Optimization of multipartite table methods to approximate the elementary functions

This paper presents the optimized methodology of the table-lookup-and-addition methods to approximate the elementary functions. Compared to the previously published methods including SBTM, STAM and their improved method in the paper, our method uses three small look-up tables to replace the biggest look-up tables in the previous methods and shortens the number of address bits to some look-up tables in the previous methods to reduce the memory requirements significantly. For example, when both our method and the method in the de Dinechin and Tisserand (2001) require the least number of bits, the compression ratio can reach to 1.57 using 16 bits operand for function 1/x. The data in this paper have been validated by using a set of C programs; and the designs have been synthesized with EDA tools.