# bibtab

bibtype: article
filename: elefunt.bib
label: Qi:2019:CMD
author: Feng Qi and Ai-Qi Liu
title: Completely monotonic degrees for a difference between the logarithmic and psi functions
journal: j-J-COMPUT-APPL-MATH
volume: 361
pages: 366--371
day: 1
month: dec
monthnumber: 12
year: 2019
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Fri Sep 6 08:23:29 MDT 2019
bibtimestamp: 2019.09.06 08:23:29 MDT
URL: https://www.sciencedirect.com/science/article/pii/S0377042719302298
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Feng Qi and Ai-Qi Liu
rawtitle: Completely monotonic degrees for a difference between the logarithmic and psi functions
entry:
@Article{Qi:2019:CMD,
  author =       "Feng Qi and Ai-Qi Liu",
  title =        "Completely monotonic degrees for a difference between
                 the logarithmic and psi functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "361",
  number =       "??",
  pages =        "366--371",
  day =          "1",
  month =        dec,
  year =         "2019",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Fri Sep 6 08:23:29 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2015.bib",
  URL =          "https://www.sciencedirect.com/science/article/pii/S0377042719302298",
  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: Shterenlikht:2019:QIF
author: A. Shterenlikht
title: On Quality of Implementation of Fortran 2008 Complex Intrinsic Functions on Branch Cuts
journal: j-TOMS
volume: 45
number: 1
pages: 11:1--11:9
month: mar
monthnumber: 3
year: 2019
CODEN: ACMSCU
DOI: https://doi.org/10.1145/3301318
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Mon May 6 18:23:42 MDT 2019
bibtimestamp: 2019.05.06 18:23:42 MDT
URL: https://dl.acm.org/citation.cfm?id=3301318
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
articleno: 11
journalURL: https://dl.acm.org/loi/toms
rawauthor: A. Shterenlikht
rawtitle: On Quality of Implementation of {Fortran 2008} Complex Intrinsic Functions on Branch Cuts
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib

abstract:
Branch cuts in complex functions have important uses in fracture mechanics, jet flow, and aerofoil analysis. This article introduces tests for validating Fortran 2008 complex functions-LOG, SQRT, ASIN, ACOS, ATAN, ASINH, ACOSH, and ATANH-on branch cuts with arguments of all 3 IEEE floating-point binary formats: binary32, binary64, and binary128, including signed zero and signed infinity. Multiple test failures were revealed, such as wrong signs of results or unexpected overflow, underflow, or NaN. We conclude that the quality of implementation of these Fortran 2008 intrinsics in many compilers is not yet sufficient to remove the need for special code for branch cuts. The electronic appendix contains the full test results with 8 Fortran 2008 compilers: GCC, Flang, Cray, Oracle, PGI, Intel, NAG, and IBM, detailed derivations of the values of these functions on branch cuts and conformal maps of the branch cuts, to be used as a reference. The tests and the results are freely available from https://cmplx.sourceforge.io. This work will be of interest to engineers who use complex functions, as well as to compiler and math library developers.

rawabstract:
Branch cuts in complex functions have important uses in fracture mechanics, jet flow, and aerofoil analysis. This article introduces tests for validating Fortran 2008 complex functions-LOG, SQRT, ASIN, ACOS, ATAN, ASINH, ACOSH, and ATANH-on branch cuts with arguments of all 3 IEEE floating-point binary formats: binary32, binary64, and binary128, including signed zero and signed infinity. Multiple test failures were revealed, such as wrong signs of results or unexpected overflow, underflow, or NaN. We conclude that the quality of implementation of these Fortran 2008 intrinsics in many compilers is not yet sufficient to remove the need for special code for branch cuts. The electronic appendix contains the full test results with 8 Fortran 2008 compilers: GCC, Flang, Cray, Oracle, PGI, Intel, NAG, and IBM, detailed derivations of the values of these functions on branch cuts and conformal maps of the branch cuts, to be used as a reference. The tests and the results are freely available from https://cmplx.sourceforge.io. This work will be of interest to engineers who use complex functions, as well as to compiler and math library developers.

entry:
@Article{Shterenlikht:2019:QIF,
  author =       "A. Shterenlikht",
  title =        "On Quality of Implementation of {Fortran 2008} Complex
                 Intrinsic Functions on Branch Cuts",
  journal =      j-TOMS,
  volume =       "45",
  number =       "1",
  pages =        "11:1--11:9",
  month =        mar,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3301318",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon May 6 18:23:42 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3301318",
  abstract =     "Branch cuts in complex functions have important uses
                 in fracture mechanics, jet flow, and aerofoil analysis.
                 This article introduces tests for validating Fortran
                 2008 complex functions-LOG, SQRT, ASIN, ACOS, ATAN,
                 ASINH, ACOSH, and ATANH-on branch cuts with arguments
                 of all 3 IEEE floating-point binary formats: binary32,
                 binary64, and binary128, including signed zero and
                 signed infinity. Multiple test failures were revealed,
                 such as wrong signs of results or unexpected overflow,
                 underflow, or NaN. We conclude that the quality of
                 implementation of these Fortran 2008 intrinsics in many
                 compilers is not yet sufficient to remove the need for
                 special code for branch cuts. The electronic appendix
                 contains the full test results with 8 Fortran 2008
                 compilers: GCC, Flang, Cray, Oracle, PGI, Intel, NAG,
                 and IBM, detailed derivations of the values of these
                 functions on branch cuts and conformal maps of the
                 branch cuts, to be used as a reference. The tests and
                 the results are freely available from
                 https://cmplx.sourceforge.io. This work will be of
                 interest to engineers who use complex functions, as
                 well as to compiler and math library developers.",
  acknowledgement = ack-nhfb,
  articleno =    "11",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: inproceedings
filename: elefunt.bib
label: Volkova:2019:SAI
author: Anastasia Volkova and Jean-Michel Muller
title: Semi-Automatic Implementation of the Complementary Error Function
crossref: Takagi:2019:ISC
pages: 167--174
month: jun
monthnumber: 6
year: 2019
DOI: https://doi.org/10.1109/ARITH.2019.00039
bibdate: Fri Jan 31 08:18:07 2020
bibtimestamp: 2020.01.31 08:18:07 ???
acknowledgement: ack-nhfb
rawauthor: Anastasia Volkova and Jean-Michel Muller
rawtitle: Semi-Automatic Implementation of the Complementary Error Function
abstract:
The normal and complementary error functions are ubiquitous special functions for any mathematical library. They have a wide range of applications. Practical applications call for customized implementations that have strict accuracy requirements. Accurate numerical implementation of these functions is, however, non-trivial. In particular, the complementary error function erfc for large positive arguments heavily suffers from cancellation, which is largely due to its asymptotic behavior. We provide a semi-automatic code generator for the erfc function which is parameterized by the user-given bound on the relative error. Our solution exploits the asymptotic expression of erfc and leverages the automatic code generator Metalibm that provides accurate polynomial approximations. A fine-grained a priori error analysis provides a libm developer with the required accuracy for each step of the evaluation. In critical parts, we exploit double-word arithmetic to achieve implementations that are fast, yet accurate up to 50 bits, even for large input arguments. We demonstrate that for high required accuracies the automatically generated code has performance comparable to that of the standard libm and for lower ones our code demonstrated roughly 25% speedup.

keywords:
a priori error analysis; ARITH-26; asymptotic behavior; asymptotic expression; complementary error functions; Digital arithmetic; Error analysis; error analysis; error function; floating-point arithmetic; Generators; Libraries; Lips; mathematical library; Metalibm; normal error functions; polynomial approximation; polynomial approximations; program compilers; semi-automated code generation; semiautomatic code generator; semiautomatic implementation; Standards; Tools; ubiquitous special functions

rawabstract:
The normal and complementary error functions are ubiquitous special functions for any mathematical library. They have a wide range of applications. Practical applications call for customized implementations that have strict accuracy requirements. Accurate numerical implementation of these functions is, however, non-trivial. In particular, the complementary error function erfc for large positive arguments heavily suffers from cancellation, which is largely due to its asymptotic behavior. We provide a semi-automatic code generator for the erfc function which is parameterized by the user-given bound on the relative error. Our solution exploits the asymptotic expression of erfc and leverages the automatic code generator Metalibm that provides accurate polynomial approximations. A fine-grained a priori error analysis provides a libm developer with the required accuracy for each step of the evaluation. In critical parts, we exploit double-word arithmetic to achieve implementations that are fast, yet accurate up to 50 bits, even for large input arguments. We demonstrate that for high required accuracies the automatically generated code has performance comparable to that of the standard libm and for lower ones our code demonstrated roughly 25\% speedup.

entry:
@InProceedings{Volkova:2019:SAI,
  author =       "Anastasia Volkova and Jean-Michel Muller",
  title =        "Semi-Automatic Implementation of the Complementary
                 Error Function",
  crossref =     "Takagi:2019:ISC",
  pages =        "167--174",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00039",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The normal and complementary error functions are
                 ubiquitous special functions for any mathematical
                 library. They have a wide range of applications.
                 Practical applications call for customized
                 implementations that have strict accuracy requirements.
                 Accurate numerical implementation of these functions
                 is, however, non-trivial. In particular, the
                 complementary error function erfc for large positive
                 arguments heavily suffers from cancellation, which is
                 largely due to its asymptotic behavior. We provide a
                 semi-automatic code generator for the erfc function
                 which is parameterized by the user-given bound on the
                 relative error. Our solution exploits the asymptotic
                 expression of erfc and leverages the automatic code
                 generator Metalibm that provides accurate polynomial
                 approximations. A fine-grained a priori error analysis
                 provides a libm developer with the required accuracy
                 for each step of the evaluation. In critical parts, we
                 exploit double-word arithmetic to achieve
                 implementations that are fast, yet accurate up to 50
                 bits, even for large input arguments. We demonstrate
                 that for high required accuracies the automatically
                 generated code has performance comparable to that of
                 the standard libm and for lower ones our code
                 demonstrated roughly 25\% speedup.",
  acknowledgement = ack-nhfb,
  keywords =     "a priori error analysis; ARITH-26; asymptotic
                 behavior; asymptotic expression; complementary error
                 functions; Digital arithmetic; Error analysis; error
                 analysis; error function; floating-point arithmetic;
                 Generators; Libraries; Lips; mathematical library;
                 Metalibm; normal error functions; polynomial
                 approximation; polynomial approximations; program
                 compilers; semi-automated code generation;
                 semiautomatic code generator; semiautomatic
                 implementation; Standards; Tools; ubiquitous special
                 functions",
}


bibtype: article
filename: elefunt.bib
label: Walczyk:2019:MFI
author: Cezary J. Walczyk and Leonid V. Moroz and Jan L. Cieslinski
title: A Modification of the Fast Inverse Square Root Algorithm
journal: Computation
volume: 7
number: 3
pages: 41
month: aug
monthnumber: 8
year: 2019
DOI: https://doi.org/10.3390/computation7030041
ISSN: 2079-3197 OR 20793197
ISSNL: 2079-3197 OR 20793197
bibdate: Thu Apr 10 15:20:23 2025
bibtimestamp: 2025.04.10 15:20:23 ???
acknowledgement: ack-nhfb
rawauthor: Cezary J. Walczyk and Leonid V. Moroz and Jan L. Cie{\'s}li{\'n}ski
rawtitle: A Modification of the Fast Inverse Square Root Algorithm
entry:
@Article{Walczyk:2019:MFI,
  author =       "Cezary J. Walczyk and Leonid V. Moroz and Jan L.
                 Cie{\'s}li{\'n}ski",
  title =        "A Modification of the Fast Inverse Square Root
                 Algorithm",
  journal =      "Computation",
  volume =       "7",
  number =       "3",
  pages =        "41",
  month =        aug,
  year =         "2019",
  DOI =          "https://doi.org/10.3390/computation7030041",
  ISSN =         "2079-3197",
  ISSN-L =       "2079-3197",
  bibdate =      "Thu Apr 10 15:20:23 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Zaghloul:2019:RO
author: Mofreh R. Zaghloul
journal: j-TOMS
volume: 45
number: 2
pages: 24:1--24:3
month: apr
monthnumber: 4
year: 2019
CODEN: ACMSCU
DOI: https://doi.org/10.1145/3309681
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Mon May 6 18:23:42 MDT 2019
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib
bibtimestamp: 2019.05.06 18:23:42 MDT
URL: https://dl.acm.org/citation.cfm?id=3309681
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
articleno: 24
journalURL: https://dl.acm.org/loi/toms
rawauthor: Mofreh R. Zaghloul
title:
Remark on `Algorithm 680: Evaluation of the Complex Error Function': Cause and Remedy for the Loss of Accuracy Near the Real Axis

abstract:
In this remark, we identify the cause of the loss of accuracy in the computation of the Faddeyeva function, $ w(z) $, near the real axis when using Algorithm 680. We provide a simple correction to this problem that allows us to restore this code as one of the important reference routines for accuracy comparisons.

rawabstract:
In this remark, we identify the cause of the loss of accuracy in the computation of the Faddeyeva function, $ w(z) $, near the real axis when using Algorithm 680. We provide a simple correction to this problem that allows us to restore this code as one of the important reference routines for accuracy comparisons.

rawtitle:
Remark on {`Algorithm 680: Evaluation of the Complex Error Function': Cause and Remedy for the Loss of Accuracy Near the Real Axis}

entry:
@Article{Zaghloul:2019:RO,
  author =       "Mofreh R. Zaghloul",
  title =        "Remark on {`Algorithm 680: Evaluation of the Complex
                 Error Function': Cause and Remedy for the Loss of
                 Accuracy Near the Real Axis}",
  journal =      j-TOMS,
  volume =       "45",
  number =       "2",
  pages =        "24:1--24:3",
  month =        apr,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3309681",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon May 6 18:23:42 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3309681",
  abstract =     "In this remark, we identify the cause of the loss of
                 accuracy in the computation of the Faddeyeva function,
                 $ w(z) $, near the real axis when using Algorithm 680.
                 We provide a simple correction to this problem that
                 allows us to restore this code as one of the important
                 reference routines for accuracy comparisons.",
  acknowledgement = ack-nhfb,
  articleno =    "24",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Abergel:2020:AFA
author: Remy Abergel and Lionel Moisan
title: Algorithm 1006: Fast and Accurate Evaluation of a Generalized Incomplete Gamma Function
journal: j-TOMS
volume: 46
number: 1
pages: 10:1--10:24
month: mar
monthnumber: 3
year: 2020
CODEN: ACMSCU
DOI: https://doi.org/10.1145/3365983
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Apr 7 10:39:23 MDT 2020
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib
bibtimestamp: 2020.04.07 10:39:23 MDT
URL: https://dl.acm.org/doi/abs/10.1145/3365983
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
articleno: 10
journalURL: https://dl.acm.org/loi/toms
rawauthor: R{\'e}my Abergel and Lionel Moisan
rawtitle: {Algorithm 1006}: Fast and Accurate Evaluation of a Generalized Incomplete Gamma Function
abstract:
We present a computational procedure to evaluate the integral $ int ^y_x s^p - 1 e^- mu s d s $ for $ 0 leq x < y leq + infty $, $ mu = pm 1 $, $ p > 0 $, which generalizes the lower $ (x = 0) $ and upper $ (y = + infty ) $ incomplete gamma functions. To allow for large values of $x$, $y$, and $p$ while avoiding under / overflow issues in the standard double precision floating point arithmetic, we use an explicit normalization that is much more efficient than the classical ratio with the complete gamma function. The generalized incomplete gamma function is estimated with continued fractions, with integrations by parts, or, when $ x approx y$, with the Romberg numerical integration algorithm. We show that the accuracy reached by our algorithm improves a recent state-of-the-art method by two orders of magnitude, and it is essentially optimal considering the limitations imposed by floating point arithmetic. Moreover, the admissible parameter range of our algorithm $ (0 leq p, x, y leq 10^15)$ is much larger than competing algorithms, and its robustness is assessed through massive usage in an image processing application.

rawabstract:
We present a computational procedure to evaluate the integral $ \int^y_x s^{p - 1} e^{- \mu s} \, d s $ for $ 0 \leq x < y \leq + \infty $, $ \mu = \pm 1 $, $ p > 0 $, which generalizes the lower $ (x = 0) $ and upper $ (y = + \infty) $ incomplete gamma functions. To allow for large values of $x$, $y$, and $p$ while avoiding under\slash overflow issues in the standard double precision floating point arithmetic, we use an explicit normalization that is much more efficient than the classical ratio with the complete gamma function. The generalized incomplete gamma function is estimated with continued fractions, with integrations by parts, or, when $ x \approx y$, with the Romberg numerical integration algorithm. We show that the accuracy reached by our algorithm improves a recent state-of-the-art method by two orders of magnitude, and it is essentially optimal considering the limitations imposed by floating point arithmetic. Moreover, the admissible parameter range of our algorithm $ (0 \leq p, x, y \leq 10^{15})$ is much larger than competing algorithms, and its robustness is assessed through massive usage in an image processing application.

entry:
@Article{Abergel:2020:AFA,
  author =       "R{\'e}my Abergel and Lionel Moisan",
  title =        "{Algorithm 1006}: Fast and Accurate Evaluation of a
                 Generalized Incomplete Gamma Function",
  journal =      j-TOMS,
  volume =       "46",
  number =       "1",
  pages =        "10:1--10:24",
  month =        mar,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3365983",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 7 10:39:23 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/abs/10.1145/3365983",
  abstract =     "We present a computational procedure to evaluate the
                 integral $ \int^y_x s^{p - 1} e^{- \mu s} \, d s $ for
                 $ 0 \leq x < y \leq + \infty $, $ \mu = \pm 1 $, $ p >
                 0 $, which generalizes the lower $ (x = 0) $ and upper
                 $ (y = + \infty) $ incomplete gamma functions. To allow
                 for large values of $x$, $y$, and $p$ while avoiding
                 under\slash overflow issues in the standard double
                 precision floating point arithmetic, we use an explicit
                 normalization that is much more efficient than the
                 classical ratio with the complete gamma function. The
                 generalized incomplete gamma function is estimated with
                 continued fractions, with integrations by parts, or,
                 when $ x \approx y$, with the Romberg numerical
                 integration algorithm. We show that the accuracy
                 reached by our algorithm improves a recent
                 state-of-the-art method by two orders of magnitude, and
                 it is essentially optimal considering the limitations
                 imposed by floating point arithmetic. Moreover, the
                 admissible parameter range of our algorithm $ (0 \leq
                 p, x, y \leq 10^{15})$ is much larger than competing
                 algorithms, and its robustness is assessed through
                 massive usage in an image processing application.",
  acknowledgement = ack-nhfb,
  articleno =    "10",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Adell:2020:RAE
author: Jose A. Adell and Alberto Lekuona
title: Rational approximation to Euler's constant at a geometric rate of convergence
journal: j-MATH-COMPUT
volume: 89
number: 325
pages: 2553--2561
month: jan
monthnumber: 1
year: 2020
CODEN: MCMPAF
DOI: https://doi.org/10.1090/mcom/3528
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Jul 14 07:56:12 MDT 2020
bibtimestamp: 2020.07.14 07:56:12 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Jos{\'e} A. Adell and Alberto Lekuona
rawtitle: Rational approximation to {Euler}'s constant at a geometric rate of convergence
bibsource:
http://www.ams.org/mcom/2020-89-325; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp2020.bib

URL:
https://www.ams.org/AMSMathViewer; https://www.ams.org/journals/mcom/2020-89-325/S0025-5718-2020-03528-5; https://www.ams.org/journals/mcom/2020-89-325/S0025-5718-2020-03528-5/S0025-5718-2020-03528-5.pdf; https://www.ams.org/mathscinet/search/authors.html?mrauthid=340766; https://www.ams.org/mathscinet/search/authors.html?mrauthid=663604

entry:
@Article{Adell:2020:RAE,
  author =       "Jos{\'e} A. Adell and Alberto Lekuona",
  title =        "Rational approximation to {Euler}'s constant at a
                 geometric rate of convergence",
  journal =      j-MATH-COMPUT,
  volume =       "89",
  number =       "325",
  pages =        "2553--2561",
  month =        jan,
  year =         "2020",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.1090/mcom/3528",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Jul 14 07:56:12 MDT 2020",
  bibsource =    "http://www.ams.org/mcom/2020-89-325;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp2020.bib",
  URL =          "https://www.ams.org/AMSMathViewer;
                 https://www.ams.org/journals/mcom/2020-89-325/S0025-5718-2020-03528-5;
                 https://www.ams.org/journals/mcom/2020-89-325/S0025-5718-2020-03528-5/S0025-5718-2020-03528-5.pdf;
                 https://www.ams.org/mathscinet/search/authors.html?mrauthid=340766;
                 https://www.ams.org/mathscinet/search/authors.html?mrauthid=663604",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Chin:2020:PPW
author: Wooyoung Chin
title: A Probabilistic Proof of a Wallis-type Formula for the Gamma Function
journal: j-AMER-MATH-MONTHLY
volume: 127
number: 1
pages: 75--79
year: 2020
CODEN: AMMYAE
DOI: https://doi.org/10.1080/00029890.2020.1668708
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
bibdate: Mon Dec 13 15:45:45 MST 2021
bibtimestamp: 2021.12.13 15:45:45 MST
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
journalURL: http://www.jstor.org/journals/00029890.html; https://www.tandfonline.com/loi/uamm20
onlinedate: 19 Dec 2019
rawauthor: Wooyoung Chin
rawtitle: A Probabilistic Proof of a {Wallis}-type Formula for the Gamma Function
bibsource:
https://www.math.utah.edu/pub/tex/bib/amermathmonthly2020.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Chin:2020:PPW,
  author =       "Wooyoung Chin",
  title =        "A Probabilistic Proof of a {Wallis}-type Formula for
                 the Gamma Function",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "127",
  number =       "1",
  pages =        "75--79",
  year =         "2020",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.1080/00029890.2020.1668708",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Dec 13 15:45:45 MST 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/amermathmonthly2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html;
                 https://www.tandfonline.com/loi/uamm20",
  onlinedate =   "19 Dec 2019",
}


bibtype: article
filename: elefunt.bib
label: Ewart:2020:PES
author: Timothee Ewart and Francesco Cremonesi and Felix Schurmann and Fabien Delalondre
title: Polynomial Evaluation on Superscalar Architecture, Applied to the Elementary Function $ e^x $
journal: j-TOMS
volume: 46
number: 3
pages: 28:1--28:22
month: sep
monthnumber: 9
year: 2020
CODEN: ACMSCU
DOI: https://doi.org/10.1145/3408893
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sat Sep 26 07:28:19 MDT 2020
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib
bibtimestamp: 2020.09.26 07:28:19 MDT
URL: https://dl.acm.org/doi/10.1145/3408893
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
articleno: 28
journalURL: https://dl.acm.org/loi/toms
rawauthor: Timoth{\'e}e Ewart and Francesco Cremonesi and Felix Sch{\"u}rmann and Fabien Delalondre
rawtitle: Polynomial Evaluation on Superscalar Architecture, Applied to the Elementary Function $ e^x $
abstract:
The evaluation of small degree polynomials is critical for the computation of elementary functions. It has been extensively studied and is well documented. In this article, we evaluate existing methods for polynomial evaluation on superscalar architecture. In addition, we have completed this work with a factorization method, which is surprisingly neglected in the literature. This work focuses on out-of-order Intel processors, amongst others, of which computational units are available. Moreover, we applied our work on the elementary function $ e^x $ that requires, in the current implementation, an evaluation of a polynomial of degree 10 for a satisfying precision and performance. Our results show that the factorization scheme is the fastest in benchmarks, and that latency and throughput are intrinsically dependent on each other on superscalar architecture.

rawabstract:
The evaluation of small degree polynomials is critical for the computation of elementary functions. It has been extensively studied and is well documented. In this article, we evaluate existing methods for polynomial evaluation on superscalar architecture. In addition, we have completed this work with a factorization method, which is surprisingly neglected in the literature. This work focuses on out-of-order Intel processors, amongst others, of which computational units are available. Moreover, we applied our work on the elementary function $ e^x $ that requires, in the current implementation, an evaluation of a polynomial of degree 10 for a satisfying precision and performance. Our results show that the factorization scheme is the fastest in benchmarks, and that latency and throughput are intrinsically dependent on each other on superscalar architecture.

entry:
@Article{Ewart:2020:PES,
  author =       "Timoth{\'e}e Ewart and Francesco Cremonesi and Felix
                 Sch{\"u}rmann and Fabien Delalondre",
  title =        "Polynomial Evaluation on Superscalar Architecture,
                 Applied to the Elementary Function $ e^x $",
  journal =      j-TOMS,
  volume =       "46",
  number =       "3",
  pages =        "28:1--28:22",
  month =        sep,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3408893",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Sep 26 07:28:19 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3408893",
  abstract =     "The evaluation of small degree polynomials is critical
                 for the computation of elementary functions. It has
                 been extensively studied and is well documented. In
                 this article, we evaluate existing methods for
                 polynomial evaluation on superscalar architecture. In
                 addition, we have completed this work with a
                 factorization method, which is surprisingly neglected
                 in the literature. This work focuses on out-of-order
                 Intel processors, amongst others, of which
                 computational units are available. Moreover, we applied
                 our work on the elementary function $ e^x $ that
                 requires, in the current implementation, an evaluation
                 of a polynomial of degree 10 for a satisfying precision
                 and performance. Our results show that the
                 factorization scheme is the fastest in benchmarks, and
                 that latency and throughput are intrinsically dependent
                 on each other on superscalar architecture.",
  acknowledgement = ack-nhfb,
  articleno =    "28",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Gil:2020:NEA
author: A. Gil and J. Segura and N. M. Temme
title: Numerical evaluation of Airy-type integrals arising in uniform asymptotic analysis
journal: j-J-COMPUT-APPL-MATH
volume: 371
pages: Article 112717
month: jun
monthnumber: 6
year: 2020
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Wed May 13 06:58:32 MDT 2020
bibtimestamp: 2020.05.13 06:58:32 MDT
URL: http://www.sciencedirect.com/science/article/pii/S037704272030008X
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: A. Gil and J. Segura and N. M. Temme
rawtitle: Numerical evaluation of {Airy}-type integrals arising in uniform asymptotic analysis
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2020.bib

entry:
@Article{Gil:2020:NEA,
  author =       "A. Gil and J. Segura and N. M. Temme",
  title =        "Numerical evaluation of {Airy}-type integrals arising
                 in uniform asymptotic analysis",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "371",
  number =       "??",
  pages =        "Article 112717",
  month =        jun,
  year =         "2020",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Wed May 13 06:58:32 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2020.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S037704272030008X",
  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: Gimbutas:2020:EAF
author: Zydrunas Gimbutas and Shidong Jiang and Li-Shi Luo
title: Evaluation of Abramowitz functions in the right half of the complex plane
journal: j-J-COMPUT-PHYS
volume: 405
pages: Article 109169
day: 15
month: mar
monthnumber: 3
year: 2020
CODEN: JCTPAH
DOI: https://doi.org/10.1016/j.jcp.2019.109169
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Mon Mar 9 18:28:24 MDT 2020
bibtimestamp: 2020.03.09 18:28:24 MDT
URL: http://www.sciencedirect.com/science/article/pii/S0021999119308745
fjournal: Journal of Computational Physics
keywords: Abramowitz functions; Laurent series; Least squares method
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991
rawauthor: Zydrunas Gimbutas and Shidong Jiang and Li-Shi Luo
rawtitle: Evaluation of {Abramowitz} functions in the right half of the complex plane
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jcomputphys2020.bib

remark:
The Abramowitz functions of order n, defined by $ J_n(z) = int _0^infty t^n exp ( - t^2 - z / t) d t $, for $ n in mathbb Z $.

entry:
@Article{Gimbutas:2020:EAF,
  author =       "Zydrunas Gimbutas and Shidong Jiang and Li-Shi Luo",
  title =        "Evaluation of {Abramowitz} functions in the right half
                 of the complex plane",
  journal =      j-J-COMPUT-PHYS,
  volume =       "405",
  number =       "??",
  pages =        "Article 109169",
  day =          "15",
  month =        mar,
  year =         "2020",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/j.jcp.2019.109169",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Mon Mar 9 18:28:24 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys2020.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0021999119308745",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991",
  keywords =     "Abramowitz functions; Laurent series; Least squares
                 method",
  remark =       "The Abramowitz functions of order n, defined by $
                 J_n(z) = \int_0^\infty t^n \exp ( - t^2 - z / t) \, d t
                 $, for $ n \in \mathbb {Z} $.",
}


bibtype: article
filename: elefunt.bib
label: Godunov:2020:ACC
author: A. Godunov
title: Algorithms for Calculating Correctly Rounded Exponential Function in Double-Precision Arithmetic
journal: j-IEEE-TRANS-COMPUT
volume: 69
number: 9
pages: 1388--1400
month: sep
monthnumber: 9
year: 2020
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.2020.2972901
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Aug 12 14:58:16 2020
bibtimestamp: 2020.08.12 14:58:16 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: A. Godunov
rawtitle: Algorithms for Calculating Correctly Rounded Exponential Function in Double-Precision Arithmetic
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/ieeetranscomput2020.bib

abstract:
Correct rounding provides the best approximation of the exponential function by double-precision numbers. To obtain the correctly rounded exponential of some arguments, the exponential should be calculated with high accuracy. For small arguments, even higher accuracy is required. This article presents simple and very fast algorithms for small arguments. Yet another algorithm presented here demonstrates a good maximum execution time, which may be important for critical applications. This algorithm can be combined with some other already existing algorithms to achieve the best maximum and average execution times. All proposed algorithms calculate the correctly rounded exponential function for all rounding modes and use only double-precision arithmetic for computation. In the argument reduction step, precalculated tables are used. Test implementations of these algorithms were developed in C language and are portable. Full proofs are presented either in this article itself or in its appendices.

rawabstract:
Correct rounding provides the best approximation of the exponential function by double-precision numbers. To obtain the correctly rounded exponential of some arguments, the exponential should be calculated with high accuracy. For small arguments, even higher accuracy is required. This article presents simple and very fast algorithms for small arguments. Yet another algorithm presented here demonstrates a good maximum execution time, which may be important for critical applications. This algorithm can be combined with some other already existing algorithms to achieve the best maximum and average execution times. All proposed algorithms calculate the correctly rounded exponential function for all rounding modes and use only double-precision arithmetic for computation. In the argument reduction step, precalculated tables are used. Test implementations of these algorithms were developed in C language and are portable. Full proofs are presented either in this article itself or in its appendices.

entry:
@Article{Godunov:2020:ACC,
  author =       "A. Godunov",
  title =        "Algorithms for Calculating Correctly Rounded
                 Exponential Function in Double-Precision Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "69",
  number =       "9",
  pages =        "1388--1400",
  month =        sep,
  year =         "2020",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2020.2972901",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Aug 12 14:58:16 2020",
  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/ieeetranscomput2020.bib",
  abstract =     "Correct rounding provides the best approximation of
                 the exponential function by double-precision numbers.
                 To obtain the correctly rounded exponential of some
                 arguments, the exponential should be calculated with
                 high accuracy. For small arguments, even higher
                 accuracy is required. This article presents simple and
                 very fast algorithms for small arguments. Yet another
                 algorithm presented here demonstrates a good maximum
                 execution time, which may be important for critical
                 applications. This algorithm can be combined with some
                 other already existing algorithms to achieve the best
                 maximum and average execution times. All proposed
                 algorithms calculate the correctly rounded exponential
                 function for all rounding modes and use only
                 double-precision arithmetic for computation. In the
                 argument reduction step, precalculated tables are used.
                 Test implementations of these algorithms were developed
                 in C language and are portable. Full proofs are
                 presented either in this article itself or in its
                 appendices.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: elefunt.bib
label: Harper:2020:AGH
author: J. F. Harper
title: Asymptotics of a Gauss hypergeometric function with two large parameters: a new case
journal: j-ANZIAM-J
volume: 62
number: 4
pages: 446--452
month: oct
monthnumber: 10
year: 2020
CODEN: AJNOA2
DOI: https://doi.org/10.1017/S1446181119000166
ISSN: 1446-1811 (print), 1446-8735 (electronic) OR 14461811 (print), 14468735 (electronic)
ISSNL: 1446-1811 OR 14461811
bibdate: Fri May 14 17:04:43 MDT 2021
bibtimestamp: 2021.05.14 17:04:43 MDT
fjournal: The ANZIAM Journal. The Australian & New Zealand Industrial and Applied Mathematics Journal
acknowledgement: ack-nhfb
ajournal: ANZIAM J.
journalURL: http://journals.cambridge.org/action/displayJournal?jid=ANZ
onlinedate: 10 December 2019
rawauthor: J. F. Harper
rawtitle: Asymptotics of a {Gauss} hypergeometric function with two large parameters: a new case
URL:
https://www.cambridge.org/core/journals/anziam-journal/article/asymptotics-of-a-gauss-hypergeometric-function-with-two-large-parameters-a-new-case/32B40986E7DB85F500FC9024F846E527

entry:
@Article{Harper:2020:AGH,
  author =       "J. F. Harper",
  title =        "Asymptotics of a {Gauss} hypergeometric function with
                 two large parameters: a new case",
  journal =      j-ANZIAM-J,
  volume =       "62",
  number =       "4",
  pages =        "446--452",
  month =        oct,
  year =         "2020",
  CODEN =        "AJNOA2",
  DOI =          "https://doi.org/10.1017/S1446181119000166",
  ISSN =         "1446-1811 (print), 1446-8735 (electronic)",
  ISSN-L =       "1446-1811",
  bibdate =      "Fri May 14 17:04:43 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/anziamj.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://www.cambridge.org/core/journals/anziam-journal/article/asymptotics-of-a-gauss-hypergeometric-function-with-two-large-parameters-a-new-case/32B40986E7DB85F500FC9024F846E527",
  acknowledgement = ack-nhfb,
  ajournal =     "ANZIAM J.",
  fjournal =     "The ANZIAM Journal. The Australian \& New Zealand
                 Industrial and Applied Mathematics Journal",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=ANZ",
  onlinedate =   "10 December 2019",
}


bibtype: article
filename: elefunt.bib
label: Hrycak:2020:ELP
author: Tomasz Hrycak and Sebastian Schmutzhard
title: Evaluation of Legendre polynomials by a three-term recurrence in floating-point arithmetic
journal: j-IMA-J-NUMER-ANAL
volume: 40
number: 1
pages: 587--605
month: jan
monthnumber: 1
year: 2020
CODEN: IJNADH
DOI: https://doi.org/10.1093/imanum/dry079
ISSN: 0272-4979 (print), 1464-3642 (electronic) OR 02724979 (print), 14643642 (electronic)
ISSNL: 0272-4979 OR 02724979
bibdate: Sat Feb 29 14:22:43 MST 2020
bibtimestamp: 2020.02.29 14:22:43 MST
URL: http://academic.oup.com/imajna/article/40/1/587/5162990
fjournal: IMA Journal of Numerical Analysis
acknowledgement: ack-nhfb
journalURL: http://imajna.oxfordjournals.org/content/by/year
rawauthor: Tomasz Hrycak and Sebastian Schmutzhard
rawtitle: Evaluation of {Legendre} polynomials by a three-term recurrence in floating-point arithmetic
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/imajnumeranal.bib

entry:
@Article{Hrycak:2020:ELP,
  author =       "Tomasz Hrycak and Sebastian Schmutzhard",
  title =        "Evaluation of {Legendre} polynomials by a three-term
                 recurrence in floating-point arithmetic",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "40",
  number =       "1",
  pages =        "587--605",
  month =        jan,
  year =         "2020",
  CODEN =        "IJNADH",
  DOI =          "https://doi.org/10.1093/imanum/dry079",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  bibdate =      "Sat Feb 29 14:22:43 MST 2020",
  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/imajnumeranal.bib",
  URL =          "http://academic.oup.com/imajna/article/40/1/587/5162990",
  acknowledgement = ack-nhfb,
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
}


bibtype: article
filename: elefunt.bib
label: Jablonski:2020:IAC
author: A. Jablonski
title: Improved algorithm for calculating high accuracy values of the Chandrasekhar function
journal: j-COMP-PHYS-COMM
volume: 251
pages: Article 107237
month: jun
monthnumber: 6
year: 2020
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/j.cpc.2020.107237
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Fri May 29 07:03:02 MDT 2020
bibtimestamp: 2020.05.29 07:03:02 MDT
URL: http://www.sciencedirect.com/science/article/pii/S0010465520300709
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: A. Jablonski
rawtitle: Improved algorithm for calculating high accuracy values of the {Chandrasekhar} function
bibsource:
https://www.math.utah.edu/pub/tex/bib/compphyscomm2020.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Jablonski:2020:IAC,
  author =       "A. Jablonski",
  title =        "Improved algorithm for calculating high accuracy
                 values of the {Chandrasekhar} function",
  journal =      j-COMP-PHYS-COMM,
  volume =       "251",
  number =       "??",
  pages =        "Article 107237",
  month =        jun,
  year =         "2020",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2020.107237",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Fri May 29 07:03:02 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465520300709",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: article
filename: elefunt.bib
label: Johansson:2020:CLW
author: Fredrik Johansson
title: Computing the Lambert $W$ function in arbitrary-precision complex interval arithmetic
journal: j-NUMER-ALGORITHMS
volume: 83
number: 1
pages: 221--242
month: jan
monthnumber: 1
year: 2020
CODEN: NUALEG
DOI: https://doi.org/10.1007/s11075-019-00678-x
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
bibdate: Wed Jan 22 08:40:22 MST 2020
bibtimestamp: 2020.01.22 08:40:22 MST
fjournal: Numerical Algorithms
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/11075
rawauthor: Fredrik Johansson
rawtitle: Computing the {Lambert $W$} function in arbitrary-precision complex interval arithmetic
bibsource:
http://link.springer.com/journal/11075/83/1; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib

entry:
@Article{Johansson:2020:CLW,
  author =       "Fredrik Johansson",
  title =        "Computing the {Lambert $W$} function in
                 arbitrary-precision complex interval arithmetic",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "83",
  number =       "1",
  pages =        "221--242",
  month =        jan,
  year =         "2020",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-019-00678-x",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Wed Jan 22 08:40:22 MST 2020",
  bibsource =    "http://link.springer.com/journal/11075/83/1;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}


bibtype: incollection
filename: elefunt.bib
label: Johansson:2020:FSL
author: Fredrik Johansson
title: FunGrim: A Symbolic Library for Special Functions
crossref: Bigatti:2020:MSI
pages: 315--323
year: 2020
DOI: https://doi.org/10.1007/978-3-030-52200-1_31
bibdate: Sat Sep 23 06:47:37 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2023.09.23 06:47:37 ???
acknowledgement: ack-nhfb
rawauthor: Fredrik Johansson
rawtitle: {FunGrim}: A Symbolic Library for Special Functions
entry:
@InCollection{Johansson:2020:FSL,
  author =       "Fredrik Johansson",
  title =        "{FunGrim}: A Symbolic Library for Special Functions",
  crossref =     "Bigatti:2020:MSI",
  pages =        "315--323",
  year =         "2020",
  DOI =          "https://doi.org/10.1007/978-3-030-52200-1_31",
  bibdate =      "Sat Sep 23 06:47:37 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Johnson:2020:EAHa
author: Jeff Johnson
title: Efficient, arbitrarily high precision hardware logarithmic arithmetic for linear algebra
journal: arxiv.org
pages: 1--8
day: 14
month: may
monthnumber: 5
year: 2020
bibdate: Tue Jul 06 18:17:13 2021
bibtimestamp: 2021.07.06 18:17:13 ???
URL: https://arxiv.org/pdf/2004.09313.pdf
remark: Published in cite Johnson:2020:EAHb.
acknowledgement: ack-nhfb
rawauthor: Jeff Johnson
rawtitle: Efficient, arbitrarily high precision hardware logarithmic arithmetic for linear algebra
bibsource:
https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
The logarithmic number system (LNS) is arguably not broadly used due to exponential circuit overheads for summation tables relative to arithmetic precision. Methods to reduce this overhead have been proposed, yet still yield designs with high chip area and power requirements. Use remains limited to lower precision or high multiply/add ratio cases, while much of linear algebra (near 1:1 multiply/add ratio) does not qualify.par We present a dual-base approximate logarithmic arithmetic comparable to floating point in use, yet unlike LNS it is easily fully pipelined, extendable to arbitrary precision with $ O(n^2) $ overhead, and energy efficient at a 1:1 multiply/add ratio.Compared to float32 or float64 vector inner product with FMA, our design is respectively $ 2.3 times $ and $ 4.6 times $ more energy efficient in 7 nm CMOS. It depends on exp and log evaluation $ 5.4 times $ and $ 3.2 times $ more energy efficient, at $ 0.23 times $ and $ 0.37 times $ the chip area for equivalent accuracy versus standard hyperbolic CORDIC using shift-and-add and approximated ODE integration in the style of Revol and Yakoubsohn. This technique is a novel alternative for low power, high precision hardened linear algebra in computer vision, graphics and machine learning applications.

