Eyecharts: Constructive benchmarking of gate sizing heuristics

Discrete gate sizing is one of the most commonly used, flexible, and powerful techniques for digital circuit optimization. The underlying problem has been proven to be NP-hard. Several (suboptimal) gate sizing heuristics have been proposed over the past two decades, but research has suffered from the lack of any systematic way of assessing the quality of the proposed algorithms. We develop a method to generate benchmark circuits (called eyecharts) of arbitrary size along with a method to compute their optimal solutions using dynamic programming. We evaluate the suboptimalities of some popular gate sizing algorithms. Eyecharts help diagnose the weaknesses of existing gate sizing algorithms, enable systematic and quantitative comparison of sizing algorithms, and catalyze further gate sizing research. Our results show that common sizing methods (including commercial tools) can be suboptimal by as much as 54% (V
_t
-assignment), 46% (gate sizing) and 49% (gate-length biasing) for realistic libraries and circuit topologies.