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

Vincent Lefèvre 1 Damien Stehlé 1 Paul Zimmermann 2
1 ARENAIRE - Computer arithmetic
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
2 CACAO - Curves, Algebra, Computer Arithmetic, and so On
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : We show how one can search for the worst cases for correct rounding of the exponential function in the IEEE 754r 64-bit decimal format, and give such bad cases that have been found so far. 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.
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Contributor : Vincent Lefèvre <>
Submitted on : Wednesday, September 3, 2008 - 1:07:06 PM
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Vincent Lefèvre, Damien Stehlé, Paul Zimmermann. Worst Cases for the Exponential Function in the IEEE 754r decimal64 Format. P. Hertling; C.M. Hoffmann; W. Luther; N. Revol. Reliable Implementation of Real Number Algorithms: Theory and Practice, 5045, Springer, pp.114-126, 2008, Lecture Notes in Computer Science, 978-3-540-85521-7. ⟨10.1007/978-3-540-85521-7_7⟩. ⟨http://www.dagstuhl.de/06021⟩. ⟨inria-00068731v2⟩

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