A Multi-width Parametric Bitvector Equivalence Solver

Abstract

Abstract At the core of modern electronic design automation (EDA) tools is rewriting : a mechanism by which local transformations are iteratively applied to circuits to make them faster and more efficient. These rewrites are crucial for producing high-quality hardware, and they often depend on extremely delicate conditions, relating, for example, to the widths of the various bitvectors involved. As such, it is both desirable and difficult to prove them correct. Prior work has studied the correctness of parametric-bitwidth rewrites in the context of software compilers and SMT solvers, but those approaches struggle to handle rewrites that have multiple bitwidth parameters, as are commonplace in EDA. We propose a language for expressing these multi-width parametric rewrites and provide a translation into equivalences in modular arithmetic. We then show how these equivalences can be automatically and efficiently proved using equality saturation over a set of carefully chosen axioms, and finally reconstructed automatically as theorems in Isabelle. This process is implemented in our solver, ParaBit. Using benchmarks from prior compilers work and from industrial EDA tools, we demonstrate that ParaBit can solve a class of problems that are intractable using existing techniques.