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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.

Keywords : FLOATING-POINT ARITHMETIC FUSED-MAC MULTIPLICATION BY A CONSTANT CORRECT ROUNDING COMPUTER ARITHMETIC





Author: Nicolas Brisebarre - Jean-Michel Muller -

Source: https://hal.archives-ouvertes.fr/



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