Rectification of Integer Arithmetic Circuits using Computer Algebra Techniques

This paper proposes a symbolic algebra approach for multi-target rectification of integer arithmetic circuits. The circuit is represented as a system of polynomials and rectified against a polynomial specification with computations modeled over the field of rationals. Given a set of nets as potential rectification targets, we formulate a check to ascertain the existence of rectification functions at these targets. Upon confirmation, we compute the patch functions collectively for the targets. In this regard, we show how to synthesize a logic sub-circuit from polynomial artifacts generated over the field of rationals. We present new mathematical contributions and results to substantiate this synthesis process. We present two approaches for patch function computation: a greedy approach that resolves the rectification functions for the targets and an approach that explores a subset of don’t care conditions for the targets. Our approach is implemented as custom software and utilizes the existing open-source symbolic algebra libraries for computations. We present experimental results of our approach on several integer multipliers benchmark and discuss the quality of the patch sub-circuits generated.