keywords:
approximate arithmetic; elementary function evaluation; hardware linear algebra; logarithmic arithmetic

rawabstract:
The logarithmic number system (LNS) is arguably not broadly used due to exponential circuit overheads for summation tables relative to arithmetic precision. Methods to reduce this overhead have been proposed, yet still yield designs with high chip area and power requirements. Use remains limited to lower precision or high multiply/add ratio cases, while much of linear algebra (near 1:1 multiply/add ratio) does not qualify.\par We present a dual-base approximate logarithmic arithmetic comparable to floating point in use, yet unlike LNS it is easily fully pipelined, extendable to arbitrary precision with $ O(n^2) $ overhead, and energy efficient at a 1:1 multiply/add ratio.Compared to float32 or float64 vector inner product with FMA, our design is respectively $ 2.3 \times $ and $ 4.6 \times $ more energy efficient in 7 nm CMOS. It depends on exp and log evaluation $ 5.4 \times $ and $ 3.2 \times $ more energy efficient, at $ 0.23 \times $ and $ 0.37 \times $ the chip area for equivalent accuracy versus standard hyperbolic CORDIC using shift-and-add and approximated ODE integration in the style of Revol and Yakoubsohn. This technique is a novel alternative for low power, high precision hardened linear algebra in computer vision, graphics and machine learning applications.

entry:
@Article{Johnson:2020:EAHa,
  author =       "Jeff Johnson",
  title =        "Efficient, arbitrarily high precision hardware
                 logarithmic arithmetic for linear algebra",
  journal =      "arxiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--8",
  day =          "14",
  month =        may,
  year =         "2020",
  bibdate =      "Tue Jul 06 18:17:13 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://arxiv.org/pdf/2004.09313.pdf",
  abstract =     "The logarithmic number system (LNS) is arguably not
                 broadly used due to exponential circuit overheads for
                 summation tables relative to arithmetic precision.
                 Methods to reduce this overhead have been proposed, yet
                 still yield designs with high chip area and power
                 requirements. Use remains limited to lower precision or
                 high multiply/add ratio cases, while much of linear
                 algebra (near 1:1 multiply/add ratio) does not
                 qualify.\par

                 We present a dual-base approximate logarithmic
                 arithmetic comparable to floating point in use, yet
                 unlike LNS it is easily fully pipelined, extendable to
                 arbitrary precision with $ O(n^2) $ overhead, and
                 energy efficient at a 1:1 multiply/add ratio.Compared
                 to float32 or float64 vector inner product with FMA,
                 our design is respectively $ 2.3 \times $ and $ 4.6
                 \times $ more energy efficient in 7 nm CMOS. It depends
                 on exp and log evaluation $ 5.4 \times $ and $ 3.2
                 \times $ more energy efficient, at $ 0.23 \times $ and
                 $ 0.37 \times $ the chip area for equivalent accuracy
                 versus standard hyperbolic CORDIC using shift-and-add
                 and approximated ODE integration in the style of Revol
                 and Yakoubsohn. This technique is a novel alternative
                 for low power, high precision hardened linear algebra
                 in computer vision, graphics and machine learning
                 applications.",
  acknowledgement = ack-nhfb,
  keywords =     "approximate arithmetic; elementary function
                 evaluation; hardware linear algebra; logarithmic
                 arithmetic",
  remark =       "Published in \cite{Johnson:2020:EAHb}.",
}


bibtype: inproceedings
filename: elefunt.bib
label: Johnson:2020:EAHb
author: Jeff Johnson
title: Efficient, arbitrarily high precision hardware logarithmic arithmetic for linear algebra
crossref: Cornea:2020:ISC
pages: 25--32
month: jun
monthnumber: 6
year: 2020
DOI: https://doi.org/10.1109/ARITH48897.2020.00013
ISSN: 2576-2265 OR 25762265
bibdate: Wed Jul 7 06:24:52 2021
bibtimestamp: 2021.07.07 06:24:52 ???
acknowledgement: ack-nhfb
rawauthor: Jeff Johnson
rawtitle: Efficient, arbitrarily high precision hardware logarithmic arithmetic for linear algebra
abstract:
The logarithmic number system (LNS) is arguably not broadly used due to exponential circuit overheads for summation tables relative to arithmetic precision. Methods to reduce this overhead have been proposed, yet still yield designs with high chip area and power requirements. Use remains limited to lower precision or high multiply/add ratio cases, while much of linear algebra (near 1:1 multiply/add ratio) does not qualify. We present a dual-base approximate logarithmic arithmetic comparable to floating point in use, yet unlike LNS it is easily fully pipelined, extendable to arbitrary precision with $ O(n^2) $ overhead, and energy efficient at a 1:1 multiply/add ratio. Compared to float32 or float64 vector inner product with FMA, our design is respectively $ 2.3 times $ and $ 4.6 times $ more energy efficient in 7 nm CMOS. It depends on exp and log evaluation 5.4 and $ 3.2 times $ more energy efficient, at $ 0.23 times $ and $ 0.37 times $ the chip area for equivalent accuracy versus standard hyperbolic CORDIC using shift-and-add and approximated ODE integration in the style of Revol and Yakoubsohn. This technique is a novel alternative for low power, high precision hardened linear algebra in computer vision, graphics and machine learning applications.

keywords:
Adders; approximate arithmetic; Clocks; elementary function evaluation; Hardware; hardware linear algebra; Linear algebra; logarithmic arithmetic; Pipeline processing; Read only memory; Switches

rawabstract:
The logarithmic number system (LNS) is arguably not broadly used due to exponential circuit overheads for summation tables relative to arithmetic precision. Methods to reduce this overhead have been proposed, yet still yield designs with high chip area and power requirements. Use remains limited to lower precision or high multiply/add ratio cases, while much of linear algebra (near 1:1 multiply/add ratio) does not qualify. We present a dual-base approximate logarithmic arithmetic comparable to floating point in use, yet unlike LNS it is easily fully pipelined, extendable to arbitrary precision with $ O(n^2) $ overhead, and energy efficient at a 1:1 multiply/add ratio. Compared to float32 or float64 vector inner product with FMA, our design is respectively $ 2.3 \times $ and $ 4.6 \times $ more energy efficient in 7 nm CMOS. It depends on exp and log evaluation 5.4 and $ 3.2 \times $ more energy efficient, at $ 0.23 \times $ and $ 0.37 \times $ the chip area for equivalent accuracy versus standard hyperbolic CORDIC using shift-and-add and approximated ODE integration in the style of Revol and Yakoubsohn. This technique is a novel alternative for low power, high precision hardened linear algebra in computer vision, graphics and machine learning applications.

entry:
@InProceedings{Johnson:2020:EAHb,
  author =       "Jeff Johnson",
  title =        "Efficient, arbitrarily high precision hardware
                 logarithmic arithmetic for linear algebra",
  crossref =     "Cornea:2020:ISC",
  pages =        "25--32",
  month =        jun,
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ARITH48897.2020.00013",
  ISSN =         "2576-2265",
  bibdate =      "Wed Jul 7 06:24:52 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The logarithmic number system (LNS) is arguably not
                 broadly used due to exponential circuit overheads for
                 summation tables relative to arithmetic precision.
                 Methods to reduce this overhead have been proposed, yet
                 still yield designs with high chip area and power
                 requirements. Use remains limited to lower precision or
                 high multiply/add ratio cases, while much of linear
                 algebra (near 1:1 multiply/add ratio) does not qualify.
                 We present a dual-base approximate logarithmic
                 arithmetic comparable to floating point in use, yet
                 unlike LNS it is easily fully pipelined, extendable to
                 arbitrary precision with $ O(n^2) $ overhead, and
                 energy efficient at a 1:1 multiply/add ratio. Compared
                 to float32 or float64 vector inner product with FMA,
                 our design is respectively $ 2.3 \times $ and $ 4.6
                 \times $ more energy efficient in 7 nm CMOS. It depends
                 on exp and log evaluation 5.4 and $ 3.2 \times $ more
                 energy efficient, at $ 0.23 \times $ and $ 0.37 \times
                 $ the chip area for equivalent accuracy versus standard
                 hyperbolic CORDIC using shift-and-add and approximated
                 ODE integration in the style of Revol and Yakoubsohn.
                 This technique is a novel alternative for low power,
                 high precision hardened linear algebra in computer
                 vision, graphics and machine learning applications.",
  acknowledgement = ack-nhfb,
  keywords =     "Adders; approximate arithmetic; Clocks; elementary
                 function evaluation; Hardware; hardware linear algebra;
                 Linear algebra; logarithmic arithmetic; Pipeline
                 processing; Read only memory; Switches",
}


bibtype: book
filename: elefunt.bib
label: Korotkov:2020:IRE
author: N. E. (Nikolayi Efimovich) Korotkov and Alexander N. Korotkov
title: Integrals Related to the Error Function
publisher: CRC Press, Taylor and Francis Group
address: Boca Raton, FL, USA
pages: xx + 227
year: 2020
LCCN: QA308 .K67 2020
bibdate: Fri Feb 5 17:54:22 MST 2021
bibsource: fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2021.02.05 17:54:22 MST
subject: Integrals; Tables; Error functions
acknowledgement: ack-nhfb
rawauthor: N. E. (Nikola{\'y}i Efimovich) Korotkov and Alexander N. Korotkov
rawtitle: Integrals Related to the Error Function
ISBN:
0-367-40820-1 (hardcover), 0-367-80923-0 (e-book), 1-000-03307-4 (e-book), 1-000-03308-2 (Mobipocket e-book), 1-000-03309-0 (e-Pub) OR 0367408201 (hardcover), 0367809230 (ebook), 1000033074 (ebook), 1000033082 (Mobipocket ebook), 1000033090 (ePub)

ISBN13:
978-0-367-40820-6 (hardcover), 978-0-367-80923-2 (e-book), 978-1-000-03307-6 (e-book), 978-1-000-03308-3 (Mobipocket e-book), 978-1-000-03309-0 (e-Pub) OR 9780367408206 (hardcover), 9780367809232 (ebook), 9781000033076 (ebook), 9781000033083 (Mobipocket ebook), 9781000033090 (ePub)

abstract:
booktitle Integrals Related to the Error Function presents a table of integrals related to the error function, including indefinite and improper definite integrals. Most of the formulas in this book have not been presented in other tables of integrals or have been presented only for some special cases of parameters or for integration only along the real axis of the complex plane. Many of the integrals presented here cannot be obtained using a computer (except via an approximate numerical integration). Additionally, for improper integrals, this book emphasizes the necessary and sufficient conditions for the validity of the presented formulas, including trajectory for going to infinity on the complex plane; such conditions are usually not given in computer-assisted analytical integration and often not presented in the previously published tables of integrals. Features The first book in English language to present a comprehensive collection of integrals related to the error function Useful for researchers whose work involves the error function (e.g., via probability integrals in communication theory). Additionally, it can also be used by broader audience.

TOC:
Indefinite integrals Definite integrals Appendix: Some useful formulas for obtaining other integrals.

rawabstract:
\booktitle{Integrals Related to the Error Function} presents a table of integrals related to the error function, including indefinite and improper definite integrals. Most of the formulas in this book have not been presented in other tables of integrals or have been presented only for some special cases of parameters or for integration only along the real axis of the complex plane. Many of the integrals presented here cannot be obtained using a computer (except via an approximate numerical integration). Additionally, for improper integrals, this book emphasizes the necessary and sufficient conditions for the validity of the presented formulas, including trajectory for going to infinity on the complex plane; such conditions are usually not given in computer-assisted analytical integration and often not presented in the previously published tables of integrals. Features The first book in English language to present a comprehensive collection of integrals related to the error function Useful for researchers whose work involves the error function (e.g., via probability integrals in communication theory). Additionally, it can also be used by broader audience.

rawTOC:
Indefinite integrals \\ Definite integrals \\ Appendix: Some useful formulas for obtaining other integrals.

entry:
@Book{Korotkov:2020:IRE,
  author =       "N. E. (Nikola{\'y}i Efimovich) Korotkov and Alexander
                 N. Korotkov",
  title =        "Integrals Related to the Error Function",
  publisher =    "CRC Press, Taylor and Francis Group",
  address =      "Boca Raton, FL, USA",
  pages =        "xx + 227",
  year =         "2020",
  ISBN =         "0-367-40820-1 (hardcover), 0-367-80923-0 (e-book),
                 1-000-03307-4 (e-book), 1-000-03308-2 (Mobipocket
                 e-book), 1-000-03309-0 (e-Pub)",
  ISBN-13 =      "978-0-367-40820-6 (hardcover), 978-0-367-80923-2
                 (e-book), 978-1-000-03307-6 (e-book), 978-1-000-03308-3
                 (Mobipocket e-book), 978-1-000-03309-0 (e-Pub)",
  LCCN =         "QA308 .K67 2020",
  bibdate =      "Fri Feb 5 17:54:22 MST 2021",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "\booktitle{Integrals Related to the Error Function}
                 presents a table of integrals related to the error
                 function, including indefinite and improper definite
                 integrals. Most of the formulas in this book have not
                 been presented in other tables of integrals or have
                 been presented only for some special cases of
                 parameters or for integration only along the real axis
                 of the complex plane. Many of the integrals presented
                 here cannot be obtained using a computer (except via an
                 approximate numerical integration). Additionally, for
                 improper integrals, this book emphasizes the necessary
                 and sufficient conditions for the validity of the
                 presented formulas, including trajectory for going to
                 infinity on the complex plane; such conditions are
                 usually not given in computer-assisted analytical
                 integration and often not presented in the previously
                 published tables of integrals. Features The first book
                 in English language to present a comprehensive
                 collection of integrals related to the error function
                 Useful for researchers whose work involves the error
                 function (e.g., via probability integrals in
                 communication theory). Additionally, it can also be
                 used by broader audience.",
  acknowledgement = ack-nhfb,
  subject =      "Integrals; Tables; Error functions",
  tableofcontents = "Indefinite integrals \\
                 Definite integrals \\
                 Appendix: Some useful formulas for obtaining other
                 integrals.",
}


bibtype: article
filename: elefunt.bib
label: Muller:2020:EFA
author: Jean-Michel Muller
title: Elementary Functions and Approximate Computing
journal: j-PROC-IEEE
volume: 108
number: 12
pages: 2136--2149
month: dec
monthnumber: 12
year: 2020
CODEN: IEEPAD
DOI: https://doi.org/10.1109/jproc.2020.2991885
ISSN: 0018-9219 (print), 1558-2256 (electronic) OR 00189219 (print), 15582256 (electronic)
ISSNL: 0018-9219 OR 00189219
bibdate: Tue Mar 1 06:07:02 2022
bibtimestamp: 2022.03.01 06:07:02 ???
fjournal: Proceedings of the IEEE
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5
rawauthor: Jean-Michel Muller
rawtitle: Elementary Functions and Approximate Computing
abstract:
In this article, we review some of the classical methods used for quickly obtaining low-precision approximations to the elementary functions. Then, for each of the three main classes of elementary function algorithms (shift-and-add algorithms, polynomial or rational approximations, and table-based methods) and for the additional, specific to approximate computing, ``bit-manipulation'' techniques, we examine what can be done for obtaining very fast estimates of a function, at the cost of a (controlled) loss in terms of accuracy.

rawabstract:
In this article, we review some of the classical methods used for quickly obtaining low-precision approximations to the elementary functions. Then, for each of the three main classes of elementary function algorithms (shift-and-add algorithms, polynomial or rational approximations, and table-based methods) and for the additional, specific to approximate computing, ``bit-manipulation'' techniques, we examine what can be done for obtaining very fast estimates of a function, at the cost of a (controlled) loss in terms of accuracy.

entry:
@Article{Muller:2020:EFA,
  author =       "Jean-Michel Muller",
  title =        "Elementary Functions and Approximate Computing",
  journal =      j-PROC-IEEE,
  volume =       "108",
  number =       "12",
  pages =        "2136--2149",
  month =        dec,
  year =         "2020",
  CODEN =        "IEEPAD",
  DOI =          "https://doi.org/10.1109/jproc.2020.2991885",
  ISSN =         "0018-9219 (print), 1558-2256 (electronic)",
  ISSN-L =       "0018-9219",
  bibdate =      "Tue Mar 1 06:07:02 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In this article, we review some of the classical
                 methods used for quickly obtaining low-precision
                 approximations to the elementary functions. Then, for
                 each of the three main classes of elementary function
                 algorithms (shift-and-add algorithms, polynomial or
                 rational approximations, and table-based methods) and
                 for the additional, specific to approximate computing,
                 ``bit-manipulation'' techniques, we examine what can be
                 done for obtaining very fast estimates of a function,
                 at the cost of a (controlled) loss in terms of
                 accuracy.",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the IEEE",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
}


bibtype: article
filename: elefunt.bib
label: Naterop:2020:HRN
author: L. Naterop and A. Signer and Y. Ulrich
title: handyG --- Rapid numerical evaluation of generalised polylogarithms in Fortran
journal: j-COMP-PHYS-COMM
volume: 253
pages: Article 107165
month: aug
monthnumber: 8
year: 2020
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/j.cpc.2020.107165
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Fri Jun 19 07:19:48 MDT 2020
bibtimestamp: 2020.06.19 07:19:48 MDT
URL: http://www.sciencedirect.com/science/article/pii/S0010465520300230
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: L. Naterop and A. Signer and Y. Ulrich
rawtitle: {handyG} --- Rapid numerical evaluation of generalised polylogarithms in {Fortran}
bibsource:
https://www.math.utah.edu/pub/tex/bib/compphyscomm2020.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fortran3.bib

entry:
@Article{Naterop:2020:HRN,
  author =       "L. Naterop and A. Signer and Y. Ulrich",
  title =        "{handyG} --- Rapid numerical evaluation of generalised
                 polylogarithms in {Fortran}",
  journal =      j-COMP-PHYS-COMM,
  volume =       "253",
  number =       "??",
  pages =        "Article 107165",
  month =        aug,
  year =         "2020",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2020.107165",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Fri Jun 19 07:19:48 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran3.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465520300230",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: techreport
filename: elefunt.bib
label: Pornin:2020:OBG
author: Thomas Pornin
title: Optimized Binary GCD for Modular Inversion
type: Report
institution: International Association for Cryptologic Research
pages: 16
day: 23
month: aug
monthnumber: 8
year: 2020
bibdate: Mon May 30 07:10:10 2022
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2022.05.30 07:10:10 ???
URL: https://eprint.iacr.org/2020/972.pdf
acknowledgement: ack-nhfb
rawauthor: Thomas Pornin
rawtitle: Optimized Binary {GCD} for Modular Inversion
abstract:
In this short note, we describe a practical optimization of the well-known extended binary GCD algorithm, for the purpose of computing modular inverses. The method is conceptually simple and is applicable to all odd moduli (including non-prime moduli). When implemented for inversion in the field of integers modulo the prime $ 2^255 - 19 $, on a recent x86 CPU (Coffee Lake core), we compute the inverse in 6253 cycles, with a fully constant-time implementation.

rawabstract:
In this short note, we describe a practical optimization of the well-known extended binary GCD algorithm, for the purpose of computing modular inverses. The method is conceptually simple and is applicable to all odd moduli (including non-prime moduli). When implemented for inversion in the field of integers modulo the prime $ 2^{255} - 19 $, on a recent x86 CPU (Coffee Lake core), we compute the inverse in 6253 cycles, with a fully constant-time implementation.

entry:
@TechReport{Pornin:2020:OBG,
  author =       "Thomas Pornin",
  title =        "Optimized Binary {GCD} for Modular Inversion",
  type =         "Report",
  number =       "??",
  institution =  "International Association for Cryptologic Research",
  address =      "????",
  pages =        "16",
  day =          "23",
  month =        aug,
  year =         "2020",
  bibdate =      "Mon May 30 07:10:10 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://eprint.iacr.org/2020/972.pdf",
  abstract =     "In this short note, we describe a practical
                 optimization of the well-known extended binary GCD
                 algorithm, for the purpose of computing modular
                 inverses. The method is conceptually simple and is
                 applicable to all odd moduli (including non-prime
                 moduli). When implemented for inversion in the field of
                 integers modulo the prime $ 2^{255} - 19 $, on a recent
                 x86 CPU (Coffee Lake core), we compute the inverse in
                 6253 cycles, with a fully constant-time
                 implementation.",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: elefunt.bib
label: Raveendran:2020:NPF
author: Aneesh Raveendran and Sandra Jean and J. Mervin and D. Vivian and David Selvakumar
editor: IEEE
title: A Novel Parametrized Fused Division and Square-Root POSIT Arithmetic Architecture
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 207--212
month: jan
monthnumber: 1
year: 2020
DOI: https://doi.org/10.1109/vlsid49098.2020.00053
ISBN: 1-72815-701-3 OR 1728157013
ISBN13: 978-1-72815-701-6 OR 9781728157016
ISSN: 1063-9667 (print), 2380-6923 (electronic) OR 10639667 (print), 23806923 (electronic)
ISSNL: 1063-9667 OR 10639667
bibdate: Fri Dec 15 07:29:26 2023
bibtimestamp: 2023.12.15 07:29:26 ???
acknowledgement: ack-nhfb
rawauthor: Aneesh Raveendran and Sandra Jean and J. Mervin and D. Vivian and David Selvakumar
raweditor: {IEEE}
rawtitle: A Novel Parametrized Fused Division and Square-Root {POSIT} Arithmetic Architecture
booktitle:
2020 33rd International Conference on VLSI Design and 2020 19th International Conference on Embedded Systems (VLSID), Bengaluru, India, 4--8 January 2020

rawbooktitle:
{2020 33rd International Conference on VLSI Design and 2020 19th International Conference on Embedded Systems (VLSID), Bengaluru, India, 4--8 January 2020}

entry:
@InProceedings{Raveendran:2020:NPF,
  author =       "Aneesh Raveendran and Sandra Jean and J. Mervin and D.
                 Vivian and David Selvakumar",
  editor =       "{IEEE}",
  booktitle =    "{2020 33rd International Conference on VLSI Design and
                 2020 19th International Conference on Embedded Systems
                 (VLSID), Bengaluru, India, 4--8 January 2020}",
  title =        "A Novel Parametrized Fused Division and Square-Root
                 {POSIT} Arithmetic Architecture",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "207--212",
  month =        jan,
  year =         "2020",
  DOI =          "https://doi.org/10.1109/vlsid49098.2020.00053",
  ISBN =         "1-72815-701-3",
  ISBN-13 =      "978-1-72815-701-6",
  ISSN =         "1063-9667 (print), 2380-6923 (electronic)",
  ISSN-L =       "1063-9667",
  bibdate =      "Fri Dec 15 07:29:26 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Shibata:2020:SPV
author: Naoki Shibata and Francesco Petrogalli
title: SLEEF: A Portable Vectorized Library of C Standard Mathematical Functions
journal: j-IEEE-TRANS-PAR-DIST-SYS
volume: 31
number: 6
pages: 1316--1327
month: jun
monthnumber: 6
year: 2020
CODEN: ITDSEO
DOI: https://doi.org/10.1109/TPDS.2019.2960333
ISSN: 1045-9219 (print), 1558-2183 (electronic) OR 10459219 (print), 15582183 (electronic)
ISSNL: 1045-9219 OR 10459219
bibdate: Thu Feb 20 10:08:58 2020
bibtimestamp: 2020.02.20 10:08:58 ???
fjournal: IEEE Transactions on Parallel and Distributed Systems
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=71
rawauthor: Naoki Shibata and Francesco Petrogalli
rawtitle: {SLEEF}: A Portable Vectorized Library of {C} Standard Mathematical Functions
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/ieeetranspardistsys.bib

keywords:
elementary functions; floating-point arithmetic; Parallel and vector implementations; SIMD processors

entry:
@Article{Shibata:2020:SPV,
  author =       "Naoki Shibata and Francesco Petrogalli",
  title =        "{SLEEF}: A Portable Vectorized Library of {C} Standard
                 Mathematical Functions",
  journal =      j-IEEE-TRANS-PAR-DIST-SYS,
  volume =       "31",
  number =       "6",
  pages =        "1316--1327",
  month =        jun,
  year =         "2020",
  CODEN =        "ITDSEO",
  DOI =          "https://doi.org/10.1109/TPDS.2019.2960333",
  ISSN =         "1045-9219 (print), 1558-2183 (electronic)",
  ISSN-L =       "1045-9219",
  bibdate =      "Thu Feb 20 10:08:58 2020",
  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/ieeetranspardistsys.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Parallel and Distributed
                 Systems",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=71",
  keywords =     "elementary functions; floating-point arithmetic;
                 Parallel and vector implementations; SIMD processors",
}


bibtype: article
filename: elefunt.bib
label: Wakhare:2020:TCJ
author: Tanay Wakhare and Christophe Vignat
title: Taylor coefficients of the Jacobi $ theta _3 (q) $ function
journal: j-J-NUMBER-THEORY
volume: 216
pages: 280--306
month: nov
monthnumber: 11
year: 2020
CODEN: JNUTA9
DOI: https://doi.org/10.1016/j.jnt.2020.03.002
ISSN: 0022-314X (print), 1096-1658 (electronic) OR 0022314X (print), 10961658 (electronic)
ISSNL: 0022-314X OR 0022314X
bibdate: Sat Aug 8 09:41:52 MDT 2020
bibtimestamp: 2020.08.08 09:41:52 MDT
URL: http://www.sciencedirect.com/science/article/pii/S0022314X20300858
fjournal: Journal of Number Theory
acknowledgement: ack-nhfb
ajournal: J. Number Theory
journalURL: http://www.sciencedirect.com/science/journal/0022314X
rawauthor: Tanay Wakhare and Christophe Vignat
rawtitle: {Taylor} coefficients of the {Jacobi} $ \theta_3 (q) $ function
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jnumbertheory2020.bib

entry:
@Article{Wakhare:2020:TCJ,
  author =       "Tanay Wakhare and Christophe Vignat",
  title =        "{Taylor} coefficients of the {Jacobi} $ \theta_3 (q) $
                 function",
  journal =      j-J-NUMBER-THEORY,
  volume =       "216",
  number =       "??",
  pages =        "280--306",
  month =        nov,
  year =         "2020",
  CODEN =        "JNUTA9",
  DOI =          "https://doi.org/10.1016/j.jnt.2020.03.002",
  ISSN =         "0022-314X (print), 1096-1658 (electronic)",
  ISSN-L =       "0022-314X",
  bibdate =      "Sat Aug 8 09:41:52 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jnumbertheory2020.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022314X20300858",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Number Theory",
  fjournal =     "Journal of Number Theory",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022314X",
}


bibtype: article
filename: elefunt.bib
label: Xiao:2020:PAH
author: Feibao Xiao and Feng Liang and Bin Wu and Junzhe Liang and Shuting Cheng and Guohe Zhang
title: Posit Arithmetic Hardware Implementations with The Minimum Cost Divider and Square Root
journal: j-ELECTRONICS
volume: 9
number: 10
pages: 1622:1--1622:16
month: oct
monthnumber: 10
year: 2020
DOI: https://doi.org/10.3390/electronics9101622
ISSN: 2079-9292 OR 20799292
ISSNL: 2079-9292 OR 20799292
bibdate: Fri Dec 15 07:25:40 2023
bibtimestamp: 2023.12.15 07:25:40 ???
fjournal: Electronics
acknowledgement: ack-nhfb
journalURL: https://www.mdpi.com/journal/electronics
rawauthor: Feibao Xiao and Feng Liang and Bin Wu and Junzhe Liang and Shuting Cheng and Guohe Zhang
rawtitle: Posit Arithmetic Hardware Implementations with The Minimum Cost Divider and Square Root
entry:
@Article{Xiao:2020:PAH,
  author =       "Feibao Xiao and Feng Liang and Bin Wu and Junzhe Liang
                 and Shuting Cheng and Guohe Zhang",
  title =        "Posit Arithmetic Hardware Implementations with The
                 Minimum Cost Divider and Square Root",
  journal =      j-ELECTRONICS,
  volume =       "9",
  number =       "10",
  pages =        "1622:1--1622:16",
  month =        oct,
  year =         "2020",
  DOI =          "https://doi.org/10.3390/electronics9101622",
  ISSN =         "2079-9292",
  ISSN-L =       "2079-9292",
  bibdate =      "Fri Dec 15 07:25:40 2023",
  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 =     "Electronics",
  journal-URL =  "https://www.mdpi.com/journal/electronics",
}


bibtype: article
filename: elefunt.bib
label: Akram:2021:XFA
author: Riad Akram and Shantanu Mandal and Abdullah Muzahid
title: XMeter: Finding Approximable Functions and Predicting Their Accuracy
journal: j-IEEE-TRANS-COMPUT
volume: 70
number: 7
pages: 1081--1093
month: jul
monthnumber: 7
year: 2021
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.2020.3005083
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jun 10 15:51:57 2021
bibtimestamp: 2021.06.10 15:51:57 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Riad Akram and Shantanu Mandal and Abdullah Muzahid
rawtitle: {XMeter}: Finding Approximable Functions and Predicting Their Accuracy
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib

entry:
@Article{Akram:2021:XFA,
  author =       "Riad Akram and Shantanu Mandal and Abdullah Muzahid",
  title =        "{XMeter}: Finding Approximable Functions and
                 Predicting Their Accuracy",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "70",
  number =       "7",
  pages =        "1081--1093",
  month =        jul,
  year =         "2021",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2020.3005083",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jun 10 15:51:57 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: misc
filename: elefunt.bib
label: Bailey:2021:PMN
author: David H. Bailey
title: pkg MPFUN2020: a new thread-safe arbitrary precision package
pages: 54
day: 18
month: may
monthnumber: 5
year: 2021
bibdate: Mon Dec 05 07:32:16 2022
bibtimestamp: 2022.12.05 07:32:16 ???
URL: https://www.davidhbailey.com/dhbpapers/mpfun2020.pdf
acknowledgement: ack-nhfb
howpublished: Web document
rawauthor: David H. Bailey
rawtitle: \pkg{MPFUN2020}: a new thread-safe arbitrary precision package
abstract:
Numerous research studies have arisen, particularly in mathematical physics and experimental mathematics, that require extremely high numeric precision. Such precision greatly magnifies computer run times, so software packages to support high-precision computing must be designed for thread-based parallel processing. This paper describes a new arbitrary precision software package (``MPFUN2020'') that features several significant improvements over an earlier package. It comes in two versions: a self-contained all-Fortran version, and a version based on the MPFR package, which is even faster. Both versions feature: (a) a completely thread-safe design, so user codes can be converted for parallel execution at the application level; (b) a full-featured high-level Fortran interface, so that most applications can be converted to multiprecision with relatively minor changes to source code; (c) full support for both real and complex datatypes; (d) a wide variety of transcendental functions and special functions; (e) run-time checking and other facilities to overcome problems with converting double precision constants and data; (f) a medium precision datatype, which improves performance and reduces memory cost on large variable precision applications; and (g) interoperability --- with a simple restriction, application codes written for one version can be run with the other without change.

rawabstract:
Numerous research studies have arisen, particularly in mathematical physics and experimental mathematics, that require extremely high numeric precision. Such precision greatly magnifies computer run times, so software packages to support high-precision computing must be designed for thread-based parallel processing. This paper describes a new arbitrary precision software package (``MPFUN2020'') that features several significant improvements over an earlier package. It comes in two versions: a self-contained all-Fortran version, and a version based on the MPFR package, which is even faster. Both versions feature: (a) a completely thread-safe design, so user codes can be converted for parallel execution at the application level; (b) a full-featured high-level Fortran interface, so that most applications can be converted to multiprecision with relatively minor changes to source code; (c) full support for both real and complex datatypes; (d) a wide variety of transcendental functions and special functions; (e) run-time checking and other facilities to overcome problems with converting double precision constants and data; (f) a medium precision datatype, which improves performance and reduces memory cost on large variable precision applications; and (g) interoperability --- with a simple restriction, application codes written for one version can be run with the other without change.

entry:
@Misc{Bailey:2021:PMN,
  author =       "David H. Bailey",
  title =        "\pkg{MPFUN2020}: a new thread-safe arbitrary precision
                 package",
  howpublished = "Web document",
  pages =        "54",
  day =          "18",
  month =        may,
  year =         "2021",
  bibdate =      "Mon Dec 05 07:32:16 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.davidhbailey.com/dhbpapers/mpfun2020.pdf",
  abstract =     "Numerous research studies have arisen, particularly in
                 mathematical physics and experimental mathematics, that
                 require extremely high numeric precision. Such
                 precision greatly magnifies computer run times, so
                 software packages to support high-precision computing
                 must be designed for thread-based parallel
                 processing.

                 This paper describes a new arbitrary precision software
                 package (``MPFUN2020'') that features several
                 significant improvements over an earlier package. It
                 comes in two versions: a self-contained all-Fortran
                 version, and a version based on the MPFR package, which
                 is even faster. Both versions feature: (a) a completely
                 thread-safe design, so user codes can be converted for
                 parallel execution at the application level; (b) a
                 full-featured high-level Fortran interface, so that
                 most applications can be converted to multiprecision
                 with relatively minor changes to source code; (c) full
                 support for both real and complex datatypes; (d) a wide
                 variety of transcendental functions and special
                 functions; (e) run-time checking and other facilities
                 to overcome problems with converting double precision
                 constants and data; (f) a medium precision datatype,
                 which improves performance and reduces memory cost on
                 large variable precision applications; and (g)
                 interoperability --- with a simple restriction,
                 application codes written for one version can be run
                 with the other without change.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Borges:2021:AIA
author: Carlos F. Borges
title: Algorithm 1014: an Improved Algorithm for tt hypot(x,y)
journal: j-TOMS
volume: 47
number: 1
pages: 9:1--9:12
month: jan
monthnumber: 1
year: 2021
CODEN: ACMSCU
DOI: https://doi.org/10.1145/3428446
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Thu Jan 7 10:31:04 MST 2021
bibtimestamp: 2021.01.07 10:31:04 MST
URL: https://dl.acm.org/doi/10.1145/3428446
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
articleno: 9
journalURL: https://dl.acm.org/loi/toms
rawauthor: Carlos F. Borges
rawtitle: {Algorithm 1014}: an Improved Algorithm for {\tt hypot(x,y)}
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/julia.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib

abstract:
We develop fast and accurate algorithms for evaluating $ sqrt x^2 + y^2 $ for two floating-point numbers $x$ and $y$. Library functions that perform this computation are generally named tt hypot(x,y). We compare five approaches that we will develop in this article to the current resident library function that is delivered with Julia 1.1 and to the code that has been distributed with the C math library for decades. We will investigate the accuracy of our algorithms by simulation.

rawabstract:
We develop fast and accurate algorithms for evaluating $ \sqrt {x^2 + y^2} $ for two floating-point numbers $x$ and $y$. Library functions that perform this computation are generally named {\tt hypot(x,y)}. We compare five approaches that we will develop in this article to the current resident library function that is delivered with Julia 1.1 and to the code that has been distributed with the C math library for decades. We will investigate the accuracy of our algorithms by simulation.

entry:
@Article{Borges:2021:AIA,
  author =       "Carlos F. Borges",
  title =        "{Algorithm 1014}: an Improved Algorithm for {\tt
                 hypot(x,y)}",
  journal =      j-TOMS,
  volume =       "47",
  number =       "1",
  pages =        "9:1--9:12",
  month =        jan,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3428446",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jan 7 10:31:04 MST 2021",
  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/julia.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3428446",
  abstract =     "We develop fast and accurate algorithms for evaluating
                 $ \sqrt {x^2 + y^2} $ for two floating-point numbers
                 $x$ and $y$. Library functions that perform this
                 computation are generally named {\tt hypot(x,y)}. We
                 compare five approaches that we will develop in this
                 article to the current resident library function that
                 is delivered with Julia 1.1 and to the code that has
                 been distributed with the C math library for decades.
                 We will investigate the accuracy of our algorithms by
                 simulation.",
  acknowledgement = ack-nhfb,
  articleno =    "9",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Borges:2021:CRN
author: Carlos F. Borges
title: A Correctly Rounded Newton Step for the Reciprocal Square Root
journal: arXiv.org
pages: 1--8
day: 28
month: dec
monthnumber: 12
year: 2021
bibdate: Fri Sep 22 16:08:53 2023
bibtimestamp: 2023.09.22 16:08:53 ???
URL: https://arxiv.org/abs/2112.14321
acknowledgement: ack-nhfb
rawauthor: Carlos F. Borges
rawtitle: A Correctly Rounded {Newton} Step for the Reciprocal Square Root
abstract:
The reciprocal square root is an important computation for which many sophisticated algorithms exist (see for example cite Moroz,863046,863031 and the references therein). A common theme is the use of Newton's method to refine the estimates. In this paper we develop a correctly rounded Newton step that can be used to improve the accuracy of a naive calculation (using methods similar to those developed in cite borges) The approach relies on the use of the fused multiply-add (FMA) which is widely available in hardware on a variety of modern computer architectures. We then introduce the notion of em weak rounding and prove that our proposed algorithm meets this standard. We then show how to leverage the exact Newton step to get a Halley's method compensation which requires one additional FMA and one additional multiplication. This method appears to give correctly rounded results experimentally and we show that it can be combined with a square root free method for estimating the reciprocal square root to get a method that is both very fast (in computing environments with a slow square root) and, experimentally, highly accurate.

rawabstract:
The reciprocal square root is an important computation for which many sophisticated algorithms exist (see for example \cite{Moroz,863046,863031} and the references therein). A common theme is the use of Newton's method to refine the estimates. In this paper we develop a correctly rounded Newton step that can be used to improve the accuracy of a naive calculation (using methods similar to those developed in \cite{borges}) The approach relies on the use of the fused multiply-add (FMA) which is widely available in hardware on a variety of modern computer architectures. We then introduce the notion of {\em weak rounding} and prove that our proposed algorithm meets this standard. We then show how to leverage the exact Newton step to get a Halley's method compensation which requires one additional FMA and one additional multiplication. This method appears to give correctly rounded results experimentally and we show that it can be combined with a square root free method for estimating the reciprocal square root to get a method that is both very fast (in computing environments with a slow square root) and, experimentally, highly accurate.

