Using Machine Learning to Predict Path-Based Slack from Graph-Based Timing Analysis

Abstract

With diminishing margins in advanced technology nodes, accuracy of timing analysis is a serious concern. Improved accuracy helps to reduce overdesign, particularly in P&R-based optimization and timing closure steps, but comes at the cost of runtime. A major factor in accurate estimation of timing slack, especially for low-voltage corners, is the propagation of transition time. In graph-based analysis (GBA), worst-case transition time is propagated through a given gate, independent of the path under analysis, and is hence pessimistic. The timing pessimism results in overdesign and/or inability to fully recover power and area during optimization. In path-based analysis (PBA), pathspeci?c transition times are propagated, reducing pessimism. However, PBA incurs severe (4X or more) runtime overheads relative to GBA, and is often avoided in the early stages of physical implementation. With numerous operating corners, use of PBA is even more burdensome. In this paper, we propose a machine learning model, based on bigrams of path stages, to predict expensive PBA results from relatively inexpensive GBA results. We identify electrical and structural features of the circuit that affect PBA-GBA divergence with respect to endpoint arrival times. We use GBA and PBA analysis of a given testcase design along with arti?cially generated timing paths, in combination with a classi?cation and regression tree (CART) approach, to develop a predictive model for PBA-GBA divergence. Empirical studies demonstrate that our model has the potential to substantially reduce pessimism while retaining the lower turnaround time of GBA analysis. For example, a model trained on a post-CTS and tested on a post-route database for the leon3mp design in 28nm FDSOI foundry enablement reduces divergence from true PBA slack (i.e., model prediction divergence, versus GBA divergence) from 9.43ps to 6.06ps (mean absolute error), 26.79ps to 19.72ps (99th percentile error), and 50.78ps to 39.46ps (maximum error).