Integrating proxy theories and numeric model lifting for floating-point arithmetic

Precise reasoning for floating-point arithmetic (FPA) is as critical for accurate software analysis as it is hard to achieve. Several recent approaches reduce solving an FPA formula f to reasoning over a related but easier-to-solve proxy theory. The rationale is that a satisfying proxy assignment may directly correspond to a model for f. But what if it doesn't? Prior work deals with this case somewhat crudely, or discards the proxy assignment altogether. In this paper we present an FPA decision framework, parameterized by the choice of proxy theory T, that attempts to lift an encountered T model to a numerically close FPA model. Other than assuming some “proximity” of T to FPA, our lifting procedure is T-agnostic; it is in fact designed to work independently of how the proxy assignment was obtained. Should the lifting fail, our procedure gradually reduces the gap between the FPA and the proxy interpretations of f. We have instantiated the framework using real arithmetic and reduced-precision FPA as proxy theories, and demonstrate that we can, in many cases, decide f more efficiently than earlier work.