entry:
@Article{Borges:2021:CRN,
  author =       "Carlos F. Borges",
  title =        "A Correctly Rounded {Newton} Step for the Reciprocal
                 Square Root",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--8",
  day =          "28",
  month =        dec,
  year =         "2021",
  bibdate =      "Fri Sep 22 16:08:53 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://arxiv.org/abs/2112.14321",
  abstract =     "The reciprocal square root is an important computation
                 for which many sophisticated algorithms exist (see for
                 example \cite{Moroz,863046,863031} and the references
                 therein). A common theme is the use of Newton's method
                 to refine the estimates. In this paper we develop a
                 correctly rounded Newton step that can be used to
                 improve the accuracy of a naive calculation (using
                 methods similar to those developed in \cite{borges})
                 The approach relies on the use of the fused
                 multiply-add (FMA) which is widely available in
                 hardware on a variety of modern computer architectures.
                 We then introduce the notion of {\em weak rounding} and
                 prove that our proposed algorithm meets this standard.
                 We then show how to leverage the exact Newton step to
                 get a Halley's method compensation which requires one
                 additional FMA and one additional multiplication. This
                 method appears to give correctly rounded results
                 experimentally and we show that it can be combined with
                 a square root free method for estimating the reciprocal
                 square root to get a method that is both very fast (in
                 computing environments with a slow square root) and,
                 experimentally, highly accurate.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Borges:2021:FCA
author: Carlos F. Borges
journal: arXiv.org
pages: 1--11
day: 23
month: feb
monthnumber: 2
year: 2021
bibdate: Fri Sep 22 16:05:47 2023
bibtimestamp: 2023.09.22 16:05:47 ???
URL: https://arxiv.org/abs/2103.08694
acknowledgement: ack-nhfb
rawauthor: Carlos F. Borges
title:
Fast compensated algorithms for the reciprocal square root, the reciprocal hypotenuse, and Givens rotations

abstract:
The reciprocal square root is an important computation for which many very sophisticated algorithms exist (see for example cite 863046,863031 and the references therein). In this paper we develop a simple differential compensation (much like those developed in cite borges) that can be used to improve the accuracy of a naive calculation. The approach relies on the use of the fused multiply-add (FMA) which is widely available in hardware on a variety of modern computer architectures. We then demonstrate how to combine this approach with a somewhat inaccurate but fast square root free method for estimating the reciprocal square root to get a method that is both fast (in computing environments with a slow square root) and, experimentally, highly accurate. Finally, we show how this same approach can be extended to the reciprocal hypotenuse calculation and, most importantly, to the construction of Givens rotations.

rawabstract:
The reciprocal square root is an important computation for which many very sophisticated algorithms exist (see for example \cite{863046,863031} and the references therein). In this paper we develop a simple differential compensation (much like those developed in \cite{borges}) that can be used to improve the accuracy of a naive calculation. The approach relies on the use of the fused multiply-add (FMA) which is widely available in hardware on a variety of modern computer architectures. We then demonstrate how to combine this approach with a somewhat inaccurate but fast square root free method for estimating the reciprocal square root to get a method that is both fast (in computing environments with a slow square root) and, experimentally, highly accurate. Finally, we show how this same approach can be extended to the reciprocal hypotenuse calculation and, most importantly, to the construction of Givens rotations.

rawtitle:
Fast compensated algorithms for the reciprocal square root, the reciprocal hypotenuse, and {Givens} rotations

entry:
@Article{Borges:2021:FCA,
  author =       "Carlos F. Borges",
  title =        "Fast compensated algorithms for the reciprocal square
                 root, the reciprocal hypotenuse, and {Givens}
                 rotations",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--11",
  day =          "23",
  month =        feb,
  year =         "2021",
  bibdate =      "Fri Sep 22 16:05:47 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://arxiv.org/abs/2103.08694",
  abstract =     "The reciprocal square root is an important computation
                 for which many very sophisticated algorithms exist (see
                 for example \cite{863046,863031} and the references
                 therein). In this paper we develop a simple
                 differential compensation (much like those developed in
                 \cite{borges}) that can be used to improve the accuracy
                 of a naive calculation. The approach relies on the use
                 of the fused multiply-add (FMA) which is widely
                 available in hardware on a variety of modern computer
                 architectures. We then demonstrate how to combine this
                 approach with a somewhat inaccurate but fast square
                 root free method for estimating the reciprocal square
                 root to get a method that is both fast (in computing
                 environments with a slow square root) and,
                 experimentally, highly accurate. Finally, we show how
                 this same approach can be extended to the reciprocal
                 hypotenuse calculation and, most importantly, to the
                 construction of Givens rotations.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Iacono:2021:BEF
author: Roberto Iacono
title: Bounding the Error Function
journal: j-COMPUT-SCI-ENG
volume: 23
number: 4
pages: 65--68
year: 2021
CODEN: CSENFA
DOI: https://doi.org/10.1109/MCSE.2021.3083778
ISSN: 1521-9615 (print), 1558-366X (electronic) OR 15219615 (print), 1558366X (electronic)
ISSNL: 1521-9615 OR 15219615
bibdate: Thu Jul 29 07:00:57 2021
bibtimestamp: 2021.07.29 07:00:57 ???
fjournal: Computing in Science and Engineering
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5992
rawauthor: Roberto Iacono
rawtitle: Bounding the Error Function
bibsource:
https://www.math.utah.edu/pub/tex/bib/computscieng.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

abstract:
Prompted by previous work published in this magazine, in this article we focus on the derivation of global analytical bounds for the error function of a real argument. Using an integral representation of this function, we obtain two simple and accurate lower bounds, which complement a well-known upper bound given long ago by Polya.

rawabstract:
Prompted by previous work published in this magazine, in this article we focus on the derivation of global analytical bounds for the error function of a real argument. Using an integral representation of this function, we obtain two simple and accurate lower bounds, which complement a well-known upper bound given long ago by P{\'o}lya.

entry:
@Article{Iacono:2021:BEF,
  author =       "Roberto Iacono",
  title =        "Bounding the Error Function",
  journal =      j-COMPUT-SCI-ENG,
  volume =       "23",
  number =       "4",
  pages =        "65--68",
  year =         "2021",
  CODEN =        "CSENFA",
  DOI =          "https://doi.org/10.1109/MCSE.2021.3083778",
  ISSN =         "1521-9615 (print), 1558-366X (electronic)",
  ISSN-L =       "1521-9615",
  bibdate =      "Thu Jul 29 07:00:57 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computscieng.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Prompted by previous work published in this magazine,
                 in this article we focus on the derivation of global
                 analytical bounds for the error function of a real
                 argument. Using an integral representation of this
                 function, we obtain two simple and accurate lower
                 bounds, which complement a well-known upper bound given
                 long ago by P{\'o}lya.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing in Science and Engineering",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5992",
}


bibtype: article
filename: elefunt.bib
label: Johansson:2021:APC
author: Fredrik Johansson
title: Arbitrary-Precision Computation of the Gamma Function
journal: arXiv.org
pages: 1--51
day: 17
month: sep
monthnumber: 9
year: 2021
DOI: https://doi.org/10.48550/arXiv.2109.0839
bibdate: Sun Dec 04 11:01:23 2022
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2022.12.04 11:01:23 ???
URL: https://arxiv.org/abs/2109.08392
acknowledgement: ack-nhfb
rawauthor: Fredrik Johansson
rawtitle: Arbitrary-Precision Computation of the Gamma Function
abstract:
We discuss the best methods available for computing the gamma function $ Gamma (z) $ in arbitrary-precision arithmetic with rigorous error bounds. We address different cases: rational, algebraic, real or complex arguments; large or small arguments; low or high precision; with or without precomputation. The methods also cover the log-gamma function $ log Gamma (z) $, the digamma function $ psi (z) $, and derivatives $ Gamma ^(n)(z) $ and $ psi ^(n)(z) $. Besides attempting to summarize the existing state of the art, we present some new formulas, estimates, bounds and algorithmic improvements and discuss implementation results.

rawabstract:
We discuss the best methods available for computing the gamma function $ \Gamma (z) $ in arbitrary-precision arithmetic with rigorous error bounds. We address different cases: rational, algebraic, real or complex arguments; large or small arguments; low or high precision; with or without precomputation. The methods also cover the log-gamma function $ \log \Gamma (z) $, the digamma function $ \psi (z) $, and derivatives $ \Gamma^{(n)}(z) $ and $ \psi^{(n)}(z) $. Besides attempting to summarize the existing state of the art, we present some new formulas, estimates, bounds and algorithmic improvements and discuss implementation results.

entry:
@Article{Johansson:2021:APC,
  author =       "Fredrik Johansson",
  title =        "Arbitrary-Precision Computation of the Gamma
                 Function",
  journal =      "arXiv.org",
  pages =        "1--51",
  day =          "17",
  month =        sep,
  year =         "2021",
  DOI =          "https://doi.org/10.48550/arXiv.2109.0839",
  bibdate =      "Sun Dec 04 11:01:23 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://arxiv.org/abs/2109.08392",
  abstract =     "We discuss the best methods available for computing
                 the gamma function $ \Gamma (z) $ in
                 arbitrary-precision arithmetic with rigorous error
                 bounds. We address different cases: rational,
                 algebraic, real or complex arguments; large or small
                 arguments; low or high precision; with or without
                 precomputation. The methods also cover the log-gamma
                 function $ \log \Gamma (z) $, the digamma function $
                 \psi (z) $, and derivatives $ \Gamma^{(n)}(z) $ and $
                 \psi^{(n)}(z) $. Besides attempting to summarize the
                 existing state of the art, we present some new
                 formulas, estimates, bounds and algorithmic
                 improvements and discuss implementation results.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Kang:2021:NEE
author: Hongchao Kang and Hong Wang
journal: j-APPL-NUM-MATH
volume: 160
pages: 23--41
month: feb
monthnumber: 2
year: 2021
CODEN: ANMAEL
ISSN: 0168-9274 (print), 1873-5460 (electronic) OR 01689274 (print), 18735460 (electronic)
ISSNL: 0168-9274 OR 01689274
bibdate: Tue Dec 29 07:52:55 MST 2020
bibtimestamp: 2020.12.29 07:52:55 MST
URL: http://www.sciencedirect.com/science/article/pii/S0168927420302932
fjournal: Applied Numerical Mathematics: Transactions of IMACS
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01689274
rawauthor: Hongchao Kang and Hong Wang
title:
Numerical evaluation and error analysis of many different oscillatory Bessel transforms via confluent hypergeometric function

rawtitle:
Numerical evaluation and error analysis of many different oscillatory {Bessel} transforms via confluent hypergeometric function

entry:
@Article{Kang:2021:NEE,
  author =       "Hongchao Kang and Hong Wang",
  title =        "Numerical evaluation and error analysis of many
                 different oscillatory {Bessel} transforms via confluent
                 hypergeometric function",
  journal =      j-APPL-NUM-MATH,
  volume =       "160",
  number =       "??",
  pages =        "23--41",
  month =        feb,
  year =         "2021",
  CODEN =        "ANMAEL",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  bibdate =      "Tue Dec 29 07:52:55 MST 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0168927420302932",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274",
}


bibtype: article
filename: elefunt.bib
label: Langdon:2021:GID
author: William B. Langdon and Oliver Krauss
title: Genetic Improvement of Data for Maths Functions
journal: j-TELO
volume: 1
number: 2
pages: 7:1--7:30
month: jun
monthnumber: 6
year: 2021
DOI: https://doi.org/10.1145/3461016
ISSN: 2688-299X (print), 2688-3007 (electronic) OR 2688299X (print), 26883007 (electronic)
ISSNL: 2688-299X OR 2688299X
bibdate: Sat Aug 21 15:11:10 MDT 2021
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/telo.bib
bibtimestamp: 2021.08.21 15:11:10 MDT
URL: https://dl.acm.org/doi/10.1145/3461016
fjournal: ACM Transactions on Evolutionary Learning and Optimization
acknowledgement: ack-nhfb
articleno: 7
journalURL: https://dl.acm.org/loi/telo
rawauthor: William B. Langdon and Oliver Krauss
rawtitle: Genetic Improvement of Data for Maths Functions
abstract:
We use continuous optimisation and manual code changes to evolve up to 1024 Newton--Raphson numerical values embedded in an open source GNU C library glibc square root sqrt to implement a double precision cube root routine cbrt, binary logarithm log2 and reciprocal square root function for C in seconds. The GI inverted square root $ x-1 / 2 $ is far more accurate than Quake's InvSqrt, Quare root. GI shows potential for automatically creating mobile or low resource mote smart dust bespoke custom mathematical libraries with new functionality.

rawabstract:
We use continuous optimisation and manual code changes to evolve up to 1024 Newton--Raphson numerical values embedded in an open source GNU C library glibc square root sqrt to implement a double precision cube root routine cbrt, binary logarithm log2 and reciprocal square root function for C in seconds. The GI inverted square root $ x{-1 / 2} $ is far more accurate than Quake's InvSqrt, Quare root. GI shows potential for automatically creating mobile or low resource mote smart dust bespoke custom mathematical libraries with new functionality.

entry:
@Article{Langdon:2021:GID,
  author =       "William B. Langdon and Oliver Krauss",
  title =        "Genetic Improvement of Data for Maths Functions",
  journal =      j-TELO,
  volume =       "1",
  number =       "2",
  pages =        "7:1--7:30",
  month =        jun,
  year =         "2021",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3461016",
  ISSN =         "2688-299X (print), 2688-3007 (electronic)",
  ISSN-L =       "2688-299X",
  bibdate =      "Sat Aug 21 15:11:10 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/telo.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3461016",
  abstract =     "We use continuous optimisation and manual code changes
                 to evolve up to 1024 Newton--Raphson numerical values
                 embedded in an open source GNU C library glibc square
                 root sqrt to implement a double precision cube root
                 routine cbrt, binary logarithm log2 and reciprocal
                 square root function for C in seconds. The GI inverted
                 square root $ x{-1 / 2} $ is far more accurate than
                 Quake's InvSqrt, Quare root. GI shows potential for
                 automatically creating mobile or low resource mote
                 smart dust bespoke custom mathematical libraries with
                 new functionality.",
  acknowledgement = ack-nhfb,
  articleno =    "7",
  fjournal =     "ACM Transactions on Evolutionary Learning and
                 Optimization",
  journal-URL =  "https://dl.acm.org/loi/telo",
}


bibtype: inproceedings
filename: elefunt.bib
label: Lim:2021:HPC
author: Jay P. Lim and Santosh Nagarakatte
title: High performance correctly rounded math libraries for 32-bit floating point representations
publisher: pub-ACM
address: pub-ACM:adr
pages: 7:1--7:30
month: jun
monthnumber: 6
year: 2021
DOI: https://doi.org/10.1145/3453483.3454049
bibdate: Tue Sep 24 15:06:44 2024
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2024.09.24 15:06:44 ???
URL: https://github.com/rutgers-apl/rlibm-32
keywords: binary32; correctly rounded functions; posit32
acknowledgement: ack-nhfb
rawauthor: Jay P. Lim and Santosh Nagarakatte
rawtitle: High performance correctly rounded math libraries for 32-bit floating point representations
booktitle:
Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation

abstract:
This paper proposes a set of techniques to develop correctly rounded math libraries for 32-bit float and posit types. It enhances our RLIBM approach that frames the problem of generating correctly rounded libraries as a linear programming problem in the context of 16-bit types to scale to 32-bit types. Specifically, this paper proposes new algorithms to (1) generate polynomials that produce correctly rounded outputs for all inputs using counterexample guided polynomial generation, (2) generate efficient piecewise polynomials with bit-pattern based domain splitting, and (3) deduce the amount of freedom available to produce correct results when range reduction involves multiple elementary functions. The resultant math library for the 32-bit float type is faster than state-of-the-art math libraries while producing the correct output for all inputs. We have also developed a set of correctly rounded elementary functions for 32-bit posits.

rawabstract:
This paper proposes a set of techniques to develop correctly rounded math libraries for 32-bit float and posit types. It enhances our RLIBM approach that frames the problem of generating correctly rounded libraries as a linear programming problem in the context of 16-bit types to scale to 32-bit types. Specifically, this paper proposes new algorithms to (1) generate polynomials that produce correctly rounded outputs for all inputs using counterexample guided polynomial generation, (2) generate efficient piecewise polynomials with bit-pattern based domain splitting, and (3) deduce the amount of freedom available to produce correct results when range reduction involves multiple elementary functions. The resultant math library for the 32-bit float type is faster than state-of-the-art math libraries while producing the correct output for all inputs. We have also developed a set of correctly rounded elementary functions for 32-bit posits.

rawbooktitle:
Proceedings of the {42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation}

entry:
@InProceedings{Lim:2021:HPC,
  author =       "Jay P. Lim and Santosh Nagarakatte",
  booktitle =    "Proceedings of the {42nd ACM SIGPLAN International
                 Conference on Programming Language Design and
                 Implementation}",
  title =        "High performance correctly rounded math libraries for
                 32-bit floating point representations",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  month =        jun,
  year =         "2021",
  DOI =          "https://doi.org/10.1145/3453483.3454049",
  bibdate =      "Tue Sep 24 15:06:44 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://github.com/rutgers-apl/rlibm-32",
  abstract =     "This paper proposes a set of techniques to develop
                 correctly rounded math libraries for 32-bit float and
                 posit types. It enhances our RLIBM approach that frames
                 the problem of generating correctly rounded libraries
                 as a linear programming problem in the context of
                 16-bit types to scale to 32-bit types. Specifically,
                 this paper proposes new algorithms to (1) generate
                 polynomials that produce correctly rounded outputs for
                 all inputs using counterexample guided polynomial
                 generation, (2) generate efficient piecewise
                 polynomials with bit-pattern based domain splitting,
                 and (3) deduce the amount of freedom available to
                 produce correct results when range reduction involves
                 multiple elementary functions. The resultant math
                 library for the 32-bit float type is faster than
                 state-of-the-art math libraries while producing the
                 correct output for all inputs. We have also developed a
                 set of correctly rounded elementary functions for
                 32-bit posits.",
  acknowledgement = ack-nhfb,
  description =  "RLIBM-32 is both a math library that provides
                 correctly rounded result for all inputs and tools used
                 to generate the correct polynomials. The techniques
                 behind the tools will be appearing at PLDI 2021.
                 Currently, RLIBM-32 supports a number of elementary
                 functions for float and posit32
                 representations.\par

                 List of float functions supported by
                 RLIBM-32:\par

                 log(x), log2(x), log10(x) \\
                 exp(x), exp2(x), exp10(x) \\
                 sinh(x), cosh(x) \\
                 sinpi(x), cospi(x)\par

                 List of posit32 functions supported by
                 RLIBM-32:\par

                 log(x), log2(x), log10(x) \\
                 exp(x), exp2(x), exp10(x) \\
                 sinh(x), cosh(x)",
  keywords =     "binary32; correctly rounded functions; posit32",
  remark-1 =     "From page 360: ``Our RLibm approach [31, 32] generates
                 polynomials that approximate the correctly rounded
                 result rather than the real value of the elementary
                 function. \ldots{} Using the RLibm approach, we have
                 been successful in generating correctly rounded
                 libraries with 16-bit types such as bfloat16 and
                 posit16.''",
  remark-2 =     "From page 360: ``A naive use of the RLibm approach
                 with 32-bit types will generate more than a billion
                 constraints, which is beyond the capabilities of
                 current LP solvers.''",
  remark-3 =     "From page 361: ``Our elementary functions for floats
                 are faster than existing libraries: Intel's libm,
                 Glibc's libm, CR-LIBM [13], and Metalibm [25]. Unlike
                 existing libraries, our functions produce correctly
                 rounded results for all inputs. We have developed the
                 first correctly rounded implementations of functions
                 for 32-bit posits.''",
  remark-4 =     "From page 363: ``All internal computation such as
                 range reduction, polynomial evaluation, and output
                 compensation is performed in representation H where H
                 has higher precision than T. To attain good
                 performance, H is a representation that is supported in
                 hardware (e.g., double).''",
  remark-5 =     "From page 368: ``CR-LIBM has correctly rounded
                 functions for double precision. However, CR-LIBM does
                 not produce correctly rounded results for 32-bit floats
                 due to double rounding. There are no math libraries
                 available for posit32. All posit32 values can be
                 exactly represented in double.''",
  remark-6 =     "From page 370: ``All three re-purposed math libraries
                 produce wrong results for some inputs. RLibm-32
                 provides the first correctly rounded functions for the
                 posit32 type.''",
  remark-7 =     "From page 372: ``This paper extends our prior work on
                 RLibm [31, 32] and John Gustafson's Minefield method
                 [20], which advocate approximating the correctly
                 rounded value rather than real value of an elementary
                 function.''",
  remark-8 =     "From page 372: ``We have used RLibm to create
                 correctly rounded functions for 16-bit types: bfloat16
                 and posit16.''",
}


bibtype: article
filename: elefunt.bib
label: Lipovetsky:2021:BRI
author: Stan Lipovetsky
journal: j-TECHNOMETRICS
volume: 62
number: 4
pages: 560--560
year: 2021
CODEN: TCMTA2
DOI: https://doi.org/10.1080/00401706.2020.1825632
ISSN: 0040-1706 (print), 1537-2723 (electronic) OR 00401706 (print), 15372723 (electronic)
ISSNL: 0040-1706 OR 00401706
bibdate: Fri Feb 5 17:42:52 MST 2021
bibtimestamp: 2021.02.05 17:42:52 MST
fjournal: Technometrics
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/utch20
onlinedate: 23 Oct 2020
rawauthor: Stan Lipovetsky
title:
Book Review: booktitle Integrals Related to the Error Function, by Nikolai E. Korotkov and Alexander N. Korotkov. Boca Raton, FL: Chapman and Hall / CRC Press, Taylor & Francis Group, 2020, 228 pp., $140.00 (hardback), $46.36 (eBook), ISBN: 978-0-367-40820-6 (hardback)

bibsource:
http://www.tandf.co.uk/journals/titles/00401706.html; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/technometrics2020.bib

rawtitle:
Book Review: {{\booktitle{Integrals Related to the Error Function}}, by Nikolai E. Korotkov and Alexander N. Korotkov. Boca Raton, FL: Chapman and Hall\slash CRC Press, Taylor \& Francis Group, 2020, 228 pp., \$140.00 (hardback), \$46.36 (eBook), ISBN: 978-0-367-40820-6 (hardback)}

entry:
@Article{Lipovetsky:2021:BRI,
  author =       "Stan Lipovetsky",
  title =        "Book Review: {{\booktitle{Integrals Related to the
                 Error Function}}, by Nikolai E. Korotkov and Alexander
                 N. Korotkov. Boca Raton, FL: Chapman and Hall\slash CRC
                 Press, Taylor \& Francis Group, 2020, 228 pp., \$140.00
                 (hardback), \$46.36 (eBook), ISBN: 978-0-367-40820-6
                 (hardback)}",
  journal =      j-TECHNOMETRICS,
  volume =       "62",
  number =       "4",
  pages =        "560--560",
  year =         "2021",
  CODEN =        "TCMTA2",
  DOI =          "https://doi.org/10.1080/00401706.2020.1825632",
  ISSN =         "0040-1706 (print), 1537-2723 (electronic)",
  ISSN-L =       "0040-1706",
  bibdate =      "Fri Feb 5 17:42:52 MST 2021",
  bibsource =    "http://www.tandf.co.uk/journals/titles/00401706.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/technometrics2020.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Technometrics",
  journal-URL =  "http://www.tandfonline.com/loi/utch20",
  onlinedate =   "23 Oct 2020",
}


bibtype: techreport
filename: elefunt.bib
label: MPFR:2021:MLA
author: The MPFR Team
title: The MPFR Library: Algorithms and Proofs
type: Report
pages: 69
day: 5
month: nov
monthnumber: 11
year: 2021
bibdate: Tue Mar 14 13:13:13 2023
bibtimestamp: 2023.03.14 13:13:13 ???
URL: https://www.mpfr.org/algorithms.pdf
acknowledgement: ack-nhfb
rawauthor: {The MPFR Team}
rawtitle: The {MPFR} Library: Algorithms and Proofs
entry:
@TechReport{MPFR:2021:MLA,
  author =       "{The MPFR Team}",
  title =        "The {MPFR} Library: Algorithms and Proofs",
  type =         "Report",
  institution =  "????",
  address =      "????",
  pages =        "69",
  day =          "5",
  month =        nov,
  year =         "2021",
  bibdate =      "Tue Mar 14 13:13:13 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.mpfr.org/algorithms.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Patankar:2021:RBC
author: Udayan S. Patankar and Ants Koel
title: Review of Basic Classes of Dividers Based on Division Algorithm
journal: j-IEEE-ACCESS
volume: 9
pages: 23035--23069
year: 2021
DOI: https://doi.org/10.1109/access.2021.3055735
ISSN: 2169-3536 OR 21693536
ISSNL: 2169-3536 OR 21693536
bibdate: Thu Apr 10 15:08:12 2025
bibtimestamp: 2025.04.10 15:08:12 ???
fjournal: IEEE Access
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639
rawauthor: Udayan S. Patankar and Ants Koel
rawtitle: Review of Basic Classes of Dividers Based on Division Algorithm
entry:
@Article{Patankar:2021:RBC,
  author =       "Udayan S. Patankar and Ants Koel",
  title =        "Review of Basic Classes of Dividers Based on Division
                 Algorithm",
  journal =      j-IEEE-ACCESS,
  volume =       "9",
  pages =        "23035--23069",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/access.2021.3055735",
  ISSN =         "2169-3536",
  ISSN-L =       "2169-3536",
  bibdate =      "Thu Apr 10 15:08:12 2025",
  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 =     "IEEE Access",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
}


bibtype: article
filename: elefunt.bib
label: Snyder:2021:CRA
author: W. Van Snyder
title: Corrigendum: Remark on Algorithm 723: Fresnel Integrals
journal: j-TOMS
volume: 47
number: 4
pages: 37:1--37:1
month: dec
monthnumber: 12
year: 2021
CODEN: ACMSCU
DOI: https://doi.org/10.1145/3452336
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Wed Sep 29 06:58:41 MDT 2021
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib
bibtimestamp: 2021.09.29 06:58:41 MDT
note: See cite Snyder:1993:AFI.
URL: https://dl.acm.org/doi/10.1145/3452336
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
articleno: 37
journalURL: https://dl.acm.org/loi/toms
rawauthor: W. Van Snyder
rawnote: See \cite{Snyder:1993:AFI}.
rawtitle: Corrigendum: {Remark on Algorithm 723: Fresnel Integrals}
abstract:
There are mistakes and typographical errors in Remark on Algorithm 723: Fresnel Integrals, which appeared in ACM Transactions on Mathematical Software 22, 4 (December 1996). This remark corrects those errors. The software provided to Collected Algorithms of the ACM was correct.

rawabstract:
There are mistakes and typographical errors in Remark on Algorithm 723: Fresnel Integrals, which appeared in ACM Transactions on Mathematical Software 22, 4 (December 1996). This remark corrects those errors. The software provided to Collected Algorithms of the ACM was correct.

entry:
@Article{Snyder:2021:CRA,
  author =       "W. Van Snyder",
  title =        "Corrigendum: {Remark on Algorithm 723: Fresnel
                 Integrals}",
  journal =      j-TOMS,
  volume =       "47",
  number =       "4",
  pages =        "37:1--37:1",
  month =        dec,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3452336",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Sep 29 06:58:41 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Snyder:1993:AFI}.",
  URL =          "https://dl.acm.org/doi/10.1145/3452336",
  abstract =     "There are mistakes and typographical errors in Remark
                 on Algorithm 723: Fresnel Integrals, which appeared in
                 ACM Transactions on Mathematical Software 22, 4
                 (December 1996). This remark corrects those errors. The
                 software provided to Collected Algorithms of the ACM
                 was correct.",
  acknowledgement = ack-nhfb,
  articleno =    "37",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Walczyk:2021:IAF
author: Cezary J. Walczyk and Leonid V. Moroz and Jan L. Cieslinski
title: Improving the Accuracy of the Fast Inverse Square Root by Modifying Newton--Raphson Corrections
journal: j-ENTROPY
volume: 23
number: 1
pages: 86:1--86:20
month: jan
monthnumber: 1
year: 2021
CODEN: ENTRFG
DOI: https://doi.org/10.3390/e23010086
ISSN: 1099-4300 OR 10994300
ISSNL: 1099-4300 OR 10994300
bibdate: Wed Dec 20 07:52:39 2023
bibtimestamp: 2023.12.20 07:52:39 ???
fjournal: Entropy
acknowledgement: ack-nhfb
journalURL: https://www.mdpi.com/journal/entropy/
rawauthor: Cezary J. Walczyk and Leonid V. Moroz and Jan L. Cie{\'s}li{\'n}ski
rawtitle: Improving the Accuracy of the Fast Inverse Square Root by Modifying {Newton--Raphson} Corrections
entry:
@Article{Walczyk:2021:IAF,
  author =       "Cezary J. Walczyk and Leonid V. Moroz and Jan L.
                 Cie{\'s}li{\'n}ski",
  title =        "Improving the Accuracy of the Fast Inverse Square Root
                 by Modifying {Newton--Raphson} Corrections",
  journal =      j-ENTROPY,
  volume =       "23",
  number =       "1",
  pages =        "86:1--86:20",
  month =        jan,
  year =         "2021",
  CODEN =        "ENTRFG",
  DOI =          "https://doi.org/10.3390/e23010086",
  ISSN =         "1099-4300",
  ISSN-L =       "1099-4300",
  bibdate =      "Wed Dec 20 07:52:39 2023",
  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 =     "Entropy",
  journal-URL =  "https://www.mdpi.com/journal/entropy/",
}


bibtype: misc
filename: elefunt.bib
label: Anonymous:2022:DLM
author: Anonymous
title: Digital Library of Mathematical Functions: Date: 2010
pages: 86:1--86:20
day: 14
month: mar
monthnumber: 3
year: 2022
bibdate: Wed Oct 25 18:20:12 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2023.10.25 18:20:12 ???
acknowledgement: ack-nhfb
howpublished: NIST Web site
rawauthor: Anonymous
rawtitle: Digital Library of Mathematical Functions: Date: 2010
URL:
https://dlmf.nist.gov/; https://www.nist.gov/mathematics-statistics/digital-library-mathematical-functions

abstract:
In 2010, NIST released the Digital Library of Mathematical Functions (DLMF), an online successor to the classic Abramowitz and Stegun booktitle Handbook of Mathematical Functions. [cite Abramowitz:1964:HMF]

remark:
From the site: ``By the late 1990s it [the 1964 Handbook] was still the most widely distributed and cited publication of all time, regularly seeing more than 2000 citations per year.''

rawabstract:
In 2010, NIST released the Digital Library of Mathematical Functions (DLMF), an online successor to the classic Abramowitz and Stegun \booktitle{Handbook of Mathematical Functions}. [\cite{Abramowitz:1964:HMF}]

entry:
@Misc{Anonymous:2022:DLM,
  author =       "Anonymous",
  title =        "Digital Library of Mathematical Functions: Date:
                 2010",
  howpublished = "NIST Web site",
  day =          "14",
  month =        mar,
  year =         "2022",
  bibdate =      "Wed Oct 25 18:20:12 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://dlmf.nist.gov/;
                 https://www.nist.gov/mathematics-statistics/digital-library-mathematical-functions",
  abstract =     "In 2010, NIST released the Digital Library of
                 Mathematical Functions (DLMF), an online successor to
                 the classic Abramowitz and Stegun \booktitle{Handbook
                 of Mathematical Functions}.
                 [\cite{Abramowitz:1964:HMF}]",
  acknowledgement = ack-nhfb,
  remark =       "From the site: ``By the late 1990s it [the 1964
                 Handbook] was still the most widely distributed and
                 cited publication of all time, regularly seeing more
                 than 2000 citations per year.''",
}


bibtype: inproceedings
filename: elefunt.bib
label: Borges:2022:HLA
author: Carlos F. Borges and Claude-Pierre Jeannerod and Jean-Michel Muller
title: High-level algorithms for correctly-rounded reciprocal square roots
crossref: IEEE:2022:ISC
pages: 18--25
year: 2022
DOI: https://doi.org/10.1109/ARITH54963.2022.00013
bibdate: Thu Sep 21 10:14:25 2023
bibtimestamp: 2023.09.21 10:14:25 ???
keywords: ARITH-29
acknowledgement: ack-nhfb
rawauthor: Carlos F. Borges and Claude-Pierre Jeannerod and Jean-Michel Muller
rawtitle: High-level algorithms for correctly-rounded reciprocal square roots
entry:
@InProceedings{Borges:2022:HLA,
  author =       "Carlos F. Borges and Claude-Pierre Jeannerod and
                 Jean-Michel Muller",
  title =        "High-level algorithms for correctly-rounded reciprocal
                 square roots",
  crossref =     "IEEE:2022:ISC",
  pages =        "18--25",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00013",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  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 =     "ARITH-29",
}


bibtype: inproceedings
filename: elefunt.bib
label: Bruguera:2022:LLH
author: Javier D. Bruguera
title: Low-Latency and High-Bandwidth Pipelined Radix-64 Division and Square Root Unit
crossref: IEEE:2022:ISC
pages: 10--17
year: 2022
DOI: https://doi.org/10.1109/ARITH54963.2022.00012
bibdate: Thu Sep 21 10:14:25 2023
bibtimestamp: 2023.09.21 10:14:25 ???
keywords: ARITH-29
acknowledgement: ack-nhfb
rawauthor: Javier D. Bruguera
rawtitle: Low-Latency and High-Bandwidth Pipelined Radix-64 Division and Square Root Unit
entry:
@InProceedings{Bruguera:2022:LLH,
  author =       "Javier D. Bruguera",
  title =        "Low-Latency and High-Bandwidth Pipelined Radix-64
                 Division and Square Root Unit",
  crossref =     "IEEE:2022:ISC",
  pages =        "10--17",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00012",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  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 =     "ARITH-29",
}


bibtype: article
filename: elefunt.bib
label: Causley:2022:GFI
author: Matthew F. Causley
title: The gamma function via interpolation
journal: j-NUMER-ALGORITHMS
volume: 90
number: 2
pages: 687--707
month: jun
monthnumber: 6
year: 2022
CODEN: NUALEG
DOI: https://doi.org/10.1007/s11075-021-01204-8
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
bibdate: Sun May 8 06:36:19 MDT 2022
bibtimestamp: 2022.05.08 06:36:19 MDT
URL: https://link.springer.com/article/10.1007/s11075-021-01204-8
fjournal: Numerical Algorithms
acknowledgement: ack-nhfb
ajournal: Numer. Algorithms
journalURL: http://link.springer.com/journal/11075
rawauthor: Matthew F. Causley
rawtitle: The gamma function via interpolation
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib

entry:
@Article{Causley:2022:GFI,
  author =       "Matthew F. Causley",
  title =        "The gamma function via interpolation",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "90",
  number =       "2",
  pages =        "687--707",
  month =        jun,
  year =         "2022",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-021-01204-8",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Sun May 8 06:36:19 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  URL =          "https://link.springer.com/article/10.1007/s11075-021-01204-8",
  acknowledgement = ack-nhfb,
  ajournal =     "Numer. Algorithms",
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}


bibtype: article
filename: elefunt.bib
label: Cojean:2022:GML
author: Terry Cojean and Yu-Hsiang Mike Tsai and Hartwig Anzt
title: Ginkgo --- a math library designed for platform portability
journal: j-PARALLEL-COMPUTING
volume: 111
pages: ??--??
month: jul
monthnumber: 7
year: 2022
CODEN: PACOEJ
DOI: https://doi.org/10.1016/j.parco.2022.102902
ISSN: 0167-8191 (print), 1872-7336 (electronic) OR 01678191 (print), 18727336 (electronic)
ISSNL: 0167-8191 OR 01678191
bibdate: Mon May 9 07:06:37 MDT 2022
bibtimestamp: 2022.05.09 07:06:37 MDT
URL: http://www.sciencedirect.com/science/article/pii/S0167819122000096
fjournal: Parallel Computing
acknowledgement: ack-nhfb
articleno: 102902
journalURL: http://www.sciencedirect.com/science/journal/01678191
rawauthor: Terry Cojean and Yu-Hsiang Mike Tsai and Hartwig Anzt
rawtitle: {Ginkgo} --- a math library designed for platform portability
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/parallelcomputing.bib

abstract:
In an era of increasing computer system diversity, the portability of software from one system to another plays a central role. Software portability is important for the software developers as many software projects have a lifetime longer than a specific system, e.g., a supercomputer, and it is important for the domain scientists that realize their scientific application in a software framework and want to be able to run on one or another system. On a high level, there exist two approaches for realizing platform portability: (1) implementing software using a portability layer leveraging any technique which always generates specific kernels from another language or through an interface for running on different architectures; and (2) providing backends for different hardware architectures, with the backends typically differing in how and in which programming language functionality is realized due to using the language of choice for each hardware (e.g., CUDA kernels for NVIDIA GPUs, SYCL (DPC++) kernels to targeting Intel GPUs and other supported hardware, ldots ). In practice, these two approaches can be combined in applications to leverage their respective strengths. In this paper, we present how we realize portability across different hardware architectures for the Ginkgo library by following the second strategy and the goal to not only port to new hardware architectures but also achieve good performance. We present the Ginkgo library design, separating algorithms from hardware-specific kernels forming the distinct hardware executors, and report our experience when adding execution backends for NVIDIA, AMD, and Intel GPUs. We also present the performance we achieve with this approach for distinct hardware backends.

rawabstract:
In an era of increasing computer system diversity, the portability of software from one system to another plays a central role. Software portability is important for the software developers as many software projects have a lifetime longer than a specific system, e.g., a supercomputer, and it is important for the domain scientists that realize their scientific application in a software framework and want to be able to run on one or another system. On a high level, there exist two approaches for realizing platform portability: (1) implementing software using a portability layer leveraging any technique which always generates specific kernels from another language or through an interface for running on different architectures; and (2) providing backends for different hardware architectures, with the backends typically differing in how and in which programming language functionality is realized due to using the language of choice for each hardware (e.g., CUDA kernels for NVIDIA GPUs, SYCL (DPC++) kernels to targeting Intel GPUs and other supported hardware, \ldots). In practice, these two approaches can be combined in applications to leverage their respective strengths. In this paper, we present how we realize portability across different hardware architectures for the Ginkgo library by following the second strategy and the goal to not only port to new hardware architectures but also achieve good performance. We present the Ginkgo library design, separating algorithms from hardware-specific kernels forming the distinct hardware executors, and report our experience when adding execution backends for NVIDIA, AMD, and Intel GPUs. We also present the performance we achieve with this approach for distinct hardware backends.

