Towards the post-ultimate libm

Florent de Dinechin 1 Nicolas Gast 1
1 ARENAIRE - Computer arithmetic
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : This article presents advances in the subject of double-precision correctly rounded elementary functions since the publication of the libultim mathematical library developed by Ziv at IBM. This library demonstrated that the performance overhead of correct rounding could be made negligible in average. However, the worst case execution time was up to 1000 times the average time, and memory consumption was also a problem. To address these questions, a range of new techniques, from the more portable to the more efficient, are presented, and demonstrated on two typical functions, exponential and arctangent. The main result of this paper is to show that the worst-case execution time can be bounded within a factor of 2 to 10 of the average time, with memory consumption comparable to current libms. This has in turn implications on the techniques and tradeoffs for correctly rounded functions. This article also shows that these techniques make it much easier to prove the correct rounding property. Thus, this article lifts the last technical obstacles to a widespread use of (at least some) correctly rounded double precision elementary functions.
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https://hal.inria.fr/inria-00070636
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Submitted on : Friday, May 19, 2006 - 9:05:30 PM
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Florent de Dinechin, Nicolas Gast. Towards the post-ultimate libm. [Research Report] RR-5367, LIP RR 2004-47, INRIA, LIP. 2004, pp.18. ⟨inria-00070636⟩

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