i n v e n t i v ei n v e n t i v e a morphing approach to address placement stability philip chong...
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I N
V E
N T
I V
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A Morphing Approach To Address Placement Stability
Philip Chong
Christian Szegedy
March 20, 2007 2
Overview
• Motivation/Background• Our Algorithm• Results/Conclusions• Future Work
March 20, 2007 3
Motivation
• Design process has become tremendously complex– Timing, power, noise/crosstalk, manufacturability, etc. play
increasingly important roles
• Placement must account for all these metrics• Pure “top-down” design flow impossible
– Impossible to predict physical effects prior to placement
• Iteration and incremental design are critical for closure• Need to have stability in placement
– Also need stability throughout entire design flow
March 20, 2007 4
Stability
• An algorithm is stable if, when given two similar inputs, it produces two similar outputs– A small change in the input only causes a small change in the
output
• Stability is necessary to be able to obtain closure in an incremental design flow– E.g. a single buffer insertion should not cause a significant
change in the layout
March 20, 2007 5
Our Work
• We have developed a global placement approach called grid morphing which focuses on stability and is targeted towards an incremental design flow
March 20, 2007 6
Existing Work
• Brenner, Vygen, “Legalizing A Placement With Minimum Total Movement”, IEEE Trans. CAD, Dec. 2004– Optimizes total absolute perturbation; we optimize relative
perturbation
• Ren et al, “Diffusion-based Placement Migration”, DAC 2005– Focus on final placement stage and less efficient; we look at
global placement and are more efficient
• Xiu et al, “Large-scale Placement By Grid-Warping”, DAC 2004– Inefficient non-linear formulation and restricted to
quadrisectioning; we have a more efficient approach which optimizes over a global grid
March 20, 2007 7
Overall Placement Flow
Start
Initial QP Solution
Grid Morphing
Local Optimization
Evenly Spread?
Final Placement
Stop
N
March 20, 2007 8
Grid Morphing Overview
• All cell movements are computed using an ordinary bilinear transform
March 20, 2007 9
Grid Morphing Example
InitialPlacement
After FirstMorphing
After SecondMorphing
After FirstIteration
March 20, 2007 10
Morphing Formulation
• Find new control points for the grid which minimizes distortion relative to the original grid
• Tiles in new grid must be large enough to fit their contained gates
• Difficulty: Straightforward Lagrangian relaxation using subgradient method yields poor convergence
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March 20, 2007 11
Our Approach
• Based on an intuitive physical model• Imagine each tile is a flexible container for some gas
under pressure proportional to its placement utilization• Walls between containers move to equalize the pressure
between them• Containers under high pressure expand to occupy a
larger volume, containers under low pressure are squished to occupy a smaller volume
March 20, 2007 12
Control Point Movement
• First move border points according to pressures• Then move control points according to border point
movements
March 20, 2007 13
Algorithmic Improvements
• Multilevel Morphing– Improve runtime: Start with a coarse grid, solve the morphing
problem, then use the solution as an initial solution for a finer grid
• Maximum Blowup Control– Improve stability: Limit the Aj values so that no one grid tile
expands too greatly in one iteration
March 20, 2007 14
Algorithmic Improvements (cont.)
• Netlength Guided Morphing– Improve netlength: First estimate sensitivity of wirelength to grid
control point positions (i.e. how much wirelength degrades when a control point is moved), then add penalty terms to the optimization objective function weighted by the sensitivities
• Local Optimization– Improve netlength: After each iteration perform greedy
optimization of netlength
March 20, 2007 15
Comparison With MetaPlacer
MetaPlacer
Our Placer
Original 10% Resized 20% Resized
March 20, 2007 16
Placement Results
• Net perturbation (Alpert et al, ASPDAC 2005):
• Run times: MetaPlacer 2-3 hours, Our Placer <1 hour
Placement Net Len Avg Pert RMS Pert Max PertMeta Orig 1.10E+11Meta 10% 1.16E+11 1.19E+06 9.87E+06 3.49E+09Meta 20% 1.20E+11 1.20E+06 9.08E+06 2.88E+09
Our Orig 1.02E+11Our 10% 1.06E+11 6.34E+05 3.59E+06 1.01E+09Our 20% 1.09E+11 6.45E+05 3.74E+06 1.18E+09
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March 20, 2007 17
Perturbation Distributions
MetaPlacer Our Placer
5218 1790
• Often makes sense to reduce largest perturbations at the expense of introducing many tiny movements
March 20, 2007 18
Perturbation Maps
MetaPlacer
Our Placer
10% Resized 20% Resized
March 20, 2007 19
Future Work
• More testcases– Wider variety of designs– Examine effect of different kinds of incremental changes– Comparisons with other placers
• Incorporate different metrics– Timing, routability, crosstalk, manufacturability, etc.
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