Adaptive Stochastic Collocation Method for Parameterized Statistical Timing Analysis with Quadratic Delay Model

Wang, Yi; Zeng, Xuan; Tao, Jun; Zhu, Hengliang; Cai, Wei

doi:10.1093/ietfec/e91-a.12.3465

Cited by 1 publication

(26 citation statements)

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“…Traditional Deterministic Static Timing Analysis (DSTA), which computes the circuit delay for a specific process condition, is unable to cope with a large process corner space [1]. An alternative approach that overcomes these problems is Statistical Static Timing Analysis (SSTA) [2]- [9], which treats delays of gates and interconnects not as fixed numbers, but as probability density functions.…”

Section: Introductionmentioning

confidence: 99%

“…SSTA methods can be categorized into path-based approaches [2], [3] and block-based approaches [4]- [9]. Pathbased SSTA methods require the enumeration of paths and suffer from the exponential number of paths with respect to the circuit size.…”

Section: Introductionmentioning

confidence: 99%

“…SUM is a linear operator and not difficult to be approximated, while MAX is nonlinear and the key operator of the block-based SSTA [1]. To approximate the MAX operator, two kinds of approaches have been proposed, i.e., moment match based methods [4], [6] and stochastic collocation methods [7]- [9]. Most of the available moment match based methods adopt the first two order moments to approximate the statistical MAX operator.…”

Section: Introductionmentioning

confidence: 99%

“…Most of the available moment match based methods adopt the first two order moments to approximate the statistical MAX operator. However, the first two order moments are not accurate enough to capture the nonlinear effect of MAX operator [8], [9]. In contrary to moment match based methods, stochastic collocation methods [7]- [9] approximate the MAX operator in the full random space by minimizing the mean square error, and offer much higher accuracy.…”

Section: Introductionmentioning

confidence: 99%

“…However, the first two order moments are not accurate enough to capture the nonlinear effect of MAX operator [8], [9]. In contrary to moment match based methods, stochastic collocation methods [7]- [9] approximate the MAX operator in the full random space by minimizing the mean square error, and offer much higher accuracy. In stochastic collocation methods [7]- [9], the random delays of gates and interconnects are modeled by quadratic polynomial chaos expansions.…”

Section: Introductionmentioning

confidence: 99%

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A Modified Nested Sparse Grid Based Adaptive Stochastic Collocation Method for Statistical Static Timing Analysis

Luo

Yang

Zeng

et al. 2009

IEICE Trans. Fundamentals

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In this paper, we propose a Modified nested sparse grid based Adaptive Stochastic Collocation Method (MASCM) for block-based Statistical Static Timing Analysis (SSTA). The proposed MASCM employs an improved adaptive strategy derived from the existing Adaptive Stochastic Collocation Method (ASCM) to approximate the key operator MAX during timing analysis. In contrast to ASCM which uses non-nested sparse grid and tensor product quadratures to approximate the MAX operator for weakly and strongly nonlinear conditions respectively, MASCM proposes a modified nested sparse grid quadrature to approximate the MAX operator for both weakly and strongly nonlinear conditions. In the modified nested sparse grid quadrature, we firstly construct the second order quadrature points based on extended Gauss-Hermite quadrature and nested sparse grid technique, and then discard those quadrature points that do not contribute significantly to the computation accuracy to enhance the efficiency of the MAX approximation. Compared with the non-nested sparse grid quadrature, the proposed modified nested sparse grid quadrature not only employs much fewer collocation points, but also offers much higher accuracy. Compared with the tensor product quadrature, the modified nested sparse grid quadrature greatly reduced the computational cost, while still maintains sufficient accuracy for the MAX operator approximation. As a result, the proposed MASCM provides comparable accuracy while remarkably reduces the computational cost compared with ASCM. The numerical results show that with comparable accuracy MASCM has 50% reduction in run time compared with ASCM.

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Section: Introductionmentioning

confidence: 99%