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2008
IEEE

An efficient method for evaluating polynomial and rational function approximations

9 years 6 days ago
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 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.
Nicolas Brisebarre, Sylvain Chevillard, Milos D. E
Added 12 Oct 2010
Updated 12 Oct 2010
Type Conference
Year 2008
Where ASAP
Authors Nicolas Brisebarre, Sylvain Chevillard, Milos D. Ercegovac, Jean-Michel Muller, Serge Torres
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