Integrated ESOP Refactoring for Industrial Designs

We present a multi-level logic refactoring algorithm based on exclusive sum-of-product (ESOP) expressions. ESOP expressions are two-level logic representation forms, similar to sum of -product (SOP) expressions. However, ESOPs use EXOR instead of OR operators. It has been shown that this allows ESOPs to be exponentially more compact than SOP expressions for important classes of functions. Our algorithm is based on a combination of ESOP collapsing, minimization, and refactoring. In EXOR-heavy logic, such as arithmetic units, it unlocks optimizations that may be outside the reach of SOP based methods. We show that our method is able to significantly improve upon logic optimization results, as compared to a similar SOP based flow. On a set of EXOR-heavy benchmarks, we reduce logic levels by up to 833% in the best case, and by 44.6% on average. Further, we are able to reduce logic network size by 21.4% on average. We have integrated our method into a commercial synthesis flow. On a set of 46 industrial benchmarks, the optimizations introduced by our algorithm improve design results after physical synthesis.