MIP-based Detailed Placer for Mixed-size Circuits Shuai Li, Cheng-Kok Koh ECE, Purdue University {li263,

Outline Motivation Incomplete SCP model Experimental results Summary

Background Placement minimize total wirelength, estimated with half parameter wirelength (HPWL) routability-driven placement avoid routing congestion Global placement optimized approximate locations; Detailed placement after legalization; rearrange cells to reduce HPWL

Detailed placement cell swap/move technique FastPlace-DP, global and vertical cell swap/move congestion-aware FastPlace-DP, routability-driven placers sliding window technique partition the whole chip into overlapping windows moving cells locally in windows has less perturbance to routability enumeration approach; solution space O(n!) for n -cell window; windows with no more than 6 cells alternative approaches to optimize larger windows branch-and-bound technique, cell matching technique, etc.

MIP approach for detailed placement Mixed Integer Programming (MIP) approach placement of each window is formulated into an MIP problem: linear objective function & linear constraints; integer variables mature mathematical techniques for solving MIP problems a branch-and-bound tree is built during solution, whose size is dependent on the number of integer variables MIP models for detailed placement the S model, the RQ model, the SCP model the single-cell-placement (SCP) model over 10 times more efficient than the other MIP models

MIP-based detailed placer Parallelized MIP-based detailed placer IBM Version 2 benchmark circuits Initial placement results generated with enumeration approach; 1.684% further reduction in HPWL; 0.827% and 1.707% further reduction in routed wirelength and via count, respectively. Apply it to recent mixed-size circuits? benchmark circuits in ISPD11, DAC12, ICCAD12 routability-driven contests

IBM Version 2 DAC12 Challenges with recent mixed-size circuits DAC12 benchmark circuits n.c. number of cells o.r. occupation rate, the rate that sites are occupied by cells 400 extracted 10-cell windows n.s. average number of sites n.v. average number of integer variables in SCP model;

Our contribution DAC12 benchmark circuits over 10 times more cells over 2 times more sites in sliding windows over 10 times increase in solution time of each window Incomplete SCP model ignore a portion of integer variables in SCP model great reduction in solution time without much degradation in solution quality MIP-based detailed placer for DAC12 benchmark circuits

Outline Motivation Incomplete SCP model Experimental results Summary

Problem description Objective: minimize HPWL Constraints: 1. no cell overlap; 2. each cell is placed legally, i.e. cell c occupies exactly w c consecutive sites in one row R : set of rows Q : set of columns C : set of cells w c : width of cell c N : set of nets

Single-cell-placement variables single-cell-placement (SCP) variable: whether the kth pattern to place single cell c is chosen or not Single-cell-placement patterns and corresponding vectors e.g. cell 1 in the 3X7 window; |R|(|Q|-w c +1)= 18 variables in all

SCP Model (llx n, lly n, urx n, ury n ): bounding box of net n ; (x c, y c ): centroid of cell c; p crq : whether cell c occupies the site at row r and column q definition of bounding box site occupation cell centroid and site occupation variables derived from SCP variables one pattern for each cell

Incomplete SCP Model definition of bounding box site occupation cell centroid and site occupation variables derived from SCP variables one pattern for each cell skipping patterns

Incomplete SCP Model (contd) o c = 1, when skip =3, only the 1 st, 4 th, 7 th, 10 th, 13 th, 16 th are kept e.g. cell 1 in the 3X7 window; |R|(|Q|-w c +1)= 18 variables in all

Incomplete SCP Model (contd) Guideline to set skip exact locations in the solution may be non-optimal guarantee different orders of placing cells are still in the solution space skip=1 for compact windows; larger skip for sparse windows with low occupation rate (ocp_rt) and more empty sites

Two incomplete SCP models Number of variables for cell c in SCP model: v c is close to summation of cell width, the same as in the SCP model of placing the same cells in a compact window SCP_ES model, set skip based on number of empty sites In compact windows, skip =1 In sparse windows with ocp_rt close to 0.0, v c is close to |C|, the same as in the SCP model of placing the same number of uniform-width cells SCP_OR model, set skip based on occupation rate

Outline Motivation Incomplete SCP model Experimental results Summary

Effect of incomplete models tolerance time 40s, 60s, 800s for 8-cell, 10-cell, 12-cell windows SCP_OR model, a good compromise of the SCP model fewer than a half integer variables (n.v. ) over 6 times faster (t(s)), within 10% degradation in HPWL reduction (red.) SCP_ES model 1/5 variables, 100 times faster with 40% degradation used in our parallelized MIP-based detailed placer Enumeration approach (ENUM) few windows are optimized with the same tolerance time

Results on DAC12 benchmark circuits MIP-based detailed placer 2-row and 4-row windows with no more than 10 cells windows are scanned for 3 times Initial placement results generated by different placers Ripple NTUPlace4 Two commercial routers to generate detailed routing solutions Router A, Router B existing translator from Bookshelf files to LEF/DEF files W.-H. Liu et al. Case study for placement solutions in ISPD11 and DAC12 routability-driven placement contests. In Proc. ISPD, pages 114–119, 2013.

Effects on Ripples results INIT: initial results generated with congestion-aware FastPlace-DP MIP: results after MIP-based detailed placer Router A WL(e7): routed wirelength VIA(e7): via count VIO: number of detailed routing violations T(m): routing run-time OF: overflows in global routing

Effects on NTUPlace4s results INIT: initial results generated with cell matching technique MIP: results after MIP-based detailed placer Router A WL(e7): routed wirelength VIA(e7): via count VIO: number of detailed routing violations T(m): routing run-time OF: overflows in global routing

Effects on Ripples results INIT: initial results generated with congestion-aware FastPlace-DP MIP: results after MIP-based detailed placer Router B

Effects on NTUPlace4s results INIT: initial results generated with cell matching technique MIP: results after MIP-based detailed placer Router B

Outline Motivation Incomplete SCP model Experimental results Summary

MIP approach for detailed placement optimize larger sliding windows to further reduce wirelength Application in recent large-scale benchmark circuits Over 10 times more cells; Lower occupation rate leading to significant increase in the solution time of each window Incomplete SCP model ignore variables to significantly decrease solution time; Despite degradation in solution quality, still effective reduction in wirelength is achieved without perturbance of routability

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Large-scale mixed-size circuits #cellt(s)opt ibm01 8-cell % 10-cell % 12-cell % s16 8-cell % 10-cell % 12-cell % Over 300 randomly extracted windows for each size ibm01: IBM Version 2 benchmark tolerance time 40s s16: DAC12 benchmark tolerance time 40s, 60s, 800s for 8-cell, 10-cell, 12-cell windows, respectively longer average solution time t(s) lower optimization rate opt Larger solution space for windows with more empty sites 1-row window with n cells and m empty sites More integer variables in MIP results in the increase of solution time