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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, * 
* Corresponding author
1 ARENAIRE - Computer arithmetic
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : 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.
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Submitted on : Wednesday, December 5, 2012 - 7:09:13 PM
Last modification on : Tuesday, November 29, 2022 - 12:06:07 PM


  • HAL Id : hal-00761652, version 1



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⟩



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