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Primitive Floats in Coq

Authors Guillaume Bertholon , Érik Martin-Dorel , Pierre Roux

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Subject Classification

ACM Subject Classification
  • Theory of computation → Type theory
  • Mathematics of computing → Numerical analysis
  • General and reference → Performance
Keywords
  • Coq formal proofs
  • floating-point arithmetic
  • reflexive tactics
  • Cholesky decomposition

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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.

Cite As Get BibTex

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) https://doi.org/10.4230/LIPIcs.ITP.2019.7

Author Details

Guillaume Bertholon
  • École Normale Supérieure, Paris, France
Érik Martin-Dorel
  • Lab. IRIT, University of Toulouse, CNRS, France
Pierre Roux
  • ONERA, Toulouse, France

Acknowledgements

The authors would like to thank Maxime Dénès and Guillaume Melquiond for helpful discussions.

Supplementary Materials

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