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Rigorous Estimation of Floating-Point Round-off Errors with Symbolic Taylor Expansions

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FM 2015: Formal Methods (FM 2015)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9109))

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Abstract

Rigorous estimation of maximum floating-point round-off errors is an important capability central to many formal verification tools. Unfortunately, available techniques for this task often provide overestimates. Also, there are no available rigorous approaches that handle transcendental functions. We have developed a new approach called Symbolic Taylor Expansions that avoids this difficulty, and implemented a new tool called FPTaylor embodying this approach. Key to our approach is the use of rigorous global optimization, instead of the more familiar interval arithmetic, affine arithmetic, and/or SMT solvers. In addition to providing far tighter upper bounds of round-off error in a vast majority of cases, FPTaylor also emits analysis certificates in the form of HOL Light proofs. We release FPTaylor along with our benchmarks for evaluation.

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Authors and Affiliations

  1. School of Computing, University of Utah, Salt Lake City, UT, 84112, USA

    Alexey Solovyev, Charles Jacobsen, Zvonimir Rakamarić & Ganesh Gopalakrishnan

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  1. Alexey Solovyev
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  2. Charles Jacobsen
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  3. Zvonimir Rakamarić
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  4. Ganesh Gopalakrishnan
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Correspondence to Alexey Solovyev .

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Editors and Affiliations

  1. Microsoft Research, Redmond, Washington, USA

    Nikolaj Bjørner

  2. Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands

    Frank de Boer

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Solovyev, A., Jacobsen, C., Rakamarić, Z., Gopalakrishnan, G. (2015). Rigorous Estimation of Floating-Point Round-off Errors with Symbolic Taylor Expansions. In: Bjørner, N., de Boer, F. (eds) FM 2015: Formal Methods. FM 2015. Lecture Notes in Computer Science(), vol 9109. Springer, Cham. https://doi.org/10.1007/978-3-319-19249-9_33

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  • DOI: https://doi.org/10.1007/978-3-319-19249-9_33

  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-319-19249-9

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