On Ziv's rounding test

Abstract : A very simple test, introduced by Ziv, allows one to determine if an approximation to the value f (x) of an elementary function at a given point x suffices to return the floating-point number nearest f(x). The same test may be used when implementing floating-point operations with input and output operands of different formats, using arithmetic operators tailored for manipulating operands of the same format. That test depends on a "magic constant" e. We show how to choose that constant e to make the test reliable and efficient. Various cases are considered, depending on the availability of an fma instruction, and on the range of f (x).
Type de document :
Pré-publication, Document de travail
2012
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https://hal-ens-lyon.archives-ouvertes.fr/ensl-00693317
Contributeur : Jean-Michel Muller <>
Soumis le : mercredi 2 mai 2012 - 13:55:57
Dernière modification le : vendredi 31 août 2018 - 09:25:53
Document(s) archivé(s) le : lundi 26 novembre 2012 - 16:05:18

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ZivRounding_PreprintVersion.pd...
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  • HAL Id : ensl-00693317, version 1

Citation

Florent De Dinechin, Christoph Lauter, Jean-Michel Muller, Serge Torres. On Ziv's rounding test. 2012. 〈ensl-00693317v1〉

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