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Author Dinechin, Florent De ♦ Defour, David ♦ Lauter, Christoph
Source Hyper Articles en Ligne (HAL)
Content type Text
File Format PDF
Language English
Subject Keyword ELEMENTARY FUNCTIONS ♦ CORRECT ROUNDING ♦ IEEE-754 ♦ DOUBLE-EXTENDED PRECISION ♦ FONCTIONS ELEMENTAIRES ♦ ARRONDI CORRECT ♦ PRECISION DOUBLE ETENDUE ♦ info ♦ Computer Science [cs]/Other [cs.OH]
Abstract This article shows that IEEE-754 double-precision correct rounding of the most common elementary functions (exp/log, trigonometric and hyperbolic) is achievable on current processors using only double-double-extended arithmetic. This allows to improve by several orders of magnitude the worst case performance of a correctly-rounded mathematical library, compared to the current state of the art. This article builds up on previous work by Lefèvre and Muller, who have shown that an intermediate accuracy of up to 158 bits is required for the evaluation of some functions. We show that the practical accuracy required can always be reduced to less than 119 bits, which is easy to obtain using well-known and well-proven techniques of double-double-extended arithmetic. As an example, a prototype implementation of the exponential function on the Itanium has a worst-case time about twice that of the standard, highly optimized libm by Intel, which doesn't offer correct rounding. Such a small performance penalty should allow correct rounding of elementary functions to become the standard.
Educational Use Research
Learning Resource Type Report ♦ Article
Publisher Date 2004-01-01
Publisher Institution INRIA, LIP