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Runtime Abstract Interpretation for Numerical Accuracy and Robustness

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Verification, Model Checking, and Abstract Interpretation (VMCAI 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12597))

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Abstract

Verification of numerical accuracy properties in modern software remains an important and challenging task. One of its difficulties is related to unstable tests, where the execution can take different branches for real and floating-point numbers. This paper presents a new verification technique for numerical properties, named Runtime Abstract Interpretation (RAI), that, given an annotated source code, embeds into it an abstract analyzer in order to analyze the program behavior at runtime. RAI is a hybrid technique combining abstract interpretation and runtime verification that aims at being sound as the former while taking benefit from the concrete run to gain greater precision from the latter when necessary. It solves the problem of unstable tests by surrounding an unstable test by two carefully defined program points, forming a so-called split-merge section, for which it separately analyzes different executions and merges the computed domains at the end of the section. Our implementation of this technique in a toolchain called FLDBox relies on two basic tools, FLDCompiler, that performs a source-to-source transformation of the given program and defines the split-merge sections, and an instrumentation library FLDLib that provides necessary primitives to explore relevant (partial) executions of each section and propagate accuracy properties. Initial experiments show that the proposed technique can efficiently and soundly analyze numerical accuracy for industrial programs on thin numerical scenarios.

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Notes

  1. 1.

    http://www-users.math.umn.edu/arnold/disasters/patriot.html.

  2. 2.

    https://en.wikipedia.org/wiki/Vancouver_Stock_Exchange.

  3. 3.

    http://www-users.math.umn.edu/arnold/disasters/sleipner.html.

  4. 4.

    The source code of FLDLib is available at https://github.com/fvedrine/fldlib.

  5. 5.

    https://gmplib.org/.

  6. 6.

    https://github.com/AdaCore/libadalang.

  7. 7.

    https://gitlab.com/libeigen/eigen.

  8. 8.

    https://www.mpfr.org.

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Acknowledgement

The authors thank Romain Soulat and Thales Research and Technology for providing case studies and participation in the evaluation. We are also grateful to Jean Gassino, Gregory de la Grange and IRSN for their support and evaluation on additional case studies, as well as to the anonymous reviewers for their valuable comments.

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Authors and Affiliations

  1. Université Paris -Saclay, CEA, List, Palaiseau, France

    Franck Védrine, Maxime Jacquemin, Nikolai Kosmatov & Julien Signoles

  2. Thales Research and Technology, Palaiseau, France

    Nikolai Kosmatov

Authors
  1. Franck Védrine
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  2. Maxime Jacquemin
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  3. Nikolai Kosmatov
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  4. Julien Signoles
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Corresponding author

Correspondence to Nikolai Kosmatov .

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Editors and Affiliations

  1. University of Copenhagen, Copenhagen, Denmark

    Fritz Henglein

  2. Tel Aviv University, Tel Aviv, Israel

    Sharon Shoham

  3. Technion, Haifa, Israel

    Yakir Vizel

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Védrine, F., Jacquemin, M., Kosmatov, N., Signoles, J. (2021). Runtime Abstract Interpretation for Numerical Accuracy and Robustness. In: Henglein, F., Shoham, S., Vizel, Y. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2021. Lecture Notes in Computer Science(), vol 12597. Springer, Cham. https://doi.org/10.1007/978-3-030-67067-2_12

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  • DOI: https://doi.org/10.1007/978-3-030-67067-2_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-67066-5

  • Online ISBN: 978-3-030-67067-2

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