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An Abstract Interpretation Framework for the Round-Off Error Analysis of Floating-Point Programs

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Verification, Model Checking, and Abstract Interpretation (VMCAI 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10747))

Abstract

This paper presents an abstract interpretation framework for the round-off error analysis of floating-point programs. This framework defines a parametric abstract analysis that computes, for each combination of ideal and floating-point execution path of the program, a sound over-approximation of the accumulated floating-point round-off error that may occur. In addition, a Boolean expression that characterizes the input values leading to the computed error approximation is also computed. An abstraction on the control flow of the program is proposed to mitigate the explosion of the number of elements generated by the analysis. Additionally, a widening operator is defined to ensure the convergence of recursive functions and loops. An instantiation of this framework is implemented in the prototype tool PRECiSA that generates formal proof certificates stating the correctness of the computed round-off errors.

M. Moscato—Research by the first three authors was supported by the National Aeronautics and Space Administration under NASA/NIA Cooperative Agreement NNL09AA00A.

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Author information

Authors and Affiliations

  1. National Institute of Aerospace, Hampton, USA

    Laura Titolo, Marco A. Feliú & Mariano Moscato

  2. NASA Langley Research Center, Hampton, USA

    César A. Muñoz

Authors
  1. Laura Titolo
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  2. Marco A. Feliú
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  3. Mariano Moscato
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  4. César A. Muñoz
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Corresponding author

Correspondence to Laura Titolo .

Editor information

Editors and Affiliations

  1. University of Texas , Austin, Texas, USA

    Isil Dillig

  2. University of California , Los Angeles, California, USA

    Jens Palsberg

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Titolo, L., Feliú, M.A., Moscato, M., Muñoz, C.A. (2018). An Abstract Interpretation Framework for the Round-Off Error Analysis of Floating-Point Programs. In: Dillig, I., Palsberg, J. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2018. Lecture Notes in Computer Science(), vol 10747. Springer, Cham. https://doi.org/10.1007/978-3-319-73721-8_24

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  • DOI: https://doi.org/10.1007/978-3-319-73721-8_24

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