## Section: New Results

### Formal study of double-word arithmetic algorithms

Participants : Laurence Rideau, Erik Martin-Dorel [IRIT Toulouse] , Jean-Michel Muller [CNRS and ENS Lyon] , Valentina Popescu [CNRS and ENS Lyon] .

As part of the ANR Fastrelax project, we have started to formalize 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" [24]. The formalization is progressing. A notable event is that we detected a small error in the article proof, which required a correction by the authors.