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Introduction to the IEEE 1788-2015 Standard for Interval Arithmetic

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Numerical Software Verification (NSV 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10381))

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Abstract

Interval arithmetic is a tool of choice for numerical software verification, as every result computed using this arithmetic is self-verified: every result is an interval that is guaranteed to contain the exact numerical values, regardless of uncertainty or roundoff errors.

From 2008 to 2015, interval arithmetic underwent a standardization effort, resulting in the IEEE 1788-2015 standard. The main features of this standard are developed: the structure into levels, from the mathematic model to the implementation on computers; the possibility to accommodate different mathematical models, called flavors; the decoration system that keeps track of relevant events during the course of a calculation; the exact dot product for point (as opposed to interval) vectors.

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Acknowledgments

The author would like to thank Alessandro Abate and Sylvie Boldo for their kind invitation. The author would also like to thank all participants to the working group that developed the IEEE 1788-2015 standard for providing the material for this standard, for their differing points of view that questioned every proposal and that eventually contributed to create a solid standard, and for their never-fading enthusiasm. Last but not least, special thanks go to Kearfott [8] and Pryce [15] for the collective work and for their inspiring papers.

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Authors and Affiliations

  1. Inria – LIP, ENS de Lyon, University of Lyon, 46 allée d’Italie, 69364, Lyon Cedex 07, France

    Nathalie Revol

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  1. Nathalie Revol
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Correspondence to Nathalie Revol .

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Editors and Affiliations

  1. University of Oxford , Oxford, United Kingdom

    Alessandro Abate

  2. Université Paris-Sud, Inria , Orsay, France

    Sylvie Boldo

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Revol, N. (2017). Introduction to the IEEE 1788-2015 Standard for Interval Arithmetic. In: Abate, A., Boldo, S. (eds) Numerical Software Verification. NSV 2017. Lecture Notes in Computer Science(), vol 10381. Springer, Cham. https://doi.org/10.1007/978-3-319-63501-9_2

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  • DOI: https://doi.org/10.1007/978-3-319-63501-9_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-63500-2

  • Online ISBN: 978-3-319-63501-9

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