An Efficient Method for Evaluating Polynomial and Rational Function Approximations

Nicolas Brisebarre (1) , Sylvain Chevillard (1) , Milos Ercegovac (2) , Jean-Michel Muller (1) , Serge Torres (1)

1 ARENAIRE - Computer arithmetic
2 Digital Arithmetic and Reconfigurable Architecture Laboratory

In this paper we extend the domain of applicability of the E-method, as a hardware-oriented method for evaluating elementary functions using polynomial and rational function approximations. The polynomials and rational 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 dominance condition. Until now, there was no systematic approach to obtain good approximations to f over an interval [a,b] by rational functions satisfying the constraints required 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.

Domaines: Arithmétique des ordinateurs; Architectures Matérielles [cs.AR]

Nicolas Brisebarre, Sylvain Chevillard, Milos Ercegovac, Jean-Michel Muller, Serge Torres. An Efficient Method for Evaluating Polynomial and Rational Function Approximations. ASAP 08, Jul 2008, Leuven, Belgium. pp.233 -- 238. ⟨hal-00761652⟩