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DOI: 10.4230/LIPIcs.ITP.2019.7

Primitive Floats in Coq

Authors: Guillaume Bertholon, Érik Martin-Dorel, and Pierre Roux

Published in: LIPIcs, Volume 141, 10th International Conference on Interactive Theorem Proving (ITP 2019)

Abstract

Some mathematical proofs involve intensive computations, for instance: the four-color theorem, Hales' theorem on sphere packing (formerly known as the Kepler conjecture) or interval arithmetic. For numerical computations, floating-point arithmetic enjoys widespread usage thanks to its efficiency, despite the introduction of rounding errors. Formal guarantees can be obtained on floating-point algorithms based on the IEEE 754 standard, which precisely specifies floating-point arithmetic and its rounding modes, and a proof assistant such as Coq, that enjoys efficient computation capabilities. Coq offers machine integers, however floating-point arithmetic still needed to be emulated using these integers. A modified version of Coq is presented that enables using the machine floating-point operators. The main obstacles to such an implementation and its soundness are discussed. Benchmarks show potential performance gains of two orders of magnitude.

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Guillaume Bertholon, Érik Martin-Dorel, and Pierre Roux. Primitive Floats in Coq. In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, pp. 7:1-7:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{bertholon_et_al:LIPIcs.ITP.2019.7,
  author =	{Bertholon, Guillaume and Martin-Dorel, \'{E}rik and Roux, Pierre},
  title =	{{Primitive Floats in Coq}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{7:1--7:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-122-1},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{141},
  editor =	{Harrison, John and O'Leary, John and Tolmach, Andrew},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2019.7},
  URN =		{urn:nbn:de:0030-drops-110629},
  doi =		{10.4230/LIPIcs.ITP.2019.7},
  annote =	{Keywords: Coq formal proofs, floating-point arithmetic, reflexive tactics, Cholesky decomposition}
}

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Primitive Floats in Coq

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