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How to Get an Efficient yet Verified Arbitrary-Precision Integer Library

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Verified Software. Theories, Tools, and Experiments (VSTTE 2017)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 10712))

Abstract

The GNU Multi-Precision library is a widely used, safety-critical, library for arbitrary-precision arithmetic. Its source code is written in C and assembly, and includes intricate state-of-the-art algorithms for the sake of high performance. Formally verifying the functional behavior of such highly optimized code, not designed with verification in mind, is challenging. We present a fully verified library designed using the Why3 program verifier. The use of a dedicated memory model makes it possible to have the Why3 code be very similar to the original GMP code. This library is extracted to C and is compatible and performance-competitive with GMP.

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Notes

  1. 1.

    http://gmplib.org/.

  2. 2.

    Look for ‘division’ at https://gmplib.org/gmp5.0.html.

  3. 3.

    http://why3.lri.fr/.

  4. 4.

    http://gmplib.org/manual/Low_002dlevel-Functions.html.

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Acknowledgments

We gratefully thank Pascal Cuoq, Jean-Christophe Filliâtre and Mário Pereira for their comments on preliminary versions of this article.

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Authors and Affiliations

  1. École Normale Supérieure, 75230, Paris, France

    Raphaël Rieu-Helft

  2. Inria, Université Paris-Saclay, 91120, Palaiseau, France

    Raphaël Rieu-Helft, Claude Marché & Guillaume Melquiond

  3. LRI (CNRS & Univ. Paris-Sud), Université Paris-Saclay, 91405, Orsay, France

    Raphaël Rieu-Helft, Claude Marché & Guillaume Melquiond

Authors
  1. Raphaël Rieu-Helft
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  2. Claude Marché
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  3. Guillaume Melquiond
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Corresponding author

Correspondence to Claude Marché .

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Editors and Affiliations

  1. Paris-Sud University, Orsay, France

    Andrei Paskevich

  2. New York University, New York, New York, USA

    Thomas Wies

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Rieu-Helft, R., Marché, C., Melquiond, G. (2017). How to Get an Efficient yet Verified Arbitrary-Precision Integer Library. In: Paskevich, A., Wies, T. (eds) Verified Software. Theories, Tools, and Experiments. VSTTE 2017. Lecture Notes in Computer Science(), vol 10712. Springer, Cham. https://doi.org/10.1007/978-3-319-72308-2_6

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  • DOI: https://doi.org/10.1007/978-3-319-72308-2_6

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  • Online ISBN: 978-3-319-72308-2

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