Correctly rounded multiplication by arbitrary precision constants

Nicolas Brisebarre 1 Jean-Michel Muller 1
1 ARENAIRE - Computer arithmetic
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : We introduce an algorithm for multiplying a floating-point number $x$ by a constant $C$ that is not exactly representable in floating-point arithmetic. Our algorithm uses a multiplication and a fused multiply accumulate instruction. We give methods for checking whether, for a given value of $C$ and a given floating-point format, our algorithm returns a correctly rounded result for any $x$. When it does not, our methods give the values $x$ for which the multiplication is not correctly rounded.
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https://hal.inria.fr/inria-00070649
Contributor : Rapport de Recherche Inria <>
Submitted on : Friday, May 19, 2006 - 9:06:52 PM
Last modification on : Tuesday, April 30, 2019 - 9:19:23 AM

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  • HAL Id : inria-00070649, version 1

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Nicolas Brisebarre, Jean-Michel Muller. Correctly rounded multiplication by arbitrary precision constants. [Research Report] RR-5354, LIP RR-2004-44, INRIA, LIP. 2004, pp.14. ⟨inria-00070649⟩

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