Computing correctly rounded integer powers in floating-point arithmetic

Abstract

We introduce several algorithms for accurately evaluating powers to a positive integer in floating-point arithmetic, assuming a <i>fused multiply-add</i> (fma) instruction is available. For bounded, yet very large values of the exponent, we aim at obtaining correctly rounded results in round-to-nearest mode, that is, our algorithms return the floating-point number that is nearest the exact value.

DOI: 10.1145/1644001.1644005

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@article{Kornerup2010ComputingCR, title={Computing correctly rounded integer powers in floating-point arithmetic}, author={Peter Kornerup and Christoph Quirin Lauter and Vincent Lef{\`e}vre and Nicolas Louvet and Jean-Michel Muller}, journal={ACM Trans. Math. Softw.}, year={2010}, volume={37}, pages={4:1-4:23} }