entry:
@Article{Cojean:2022:GML,
  author =       "Terry Cojean and Yu-Hsiang Mike Tsai and Hartwig
                 Anzt",
  title =        "{Ginkgo} --- a math library designed for platform
                 portability",
  journal =      j-PARALLEL-COMPUTING,
  volume =       "111",
  number =       "??",
  pages =        "??--??",
  month =        jul,
  year =         "2022",
  CODEN =        "PACOEJ",
  DOI =          "https://doi.org/10.1016/j.parco.2022.102902",
  ISSN =         "0167-8191 (print), 1872-7336 (electronic)",
  ISSN-L =       "0167-8191",
  bibdate =      "Mon May 9 07:06:37 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/parallelcomputing.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167819122000096",
  abstract =     "In an era of increasing computer system diversity, the
                 portability of software from one system to another
                 plays a central role. Software portability is important
                 for the software developers as many software projects
                 have a lifetime longer than a specific system, e.g., a
                 supercomputer, and it is important for the domain
                 scientists that realize their scientific application in
                 a software framework and want to be able to run on one
                 or another system. On a high level, there exist two
                 approaches for realizing platform portability: (1)
                 implementing software using a portability layer
                 leveraging any technique which always generates
                 specific kernels from another language or through an
                 interface for running on different architectures; and
                 (2) providing backends for different hardware
                 architectures, with the backends typically differing in
                 how and in which programming language functionality is
                 realized due to using the language of choice for each
                 hardware (e.g., CUDA kernels for NVIDIA GPUs, SYCL
                 (DPC++) kernels to targeting Intel GPUs and other
                 supported hardware, \ldots). In practice, these two
                 approaches can be combined in applications to leverage
                 their respective strengths. In this paper, we present
                 how we realize portability across different hardware
                 architectures for the Ginkgo library by following the
                 second strategy and the goal to not only port to new
                 hardware architectures but also achieve good
                 performance. We present the Ginkgo library design,
                 separating algorithms from hardware-specific kernels
                 forming the distinct hardware executors, and report our
                 experience when adding execution backends for NVIDIA,
                 AMD, and Intel GPUs. We also present the performance we
                 achieve with this approach for distinct hardware
                 backends.",
  acknowledgement = ack-nhfb,
  articleno =    "102902",
  fjournal =     "Parallel Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01678191",
}


bibtype: inproceedings
filename: elefunt.bib
label: Gao:2022:TFI
author: Zhanyuan Gao and Laiping Zhao and Haonan Chen
editor: IEEE
booktitle: 2022 IEEE / ACIS 22nd International Conference on Computer and Information Science (ICIS)
title: A Trigonometric Function Instruction Set Extension Method Based on RISC-V
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 119--126
year: 2022
DOI: https://doi.org/10.1109/ICIS54925.2022.9882453
bibdate: Sat Dec 16 15:51:40 2023
bibtimestamp: 2023.12.16 15:51:40 ???
acknowledgement: ack-nhfb
rawauthor: Zhanyuan Gao and Laiping Zhao and Haonan Chen
rawbooktitle: {2022 IEEE\slash ACIS 22nd International Conference on Computer and Information Science (ICIS)}
raweditor: {IEEE}
rawtitle: A Trigonometric Function Instruction Set Extension Method Based on {RISC-V}
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/risc-v.bib

entry:
@InProceedings{Gao:2022:TFI,
  author =       "Zhanyuan Gao and Laiping Zhao and Haonan Chen",
  editor =       "{IEEE}",
  booktitle =    "{2022 IEEE\slash ACIS 22nd International Conference on
                 Computer and Information Science (ICIS)}",
  title =        "A Trigonometric Function Instruction Set Extension
                 Method Based on {RISC-V}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "119--126",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ICIS54925.2022.9882453",
  bibdate =      "Sat Dec 16 15:51:40 2023",
  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/risc-v.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Hao:2022:DVP
author: Jiangwei Hao and Jinchen Xu and YuanYuan Xia
title: Design of variable precision transcendental function automatic generator
journal: j-J-SUPERCOMPUTING
volume: 78
number: 2
pages: 2196--2218
month: feb
monthnumber: 2
year: 2022
CODEN: JOSUED
DOI: https://doi.org/10.1007/s11227-021-03937-8
ISSN: 0920-8542 (print), 1573-0484 (electronic) OR 09208542 (print), 15730484 (electronic)
ISSNL: 0920-8542 OR 09208542
bibdate: Mon Feb 28 16:44:34 MST 2022
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jsuper.bib
bibtimestamp: 2022.02.28 16:44:34 MST
URL: https://link.springer.com/article/10.1007/s11227-021-03937-8
fjournal: The Journal of Supercomputing
acknowledgement: ack-nhfb
ajournal: J. Supercomputing
journalURL: http://link.springer.com/journal/11227
rawauthor: Jiangwei Hao and Jinchen Xu and YuanYuan Xia
rawtitle: Design of variable precision transcendental function automatic generator
entry:
@Article{Hao:2022:DVP,
  author =       "Jiangwei Hao and Jinchen Xu and YuanYuan Xia",
  title =        "Design of variable precision transcendental function
                 automatic generator",
  journal =      j-J-SUPERCOMPUTING,
  volume =       "78",
  number =       "2",
  pages =        "2196--2218",
  month =        feb,
  year =         "2022",
  CODEN =        "JOSUED",
  DOI =          "https://doi.org/10.1007/s11227-021-03937-8",
  ISSN =         "0920-8542 (print), 1573-0484 (electronic)",
  ISSN-L =       "0920-8542",
  bibdate =      "Mon Feb 28 16:44:34 MST 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jsuper.bib",
  URL =          "https://link.springer.com/article/10.1007/s11227-021-03937-8",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Supercomputing",
  fjournal =     "The Journal of Supercomputing",
  journal-URL =  "http://link.springer.com/journal/11227",
}


bibtype: article
filename: elefunt.bib
label: Howard:2022:AAA
author: Roy M. Howard
title: Arbitrarily Accurate Analytical Approximations for the Error Function
journal: j-MATH-COMPUT-APPL
volume: 27
number: 1
pages: 14:1--14:44
month: feb
monthnumber: 2
year: 2022
DOI: https://doi.org/10.3390/mca27010014
ISSN: 2297-8747 OR 22978747
ISSNL: 2297-8747 OR 22978747
bibdate: Sun Feb 18 06:28:42 MST 2024
bibtimestamp: 2024.02.18 06:28:42 MST
URL: https://www.mdpi.com/2297-8747/27/1/14
fjournal: Mathematical and Computational Applications
acknowledgement: ack-nhfb
ajournal: Math. Comput. Appl.
articleno: 14
journalURL: https://www.mdpi.com/journal/mca
rawauthor: Roy M. Howard
rawtitle: Arbitrarily Accurate Analytical Approximations for the Error Function
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/math-comput-appl.bib

entry:
@Article{Howard:2022:AAA,
  author =       "Roy M. Howard",
  title =        "Arbitrarily Accurate Analytical Approximations for the
                 Error Function",
  journal =      j-MATH-COMPUT-APPL,
  volume =       "27",
  number =       "1",
  pages =        "14:1--14:44",
  month =        feb,
  year =         "2022",
  CODEN =        "????",
  DOI =          "https://doi.org/10.3390/mca27010014",
  ISSN =         "2297-8747",
  ISSN-L =       "2297-8747",
  bibdate =      "Sun Feb 18 06:28:42 MST 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/math-comput-appl.bib",
  URL =          "https://www.mdpi.com/2297-8747/27/1/14",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput. Appl.",
  articleno =    "14",
  fjournal =     "Mathematical and Computational Applications",
  journal-URL =  "https://www.mdpi.com/journal/mca",
}


bibtype: article
filename: elefunt.bib
label: Lim:2022:OPA
author: Jay P. Lim and Santosh Nagarakatte
journal: j-PACMPL
volume: 6
number: POPL
pages: 3:1--3:28
month: jan
monthnumber: 1
year: 2022
DOI: https://doi.org/10.1145/3498664
ISSN: 2475-1421 (electronic) OR 24751421 (electronic)
ISSNL: 2475-1421 OR 24751421
bibdate: Thu May 26 06:32:48 MDT 2022
bibtimestamp: 2022.05.26 06:32:48 MDT
URL: https://dl.acm.org/doi/10.1145/3498664
fjournal: Proceedings of the ACM on Programming Languages (PACMPL)
keywords: correct rounding; elementary functions
acknowledgement: ack-nhfb
articleno: 3
journalURL: https://dl.acm.org/loi/pacmpl
rawauthor: Jay P. Lim and Santosh Nagarakatte
title:
One polynomial approximation to produce correctly rounded results of an elementary function for multiple representations and rounding modes

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/pacmpl.bib

abstract:
Mainstream math libraries for floating point (FP) do not produce correctly rounded results for all inputs. In contrast, CR-LIBM and RLIBM provide correctly rounded implementations for a specific FP representation with one rounding mode. Using such libraries for a representation with a new rounding mode or with different precision will result in wrong results due to double rounding. This paper proposes a novel method to generate a single polynomial approximation that produces correctly rounded results for all inputs for multiple rounding modes and multiple precision configurations. To generate a correctly rounded library for n-bits, our key idea is to generate a polynomial approximation for a representation with n+2-bits using the round-to-odd mode. We prove that the resulting polynomial approximation will produce correctly rounded results for all five rounding modes in the standard and for multiple representations with k-bits such that $ |E| + 1 < k leq n $, where $ |E| $ is the number of exponent bits in the representation. Similar to our prior work in the RLIBM project, we approximate the correctly rounded result when we generate the library with n+2-bits using the round-to-odd mode. We also generate polynomial approximations by structuring it as a linear programming problem but propose enhancements to polynomial generation to handle the round-to-odd mode. Our prototype is the first 32-bit float library that produces correctly rounded results with all rounding modes in the IEEE standard for all inputs with a single polynomial approximation. It also produces correctly rounded results for any FP configuration ranging from 10-bits to 32-bits while also being faster than mainstream libraries.

rawabstract:
Mainstream math libraries for floating point (FP) do not produce correctly rounded results for all inputs. In contrast, CR-LIBM and RLIBM provide correctly rounded implementations for a specific FP representation with one rounding mode. Using such libraries for a representation with a new rounding mode or with different precision will result in wrong results due to double rounding. This paper proposes a novel method to generate a single polynomial approximation that produces correctly rounded results for all inputs for multiple rounding modes and multiple precision configurations. To generate a correctly rounded library for n-bits, our key idea is to generate a polynomial approximation for a representation with n+2-bits using the round-to-odd mode. We prove that the resulting polynomial approximation will produce correctly rounded results for all five rounding modes in the standard and for multiple representations with k-bits such that $ |E| + 1 < k \leq n $, where $ |E| $ is the number of exponent bits in the representation. Similar to our prior work in the RLIBM project, we approximate the correctly rounded result when we generate the library with n+2-bits using the round-to-odd mode. We also generate polynomial approximations by structuring it as a linear programming problem but propose enhancements to polynomial generation to handle the round-to-odd mode. Our prototype is the first 32-bit float library that produces correctly rounded results with all rounding modes in the IEEE standard for all inputs with a single polynomial approximation. It also produces correctly rounded results for any FP configuration ranging from 10-bits to 32-bits while also being faster than mainstream libraries.

rawtitle:
One polynomial approximation to produce correctly rounded results of an elementary function for multiple representations and rounding modes

entry:
@Article{Lim:2022:OPA,
  author =       "Jay P. Lim and Santosh Nagarakatte",
  title =        "One polynomial approximation to produce correctly
                 rounded results of an elementary function for multiple
                 representations and rounding modes",
  journal =      j-PACMPL,
  volume =       "6",
  number =       "POPL",
  pages =        "3:1--3:28",
  month =        jan,
  year =         "2022",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3498664",
  ISSN =         "2475-1421 (electronic)",
  ISSN-L =       "2475-1421",
  bibdate =      "Thu May 26 06:32:48 MDT 2022",
  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/pacmpl.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3498664",
  abstract =     "Mainstream math libraries for floating point (FP) do
                 not produce correctly rounded results for all inputs.
                 In contrast, CR-LIBM and RLIBM provide correctly
                 rounded implementations for a specific FP
                 representation with one rounding mode. Using such
                 libraries for a representation with a new rounding mode
                 or with different precision will result in wrong
                 results due to double rounding. This paper proposes a
                 novel method to generate a single polynomial
                 approximation that produces correctly rounded results
                 for all inputs for multiple rounding modes and multiple
                 precision configurations. To generate a correctly
                 rounded library for n-bits, our key idea is to generate
                 a polynomial approximation for a representation with
                 n+2-bits using the round-to-odd mode. We prove that the
                 resulting polynomial approximation will produce
                 correctly rounded results for all five rounding modes
                 in the standard and for multiple representations with
                 k-bits such that $ |E| + 1 < k \leq n $, where $ |E| $
                 is the number of exponent bits in the representation.
                 Similar to our prior work in the RLIBM project, we
                 approximate the correctly rounded result when we
                 generate the library with n+2-bits using the
                 round-to-odd mode. We also generate polynomial
                 approximations by structuring it as a linear
                 programming problem but propose enhancements to
                 polynomial generation to handle the round-to-odd mode.
                 Our prototype is the first 32-bit float library that
                 produces correctly rounded results with all rounding
                 modes in the IEEE standard for all inputs with a single
                 polynomial approximation. It also produces correctly
                 rounded results for any FP configuration ranging from
                 10-bits to 32-bits while also being faster than
                 mainstream libraries.",
  acknowledgement = ack-nhfb,
  articleno =    "3",
  fjournal =     "Proceedings of the ACM on Programming Languages
                 (PACMPL)",
  journal-URL =  "https://dl.acm.org/loi/pacmpl",
  keywords =     "correct rounding; elementary functions",
}


bibtype: inproceedings
filename: elefunt.bib
label: Oh:2022:EPA
author: Hyun Woo Oh and Won Sik Jeong and Seung Eun Lee
editor: IEEE
booktitle: 2022 19th International SoC Design Conference (ISOCC)
title: Evaluation of Posit Arithmetic on Machine Learning based on Approximate Exponential Functions
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 358--359
year: 2022
DOI: https://doi.org/10.1109/ISOCC56007.2022.10031524
bibdate: Fri Dec 15 09:21:55 2023
bibtimestamp: 2023.12.15 09:21:55 ???
acknowledgement: ack-nhfb
rawauthor: Hyun Woo Oh and Won Sik Jeong and Seung Eun Lee
rawbooktitle: {2022 19th International SoC Design Conference (ISOCC)}
raweditor: {IEEE}
rawtitle: Evaluation of Posit Arithmetic on Machine Learning based on Approximate Exponential Functions
entry:
@InProceedings{Oh:2022:EPA,
  author =       "Hyun Woo Oh and Won Sik Jeong and Seung Eun Lee",
  editor =       "{IEEE}",
  booktitle =    "{2022 19th International SoC Design Conference
                 (ISOCC)}",
  title =        "Evaluation of Posit Arithmetic on Machine Learning
                 based on Approximate Exponential Functions",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "358--359",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ISOCC56007.2022.10031524",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: elefunt.bib
label: Patel:2022:LPG
author: Pragnesh Patel and Aman Arora and Earl Swartzlander and Lizy John
booktitle: 2022 23rd International Symposium on Quality Electronic Design (ISQED)
title: LogGen: a Parameterized Generator for Designing Floating-Point Logarithm Units for Deep Learning
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1--7
year: 2022
DOI: https://doi.org/10.1109/ISQED54688.2022.9806139
bibdate: Wed Oct 1 06:40:18 2025
bibtimestamp: 2025.10.01 06:40:18 ???
acknowledgement: ack-nhfb
rawauthor: Pragnesh Patel and Aman Arora and Earl Swartzlander and Lizy John
rawbooktitle: {2022 23rd International Symposium on Quality Electronic Design (ISQED)}
rawtitle: {LogGen}: a Parameterized Generator for Designing Floating-Point Logarithm Units for Deep Learning
keywords:
ASIC; Deep learning; Deep Learning Hardware; Delays; Digital signal processing; Floating-point Arithmetic; FPGA; Generator; Generators; Logarithm; Measurement; Memory management; Pipelines; Tools

entry:
@InProceedings{Patel:2022:LPG,
  author =       "Pragnesh Patel and Aman Arora and Earl Swartzlander
                 and Lizy John",
  booktitle =    "{2022 23rd International Symposium on Quality
                 Electronic Design (ISQED)}",
  title =        "{LogGen}: a Parameterized Generator for Designing
                 Floating-Point Logarithm Units for Deep Learning",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--7",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ISQED54688.2022.9806139",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  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 =     "ASIC; Deep learning; Deep Learning Hardware; Delays;
                 Digital signal processing; Floating-point Arithmetic;
                 FPGA; Generator; Generators; Logarithm; Measurement;
                 Memory management; Pipelines; Tools",
}


bibtype: article
filename: elefunt.bib
label: Takekawa:2022:FPC
author: Takashi Takekawa
title: Fast parallel calculation of modified Bessel function of the second kind and its derivatives
journal: j-SOFTWAREX
volume: 17
pages: ??--??
month: jan
monthnumber: 1
year: 2022
DOI: https://doi.org/10.1016/j.softx.2021.100923
ISSN: 2352-7110 OR 23527110
ISSNL: 2352-7110 OR 23527110
bibdate: Mon Feb 28 10:41:25 MST 2022
bibtimestamp: 2022.02.28 10:41:25 MST
URL: http://www.sciencedirect.com/science/article/pii/S2352711021001655
fjournal: SoftwareX
acknowledgement: ack-nhfb
articleno: 100923
journalURL: https://www.sciencedirect.com/journal/softwarex/issues
rawauthor: Takashi Takekawa
rawtitle: Fast parallel calculation of modified {Bessel} function of the second kind and its derivatives
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/softwarex.bib

entry:
@Article{Takekawa:2022:FPC,
  author =       "Takashi Takekawa",
  title =        "Fast parallel calculation of modified {Bessel}
                 function of the second kind and its derivatives",
  journal =      j-SOFTWAREX,
  volume =       "17",
  number =       "??",
  pages =        "??--??",
  month =        jan,
  year =         "2022",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1016/j.softx.2021.100923",
  ISSN =         "2352-7110",
  ISSN-L =       "2352-7110",
  bibdate =      "Mon Feb 28 10:41:25 MST 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/softwarex.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S2352711021001655",
  acknowledgement = ack-nhfb,
  articleno =    "100923",
  fjournal =     "SoftwareX",
  journal-URL =  "https://www.sciencedirect.com/journal/softwarex/issues",
}


bibtype: article
filename: elefunt.bib
label: Akdemir:2023:ABC
author: S. Akdemir and S. Ozay and E. Oztekin
title: Asymptotic behavior of Clebsch--Gordan coefficients
journal: j-J-MATH-CHEM
volume: 62
number: 10
pages: 2761--2775
month: nov
monthnumber: 11
year: 2023
CODEN: JMCHEG
DOI: https://doi.org/10.1007/s10910-023-01544-x
ISSN: 0259-9791 (print), 1572-8897 (electronic) OR 02599791 (print), 15728897 (electronic)
ISSNL: 0259-9791 OR 02599791
bibdate: Tue Aug 5 06:18:24 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.08.05 06:18:24 ???
fjournal: Journal of Mathematical Chemistry
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10910
rawauthor: S. Akdemir and S. {\"O}zay and E. {\"O}ztekin
rawtitle: Asymptotic behavior of {Clebsch--Gordan} coefficients
entry:
@Article{Akdemir:2023:ABC,
  author =       "S. Akdemir and S. {\"O}zay and E. {\"O}ztekin",
  title =        "Asymptotic behavior of {Clebsch--Gordan}
                 coefficients",
  journal =      j-J-MATH-CHEM,
  volume =       "62",
  number =       "10",
  pages =        "2761--2775",
  month =        nov,
  year =         "2023",
  CODEN =        "JMCHEG",
  DOI =          "https://doi.org/10.1007/s10910-023-01544-x",
  ISSN =         "0259-9791 (print), 1572-8897 (electronic)",
  ISSN-L =       "0259-9791",
  bibdate =      "Tue Aug 5 06:18:24 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Chemistry",
  journal-URL =  "http://link.springer.com/journal/10910",
}


bibtype: article
filename: elefunt.bib
label: Ananthanarayan:2023:EAD
author: B. Ananthanarayan and Souvik Bera and S. Friot and O. Marichev and Tanay Pathak
title: On the evaluation of the Appell $ F_2 $ double hypergeometric function
journal: j-COMP-PHYS-COMM
volume: 284
pages: Article 108589
month: mar
monthnumber: 3
year: 2023
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/j.cpc.2022.108589
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Sat Feb 25 06:01:54 MST 2023
bibtimestamp: 2023.02.25 06:01:54 MST
URL: http://www.sciencedirect.com/science/article/pii/S0010465522003083
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: B. Ananthanarayan and Souvik Bera and S. Friot and O. Marichev and Tanay Pathak
rawtitle: On the evaluation of the {Appell} {$ F_2 $} double hypergeometric function
bibsource:
https://www.math.utah.edu/pub/tex/bib/compphyscomm2020.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Ananthanarayan:2023:EAD,
  author =       "B. Ananthanarayan and Souvik Bera and S. Friot and O.
                 Marichev and Tanay Pathak",
  title =        "On the evaluation of the {Appell} {$ F_2 $} double
                 hypergeometric function",
  journal =      j-COMP-PHYS-COMM,
  volume =       "284",
  number =       "??",
  pages =        "Article 108589",
  month =        mar,
  year =         "2023",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2022.108589",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Feb 25 06:01:54 MST 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465522003083",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: inproceedings
filename: elefunt.bib
label: Bavier:2023:VNF
author: Eric Bavier and Nicholas Knight and Hugues de Lassus Saint-Genies and Eric Love
title: Vectorized Nonlinear Functions with the RISC-V Vector Extension
crossref: IEEE:2023:PIS
pages: 127--130
year: 2023
DOI: https://doi.org/10.1109/ARITH58626.2023.00032
bibdate: Wed May 8 09:17:31 2024
bibtimestamp: 2024.05.08 09:17:31 ???
acknowledgement: ack-nhfb
rawauthor: Eric Bavier and Nicholas Knight and Hugues de Lassus Saint-Geni{\`e}s and Eric Love
rawtitle: Vectorized Nonlinear Functions with the {RISC-V} Vector Extension
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/risc-v.bib

keywords:
ARITH-30; floating point; Instruction sets; Libraries; Pipelines; RISC-V vectors; scalable vectors; Software; Software algorithms; vector mathematical functions; Vectors; Writing

entry:
@InProceedings{Bavier:2023:VNF,
  author =       "Eric Bavier and Nicholas Knight and Hugues de Lassus
                 Saint-Geni{\`e}s and Eric Love",
  title =        "Vectorized Nonlinear Functions with the {RISC-V}
                 Vector Extension",
  crossref =     "IEEE:2023:PIS",
  pages =        "127--130",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ARITH58626.2023.00032",
  bibdate =      "Wed May 8 09:17:31 2024",
  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/risc-v.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-30; floating point; Instruction sets; Libraries;
                 Pipelines; RISC-V vectors; scalable vectors; Software;
                 Software algorithms; vector mathematical functions;
                 Vectors; Writing",
}


bibtype: article
filename: elefunt.bib
label: Blanchard:2023:NMD
author: Jeffrey D. Blanchard and Marc Chamberland
title: Newton's Method Without Division
journal: j-AMER-MATH-MONTHLY
volume: 130
number: 7
pages: 606--617
year: 2023
CODEN: AMMYAE
DOI: https://doi.org/10.1080/00029890.2022.2093573
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
bibdate: Fri Aug 25 08:24:37 MDT 2023
bibtimestamp: 2023.08.25 08:24:37 MDT
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
journalURL: http://www.jstor.org/journals/00029890.html; https://www.tandfonline.com/loi/uamm20
onlinedate: 04 Aug 2023
rawauthor: Jeffrey D. Blanchard and Marc Chamberland
rawtitle: {Newton}'s Method Without Division
bibsource:
https://www.math.utah.edu/pub/tex/bib/amermathmonthly2020.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Blanchard:2023:NMD,
  author =       "Jeffrey D. Blanchard and Marc Chamberland",
  title =        "{Newton}'s Method Without Division",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "130",
  number =       "7",
  pages =        "606--617",
  year =         "2023",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.1080/00029890.2022.2093573",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Fri Aug 25 08:24:37 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/amermathmonthly2020.bib;
                 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 =  "http://www.jstor.org/journals/00029890.html;
                 https://www.tandfonline.com/loi/uamm20",
  onlinedate =   "04 Aug 2023",
}


bibtype: inproceedings
filename: elefunt.bib
label: Brisebarre:2023:TME
author: Nicolas Brisebarre and Silviu-Ioan Filip
title: Towards Machine-Efficient Rational $ L^infty $-Approximations of Mathematical Functions
crossref: IEEE:2023:PIS
pages: 119--126
year: 2023
DOI: https://doi.org/10.1109/ARITH58626.2023.00029
bibdate: Wed May 8 09:17:31 2024
bibtimestamp: 2024.05.08 09:17:31 ???
keywords: Approximation algorithms; ARITH-30; Behavioral sciences; Digital arithmetic; Software
acknowledgement: ack-nhfb
rawauthor: Nicolas Brisebarre and Silviu-Ioan Filip
rawtitle: Towards Machine-Efficient Rational {$ L^\infty $}-Approximations of Mathematical Functions
entry:
@InProceedings{Brisebarre:2023:TME,
  author =       "Nicolas Brisebarre and Silviu-Ioan Filip",
  title =        "Towards Machine-Efficient Rational {$ L^\infty
                 $}-Approximations of Mathematical Functions",
  crossref =     "IEEE:2023:PIS",
  pages =        "119--126",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ARITH58626.2023.00029",
  bibdate =      "Wed May 8 09:17:31 2024",
  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 =     "Approximation algorithms; ARITH-30; Behavioral
                 sciences; Digital arithmetic; Software",
}


bibtype: inproceedings
filename: elefunt.bib
label: deLamarliere:2023:SFP
author: Paul Geneau de Lamarliere and Guillaume Melquiond and Florian Faissole
title: Slimmer Formal Proofs for Mathematical Libraries
crossref: IEEE:2023:PIS
pages: 32--35
year: 2023
DOI: https://doi.org/10.1109/ARITH58626.2023.00026
bibdate: Wed May 8 09:17:31 2024
bibtimestamp: 2024.05.08 09:17:31 ???
acknowledgement: ack-nhfb
rawauthor: Paul Geneau de Lamarli{\`e}re and Guillaume Melquiond and Florian Faissole
rawtitle: Slimmer Formal Proofs for Mathematical Libraries
keywords:
ARITH-30; Behavioral sciences; Codes; Coq proof assistant; Costs; Digital arithmetic; Floating-point arithmetic; Formal methods; Libraries; Mathematical libraries; Writing

entry:
@InProceedings{deLamarliere:2023:SFP,
  author =       "Paul Geneau de Lamarli{\`e}re and Guillaume Melquiond
                 and Florian Faissole",
  title =        "Slimmer Formal Proofs for Mathematical Libraries",
  crossref =     "IEEE:2023:PIS",
  pages =        "32--35",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ARITH58626.2023.00026",
  bibdate =      "Wed May 8 09:17:31 2024",
  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 =     "ARITH-30; Behavioral sciences; Codes; Coq proof
                 assistant; Costs; Digital arithmetic; Floating-point
                 arithmetic; Formal methods; Libraries; Mathematical
                 libraries; Writing",
}


bibtype: article
filename: elefunt.bib
label: Gil:2023:EGF
author: Amparo Gil and Andrzej Odrzywolek and Javier Segura and Nico M. Temme
journal: j-COMP-PHYS-COMM
volume: 283
pages: Article 108563
month: feb
monthnumber: 2
year: 2023
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/j.cpc.2022.108563
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Mon Dec 5 09:16:39 MST 2022
bibtimestamp: 2022.12.05 09:16:39 MST
URL: http://www.sciencedirect.com/science/article/pii/S001046552200282X
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: Amparo Gil and Andrzej Odrzywo{\l}ek and Javier Segura and Nico M. Temme
title:
Evaluation of the generalized Fermi--Dirac integral and its derivatives for moderate / large values of the parameters

bibsource:
https://www.math.utah.edu/pub/tex/bib/compphyscomm2020.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

rawtitle:
Evaluation of the generalized {Fermi--Dirac} integral and its derivatives for moderate\slash large values of the parameters

entry:
@Article{Gil:2023:EGF,
  author =       "Amparo Gil and Andrzej Odrzywo{\l}ek and Javier Segura
                 and Nico M. Temme",
  title =        "Evaluation of the generalized {Fermi--Dirac} integral
                 and its derivatives for moderate\slash large values of
                 the parameters",
  journal =      j-COMP-PHYS-COMM,
  volume =       "283",
  number =       "??",
  pages =        "Article 108563",
  month =        feb,
  year =         "2023",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2022.108563",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Dec 5 09:16:39 MST 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S001046552200282X",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: inproceedings
filename: elefunt.bib
label: Graillat:2023:PCH
author: Stef Graillat and Youness Ibrahimy and Clothilde Jeangoudoux and Christoph Lauter
title: A parallel compensated Horner scheme for SIMD architecture
crossref: IEEE:2023:PIS
pages: 131--138
year: 2023
DOI: https://doi.org/10.1109/ARITH58626.2023.00010
bibdate: Wed May 8 09:17:31 2024
bibtimestamp: 2024.05.08 09:17:31 ???
acknowledgement: ack-nhfb
rawauthor: Stef Graillat and Youness Ibrahimy and Clothilde Jeangoudoux and Christoph Lauter
rawtitle: A parallel compensated {Horner} scheme for {SIMD} architecture
keywords:
ARITH-30; AVX; compensated algorithms; Computer architecture; Computers; Costs; Digital arithmetic; error-free transformations; Horner scheme; Limiting; parallel algorithms; polynomial evaluation; Registers; rounding errors; Scalability; SIMD

entry:
@InProceedings{Graillat:2023:PCH,
  author =       "Stef Graillat and Youness Ibrahimy and Clothilde
                 Jeangoudoux and Christoph Lauter",
  title =        "A parallel compensated {Horner} scheme for {SIMD}
                 architecture",
  crossref =     "IEEE:2023:PIS",
  pages =        "131--138",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ARITH58626.2023.00010",
  bibdate =      "Wed May 8 09:17:31 2024",
  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 =     "ARITH-30; AVX; compensated algorithms; Computer
                 architecture; Computers; Costs; Digital arithmetic;
                 error-free transformations; Horner scheme; Limiting;
                 parallel algorithms; polynomial evaluation; Registers;
                 rounding errors; Scalability; SIMD",
}


bibtype: techreport
filename: elefunt.bib
label: Hubrecht:2023:TCRa
author: Tom Hubrecht and Claude-Pierre Jeannerod and Paul Zimmermann
title: Towards a correctly-rounded and fast power function in binary64 arithmetic
type: Report
institution: DI-ENS --- Departement d'informatique --- ENS Paris
address: Paris, France
pages: 131--138
day: 12
month: jul
monthnumber: 7
year: 2023
bibdate: Mon May 13 12:00:21 2024
bibtimestamp: 2024.05.13 12:00:21 ???
URL: https://inria.hal.science/hal-04159652v1/
remark: This is a longer version of cite Hubrecht:2023:TCRb with proofs.
acknowledgement: ack-nhfb
rawauthor: Tom Hubrecht and Claude-Pierre Jeannerod and Paul Zimmermann
rawtitle: Towards a correctly-rounded and fast power function in binary64 arithmetic
abstract:
We design algorithms for the correct rounding of the power function $ x^y $ in the binary64 IEEE 754 format, for all rounding modes, modulo the knowledge of hardest-to-round cases. Our implementation of these algorithms largely outperforms previous correctly-rounded implementations and is not far from the efficiency of current mathematical libraries, which are not correctly-rounded. Still, we expect our algorithms can be further improved for speed. The proofs of correctness are fully detailed in an extended version of this paper, with the goal to enable a formal proof of these algorithms. We hope this work will motivate the next IEEE 754 revision committee to require correct rounding for mathematical functions.

rawabstract:
We design algorithms for the correct rounding of the power function $ x^y $ in the binary64 IEEE 754 format, for all rounding modes, modulo the knowledge of hardest-to-round cases. Our implementation of these algorithms largely outperforms previous correctly-rounded implementations and is not far from the efficiency of current mathematical libraries, which are not correctly-rounded. Still, we expect our algorithms can be further improved for speed. The proofs of correctness are fully detailed in an extended version of this paper, with the goal to enable a formal proof of these algorithms. We hope this work will motivate the next IEEE 754 revision committee to require correct rounding for mathematical functions.

entry:
@TechReport{Hubrecht:2023:TCRa,
  author =       "Tom Hubrecht and Claude-Pierre Jeannerod and Paul
                 Zimmermann",
  title =        "Towards a correctly-rounded and fast power function in
                 binary64 arithmetic",
  type =         "Report",
  institution =  "DI-ENS --- D{\'e}partement d'informatique --- ENS
                 Paris",
  address =      "Paris, France",
  day =          "12",
  month =        jul,
  year =         "2023",
  bibdate =      "Mon May 13 12:00:21 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://inria.hal.science/hal-04159652v1/",
  abstract =     "We design algorithms for the correct rounding of the
                 power function $ x^y $ in the binary64 IEEE 754 format,
                 for all rounding modes, modulo the knowledge of
                 hardest-to-round cases. Our implementation of these
                 algorithms largely outperforms previous
                 correctly-rounded implementations and is not far from
                 the efficiency of current mathematical libraries, which
                 are not correctly-rounded. Still, we expect our
                 algorithms can be further improved for speed. The
                 proofs of correctness are fully detailed in an extended
                 version of this paper, with the goal to enable a formal
                 proof of these algorithms. We hope this work will
                 motivate the next IEEE 754 revision committee to
                 require correct rounding for mathematical functions.",
  acknowledgement = ack-nhfb,
  remark =       "This is a longer version of \cite{Hubrecht:2023:TCRb}
                 with proofs.",
}


bibtype: inproceedings
filename: elefunt.bib
label: Hubrecht:2023:TCRb
author: Tom Hubrecht and Claude-Pierre Jeannerod and Paul Zimmermann
title: Towards a correctly-rounded and fast power function in binary64 arithmetic
crossref: IEEE:2023:PIS
pages: 111--118
year: 2023
DOI: https://doi.org/10.1109/ARITH58626.2023.00028
bibdate: Fri Dec 08 15:03:08 2023
bibtimestamp: 2023.12.08 15:03:08 ???
remark: See also longer versions cite Hubrecht:2023:TCRa,Hubrecht:2024:TCR.
acknowledgement: ack-nhfb
rawauthor: Tom Hubrecht and Claude-Pierre Jeannerod and Paul Zimmermann
rawtitle: Towards a correctly-rounded and fast power function in binary64 arithmetic
URL:
https://arith2023.arithsymposium.org/slides/S6_PaulZimmermannS6P1.pdf; https://inria.hal.science/hal-04159652v1/file/pow.pdf; https://inria.hal.science/hal-04326201

abstract:
We design algorithms for the correct rounding of the power function $ x^y $ in the binary64 IEEE 754 format, for all rounding modes, modulo the knowledge of hardest-to-round cases. Our implementation of these algorithms largely outperforms previous correctly-rounded implementations and is not far from the efficiency of current mathematical libraries, which are not correctly-rounded. Still, we expect our algorithms can be further improved for speed. The proofs of correctness are fully detailed, with the goal to enable a formal proof of these algorithms. We hope this work will motivate the next IEEE 754 revision committee to require correct rounding for mathematical functions.

keywords:
ARITH-30; binary64 format; correct rounding; Digital arithmetic; double precision; efficiency; Error analysis; IEEE 754; Libraries; power function; Prediction algorithms; Software; Software algorithms; Switches

rawabstract:
We design algorithms for the correct rounding of the power function $ x^y $ in the binary64 IEEE 754 format, for all rounding modes, modulo the knowledge of hardest-to-round cases. Our implementation of these algorithms largely outperforms previous correctly-rounded implementations and is not far from the efficiency of current mathematical libraries, which are not correctly-rounded. Still, we expect our algorithms can be further improved for speed. The proofs of correctness are fully detailed, with the goal to enable a formal proof of these algorithms. We hope this work will motivate the next IEEE 754 revision committee to require correct rounding for mathematical functions.

entry:
@InProceedings{Hubrecht:2023:TCRb,
  author =       "Tom Hubrecht and Claude-Pierre Jeannerod and Paul
                 Zimmermann",
  title =        "Towards a correctly-rounded and fast power function in
                 binary64 arithmetic",
  crossref =     "IEEE:2023:PIS",
  pages =        "111--118",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ARITH58626.2023.00028",
  bibdate =      "Fri Dec 08 15:03:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://arith2023.arithsymposium.org/slides/S6_PaulZimmermannS6P1.pdf;
                 https://inria.hal.science/hal-04159652v1/file/pow.pdf;
                 https://inria.hal.science/hal-04326201",
  abstract =     "We design algorithms for the correct rounding of the
                 power function $ x^y $ in the binary64 IEEE 754 format,
                 for all rounding modes, modulo the knowledge of
                 hardest-to-round cases. Our implementation of these
                 algorithms largely outperforms previous
                 correctly-rounded implementations and is not far from
                 the efficiency of current mathematical libraries, which
                 are not correctly-rounded. Still, we expect our
                 algorithms can be further improved for speed. The
                 proofs of correctness are fully detailed, with the goal
                 to enable a formal proof of these algorithms. We hope
                 this work will motivate the next IEEE 754 revision
                 committee to require correct rounding for mathematical
                 functions.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-30; binary64 format; correct rounding; Digital
                 arithmetic; double precision; efficiency; Error
                 analysis; IEEE 754; Libraries; power function;
                 Prediction algorithms; Software; Software algorithms;
                 Switches",
  remark =       "See also longer versions
                 \cite{Hubrecht:2023:TCRa,Hubrecht:2024:TCR}.",
}


bibtype: article
filename: elefunt.bib
label: Mansfield:2023:MSR
author: Daniel F. Mansfield
title: Mesopotamian square root approximation by a sequence of rectangles
journal: j-BRITISH-J-HIST-MATH
volume: 38
number: 3
pages: 175--188
year: 2023
DOI: https://doi.org/10.1080/26375451.2023.2215652
ISSN: 1749-8430 (print), 1749-8341 (electronic) OR 17498430 (print), 17498341 (electronic)
ISSNL: 1749-8341 OR 17498341
bibdate: Thu Apr 25 11:06:30 MDT 2024
bibtimestamp: 2024.04.25 11:06:30 MDT
URL: http://www.tandfonline.com/doi/full/10.1080/26375451.2023.2215652
fjournal: BSHM Bulletin: Journal of the British Society for the History of Mathematics
acknowledgement: ack-nhfb
ajournal: BSHM Bull.
journalURL: http://www.tandfonline.com/loi/tbsh20
onlinedate: 09 Jun 2023
rawauthor: Daniel F. Mansfield
rawtitle: {Mesopotamian} square root approximation by a sequence of rectangles
bibsource:
https://www.math.utah.edu/pub/tex/bib/bshm.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Mansfield:2023:MSR,
  author =       "Daniel F. Mansfield",
  title =        "{Mesopotamian} square root approximation by a sequence
                 of rectangles",
  journal =      j-BRITISH-J-HIST-MATH,
  volume =       "38",
  number =       "3",
  pages =        "175--188",
  year =         "2023",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/26375451.2023.2215652",
  ISSN =         "1749-8430 (print), 1749-8341 (electronic)",
  ISSN-L =       "1749-8341",
  bibdate =      "Thu Apr 25 11:06:30 MDT 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/bshm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.tandfonline.com/doi/full/10.1080/26375451.2023.2215652",
  acknowledgement = ack-nhfb,
  ajournal =     "BSHM Bull.",
  fjournal =     "BSHM Bulletin: Journal of the British Society for the
                 History of Mathematics",
  journal-URL =  "http://www.tandfonline.com/loi/tbsh20",
  onlinedate =   "09 Jun 2023",
}


bibtype: article
filename: elefunt.bib
label: Pradhan:2023:ETB
author: Chetana Pradhan and Martin Letras and Jurgen Teich
journal: j-TECS
volume: 22
number: 4
pages: 73:1--73:??
month: jul
monthnumber: 7
year: 2023
DOI: https://doi.org/10.1145/3580737
ISSN: 1539-9087 (print), 1558-3465 (electronic) OR 15399087 (print), 15583465 (electronic)
ISSNL: 1539-9087 OR 15399087
bibdate: Thu Aug 10 07:21:24 MDT 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/tecs.bib
bibtimestamp: 2023.08.10 07:21:24 MDT
URL: https://dl.acm.org/doi/10.1145/3580737
fjournal: ACM Transactions on Embedded Computing Systems
acknowledgement: ack-nhfb
ajournal: ACM Trans. Embed. Comput. Syst.
articleno: 73
journalURL: https://dl.acm.org/loi/tecs
rawauthor: Chetana Pradhan and Martin Letras and J{\"u}rgen Teich
title:
Efficient Table-based Function Approximation on FPGAs Using Interval Splitting and BRAM Instantiation

abstract:
This article proposes a novel approach for the generation of memory-efficient table-based function approximation circuits for edge devices in general and FPGAs in particular. Given a function $ f(x) $ to be approximated in a given interval $ [x_0, x_0 + a) $ and a maximum approximation error $ E_a $, the goal is to determine a function table implementation with a minimized memory footprint, i.e., number of entries that need to be stored. Rather than state-of-the-art work performing an equidistant sampling of the given interval by so-called breakpoints and using linear interpolation between two adjacent breakpoints to determine $ f(x) $ at the maximum error bound, we propose and compare three algorithms for splitting the given interval into sub-intervals to reduce the required memory footprint drastically based on the observation that in sub-intervals of low gradient, a coarser sampling grid may be assumed while guaranteeing the maximum interpolation error bound $ E_a $. Experiments on elementary mathematical functions show that a large fraction in memory footprint may be saved. Second, a hardware architecture implementing the sub-interval selection, breakpoint lookup, and interpolation at a latency of just 9 clock cycles is introduced. Third, for each generated circuit design, BRAMs are automatically instantiated rather than synthesizing the reduced footprint function table using LUT primitives, providing an additional degree of resource efficiency. The approach presented here for FPGAs can equally be applied to other circuit technologies for fast and, at the same time, memory-optimized function approximation at the edge.

