Self-contained exponentiation

Abstract

The traditional implementation for floating-point exponentiation, x raised to the y power, is to compute exp (y ln(x)) using standard subroutines for the logarithm and the exponential function. While it is possible to provide extremely accurate subroutines for these latter functions, we shall shortly see that this is seldom done. Even in those rare cases where excellent subroutines are available, the exponentiation routine, for sound theoretical reasons, is poor. In this paper, we present brief statistics indicative of the quality of these three subroutines in the basic Fortran libraries provided by various manufacturers, a detailed error analysis for exponentiation, and a method for exponentiation via self-contained subroutines.