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Computing Correctly Rounded Integer Powers in Floating-Point Arithmetic

Peter Kornerup 1 Christoph Lauter 2 Vincent Lefèvre 2 Nicolas Louvet 2 Jean-Michel Muller 2
1 IMADA - Department of Mathematics and Computer Science [Odense]
2 ARENAIRE - Computer arithmetic
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : We introduce several algorithms for accurately evaluating powers to a positive integer in floating-point arithmetic, assuming a fused multiply-add (fma) instruction is available. For bounded, yet very large values of the exponent, we aim at obtaining correctly-rounded results in round-to-nearest mode, that is, our algorithms return the floating-point number that is nearest the exact value.
Keywords : correct rounding floating-point arithmetic integer power function
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https://hal.inria.fr/inria-00388501
Contributor : Vincent Lefèvre Connect in order to contact the contributor
Submitted on : Tuesday, May 26, 2009 - 6:03:21 PM
Last modification on : Friday, February 4, 2022 - 3:19:08 AM

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CNRS | INRIA | ENS-LYON | UNIV-LYON1 | UDL | ANR | INRIA2

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Peter Kornerup, Christoph Lauter, Vincent Lefèvre, Nicolas Louvet, Jean-Michel Muller. Computing Correctly Rounded Integer Powers in Floating-Point Arithmetic. ACM Transactions on Mathematical Software, Association for Computing Machinery, 2010, 37 (1), pp.4:1-4:23. ⟨10.1145/1644001.1644005⟩. ⟨inria-00388501⟩

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