rawabstract:
This article proposes a novel approach for the generation of memory-efficient table-based function approximation circuits for edge devices in general and FPGAs in particular. Given a function $ f(x) $ to be approximated in a given interval $ [x_0, x_0 + a) $ and a maximum approximation error $ E_a $, the goal is to determine a function table implementation with a minimized memory footprint, i.e., number of entries that need to be stored. Rather than state-of-the-art work performing an equidistant sampling of the given interval by so-called breakpoints and using linear interpolation between two adjacent breakpoints to determine $ f(x) $ at the maximum error bound, we propose and compare three algorithms for splitting the given interval into sub-intervals to reduce the required memory footprint drastically based on the observation that in sub-intervals of low gradient, a coarser sampling grid may be assumed while guaranteeing the maximum interpolation error bound $ E_a $. Experiments on elementary mathematical functions show that a large fraction in memory footprint may be saved. Second, a hardware architecture implementing the sub-interval selection, breakpoint lookup, and interpolation at a latency of just 9 clock cycles is introduced. Third, for each generated circuit design, BRAMs are automatically instantiated rather than synthesizing the reduced footprint function table using LUT primitives, providing an additional degree of resource efficiency. The approach presented here for FPGAs can equally be applied to other circuit technologies for fast and, at the same time, memory-optimized function approximation at the edge.

rawtitle:
Efficient Table-based Function Approximation on {FPGAs} Using Interval Splitting and {BRAM} Instantiation

entry:
@Article{Pradhan:2023:ETB,
  author =       "Chetana Pradhan and Martin Letras and J{\"u}rgen
                 Teich",
  title =        "Efficient Table-based Function Approximation on
                 {FPGAs} Using Interval Splitting and {BRAM}
                 Instantiation",
  journal =      j-TECS,
  volume =       "22",
  number =       "4",
  pages =        "73:1--73:??",
  month =        jul,
  year =         "2023",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3580737",
  ISSN =         "1539-9087 (print), 1558-3465 (electronic)",
  ISSN-L =       "1539-9087",
  bibdate =      "Thu Aug 10 07:21:24 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/tecs.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3580737",
  abstract =     "This article proposes a novel approach for the
                 generation of memory-efficient table-based function
                 approximation circuits for edge devices in general and
                 FPGAs in particular. Given a function $ f(x) $ to be
                 approximated in a given interval $ [x_0, x_0 + a) $ and
                 a maximum approximation error $ E_a $, the goal is to
                 determine a function table implementation with a
                 minimized memory footprint, i.e., number of entries
                 that need to be stored. Rather than state-of-the-art
                 work performing an equidistant sampling of the given
                 interval by so-called breakpoints and using linear
                 interpolation between two adjacent breakpoints to
                 determine $ f(x) $ at the maximum error bound, we
                 propose and compare three algorithms for splitting the
                 given interval into sub-intervals to reduce the
                 required memory footprint drastically based on the
                 observation that in sub-intervals of low gradient, a
                 coarser sampling grid may be assumed while guaranteeing
                 the maximum interpolation error bound $ E_a $.
                 Experiments on elementary mathematical functions show
                 that a large fraction in memory footprint may be saved.
                 Second, a hardware architecture implementing the
                 sub-interval selection, breakpoint lookup, and
                 interpolation at a latency of just 9 clock cycles is
                 introduced. Third, for each generated circuit design,
                 BRAMs are automatically instantiated rather than
                 synthesizing the reduced footprint function table using
                 LUT primitives, providing an additional degree of
                 resource efficiency. The approach presented here for
                 FPGAs can equally be applied to other circuit
                 technologies for fast and, at the same time,
                 memory-optimized function approximation at the edge.",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Embed. Comput. Syst.",
  articleno =    "73",
  fjournal =     "ACM Transactions on Embedded Computing Systems",
  journal-URL =  "https://dl.acm.org/loi/tecs",
}


bibtype: article
filename: elefunt.bib
label: Slevinsky:2023:RAE
author: Richard M. Slevinsky and Hassan Safouhi
title: A recursive algorithm for an efficient and accurate computation of incomplete Bessel functions
journal: j-NUMER-ALGORITHMS
volume: 92
number: 1
pages: 973--983
month: jan
monthnumber: 1
year: 2023
CODEN: NUALEG
DOI: https://doi.org/10.1007/s11075-022-01438-0
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
bibdate: Mon Jan 30 12:22:09 MST 2023
bibtimestamp: 2023.01.30 12:22:09 MST
URL: https://link.springer.com/article/10.1007/s11075-022-01438-0
fjournal: Numerical Algorithms
acknowledgement: ack-nhfb
ajournal: Numer. Algorithms
journalURL: http://link.springer.com/journal/11075
rawauthor: Richard M. Slevinsky and Hassan Safouhi
rawtitle: A recursive algorithm for an efficient and accurate computation of incomplete {Bessel} functions
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib

entry:
@Article{Slevinsky:2023:RAE,
  author =       "Richard M. Slevinsky and Hassan Safouhi",
  title =        "A recursive algorithm for an efficient and accurate
                 computation of incomplete {Bessel} functions",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "92",
  number =       "1",
  pages =        "973--983",
  month =        jan,
  year =         "2023",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-022-01438-0",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Mon Jan 30 12:22:09 MST 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  URL =          "https://link.springer.com/article/10.1007/s11075-022-01438-0",
  acknowledgement = ack-nhfb,
  ajournal =     "Numer. Algorithms",
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}


bibtype: article
filename: elefunt.bib
label: Ananthanarayan:2024:OWR
author: B. Ananthanarayan and Souvik Bera and S. Friot and Tanay Pathak
journal: j-COMP-PHYS-COMM
volume: 300
pages: ??--??
month: jul
monthnumber: 7
year: 2024
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/j.cpc.2024.109162
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Mon May 6 07:51:16 MDT 2024
bibtimestamp: 2024.05.06 07:51:16 MDT
URL: http://www.sciencedirect.com/science/article/pii/S0010465524000857
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
articleno: 109162
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: B. Ananthanarayan and Souvik Bera and S. Friot and Tanay Pathak
title:
pkg Olsson.wl and pkg ROC2.wl: Mathematica packages for transformations of multivariable hypergeometric functions and regions of convergence for their series representations in the two variables case

bibsource:
https://www.math.utah.edu/pub/tex/bib/compphyscomm2020.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathematica.bib

rawtitle:
\pkg{Olsson.wl} and \pkg{ROC2.wl}: {Mathematica} packages for transformations of multivariable hypergeometric functions and regions of convergence for their series representations in the two variables case

entry:
@Article{Ananthanarayan:2024:OWR,
  author =       "B. Ananthanarayan and Souvik Bera and S. Friot and
                 Tanay Pathak",
  title =        "\pkg{Olsson.wl} and \pkg{ROC2.wl}: {Mathematica}
                 packages for transformations of multivariable
                 hypergeometric functions and regions of convergence for
                 their series representations in the two variables
                 case",
  journal =      j-COMP-PHYS-COMM,
  volume =       "300",
  number =       "??",
  pages =        "??--??",
  month =        jul,
  year =         "2024",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2024.109162",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon May 6 07:51:16 MDT 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathematica.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465524000857",
  acknowledgement = ack-nhfb,
  articleno =    "109162",
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: article
filename: elefunt.bib
label: Briggs:2024:ISM
author: Ian Briggs and Yash Lad and Pavel Panchekha
title: Implementation and Synthesis of Math Library Functions
journal: j-PACMPL
volume: 8
number: POPL
pages: 32:1--32:??
month: jan
monthnumber: 1
year: 2024
DOI: https://doi.org/10.1145/3632874
ISSN: 2475-1421 (electronic) OR 24751421 (electronic)
ISSNL: 2475-1421 OR 24751421
bibdate: Fri May 10 10:23:39 MDT 2024
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/pacmpl.bib
bibtimestamp: 2024.05.10 10:23:39 MDT
URL: https://dl.acm.org/doi/10.1145/3632874
fjournal: Proceedings of the ACM on Programming Languages (PACMPL)
acknowledgement: ack-nhfb
ajournal: Proc. ACM Program. Lang.
articleno: 32
journalURL: https://dl.acm.org/loi/pacmpl
rawauthor: Ian Briggs and Yash Lad and Pavel Panchekha
rawtitle: Implementation and Synthesis of Math Library Functions
abstract:
Achieving speed and accuracy for math library functions like exp, sin, and log is difficult. This is because low-level implementation languages like C do not help math library developers catch mathematical errors, build implementations incrementally, or separate high-level and low-level decision making. This ultimately puts development of such functions out of reach for all but the most experienced experts. To address this, we introduce MegaLibm, a domain-specific language for implementing, testing, and tuning math library implementations. MegaLibm is safe, modular, and tunable. Implementations in MegaLibm can automatically detect mathematical mistakes like sign flips via semantic wellformedness checks, and components like range reductions can be implemented in a modular, composable way, simplifying implementations. Once the high-level algorithm is done, tuning parameters like working precisions and evaluation schemes can be adjusted through orthogonal tuning parameters to achieve the desired speed and accuracy. MegaLibm also enables math library developers to work interactively, compiling, testing, and tuning their implementations and invoking tools like Sollya and type-directed synthesis to complete components and synthesize entire implementations. MegaLibm can express 8 state-of-the-art math library implementations with comparable speed and accuracy to the original C code, and can synthesize 5 variations and 3 from-scratch implementations with minimal guidance.

rawabstract:
Achieving speed and accuracy for math library functions like exp, sin, and log is difficult. This is because low-level implementation languages like C do not help math library developers catch mathematical errors, build implementations incrementally, or separate high-level and low-level decision making. This ultimately puts development of such functions out of reach for all but the most experienced experts. To address this, we introduce MegaLibm, a domain-specific language for implementing, testing, and tuning math library implementations. MegaLibm is safe, modular, and tunable. Implementations in MegaLibm can automatically detect mathematical mistakes like sign flips via semantic wellformedness checks, and components like range reductions can be implemented in a modular, composable way, simplifying implementations. Once the high-level algorithm is done, tuning parameters like working precisions and evaluation schemes can be adjusted through orthogonal tuning parameters to achieve the desired speed and accuracy. MegaLibm also enables math library developers to work interactively, compiling, testing, and tuning their implementations and invoking tools like Sollya and type-directed synthesis to complete components and synthesize entire implementations. MegaLibm can express 8 state-of-the-art math library implementations with comparable speed and accuracy to the original C code, and can synthesize 5 variations and 3 from-scratch implementations with minimal guidance.

entry:
@Article{Briggs:2024:ISM,
  author =       "Ian Briggs and Yash Lad and Pavel Panchekha",
  title =        "Implementation and Synthesis of Math Library
                 Functions",
  journal =      j-PACMPL,
  volume =       "8",
  number =       "POPL",
  pages =        "32:1--32:??",
  month =        jan,
  year =         "2024",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3632874",
  ISSN =         "2475-1421 (electronic)",
  ISSN-L =       "2475-1421",
  bibdate =      "Fri May 10 10:23:39 MDT 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/pacmpl.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3632874",
  abstract =     "Achieving speed and accuracy for math library
                 functions like exp, sin, and log is difficult. This is
                 because low-level implementation languages like C do
                 not help math library developers catch mathematical
                 errors, build implementations incrementally, or
                 separate high-level and low-level decision making. This
                 ultimately puts development of such functions out of
                 reach for all but the most experienced experts. To
                 address this, we introduce MegaLibm, a domain-specific
                 language for implementing, testing, and tuning math
                 library implementations. MegaLibm is safe, modular, and
                 tunable. Implementations in MegaLibm can automatically
                 detect mathematical mistakes like sign flips via
                 semantic wellformedness checks, and components like
                 range reductions can be implemented in a modular,
                 composable way, simplifying implementations. Once the
                 high-level algorithm is done, tuning parameters like
                 working precisions and evaluation schemes can be
                 adjusted through orthogonal tuning parameters to
                 achieve the desired speed and accuracy. MegaLibm also
                 enables math library developers to work interactively,
                 compiling, testing, and tuning their implementations
                 and invoking tools like Sollya and type-directed
                 synthesis to complete components and synthesize entire
                 implementations. MegaLibm can express 8
                 state-of-the-art math library implementations with
                 comparable speed and accuracy to the original C code,
                 and can synthesize 5 variations and 3 from-scratch
                 implementations with minimal guidance.",
  acknowledgement = ack-nhfb,
  ajournal =     "Proc. ACM Program. Lang.",
  articleno =    "32",
  fjournal =     "Proceedings of the ACM on Programming Languages
                 (PACMPL)",
  journal-URL =  "https://dl.acm.org/loi/pacmpl",
}


bibtype: techreport
filename: elefunt.bib
label: Brisebarre:2024:CRE
author: Nicolas Brisebarre and Guillaume Hanrot and Jean-Michel Muller and Paul Zimmermann
title: Correctly-rounded evaluation of a function: why, how, and at what cost?
type: Report
number: hal-04474530
institution: CNRS --- Centre National de la Recherche Scientifique and others
address: Paris, France
pages: 29
day: 23
month: feb
monthnumber: 2
year: 2024
bibdate: Fri Feb 23 16:11:08 2024
bibtimestamp: 2024.02.23 16:11:08 ???
URL: https://hal.science/hal-04474530
acknowledgement: ack-nhfb
rawauthor: Nicolas Brisebarre and Guillaume Hanrot and Jean-Michel Muller and Paul Zimmermann
rawtitle: Correctly-rounded evaluation of a function: why, how, and at what cost?
abstract:
The goal of this paper is to convince the reader that a future standard for floating-point arithmetic should require the availability of a correctly-rounded version of a well-chosen core set of elementary functions. We discuss the interest and feasibility of this requirement. We also give answers to common objections we have received over the last 10 years.

keywords:
algorithmic number theory; approximation theory; Computer arithmetic; elementary functions; floating-point arithmetic; lattice basis reduction; LLL algorithm; standardization

rawabstract:
The goal of this paper is to convince the reader that a future standard for floating-point arithmetic should require the availability of a correctly-rounded version of a well-chosen core set of elementary functions. We discuss the interest and feasibility of this requirement. We also give answers to common objections we have received over the last 10 years.

entry:
@TechReport{Brisebarre:2024:CRE,
  author =       "Nicolas Brisebarre and Guillaume Hanrot and
                 Jean-Michel Muller and Paul Zimmermann",
  title =        "Correctly-rounded evaluation of a function: why, how,
                 and at what cost?",
  type =         "Report",
  number =       "hal-04474530",
  institution =  "CNRS --- Centre National de la Recherche Scientifique
                 and others",
  address =      "Paris, France",
  pages =        "29",
  day =          "23",
  month =        feb,
  year =         "2024",
  bibdate =      "Fri Feb 23 16:11:08 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://hal.science/hal-04474530",
  abstract =     "The goal of this paper is to convince the reader that
                 a future standard for floating-point arithmetic should
                 require the availability of a correctly-rounded version
                 of a well-chosen core set of elementary functions. We
                 discuss the interest and feasibility of this
                 requirement. We also give answers to common objections
                 we have received over the last 10 years.",
  acknowledgement = ack-nhfb,
  keywords =     "algorithmic number theory; approximation theory;
                 Computer arithmetic; elementary functions;
                 floating-point arithmetic; lattice basis reduction; LLL
                 algorithm; standardization",
}


bibtype: article
filename: elefunt.bib
label: Cameron:2024:AHM
author: Thomas R. Cameron and Stef Graillat
title: Accurate Horner methods in real and complex floating-point arithmetic
journal: j-BIT-NUM-MATH
volume: 64
number: 2
pages: ??--??
month: jun
monthnumber: 6
year: 2024
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/s10543-024-01017-w
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
bibdate: Tue May 28 15:02:24 MDT 2024
bibtimestamp: 2024.05.28 15:02:24 MDT
URL: https://link.springer.com/article/10.1007/s10543-024-01017-w
fjournal: BIT Numerical Mathematics
acknowledgement: ack-nhfb
ajournal: Bit Num. Math.
articleno: 17
journalURL: http://link.springer.com/journal/10543
rawauthor: Thomas R. Cameron and Stef Graillat
rawtitle: Accurate {Horner} methods in real and complex floating-point arithmetic
bibsource:
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

entry:
@Article{Cameron:2024:AHM,
  author =       "Thomas R. Cameron and Stef Graillat",
  title =        "Accurate {Horner} methods in real and complex
                 floating-point arithmetic",
  journal =      j-BIT-NUM-MATH,
  volume =       "64",
  number =       "2",
  pages =        "??--??",
  month =        jun,
  year =         "2024",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/s10543-024-01017-w",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Tue May 28 15:02:24 MDT 2024",
  bibsource =    "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 =          "https://link.springer.com/article/10.1007/s10543-024-01017-w",
  acknowledgement = ack-nhfb,
  ajournal =     "Bit Num. Math.",
  articleno =    "17",
  fjournal =     "BIT Numerical Mathematics",
  journal-URL =  "http://link.springer.com/journal/10543",
}


bibtype: book
filename: elefunt.bib
label: deDinechin:2024:ASA
author: Florent de Dinechin and Martin Kumm
publisher: pub-SV-CHAM
address: pub-SV-CHAM:adr
pages: xxiii + 804
year: 2024
DOI: https://doi.org/10.1007/978-3-031-42808-1
LCCN: QA76.9.C62 D56 2024
bibdate: Fri Dec 8 13:09:29 MST 2023
bibtimestamp: 2023.12.08 13:09:29 MST
acknowledgement: ack-nhfb
rawauthor: Florent de Dinechin and Martin Kumm
title:
Application-specific Arithmetic: Computing Just Right for the Reconfigurable Computer and the Dark Silicon Era

ISBN:
3-031-42807-2, 3-031-42808-0 (e-book), 3-031-42809-9, 3-031-42810-2 OR 3031428072, 3031428080 (ebook), 3031428099, 3031428102

ISBN13:
978-3-031-42807-4, 978-3-031-42808-1 (e-book), 978-3-031-42809-8, 978-3-031-42810-4 OR 9783031428074, 9783031428081 (ebook), 9783031428098, 9783031428104

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

URL:
http://perso.citi-lab.fr/fdedinec/ASA-book/errata.pdf; https://link.springer.com/book/10.1007/978-3-031-42808-1

abstract:
Written by two experts of the domain, this book presents the most recent advances in computer arithmetic hardware, with a focus on application-specific arithmetic beyond the classic operators and the standard precisions. It targets silicon designers who have to do better with less in the post-Moore era, and FPGA developers who want to exploit the full possibilities of reconfigurable computing platforms. Presents a unique focus on application-specific computer arithmetic; Helps developers gain a deep understanding of the arithmetic in their projects, and tailor it to their application; Illustrates concepts and architectures by actual implementations, using the FloPoCo open-source hardware generator.

TOC:
1: Introduction 2: Number Formats 3: Computing Just Right: Accuracy Specification and Error Analysis 4: Field Programmable Gate Arrays Part 1 Revisiting Classic Arithmetic 5: Fixed-Point Addition 6: Fixed-Point Comparison 7: Sums of Weighted Bits 8: Fixed-Point Multiplication 9: Fixed-Point Division 10: Shifters and Leading Bit Counters 11: Basic Floating-Point Operators Part 2 Operator Specialization 12: Multiplication by Constants 13: Division by Constants 14: Fixed-Point Squares, Cubes, and Other Integer Powers 15: Specialization and Fusion of Floating-Point Operators Part 3 Generic Methods for Fixed-Point Function Approximation 16: Generalities on Fixed-Point Function Approximation 17: Function Evaluation Using Tables and Additions 18: Polynomial-Based Architectures for Function Evaluation 19: Digit Recurrence for Algebraic Functions Part 4 Example Composite Operators 20: Fixed-Point Sine and Cosine 21: Floating-Point Accumulation and Sum-of-Products 22: Floating-Point Exponential Part 5 Application Domains 23: Arithmetic in The Design of Linear Time-Invariant Filters 24: Arithmetic for Deep Learning Part 6 Appendix 25: Appendix A: Custom Arithmetic Datapath Design with FloPoCo 26: Appendix B: Optimization Using Integer Linear Programming

rawabstract:
Written by two experts of the domain, this book presents the most recent advances in computer arithmetic hardware, with a focus on application-specific arithmetic beyond the classic operators and the standard precisions. It targets silicon designers who have to do better with less in the post-Moore era, and FPGA developers who want to exploit the full possibilities of reconfigurable computing platforms. Presents a unique focus on application-specific computer arithmetic; Helps developers gain a deep understanding of the arithmetic in their projects, and tailor it to their application; Illustrates concepts and architectures by actual implementations, using the FloPoCo open-source hardware generator.

rawtitle:
Application-specific Arithmetic: Computing Just Right for the Reconfigurable Computer and the Dark Silicon Era

rawTOC:
1: Introduction \\ 2: Number Formats \\ 3: Computing Just Right: Accuracy Specification and Error Analysis \\ 4: Field Programmable Gate Arrays \\ \\ Part 1 Revisiting Classic Arithmetic \\ 5: Fixed-Point Addition \\ 6: Fixed-Point Comparison \\ 7: Sums of Weighted Bits \\ 8: Fixed-Point Multiplication \\ 9: Fixed-Point Division \\ 10: Shifters and Leading Bit Counters \\ 11: Basic Floating-Point Operators \\ \\ Part 2 Operator Specialization \\ 12: Multiplication by Constants \\ 13: Division by Constants \\ 14: Fixed-Point Squares, Cubes, and Other Integer Powers \\ 15: Specialization and Fusion of Floating-Point Operators \\ \\ Part 3 Generic Methods for Fixed-Point Function Approximation \\ 16: Generalities on Fixed-Point Function Approximation \\ 17: Function Evaluation Using Tables and Additions \\ 18: Polynomial-Based Architectures for Function Evaluation \\ 19: Digit Recurrence for Algebraic Functions \\ \\ Part 4 Example Composite Operators \\ 20: Fixed-Point Sine and Cosine \\ 21: Floating-Point Accumulation and Sum-of-Products \\ 22: Floating-Point Exponential \\ \\ Part 5 Application Domains \\ 23: Arithmetic in The Design of Linear Time-Invariant Filters \\ 24: Arithmetic for Deep Learning \\ \\ Part 6 Appendix \\ 25: Appendix A: Custom Arithmetic Datapath Design with FloPoCo \\ 26: Appendix B: Optimization Using Integer Linear Programming

entry:
@Book{deDinechin:2024:ASA,
  author =       "Florent de Dinechin and Martin Kumm",
  title =        "Application-specific Arithmetic: Computing Just Right
                 for the Reconfigurable Computer and the Dark Silicon
                 Era",
  publisher =    pub-SV-CHAM,
  address =      pub-SV-CHAM:adr,
  pages =        "xxiii + 804",
  year =         "2024",
  DOI =          "https://doi.org/10.1007/978-3-031-42808-1",
  ISBN =         "3-031-42807-2, 3-031-42808-0 (e-book), 3-031-42809-9,
                 3-031-42810-2",
  ISBN-13 =      "978-3-031-42807-4, 978-3-031-42808-1 (e-book),
                 978-3-031-42809-8, 978-3-031-42810-4",
  LCCN =         "QA76.9.C62 D56 2024",
  bibdate =      "Fri Dec 8 13:09:29 MST 2023",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://perso.citi-lab.fr/fdedinec/ASA-book/errata.pdf;
                 https://link.springer.com/book/10.1007/978-3-031-42808-1",
  abstract =     "Written by two experts of the domain, this book
                 presents the most recent advances in computer
                 arithmetic hardware, with a focus on
                 application-specific arithmetic beyond the classic
                 operators and the standard precisions. It targets
                 silicon designers who have to do better with less in
                 the post-Moore era, and FPGA developers who want to
                 exploit the full possibilities of reconfigurable
                 computing platforms. Presents a unique focus on
                 application-specific computer arithmetic; Helps
                 developers gain a deep understanding of the arithmetic
                 in their projects, and tailor it to their application;
                 Illustrates concepts and architectures by actual
                 implementations, using the FloPoCo open-source hardware
                 generator.",
  acknowledgement = ack-nhfb,
  tableofcontents = "1: Introduction \\
                 2: Number Formats \\
                 3: Computing Just Right: Accuracy Specification and
                 Error Analysis \\
                 4: Field Programmable Gate Arrays \\
                 \\
                 Part 1 Revisiting Classic Arithmetic \\
                 5: Fixed-Point Addition \\
                 6: Fixed-Point Comparison \\
                 7: Sums of Weighted Bits \\
                 8: Fixed-Point Multiplication \\
                 9: Fixed-Point Division \\
                 10: Shifters and Leading Bit Counters \\
                 11: Basic Floating-Point Operators \\
                 \\
                 Part 2 Operator Specialization \\
                 12: Multiplication by Constants \\
                 13: Division by Constants \\
                 14: Fixed-Point Squares, Cubes, and Other Integer
                 Powers \\
                 15: Specialization and Fusion of Floating-Point
                 Operators \\
                 \\
                 Part 3 Generic Methods for Fixed-Point Function
                 Approximation \\
                 16: Generalities on Fixed-Point Function Approximation
                 \\
                 17: Function Evaluation Using Tables and Additions \\
                 18: Polynomial-Based Architectures for Function
                 Evaluation \\
                 19: Digit Recurrence for Algebraic Functions \\
                 \\
                 Part 4 Example Composite Operators \\
                 20: Fixed-Point Sine and Cosine \\
                 21: Floating-Point Accumulation and Sum-of-Products \\
                 22: Floating-Point Exponential \\
                 \\
                 Part 5 Application Domains \\
                 23: Arithmetic in The Design of Linear Time-Invariant
                 Filters \\
                 24: Arithmetic for Deep Learning \\
                 \\
                 Part 6 Appendix \\
                 25: Appendix A: Custom Arithmetic Datapath Design with
                 FloPoCo \\
                 26: Appendix B: Optimization Using Integer Linear
                 Programming",
}


bibtype: article
filename: elefunt.bib
label: Dempsey:2024:PBI
author: Kevin M. Dempsey
title: Principal Branches of Inverse Trigonometric and Inverse Hyperbolic Functions
journal: j-ACM-COMM-COMP-ALGEBRA
volume: 58
number: 3
pages: 45--56
month: sep
monthnumber: 9
year: 2024
DOI: https://doi.org/10.1145/3717582.3717583
ISSN: 1932-2232 (print), 1932-2240 (electronic) OR 19322232 (print), 19322240 (electronic)
ISSNL: 1932-2232 OR 19322232
bibdate: Sat Apr 19 05:48:11 MDT 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/sigsam.bib
bibtimestamp: 2025.04.19 05:48:11 MDT
fjournal: ACM Communications in Computer Algebra
acknowledgement: ack-nhfb
ajournal: ACM Commun. Computer Algebr.
journalURL: https://dl.acm.org/loi/sigsam-cca
rawauthor: Kevin M. Dempsey
rawtitle: Principal Branches of Inverse Trigonometric and Inverse Hyperbolic Functions
abstract:
We discuss principal branches for five square root functions and for the inverse trigonometric and inverse hyperbolic functions. We take the standard reference in this area to be the NIST Digital Library of Mathematical Functions (DLMF). We adopt the notation for and the definitions of the principal branches of the inverse functions in the DLMF. Similarly, the branch cuts for the inverse functions are defined as per the DLMF. Our goal is to use complex analysis to turn the definitions of the principal branches in the DLMF into concrete expressions that hold on the entirety of their respective cut planes. The square root principal branch expressions are new breakthrough discoveries that lead smoothly to four of the concrete expressions. We expand the number of concrete expressions in Sections 4.23 and 4.37 in the DLMF from two to eight. Three of these eight concrete expressions were in print in 1924. One of the latter is still awaiting inclusion in the DLMF. Taken altogether, we provide a computationally efficient resource for computer algebra in programming languages, specifically for the principal branches of the inverse trigonometric and inverse hyperbolic functions.

rawabstract:
We discuss principal branches for five square root functions and for the inverse trigonometric and inverse hyperbolic functions. We take the standard reference in this area to be the NIST Digital Library of Mathematical Functions (DLMF). We adopt the notation for and the definitions of the principal branches of the inverse functions in the DLMF. Similarly, the branch cuts for the inverse functions are defined as per the DLMF. Our goal is to use complex analysis to turn the definitions of the principal branches in the DLMF into concrete expressions that hold on the entirety of their respective cut planes. The square root principal branch expressions are new breakthrough discoveries that lead smoothly to four of the concrete expressions. We expand the number of concrete expressions in Sections 4.23 and 4.37 in the DLMF from two to eight. Three of these eight concrete expressions were in print in 1924. One of the latter is still awaiting inclusion in the DLMF. Taken altogether, we provide a computationally efficient resource for computer algebra in programming languages, specifically for the principal branches of the inverse trigonometric and inverse hyperbolic functions.

entry:
@Article{Dempsey:2024:PBI,
  author =       "Kevin M. Dempsey",
  title =        "Principal Branches of Inverse Trigonometric and
                 Inverse Hyperbolic Functions",
  journal =      j-ACM-COMM-COMP-ALGEBRA,
  volume =       "58",
  number =       "3",
  pages =        "45--56",
  month =        sep,
  year =         "2024",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3717582.3717583",
  ISSN =         "1932-2232 (print), 1932-2240 (electronic)",
  ISSN-L =       "1932-2232",
  bibdate =      "Sat Apr 19 05:48:11 MDT 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigsam.bib",
  abstract =     "We discuss principal branches for five square root
                 functions and for the inverse trigonometric and inverse
                 hyperbolic functions. We take the standard reference in
                 this area to be the NIST Digital Library of
                 Mathematical Functions (DLMF). We adopt the notation
                 for and the definitions of the principal branches of
                 the inverse functions in the DLMF. Similarly, the
                 branch cuts for the inverse functions are defined as
                 per the DLMF. Our goal is to use complex analysis to
                 turn the definitions of the principal branches in the
                 DLMF into concrete expressions that hold on the
                 entirety of their respective cut planes. The square
                 root principal branch expressions are new breakthrough
                 discoveries that lead smoothly to four of the concrete
                 expressions. We expand the number of concrete
                 expressions in Sections 4.23 and 4.37 in the DLMF from
                 two to eight. Three of these eight concrete expressions
                 were in print in 1924. One of the latter is still
                 awaiting inclusion in the DLMF. Taken altogether, we
                 provide a computationally efficient resource for
                 computer algebra in programming languages, specifically
                 for the principal branches of the inverse trigonometric
                 and inverse hyperbolic functions.",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Commun. Computer Algebr.",
  fjournal =     "ACM Communications in Computer Algebra",
  journal-URL =  "https://dl.acm.org/loi/sigsam-cca",
}


bibtype: article
filename: elefunt.bib
label: Harris:2024:UDS
title: Unified Digit Selection for Radix-4 Recurrence Division and Square Root
journal: j-IEEE-TRANS-COMPUT
volume: 73
number: 1
pages: 292--300
month: jan
monthnumber: 1
year: 2024
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.2023.3305760
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Dec 27 15:37:27 2023
bibtimestamp: 2023.12.27 15:37:27 ???
fjournal: IEEE Transactions on Computers
keywords: division; minimally-redundant radix-4; RISC-V; square root; SRT
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawtitle: Unified Digit Selection for Radix-4 Recurrence Division and Square Root
author:
David Harris and James Stine and Milo Ercegovac and Alberto Nannarelli and Katherine Parry and Cedar Turek

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/ieeetranscomput2020.bib; https://www.math.utah.edu/pub/tex/bib/risc-v.bib

rawauthor:
David Harris and James Stine and Milo Ercegovac and Alberto Nannarelli and Katherine Parry and Cedar Turek

entry:
@Article{Harris:2024:UDS,
  author =       "David Harris and James Stine and Milo Ercegovac and
                 Alberto Nannarelli and Katherine Parry and Cedar
                 Turek",
  title =        "Unified Digit Selection for Radix-4 Recurrence
                 Division and Square Root",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "73",
  number =       "1",
  pages =        "292--300",
  month =        jan,
  year =         "2024",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2023.3305760",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Dec 27 15:37:27 2023",
  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/ieeetranscomput2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "division; minimally-redundant radix-4; RISC-V; square
                 root; SRT",
}


bibtype: techreport
filename: elefunt.bib
label: Hubrecht:2024:TCR
author: Tom Hubrecht and Claude-Pierre Jeannerod and Paul Zimmermann and Laurence Rideau and Laurent Thery
title: Towards a correctly-rounded and fast power function in binary64 arithmetic
type: Report
institution: DI-ENS --- Departement d'informatique --- ENS Paris
address: Paris, France
pages: 292--300
day: 8
month: feb
monthnumber: 2
year: 2024
bibdate: Mon May 13 12:00:21 2024
bibtimestamp: 2024.05.13 12:00:21 ???
URL: https://inria.hal.science/hal-04159652v2/
acknowledgement: ack-nhfb
rawtitle: Towards a correctly-rounded and fast power function in binary64 arithmetic
abstract:
We design algorithms for the correct rounding of the power function $ x^y $ in the binary64 IEEE 754 format, for all rounding modes, modulo the knowledge of hardest-to-round cases. Our implementation of these algorithms largely outperforms previous correctly-rounded implementations and is not far from the efficiency of current mathematical libraries, which are not correctly-rounded. Still, we expect our algorithms can be further improved for speed. The proofs of correctness are fully detailed and have been formally verified. We hope this work will motivate the next IEEE 754 revision committee to require correct rounding for mathematical functions.

remark:
This is a longer version of cite Hubrecht:2023:TCRb with proofs and remarks by the final two authors on the formal verification.

rawabstract:
We design algorithms for the correct rounding of the power function $ x^y $ in the binary64 IEEE 754 format, for all rounding modes, modulo the knowledge of hardest-to-round cases. Our implementation of these algorithms largely outperforms previous correctly-rounded implementations and is not far from the efficiency of current mathematical libraries, which are not correctly-rounded. Still, we expect our algorithms can be further improved for speed. The proofs of correctness are fully detailed and have been formally verified. We hope this work will motivate the next IEEE 754 revision committee to require correct rounding for mathematical functions.

rawauthor:
Tom Hubrecht and Claude-Pierre Jeannerod and Paul Zimmermann and Laurence Rideau and Laurent Th{\'e}ry

entry:
@TechReport{Hubrecht:2024:TCR,
  author =       "Tom Hubrecht and Claude-Pierre Jeannerod and Paul
                 Zimmermann and Laurence Rideau and Laurent Th{\'e}ry",
  title =        "Towards a correctly-rounded and fast power function in
                 binary64 arithmetic",
  type =         "Report",
  institution =  "DI-ENS --- D{\'e}partement d'informatique --- ENS
                 Paris",
  address =      "Paris, France",
  day =          "8",
  month =        feb,
  year =         "2024",
  bibdate =      "Mon May 13 12:00:21 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://inria.hal.science/hal-04159652v2/",
  abstract =     "We design algorithms for the correct rounding of the
                 power function $ x^y $ in the binary64 IEEE 754 format,
                 for all rounding modes, modulo the knowledge of
                 hardest-to-round cases. Our implementation of these
                 algorithms largely outperforms previous
                 correctly-rounded implementations and is not far from
                 the efficiency of current mathematical libraries, which
                 are not correctly-rounded. Still, we expect our
                 algorithms can be further improved for speed. The
                 proofs of correctness are fully detailed and have been
                 formally verified. We hope this work will motivate the
                 next IEEE 754 revision committee to require correct
                 rounding for mathematical functions.",
  acknowledgement = ack-nhfb,
  remark =       "This is a longer version of \cite{Hubrecht:2023:TCRb}
                 with proofs and remarks by the final two authors on the
                 formal verification.",
}


bibtype: article
filename: elefunt.bib
label: Kowalenko:2024:AVT
author: Victor Kowalenko
title: Algorithms for Various Trigonometric Power Sums
journal: j-ALGORITHMS-BASEL
volume: 17
number: 8
pages: 292--300
year: 2024
CODEN: ALGOCH
DOI: https://doi.org/10.3390/a17080373
ISSN: 1999-4893 (electronic) OR 19994893 (electronic)
ISSNL: 1999-4893 OR 19994893
bibdate: Fri Aug 30 05:57:31 2024
bibtimestamp: 2024.08.30 05:57:31 ???
URL: https://www.mdpi.com/1999-4893/17/8/373
fjournal: Algorithms (Basel)
remark: See cite Rosenberg:1963:FTP,Dronyuk:2025:ACG.
acknowledgement: ack-nhfb
articleno: 373
journalURL: https://www.mdpi.com/journal/algorithms
rawauthor: Victor Kowalenko
rawtitle: Algorithms for Various Trigonometric Power Sums
bibsource:
https://www.math.utah.edu/pub/tex/bib/algorithms.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

abstract:
In this paper, algorithms for different types of trigonometric power sums are developed and presented. Although interesting in their own right, these trigonometric power sums arise during the creation of an algorithm for the four types of twisted trigonometric power sums defined in the introduction. The primary aim in evaluating these sums is to obtain exact results in a rational form, as opposed to standard or direct evaluation, which often results in machine-dependent decimal values that can be affected by round-off errors. Moreover, since the variable, m, appearing in the denominators of the arguments of the trigonometric functions in these sums, can remain algebraic in the algorithms/codes, one can also obtain polynomial solutions in powers of m and the variable r that appears in the cosine factor accompanying the trigonometric power. The degrees of these polynomials are found to be dependent upon v, the value of the trigonometric power in the sum, which must always be specified.

rawabstract:
In this paper, algorithms for different types of trigonometric power sums are developed and presented. Although interesting in their own right, these trigonometric power sums arise during the creation of an algorithm for the four types of twisted trigonometric power sums defined in the introduction. The primary aim in evaluating these sums is to obtain exact results in a rational form, as opposed to standard or direct evaluation, which often results in machine-dependent decimal values that can be affected by round-off errors. Moreover, since the variable, m, appearing in the denominators of the arguments of the trigonometric functions in these sums, can remain algebraic in the algorithms/codes, one can also obtain polynomial solutions in powers of m and the variable r that appears in the cosine factor accompanying the trigonometric power. The degrees of these polynomials are found to be dependent upon v, the value of the trigonometric power in the sum, which must always be specified.

