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| HAL : hal-00135090, version 3 |
| arXiv : cs/0703026 |
| Fiche détaillée |  Récupérer au format |
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| 8th Conference on Real Numbers and Computers, Saint Jacques de Compostelle : Spain (2008) |
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| Versions disponibles : | v1 (06-03-2007) | v2 (24-05-2007) | v3 (14-05-2008) |
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| Formal proof for delayed finite field arithmetic using floating point operators |
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| Sylvie Boldo 1Marc Daumas 2 |
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| (07/2008) |
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| Formal proof checkers such as Coq are capable of validating proofs of correction of algorithms for finite field arithmetics but they require extensive training from potential users. The delayed solution of a triangular system over a finite field mixes operations on integers and operations on floating point numbers. We focus in this report on verifying proof obligations that state that no round off error occurred on any of the floating point operations. We use a tool named Gappa that can be learned in a matter of minutes to generate proofs related to floating point arithmetic and hide technicalities of formal proof checkers. We found that three facilities are missing from existing tools. The first one is the ability to use in Gappa new lemmas that cannot be easily expressed as rewriting rules. We coined the second one ``variable interchange'' as it would be required to validate loop interchanges. The third facility handles massive loop unrolling and argument instantiation by generating traces of execution for a large number of cases. We hope that these facilities may sometime in the future be integrated into mainstream code validation. |
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| 1 : | PROVAL (INRIA Futurs) |
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INRIA – Université Paris XI - Paris Sud |
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| 2 : | Electronique, Informatique, Automatique et Systèmes (ELIAUS) |
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Université de Perpignan |
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| 3 : | 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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| Domaine | : | Informatique/Arithmétique des ordinateurs Informatique/Calcul formel |
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| hal-00135090, version 3 | |
| http://hal.archives-ouvertes.fr/hal-00135090 | |
| oai:hal.archives-ouvertes.fr:hal-00135090 | |
| Contributeur : Marc Daumas | |
| Soumis le : Mercredi 14 Mai 2008, 15:05:42 | |
| Dernière modification le : Mercredi 9 Juillet 2008, 09:36:18 | |
