COSMOS: A continuous optimization approach for maximum power estimation of CMOS circuits

Maximum instantaneous power in VLSI circuits has a great impact on circuit's reliability and the design of power and ground lines. To synthesize highly reliable systems, accurate estimates of maximum power must be obtained in various design phases, Unfortunately, determining the input patterns to induce the maximum current (power) is essentially a combinatorial optimization problem. Even for circuits with small number of primary inputs (PI's), it is CPU time intensive to conduct exhaustive search in the input vector space. The only feasible way is to find good upper and lower bounds of the maximum power, and to make the gap between these two bounds as narrow as possible. In this paper, we present a continuous optimization approach to efficiently generate tight lower bounds of the maximum instantaneous power for CMOS circuits. In our approach. each primary input (PI) of the circuit is allowed to assume any real number between 0 and 1. Maximum power estimation far CMOS circuits is then transformed into a continuous optimization problem, in which a smooth function is maximized over a unit hypercube in the Euclidean space. The continuous problem can be solved efficiently to generate good lower bounds of the maximum power. Our experiments with ISCAS and MCNC benchmark circuits demonstrate the superiority of this approach. For all the circuits tested, the mean value of the ratio ''CPU time of the continuous optimization approach divided by CPU time of the simulation-based technique'' is equal to 0.41. For 60% of the circuits tested, our approach gives a better estimate (1.16 times larger, on an average) than the simulation-based technique does, Compared to the ATPG-based technique [3], the continuous optimization approach generates a tighter lower bound (1.19 times larger, on an average) of maximum power for 60% of all the circuits tested.