Second order function approximation using a single multiplication on FPGAs

Abstract

This paper presents a new scheme for the hardware evaluation of elementary functions, based on a piecewise second order minimax approximation. The novelty is that this evaluation requires only one small rectangular multiplication. Therefore the resulting architecture combines a small table size, thanks to second-order evaluation, with a short critical path: Consisting of one table lookup, the rectangular multiplication, and one addition, the critical path is shorter than that of a plain first-order evaluation. Synthesis results for several functions show that this method outperforms all the previously published methods in both area and speed for precisions ranging from 12 to 24 bits and over. © Springer-Verlag Berlin Heidelberg 2004.