Exploring Approximations for Floating-Point Arithmetic using UppSAT

We consider the problem of solving floating-point constraints obtained from software verification. We present UppSAT—an new implementation of a systematic approximation refinement framework as an abstract SMT solver. Provided with an approximation and a decision procedure (implemented in an off-the-shelf SMT solver), UppSAT yields an approximating SMT solver. Additionally, UppSAT includes a library of predefined approximation components which can be combined and extended to define new encodings, orderings and solving strategies. We propose that UppSAT can be used as a sandbox for easy and flexible exploration of new approximations. To substantiate this, we explore encodings of floating-point arithmetic into reduced precision floating-point arithmetic, real-arithmetic, and fixed-point arithmetic (encoded into the theory of bit-vectors in practice). In an experimental evaluation we compare the advantages and disadvantages of approximating solvers obtained by combining various encodings and decision procedures