On the futility of statistical power optimization

In response to the increasing variations in integrated-circuit manufacturing, the current trend is to create designs that take these variations into account statistically. In this paper we try to quantify the difference between the statistical and deterministic optima of leakage power while making no assumptions about the delay model. We develop a framework for deriving a theoretical upper-bound on the suboptimality that is incurred by using the deterministic optimum as an approximation for the statistical optimum. On average, the bound is 2.4% for a suite of benchmark circuits in a 45 nm technology. We further give an intuitive explanation and show, by using solution rank orders, that the practical suboptimality gap is much lower. Therefore, the need for statistical power modeling for the purpose of optimization is questionable.