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Fast and correctly rounded logarithms in double-precision

Florent de Dinechin 1 Christoph Lauter Jean-Michel Muller
1 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 optimizations 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.
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Contributor : Rapport de Recherche Inria <>
Submitted on : Friday, May 19, 2006 - 8:08:32 PM
Last modification on : Thursday, November 21, 2019 - 2:31:50 AM


  • HAL Id : inria-00070331, version 1



Florent de Dinechin, Christoph Lauter, Jean-Michel Muller. Fast and correctly rounded logarithms in double-precision. [Research Report] RR-5682, LIP RR-2005-37, INRIA, LIP. 2005, pp.15. ⟨inria-00070331⟩



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