A Provably Good and Practically Efficient Algorithm for Common Path Pessimism Removal in Large Designs

Abstract

Common path pessimism removal (CPPR) is imperative for eliminating redundant pessimism during static timing analysis (STA). However, turning on CPPR can significantly increase the analysis runtime by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$10\times $ </tex-math></inline-formula> – <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$100\times $ </tex-math></inline-formula> in large designs. Recent years have seen much research on improving the algorithmic efficiencies of CPPR, but most are architecturally constrained by either the speed–accuracy tradeoff or design-specific pruning heuristics. In this article, we introduce a novel CPPR algorithm that is provably good and practically efficient. We have evaluated our algorithm on large industrial designs and demonstrated promising performance over the current state of the art. As an example, our algorithm outperforms the baseline by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$36\times $ </tex-math></inline-formula> – <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$135\times $ </tex-math></inline-formula> faster when generating the top-10K post-CPPR critical paths on a million-gate design. At the extreme, our algorithm with one core is even <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4\times $ </tex-math></inline-formula> – <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$16\times $ </tex-math></inline-formula> faster than the baseline with eight cores. Our algorithm also outperforms the commercial STA engine PrimeTime up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$26.99\times $ </tex-math></inline-formula> faster. By exploiting parallelism within the circuit graph, we can reduce the memory consumption of our algorithm by 30%, with only 3% runtime increase.