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Gal's Accurate Tables Method Revisited

Damien Stehlé 1 Paul Zimmermann 1 
1 SPACES - Solving problems through algebraic computation and efficient software
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : Gal's accurate tables algorithm aims at providing an ef- ficient 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 ef- ficiency 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 2 [ 1 2 , 1[, in double precision.
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Submitted on : Thursday, September 29, 2005 - 5:50:50 PM
Last modification on : Friday, February 4, 2022 - 3:31:47 AM

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Damien Stehlé, Paul Zimmermann. Gal's Accurate Tables Method Revisited. 17th IEEE Symposium on Computer Arithmetic - ARITH'17, 2005, Cape Cod/USA, pp.236-257, ⟨10.1109/ARITH.2005.24⟩. ⟨inria-00000378⟩



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