Correctly rounded multiplication by arbitrary precision constants

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
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Submitted on : Friday, May 19, 2006 - 9:06:52 PM
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• HAL Id : inria-00070649, version 1

Citation

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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