Gal's accurate tables method revisited

Damien Stehlé; Paul Zimmermann

doi:10.1109/ARITH.2005.24

Gal's accurate tables method revisited

Damien Stehlé, Paul Zimmermann

School of Computing

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

3 Citations (Scopus)

Abstract

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 language	English
Title of host publication	Proceedings
Subtitle of host publication	17th IEEE Symposium on Computer Arithmetic, ARITH-17 2005, 27-29 June 2005, Cape Cod, Massachusetts, USA
Editors	Paolo Montuschi, Eric Schwarz
Place of Publication	Los Alamitos, Calif.
Publisher	Institute of Electrical and Electronics Engineers (IEEE)
Pages	257-264
Number of pages	8
ISBN (Print)	0769523668
DOIs	https://doi.org/10.1109/ARITH.2005.24
Publication status	Published - 2005
Event	Symposium on Computer Arithmetic (17th : 2005) - Cape Cod, USA Duration: 27 Jun 2005 → 29 Jun 2005

Conference

Conference	Symposium on Computer Arithmetic (17th : 2005)
City	Cape Cod, USA
Period	27/06/05 → 29/06/05

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10.1109/ARITH.2005.24

Cite this

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title = "Gal's accurate tables method revisited",

abstract = "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.",

author = "Damien Stehl{\'e} and Paul Zimmermann",

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editor = "Paolo Montuschi and Eric Schwarz",

booktitle = "Proceedings",

publisher = "Institute of Electrical and Electronics Engineers (IEEE)",

address = "United States",

note = "Symposium on Computer Arithmetic (17th : 2005) ; Conference date: 27-06-2005 Through 29-06-2005",

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Stehlé, D & Zimmermann, P 2005, Gal's accurate tables method revisited. in P Montuschi & E Schwarz (eds), Proceedings: 17th IEEE Symposium on Computer Arithmetic, ARITH-17 2005, 27-29 June 2005, Cape Cod, Massachusetts, USA. Institute of Electrical and Electronics Engineers (IEEE), Los Alamitos, Calif., pp. 257-264, Symposium on Computer Arithmetic (17th : 2005), Cape Cod, USA, 27/06/05. https://doi.org/10.1109/ARITH.2005.24

Gal's accurate tables method revisited. / Stehlé, Damien; Zimmermann, Paul.
Proceedings: 17th IEEE Symposium on Computer Arithmetic, ARITH-17 2005, 27-29 June 2005, Cape Cod, Massachusetts, USA. ed. / Paolo Montuschi; Eric Schwarz. Los Alamitos, Calif.: Institute of Electrical and Electronics Engineers (IEEE), 2005. p. 257-264.

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

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Gal's accurate tables method revisited

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