Approximating xⁿ efficiently

Abstract

A fast technique to evaluate xn to an accuracy of one part in N for 0.0 ≤ x ≤ 1.0 is discussed. Such approximations are useful in several scientific applications. The main features of the technique are as follows: Novelty: The fundamental and distinguishing contribution of our technique is the drastic reduction in the size of look-up tables used in the evaluation without a commensurate loss in performance or accuracy. Generality: The technique presented herein can be used in both hardware and software products depending on the performance requirements and amount of silicon available. The technique is illustrated more elaborately by discussing its use for computing light intensities in graphics modeling. © 1994.