Path criticality computation in parameterized statistical timing analysis

  • Authors:
  • Jaeyong Chung;Jinjun Xiong;Vladimir Zolotov;Jacob A. Abraham

  • Affiliations:
  • The University of Texas at Austin, Austin, TX;IBM Research Center, Yorktown Heights, NY;IBM Research Center, Yorktown Heights, NY;The University of Texas at Austin, Austin, TX

  • Venue:
  • Proceedings of the 16th Asia and South Pacific Design Automation Conference
  • Year:
  • 2011

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Abstract

This paper presents a method to compute criticality probabilities of paths in parameterized statistical static timing analysis (SSTA). We partition the set of all the paths into several groups and formulate the path criticality into a joint probability of inequalities. Before evaluating the joint probability directly, we simplify the inequalities through algebraic elimination, handling topological correlation. Our proposed method uses conditional probabilities to obtain the joint probability, and statistics of random variables representing process parameters are changed due to given conditions. To calculate the conditional statistics of the random variables, we derive analytic formulas by extending Clark's work. This allows us to obtain the conditional probability density function of a path delay, given the path is critical, as well as to compute criticality probabilities of paths. Our experimental results show that the proposed method provides 4.2X better accuracy on average in comparison to the state-of-art method.