Computing Integer Powers in Floating-Point Arithmetic

2007/05/30 by Kornerup, Peter, Lefèvre, Vincent, Muller, Jean-Michel
#FOS: Computer and information sciences #FOS: Mathematics #Mathematical Software (cs.MS) #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.0705.4369

Abstract

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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