GTFUZZ: A novel algorithm for robust dynamic power optimization via gate sizing with fuzzy games

As CMOS technology continues to scale, the effects of variation inject a greater proportion of error and uncertainty into the design process. Ultra-deep submicron circuits require accurate modeling of gate delay in order to meet challenging timing constraints. With the lack of statistical data, designers are faced with a arduous task to optimize a circuit which is greatly affected by variability due to the mechanical and chemical manufacturing process. Discrete gate sizing is a complex problem which requires (1) accurate models that take into account random parametric variation and (2) a fair allocation of resources to maximize the solution in the delay-energy space. The GTFUZZ algorithm is presented which handles both of these tasks. Fuzzy games are used to model the problem of gate sizing as a resource allocation problem. In fuzzy games, delay is considered a fuzzy goal with fuzzy parameters to capture the imprecision of gate delay early in the design phase when empirical data is absent. Dynamic power is normalized as a fuzzy goal without varying coefficients. The fuzzy goals also provide a flexible platform for multimetric optimization. The robust GTFUZZ (Fuzzy Game Theory) algorithm is compared against fuzzy linear programming (FLP) and deterministic worst-case FLP (DWCFLP) algorithms. 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 most critical paths using HSPICE.