Computer Arithmetic and Formal Proofs: Verifying Floating-point Algorithms with the Coq System

Sylvie Boldo 1, 2 Guillaume Melquiond 1, 2
2 TOCCATA - Certified Programs, Certified Tools, Certified Floating-Point Computations
LRI - Laboratoire de Recherche en Informatique, UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France, CNRS - Centre National de la Recherche Scientifique : UMR8623
Abstract : Floating-point arithmetic is ubiquitous in modern computing, as it is the tool of choice to approximate real numbers. Due to its limited range and precision, its use can become quite involved and potentially lead to numerous failures. One way to greatly increase confidence in floating-point software is by computer-assisted verification of its correctness proofs. This book provides a comprehensive view of how to formally specify and verify tricky floating-point algorithms with the Coq proof assistant. It describes the Flocq formalization of floating-point arithmetic and some methods to automate theorem proofs. It then presents the specification and verification of various algorithms, from error-free transformations to a numerical scheme for a partial differential equation. The examples cover not only mathematical algorithms but also C programs as well as issues related to compilation.
Type de document :
Ouvrage (y compris édition critique et traduction)
ISTE Press - Elsevier, pp.326, 2017, 9781785481123
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https://hal.inria.fr/hal-01632617
Contributeur : Guillaume Melquiond <>
Soumis le : vendredi 10 novembre 2017 - 14:28:19
Dernière modification le : jeudi 5 avril 2018 - 12:30:22

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  • HAL Id : hal-01632617, version 1

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Sylvie Boldo, Guillaume Melquiond. Computer Arithmetic and Formal Proofs: Verifying Floating-point Algorithms with the Coq System. ISTE Press - Elsevier, pp.326, 2017, 9781785481123. 〈hal-01632617〉

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