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Published Articles >> Table of Contents >> Abstract
17th IEEE Symposium on Computer Arithmetic (ARITH'05)
pp. 257-264
Gal's Accurate Tables Method Revisited
Damien Stehlé, UHP/LORIA
Paul Zimmermann, INRIA Lorraine/LORIA
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DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/ARITH.2005.24
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| Abstract |
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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 2^x and sin x for x ∊ [½, 1], in double precision.
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 Additional Information
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Citation:
Damien Stehlé, Paul Zimmermann,
"Gal's Accurate Tables Method Revisited,"
arith,
pp. 257-264,
17th IEEE Symposium on Computer Arithmetic (ARITH'05),
2005
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