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Termination of Floating-Point Computations

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Abstract

Numerical computations form an essential part of almost any real-world program. Traditional approaches to termination of logic programs are restricted to domains isomorphic to (ℕ,>); more recent works study termination of integer computations where the lack of well-foundedness of the integers has to be taken into account. Termination of computations involving floating-point numbers can be counterintuitive because of rounding errors and implementation conventions. We present a novel technique that allows us to prove termination of such computations. Our approach extends the previous work on termination of integer computations.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, TU Eindhoven, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Alexander Serebrenik

  2. Department of Computer Science, K.U. Leuven, Celestijnenlaan 200A, B-3001, Heverlee, Belgium

    Danny De Schreye

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  1. Alexander Serebrenik
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Correspondence to Alexander Serebrenik.

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Alexander Serebrenik: This research has been carried out during the first author's stay at the Department of Computer Science, K.U. Leuven, Belgium and STIX, École Polytechnique, France.

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Serebrenik, A., De Schreye, D. Termination of Floating-Point Computations. J Autom Reasoning 34, 141–177 (2005). https://doi.org/10.1007/s10817-005-6546-z

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