Computing Integer Powers in Floating-Point Arithmetic

Details Computing Integer Powers in Floating-Point Arithmetic Computing Integer Powers in Floating-Point Arithmetic

2007-05-30

arxiv.org/abs/0705.4369v1

Computer Science

Numerical Analysis

Laboratoire LIP : CNRS/ENS Lyon/INRIA/Universit\'e Lyon 1

Scientific paper

We introduce two algorithms for accurately evaluating powers to a positive integer in floating-point arithmetic, assuming a fused multiply-add (fma) instruction is available. We show that our log-time algorithm always produce faithfully-rounded results, discuss the possibility of getting correctly rounded results, and show that results correctly rounded in double precision can be obtained if extended-precision is available with the possibility to round into double precision (with a single rounding).

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