Fast statistical timing analysis handling arbitrary delay correlations

Abstract

An efficient statistical timing analysis algorithm that can handle arbitrary (spatial and structural) causes of delay correlation is described. The algorithm derives the entire cumulative distribution function of the circuit delay using a new mathematical formulation. Spatial as well as structural correlations between gate and wire delays can be taken into account. The algorithm can handle node delays described by non-Gaussian distributions. Because the analytical computation of an exact cumulative distribution function for a probabilistic graph with arbitrary distributions is infeasible, we find tight upper and lower bounds on the true cumulative distribution. An efficient algorithm to compute the bounds is based on a PERT-like single traversal of the sub-graph containing the set of N deterministically longest paths. The efficiency and accuracy of the algorithm is demonstrated on a set of ISCAS'85 benchmarks. Across all the benchmarks, the average rms error between the exact distribution and lower bound is 0.7%, and the average maximum error at 95th percentile is 0.6%. The computation of bounds for the largest benchmark takes 39 seconds.