Flottants primitifs en Coq

Abstract

International audienceSome 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