Radial basis functions based algorithms for non-gaussian delay propagation in very large circuits

Abstract

In this paper, we discuss methods for determining delay distributions in modern Very Large Scale Integration design. The delays have a non-Gaussian nature, which is a challenging task to solve and is a stumbling block for many approaches. The problem of finding delays in VLSI circuits is equivalent to a graph optimisation problem. We propose algorithms that aim at fast and very accurate calculations of statistical delay distributions. The speed of execution is achieved by utilising previously obtained analytical results for delay propagation through one logic gate. The accuracy is achieved by preserving the shapes of non-Gaussian delay distribution while traversing the graph of a circuit. The discussion on the methodology to handle non-Gaussian delay distributions is the core of the present study. The proposed algorithms are tested and compared with delay distributions obtained through Monte Carlo simulations, which is the standard verification procedure for this class of problems.