Worst cases for the exponential function in the IEEE 754r decimal64 format

Vincent Lefevre, Damien Stehlé, Paul Zimmermann

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contribution

5 Citations (Scopus)

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| ≥ 3 × 10⁻¹¹ is exp(9.407822313572878 × 10⁻²) = 1.098645682066338 5 0000000000000000 278 . . .. 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.
Original languageEnglish
Title of host publicationReliable implementation of real number algorithms
Subtitle of host publicationtheory and practice
EditorsPeter Hertling, Christoph M. Hoffmann, Wolfram Luther, Nathalie Revol
Place of PublicationBerlin/Heidelberg, Germany
PublisherSpringer, Springer Nature
Pages114-126
Number of pages13
ISBN (Print)9783540855200
DOIs
Publication statusPublished - 2008
EventInternational seminar on reliable implementation of real number algorithms : theory and practice - Germany
Duration: 8 Jan 200613 Jan 2006

Publication series

NameLecture notes in computer science
PublisherSpringer
Volume5045

Seminar

SeminarInternational seminar on reliable implementation of real number algorithms : theory and practice
CityGermany
Period8/01/0613/01/06

Fingerprint Dive into the research topics of 'Worst cases for the exponential function in the IEEE 754r decimal64 format'. Together they form a unique fingerprint.

  • Cite this

    Lefevre, V., Stehlé, D., & Zimmermann, P. (2008). Worst cases for the exponential function in the IEEE 754r decimal64 format. In P. Hertling, C. M. Hoffmann, W. Luther, & N. Revol (Eds.), Reliable implementation of real number algorithms: theory and practice (pp. 114-126). (Lecture notes in computer science; Vol. 5045). Berlin/Heidelberg, Germany: Springer, Springer Nature. https://doi.org/10.1007/978-3-540-85521-7_7