@MISC{Melquiond_floating-pointarithmetic, author = {Guillaume Melquiond}, title = {Floating-point arithmetic in the Coq system}, year = {} }

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Abstract

The process of proving some mathematical theorems can be greatly reduced by relying on numericallyintensive computations with a certified arithmetic. This article presents a formalization of floatingpoint arithmetic that makes it possible to efficiently compute inside the proofs of the Coq system. This certified library is a multi-radix and multi-precision implementation free from underflow and overflow. It provides the basic arithmetic operators and a few elementary functions. 1