Computing Integer Powers in Floating-Point Arithmetic

Peter Kornerup (1) , Vincent Lefèvre (2) , Jean-Michel Muller (2)

1 IMADA - Department of Mathematics and Computer Science [Odense]
2 LIP - Laboratoire de l'Informatique du Parallélisme

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).

Mots clés: Floating-point arithmetic; Integer powers; Computer arithmetic; Correct rounding

Domaines: Analyse numérique [cs.NA]; Autre [cs.OH]

Peter Kornerup, Vincent Lefèvre, Jean-Michel Muller. Computing Integer Powers in Floating-Point Arithmetic. 2007. ⟨ensl-00150406⟩