Gal's accurate tables method revisited

Damien Stehlé, Paul Zimmermann

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contribution

3 Citations (Scopus)


Gal's accurate tables algorithm aims at providing an efficient implementation of mathematical functions with correct rounding as often as possible. This method requires an expensive pre-computation of the values taken by the function - or by several related functions - at some distinguished points. Our improvements of Gal's method are two-fold: on the one hand we describe what is the arguably best set of distinguished values and how it improves the efficiency and accuracy of the function implementation, and on the other hand we give an algorithm which drastically decreases the cost of the pre-computation. These improvements are related to the worst cases for the correct rounding of mathematical functions and to the algorithms for finding them. We demonstrate how the whole method can be turned into practice for 2x and sin x for x∈[1/2,1[, in double precision.
Original languageEnglish
Title of host publicationProceedings
Subtitle of host publication17th IEEE Symposium on Computer Arithmetic, ARITH-17 2005, 27-29 June 2005, Cape Cod, Massachusetts, USA
EditorsPaolo Montuschi, Eric Schwarz
Place of PublicationLos Alamitos, Calif.
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Number of pages8
ISBN (Print)0769523668
Publication statusPublished - 2005
EventSymposium on Computer Arithmetic (17th : 2005) - Cape Cod, USA
Duration: 27 Jun 200529 Jun 2005


ConferenceSymposium on Computer Arithmetic (17th : 2005)
CityCape Cod, USA

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