We propose a scalable and efficient parameterized block-based statistical static timing analysis algorithm incorporating both Gaussian and non-Gaussian parameter distributions, capturing spatial correlations using a grid-based model. As a preprocessing step, we employ independent component analysis to transform the set of correlated non-Gaussian parameters to a basis set of parameters that are statistically independent, and principal components analysis to orthogonalize the Gaussian parameters. The procedure requires minimal input information: given the moments of the variational parameters, we use a Pade approximation-based moment matching scheme to generate the distributions of the random variables representing the signal arrival times, and preserve correlation information by propagating arrival times in a canonical form. For the ISCAS89 benchmark circuits, as compared to Monte Carlo simulations, we obtain average errors of 0.99% and 2.05%, respectively, in the mean and standard deviation of thecircuit delay. For a circuit with G gates and a layout with g spatial correlation grids,the complexity of our approach is O(gG).
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机译:我们提出了一种可扩展且高效的基于参数的基于块的统计静态时序分析算法,该算法结合了高斯和非高斯参数分布,并使用基于网格的模型来捕获空间相关性。作为预处理步骤,我们使用独立成分分析将相关的非高斯参数集转换为统计上独立的基本参数集,并使用主成分分析将高斯参数正交化。该过程需要最少的输入信息:给定变分参数的矩,我们使用基于Pade近似的矩匹配方案来生成表示信号到达时间的随机变量的分布,并通过在规范中传播到达时间来保留相关信息。形式。对于ISCAS89基准电路,与蒙特卡罗模拟相比,我们获得的平均延迟分别为0.99%和2.05%,电路延迟的平均值和标准偏差。对于具有 G I>个门和具有 g I>个空间相关网格的布局的电路,我们方法的复杂度为 O I>( g I> G I>)。
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