A Universal Method of Linear Approximation With Controllable Error for the Efficient Implementation of Transcendental Functions

Abstract

Transcendental functions are commonly used in many fields such as nonlinear functions of artificial neural networks (ANNs). Due to nonlinearity of these functions, hardware implementation of the functions faces many challenges. Some methods cannot control the approximation accuracy beforehand, or they cannot approximate target functions accurately and efficiently. Other methods can only approximate a particular function without generality. A universal piecewise linear (PWL) approximation method is proposed to solve the problems existing in the above methods. In this paper, a general piecewise linear (PWL) approximation method with controllable maximum absolute error for transcend-ental functions is proposed. The method has the self-adaptive capability to choose the smallest number of segments under the constraint of a controllable maximum absolute error. Therefore, it requires fewer segments and incurs less hardware overhead. Moreover, it can approximate any transcendental functions and does not rely on any properties of the target function. Comparing our work with other methods used in three transcendental functions, including the sigmoid, hyperbolic tangent, and logarithmic function, our method improves the approximation accuracy by 4.5 times, 2.1 times, and 1.3 times, respectively; in addition, our method is more efficient and it reduces the circuit area by 49.9%, 22.4%, and 28.5%, respectively.