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Worst Cases for the Exponential Function in the IEEE 754r decimal64 Format Lefèvre, Vincent Stehlé, Damien Zimmermann, Paul Floating-point arithmetic decimal arithmetic table maker's dilemma correct rounding elementary functions 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Vincent Lefèvre and Damien Stehlé and Paul Zimmermann 2006 Is Part Of Dagstuhl Seminar Proceedings, Volume 6021, Reliable Implementation of Real Number Algorithms: Theory and Practice (2006) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/DagSemProc.06021.11 urn:nbn:de:0030-drops-7483 https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.06021.11 eng https://creativecommons.org/licenses/by/4.0/legalcode