## Section: New Results

### Formal study of double-word arithmetic algorithms

Participants : Laurence Rideau, Jean-Michel Muller [CNRS and ENS Lyon] , Valentina Popescu [CNRS and ENS Lyon] , Mioara Joldes [CNRS LAAS] .

As part of the ANR Fastrelax project, we are formalizing double-word arithmetic algorithms, in particular the sum of a double-word and a floating point number and the sum of two double-word numbers described in the article " Tight and rigourous error bounds for basic building blocks of double-word arithmetic" [27]. The formalization is progressing, moving from addition to multiplication. The progress is slowed down because minor errors in the informal proofs are regularly uncovered, which requires a dialog with the initial authors.