Computing Integer Powers in Floating-Point Arithmetic

TL;DR

This paper presents two algorithms for accurately computing integer powers in floating-point arithmetic, leveraging fused multiply-add instructions to achieve faithful or correct rounding, especially in double precision.

Contribution

It introduces two novel algorithms for integer power computation that ensure faithful or correct rounding in floating-point arithmetic, assuming availability of fused multiply-add instructions.

Findings

Log-time algorithm always produces faithfully-rounded results.

Discussion on achieving correctly rounded results.

Correctly rounded results in double precision are possible with extended precision.

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).