Efficient algorithms and VLSI architectures for trigonometric functions in the logarithmic number system based on the subtraction function

Abstract

In this paper, algorithms and architectures for the evaluation of trigonometric functions in the Logarithmic Number System (LNS) are described. A novel algorithm for the computation of the LNS cosine, based on the subtraction function, is presented and extended to compute all trigonometric functions. The proposed algorithms show a major advantage over other methods in terms of memory requirements (up to 94% improvement as opposed to direct polynomial approximation) and computational speed. A hardware implementation of an elementary LNS trigonometric processor with 12-bit accuracy is also presented, to illustrate the feasibility of extending the LNS processors to include trigonometric functions.