## Section: New Results

### Approximation of Mathematical functions

Participants : Guillaume Hanrot, Érik Martin-Dorel, Micaela Mayero [Université de Paris 13] , Ioana Paşca [Université de Nimes] , Laurence Rideau, Laurent Théry [correspondant] .

In a collaboration supported by ANR project Tamadi, we study the approximation of mathematical functions (exponential and trigonometric functions) using polynomial functions.

This year, we completed the formal verification of our library that computes Taylor Models for the usual mathematical functions of one variable within Coq. A presentation of this work has been done at SYNASC'2013.

The SLZ algorithm checks that there is no hard-to-round floating numbers for a given range in a given floating-point format. It usually consists of a very long computation returning a yes/no answer. Formally proving the implementation of the algorithm is current outside reach since it requires very sophisticated numerical libraries that are currently impossible to verify formally. We have defined a notion of certificate for these computations based on Hensel's lemma and derived an executable checker within Coq that is capable to verify such computations. A publication has been submitted.