entry:
@Article{Kowalenko:2024:AVT,
  author =       "Victor Kowalenko",
  title =        "Algorithms for Various Trigonometric Power Sums",
  journal =      j-ALGORITHMS-BASEL,
  volume =       "17",
  number =       "8",
  year =         "2024",
  CODEN =        "ALGOCH",
  DOI =          "https://doi.org/10.3390/a17080373",
  ISSN =         "1999-4893 (electronic)",
  ISSN-L =       "1999-4893",
  bibdate =      "Fri Aug 30 05:57:31 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/algorithms.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://www.mdpi.com/1999-4893/17/8/373",
  abstract =     "In this paper, algorithms for different types of
                 trigonometric power sums are developed and presented.
                 Although interesting in their own right, these
                 trigonometric power sums arise during the creation of
                 an algorithm for the four types of twisted
                 trigonometric power sums defined in the introduction.
                 The primary aim in evaluating these sums is to obtain
                 exact results in a rational form, as opposed to
                 standard or direct evaluation, which often results in
                 machine-dependent decimal values that can be affected
                 by round-off errors. Moreover, since the variable, m,
                 appearing in the denominators of the arguments of the
                 trigonometric functions in these sums, can remain
                 algebraic in the algorithms/codes, one can also obtain
                 polynomial solutions in powers of m and the variable r
                 that appears in the cosine factor accompanying the
                 trigonometric power. The degrees of these polynomials
                 are found to be dependent upon v, the value of the
                 trigonometric power in the sum, which must always be
                 specified.",
  acknowledgement = ack-nhfb,
  articleno =    "373",
  fjournal =     "Algorithms (Basel)",
  journal-URL =  "https://www.mdpi.com/journal/algorithms",
  remark =       "See \cite{Rosenberg:1963:FTP,Dronyuk:2025:ACG}.",
}


bibtype: misc
filename: elefunt.bib
label: Muller:2024:SNC
author: Jean-Michel Muller
title: Some notes on correct rounding of functions
pages: 31
day: 18
month: sep
monthnumber: 9
year: 2024
bibdate: Thu Sep 19 15:27:07 2024
bibtimestamp: 2024.09.19 15:27:07 ???
acknowledgement: ack-nhfb
howpublished: Attachment to STDS-754 mailing list
rawauthor: Jean-Michel Muller
rawtitle: Some notes on correct rounding of functions
entry:
@Misc{Muller:2024:SNC,
  author =       "Jean-Michel Muller",
  title =        "Some notes on correct rounding of functions",
  howpublished = "Attachment to STDS-754 mailing list",
  pages =        "31",
  day =          "18",
  month =        sep,
  year =         "2024",
  bibdate =      "Thu Sep 19 15:27:07 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Yoshida:2024:CIB
author: Toshio Yoshida and Yoshinori Adachi
title: Computation of incomplete beta function ratios $ I_x(a, b) $ with Deuflhard's algorithm
journal: j-NUMER-ALGORITHMS
volume: 97
number: 1
pages: 373--390
month: sep
monthnumber: 9
year: 2024
CODEN: NUALEG
DOI: https://doi.org/10.1007/s11075-023-01707-6
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
bibdate: Wed Aug 7 06:17:56 MDT 2024
bibtimestamp: 2024.08.07 06:17:56 MDT
URL: https://link.springer.com/article/10.1007/s11075-023-01707-6
fjournal: Numerical Algorithms
acknowledgement: ack-nhfb
ajournal: Numer. Algorithms
journalURL: http://link.springer.com/journal/11075
rawauthor: Toshio Yoshida and Yoshinori Adachi
rawtitle: Computation of incomplete beta function ratios {$ I_x(a, b) $} with {Deuflhard}'s algorithm
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib

entry:
@Article{Yoshida:2024:CIB,
  author =       "Toshio Yoshida and Yoshinori Adachi",
  title =        "Computation of incomplete beta function ratios {$
                 I_x(a, b) $} with {Deuflhard}'s algorithm",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "97",
  number =       "1",
  pages =        "373--390",
  month =        sep,
  year =         "2024",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-023-01707-6",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Wed Aug 7 06:17:56 MDT 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  URL =          "https://link.springer.com/article/10.1007/s11075-023-01707-6",
  acknowledgement = ack-nhfb,
  ajournal =     "Numer. Algorithms",
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}


bibtype: article
filename: elefunt.bib
label: Zaghloul:2024:CFI
author: Mofreh R. Zaghloul and Leen Alrawas
title: Calculation of Fresnel integrals of real and complex arguments up to 28 significant digits
journal: j-NUMER-ALGORITHMS
volume: 96
number: 2
pages: 489--506
month: jun
monthnumber: 6
year: 2024
CODEN: NUALEG
DOI: https://doi.org/10.1007/s11075-023-01654-2
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
bibdate: Tue May 21 07:35:40 MDT 2024
bibtimestamp: 2024.05.21 07:35:40 MDT
URL: https://link.springer.com/article/10.1007/s11075-023-01654-2
fjournal: Numerical Algorithms
acknowledgement: ack-nhfb
ajournal: Numer. Algorithms
journalURL: http://link.springer.com/journal/11075
rawauthor: Mofreh R. Zaghloul and Leen Alrawas
rawtitle: Calculation of {Fresnel} integrals of real and complex arguments up to 28 significant digits
keywords:
complex cosine integral C(z); complex sine integral S(z); Fresnel functions; real cosine integral C(x); real sine integral S(x)

entry:
@Article{Zaghloul:2024:CFI,
  author =       "Mofreh R. Zaghloul and Leen Alrawas",
  title =        "Calculation of {Fresnel} integrals of real and complex
                 arguments up to 28 significant digits",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "96",
  number =       "2",
  pages =        "489--506",
  month =        jun,
  year =         "2024",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-023-01654-2",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Tue May 21 07:35:40 MDT 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  URL =          "https://link.springer.com/article/10.1007/s11075-023-01654-2",
  acknowledgement = ack-nhfb,
  ajournal =     "Numer. Algorithms",
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "complex cosine integral C(z); complex sine integral
                 S(z); Fresnel functions; real cosine integral C(x);
                 real sine integral S(x)",
}


bibtype: article
filename: elefunt.bib
label: Zaghloul:2024:EMP
author: Mofreh R. Zaghloul
journal: j-NUMER-ALGORITHMS
volume: 95
number: 3
pages: 1291--1308
month: mar
monthnumber: 3
year: 2024
CODEN: NUALEG
DOI: https://doi.org/10.1007/s11075-023-01608-8
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
bibdate: Wed Feb 14 08:54:32 MST 2024
bibtimestamp: 2024.02.14 08:54:32 MST
URL: https://link.springer.com/article/10.1007/s11075-023-01608-8
fjournal: Numerical Algorithms
keywords: Dawson(x); erf(x); erfc(x)
acknowledgement: ack-nhfb
ajournal: Numer. Algorithms
journalURL: http://link.springer.com/journal/11075
rawauthor: Mofreh R. Zaghloul
title:
Efficient multiple-precision computation of the scaled complementary error function and the Dawson integral

rawtitle:
Efficient multiple-precision computation of the scaled complementary error function and the {Dawson} integral

entry:
@Article{Zaghloul:2024:EMP,
  author =       "Mofreh R. Zaghloul",
  title =        "Efficient multiple-precision computation of the scaled
                 complementary error function and the {Dawson}
                 integral",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "95",
  number =       "3",
  pages =        "1291--1308",
  month =        mar,
  year =         "2024",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-023-01608-8",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Wed Feb 14 08:54:32 MST 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  URL =          "https://link.springer.com/article/10.1007/s11075-023-01608-8",
  acknowledgement = ack-nhfb,
  ajournal =     "Numer. Algorithms",
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "Dawson(x); erf(x); erfc(x)",
}


bibtype: article
filename: elefunt.bib
label: Zaghloul:2024:ENA
author: Mofreh R. Zaghloul
journal: j-NUMER-ALGORITHMS
volume: 95
pages: 1--19
year: 2024
CODEN: NUALEG
DOI: https://doi.org/10.1007/s11075-023-01727-2
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
bibdate: Tue Feb 20 15:50:26 2024
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2024.02.20 15:50:26 ???
fjournal: Numerical Algorithms
keywords: Dawson(x); erf(x); erfc(x)
remark: [20-Feb-2024] Available at journal Web site, but not yet assigned to a journal volume.
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/11075
rawauthor: Mofreh R. Zaghloul
title:
Efficient numerical algorithms for multi-precision and multi-accuracy calculation of the error functions and Dawson integral with complex arguments

rawtitle:
Efficient numerical algorithms for multi-precision and multi-accuracy calculation of the error functions and {Dawson} integral with complex arguments

entry:
@Article{Zaghloul:2024:ENA,
  author =       "Mofreh R. Zaghloul",
  title =        "Efficient numerical algorithms for multi-precision and
                 multi-accuracy calculation of the error functions and
                 {Dawson} integral with complex arguments",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "95",
  number =       "??",
  pages =        "1--19",
  month =        "????",
  year =         "2024",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-023-01727-2",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Tue Feb 20 15:50:26 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "Dawson(x); erf(x); erfc(x)",
  remark =       "[20-Feb-2024] Available at journal Web site, but not
                 yet assigned to a journal volume.",
}


bibtype: article
filename: elefunt.bib
label: Anonymous:2025:Cd
author: Anonymous
title: Correction
journal: j-J-STAT-COMPUT-SIMUL
volume: 95
number: 15
pages: 3397--3399
year: 2025
CODEN: JSCSAJ
DOI: https://doi.org/10.1080/00949655.2025.2525617
ISSNL: 0094-9655 OR 00949655
bibdate: Thu Oct 2 07:55:18 MDT 2025
bibtimestamp: 2025.10.02 07:55:18 MDT
note: See cite Das:2025:NMC.
fjournal: Journal of Statistical Computation and Simulation
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/gscs20
onlinedate: 16 Jul 2025
rawauthor: Anonymous
rawnote: See \cite{Das:2025:NMC}.
rawtitle: Correction
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jstatcomputsimul2020.bib

entry:
@Article{Anonymous:2025:Cd,
  author =       "Anonymous",
  title =        "Correction",
  journal =      j-J-STAT-COMPUT-SIMUL,
  volume =       "95",
  number =       "15",
  pages =        "3397--3399",
  year =         "2025",
  CODEN =        "JSCSAJ",
  DOI =          "https://doi.org/10.1080/00949655.2025.2525617",
  ISSN =         "0094-9655 (print), 1026-7778 (electronic), 1563-5163",
  ISSN-L =       "0094-9655",
  bibdate =      "Thu Oct 2 07:55:18 MDT 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jstatcomputsimul2020.bib",
  note =         "See \cite{Das:2025:NMC}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Statistical Computation and Simulation",
  journal-URL =  "http://www.tandfonline.com/loi/gscs20",
  onlinedate =   "16 Jul 2025",
}


bibtype: article
filename: elefunt.bib
label: Anton:2025:FER
author: Ramona Anton and Nicolae Mihalache and Francois Vigneron
title: Fast evaluation of real and complex polynomials
journal: j-NUM-MATH
volume: 157
number: 1
pages: 355--408
month: feb
monthnumber: 2
year: 2025
CODEN: NUMMA7
DOI: https://doi.org/10.1007/s00211-025-01454-x
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
bibdate: Sat Feb 1 09:47:51 MST 2025
bibtimestamp: 2025.02.01 09:47:51 MST
URL: https://link.springer.com/article/10.1007/s00211-025-01454-x
fjournal: Numerische Mathematik
keywords: Horner's nested form; number of multiplications to evaluate a polynomial
acknowledgement: ack-nhfb
ajournal: Num. Math.
journalURL: http://link.springer.com/journal/211
rawauthor: Ramona Anton and Nicolae Mihalache and Fran{\c{c}}ois Vigneron
rawtitle: Fast evaluation of real and complex polynomials
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/nummath2020.bib

entry:
@Article{Anton:2025:FER,
  author =       "Ramona Anton and Nicolae Mihalache and Fran{\c{c}}ois
                 Vigneron",
  title =        "Fast evaluation of real and complex polynomials",
  journal =      j-NUM-MATH,
  volume =       "157",
  number =       "1",
  pages =        "355--408",
  month =        feb,
  year =         "2025",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/s00211-025-01454-x",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Sat Feb 1 09:47:51 MST 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/nummath2020.bib",
  URL =          "https://link.springer.com/article/10.1007/s00211-025-01454-x",
  acknowledgement = ack-nhfb,
  ajournal =     "Num. Math.",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "Horner's nested form; number of multiplications to
                 evaluate a polynomial",
}


bibtype: article
filename: elefunt.bib
label: Das:2025:NMC
author: Abhranil Das
title: New methods to compute the generalized chi-square distribution
journal: j-J-STAT-COMPUT-SIMUL
volume: 95
number: 12
pages: 2608--2642
year: 2025
CODEN: JSCSAJ
DOI: https://doi.org/10.1080/00949655.2025.2501401
ISSNL: 0094-9655 OR 00949655
bibdate: Thu Aug 7 05:47:44 MDT 2025
bibtimestamp: 2025.08.07 05:47:44 MDT
note: See correction cite Anonymous:2025:Cd.
fjournal: Journal of Statistical Computation and Simulation
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/gscs20
onlinedate: 19 May 2025
rawauthor: Abhranil Das
rawnote: See correction \cite{Anonymous:2025:Cd}.
rawtitle: New methods to compute the generalized chi-square distribution
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jstatcomputsimul2020.bib

entry:
@Article{Das:2025:NMC,
  author =       "Abhranil Das",
  title =        "New methods to compute the generalized chi-square
                 distribution",
  journal =      j-J-STAT-COMPUT-SIMUL,
  volume =       "95",
  number =       "12",
  pages =        "2608--2642",
  year =         "2025",
  CODEN =        "JSCSAJ",
  DOI =          "https://doi.org/10.1080/00949655.2025.2501401",
  ISSN =         "0094-9655 (print), 1026-7778 (electronic), 1563-5163",
  ISSN-L =       "0094-9655",
  bibdate =      "Thu Aug 7 05:47:44 MDT 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jstatcomputsimul2020.bib",
  note =         "See correction \cite{Anonymous:2025:Cd}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Statistical Computation and Simulation",
  journal-URL =  "http://www.tandfonline.com/loi/gscs20",
  onlinedate =   "19 May 2025",
}


bibtype: article
filename: elefunt.bib
label: Dronyuk:2025:ACG
author: Ivanna Dronyuk
title: Algorithms for Calculating Generalized Trigonometric Functions
journal: j-ALGORITHMS-BASEL
volume: 18
number: 2
pages: 2608--2642
month: feb
monthnumber: 2
year: 2025
CODEN: ALGOCH
DOI: https://doi.org/10.3390/a18020060
ISSN: 1999-4893 (electronic) OR 19994893 (electronic)
ISSNL: 1999-4893 OR 19994893
bibdate: Fri Feb 28 06:02:21 MST 2025
bibtimestamp: 2025.02.28 06:02:21 MST
URL: https://www.mdpi.com/1999-4893/18/2/60
fjournal: Algorithms (Basel)
remark: See cite Rosenberg:1963:FTP,Kowalenko:2024:AVT.
acknowledgement: ack-nhfb
articleno: 60
journalURL: https://www.mdpi.com/journal/algorithms
rawauthor: Ivanna Dronyuk
rawtitle: Algorithms for Calculating Generalized Trigonometric Functions
bibsource:
https://www.math.utah.edu/pub/tex/bib/algorithms.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Dronyuk:2025:ACG,
  author =       "Ivanna Dronyuk",
  title =        "Algorithms for Calculating Generalized Trigonometric
                 Functions",
  journal =      j-ALGORITHMS-BASEL,
  volume =       "18",
  number =       "2",
  month =        feb,
  year =         "2025",
  CODEN =        "ALGOCH",
  DOI =          "https://doi.org/10.3390/a18020060",
  ISSN =         "1999-4893 (electronic)",
  ISSN-L =       "1999-4893",
  bibdate =      "Fri Feb 28 06:02:21 MST 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/algorithms.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://www.mdpi.com/1999-4893/18/2/60",
  acknowledgement = ack-nhfb,
  articleno =    "60",
  fjournal =     "Algorithms (Basel)",
  journal-URL =  "https://www.mdpi.com/journal/algorithms",
  pagecount =    "13",
  remark =       "See \cite{Rosenberg:1963:FTP,Kowalenko:2024:AVT}.",
}


bibtype: article
filename: elefunt.bib
label: Dunster:2025:NAC
author: T. M. Dunster and A. Gil and J. Segura
title: A numerical algorithm for computing the zeros of parabolic cylinder functions in the complex plane
journal: j-BIT-NUM-MATH
volume: 65
number: 2
pages: ??--??
month: jun
monthnumber: 6
year: 2025
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/s10543-025-01065-w
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
bibdate: Wed Jul 16 14:17:01 MDT 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.07.16 14:17:01 MDT
URL: https://link.springer.com/article/10.1007/s10543-025-01065-w
fjournal: BIT Numerical Mathematics
acknowledgement: ack-nhfb
ajournal: Bit Num. Math.
articleno: 21
journalURL: http://link.springer.com/journal/10543
rawauthor: T. M. Dunster and A. Gil and J. Segura
rawtitle: A numerical algorithm for computing the zeros of parabolic cylinder functions in the complex plane
entry:
@Article{Dunster:2025:NAC,
  author =       "T. M. Dunster and A. Gil and J. Segura",
  title =        "A numerical algorithm for computing the zeros of
                 parabolic cylinder functions in the complex plane",
  journal =      j-BIT-NUM-MATH,
  volume =       "65",
  number =       "2",
  pages =        "??--??",
  month =        jun,
  year =         "2025",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/s10543-025-01065-w",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jul 16 14:17:01 MDT 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://link.springer.com/article/10.1007/s10543-025-01065-w",
  acknowledgement = ack-nhfb,
  ajournal =     "Bit Num. Math.",
  articleno =    "21",
  fjournal =     "BIT Numerical Mathematics",
  journal-URL =  "http://link.springer.com/journal/10543",
}


bibtype: article
filename: elefunt.bib
label: Guseinov:2025:CEI
author: I. I. Guseinov and B. A. Mamedov
journal: j-J-MATH-CHEM
volume: 63
number: 2
pages: 650--650
month: feb
monthnumber: 2
year: 2025
CODEN: JMCHEG
DOI: https://doi.org/10.1007/s10910-024-01686-6
ISSN: 0259-9791 (print), 1572-8897 (electronic) OR 02599791 (print), 15728897 (electronic)
ISSNL: 0259-9791 OR 02599791
bibdate: Tue Mar 4 11:35:40 MST 2025
bibtimestamp: 2025.03.04 11:35:40 MST
note: See cite Guseinov:2004:EIG.
URL: https://link.springer.com/article/10.1007/s10910-024-01686-6
fjournal: Journal of Mathematical Chemistry
acknowledgement: ack-nhfb
ajournal: J. Math. Chem.
journalURL: http://link.springer.com/journal/10910
rawauthor: I. I. Guseinov and B. A. Mamedov
rawnote: See \cite{Guseinov:2004:EIG}.
title:
Correction to: Evaluation of incomplete gamma functions using downward recursion and analytical relations

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

rawtitle:
Correction to: {Evaluation} of incomplete gamma functions using downward recursion and analytical relations

entry:
@Article{Guseinov:2025:CEI,
  author =       "I. I. Guseinov and B. A. Mamedov",
  title =        "Correction to: {Evaluation} of incomplete gamma
                 functions using downward recursion and analytical
                 relations",
  journal =      j-J-MATH-CHEM,
  volume =       "63",
  number =       "2",
  pages =        "650--650",
  month =        feb,
  year =         "2025",
  CODEN =        "JMCHEG",
  DOI =          "https://doi.org/10.1007/s10910-024-01686-6",
  ISSN =         "0259-9791 (print), 1572-8897 (electronic)",
  ISSN-L =       "0259-9791",
  bibdate =      "Tue Mar 4 11:35:40 MST 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathchem.bib",
  note =         "See \cite{Guseinov:2004:EIG}.",
  URL =          "https://link.springer.com/article/10.1007/s10910-024-01686-6",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Math. Chem.",
  fjournal =     "Journal of Mathematical Chemistry",
  journal-URL =  "http://link.springer.com/journal/10910",
}


bibtype: article
filename: elefunt.bib
label: Kokosinski:2025:FAA
author: Zbigniew Kokosinski and Pawel Gepner and Nataliia Gavkalova
title: Fast and accurate approximation algorithms for computing floating point square root
journal: j-NUMER-ALGORITHMS
volume: 99
number: 4
pages: 1791--1804
month: aug
monthnumber: 8
year: 2025
CODEN: NUALEG
DOI: https://doi.org/10.1007/s11075-024-01932-7
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
bibdate: Wed Jul 16 11:11:45 MDT 2025
bibtimestamp: 2025.07.16 11:11:45 MDT
URL: https://link.springer.com/article/10.1007/s11075-024-01932-7
fjournal: Numerical Algorithms
acknowledgement: ack-nhfb
ajournal: Numer. Algorithms
journalURL: http://link.springer.com/journal/11075
rawauthor: Zbigniew Kokosi{\'n}ski and Pawe{\l} Gepner and Nataliia Gavkalova
rawtitle: Fast and accurate approximation algorithms for computing floating point square root
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/numeralgorithms.bib

entry:
@Article{Kokosinski:2025:FAA,
  author =       "Zbigniew Kokosi{\'n}ski and Pawe{\l} Gepner and
                 Nataliia Gavkalova",
  title =        "Fast and accurate approximation algorithms for
                 computing floating point square root",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "99",
  number =       "4",
  pages =        "1791--1804",
  month =        aug,
  year =         "2025",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-024-01932-7",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Wed Jul 16 11:11:45 MDT 2025",
  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/numeralgorithms.bib",
  URL =          "https://link.springer.com/article/10.1007/s11075-024-01932-7",
  acknowledgement = ack-nhfb,
  ajournal =     "Numer. Algorithms",
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}


bibtype: article
filename: elefunt.bib
label: Marcheva:2025:QCD
author: Plamena I. Marcheva and Ivan K. Ivanov and Stoil I. Ivanov
journal: j-ALGORITHMS-BASEL
volume: 18
number: 4
pages: 1791--1804
month: apr
monthnumber: 4
year: 2025
CODEN: ALGOCH
DOI: https://doi.org/10.3390/a18040205
ISSN: 1999-4893 (electronic) OR 19994893 (electronic)
ISSNL: 1999-4893 OR 19994893
bibdate: Mon Apr 28 09:25:31 MDT 2025
bibtimestamp: 2025.04.28 09:25:31 MDT
URL: https://www.mdpi.com/1999-4893/18/4/205
fjournal: Algorithms (Basel)
acknowledgement: ack-nhfb
articleno: 205
journalURL: https://www.mdpi.com/journal/algorithms
rawauthor: Plamena I. Marcheva and Ivan K. Ivanov and Stoil I. Ivanov
title:
On the Q-Convergence and Dynamics of a Modified Weierstrass Method for the Simultaneous Extraction of Polynomial Zeros

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

rawtitle:
On the {Q}-Convergence and Dynamics of a Modified {Weierstrass} Method for the Simultaneous Extraction of Polynomial Zeros

entry:
@Article{Marcheva:2025:QCD,
  author =       "Plamena I. Marcheva and Ivan K. Ivanov and Stoil I.
                 Ivanov",
  title =        "On the {Q}-Convergence and Dynamics of a Modified
                 {Weierstrass} Method for the Simultaneous Extraction of
                 Polynomial Zeros",
  journal =      j-ALGORITHMS-BASEL,
  volume =       "18",
  number =       "4",
  month =        apr,
  year =         "2025",
  CODEN =        "ALGOCH",
  DOI =          "https://doi.org/10.3390/a18040205",
  ISSN =         "1999-4893 (electronic)",
  ISSN-L =       "1999-4893",
  bibdate =      "Mon Apr 28 09:25:31 MDT 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/algorithms.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://www.mdpi.com/1999-4893/18/4/205",
  acknowledgement = ack-nhfb,
  articleno =    "205",
  fjournal =     "Algorithms (Basel)",
  journal-URL =  "https://www.mdpi.com/journal/algorithms",
  pagecount =    "??",
}


bibtype: article
filename: elefunt.bib
label: Ozay:2025:CCS
author: S. Ozay and S. Akdemir and E. Oztekin
title: The coupling coefficients with six parameters and the generalized hypergeometric functions
journal: j-COMP-PHYS-COMM
volume: 315
pages: ??--??
month: oct
monthnumber: 10
year: 2025
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/j.cpc.2025.109656
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Mon Aug 4 11:17:58 MDT 2025
bibtimestamp: 2025.08.04 11:17:58 MDT
URL: http://www.sciencedirect.com/science/article/pii/S0010465525001584
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
ajournal: Comput. Phys. Commun.
articleno: 109656
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: S. {\"O}zay and S. Akdemir and E. {\"O}ztekin
rawtitle: The coupling coefficients with six parameters and the generalized hypergeometric functions
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/w/wigner-eugene.bib; https://www.math.utah.edu/pub/tex/bib/compphyscomm2020.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathematica.bib

keywords:
angular momentum; binomial coefficients; Clebsch-Gordon coefficients; Gaunt coefficients; generalized hypergeometric functions; Mathematica; spherical harmonics; Wigner 3-j symbols; Wigner 6-j symbols; Wigner 9-j symbols

entry:
@Article{Ozay:2025:CCS,
  author =       "S. {\"O}zay and S. Akdemir and E. {\"O}ztekin",
  title =        "The coupling coefficients with six parameters and the
                 generalized hypergeometric functions",
  journal =      j-COMP-PHYS-COMM,
  volume =       "315",
  number =       "??",
  pages =        "??--??",
  month =        oct,
  year =         "2025",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2025.109656",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Aug 4 11:17:58 MDT 2025",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/w/wigner-eugene.bib;
                 https://www.math.utah.edu/pub/tex/bib/compphyscomm2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathematica.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465525001584",
  acknowledgement = ack-nhfb,
  ajournal =     "Comput. Phys. Commun.",
  articleno =    "109656",
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
  keywords =     "angular momentum; binomial coefficients;
                 Clebsch-Gordon coefficients; Gaunt coefficients;
                 generalized hypergeometric functions; Mathematica;
                 spherical harmonics; Wigner 3-j symbols; Wigner 6-j
                 symbols; Wigner 9-j symbols",
}


bibtype: article
filename: elefunt.bib
label: Trim:2025:AEF
author: Sean J. Trim and Raymond J. Spiteri
journal: j-TOMS
volume: 51
number: 1
pages: 6:1--6:??
month: mar
monthnumber: 3
year: 2025
CODEN: ACMSCU
DOI: https://doi.org/10.1145/3709136
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Thu Apr 10 08:03:40 MDT 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib
bibtimestamp: 2025.04.10 08:03:40 MDT
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
ajournal: ACM Trans. Math. Softw.
articleno: 6
journalURL: https://dl.acm.org/loi/toms
rawauthor: Sean J. Trim and Raymond J. Spiteri
title:
Algorithm 1054: pkg ellipFor, a Fortran Software Library for Legendre Elliptic Integrals and Jacobi Elliptic Functions with Generalized Input Arguments

abstract:
Legendre elliptic integrals and Jacobi elliptic functions arise in multiple applications within the physical sciences, including oscillations, celestial mechanics, and geodynamics. In this study, we describe the Fortran library ellipFor capable of evaluating the following for generalized input values: (1) the complete Legendre elliptic integrals of the first and second kinds, (2) the incomplete Legendre elliptic integrals of the first and second kinds, and (3) the principal Jacobi elliptic functions. Our software builds upon previously developed Fortran routines, which were designed with restrictions on input parameters that may be limiting in applications. Our routines apply multiple transformations to allow for more general input values, such as elliptic moduli greater than unity for points 1--3, arbitrary real Jacobi amplitudes for points 1--2, and complex first arguments for point 3. In addition, our routines are thread-safe, allowing for parallel computations. Our routines were compared with values from the computer algebra system SageMath over a wide range of input parameters. Values from ellipFor and SageMath agreed to within tolerances commensurate with the limitations of floating-point arithmetic used for the elliptic integrals and Jacobi elliptic functions listed in points 1, 2, and 3 above for generalized input arguments.

rawabstract:
Legendre elliptic integrals and Jacobi elliptic functions arise in multiple applications within the physical sciences, including oscillations, celestial mechanics, and geodynamics. In this study, we describe the Fortran library ellipFor capable of evaluating the following for generalized input values: (1) the complete Legendre elliptic integrals of the first and second kinds, (2) the incomplete Legendre elliptic integrals of the first and second kinds, and (3) the principal Jacobi elliptic functions. Our software builds upon previously developed Fortran routines, which were designed with restrictions on input parameters that may be limiting in applications. Our routines apply multiple transformations to allow for more general input values, such as elliptic moduli greater than unity for points 1--3, arbitrary real Jacobi amplitudes for points 1--2, and complex first arguments for point 3. In addition, our routines are thread-safe, allowing for parallel computations. Our routines were compared with values from the computer algebra system SageMath over a wide range of input parameters. Values from ellipFor and SageMath agreed to within tolerances commensurate with the limitations of floating-point arithmetic used for the elliptic integrals and Jacobi elliptic functions listed in points 1, 2, and 3 above for generalized input arguments.

rawtitle:
Algorithm 1054: \pkg{ellipFor}, a {Fortran} Software Library for {Legendre} Elliptic Integrals and {Jacobi} Elliptic Functions with Generalized Input Arguments

entry:
@Article{Trim:2025:AEF,
  author =       "Sean J. Trim and Raymond J. Spiteri",
  title =        "Algorithm 1054: \pkg{ellipFor}, a {Fortran} Software
                 Library for {Legendre} Elliptic Integrals and {Jacobi}
                 Elliptic Functions with Generalized Input Arguments",
  journal =      j-TOMS,
  volume =       "51",
  number =       "1",
  pages =        "6:1--6:??",
  month =        mar,
  year =         "2025",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3709136",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Apr 10 08:03:40 MDT 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Legendre elliptic integrals and Jacobi elliptic
                 functions arise in multiple applications within the
                 physical sciences, including oscillations, celestial
                 mechanics, and geodynamics. In this study, we describe
                 the Fortran library ellipFor capable of evaluating the
                 following for generalized input values: (1) the
                 complete Legendre elliptic integrals of the first and
                 second kinds, (2) the incomplete Legendre elliptic
                 integrals of the first and second kinds, and (3) the
                 principal Jacobi elliptic functions. Our software
                 builds upon previously developed Fortran routines,
                 which were designed with restrictions on input
                 parameters that may be limiting in applications. Our
                 routines apply multiple transformations to allow for
                 more general input values, such as elliptic moduli
                 greater than unity for points 1--3, arbitrary real
                 Jacobi amplitudes for points 1--2, and complex first
                 arguments for point 3. In addition, our routines are
                 thread-safe, allowing for parallel computations. Our
                 routines were compared with values from the computer
                 algebra system SageMath over a wide range of input
                 parameters. Values from ellipFor and SageMath agreed to
                 within tolerances commensurate with the limitations of
                 floating-point arithmetic used for the elliptic
                 integrals and Jacobi elliptic functions listed in
                 points 1, 2, and 3 above for generalized input
                 arguments.",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Math. Softw.",
  articleno =    "6",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Walczyk:2025:OAX
author: Cezary J. Walczyk and Leonid V. Moroz and Volodymyr Samotyy and Jan L. Cieslinski
title: Optimal Approximation of the $ 1 / x $ Function using Chebyshev Polynomials and Magic Constants
journal: j-TOMS
volume: 51
number: 1
pages: 2:1--2:??
month: mar
monthnumber: 3
year: 2025
CODEN: ACMSCU
DOI: https://doi.org/10.1145/3708472
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Thu Apr 10 08:03:40 MDT 2025
bibtimestamp: 2025.04.10 08:03:40 MDT
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
ajournal: ACM Trans. Math. Softw.
articleno: 2
journalURL: https://dl.acm.org/loi/toms
rawauthor: Cezary J. Walczyk and Leonid V. Moroz and Volodymyr Samotyy and Jan L. Cie{\'s}li{\'n}ski
rawtitle: Optimal Approximation of the $ 1 / x $ Function using {Chebyshev} Polynomials and Magic Constants
abstract:
In this article we analyze low-cost accurate approximation of the function $ 1 / x $ using Chebyshev polynomials of the first kind and minimizing number of elementary operations in computer codes (in particular, by using the so-called magic constants). It is shown that Newton-Raphson iterative method is not optimal and a new approach is proposed. We prove that optimal Chebyshev polynomials can be factorized in terms of Chebyshev polynomials of lower order which leads to new optimal iteration schemes. We also construct a family of new algorithms by dividing the considered interval into sub-intervals where different magic constants and multiplicative factors are used (in order to increase the accuracy). Theoretical considerations and proofs are completed with numerical tests on three types of microcontroller processors.

rawabstract:
In this article we analyze low-cost accurate approximation of the function $ 1 / x $ using Chebyshev polynomials of the first kind and minimizing number of elementary operations in computer codes (in particular, by using the so-called magic constants). It is shown that Newton-Raphson iterative method is not optimal and a new approach is proposed. We prove that optimal Chebyshev polynomials can be factorized in terms of Chebyshev polynomials of lower order which leads to new optimal iteration schemes. We also construct a family of new algorithms by dividing the considered interval into sub-intervals where different magic constants and multiplicative factors are used (in order to increase the accuracy). Theoretical considerations and proofs are completed with numerical tests on three types of microcontroller processors.

entry:
@Article{Walczyk:2025:OAX,
  author =       "Cezary J. Walczyk and Leonid V. Moroz and Volodymyr
                 Samotyy and Jan L. Cie{\'s}li{\'n}ski",
  title =        "Optimal Approximation of the $ 1 / x $ Function using
                 {Chebyshev} Polynomials and Magic Constants",
  journal =      j-TOMS,
  volume =       "51",
  number =       "1",
  pages =        "2:1--2:??",
  month =        mar,
  year =         "2025",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3708472",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Apr 10 08:03:40 MDT 2025",
  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",
  abstract =     "In this article we analyze low-cost accurate
                 approximation of the function $ 1 / x $ using Chebyshev
                 polynomials of the first kind and minimizing number of
                 elementary operations in computer codes (in particular,
                 by using the so-called magic constants). It is shown
                 that Newton-Raphson iterative method is not optimal and
                 a new approach is proposed. We prove that optimal
                 Chebyshev polynomials can be factorized in terms of
                 Chebyshev polynomials of lower order which leads to new
                 optimal iteration schemes. We also construct a family
                 of new algorithms by dividing the considered interval
                 into sub-intervals where different magic constants and
                 multiplicative factors are used (in order to increase
                 the accuracy). Theoretical considerations and proofs
                 are completed with numerical tests on three types of
                 microcontroller processors.",
  accepted =     "4 December 2024",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Math. Softw.",
  articleno =    "2",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  received =     "3 September 2022",
  revised =      "25 September 2024",
}


bibtype: article
filename: elefunt.bib
label: Zhang:2025:RRH
author: Yangyi Zhang and Xianglong Wang and Lei Chen and Fengwei An
journal: j-IEEE-TRANS-VLSI-SYST
volume: 33
number: 10
pages: 2690--2701
year: 2025
CODEN: IEVSE9
DOI: https://doi.org/10.1109/TVLSI.2025.3566433
ISSN: 1063-8210 (print), 1557-9999 (electronic) OR 10638210 (print), 15579999 (electronic)
ISSNL: 1063-8210 OR 10638210
bibdate: Wed Oct 1 06:40:18 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.10.01 06:40:18 ???
fjournal: IEEE Transactions on Very Large Scale Integration (VLSI) Systems
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/issues?punumber=92
rawauthor: Yangyi Zhang and Xianglong Wang and Lei Chen and Fengwei An
title:
ReHIT: Reconfigurable High-Radix Iterative-Taylor Architecture for Ultraprecise Logarithm / Exponential Functions in FPGA-Based Softmax Accelerators

keywords:
Accuracy; Approximation algorithms; Architecture; Computer architecture; exponential function; Field programmable gate arrays; field-programmable gate array (FPGA); Hardware; logarithm function; Logic; Polynomials; softmax function; Table lookup; Taylor formula; Taylor series; Technological innovation

rawtitle:
{ReHIT}: Reconfigurable High-Radix Iterative-Taylor Architecture for Ultraprecise Logarithm\slash Exponential Functions in {FPGA}-Based {Softmax} Accelerators

