A Multiplier-less Algorithm for Evaluating Intrinsic and Nonlinear Functions

This paper addresses the problem of efficiently approximating a function for systems-on-a-chip and other FPGA applications, hi these systems, high speed, minimal chip size, and efficient computation are necessary. Examples of common functions requiring computation include trigonometric functions and other nonlinear functions such as computing temperature using a thermistor. A generic method for determining the approximating function is based on a genetic algorithm (GA) and was published in [1]. hi general, the GA discovers a set of 3rd degree polynomials in a piecewise fashion to fit a set of training data points offline. The specific runtime algorithm implementation used to evaluate the set of 3rd degree polynomials is directly dependent on the hardware available and the tradeoffs are discussed. Specifically, we present an efficient multiplier-less method of evaluating the 3rd degree polynomials based on logarithms targeted for FPGA applications.