Multiplierless Piecewise Linear Approximation of Elementary Functions

In this work a multiplierless architecture for piecewise linear approximation of elementary functions is discussed. By limiting the slope coefficient to a given number of signed-power-of-two (SPT) terms the general multiplier can be replaced by configurable shifts and a multi-input adder. The considered architecture was proposed in an earlier work for use in direct digital frequency synthesizers (DDFS). We extend it to arbitrary functions and propose some techniques to reduce the complexity.

I. Introduction

Computation of various functions, for example, trigonometric, logarithm, exponential, and square root, are commonly used in, e.g., digital signal and video processing systems [1]. Another usage is the functions used to implement addition and subtraction in logarithmic number systems [2]. Implementation of neural networks also requires evaluation of elementary functions, such as the sigmoid function [3].