Correctly rounded multiplication by arbitrary precision constants

Jean-Michel Muller; Nicolas Brisebarre

Correctly rounded multiplication by arbitrary precision constants

Jean-Michel Muller ^{1, 2} Nicolas Brisebarre ^{2, 3}

1 LIP - Laboratoire de l'Informatique du Parallélisme

2 ARENAIRE - Computer arithmetic

Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme

3 LArAl - Laboratoire d'Arithmétique et d'Algèbre

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 and add 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 it does not.

Keywords : computer arithmetic floating-point arithmetic multiplication fused multiply-add

Document type :

Conference papers

Domain :

Computer Science [cs] / Other [cs.OH]

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https://hal-ens-lyon.archives-ouvertes.fr/ensl-00000010
Contributor : Jean-Michel Muller <>
Submitted on : Thursday, April 13, 2006 - 10:43:28 AM
Last modification on : Thursday, February 7, 2019 - 3:25:49 PM
Long-term archiving on : Saturday, April 3, 2010 - 10:17:10 PM

Correctly rounded multiplication by arbitrary precision constants

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Correctly rounded multiplication by arbitrary precision constants

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