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URN: urn:nbn:de:0030-drops-7483
URL: http://drops.dagstuhl.de/opus/volltexte/2006/748/
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Lefèvre, Vincent ; Stehlé, Damien ; Zimmermann, Paul

Worst Cases for the Exponential Function in the IEEE 754r decimal64 Format

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Abstract

We searched for the worst cases for correct rounding of the exponential function in the IEEE 754r decimal64 format, and computed all the bad cases whose distance from a breakpoint (for all rounding modes) is less than $10^{-15}$,ulp, and we give the worst ones. In particular, the worst case for $|x| geq 3 imes 10^{-11}$ is $exp(9.407822313572878 imes 10^{-2}) = 1.098645682066338,5,0000000000000000,278ldots$. This work can be extended to other elementary functions in the decimal64 format and allows the design of reasonably fast routines that will evaluate these functions with correct rounding, at least in some domains.

BibTeX - Entry

@InProceedings{lefvre_et_al:DSP:2006:748,
  author =	{Vincent Lef{\`e}vre and Damien Stehl{\'e} and Paul Zimmermann},
  title =	{Worst Cases for the Exponential Function in the IEEE 754r decimal64 Format},
  booktitle =	{Reliable Implementation of Real Number Algorithms: Theory and Practice},
  year =	{2006},
  editor =	{Peter Hertling and Christoph M. Hoffmann and Wolfram Luther and Nathalie Revol},
  number =	{06021},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Internationales Begegnungs- und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2006/748},
  annote =	{Keywords: Floating-point arithmetic, decimal arithmetic, table maker's dilemma, correct rounding, elementary functions}
}

Keywords: Floating-point arithmetic, decimal arithmetic, table maker's dilemma, correct rounding, elementary functions
Seminar: 06021 - Reliable Implementation of Real Number Algorithms: Theory and Practice
Issue Date: 2006
Date of publication: 13.09.2006


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