An efficient method for evaluating polynomial and rational function approximations

In this paper we extend the domain of applicability of the E-method [7, 8], as a hardware-oriented method for evaluating elementary functions using polynomial and ra-tional function approximations. The polynomials and ra-tional functions are computed by solving a system of linear equations using digit-serial iterations on simple and highly regular hardware. For convergence, these systems must be diagonally dominant. The E-method offers an efficient way for the fixed-point evaluation of polynomials and rational functions if their coefficients conform to the diagonal dom-inance condition. Until now, there was no systematic ap-proach to obtain good approximations to f over an inter-val [a, b] by rational functions satisfying the constraints re-quired by the E-method. In this paper, we present such an approach which is based on linear programming and lattice basis reduction. We also discuss a design and performance characteristics of a corresponding implementation. 1