# Correctly rounded multiplication by arbitrary precision constants

2 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 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.
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Conference papers
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Cited literature [10 references]

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

### Citation

Jean-Michel Muller, Nicolas Brisebarre. Correctly rounded multiplication by arbitrary precision constants. ARITH'17, 17th IEEE Symposium on Computer Arithmetic, EEE Computer Society Technical Committee on VLSI, Jun 2005, Cape Cod, United States. ⟨10.1109/ARITH.2005.13⟩. ⟨ensl-00000010⟩

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