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Correct rounding of algebraic functions

Published online by Cambridge University Press:  24 April 2007

Nicolas Brisebarre  and
Jean-Michel Muller
Nicolas Brisebarre
Affiliation:
Laboratoire LIP (CNRS/ENS Lyon/INRIA/Univ. Lyon 1), Projet Arénaire, 46 allée d'Italie, 69364 Lyon Cedex 07, France; Nicolas.Brisebarre@ens-lyon.fr; Jean-Michel.Muller@ens-lyon.fr Laboratoire LaMUSE, Université J. Monnet (Saint-Étienne), 23, rue du Dr P. Michelon, 42023 Saint-Étienne Cedex 02, France.
Jean-Michel Muller
Affiliation:
Laboratoire LIP (CNRS/ENS Lyon/INRIA/Univ. Lyon 1), Projet Arénaire, 46 allée d'Italie, 69364 Lyon Cedex 07, France; Nicolas.Brisebarre@ens-lyon.fr; Jean-Michel.Muller@ens-lyon.fr
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Abstract

We explicit the link between the computer arithmeticproblem ofproviding correctly rounded algebraic functions and somediophantine approximation issues. This allows to get bounds on the accuracy with which intermediate calculations must be performed to correctly round these functions.

Keywords

Floating-point arithmeticcomputer arithmeticalgebraic functionscorrect roundingdiophantine approximation.

Information

Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 41 , Issue 1: Real Numbers , January 2007 , pp. 71 - 83
Copyright
© EDP Sciences, 2007

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