Section: Research Program

Verification of Computer Arithmetic

Permanent researchers: S. Boldo, C. Marché, G. Melquiond

We of course want to keep this axis which is a major originality of Toccata. The main topics of the next 4 years will be:

• Fundamental studies concerning formalization of floating-point computations, algorithms, and error analysis. Related to numerical integration, we will develop the relationships between mathematical stability and floating-point stability of numerical schemes.

• A significant effort dedicated to verification of numerical programs written in C, Ada, C++. This involves combining specifications in real numbers and computation in floating-point, and underlying automated reasoning techniques with floating-point numbers and real numbers. A new approach we have in mind concerns some variant of symbolic execution of both code and specifications involving real numbers.

• We have not yet studied embedded systems. Our approach is first to tackle numerical filters. This requires more results on fixed-point arithmetic and a careful study of overflows.

• Also a specific focus on arbitrary precision integer arithmetic, in the continuation of the ongoing PhD thesis of R. Rieu-Helft.