Fast and correctly rounded logarithms in double precision

Jean-Michel Muller 1, 2 Florent De Dinechin 1, 2 Christoph Lauter 1, 2
1 LIP - Laboratoire de l'Informatique du Parallélisme
2 ARENAIRE - Computer arithmetic
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : This article is a case study in the implementation of a portable, proven and efficient correctly rounded elementary function in double-precision. We describe the methodology used to achieve these goals in the crlibm library. There are two novel aspects to this approach. The first is the proof framework, and in general the techniques used to balance performance and provability. The second is the introduction of processor-specific optimization to get performance equivalent to the best current mathematical libraries, while trying to minimize the proof work. The implementation of the natural logarithm is detailed to illustrate these questions.
Keywords : Floating-point Elementary functions Logarithm Correct rounding
Type de document :
Article dans une revue
RAIRO - Theoretical Informatics and Applications (RAIRO: ITA), EDP Sciences, 2007, 41 (1), pp.85-102. 〈10.1051/ita:2007003〉
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Contributeur : Jean-Michel Muller <>
Soumis le : mardi 24 avril 2007 - 16:52:17
Dernière modification le : vendredi 20 avril 2018 - 15:44:24
Document(s) archivé(s) le : mardi 21 septembre 2010 - 13:27:02

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Jean-Michel Muller, Florent De Dinechin, Christoph Lauter. Fast and correctly rounded logarithms in double precision. RAIRO - Theoretical Informatics and Applications (RAIRO: ITA), EDP Sciences, 2007, 41 (1), pp.85-102. 〈10.1051/ita:2007003〉. 〈ensl-00000007v2〉

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