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Floats & Ropes: a case study for formal numerical program verification

Sylvie Boldo 1, 2
1 PROVAL - Proof of Programs
UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France, CNRS - Centre National de la Recherche Scientifique : UMR
Abstract : We present a case study of a formal verification of a numerical program that computes the discretization of a simple partial differential equation. Bounding the rounding error was tricky as the usual idea, that is to bound the absolute value of the error at each step, fails. Our idea is to find out a precise analytical expression that cancels with itself at the next step, and to formally prove the correctness of this approach.
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https://hal.inria.fr/inria-00432718
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Submitted on : Tuesday, November 17, 2009 - 9:45:42 AM
Last modification on : Wednesday, February 9, 2022 - 5:26:06 PM

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Sylvie Boldo. Floats & Ropes: a case study for formal numerical program verification. Lecture Notes in Computer Science, Springer, 2009, 36th International Colloquium on Automata, Languages and Programming, 5556, pp.91--102. ⟨10.1007/978-3-642-02930-1_8⟩. ⟨inria-00432718⟩

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