Robust, Low Power, Discrete Gate Sizing

Ultra-deep submicron circuits require accurate modeling of gate delay in order to meetaggressive timing constraints. With the lack of statistical data, variability due to the mechanical manufacturing process and its chemical properties poses a challenging problem. Discrete gate sizing requires (i) accurate models that take into account random parametric variation and (ii) a fair allocation of resources to optimize the solution. The proposed GTFUZZ gate sizing algorithm handles both tasks. Gate sizing is modeled as a resource allocation problem using fuzzy game theory. Delay is modeled as a constraint and power is optimized in this algorithm. In GTFUZZ, delay is modeled as a fuzzy goal with fuzzy parameters to capture the imprecision of gate delay early in the design phase when extensive empirical data is absent. Dynamic power is modeled as a fuzzy goal without varying coefficients. The fuzzy goals provide a flexible platform for multimetric optimization. The robust GTFUZZ algorithm is compared against fuzzy linear programming (FLP) and deterministic worst-case FLP (DWCFLP) algorithms. The benchmark circuits are first synthesized, placed, routed, and optimized for performance using the Synopsys University 32/28nm standard cell library and technology files. Operating at the optimized clock frequency, results show an average power reduction of about 20% versus DWCFLP and 9% against variation-aware gate sizing with FLP. Timing and timing yield are verified by both Synopsys PrimeTime and Monte Carlo simulations of the critical paths using HSPICE