Compensated Horner algorithm in K times the working precision

Philippe Langlois 1 Nicolas Louvet 2
2 ARENAIRE - Computer arithmetic
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : We introduce an algorithm to evaluate a polynomial with floating point coefficients as accurately as the Horner scheme performed in K times the working precision, for K an arbitrary integer. The principle is to iterate the error-free transformation of the compensated Horner algorithm and to accurately sum the final decomposition. We prove this accuracy property with an apriori error analysis. We illustrate its practical efficiency with numerical experiments on significant environments and IEEE-754 arithmetic. Comparing to existing alternatives we conclude that this K-times compensated algorithm is competitive for K up to 4, i.e. up to 212 mantissa bits.
Type de document :
Rapport
[Research Report] 2008
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https://hal.inria.fr/inria-00267077
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Soumis le : mercredi 26 mars 2008 - 14:08:06
Dernière modification le : samedi 17 septembre 2016 - 01:29:18
Document(s) archivé(s) le : vendredi 28 septembre 2012 - 11:45:15

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Philippe Langlois, Nicolas Louvet. Compensated Horner algorithm in K times the working precision. [Research Report] 2008. <inria-00267077>

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