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