Speeding up computation of the max/min of a set of Gaussians for statistical timing analysis and optimization

Statistical static timing analysis (SSTA) involves computation of maximum (max) and minimum (min) of Gaussian random variables. Typically, the max or min of a set of Gaussians is performed iteratively in a pair-wise fashion, wherein the result of each pair-wise max or min operation is approximated to a Gaussian by matching moments of the true result obtained using Clark's approach [1]. The approximation error in the final result is thus a function of the order in which the pairwise operations are performed. In this paper, we analyze known “run-time expensive” ordering techniques that attempt to reduce this error in the context of SSTA and SSTA driven optimization. We propose new techniques to speeding up the computation of the max/min of a set of Gaussians by special handling of prevalent “zero error” cases. Two new methods are presented using these techniques that provide more than 60% run-time savings (3X speed-up) in max/min operations. This translates to an overall run-time improvement of 2-17% for a single SSTA run and an improvement of up to 8 hours (55%) in an SSTA driven optimization run.