Section: New Results

Formal study of double-word arithmetic algorithms

Participants : Laurence Rideau, Jean-Michel Muller [CNRS, ENS de Lyon] .

We finished the formalization of double-word arithmetic algorithms, described in the article Tight and rigourous error bounds for basic building blocks of double-word arithmetic [16].

Thanks to the formalization, errors were found in the proofs, but the stated results (correction of algorithms and error limits) were proven correct. On the other hand, for the purposes of this formalization, we had to develop a more general version of the proof of the Fast2Sum algorithm, which should soon be integrated into the Flocq library.

An article describing this work of formalisation is being written.