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Tight Error Analysis in Fixed-Point Arithmetic

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Integrated Formal Methods (IFM 2020)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 12546))

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Abstract

We consider the problem of estimating the numerical accuracy of programs with operations in fixed-point arithmetic and variables of arbitrary, mixed precision and possibly non-deterministic value. By applying a set of parameterised rewrite rules, we transform the relevant fragments of the program under consideration into sequences of operations in integer arithmetic over vectors of bits, thereby reducing the problem as to whether the error enclosures in the initial program can ever exceed a given order of magnitude to simple reachability queries on the transformed program. We present a preliminary experimental evaluation of our technique on a particularly complex industrial case study.

Partially supported by MIUR projects PRIN 2017TWRCNB SEDUCE (Designing Spatially Distributed Cyber-Physical Systems under Uncertainty) and PRIN 2017FTXR7S IT-MATTERS (Methods and Tools for Trustworthy Smart Systems).

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Author information

Authors and Affiliations

  1. IMT School for Advanced Studies, Lucca, Italy

    Stella Simić, Alberto Bemporad & Mirco Tribastone

  2. Gran Sasso Science Institute, L’Aquila, Italy

    Omar Inverso

Authors
  1. Stella Simić
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  2. Alberto Bemporad
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  3. Omar Inverso
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  4. Mirco Tribastone
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Corresponding author

Correspondence to Stella Simić .

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Editors and Affiliations

  1. University of Surrey, Guildford, UK

    Brijesh Dongol

  2. Royal Institute of Technology - KTH, Stockholm, Sweden

    Elena Troubitsyna

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Simić, S., Bemporad, A., Inverso, O., Tribastone, M. (2020). Tight Error Analysis in Fixed-Point Arithmetic. In: Dongol, B., Troubitsyna, E. (eds) Integrated Formal Methods. IFM 2020. Lecture Notes in Computer Science(), vol 12546. Springer, Cham. https://doi.org/10.1007/978-3-030-63461-2_17

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  • DOI: https://doi.org/10.1007/978-3-030-63461-2_17

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-030-63461-2

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