Computing Integer Powers in Floating-Point Arithmetic

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).