Efficient Calculation of Timed Cumulative Probability Density Function

It is well known that critical paths of a design are rarely activated because sensitization of long paths requires appropriate values applied at appropriate time for many gates. Several researches use the concept of rare activation for performance optimization but they require the accurate probability information of rare activation. We define timed cumulative probability density function (Timed-CDF) to be the probability distribution of a circuit's delay induced by input patterns. Because a Timed-CDF is very useful for many applications, in this paper, we present an efficient way for constructing a Timed-CDF. Our basic idea utilizes a concept called timed characteristic function, which allows us to perform very fast parallel simulation rather than the traditional event-driven simulation. On average, our results are 6.18 times faster then the traditional simulation.