Divide and Conquer: Floating-Point Exponential Calculation Based on Taylor-Series Expansion

Abstract

This paper presents an algorithm to compute the exponential exp(x) floating-point tails based on Taylor- series expansion with mantissa region division. exp(x) is expanded in different regions with corresponding central values using Taylor-series and the best result is selected from among the different convergence ranges obtained. We show the cases of x>0 as well as x<0, and then show the tradeoff among LUT size and the required numbers of additions, subtractions and multiplications, and also computing accuracy of exp(x) by Taylor expansion through simulation results. The designer can choose the best algorithm to build a reasonable hardware system by the method described in this paper.