Density-aware Detailed Placement with Instant Legalization Sergiy Popovych , Hung-Hao Lai, Chieh-Min Wang, Yih-Lang Li, Wen-Hao Liu, Ting-Chi Wang Outline • • • • • Introduction Problem Formulation Algorithm Experiment Result Conclusion Introduction • Modern placement process involves global placement, legalization, and detailed placement. • Global placement produce a placement solution with minimized target objective, which is usually wire-length, routability, timing, etc. Introduction • Legalization removes cell overlap and aligns the cells to the placement sites. • Detailed placement further improves the solution by relocating cells. Introduction • Since target objectives like wire-length and timing are optimized in global placement, legalization and detailed placement should not only minimize their own objectives but also preserve the global placement solution. Problem Formulation • Given a legal placement with a set of fixed macros and a set of movable cells, our algorithm move the standard cell legally to minimize the total HPWL , with consideration of user-specific placement density and maximum displacement constraint. Problem Formulation Scaled-HPWL: • OFP(Γ) denotes the overfill penalty of the top Γ% congested bins, and ABU(Γ) denotes the average bin utilization of the top Γ% congested bins. • sHPWL denotes the scaled HPWL, α is a user defined constant, AOFP denotes the weighted average of OFP(2), OFP(5), OFP(10), and OFP(20). Moving cell into a region • The basic idea of the swapping procedure: • 1) choose a set of candidate swap targets in the given region. • 2) find a number of swap target candidates, which are expected to improve them solution quality. • 3) swap the target cell with one of the swap targets found. Moving cell into a region Density-aware profit estimation • BraveDP computes the profit from swapping a cell c and a swap target t by the following equation: • ΔHPWL and ΔAOFP respectively denote the HPWL change and overfill penalty change after the swap. • OVc,t denotes the overlap penalty. • The computation of ΔAOFP is more complicated. • We use the following equation to predict the AOFP after swapping a cell c and a swap target t: • ABUct(Γ) denotes the ABU(Γ) after the swap, C is the set of bins whose densities will change after the swap. • Δd(b, Γ) denotes the effect of the density change of the bin b after the swap on the ABU(Γ). • The computation for Δd(b, Γ) can be classified into four cases. • • • • • nΓ denotes Γ% of the total number of bins. d(b) denotes the density of bin b before the swap. dct(b) denotes the density of bin b after the swap. dlow(Γ) denotes the lowest density among the bins in B(Γ). dhigh(!Γ) denotes the highest density among the bins not in B(Γ). Instant legalization and move reversal • We use very fast local legalizations, which are applied after each swap and keep the solution legal at all times. • The most important advantage of the instant legalization is that it allows the legalization consequences to be seen immediately after a swap. Design Flow • Optimal-Region Based Swap: – Optimal-Region Based Swap is applied to every cell which is not inside its optimal region already. • HPWL-Driven Swap: – We first identify cells which are placed poorly with respect to HPWL. – We evaluate the HPWL-wise optimality of the cell position by measuring the distance from the cell to its optimal region. • Density Driven Swap – Density-Driven Swap aims at improving the solution quality by identifying the cells which are placed poorly with respect to bin density, and trying to move them to positions that are suited to balance bin density. Experimental results • Our implementation is written in C++ and is compiled with g++ 4.1.2. All the benchmarks are run on a quad-core 2.4 GHz Xeon-based Linux server with 80GB RAM. Conclusion • This work develops a high quality cell swap based detailed placer. • The placer presented uses instant legalization and swap reversal technique, which allows it to efficiently control the maximal displacement constraint and solution quality deterioration during legalization. • The placer presented produces the best placement results among the top3 teams in the ICCAD13 contest.