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Modular Optimization-Based Roundoff Error Analysis of Floating-Point Programs

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Static Analysis (SAS 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14284))

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Abstract

Modular static program analyses improve over global whole-program analyses in terms of scalability at a tradeoff with analysis accuracy. This tradeoff has to-date not been explored in the context of sound floating-point roundoff error analyses; available analyses computing guaranteed absolute error bounds effectively consider only monolithic straight-line code. This paper extends the roundoff error analysis based on symbolic Taylor error expressions to non-recursive procedural floating-point programs. Our analysis achieves modularity and at the same time reasonable accuracy by automatically computing abstract procedure summaries that are a function of the input parameters. We show how to effectively use first-order Taylor approximations to compute precise procedure summaries, and how to integrate these to obtain end-to-end roundoff error bounds. Our evaluation shows that compared to an inlining of procedure calls, our modular analysis is significantly faster, while nonetheless mostly computing relatively tight error bounds.

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Author information

Authors and Affiliations

  1. MPI-SWS, Kaiserslautern and Saarbrücken, Germany

    Rosa Abbasi

  2. Uppsala University, Uppsala, Sweden

    Eva Darulova

Authors
  1. Rosa Abbasi
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  2. Eva Darulova
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Corresponding author

Correspondence to Eva Darulova .

Editor information

Editors and Affiliations

  1. U. Politécnica de Madrid (UPM) and IMDEA Software Institute, Pozuelo de Alarcón, Madrid, Spain

    Manuel V. Hermenegildo

  2. U. Politécnica de Madrid (UPM) and IMDEA Software Institute, Pozuelo de Alarcon, Spain

    José F. Morales

A Appendix

A Appendix

figure c

The code for the matrix case study is shown (partially) in Listing 1.2. The runtimes of FPTaylor for individual procedures are shown in Table 4.

Table 4. Runtimes of FPTaylor for individual procedures
Full size table

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Abbasi, R., Darulova, E. (2023). Modular Optimization-Based Roundoff Error Analysis of Floating-Point Programs. In: Hermenegildo, M.V., Morales, J.F. (eds) Static Analysis. SAS 2023. Lecture Notes in Computer Science, vol 14284. Springer, Cham. https://doi.org/10.1007/978-3-031-44245-2_4

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  • DOI: https://doi.org/10.1007/978-3-031-44245-2_4

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  • Online ISBN: 978-3-031-44245-2

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