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  author =       "Yangyi Zhang and Xianglong Wang and Lei Chen and
                 Fengwei An",
  title =        "{ReHIT}: Reconfigurable High-Radix Iterative-Taylor
                 Architecture for Ultraprecise Logarithm\slash
                 Exponential Functions in {FPGA}-Based {Softmax}
                 Accelerators",
  journal =      j-IEEE-TRANS-VLSI-SYST,
  volume =       "33",
  number =       "10",
  pages =        "2690--2701",
  year =         "2025",
  CODEN =        "IEVSE9",
  DOI =          "https://doi.org/10.1109/TVLSI.2025.3566433",
  ISSN =         "1063-8210 (print), 1557-9999 (electronic)",
  ISSN-L =       "1063-8210",
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bibtype: article
filename: elefunt.bib
label: Zullo:2025:LFP
author: Federico Zullo
title: Lommel functions, Pade approximants and hypergeometric functions
journal: j-APPL-NUM-MATH
volume: 209
pages: 275--284
month: mar
monthnumber: 3
year: 2025
CODEN: ANMAEL
DOI: https://doi.org/10.1016/j.apnum.2024.11.003
ISSN: 0168-9274 (print), 1873-5460 (electronic) OR 01689274 (print), 18735460 (electronic)
ISSNL: 0168-9274 OR 01689274
bibdate: Sat Dec 28 08:12:54 MST 2024
bibtimestamp: 2024.12.28 08:12:54 MST
URL: http://www.sciencedirect.com/science/article/pii/S016892742400299X
fjournal: Applied Numerical Mathematics: Transactions of IMACS
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01689274
rawauthor: Federico Zullo
rawtitle: {Lommel} functions, {Pad{\'e}} approximants and hypergeometric functions
entry:
@Article{Zullo:2025:LFP,
  author =       "Federico Zullo",
  title =        "{Lommel} functions, {Pad{\'e}} approximants and
                 hypergeometric functions",
  journal =      j-APPL-NUM-MATH,
  volume =       "209",
  number =       "??",
  pages =        "275--284",
  month =        mar,
  year =         "2025",
  CODEN =        "ANMAEL",
  DOI =          "https://doi.org/10.1016/j.apnum.2024.11.003",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  bibdate =      "Sat Dec 28 08:12:54 MST 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S016892742400299X",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274",
}


bibtype: inproceedings
filename: elefunt.bib
label: Ahmed:1981:VSA
author: H. M. Ahmed and M. Morf and D. T. L. Lee and P. H. Ang
booktitle: Proceedings of 1981 ICASSP. Atlanta. GA, 1981
title: A VLSI speech analysis chip set based on square-root normalized ladder forms
pages: 648--653
year: 1981
bibdate: Wed Oct 29 10:23:36 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.10.29 10:23:36 ???
acknowledgement: ack-nhfb
rawauthor: H. M. Ahmed and M. Morf and D. T. L. Lee and P. H. Ang
rawbooktitle: {Proceedings of 1981 ICASSP. Atlanta. GA, 1981}
rawtitle: A {VLSI} speech analysis chip set based on square-root normalized ladder forms
entry:
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  author =       "H. M. Ahmed and M. Morf and D. T. L. Lee and P. H.
                 Ang",
  editor =       "????",
  booktitle =    "{Proceedings of 1981 ICASSP. Atlanta. GA, 1981}",
  title =        "A {VLSI} speech analysis chip set based on square-root
                 normalized ladder forms",
  publisher =    "????",
  address =      "????",
  pages =        "648--653",
  year =         "1981",
  DOI =          "",
  ISBN =         "",
  ISBN-13 =      "",
  LCCN =         "",
  bibdate =      "Wed Oct 29 10:23:36 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: elefunt.bib
label: Considine:1989:CTF
author: V. Considine
booktitle: International Conference on Acoustics, Speech, and Signal Processing
title: CORDIC trigonometric function generator for DSP
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 2381--2384 (vol. 4)
year: 1989
DOI: https://doi.org/10.1109/ICASSP.1989.266946
bibdate: Mon Oct 27 10:32:44 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.10.27 10:32:44 ???
acknowledgement: ack-nhfb
rawauthor: V. Considine
rawbooktitle: {International Conference on Acoustics, Speech, and Signal Processing}
rawtitle: {CORDIC} trigonometric function generator for {DSP}
keywords:
Computer architecture; Digital arithmetic; Digital signal processing; Digital systems; Equations; Polynomials; Signal generators; Signal processing algorithms; Signal sampling; Table lookup

entry:
@InProceedings{Considine:1989:CTF,
  author =       "V. Considine",
  booktitle =    "{International Conference on Acoustics, Speech, and
                 Signal Processing}",
  title =        "{CORDIC} trigonometric function generator for {DSP}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "2381--2384 (vol. 4)",
  year =         "1989",
  DOI =          "https://doi.org/10.1109/ICASSP.1989.266946",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer architecture; Digital arithmetic; Digital
                 signal processing; Digital systems; Equations;
                 Polynomials; Signal generators; Signal processing
                 algorithms; Signal sampling; Table lookup",
}


bibtype: inproceedings
filename: elefunt.bib
label: Gisuthan:2000:FCU
author: B. Gisuthan and T. Srikanthan
booktitle: Proceedings of the 43rd IEEE Midwest Symposium on Circuits and Systems (Cat. No. CH37144)
volume: 3
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1414--1417 (vol. 3)
year: 2000
DOI: https://doi.org/10.1109/MWSCAS.2000.951478
bibdate: Mon Oct 27 10:32:44 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.10.27 10:32:44 ???
acknowledgement: ack-nhfb
rawauthor: B. Gisuthan and T. Srikanthan
rawbooktitle: {Proceedings of the 43rd IEEE Midwest Symposium on Circuits and Systems (Cat. No. CH37144)}
title:
Flat CORDIC: a unified architecture for high-speed generation of trigonometric and hyperbolic functions

keywords:
Arithmetic; Circuits; CMOS process; Computer architecture; Delay; Equations; Iterative algorithms; Libraries; Silicon; Very large scale integration

rawtitle:
Flat {CORDIC}: a unified architecture for high-speed generation of trigonometric and hyperbolic functions

entry:
@InProceedings{Gisuthan:2000:FCU,
  author =       "B. Gisuthan and T. Srikanthan",
  booktitle =    "{Proceedings of the 43rd IEEE Midwest Symposium on
                 Circuits and Systems (Cat. No. CH37144)}",
  title =        "Flat {CORDIC}: a unified architecture for high-speed
                 generation of trigonometric and hyperbolic functions",
  volume =       "3",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1414--1417 (vol. 3)",
  year =         "2000",
  DOI =          "https://doi.org/10.1109/MWSCAS.2000.951478",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Arithmetic; Circuits; CMOS process; Computer
                 architecture; Delay; Equations; Iterative algorithms;
                 Libraries; Silicon; Very large scale integration",
}


bibtype: article
filename: elefunt.bib
label: Lang:2000:CBC
author: Tomas Lang and Elisardo Antelo
title: CORDIC-Based Computation of ArcCos and $ sqrt 1 - t^2 $
journal: j-J-VLSI-SIGNAL-PROC-SSIVT
volume: 25
number: 1
pages: 19--38
month: may
monthnumber: 5
year: 2000
DOI: https://doi.org/10.1023/a:1008121502359
ISSN: 1387-5485 (print), 1573-0506 (electronic) OR 13875485 (print), 15730506 (electronic)
ISSNL: 1387-5485 OR 13875485
bibdate: Tue Oct 28 07:04:09 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.10.28 07:04:09 ???
fjournal: Journal of VLSI Signal Processing Systems for Signal, Image and Video Technology
acknowledgement: ack-nhfb
ajournal: J. VLSI Signal Process. Syst. Signal, Image Video Tech.
journalURL: https://link.springer.com/journal/11265
rawauthor: Tom{\'a}s Lang and Elisardo Antelo
rawtitle: {CORDIC}-Based Computation of {ArcCos} and $ \sqrt {1 - t^2} $
entry:
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  author =       "Tom{\'a}s Lang and Elisardo Antelo",
  title =        "{CORDIC}-Based Computation of {ArcCos} and $ \sqrt {1
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  journal =      j-J-VLSI-SIGNAL-PROC-SSIVT,
  volume =       "25",
  number =       "1",
  pages =        "19--38",
  month =        may,
  year =         "2000",
  DOI =          "https://doi.org/10.1023/a:1008121502359",
  ISSN =         "1387-5485 (print), 1573-0506 (electronic)",
  ISSN-L =       "1387-5485",
  bibdate =      "Tue Oct 28 07:04:09 2025",
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  fjournal =     "Journal of VLSI Signal Processing Systems for Signal,
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bibtype: article
filename: elefunt.bib
label: Gisuthan:2002:PFC
author: Bimal Gisuthan and Thambipillai Srikanthan
title: Pipelining flat CORDIC based trigonometric function generators
journal: j-MICROELECT-J
volume: 33
number: 1
pages: 77--89
year: 2002
CODEN: MICEB9
DOI: https://doi.org/10.1016/S0026-2692(01)00107-0
ISSN: 1879-2391 OR 18792391
ISSNL: 0026-2692 OR 00262692
bibdate: Wed Oct 29 14:21:46 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.10.29 14:21:46 ???
URL: https://www.sciencedirect.com/science/article/pii/S0026269201001070
fjournal: Microelectronics Journal
keywords: CORDIC; Flat CORDIC; Hyperbolic functions; Pipelining; Trigonometric functions
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00262692
rawauthor: Bimal Gisuthan and Thambipillai Srikanthan
rawtitle: Pipelining flat {CORDIC} based trigonometric function generators
entry:
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  author =       "Bimal Gisuthan and Thambipillai Srikanthan",
  title =        "Pipelining flat {CORDIC} based trigonometric function
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  journal =      j-MICROELECT-J,
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  number =       "1",
  pages =        "77--89",
  year =         "2002",
  CODEN =        "MICEB9",
  DOI =          "https://doi.org/10.1016/S0026-2692(01)00107-0",
  ISSN =         "1879-2391",
  ISSN-L =       "0026-2692",
  bibdate =      "Wed Oct 29 14:21:46 2025",
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bibtype: inproceedings
filename: elefunt.bib
label: Boudabous:2004:IHF
author: A. Boudabous and F. Ghozzi and M. W. Kharrat and N. Masmoudi
booktitle: Proceedings. The 16th International Conference on Microelectronics, 2004. ICM 2004.
title: Implementation of hyperbolic functions using CORDIC algorithm
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 738--741
year: 2004
DOI: https://doi.org/10.1109/ICM.2004.1434772
bibdate: Mon Oct 27 10:32:44 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.10.27 10:32:44 ???
acknowledgement: ack-nhfb
rawauthor: A. Boudabous and F. Ghozzi and M. W. Kharrat and N. Masmoudi
rawbooktitle: {Proceedings. The 16th International Conference on Microelectronics, 2004. ICM 2004.}
rawtitle: Implementation of hyperbolic functions using {CORDIC} algorithm
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entry:
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  author =       "A. Boudabous and F. Ghozzi and M. W. Kharrat and N.
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  booktitle =    "{Proceedings. The 16th International Conference on
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  title =        "Implementation of hyperbolic functions using {CORDIC}
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  publisher =    pub-IEEE,
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  DOI =          "https://doi.org/10.1109/ICM.2004.1434772",
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bibtype: inproceedings
filename: elefunt.bib
label: Ye:2010:FIC
author: Min Ye and Taijun Liu and Yan Ye and Gaoming Xu and Tiefeng Xu
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1--4
year: 2010
DOI: https://doi.org/10.1109/WICOM.2010.5600929
bibdate: Mon Oct 27 10:32:44 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.10.27 10:32:44 ???
acknowledgement: ack-nhfb
rawauthor: Min Ye and Taijun Liu and Yan Ye and Gaoming Xu and Tiefeng Xu
booktitle:
2010 6th International Conference on Wireless Communications Networking and Mobile Computing (WiCOM)

title:
FPGA Implementation of CORDIC-based Square Root Operation for Parameter Extraction of Digital Pre-Distortion for Power Amplifiers

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Arrays; Field programmable gate arrays; Hardware; Parameter extraction; Power amplifiers; Software; Software algorithms

rawbooktitle:
{2010 6th International Conference on Wireless Communications Networking and Mobile Computing (WiCOM)}

rawtitle:
{FPGA} Implementation of {CORDIC}-based Square Root Operation for Parameter Extraction of Digital Pre-Distortion for Power Amplifiers

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  booktitle =    "{2010 6th International Conference on Wireless
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                 (WiCOM)}",
  title =        "{FPGA} Implementation of {CORDIC}-based Square Root
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  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--4",
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  DOI =          "https://doi.org/10.1109/WICOM.2010.5600929",
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  acknowledgement = ack-nhfb,
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                 Software algorithms",
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bibtype: inproceedings
filename: elefunt.bib
label: Pouyan:2011:VIL
author: Peyman Pouyan and Erik Hertz and Peter Nilsson
booktitle: 2011 20th European Conference on Circuit Theory and Design (ECCTD)
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 709--712
year: 2011
DOI: https://doi.org/10.1109/ECCTD.2011.6043642
bibdate: Mon Oct 27 10:32:44 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.10.27 10:32:44 ???
acknowledgement: ack-nhfb
rawauthor: Peyman Pouyan and Erik Hertz and Peter Nilsson
rawbooktitle: {2011 20th European Conference on Circuit Theory and Design (ECCTD)}
title:
A VLSI implementation of logarithmic and exponential functions using a novel parabolic synthesis methodology compared to the CORDIC algorithm

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rawtitle:
A {VLSI} implementation of logarithmic and exponential functions using a novel parabolic synthesis methodology compared to the {CORDIC} algorithm

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  author =       "Peyman Pouyan and Erik Hertz and Peter Nilsson",
  booktitle =    "{2011 20th European Conference on Circuit Theory and
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  title =        "A {VLSI} implementation of logarithmic and exponential
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  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "709--712",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ECCTD.2011.6043642",
  bibdate =      "Mon Oct 27 10:32:44 2025",
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bibtype: inproceedings
filename: elefunt.bib
label: Dong:2012:ISP
author: Chen Dong and Chen He and Sun Xing and Pang Long
booktitle: 2012 International Conference on Control Engineering and Communication Technology
title: Implementation of Single-Precision Floating-Point Trigonometric Functions with Small Area
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 589--592
year: 2012
DOI: https://doi.org/10.1109/ICCECT.2012.186
bibdate: Mon Oct 27 10:32:44 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.10.27 10:32:44 ???
acknowledgement: ack-nhfb
rawauthor: Chen Dong and Chen He and Sun Xing and Pang Long
rawbooktitle: {2012 International Conference on Control Engineering and Communication Technology}
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entry:
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  title =        "Implementation of Single-Precision Floating-Point
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  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "589--592",
  year =         "2012",
  DOI =          "https://doi.org/10.1109/ICCECT.2012.186",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
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  acknowledgement = ack-nhfb,
  keywords =     "Algorithm design and analysis; Computer architecture;
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                 floating-point; FPGA; Hardware; Mathematical model;
                 Transforms; trigonometric functions",
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bibtype: inproceedings
filename: elefunt.bib
label: Mahapatra:2012:FIS
author: Chinmaya Mahapatra and Saad Mahboob and Victor C. M. Leung and Thanos Stouraitis
booktitle: 2012 International Conference on Control Engineering and Communication Technology
title: Fast Inverse Square Root Based Matrix Inverse for MIMO-LTE Systems
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 321--324
year: 2012
DOI: https://doi.org/10.1109/ICCECT.2012.253
bibdate: Mon Oct 27 10:32:44 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.10.27 10:32:44 ???
acknowledgement: ack-nhfb
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rawbooktitle: {2012 International Conference on Control Engineering and Communication Technology}
rawtitle: Fast Inverse Square Root Based Matrix Inverse for {MIMO-LTE} Systems
keywords:
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entry:
@InProceedings{Mahapatra:2012:FIS,
  author =       "Chinmaya Mahapatra and Saad Mahboob and Victor C. M.
                 Leung and Thanos Stouraitis",
  booktitle =    "{2012 International Conference on Control Engineering
                 and Communication Technology}",
  title =        "Fast Inverse Square Root Based Matrix Inverse for
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  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "321--324",
  year =         "2012",
  DOI =          "https://doi.org/10.1109/ICCECT.2012.253",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Arrays; CORDIC; Fast inverse square root; Field
                 programmable gate arrays; Hardware; Matrix
                 decomposition; MIMO; MIMO LTE; Pipeline processing;
                 Pipelining; QR decomposition; Systolic array; Xilinx
                 virtex6 FPGA",
}


bibtype: inbook
filename: elefunt.bib
label: Markovi:2012:CDS
author: Dejan Markovi and Robert W. Brodersen
booktitle: DSP Architecture Design Essentials
title: CORDIC, Divider, Square Root
publisher: Springer US
pages: 91--110
year: 2012
DOI: https://doi.org/10.1007/978-1-4419-9660-2_6
ISBN: 1-4419-9660-5 OR 1441996605
ISBN13: 978-1-4419-9660-2 OR 9781441996602
bibdate: Tue Oct 28 07:04:09 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.10.28 07:04:09 ???
acknowledgement: ack-nhfb
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rawbooktitle: {DSP} Architecture Design Essentials
rawtitle: {CORDIC}, Divider, Square Root
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bibtype: article
filename: elefunt.bib
label: Sudha:2012:NMC
author: J. Sudha and M. C. Hanumantharaju and V. Venkateswarulu and Jayalaxmi H
title: A Novel Method for Computing Exponential Function Using CORDIC Algorithm
journal: Procedia Engineering
volume: 30
pages: 519--528
year: 2012
DOI: https://doi.org/10.1016/j.proeng.2012.01.893
ISSN: 1877-7058 OR 18777058
ISSNL: 1877-7058 OR 18777058
bibdate: Wed Oct 29 14:21:46 2025
bibtimestamp: 2025.10.29 14:21:46 ???
note: International Conference on Communication Technology and System Design 2011
URL: https://www.sciencedirect.com/science/article/pii/S1877705812009034
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acknowledgement: ack-nhfb
rawauthor: J. Sudha and M. C. Hanumantharaju and V. Venkateswarulu and Jayalaxmi H
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entry:
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  journal =      "Procedia Engineering",
  volume =       "30",
  pages =        "519--528",
  year =         "2012",
  DOI =          "https://doi.org/10.1016/j.proeng.2012.01.893",
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bibtype: inproceedings
filename: elefunt.bib
label: Yang:2012:CDS
author: Bohan Yang and Dong Wang and Leibo Liu
booktitle: 2012 2nd International Conference on Consumer Electronics, Communications and Networks (CECNet)
title: Complex division and square-root using CORDIC
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 2464--2468
year: 2012
DOI: https://doi.org/10.1109/CECNet.2012.6201840
bibdate: Mon Oct 27 10:32:44 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.10.27 10:32:44 ???
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bibtype: inproceedings
filename: elefunt.bib
label: Bangqiang:2013:BLI
author: Liu Bangqiang and He Ling and Yan Xiao
booktitle: 2013 IEEE 9th International Colloquium on Signal Processing and its Applications
title: Base-$N$ logarithm implementation on FPGA for the data with random decimal point positions
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 17--20
year: 2013
DOI: https://doi.org/10.1109/CSPA.2013.6530006
bibdate: Mon Oct 27 10:32:44 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.10.27 10:32:44 ???
acknowledgement: ack-nhfb
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  author =       "Liu Bangqiang and He Ling and Yan Xiao",
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  pages =        "17--20",
  year =         "2013",
  DOI =          "https://doi.org/10.1109/CSPA.2013.6530006",
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bibtype: article
filename: elefunt.bib
label: Ray:2013:CBV
author: Kailash Chandra Ray and Anindya Sundar Dhar
journal: Journal of Signal Processing Systems
volume: 74
number: 2
pages: 235--244
month: jun
monthnumber: 6
year: 2013
DOI: https://doi.org/10.1007/s11265-013-0781-z
ISSN: 1939-8115 OR 19398115
bibdate: Tue Oct 28 07:04:09 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.10.28 07:04:09 ???
acknowledgement: ack-nhfb
rawauthor: Kailash Chandra Ray and Anindya Sundar Dhar
title:
CORDIC-Based VLSI Architecture for Implementing Kaiser--Bessel Window in Real Time Spectral Analysis

rawtitle:
{CORDIC}-Based {VLSI} Architecture for Implementing {Kaiser--Bessel} Window in Real Time Spectral Analysis

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  volume =       "74",
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bibtype: inproceedings
filename: elefunt.bib
label: Saravanan:2013:SCG
author: P. Saravanan and S. Ramasamy
title: Sine / cos generator for direct digital frequency synthesizer using pipelined CORDIC processor
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1--6
year: 2013
DOI: https://doi.org/10.1109/ICCCNT.2013.6726502
bibdate: Mon Oct 27 10:32:44 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.10.27 10:32:44 ???
acknowledgement: ack-nhfb
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Sine\slash cos generator for direct digital frequency synthesizer using pipelined {CORDIC} processor

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bibtype: inproceedings
filename: elefunt.bib
label: T:2015:IHC
author: Yamunadevi T. and Parmasivam C.
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1--5
year: 2015
DOI: https://doi.org/10.1109/ICIIECS.2015.7193234
bibdate: Mon Oct 27 10:32:44 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.10.27 10:32:44 ???
acknowledgement: ack-nhfb
rawauthor: Yamunadevi T. and Parmasivam C.
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2015 International Conference on Innovations in Information, Embedded and Communication Systems (ICIIECS)

title:
Implementation of Hyperbolic CORDIC-based VLSI architecture for Kaiser--Bessel Window techniques in spectral analysis

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Implementation of Hyperbolic {CORDIC}-based {VLSI} architecture for {Kaiser--Bessel} Window techniques in spectral analysis

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                 (ICIIECS)}",
  title =        "Implementation of Hyperbolic {CORDIC}-based {VLSI}
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  publisher =    pub-IEEE,
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bibtype: article
filename: elefunt.bib
label: Mopuri:2017:LCM
author: Suresh Mopuri and Amit Acharyya
title: Low-Complexity Methodology for Complex Square-Root Computation
journal: j-IEEE-TRANS-VLSI-SYST
volume: 25
number: 11
pages: 3255--3259
year: 2017
CODEN: IEVSE9
DOI: https://doi.org/10.1109/TVLSI.2017.2740343
ISSN: 1063-8210 (print), 1557-9999 (electronic) OR 10638210 (print), 15579999 (electronic)
ISSNL: 1063-8210 OR 10638210
bibdate: Mon Oct 27 10:32:44 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.10.27 10:32:44 ???
fjournal: IEEE Transactions on Very Large Scale Integration (VLSI) Systems
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rawauthor: Suresh Mopuri and Amit Acharyya
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entry:
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  title =        "Low-Complexity Methodology for Complex Square-Root
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bibtype: inproceedings
filename: elefunt.bib
label: Saha:2017:AEA
author: Anurup Saha and K. Gaurav Kumar and Archisman Ghosh and Mrinal Kanti Naskar
booktitle: 2017 International Conference on Circuits, Controls, and Communications (CCUBE)
title: Area efficient architecture of Hyperbolic functions for high frequency applications
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 139--142
year: 2017
DOI: https://doi.org/10.1109/CCUBE.2017.8394139
bibdate: Mon Oct 27 10:32:44 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
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bibtype: inproceedings
filename: elefunt.bib
label: De:2018:MLH
author: Debaprasad De and Archisman Ghosh and K. Gaurav Kumar and Anurup Saha and Mrinal Kanti Naskar
booktitle: 2018 IEEE Applied Signal Processing Conference (ASPCON)
title: Multiplier-less Hardware Realization of Trigonometric Functions for High Speed Applications
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 149--152
year: 2018
DOI: https://doi.org/10.1109/ASPCON.2018.8748709
bibdate: Mon Oct 27 10:32:44 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
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bibtype: inbook
filename: elefunt.bib
label: Kumari:2018:RLS
author: Aishwarya Kumari and D. P. Acharya
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publisher: Springer Singapore
pages: 219--225
year: 2018
DOI: https://doi.org/10.1007/978-981-10-8636-6_23
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ISSN: 2194-5365 OR 21945365
bibdate: Tue Oct 28 07:04:09 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.10.28 07:04:09 ???
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bibtype: inproceedings
filename: elefunt.bib
label: Rekha:2018:FIE
author: R. Rekha and Karunakara P. Menon
title: FPGA implementation of exponential function using CORDIC IP core for extended input range
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 597--600
year: 2018
DOI: https://doi.org/10.1109/RTEICT42901.2018.9012611
bibdate: Mon Oct 27 10:32:44 2025
bibtimestamp: 2025.10.27 10:32:44 ???
acknowledgement: ack-nhfb
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2018 3rd IEEE International Conference on Recent Trends in Electronics, Information & Communication Technology (RTEICT)

bibsource:
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keywords:
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rawbooktitle:
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  DOI =          "https://doi.org/10.1109/RTEICT42901.2018.9012611",
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  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer architecture; CORDIC IP Core; Exponential
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                 Signal processing algorithms; Simulation",
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bibtype: inproceedings
filename: elefunt.bib
label: Kumar:2019:FIT
author: Puli Anil Kumar
booktitle: 2019 5th International Conference on Advanced Computing & Communication Systems (ICACCS)
title: FPGA Implementation of the Trigonometric Functions Using the CORDIC Algorithm
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 894--900
year: 2019
DOI: https://doi.org/10.1109/ICACCS.2019.8728315
bibdate: Mon Oct 27 10:32:44 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.10.27 10:32:44 ???
acknowledgement: ack-nhfb
rawauthor: Puli Anil Kumar
rawbooktitle: {2019 5th International Conference on Advanced Computing \& Communication Systems (ICACCS)}
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entry:
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  author =       "Puli Anil Kumar",
  booktitle =    "{2019 5th International Conference on Advanced
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  title =        "{FPGA} Implementation of the Trigonometric Functions
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  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "894--900",
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ICACCS.2019.8728315",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
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bibtype: article
filename: elefunt.bib
label: Mopuri:2019:CRB
author: Suresh Mopuri and Swati Bhardwaj and Amit Acharyya
title: Coordinate Rotation-Based Design Methodology for Square Root and Division Computation
journal: j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS
volume: 66
number: 7
pages: 1227--1231
year: 2019
DOI: https://doi.org/10.1109/TCSII.2018.2878599
ISSN: 1549-7747 (print), 1558-3791 (electronic) OR 15497747 (print), 15583791 (electronic)
ISSNL: 1549-7747 OR 15497747
bibdate: Mon Oct 27 10:32:44 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.10.27 10:32:44 ???
fjournal: IEEE Transactions on Circuits and Systems II: Express Briefs
acknowledgement: ack-nhfb
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rawauthor: Suresh Mopuri and Swati Bhardwaj and Amit Acharyya
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  number =       "7",
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bibtype: article
filename: elefunt.bib
label: Mopuri:2019:CRM
author: Suresh Mopuri and Amit Acharyya
title: Configurable Rotation Matrix of Hyperbolic CORDIC for Any Logarithm and Its Inverse computation
journal: j-CSSP
volume: 39
number: 5
pages: 2551--2573
month: sep
monthnumber: 9
year: 2019
CODEN: CSSPEH
DOI: https://doi.org/10.1007/s00034-019-01277-w
ISSN: 1531-5878 OR 15315878
ISSNL: 0278-081X OR 0278081X
bibdate: Tue Oct 28 07:04:09 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.10.28 07:04:09 ???
fjournal: Circuits, systems, and signal processing: CSSP
acknowledgement: ack-nhfb
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rawauthor: Suresh Mopuri and Amit Acharyya
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bibtype: article
filename: elefunt.bib
label: Chen:2020:HCB
author: Hui Chen and Kaifeng Cheng and Zhonghai Lu and Yuxiang Fu and Li Li
title: Hyperbolic CORDIC-based Architecture for Computing Logarithm and Its Implementation
journal: j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS
volume: 67
number: 11
pages: 2652--2656
year: 2020
DOI: https://doi.org/10.1109/TCSII.2020.2971974
ISSN: 1549-7747 (print), 1558-3791 (electronic) OR 15497747 (print), 15583791 (electronic)
ISSNL: 1549-7747 OR 15497747
bibdate: Mon Oct 27 10:32:44 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.10.27 10:32:44 ???
fjournal: IEEE Transactions on Circuits and Systems II: Express Briefs
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journalURL: https://ieeexplore.ieee.org/xpl/issues?punumber=8920
rawauthor: Hui Chen and Kaifeng Cheng and Zhonghai Lu and Yuxiang Fu and Li Li
rawtitle: Hyperbolic {CORDIC}-based Architecture for Computing Logarithm and Its Implementation
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entry:
@Article{Chen:2020:HCB,
  author =       "Hui Chen and Kaifeng Cheng and Zhonghai Lu and Yuxiang
                 Fu and Li Li",
  title =        "Hyperbolic {CORDIC}-based Architecture for Computing
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  number =       "11",
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  bibdate =      "Mon Oct 27 10:32:44 2025",
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}


bibtype: inproceedings
filename: elefunt.bib
label: Dutt:2020:HSL
author: Rashi Dutt and Amit Acharyya
booktitle: 2020 European Conference on Circuit Theory and Design (ECCTD)
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1--4
year: 2020
DOI: https://doi.org/10.1109/ECCTD49232.2020.9218287
bibdate: Mon Oct 27 10:32:44 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.10.27 10:32:44 ???
acknowledgement: ack-nhfb
rawauthor: Rashi Dutt and Amit Acharyya
rawbooktitle: {2020 European Conference on Circuit Theory and Design (ECCTD)}
title:
A High Speed and Low Complexity Architecture Design Methodology for Square Root Unscented Kalman Filter based SLAM

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rawtitle:
A High Speed and Low Complexity Architecture Design Methodology for Square Root Unscented {Kalman} Filter based {SLAM}

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  booktitle =    "{2020 European Conference on Circuit Theory and Design
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  title =        "A High Speed and Low Complexity Architecture Design
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bibtype: article
filename: elefunt.bib
label: Chen:2021:LCH
author: Hui Chen and Zongguang Yu and Yonggang Zhang and Zhonghai Lu and Yuxiang Fu and Li Li
journal: j-IEEE-TRANS-CIRCUITS-SYST-1
volume: 68
number: 8
pages: 3293--3304
year: 2021
DOI: https://doi.org/10.1109/TCSI.2021.3081517
ISSN: 1549-8328 (print), 1558-0806 (electronic) OR 15498328 (print), 15580806 (electronic)
ISSNL: 1549-8328 OR 15498328
bibdate: Mon Oct 27 10:32:44 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.10.27 10:32:44 ???
fjournal: IEEE Transactions on Circuits and Systems I: Regular Papers
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=8919
rawauthor: Hui Chen and Zongguang Yu and Yonggang Zhang and Zhonghai Lu and Yuxiang Fu and Li Li
title:
Low-Complexity High-Precision Method and Architecture for Computing the Logarithm of Complex Numbers

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rawtitle:
Low-Complexity High-Precision Method and Architecture for Computing the Logarithm of Complex Numbers

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  journal =      j-IEEE-TRANS-CIRCUITS-SYST-1,
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  number =       "8",
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bibtype: inproceedings
filename: elefunt.bib
label: Xu:2021:LCA
author: Jin Xu and Lin Jiang and Hui Chen and Yuxiang Fu and Li Li
booktitle: 2021 18th International SoC Design Conference (ISOCC)
title: A Low-Complexity Architecture for Implementing Square to Tenth Root of Complex Numbers
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 15--16
year: 2021
DOI: https://doi.org/10.1109/ISOCC53507.2021.9613873
bibdate: Mon Oct 27 10:32:44 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.10.27 10:32:44 ???
acknowledgement: ack-nhfb
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rawbooktitle: {2021 18th International SoC Design Conference (ISOCC)}
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entry:
@InProceedings{Xu:2021:LCA,
  author =       "Jin Xu and Lin Jiang and Hui Chen and Yuxiang Fu and
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  booktitle =    "{2021 18th International SoC Design Conference
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  title =        "A Low-Complexity Architecture for Implementing Square
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  DOI =          "https://doi.org/10.1109/ISOCC53507.2021.9613873",
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  keywords =     "complex number Nth root; Complexity theory; Computer
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                 complexity; Power demand; Quantization (signal)",
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bibtype: inproceedings
filename: elefunt.bib
label: Puntsri:2022:RAG
title: Reconfigurable AWGN Generator Using Box--Muller Method with CORDIC-based Square Root Calculation
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1--4
year: 2022
DOI: https://doi.org/10.1109/ITC-CSCC55581.2022.9894924
bibdate: Mon Oct 27 10:32:44 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.10.27 10:32:44 ???
acknowledgement: ack-nhfb
author:
Kidsananapong Puntsri and Bussakorn Bunsri and Yaowarat Pittayang and Tanatip Bubpawan and Wuttichai Partipralam and Watid Phakphisut

booktitle:
2022 37th International Technical Conference on Circuits/Systems, Computers and Communications (ITC-CSCC)

keywords:
Box--Muller Method; CODIC method; Gaussian Noise Generator; Generators; Noise generators; Parity check codes; Polar codes; Real-time systems; Registers; Table lookup

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Reconfigurable {AWGN} Generator Using {Box--Muller} Method with {CORDIC}-based Square Root Calculation

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bibtype: inbook
filename: elefunt.bib
label: Ramani:2022:DDI
author: Narnindi Ramani and Saroj Mondal
booktitle: VLSI Design and Test
title: A Deep Dive into CORDIC Architectures to Implement Trigonometric Functions
publisher: Springer Nature Switzerland
pages: 551--561
year: 2022
DOI: https://doi.org/10.1007/978-3-031-21514-8_45
ISBN: 3-031-21514-1 OR 3031215141
ISBN13: 978-3-031-21514-8 OR 9783031215148
ISSN: 1865-0937 OR 18650937
bibdate: Tue Oct 28 07:04:09 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.10.28 07:04:09 ???
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bibtype: inproceedings
filename: elefunt.bib
label: Vakil:2022:TCB
author: Ardavan Vakil and Miad Faezipour
booktitle: 2022 International Conference on Computational Science and Computational Intelligence (CSCI)
title: Toward CORDIC-based Hyperbolic Function Implementation for Neural Engineering Hardware
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 416--418
year: 2022
DOI: https://doi.org/10.1109/CSCI58124.2022.00080
bibdate: Mon Oct 27 10:32:44 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.10.27 10:32:44 ???
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  title =        "Toward {CORDIC}-based Hyperbolic Function
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bibtype: inproceedings
filename: elefunt.bib
label: Vinh:2022:FIT
author: Truong Quang Vinh and Tran Ba Thanh and Dang Hoang Viet
booktitle: 2022 9th NAFOSTED Conference on Information and Computer Science (NICS)
title: FPGA Implementation of Trigonometric Function Using Loop-Optimized Radix-4 CORDIC
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 217--222
year: 2022
DOI: https://doi.org/10.1109/NICS56915.2022.10013467
bibdate: Mon Oct 27 10:32:44 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.10.27 10:32:44 ???
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  pages =        "217--222",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/NICS56915.2022.10013467",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer science; Convolution; Convolutional neural
                 networks; CORDIC; FPGA; Hardware; hardware
                 implementation; Performance evaluation; Quaternions;
                 Radix-4 CORDIC; Signal processing algorithms;
                 trigonometric function",
}


bibtype: article
filename: elefunt.bib
label: Dalloo:2024:LPL
author: Ayad M. Dalloo and Amjad Jaleel Humaidi and Ammar K. Al Mhdawi and Hamed Al-Raweshidy
journal: j-IEEE-ACCESS
volume: 12
pages: 24151--24163
year: 2024
DOI: https://doi.org/10.1109/ACCESS.2024.3364361
ISSN: 2169-3536 OR 21693536
ISSNL: 2169-3536 OR 21693536
bibdate: Mon Oct 27 10:32:44 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.10.27 10:32:44 ???
fjournal: IEEE Access
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639
rawauthor: Ayad M. Dalloo and Amjad Jaleel Humaidi and Ammar K. {Al Mhdawi} and Hamed Al-Raweshidy
title:
Low-Power and Low-Latency Hardware Implementation of Approximate Hyperbolic and Exponential Functions for Embedded System Applications

keywords:
approximate computing; Approximation algorithms; Approximation methods; Computer architecture; CORDIC; elementary functions; Exponential distribution; exponential function; Field programmable gate arrays; Hyperbolic functions; machine learning; Machine learning; Signal processing algorithms; Source coding; Table lookup; table-driven algorithm; Taylor series

rawtitle:
Low-Power and Low-Latency Hardware Implementation of Approximate Hyperbolic and Exponential Functions for Embedded System Applications

entry:
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  author =       "Ayad M. Dalloo and Amjad Jaleel Humaidi and Ammar K.
                 {Al Mhdawi} and Hamed Al-Raweshidy",
  title =        "Low-Power and Low-Latency Hardware Implementation of
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                 Embedded System Applications",
  journal =      j-IEEE-ACCESS,
  volume =       "12",
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  year =         "2024",
  DOI =          "https://doi.org/10.1109/ACCESS.2024.3364361",
  ISSN =         "2169-3536",
  ISSN-L =       "2169-3536",
  bibdate =      "Mon Oct 27 10:32:44 2025",
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                 Table lookup; table-driven algorithm; Taylor series",
}


bibtype: inproceedings
filename: elefunt.bib
label: Wong:2024:HGT
author: Paul Wong and Dania Susanne Mosuli and Xuechen Zhang and Xiaokun Yang
booktitle: 2024 IEEE International Conference on Big Data (BigData)
title: Hardware Generation on Trigonometric Functions
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 7571--7576
year: 2024
DOI: https://doi.org/10.1109/BigData62323.2024.10825243
bibdate: Mon Oct 27 10:32:44 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.10.27 10:32:44 ???
acknowledgement: ack-nhfb
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rawtitle: Hardware Generation on Trigonometric Functions
keywords:
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entry:
@InProceedings{Wong:2024:HGT,
  author =       "Paul Wong and Dania Susanne Mosuli and Xuechen Zhang
                 and Xiaokun Yang",
  booktitle =    "{2024 IEEE International Conference on Big Data
                 (BigData)}",
  title =        "Hardware Generation on Trigonometric Functions",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "7571--7576",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/BigData62323.2024.10825243",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
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                 Registers; Resource management; Scientific computing;
                 trigonometry",
}


bibtype: inproceedings
filename: elefunt.bib
label: Zhao:2025:RVP
author: Ruixiao Zhao and Min Xie and Xinchen Li and Yujie Zhang
booktitle: 2025 IEEE 14th International Conference on Communications, Circuits and Systems (ICCCAS)
title: A RISC-V Processor with Optimized CORDIC-based Trigonometric Function Accelerator
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 155--159
year: 2025
DOI: https://doi.org/10.1109/ICCCAS65806.2025.11102696
bibdate: Mon Oct 27 10:32:44 2025
bibtimestamp: 2025.10.27 10:32:44 ???
acknowledgement: ack-nhfb
rawauthor: Ruixiao Zhao and Min Xie and Xinchen Li and Yujie Zhang
rawbooktitle: {2025 IEEE 14th International Conference on Communications, Circuits and Systems (ICCCAS)}
rawtitle: A {RISC-V} Processor with Optimized {CORDIC}-based Trigonometric Function Accelerator
bibsource:
https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/risc-v.bib

keywords:
Accuracy; Circuits and systems; Computational efficiency; Computer architecture; CORDIC; Hardware; instruction set extension; Instruction sets; RISC-V; Table lookup; trigonometric function

entry:
@InProceedings{Zhao:2025:RVP,
  author =       "Ruixiao Zhao and Min Xie and Xinchen Li and Yujie
                 Zhang",
  booktitle =    "{2025 IEEE 14th International Conference on
                 Communications, Circuits and Systems (ICCCAS)}",
  title =        "A {RISC-V} Processor with Optimized {CORDIC}-based
                 Trigonometric Function Accelerator",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "155--159",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/ICCCAS65806.2025.11102696",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Accuracy; Circuits and systems; Computational
                 efficiency; Computer architecture; CORDIC; Hardware;
                 instruction set extension; Instruction sets; RISC-V;
                 Table lookup; trigonometric function",
}


bibtype: book
filename: elefunt.bib
label: Jones:1984:CFA
author: William B. (William Branham) Jones and Wolfgang J. Thron
booktitle: Continued Fractions: Analytic Theory and Applications
title: Continued Fractions: Analytic Theory and Applications
volume: 11
publisher: pub-CAMBRIDGE
address: pub-CAMBRIDGE:adr
pages: xxviii + 428
year: 1984
DOI: https://doi.org/10.1017/CBO9780511759550
ISBN: 0-521-30231-5 OR 0521302315
ISBN13: 978-0-521-30231-9 OR 9780521302319
LCCN: QA295 .J64 1984
bibdate: Sat Jul 10 09:47:15 MDT 2010
bibtimestamp: 2010.07.10 09:47:15 MDT
series: Encyclopedia of mathematics and its applications
acknowledgement: ack-nhfb
rawauthor: William B. (William Branham) Jones and Wolfgang J. Thron
rawbooktitle: Continued Fractions: Analytic Theory and Applications
rawtitle: Continued Fractions: Analytic Theory and Applications
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/h/henrici-peter.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcw.bib; z3950.bibsys.no:2100/BIBSYS

