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

Lefèvre, Vincent; Stehlé, Damien; Zimmermann, Paul

doi:10.4230/DagSemProc.06021.11

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

Authors Vincent Lefèvre, Damien Stehlé, Paul Zimmermann

Part of: Volume: Dagstuhl Seminar Proceedings, Volume 6021
Part of: Series: Dagstuhl Seminar Proceedings (DagSemProc)
License: Creative Commons Attribution 4.0 International license
Publication Date: 2006-09-13

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Document Identifiers

DOI: 10.4230/DagSemProc.06021.11
URN: urn:nbn:de:0030-drops-7483

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Keywords

Floating-point arithmetic
decimal arithmetic
table maker's dilemma
correct rounding
elementary functions

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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.

Cite As Get BibTex

Vincent Lefèvre, Damien Stehlé, and Paul Zimmermann. Worst Cases for the Exponential Function in the IEEE 754r decimal64 Format. In Reliable Implementation of Real Number Algorithms: Theory and Practice. Dagstuhl Seminar Proceedings, Volume 6021, pp. 1-10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006) https://doi.org/10.4230/DagSemProc.06021.11

Author Details

Vincent Lefèvre

Damien Stehlé

Paul Zimmermann

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