Fast and correctly rounded logarithms in double precision

Jean-Michel Muller; Florent de Dinechin; Christoph Lauter

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

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

Document type :

Journal articles

Domain :

Computer Science [cs] / Other [cs.OH]

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https://hal-ens-lyon.archives-ouvertes.fr/ensl-00000007
Contributor : Jean-Michel Muller <>
Submitted on : Tuesday, April 24, 2007 - 4:52:17 PM
Last modification on : Thursday, February 7, 2019 - 5:24:18 PM
Long-term archiving on : Tuesday, September 21, 2010 - 1:27:02 PM

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Fast and correctly rounded logarithms in double precision

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Fast and correctly rounded logarithms in double precision

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