Existing statistical static timing analysis (SSTA) techniques suffer from limited modeling capability by using a linear delay model with Gaussian distribution, or have scalability problems due to expensive operations involved to handle non-Gaussian variation sources or non-linear delays. To overcome these limitations, we propose a novel SSTA technique to handle both nonlinear delay dependency and non-Gaussian variation sources simultaneously. We develop efficient algorithms to perform all statistical atomic operations (such as max and add) efficiently via either closedform formulas or one-dimensional lookup tables. The resulting timing quantity provably preserves the correlation with variation sources to the third-order. We prove that the complexity of our algorithm is linear in both variation sources and circuit sizes, hence our algorithm scales well for

Abstract — Post-fabrication tuning provides a promising design approach to mitigate the performance and power overheads of process variation in advanced fabrication technologies. This paper explores design considerations and VLSI-CAD support for a recently proposed postfabrication tuning knob called voltage interpolation. The paper discusses design tradeoffs between circuit tuning range and static power overheads that can be performed within the synthesis flow of the design process. The paper explores the scheme for a 64-core chip-multiprocessor machine using industrial-grade design blocks and shows that the scheme can be used to mitigate overhead arising from random and correlated within-die process variations. The analysis shows that the scheme can match the nominal delay target with a 10 % power cost, or for the same power budget, incur only a 9 % delay overhead after variations. I.

Abstract—This paper quantifies the approximation error when results obtained by Clark (Oper. Res., vol. 9, p. 145, 1961) are employed to compute the maximum (max) of Gaussian random variables, which is a fundamental operation in statistical timing. We show that a finite lookup table can be used to store these errors. Based on the error computations, approaches to different orderings for pairwise max operations on a set of Gaussians are proposed. Experimental results show accuracy improvements in the computation of the max of multiple Gaussians, in comparison to the traditional approach. In addition, we present an approach to compute the tightness probabilities of Gaussian random variables with dynamic runtime-accuracy tradeoff options. We replace required numerical computations for their estimations by closed form expressions based on Taylor series expansion that involve table lookup and a few fundamental arithmetic operations. Experimental results demonstrate an average speedup of 2 × using our approach for computing the maximum of two Gaussians, in comparison to the traditional approach, without any accuracy penalty. Index Terms—Computer-aided design (CAD), Gaussian approximation, statistical timing, very large-scale integration