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Computer Certified Efficient Exact Reals in Coq

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Intelligent Computer Mathematics (CICM 2011)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6824))

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Abstract

Floating point operations are fast, but require continuous effort on the part of the user in order to ensure that the results are correct. This burden can be shifted away from the user by providing a library of exact analysis in which the computer handles the error estimates. We provide an implementation of the exact real numbers in the Coq proof assistant. This improves on the earlier Coq-implementation by O’Connor in two ways: we use dyadic rationals built from the machine integers and we optimize computation of power series by using approximate division. Moreover, we use type classes for clean mathematical interfaces. This appears to be the first time that type classes are used in heavy computation. We obtain over a 100 times speed up of the basic operations and indications for improving the Coq system.

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Author information

Authors and Affiliations

  1. Radboud University Nijmegen, The Netherlands

    Robbert Krebbers & Bas Spitters

Authors
  1. Robbert Krebbers
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  2. Bas Spitters
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Editor information

Editors and Affiliations

  1. Departments of Computer Science and Mathematics Sciences, University of Bath, BA2 7AY, United Kingdom

    James H. Davenport

  2. Department of Computing and Software, McMaster University, 1280 Main Street West, L8SK1, Hamilton, Ontario, Canada

    William M. Farmer

  3. Institute for Computing and Information Sciences, Radboud University, Heyendaalseweg 135, 6525 AJ, Nijmegen, The Netherlands

    Josef Urban

  4. Department of Computer Science, Jacobs University Bremen, Campus Ring 12, 28759, Bremen, Germany

    Florian Rabe

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Krebbers, R., Spitters, B. (2011). Computer Certified Efficient Exact Reals in Coq . In: Davenport, J.H., Farmer, W.M., Urban, J., Rabe, F. (eds) Intelligent Computer Mathematics. CICM 2011. Lecture Notes in Computer Science(), vol 6824. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22673-1_7

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  • DOI: https://doi.org/10.1007/978-3-642-22673-1_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22672-4

  • Online ISBN: 978-3-642-22673-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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