De l'arithmétique d'intervalles à la certification de programmes

Guillaume Melquiond 1
1 ARENAIRE - Computer arithmetic
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : Computer numbers are usually limited, both in range and in precision. As a consequence, a careful certification has to be performed for applications that compute with these sets of numbers. Unfortunately, performing such a certification by hand is error-prone. Formal methods can ensure that the certification is correct, but making use of them is usually long and tedious, even for experts.This thesis aims at improving the availability of these methods to developers by automatizing their implementation. The key concepts are the use of interval arithmetic, a database of theorems on computer arithmetics, and a system for rewriting expressions in order to compute tight bounds on rounding errors.This approach has led to the development of the Gappa tool. It is designed to verify the numeric properties of programs relying on floating-point or fixed-point arithmetic. When verifying these properties, the tool also generates formal proofs of their correctness. These proofs can later be mechanically checked by the Coq proof assistant. Gappa has been successfully used for certifying some functions of the CRlibm, CGAL, and FLIP libraries, among others.
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Guillaume Melquiond. De l'arithmétique d'intervalles à la certification de programmes. Arithmétique des ordinateurs. École Normale Supérieure de Lyon, 2006. Français. ⟨NNT : 2006ENSL0388⟩. ⟨tel-01094485⟩



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