## Section: New Results

### Formaly study of algorithms to compute $\pi $

Participants : Yves Bertot, Laurence Rideau, Laurent Théry.

We studied formal proofs for several algorithms used to computed $\pi $ to very high precisions, the famous BBP formula and an algorithm derived from it and another algorithm based on arithmetic-geometric means that is used in the MPFR library. These results show that Coq can be used directly to compute a million decimals or the billionth hexa-decimal in isolation [5].