TOC:
Editor's Statement Section Editor's Foreword Introduction by Peter Henrici Preface Symbols 1: Introduction 1.1 History 1.1.1 Beginnings 1.1.2 Number-Theoretic Results 1.1.3 Analytic Theory 1.2 Overview of Contents 2: Elementary Properties of Continued Fractions 2.1 Preliminaries 2.1.1 Basic Definitions and Theorems 2.1.2 Regular Continued Fractions 2.1.3 Other Continued-Fraction Expansions 2.1.4 Algorithms for Computing Approximants ldots 2.2 Sequences Generated by Linear Fractional Transformations 2.3 Equivalence Transformations 2.3.1 Equivalent Continued Fractions 2.3.2 Euler's [1748] Connection between Continued Fractions and Infinite Series 2.4 Contractions and Extensions 2.4.1 Contraction of Continued Fractions 2.4.2 Even Part of a Continued Fraction 2.4.3 Odd Part of a Continued Fraction 2.4.4 Extension of a Continued Fraction 3: Periodic Continued Fractions 3.1 Introduction 3.2 Convergence of Periodic Continued Fractions ldots 3.3 Dual Periodic Continued Fractions 4: Convergence of Continued Fractions 4.1 Introduction 4.2 Element Regions, Value Regions, and Sequences of Nested Circular Disks 4.3 Necessary Conditions for Convergence 4.3.1 Stern--Stolz Theorem 4.3.2 Necessary Conditions for Best Value Regions and Convergence Regions 4.4 Sufficient Conditions for Convergence: Constant Elements 4.4.1 Classical Results and Generalizations 4.4.2 Parabolic Convergence Regions 4.4.3 Convergence Neighborhoods for K(an/1) ldots 4.4.4 Twin Convergence Regions 4.4.5 Miscellaneous Convergence Criteria 4.5 Sufficient Conditions for Convergence Variable Elements 4.5.1 Introduction Classification of Continued Fractions 4.5.2 Regular C-fractions 4.5.3 Positive Definite/-fractions 4.5.4 General T-fractions 5: Methods for Representing Analytic Functions by Continued Fractions 5.1 Correspondence 5.2 Three-Term Recurrence Relations 5.3 Minimal Solutions of Three-Term Recurrence Relations 5.4 Uniform Convergence 5.5 Pade Table 5.5.1 Pade Approximants 5.5.2 Multiple-Point Pade Tables 6: Representations of Analytic Functions by Continued Fractions 6.1 Continued Fractions of Gauss 6.1.1 Hypergeometric Functions $F(a, b; c; z)$ ldots 6.1.2 Confluent Hypergeometric Functions $Phi (b; c; z)$ 6.1.3 Confluent Hypergeometric Functions $Psi (c; z)$ 6.1.4 Confluent Hypergeometric Functions $Omega (a, b; z)$ 6.2 Representations from Minimal Solutions 7: Types of Corresponding Continued Fractions and Related Algorithms 7.1 Regular $C$-Fractions 7.1.1 Correspondence of Regular $C$-Fractions 7.1.2 Quotient-Difference Algorithm 7.1.3 $g$-Fractions 7.2 Associated Continued Fractions and $J$-Fractions 7.2.1 Correspondence of Associated Continued Fractions 7.2.2 $J$-Fractions and Orthogonal Polynomials 7.3 General $T$-Fractions 7.3.1 Correspondence of General $T$-Fractions 7.3.2 FG Algorithms 7.3.3 Representation of Analytic Functions 7.4 Stable Polynomials 8: Truncation-Error Analysis 8.1 Introduction 8.2 General Theory of Inclusion Regions and Truncation Errors 8.3 Explicit Results on Inclusion Regions and Truncation-Error Bounds 8.4 Accelerating Convergence 9: Asymptotic Expansions and Moment Problems 9.1 Introduction 9.2 Moment Problems 9.3 Integral Representations of Continued Fractions 9.4 Asymptotic Expansions for Continued Fractions 9.5 Solutions of the Moment Problems 9.6 Representations of Analytic Functions 10: Numerical Stability in Evaluating Continued Fractions 10.1 General Estimates of Relative Roundoff Error 10.2 Methods for Estimating $g_^(n)$ 10.3 Applications 11: Application of Continued Fractions to Birth--Death Processes 11.1 Birth--Death Processes 11.2 Computational Procedures 12: Miscellaneous Results 12.1 $T$-Fraction Expansions for Families of Bounded Functions 12.2 $T$-Fractions Corresponding to Rational Functions 12.3 Location of Singular Points of Analytic Functions Represented by Continued Fractions 12.4 Univalence of Functions Represented by Continued Fractions Appendix A. Classification of Special Types of Continued Fractions Appendix B. Additional Results on Minimal Solutions of Three-Term Recurrence Relations Bibliography Author Index Subject Index

rawTOC:
Editor's Statement \\ Section Editor's Foreword \\ Introduction by Peter Henrici \\ Preface \\ Symbols \\ 1: Introduction \\ 1.1 History \\ 1.1.1 Beginnings \\ 1.1.2 Number-Theoretic Results \\ 1.1.3 Analytic Theory \\ 1.2 Overview of Contents \\ \\ 2: Elementary Properties of Continued Fractions \\ 2.1 Preliminaries \\ 2.1.1 Basic Definitions and Theorems \\ 2.1.2 Regular Continued Fractions \\ 2.1.3 Other Continued-Fraction Expansions \\ 2.1.4 Algorithms for Computing Approximants \ldots{} \\ 2.2 Sequences Generated by Linear Fractional Transformations \\ 2.3 Equivalence Transformations \\ 2.3.1 Equivalent Continued Fractions \\ 2.3.2 Euler's [1748] Connection between Continued Fractions and Infinite Series \\ 2.4 Contractions and Extensions \\ 2.4.1 Contraction of Continued Fractions \\ 2.4.2 Even Part of a Continued Fraction \\ 2.4.3 Odd Part of a Continued Fraction \\ 2.4.4 Extension of a Continued Fraction \\ \\ 3: Periodic Continued Fractions \\ 3.1 Introduction \\ 3.2 Convergence of Periodic Continued Fractions \ldots{} \\ 3.3 Dual Periodic Continued Fractions \\ \\ 4: Convergence of Continued Fractions \\ 4.1 Introduction \\ 4.2 Element Regions, Value Regions, and Sequences of Nested Circular Disks \\ 4.3 Necessary Conditions for Convergence \\ 4.3.1 Stern--Stolz Theorem \\ 4.3.2 Necessary Conditions for Best Value Regions and Convergence Regions \\ 4.4 Sufficient Conditions for Convergence: Constant Elements \\ 4.4.1 Classical Results and Generalizations \\ 4.4.2 Parabolic Convergence Regions \\ 4.4.3 Convergence Neighborhoods for K(an/1) \ldots{} \\ 4.4.4 Twin Convergence Regions \\ 4.4.5 Miscellaneous Convergence Criteria \\ 4.5 Sufficient Conditions for Convergence \\ Variable Elements \\ 4.5.1 Introduction \\ Classification of Continued Fractions \\ 4.5.2 Regular C-fractions \\ 4.5.3 Positive Definite/-fractions \\ 4.5.4 General T-fractions \\ \\ 5: Methods for Representing Analytic Functions by Continued Fractions \\ 5.1 Correspondence \\ 5.2 Three-Term Recurrence Relations \\ 5.3 Minimal Solutions of Three-Term Recurrence Relations \\ 5.4 Uniform Convergence \\ 5.5 Pad{\'e} Table \\ 5.5.1 Pad{\'e} Approximants \\ 5.5.2 Multiple-Point Pad{\'e} Tables \\ \\ 6: Representations of Analytic Functions by Continued Fractions \\ 6.1 Continued Fractions of Gauss \\ 6.1.1 Hypergeometric Functions $F(a, b; c; z)$ \ldots{} \\ 6.1.2 Confluent Hypergeometric Functions $\Phi(b; c; z)$ \\ 6.1.3 Confluent Hypergeometric Functions $\Psi(c; z)$ \\ 6.1.4 Confluent Hypergeometric Functions $\Omega(a, b; z)$ \\ 6.2 Representations from Minimal Solutions \\ \\ 7: Types of Corresponding Continued \\ Fractions and Related Algorithms \\ 7.1 Regular $C$-Fractions \\ 7.1.1 Correspondence of Regular $C$-Fractions \\ 7.1.2 Quotient-Difference Algorithm \\ 7.1.3 $g$-Fractions \\ 7.2 Associated Continued Fractions and $J$-Fractions \\ 7.2.1 Correspondence of Associated Continued Fractions \\ 7.2.2 $J$-Fractions and Orthogonal Polynomials \\ 7.3 General $T$-Fractions \\ 7.3.1 Correspondence of General $T$-Fractions \\ 7.3.2 FG Algorithms \\ 7.3.3 Representation of Analytic Functions \\ 7.4 Stable Polynomials \\ \\ 8: Truncation-Error Analysis \\ 8.1 Introduction \\ 8.2 General Theory of Inclusion Regions and Truncation Errors \\ 8.3 Explicit Results on Inclusion Regions and Truncation-Error Bounds \\ 8.4 Accelerating Convergence \\ \\ 9: Asymptotic Expansions and Moment Problems \\ 9.1 Introduction \\ 9.2 Moment Problems \\ 9.3 Integral Representations of Continued Fractions \\ 9.4 Asymptotic Expansions for Continued Fractions \\ 9.5 Solutions of the Moment Problems \\ 9.6 Representations of Analytic Functions \\ \\ 10: Numerical Stability in Evaluating Continued Fractions \\ 10.1 General Estimates of Relative Roundoff Error \\ 10.2 Methods for Estimating $g_^{(n)}$ \\ 10.3 Applications \\ \\ 11: Application of Continued Fractions to \\ Birth--Death Processes \\ 11.1 Birth--Death Processes \\ 11.2 Computational Procedures \\ \\ 12: Miscellaneous Results \\ 12.1 $T$-Fraction Expansions for Families of Bounded Functions \\ 12.2 $T$-Fractions Corresponding to Rational Functions \\ 12.3 Location of Singular Points of Analytic Functions Represented by Continued Fractions \\ 12.4 Univalence of Functions Represented by Continued Fractions \\ \\ Appendix A. Classification of Special Types of Continued Fractions \\ Appendix B. Additional Results on Minimal Solutions of Three-Term Recurrence Relations \\ Bibliography \\ Author Index \\ Subject Index

entry:
@Book{Jones:1984:CFA,
  author =       "William B. (William Branham) Jones and Wolfgang J.
                 Thron",
  booktitle =    "Continued Fractions: Analytic Theory and
                 Applications",
  title =        "Continued Fractions: Analytic Theory and
                 Applications",
  volume =       "11",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "xxviii + 428",
  year =         "1984",
  DOI =          "https://doi.org/10.1017/CBO9780511759550",
  ISBN =         "0-521-30231-5",
  ISBN-13 =      "978-0-521-30231-9",
  LCCN =         "QA295 .J64 1984",
  bibdate =      "Sat Jul 10 09:47:15 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/henrici-peter.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 z3950.bibsys.no:2100/BIBSYS",
  series =       "Encyclopedia of mathematics and its applications",
  acknowledgement = ack-nhfb,
  tableofcontents = "Editor's Statement \\
                 Section Editor's Foreword \\
                 Introduction by Peter Henrici \\
                 Preface \\
                 Symbols \\
                 1: Introduction \\
                 1.1 History \\
                 1.1.1 Beginnings \\
                 1.1.2 Number-Theoretic Results \\
                 1.1.3 Analytic Theory \\
                 1.2 Overview of Contents \\
                 \\
                 2: Elementary Properties of Continued Fractions \\
                 2.1 Preliminaries \\
                 2.1.1 Basic Definitions and Theorems \\
                 2.1.2 Regular Continued Fractions \\
                 2.1.3 Other Continued-Fraction Expansions \\
                 2.1.4 Algorithms for Computing Approximants \ldots{}
                 \\
                 2.2 Sequences Generated by Linear Fractional
                 Transformations \\
                 2.3 Equivalence Transformations \\
                 2.3.1 Equivalent Continued Fractions \\
                 2.3.2 Euler's [1748] Connection between Continued
                 Fractions and Infinite Series \\
                 2.4 Contractions and Extensions \\
                 2.4.1 Contraction of Continued Fractions \\
                 2.4.2 Even Part of a Continued Fraction \\
                 2.4.3 Odd Part of a Continued Fraction \\
                 2.4.4 Extension of a Continued Fraction \\
                 \\
                 3: Periodic Continued Fractions \\
                 3.1 Introduction \\
                 3.2 Convergence of Periodic Continued Fractions
                 \ldots{} \\
                 3.3 Dual Periodic Continued Fractions \\
                 \\
                 4: Convergence of Continued Fractions \\
                 4.1 Introduction \\
                 4.2 Element Regions, Value Regions, and Sequences of
                 Nested Circular Disks \\
                 4.3 Necessary Conditions for Convergence \\
                 4.3.1 Stern--Stolz Theorem \\
                 4.3.2 Necessary Conditions for Best Value Regions and
                 Convergence Regions \\
                 4.4 Sufficient Conditions for Convergence: Constant
                 Elements \\
                 4.4.1 Classical Results and Generalizations \\
                 4.4.2 Parabolic Convergence Regions \\
                 4.4.3 Convergence Neighborhoods for K(an/1) \ldots{}
                 \\
                 4.4.4 Twin Convergence Regions \\
                 4.4.5 Miscellaneous Convergence Criteria \\
                 4.5 Sufficient Conditions for Convergence \\
                 Variable Elements \\
                 4.5.1 Introduction \\
                 Classification of Continued Fractions \\
                 4.5.2 Regular C-fractions \\
                 4.5.3 Positive Definite/-fractions \\
                 4.5.4 General T-fractions \\
                 \\
                 5: Methods for Representing Analytic Functions by
                 Continued Fractions \\
                 5.1 Correspondence \\
                 5.2 Three-Term Recurrence Relations \\
                 5.3 Minimal Solutions of Three-Term Recurrence
                 Relations \\
                 5.4 Uniform Convergence \\
                 5.5 Pad{\'e} Table \\
                 5.5.1 Pad{\'e} Approximants \\
                 5.5.2 Multiple-Point Pad{\'e} Tables \\
                 \\
                 6: Representations of Analytic Functions by Continued
                 Fractions \\
                 6.1 Continued Fractions of Gauss \\
                 6.1.1 Hypergeometric Functions $F(a, b; c; z)$ \ldots{}
                 \\
                 6.1.2 Confluent Hypergeometric Functions $\Phi(b; c;
                 z)$ \\
                 6.1.3 Confluent Hypergeometric Functions $\Psi(c; z)$
                 \\
                 6.1.4 Confluent Hypergeometric Functions $\Omega(a, b;
                 z)$ \\
                 6.2 Representations from Minimal Solutions \\
                 \\
                 7: Types of Corresponding Continued \\
                 Fractions and Related Algorithms \\
                 7.1 Regular $C$-Fractions \\
                 7.1.1 Correspondence of Regular $C$-Fractions \\
                 7.1.2 Quotient-Difference Algorithm \\
                 7.1.3 $g$-Fractions \\
                 7.2 Associated Continued Fractions and $J$-Fractions
                 \\
                 7.2.1 Correspondence of Associated Continued Fractions
                 \\
                 7.2.2 $J$-Fractions and Orthogonal Polynomials \\
                 7.3 General $T$-Fractions \\
                 7.3.1 Correspondence of General $T$-Fractions \\
                 7.3.2 FG Algorithms \\
                 7.3.3 Representation of Analytic Functions \\
                 7.4 Stable Polynomials \\
                 \\
                 8: Truncation-Error Analysis \\
                 8.1 Introduction \\
                 8.2 General Theory of Inclusion Regions and Truncation
                 Errors \\
                 8.3 Explicit Results on Inclusion Regions and
                 Truncation-Error Bounds \\
                 8.4 Accelerating Convergence \\
                 \\
                 9: Asymptotic Expansions and Moment Problems \\
                 9.1 Introduction \\
                 9.2 Moment Problems \\
                 9.3 Integral Representations of Continued Fractions \\
                 9.4 Asymptotic Expansions for Continued Fractions \\
                 9.5 Solutions of the Moment Problems \\
                 9.6 Representations of Analytic Functions \\
                 \\
                 10: Numerical Stability in Evaluating Continued
                 Fractions \\
                 10.1 General Estimates of Relative Roundoff Error \\
                 10.2 Methods for Estimating $g_^{(n)}$ \\
                 10.3 Applications \\
                 \\
                 11: Application of Continued Fractions to \\
                 Birth--Death Processes \\
                 11.1 Birth--Death Processes \\
                 11.2 Computational Procedures \\
                 \\
                 12: Miscellaneous Results \\
                 12.1 $T$-Fraction Expansions for Families of Bounded
                 Functions \\
                 12.2 $T$-Fractions Corresponding to Rational Functions
                 \\
                 12.3 Location of Singular Points of Analytic Functions
                 Represented by Continued Fractions \\
                 12.4 Univalence of Functions Represented by Continued
                 Fractions \\
                 \\
                 Appendix A. Classification of Special Types of
                 Continued Fractions \\
                 Appendix B. Additional Results on Minimal Solutions of
                 Three-Term Recurrence Relations \\
                 Bibliography \\
                 Author Index \\
                 Subject Index",
}


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filename: elefunt.bib
label: Anonymous:1998:TIC
editor: Anonymous
volume: 147
publisher: Accademia Nazionale dei Lincei
address: Roma, Italy
pages: 322
year: 1998
ISSN: 0391-805X OR 0391805X
LCCN: QA299.6
bibdate: Fri May 31 16:34:38 MDT 2024
bibtimestamp: 2024.05.31 16:34:38 MDT
series: Atti dei convegni Lincei
acknowledgement: ack-nhfb
raweditor: Anonymous
booktitle:
Tricomi's ideas and contemporary applied mathematics: (Roma, 28--29 novembre --- Torino, 1--2 dicembre 1997)

title:
Tricomi's ideas and contemporary applied mathematics: (Roma, 28--29 novembre --- Torino, 1--2 dicembre 1997)

bibsource:
fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/bibnet/authors/g/gautschi-walter.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

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                 1997)}",
  title =        "{Tricomi's ideas and contemporary applied mathematics:
                 (Roma, 28--29 novembre --- Torino, 1--2 dicembre
                 1997)}",
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  publisher =    "Accademia Nazionale dei Lincei",
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  series =       "Atti dei convegni Lincei",
  acknowledgement = ack-nhfb,
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bibtype: book
filename: elefunt.bib
label: Knuth:1998:SA
author: Donald E. Knuth
title: Seminumerical Algorithms
volume: 2
publisher: pub-AW
address: pub-AW:adr
edition: Third
pages: xiii + 762
year: 1998
ISBN: 0-201-89684-2 OR 0201896842
ISBN13: 978-0-201-89684-8 OR 9780201896848
LCCN: QA76.6 .K64 1997
bibdate: Fri Jul 11 15:41:22 1997
bibtimestamp: 1997.07.11 15:41:22 ???
series: The Art of Computer Programming
acknowledgement: ack-nhfb
rawauthor: Donald E. Knuth
rawtitle: Seminumerical Algorithms
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/css.bib; 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/master.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/texbook2.bib

TOC:
3: Random Numbers / 1 3.1. Introduction / 1 3.2. Generating Uniform Random Numbers / 10 3.2.1. The Linear Congruential Method / 10 3.2 1.1. Choice of modulus / 12 3.2.1.2 Choice of multiplier / 16 3.2.1.3. Potency / 23 3.2.2. Other Methods / 26 3.3. Statistical Tests / 41 3.3.1. General Test Procedures for Studying Random Data / 41 3.3.2. Empirical Tests / 61 *3.3.3. Theoretical Tests / 80 3.3.4. The Spectral Test / 93 3.4. Other Types of Random Quantities / 119 3.4 1. Numerical Distributions / 119 3.4.2. Random Sampling and Shuffling / 142 *3.5. What Is a Random Sequence? / 149 3.6. Summary / 184 4: Arithmetic / 194 4.1. Positional Number Systems / 195 4.2. Floating Point Arithmetic / 214 4.2.1. Single-Precision Calculations / 214 4.2 2. Accuracy of Floating Point Arithmetic / 229 *4.2.3. Double-Precision Calculations / 246 4.2.4. Distribution of Floating Point Numbers / 253 4.3 Multiple Precision Arithmetic / 265 4.3.1. The Classical Algorithms / 265 *4.3.2. Modular Arithmetic / 284 *4.3.3. How Fast Can We Multiply? / 294 4.4. Radix Conversion / 319 4.5. Rational Arithmetic / 330 4.5.1. Fractions / 330 4.5.2. The Greatest Common Divisor / 333 *4.5.3. Analysis of Euclid's Algorithm / 356 4.5.4. Factoring into Primes / 379 4.6. Polynomial Arithmetic / 418 4.6.1. Division of Polynomials / 420 *4.6.2. Factorization of Polynomials / 439 4.6.3. Evaluation of Powers / 461 4.6.4. Evaluation of Polynomials / 485 *4.7. Manipulation of Power Series / 525 Answers to Exercises / 538 Appendix A: Tables of Numerical Quantities / 726 1. Fundamental Constants (decimal) / 726 2; Fundamental Constants ( octal) / 727 3. Harmonic Numbers, Bernoulli Numbers, Fibonacci Numbers / 728 Appendix B: Index to Notations / 730 Index and Glossary / 735

rawTOC:
3: Random Numbers / 1 \\ 3.1. Introduction / 1 \\ 3.2. Generating Uniform Random Numbers / 10 \\ 3.2.1. The Linear Congruential Method / 10 \\ 3.2 1.1. Choice of modulus / 12 \\ 3.2.1.2 Choice of multiplier / 16 \\ 3.2.1.3. Potency / 23 \\ 3.2.2. Other Methods / 26 \\ 3.3. Statistical Tests / 41 \\ 3.3.1. General Test Procedures for Studying Random Data / 41 \\ 3.3.2. Empirical Tests / 61 \\ *3.3.3. Theoretical Tests / 80 \\ 3.3.4. The Spectral Test / 93 \\ 3.4. Other Types of Random Quantities / 119 \\ 3.4 1. Numerical Distributions / 119 \\ 3.4.2. Random Sampling and Shuffling / 142 \\ *3.5. What Is a Random Sequence? / 149 \\ 3.6. Summary / 184 \\ 4: Arithmetic / 194 \\ 4.1. Positional Number Systems / 195 \\ 4.2. Floating Point Arithmetic / 214 \\ 4.2.1. Single-Precision Calculations / 214 \\ 4.2 2. Accuracy of Floating Point Arithmetic / 229 \\ *4.2.3. Double-Precision Calculations / 246 \\ 4.2.4. Distribution of Floating Point Numbers / 253 \\ 4.3 Multiple Precision Arithmetic / 265 \\ 4.3.1. The Classical Algorithms / 265 \\ *4.3.2. Modular Arithmetic / 284 \\ *4.3.3. How Fast Can We Multiply? / 294 \\ 4.4. Radix Conversion / 319 \\ 4.5. Rational Arithmetic / 330 \\ 4.5.1. Fractions / 330 \\ 4.5.2. The Greatest Common Divisor / 333 \\ *4.5.3. Analysis of Euclid's Algorithm / 356 \\ 4.5.4. Factoring into Primes / 379 \\ 4.6. Polynomial Arithmetic / 418 \\ 4.6.1. Division of Polynomials / 420 \\ *4.6.2. Factorization of Polynomials / 439 \\ 4.6.3. Evaluation of Powers / 461 \\ 4.6.4. Evaluation of Polynomials / 485 \\ *4.7. Manipulation of Power Series / 525 \\ Answers to Exercises / 538 \\ Appendix A: Tables of Numerical Quantities / 726 \\ 1. Fundamental Constants (decimal) / 726 \\ 2; Fundamental Constants ( octal) / 727 \\ 3. Harmonic Numbers, Bernoulli Numbers, Fibonacci Numbers / 728 \\ Appendix B: Index to Notations / 730 \\ Index and Glossary / 735

entry:
@Book{Knuth:1998:SA,
  author =       "Donald E. Knuth",
  title =        "Seminumerical Algorithms",
  volume =       "2",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  edition =      "Third",
  pages =        "xiii + 762",
  year =         "1998",
  ISBN =         "0-201-89684-2",
  ISBN-13 =      "978-0-201-89684-8",
  LCCN =         "QA76.6 .K64 1997",
  bibdate =      "Fri Jul 11 15:41:22 1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/css.bib;
                 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/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 https://www.math.utah.edu/pub/tex/bib/texbook2.bib",
  price =        "US\$52.75",
  series =       "The Art of Computer Programming",
  acknowledgement = ack-nhfb,
  tableofcontents = "3: Random Numbers / 1 \\
                 3.1. Introduction / 1 \\
                 3.2. Generating Uniform Random Numbers / 10 \\
                 3.2.1. The Linear Congruential Method / 10 \\
                 3.2 1.1. Choice of modulus / 12 \\
                 3.2.1.2 Choice of multiplier / 16 \\
                 3.2.1.3. Potency / 23 \\
                 3.2.2. Other Methods / 26 \\
                 3.3. Statistical Tests / 41 \\
                 3.3.1. General Test Procedures for Studying Random Data
                 / 41 \\
                 3.3.2. Empirical Tests / 61 \\
                 *3.3.3. Theoretical Tests / 80 \\
                 3.3.4. The Spectral Test / 93 \\
                 3.4. Other Types of Random Quantities / 119 \\
                 3.4 1. Numerical Distributions / 119 \\
                 3.4.2. Random Sampling and Shuffling / 142 \\
                 *3.5. What Is a Random Sequence? / 149 \\
                 3.6. Summary / 184 \\
                 4: Arithmetic / 194 \\
                 4.1. Positional Number Systems / 195 \\
                 4.2. Floating Point Arithmetic / 214 \\
                 4.2.1. Single-Precision Calculations / 214 \\
                 4.2 2. Accuracy of Floating Point Arithmetic / 229 \\
                 *4.2.3. Double-Precision Calculations / 246 \\
                 4.2.4. Distribution of Floating Point Numbers / 253 \\
                 4.3 Multiple Precision Arithmetic / 265 \\
                 4.3.1. The Classical Algorithms / 265 \\
                 *4.3.2. Modular Arithmetic / 284 \\
                 *4.3.3. How Fast Can We Multiply? / 294 \\
                 4.4. Radix Conversion / 319 \\
                 4.5. Rational Arithmetic / 330 \\
                 4.5.1. Fractions / 330 \\
                 4.5.2. The Greatest Common Divisor / 333 \\
                 *4.5.3. Analysis of Euclid's Algorithm / 356 \\
                 4.5.4. Factoring into Primes / 379 \\
                 4.6. Polynomial Arithmetic / 418 \\
                 4.6.1. Division of Polynomials / 420 \\
                 *4.6.2. Factorization of Polynomials / 439 \\
                 4.6.3. Evaluation of Powers / 461 \\
                 4.6.4. Evaluation of Polynomials / 485 \\
                 *4.7. Manipulation of Power Series / 525 \\
                 Answers to Exercises / 538 \\
                 Appendix A: Tables of Numerical Quantities / 726 \\
                 1. Fundamental Constants (decimal) / 726 \\
                 2; Fundamental Constants ( octal) / 727 \\
                 3. Harmonic Numbers, Bernoulli Numbers, Fibonacci
                 Numbers / 728 \\
                 Appendix B: Index to Notations / 730 \\
                 Index and Glossary / 735",
}


bibtype: book
filename: elefunt.bib
label: Borwein:2007:RHR
editor: Peter Borwein and Stephen Choi and Brendan Rooney and Andrea Weirathmueller and others
title: The Riemann Hypothesis: a resource for the afficionado and virtuoso alike
volume: 27
publisher: Springer Science+Business Media, LLC
address: New York, NY, USA
pages: xiv + 533
year: 2007
DOI: https://doi.org/10.1007/978-0-387-72126-2
ISBN: 0-387-72125-8 (hardcover), 0-387-72126-6 (e-book) OR 0387721258 (hardcover), 0387721266 (ebook)
LCCN: QA246 .R53 2008
bibdate: Thu Sep 1 07:07:49 MDT 2022
bibsource: fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2022.09.01 07:07:49 MDT
series: CMS books in mathematics
URL: http://libanswers.liverpool.ac.uk/faq/182315
acknowledgement: ack-nhfb
raweditor: Peter Borwein and Stephen Choi and Brendan Rooney and Andrea Weirathmueller and others
rawtitle: The {Riemann Hypothesis}: a resource for the afficionado and virtuoso alike
ISBN13:
978-0-387-72125-5 (hardcover), 978-0-387-72126-2 (e-book) OR 9780387721255 (hardcover), 9780387721262 (ebook)

abstract:
This book is an introduction to the theory surrounding the Riemann Hypothesis. Part I serves as a compendium of known results and as a primer for the material presented in the 20 original papers contained in Part II. The original papers place the material into historical context and illustrate the motivations for research on and around the Riemann Hypothesis. Several of these papers focus on computation of the zeta function, while others give proofs of the Prime Number Theorem, since the Prime Number Theorem is so closely connected to the Riemann Hypothesis. The text is suitable for a graduate course or seminar or simply as a reference for anyone interested in this extraordinary conjecture.

subject:
Mathematics; History; Number theory; Mathematiques; Histoire; Theorie des nombres; Mathematics.; Number theory.

TOC:
Part 1: Introduction to the Riemann hypothesis 1: Why this book 1.1: The Holy Grail 1.2: Riemann's zeta and Liouville's lambda 1.3: The prime number theorem 2: Analytic preliminaries 2.1: The Riemann zeta function 2.2: Zero-free region 2.3: Counting the zeros of [cedilla](s) 2.4: Hardy's theorem 3: Algorithms for calculating [cedilla](s) 3.1: Euler--MacLaurin summation 3.2: Backlund 3.3: Hardy's function 3.4: The Riemann--Siegel formula 3.5: Gram's law 3.6: Turing 3.7: The Odlyzko--Schonhage algorithm 3.8: A simple algorithm for the zeta function 3.9: Further reading 4: Empirical evidence 4.1: Verification in an interval 4.2: A brief history of computational evidence 4.3: The Riemann hypothesis and random matrices 4.4: The Skewes number 5: Equivalent statements 5.1: Number-theoretic equivalences 5.2: Analytic equivalences 5.3: Other equivalences 6: Extensions of the Riemann hypothesis 6.1: The Riemann hypothesis 6.2: The generalized Riemann hypothesis 6.3: The extended Riemann hypothesis 6.4: An equivalent extended Riemann hypothesis 6.5: Another extended Riemann hypothesis 6.6: The Grand Riemann hypothesis 7: Assuming the Riemann hypothesis and its extensions 7.1: Another proof of the prime number theorem 7.2: Goldbach's conjecture 7.3: More Goldbach 7.4: Primes in a given interval 7.5: The least prime in arithmetic progressions 7.6: Primality testing 7.7: Artin's primitive root conjecture 7.8: Bounds on Dirichlet $L$-series 7.9: The Lindelof hypothesis 7.10: Titchmarsh's [delta](T) function 7.11: Mean values of [cedilla](s)8: Failed attempts at proof 8.1: Stieltjes and Mertens' conjecture 8.2: Hans Rademacher and false hopes 8.3: Turan's condition 8.4: Louis de Branges's approach 8.5: No really good idea 9: Formulas 10: Timeline pt. 2: Original papers 11: Expert witnesses 11. 1: E. Bombieri (2000--2001) 11.2: P. Sarnak (2004) 11.3: J.B. Conrey (2003) 11.4: A. Ivic (2003) 12: The experts speak for themselves 12.1: P.L. Chebyshev (1852) 12.2: B. Riemann (1859) 12.3: J. Hadamard (1896) 12.4: C. de la Vallee Poussin (1899) 12.5: G.H. Hardy (1914) 12.6: G.H. Hardy (1915) 12.7: G.H. Hardy and J.E. Littlewood (1915) 12.8: A. Weil (1941) 12.9: P. Turan (1948) 12.10: A. Selberg (1949) 12.11: P. Erdo$cdot $s (1949) 12.12: S. Skewes (1955) 12.13: C.B. Haselgrove (1958) 12.14: H. Montgomery (1973) 12.15: D.J. Newman (1980) 12.16: J. Korevaar (1982) 12.17: H. Daboussi (1984) 12.18: A. Hildebrand (1986) 12.19: D. Goldston and H. Montgomery (1987) 12.20: M. Agrawal, N. Kayal, and N. Saxena (2004) References References Index

rawabstract:
This book is an introduction to the theory surrounding the Riemann Hypothesis. Part I serves as a compendium of known results and as a primer for the material presented in the 20 original papers contained in Part II. The original papers place the material into historical context and illustrate the motivations for research on and around the Riemann Hypothesis. Several of these papers focus on computation of the zeta function, while others give proofs of the Prime Number Theorem, since the Prime Number Theorem is so closely connected to the Riemann Hypothesis. The text is suitable for a graduate course or seminar or simply as a reference for anyone interested in this extraordinary conjecture.

shortTOC:
To the Riemann Hypothesis Why This Book Analytic Preliminaries Algorithms for Calculating ?(s) Empirical Evidence Equivalent Statements Extensions of the Riemann Hypothesis Assuming the Riemann Hypothesis and Its Extensions ldots Failed Attempts at Proof Formulas Timeline Original Papers Expert Witnesses The Experts Speak for Themselves

rawshortTOC:
To the Riemann Hypothesis \\ Why This Book \\ Analytic Preliminaries \\ Algorithms for Calculating ?(s) \\ Empirical Evidence \\ Equivalent Statements \\ Extensions of the Riemann Hypothesis \\ Assuming the Riemann Hypothesis and Its Extensions \ldots{} \\ Failed Attempts at Proof \\ Formulas \\ Timeline \\ Original Papers \\ Expert Witnesses \\ The Experts Speak for Themselves

rawTOC:
Part 1: Introduction to the Riemann hypothesis \\ 1: Why this book \\ 1.1: The Holy Grail \\ 1.2: Riemann's zeta and Liouville's lambda \\ 1.3: The prime number theorem \\ 2: Analytic preliminaries \\ 2.1: The Riemann zeta function \\ 2.2: Zero-free region \\ 2.3: Counting the zeros of [cedilla](s) \\ 2.4: Hardy's theorem \\ 3: Algorithms for calculating [cedilla](s) \\ 3.1: Euler--MacLaurin summation \\ 3.2: Backlund \\ 3.3: Hardy's function \\ 3.4: The Riemann--Siegel formula \\ 3.5: Gram's law \\ 3.6: Turing \\ 3.7: The Odlyzko--Sch{\"o}nhage algorithm \\ 3.8: A simple algorithm for the zeta function \\ 3.9: Further reading \\ 4: Empirical evidence \\ 4.1: Verification in an interval \\ 4.2: A brief history of computational evidence \\ 4.3: The Riemann hypothesis and random matrices \\ 4.4: The Skewes number \\ 5: Equivalent statements \\ 5.1: Number-theoretic equivalences \\ 5.2: Analytic equivalences \\ 5.3: Other equivalences \\ 6: Extensions of the Riemann hypothesis \\ 6.1: The Riemann hypothesis \\ 6.2: The generalized Riemann hypothesis \\ 6.3: The extended Riemann hypothesis \\ 6.4: An equivalent extended Riemann hypothesis \\ 6.5: Another extended Riemann hypothesis \\ 6.6: The Grand Riemann hypothesis \\ 7: Assuming the Riemann hypothesis and its extensions \\ 7.1: Another proof of the prime number theorem \\ 7.2: Goldbach's conjecture \\ 7.3: More Goldbach \\ 7.4: Primes in a given interval \\ 7.5: The least prime in arithmetic progressions \\ 7.6: Primality testing \\ 7.7: Artin's primitive root conjecture \\ 7.8: Bounds on Dirichlet $L$-series \\ 7.9: The Lindel{\"o}f hypothesis \\ 7.10: Titchmarsh's [delta](T) function \\ 7.11: Mean values of [cedilla](s)8: Failed attempts at proof \\ 8.1: Stieltjes and Mertens' conjecture \\ 8.2: Hans Rademacher and false hopes \\ 8.3: Tur{\'a}n's condition \\ 8.4: Louis de Branges's approach \\ 8.5: No really good idea \\ 9: Formulas \\ 10: Timeline \\ pt. 2: Original papers \\ 11: Expert witnesses \\ 11. 1: E. Bombieri (2000--2001) \\ 11.2: P. Sarnak (2004) \\ 11.3: J.B. Conrey (2003) \\ 11.4: A. Ivi{\'c} (2003) \\ 12: The experts speak for themselves \\ 12.1: P.L. Chebyshev (1852) \\ 12.2: B. Riemann (1859) \\ 12.3: J. Hadamard (1896) \\ 12.4: C. de la Vall{\'e}e Poussin (1899) \\ 12.5: G.H. Hardy (1914) \\ 12.6: G.H. Hardy (1915) \\ 12.7: G.H. Hardy and J.E. Littlewood (1915) \\ 12.8: A. Weil (1941) \\ 12.9: P. Tur{\'a}n (1948) \\ 12.10: A. Selberg (1949) \\ 12.11: P. Erdo$\cdot$s (1949) \\ 12.12: S. Skewes (1955) \\ 12.13: C.B. Haselgrove (1958) \\ 12.14: H. Montgomery (1973) \\ 12.15: D.J. Newman (1980) \\ 12.16: J. Korevaar (1982) \\ 12.17: H. Daboussi (1984) \\ 12.18: A. Hildebrand (1986) \\ 12.19: D. Goldston and H. Montgomery (1987) \\ 12.20: M. Agrawal, N. Kayal, and N. Saxena (2004) \\ References \\ References \\ Index

entry:
@Book{Borwein:2007:RHR,
  editor =       "Peter Borwein and Stephen Choi and Brendan Rooney and
                 Andrea Weirathmueller and others",
  title =        "The {Riemann Hypothesis}: a resource for the
                 afficionado and virtuoso alike",
  volume =       "27",
  publisher =    "Springer Science+Business Media, LLC",
  address =      "New York, NY, USA",
  pages =        "xiv + 533",
  year =         "2007",
  DOI =          "https://doi.org/10.1007/978-0-387-72126-2",
  ISBN =         "0-387-72125-8 (hardcover), 0-387-72126-6 (e-book)",
  ISBN-13 =      "978-0-387-72125-5 (hardcover), 978-0-387-72126-2
                 (e-book)",
  LCCN =         "QA246 .R53 2008",
  bibdate =      "Thu Sep 1 07:07:49 MDT 2022",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "CMS books in mathematics",
  URL =          "http://libanswers.liverpool.ac.uk/faq/182315",
  abstract =     "This book is an introduction to the theory surrounding
                 the Riemann Hypothesis. Part I serves as a compendium
                 of known results and as a primer for the material
                 presented in the 20 original papers contained in Part
                 II. The original papers place the material into
                 historical context and illustrate the motivations for
                 research on and around the Riemann Hypothesis. Several
                 of these papers focus on computation of the zeta
                 function, while others give proofs of the Prime Number
                 Theorem, since the Prime Number Theorem is so closely
                 connected to the Riemann Hypothesis. The text is
                 suitable for a graduate course or seminar or simply as
                 a reference for anyone interested in this extraordinary
                 conjecture.",
  acknowledgement = ack-nhfb,
  shorttableofcontents = "To the Riemann Hypothesis \\
                 Why This Book \\
                 Analytic Preliminaries \\
                 Algorithms for Calculating ?(s) \\
                 Empirical Evidence \\
                 Equivalent Statements \\
                 Extensions of the Riemann Hypothesis \\
                 Assuming the Riemann Hypothesis and Its Extensions
                 \ldots{} \\
                 Failed Attempts at Proof \\
                 Formulas \\
                 Timeline \\
                 Original Papers \\
                 Expert Witnesses \\
                 The Experts Speak for Themselves",
  subject =      "Mathematics; History; Number theory;
                 Math{\'e}matiques; Histoire; Th{\'e}orie des nombres;
                 Mathematics.; Number theory.",
  tableofcontents = "Part 1: Introduction to the Riemann hypothesis \\
                 1: Why this book \\
                 1.1: The Holy Grail \\
                 1.2: Riemann's zeta and Liouville's lambda \\
                 1.3: The prime number theorem \\
                 2: Analytic preliminaries \\
                 2.1: The Riemann zeta function \\
                 2.2: Zero-free region \\
                 2.3: Counting the zeros of [cedilla](s) \\
                 2.4: Hardy's theorem \\
                 3: Algorithms for calculating [cedilla](s) \\
                 3.1: Euler--MacLaurin summation \\
                 3.2: Backlund \\
                 3.3: Hardy's function \\
                 3.4: The Riemann--Siegel formula \\
                 3.5: Gram's law \\
                 3.6: Turing \\
                 3.7: The Odlyzko--Sch{\"o}nhage algorithm \\
                 3.8: A simple algorithm for the zeta function \\
                 3.9: Further reading \\
                 4: Empirical evidence \\
                 4.1: Verification in an interval \\
                 4.2: A brief history of computational evidence \\
                 4.3: The Riemann hypothesis and random matrices \\
                 4.4: The Skewes number \\
                 5: Equivalent statements \\
                 5.1: Number-theoretic equivalences \\
                 5.2: Analytic equivalences \\
                 5.3: Other equivalences \\
                 6: Extensions of the Riemann hypothesis \\
                 6.1: The Riemann hypothesis \\
                 6.2: The generalized Riemann hypothesis \\
                 6.3: The extended Riemann hypothesis \\
                 6.4: An equivalent extended Riemann hypothesis \\
                 6.5: Another extended Riemann hypothesis \\
                 6.6: The Grand Riemann hypothesis \\
                 7: Assuming the Riemann hypothesis and its extensions
                 \\
                 7.1: Another proof of the prime number theorem \\
                 7.2: Goldbach's conjecture \\
                 7.3: More Goldbach \\
                 7.4: Primes in a given interval \\
                 7.5: The least prime in arithmetic progressions \\
                 7.6: Primality testing \\
                 7.7: Artin's primitive root conjecture \\
                 7.8: Bounds on Dirichlet $L$-series \\
                 7.9: The Lindel{\"o}f hypothesis \\
                 7.10: Titchmarsh's [delta](T) function \\
                 7.11: Mean values of [cedilla](s)8: Failed attempts at
                 proof \\
                 8.1: Stieltjes and Mertens' conjecture \\
                 8.2: Hans Rademacher and false hopes \\
                 8.3: Tur{\'a}n's condition \\
                 8.4: Louis de Branges's approach \\
                 8.5: No really good idea \\
                 9: Formulas \\
                 10: Timeline \\
                 pt. 2: Original papers \\
                 11: Expert witnesses \\
                 11. 1: E. Bombieri (2000--2001) \\
                 11.2: P. Sarnak (2004) \\
                 11.3: J.B. Conrey (2003) \\
                 11.4: A. Ivi{\'c} (2003) \\
                 12: The experts speak for themselves \\
                 12.1: P.L. Chebyshev (1852) \\
                 12.2: B. Riemann (1859) \\
                 12.3: J. Hadamard (1896) \\
                 12.4: C. de la Vall{\'e}e Poussin (1899) \\
                 12.5: G.H. Hardy (1914) \\
                 12.6: G.H. Hardy (1915) \\
                 12.7: G.H. Hardy and J.E. Littlewood (1915) \\
                 12.8: A. Weil (1941) \\
                 12.9: P. Tur{\'a}n (1948) \\
                 12.10: A. Selberg (1949) \\
                 12.11: P. Erdo$\cdot$s (1949) \\
                 12.12: S. Skewes (1955) \\
                 12.13: C.B. Haselgrove (1958) \\
                 12.14: H. Montgomery (1973) \\
                 12.15: D.J. Newman (1980) \\
                 12.16: J. Korevaar (1982) \\
                 12.17: H. Daboussi (1984) \\
                 12.18: A. Hildebrand (1986) \\
                 12.19: D. Goldston and H. Montgomery (1987) \\
                 12.20: M. Agrawal, N. Kayal, and N. Saxena (2004) \\
                 References \\
                 References \\
                 Index",
}


