Abstract : We propose a new algorithm to find worst cases for correct rounding of an analytic function. We first reduce this problem to the Real Small Value Problem --- i.e. for polynomials with real coefficients. Then we show that this second problem can be solved efficiently, by extending Coppersmith's work on the Integer Small Value Problem --- for polynomials with integer coefficients --- using lattice reduction. For floating-point numbers with a mantissa less than N, and a polynomial approximation of degree d, our algorithm finds all worst cases at distance $
https://hal.inria.fr/inria-00099572
Contributeur : Publications Loria
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Soumis le : mardi 26 septembre 2006 - 09:38:49
Dernière modification le : mardi 25 octobre 2016 - 17:02:03
Damien Stehlé, Vincent Lefèvre, Paul Zimmermann. Worst Cases and Lattice Reduction. 16th IEEE Symposium on Computer Arithmetic 2003 - ARITH-16'03, 2003, Santiago de Compostela, Espagne, pp.142-147, 2003. 〈inria-00099572〉
