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Formally Verified Certificate Checkers for Hardest-to-Round Computation

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Abstract

In order to derive efficient and robust floating-point implementations of a given function f, it is crucial to compute its hardest-to-round points, i.e. the floating-point numbers x such that f(x) is closest to the midpoint of two consecutive floating-point numbers. Depending on the floating-point format one is aiming at, this can be highly computationally intensive. In this paper, we show how certificates based on Hensel’s lemma can be added to an algorithm using lattice basis reduction so that the result of a computation can be formally checked in the Coq proof assistant.

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Authors and Affiliations

  1. LRI, Inria Saclay - Île-de-France, Bâtiment 650 Ada Lovelace, Université Paris Sud 11, 91405, Orsay Cedex, France

    Érik Martin-Dorel

  2. École Normale Supérieure de Lyon, LIP (UMR 5668 CNRS, ENSL, Inria, UCBL), 46 allée d’Italie, 69364, Lyon Cedex 07, France

    Guillaume Hanrot

  3. Université Paris 13, LIPN (UMR 7030 CNRS), 99 avenue JB Clément, 93430, Villetaneuse, France

    Micaela Mayero

  4. Inria Sophia Antipolis, 2004 route des Lucioles, BP 93, 06902, Sophia Antipolis Cedex, France

    Laurent Théry

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  1. Érik Martin-Dorel
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  2. Guillaume Hanrot
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  3. Micaela Mayero
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  4. Laurent Théry
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Correspondence to Érik Martin-Dorel.

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Martin-Dorel, É., Hanrot, G., Mayero, M. et al. Formally Verified Certificate Checkers for Hardest-to-Round Computation. J Autom Reasoning 54, 1–29 (2015). https://doi.org/10.1007/s10817-014-9312-2

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  • DOI: https://doi.org/10.1007/s10817-014-9312-2

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