A correctly rounded implementationof the exponential function on the Intel Itanium architecture

Christoph Quirin Lauter 1
1 ARENAIRE - Computer arithmetic
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : This article presents an efficient implementation of a correctly rounded exponential function in double precision on the Intel Itanium processor family. This work combines advanced processor features (like the double-extended precision fused multiply-and-add units of the Itanium processors) with recent research results giving the worst-case precision needed for correctly rounding the exponential function. We give and prove an algorithm which returns a correctly rounded result (in any of the four IEEE-754 rounding modes) within 172 machine cycles on the 2 processor. This is about four times slower than the less accurate function present in the standard Intel mathematical library. The evaluation is performed in one phase only and is therefore fast even in the worst case, contrary to other implementations which use a multilevel strategy: We show that the worst-case required precision of 157 bits can always be stored in the sum of two double-extended floating-point numbers. Another algorithm is given with a 92 cycles execution time, but its proof has to be formally completed.
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https://hal.inria.fr/inria-00071560
Contributor : Rapport de Recherche Inria <>
Submitted on : Tuesday, May 23, 2006 - 5:57:13 PM
Last modification on : Monday, April 29, 2019 - 11:04:39 AM

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  • HAL Id : inria-00071560, version 1

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Christoph Quirin Lauter. A correctly rounded implementationof the exponential function on the Intel Itanium architecture. [Research Report] RR-5024, LIP RR 2003-54, INRIA, LIP. 2003. ⟨inria-00071560⟩

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