Correctly rounded multiplication by arbitrary precision constants
Résumé
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.
Domaines
Autre [cs.OH]
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