Deciding floating-point logic with systematic abstraction

We present a bit-precise decision procedure for the theory of binary floating-point arithmetic. The core of our approach is a non-trivial generalisation of the conflict analysis algorithm used in modern SAT solvers to lattice-based abstractions. Existing complete solvers for floating-point arithmetic employ bit-vector encodings. Propositional solvers based on the Conflict Driven Clause Learning (CDCL) algorithm are then used as a backend. We present a natural-domain SMT approach that lifts the CDCL framework to operate directly over abstractions of floating-point values. We have instantiated our method inside MATHSAT5 with the floating-point interval abstraction. The result is a sound and complete procedure for floating-point arithmetic that outperforms the state-of-the-art significantly on problems that check ranges on numerical variables. Our technique is independent of the specific abstraction and can be applied to problems beyond floating-point satisfiability checking.