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International Workshop on Verification, Model Checking, and Abstract Interpretation

VMCAI 2011: Verification, Model Checking, and Abstract Interpretation pp 232–247Cite as

Static Analysis of Finite Precision Computations

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6538))

Abstract

We define several abstract semantics for the static analysis of finite precision computations, that bound not only the ranges of values taken by numerical variables of a program, but also the difference with the result of the same sequence of operations in an idealized real number semantics. These domains point out with more or less detail (control point, block, function for instance) sources of numerical errors in the program and the way they were propagated by further computations, thus allowing to evaluate not only the rounding error, but also sensitivity to inputs or parameters of the program. We describe two classes of abstractions, a non relational one based on intervals, and a weakly relational one based on parametrized zonotopic abstract domains called affine sets, especially well suited for sensitivity analysis and test generation. These abstract domains are implemented in the Fluctuat static analyzer, and we finally present some experiments.

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Author information

Authors and Affiliations

  1. Laboratory for the Modelling and Analysis of Interacting Systems, CEA LIST, Point courrier 94, Gif-sur-Yvette, F-91191, France

    Eric Goubault & Sylvie Putot

Authors
  1. Eric Goubault
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  2. Sylvie Putot
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Editor information

Editors and Affiliations

  1. UC San Diego, USA

    Ranjit Jhala

  2. Department of Computing and Information Sciences, Kansas State University, 234 Nichols Hall, 66506, Manhattan, KS, USA

    David Schmidt

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Goubault, E., Putot, S. (2011). Static Analysis of Finite Precision Computations. In: Jhala, R., Schmidt, D. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2011. Lecture Notes in Computer Science, vol 6538. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18275-4_17

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  • DOI: https://doi.org/10.1007/978-3-642-18275-4_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-18274-7

  • Online ISBN: 978-3-642-18275-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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