Computing Integer Powers in Floating-Point Arithmetic
This work provides practical algorithms for accurate power computation, benefiting numerical computing applications that require reliable floating-point results.
The paper introduces two algorithms for computing integer powers in floating-point arithmetic with a fused multiply-add instruction, achieving faithfully-rounded results in log time and correctly rounded results when extended precision is available.
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).