Bound on Run of Zeros and Ones for Images of Floating-Point Numbers by Algebraic Functions

Tomas Lang 1 Jean-Michel Muller 2
2 ARENAIRE - Computer arithmetic
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : This paper presents upper bounds on the number of zeros and ones after the rounding bit for algebraic functions. These functions include reciprocal, division, square root, and inverse square root, which have been considered in previous work. We here propose simpler proofs for the previously given bounds given and generalize to all algebraic functions. We also determine cases for which the bound is achieved for square root. As is mentioned in the previous work, these bounds are useful for determining the precision required in the computation of approximations in order to be able to perform correct rounding.
Type de document :
Rapport
[Research Report] RR-4045, INRIA. 2000
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Soumis le : mercredi 24 mai 2006 - 10:21:31
Dernière modification le : vendredi 20 avril 2018 - 15:44:23
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Tomas Lang, Jean-Michel Muller. Bound on Run of Zeros and Ones for Images of Floating-Point Numbers by Algebraic Functions. [Research Report] RR-4045, INRIA. 2000. 〈inria-00072593〉

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