Section: New Results

Provably correct approximations of elementary functions

Participants : Erik Martin-Dorel, Laurence Rideau, Laurent Théry.

The elementary functions are general purpose mathematical functions that are often implemented in the hardware of modern micro-processors: exponential and trigonometric functions, and inverse functions like arctan or square-root. We participate in a nationally funded project (ANR-TaMaDi) where precise approximations of these functions and their combinations must be computed. A first approach is to use Taylor models. We implemented such an approach and proved its correctness in the Coq system. This led to the publication [9] .

We are now working on applying Bernstein polynomials to the problem of approximating transcendental functions.