An SMT-LIB Theory of Binary Floating-Point Arithmetic∗

Floating-point arithmetic is an essential ingredient of embedded systems, such as in the avionics and automotive industries. By nature, many of these applications are safety-critical, requiring rigorous mathematical methods such as model checking to verify the adherence to safety standards. One of the bottlenecks in comparing different approaches to the floating-point program verification problem is the lack of a standardised formal language to interface with SMT and constraint solvers. In this paper, we propose a theory, FPA, of floating-point arithmetic for the recently released SMT-LIB 2.0 standard. We rigorously define the semantics of FPA, following the IEEE binary floating-point standard 754-2008. We motivate our design decisions and deviations from the IEEE standard. The longterm goal is the development of SMT solvers with FPA support, as well as a set of FPA benchmarks in the SMT-LIB format that allow comparative studies of floating-point verification techniques.