Algorithm, Proof and Performances of a new Division of Floating Point Expansions

Marc Daumas 1 Claire Finot 1
1 ARENAIRE - Computer arithmetic
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : We present in this work a new algorithm for the division of floating point expansions. Floating expansion is a multiple precision data type developped with arithmetic operators that use the processor floating point unit for core computations instead of the integer unit. Researches on this subject have arised recently from the observation that the floating point unit becomes a more and more efficient part of modern computers. Many simple arithmetic operators and some very usefull geometric operators have already been presented on expansions. Yet previous work presented only a very simple division algorithm. We present in this work a new algorithm. We take this opportunity to extend the set of geometric operators with Bareiss' determinant on a matrix of size between 3 and 10. Running times with different determinant algorithms on different machines are compared with other multiprec- ision packages including GMP, CADNA and a computer geometry package working with modular arithmetic.
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Rapport
[Research Report] RR-3771, INRIA. 1999
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https://hal.inria.fr/inria-00072890
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Soumis le : mercredi 24 mai 2006 - 11:11:16
Dernière modification le : mardi 16 janvier 2018 - 15:50:59
Document(s) archivé(s) le : dimanche 4 avril 2010 - 23:26:54

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Marc Daumas, Claire Finot. Algorithm, Proof and Performances of a new Division of Floating Point Expansions. [Research Report] RR-3771, INRIA. 1999. 〈inria-00072890〉

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