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Sound Probabilistic Numerical Error Analysis

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Integrated Formal Methods (IFM 2019)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 11918))

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Abstract

Numerical software uses floating-point arithmetic to implement real-valued algorithms which inevitably introduces roundoff errors. Additionally, in an effort to reduce energy consumption, approximate hardware introduces further errors. As errors are propagated through a computation, the result of the approximated floating-point program can be vastly different from the real-valued ideal one. Previous work on soundly bounding (roundoff) errors has focused on worst-case absolute error analysis. However, not all inputs and not all errors are equally likely such that these methods can lead to overly pessimistic error bounds.

In this paper, we present a sound probabilistic static analysis which takes into account the probability distributions of inputs and propagates roundoff and approximation errors probabilistically through the program. We observe that the computed probability distributions of errors are hard to interpret, and propose an alternative metric and computation of refined error bounds which are valid with some probability.

D. Lohar—The author is supported by DFG grant DA 1898/2-1.

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Notes

  1. 1.

    All benchmarks are available at https://people.mpi-sws.org/~dlohar/assets/code/Benchmarks.txt.

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Authors and Affiliations

  1. MPI-SWS, Saarland Informatics Campus, Saarbrücken, Germany

    Debasmita Lohar & Eva Darulova

  2. University of Edinburgh, Edinburgh, UK

    Milos Prokop

Authors
  1. Debasmita Lohar
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  2. Milos Prokop
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  3. Eva Darulova
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Correspondence to Debasmita Lohar .

Editor information

Editors and Affiliations

  1. Chalmers University of Technology, Gothenburg, Sweden

    Wolfgang Ahrendt

  2. University of Oslo, Oslo, Norway

    Silvia Lizeth Tapia Tarifa

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Lohar, D., Prokop, M., Darulova, E. (2019). Sound Probabilistic Numerical Error Analysis. In: Ahrendt, W., Tapia Tarifa, S. (eds) Integrated Formal Methods. IFM 2019. Lecture Notes in Computer Science(), vol 11918. Springer, Cham. https://doi.org/10.1007/978-3-030-34968-4_18

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  • DOI: https://doi.org/10.1007/978-3-030-34968-4_18

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-34967-7

  • Online ISBN: 978-3-030-34968-4

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