Exploiting Binary Floating-Point Representations for Constraint Propagation: The Complete Unabridged Version

Abstract: Floating-point computations are quickly finding their way in the design of safety- and mission-critical systems, despite the fact that designing floating-point algorithms is significantly more difficult than designing integer algorithms. For this reason, verification and validation of floating-point computations is a hot research topic. An important verification technique, especially in some industrial sectors, is testing. However, generating test data for floating-point intensive programs proved to be a challenging problem. Existing approaches usually resort to random or search-based test data generation, but without symbolic reasoning it is almost impossible to generate test inputs that execute complex paths controlled by floating-point computations. Moreover, as constraint solvers over the reals or the rationals do not natively support the handling of rounding errors, the need arises for efficient constraint solvers over floating-point domains. In this paper, we present and fully justify improved algorithms for the propagation of arithmetic IEEE 754 binary floating-point constraints. The key point of these algorithms is a generalization of an idea by B. Marre and C. Michel that exploits a property of the representation of floating-point numbers.