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| HAL : hal-00168401, version 1 |
| arXiv : 0708.3722 |
| Fiche détaillée |  Récupérer au format |
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| Formally Verified Argument Reduction with a Fused-Multiply-Add |
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| Sylvie Boldo 1Marc Daumas 2, 3 |
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| (28/08/2007) |
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| Cody & Waite argument reduction technique works perfectly for reasonably large arguments but as the input grows there are no bit left to approximate the constant with enough accuracy. Under mild assumptions, we show that the result computed with a fused-multiply-add provides a fully accurate result for many possible values of the input with a constant almost accurate to the full working precision. We also present an algorithm for a fully accurate second reduction step to reach double full accuracy (all the significand bits of two numbers are significant) even in the worst cases of argument reduction. Our work recalls the common algorithms and presents proofs of correctness. All the proofs are formally verified using the Coq automatic proof checker. |
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| 1 : | PROVAL (INRIA Futurs) |
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INRIA – Université Paris XI - Paris Sud |
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| 2 : | Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier (LIRMM) |
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CNRS : UMR5506 – Université Montpellier II - Sciences et Techniques du Languedoc |
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| 3 : | Electronique, Informatique, Automatique et Systèmes (ELIAUS) |
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Université de Perpignan |
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| 4 : | Department of Mathematics of the University of Texas at Arlington |
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University of Texas at Arlington |
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| Domaine | : | Informatique/Arithmétique des ordinateurs Informatique/Logiciel mathématique Informatique/Performance et fiabilité |
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| hal-00168401, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00168401 | |
| oai:hal.archives-ouvertes.fr:hal-00168401 | |
| Contributeur : Marc Daumas | |
| Soumis le : Mardi 28 Août 2007, 06:56:20 | |
| Dernière modification le : Mardi 28 Août 2007, 09:15:22 | |
