] [pi]
                 / 260 \\
                 16.9: Complex (Exponential) Fourier Series for f(x) on
                 -L [less than or equal] x [less than or equal] L 261
                 \\
                 16.10: Representative Examples of Fourier Series 261
                 \\
                 16.11: Fourier Series and Discontinuous Functions 265
                 \\
                 17: Bessel Functions \\
                 17.1: Bessel's Differential Equation / 269 \\
                 17.2: Series Expansions for J[subscript v](x) and
                 Y[subscript v](x) / 270 \\
                 17.3: Bessel Functions of Fractional Order / 272 \\
                 17.4: Asymptotic Representations for Bessel Functions /
                 273 \\
                 17.5: Zeros of Bessel Functions / 273 \\
                 17.6: Bessel's Modified Equation / 274 \\
                 17.7: Series Expansions for I[subscript v](x) and
                 K[subscript v](x) / 276 \\
                 17.8: Modified Bessel Functions of Fractional Order /
                 277 \\
                 17.9: Asymptotic Representations of Modified Bessel
                 Functions / 278 \\
                 17.10: Relationships between Bessel Functions 278 \\
                 17.11: Integral Representations of J[subscript n](x),
                 I[subscript n](x), and K[subscript n](x) / 281 \\
                 17.12: Indefinite Integrals of Bessel Functions 281 \\
                 17.13: Definite Integrals Involving Bessel Functions /
                 282 \\
                 17.14: Spherical Bessel Functions / 283 \\
                 18: Orthogonal Polynomials \\
                 18.2: Legendre Polynomials P[subscript n](x) 286 \\
                 18.3: Chebyshev Polynomials T[subscript n](x) and
                 U[subscript n](x) / 290 \\
                 18.4: Laguerre Polynomials L[subscript n](x) 294 \\
                 18.5: Hermite Polynomials H[subscript n](x) / 296 \\
                 19: Laplace Transformation \\
                 20: Fourier Transforms \\
                 21: Numerical Integration \\
                 21.1: Classical Methods / 315 \\
                 22: Solutions of Standard Ordinary Differential
                 Equations \\
                 22.2: Separation of Variables / 323 \\
                 22.3: Linear First-Order Equations / 323 \\
                 22.4: Bernoulli's Equation / 324 \\
                 22.5: Exact Equations / 325 \\
                 22.6: Homogeneous Equations / 325 \\
                 22.7: Linear Differential Equations / 326 \\
                 22.8: Constant Coefficient Linear Differential
                 Equations \\
                 Homogeneous Case / 327 \\
                 22.9: Linear Homogeneous Second-Order Equation 330 \\
                 22.10: Constant Coefficient Linear Differential
                 Equations \\
                 Inhomogeneous Case / 331 \\
                 22.11: Linear Inhomogeneous Second-Order Equation 333
                 \\
                 22.12: Determination of Particular Integrals by the
                 Method of Undetermined Coefficients / 334 \\
                 22.13: The Cauchy-Euler Equation / 336 \\
                 22.14: Legendre's Equation / 337 \\
                 22.15: Bessel's Equations / 337 \\
                 22.16: Power Series and Frobenius Methods / 339 \\
                 22.17: The Hypergeometric Equation / 344 \\
                 22.18: Numerical Methods / 345 \\
                 23: Vector Analysis \\
                 23.1: Scalars and Vectors / 353 \\
                 23.2: Scalar Products / 358 \\
                 23.3: Vector Products / 359 \\
                 23.4: Triple Products / 360 \\
                 23.5: Products of Four Vectors / 361 \\
                 23.6: Derivatives of Vector Functions of a Scalar t /
                 361 \\
                 23.7: Derivatives of Vector Functions of Several Scalar
                 Variables / 362 \\
                 23.8: Integrals of Vector Functions of a Scalar
                 Variable t / 363 \\
                 23.9: Line Integrals / 364 \\
                 23.10: Vector Integral Theorems / 366 \\
                 23.11: A Vector Rate of Change Theorem / 368 \\
                 23.12: Useful Vector Identities and Results / 368 \\
                 24: Systems of Orthogonal Coordinates \\
                 24.1: Curvilinear Coordinates / 369 \\
                 24.2: Vector Operators in Orthogonal Coordinates 371
                 \\
                 24.3: Systems of Orthogonal Coordinates / 371 \\
                 25: Partial Differential Equations and Special
                 Functions \\
                 25.1: Fundamental Ideas / 381 \\
                 25.2: Method of Separation of Variables / 385 \\
                 25.3: The Sturm--Liouville Problem and Special
                 Functions / 387 \\
                 25.4: A First-Order System and the Wave Equation 390
                 \\
                 25.5: Conservation Equations (Laws) / 391 \\
                 25.6: The Method of Characteristics / 392 \\
                 25.7: Discontinuous Solutions (Shocks) / 396 \\
                 25.8: Similarity Solutions / 398 \\
                 25.9: Burgers's Equation, the KdV Equation, and the
                 KdVB Equation / 400 \\
                 26: The z-Transform \\
                 26.1: The z-Transform and Transform Pairs / 403 \\
                 27: Numerical Approximation \\
                 27.2: Economization of Series / 411 \\
                 27.3: Pade Approximation / 413 \\
                 27.4: Finite Difference Approximations to Ordinary and
                 Partial Derivatives / 415",
}


