Section: New Results

Floating-point algorithms and proofs

Participants : Sylvie Boldo, Guillaume Melquiond.

An established collaboration with M. Daumas (Université of Perpignan Via Domitia) and R.-C. Li (University of Texas at Arlington, USA) with S. Boldo has been carried on about argument reductions [14] and has been published in IEEE Transactions on Computers. This is the first step and a very delicate one to compute elementary functions (exponential, sine...).

S. Boldo and G. Melquiond developed with P. Zimmermann (CACAO, INRIA Lorraine) and S. Rump (Institute for Reliable Computing, Hamburg) a simple and efficient method to compute and/or estimate the predecessor and successor of a floating-point number using only floating-point operations in rounding to nearest [16] .

S. Boldo, J.-C. Filliâtre and G. Melquiond implemented a mechanism for calling Gappa (an automatic tool specialized in floating-point arithmetic) from a Coq interactive proof. This offers a significant speedup in the process of verifying floating-point programs [20] .

G. Melquiond participed to the writing of a handbook on floating-point arithmetic [29] directed by Jean-Michel Muller (Arenaire, INRIA Rhône-Alpes).