Floating-point arithmetic in the Coq system

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Abstract

The process of proving some mathematical theorems can be greatly reduced by relying on numerically-intensive computations with a certified arithmetic. This article presents a formalization of floating-point 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.

Keywords

Floating-point arithmetic
Formal proofs
Coq system

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This work was partly done while at the Microsoft Research – INRIA Joint Laboratory.