Analytical Clustering Score with Application to Postplacement Register Clustering

Circuit clustering is usually done through discrete optimizations to enable circuit size reduction or design-specific cluster formation. In this article, we are interested in the register-clustering technique for clock-power reduction by leveraging new opportunities introduced by multibit flip-flop (MBFF). Currently, INTEGRA is the only existing postplacement MBFF clustering optimizer with a subquadratic time complexity. However, it severely degrades the wirelength, especially for realistic designs, which may nullify the benefits of MBFF clustering. In contrast, we formulate an analytical clustering score with a nonlinear programming framework, in which the wirelength objective can be seamlessly integrated and the solver has empirical subquadratic time complexity. With the MBFF library, the application of our analytical clustering method achieves comparable clock power to the state-of-the-art techniques, but further reduces the wirelength by about 25%. Even without the MBFF library, we can still achieve 30% clock wirelength reduction. In addition, the proposed method can potentially be integrated into an in-placement MBFF clustering solver and be applied to other problems that require formulating clustering scores in their objective functions.