DagSemProc.06021.11.pdf
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Worst Cases for the Exponential Function in the IEEE 754r decimal64 Format
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Dagstuhl Seminar Proceedings, Volume 6021
Series: Dagstuhl Seminar Proceedings (DagSemProc) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2006-09-13
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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
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.
Subject Classification
Keywords
- Floating-point arithmetic
- decimal arithmetic
- table maker's dilemma
- correct rounding
- elementary functions
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