1 / 25

Multilevel Generalized Force-directed Method for Circuit Placement

Multilevel Generalized Force-directed Method for Circuit Placement. Tony Chan 1 , Jason Cong 2 , Kenton Sze 1 1 UCLA Mathematics Department 2 UCLA Computer Science Department. This work is partially supported by SRC, NSF, and ONR. Outline. A Brief History of mPL

eugene
Download Presentation

Multilevel Generalized Force-directed Method for Circuit Placement

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Multilevel Generalized Force-directed Method for Circuit Placement Tony Chan1, Jason Cong2, Kenton Sze1 1UCLA Mathematics Department 2UCLA Computer Science Department This work is partially supported by SRC, NSF, and ONR.

  2. Outline • A Brief History of mPL • Recent Progress in Analytical Placement • Our new contributions and enhancements [mPL5] • Generalization of force-directed method (GFD) • More accurate approximation of half-perimeter wirelength • More accurate computation of cell spreading forces • Systematic scaling of the cell spreading forces • Multilevel implementation of GFD • Overview of mPL multilevel framework • mPL5 framework • Conclusions UCLA VLSICAD LAB

  3. Relative Wirelength A Brief History of mPL • mPL 1.1 • FC-Clustering • added partitioning to legalization • mPL 1.0 [ICCAD00] • Recursive ESC clustering • NLP at coarsest level • Goto discrete relaxation • Slot Assignment legalization • Domino detailed placement UNIFORM CELL SIZE • mPL 2.0 • RDFL relaxation • primal-dual netlist pruning • mPL 3.0 [ICCAD 03] • QRS relaxation • AMG interpolation • multiple V-cycles • cell-area fragmentation • mPL 4.0 • improved DP • better coarsening • backtracking V-cycle NON-UNIFORM CELL SIZE • mPL 5.0 • Multilevel Force-Directed 2002 2003 year 2000 2001 2004 UCLA VLSICAD LAB

  4. Recent Progress on Analytical Placement • Force-directed method [Eisenmann and Johannes 98] • Efficient spreading force computation using a fast Poisson solver • Interleave with quadratic placement • Limitations: • Inaccurate objective function • Require ad hoc tuning of forces for good convergence • Aplace [Kahng and Wang 04] • More accurate approximation to half-perimeter wirelength • Log-sum-exp [Naylor. et al 01] • Solving the non-linear optimization problem in a multilevel framework • Limitations: • Local smoothing of density functions • Penalty formulation lumps all constraints together UCLA VLSICAD LAB

  5. Basic Formulation of Our Approach • Minimize the half-perimeter wirelength subject to even density constraint: UCLA VLSICAD LAB

  6. HPWL Log-Sum-Exp Quadratic Lp-norm Choices of Wirelength Objective Functions UCLA VLSICAD LAB

  7. Average bin density Equality constraint Average bin density = utilization ratio However, density function is highly non-smooth m v4 3 v5 v3 2 v6 v2 1 v7 v1 n 1 3 4 2 = a13(v7) = fractional area of cell v7 in bin B13 Bin based Density Formulation UCLA VLSICAD LAB

  8. Smoothing operator: Larger epsilon More local smoothing Slow convergence Smaller epsilon More global smoothing Faster convergence Smoothing Density Function UCLA VLSICAD LAB

  9. Smoothed Constrained WL Minimization Problem • Minimize smooth objective wirelength subject to smooth density function: UCLA VLSICAD LAB

  10. Solving Density Constrained WL Minimization • Using the Uzawa algorithm, we iteratively solve • can be viewed as “generalized force” • Advantages: • Individual scaling factor at each bin • Systematic updates of these scaling factors • No Hessian inversion is required UCLA VLSICAD LAB

  11. Summary of Generalized Force-directed (GFD) Algorithm • If initial solution not given: • Use unconstrained quadratic minimizer • Set stopping criterion • Iteratively solve: • Poisson equation to get forces • Updating the scaling factor (Lagrange multiplier) for forces based on the smoothed density • The nonlinear equation by stabilized fixed point iteration UCLA VLSICAD LAB

  12. Important Ingredients of GFD • Use of accurate objective functions • Optimization-based bin-density constraint formulation • Global smoothing of density function • Use of Uzawa algorithm enables: • Systematic bin-level adjustment of force-scaling factors • Convergence to a well defined solution via fixed-point iteration • Applying multilevel optimization can lead to better runtime and wirelength UCLA VLSICAD LAB

  13. Overview of mPL multilevel framework • Coarsening: build a hierarchy of problem approximations by First Choice clustering • Relaxation: improve the placement at each level by iterative optimization • Interpolation:transfer coarse-level solution to adjacent, finer level (AMG declustering) • Multilevel Flow: multiple traversals over multiple hierarchies (V-cycle variations) UCLA VLSICAD LAB

  14. Level 3 C+I C I I Level 2 C+I C I I Level 1 Level at which GFD is applied C Coasening I Interpolation mPL5 Framework Keep coarsening until # cells less than 500 UCLA VLSICAD LAB

  15. Improvement by Our Multilevel Framework Experiments carried out on ISPD2004 FastPlace IBM benchmarks. UCLA VLSICAD LAB

  16. Comparison on Standard Cell Designs Experiments carried out on ISPD2004 FastPlace IBM benchmarks. UCLA VLSICAD LAB

  17. Scalability Comparison mPL5-fast is slightly more scalable than FastPlace1.0 UCLA VLSICAD LAB

  18. Comparison on Mixed-Size Placement Benchmarks mPL5 has 18% shorter wirelength than Capo 9.0 mPL5 has 9 % shorter wirelength than Fengshui 5.0 Experiments carried out on ICCAD2004 Mixed-size benchmarks. UCLA VLSICAD LAB

  19. Placement Plot of Placers on ICCAD2004 Mixed-size IBM02 mPL5 Rel. WL = 1.00 Fengshui 5.0 Rel. WL = 1.11 Capo 9.0 Rel. WL = 1.17 UCLA VLSICAD LAB

  20. Placement Plot of Placers on ICCAD2004 Mixed-size IBM10 mPL5 Rel. WL = 1.00 Fengshui 5.0 Rel. WL = 1.15 Capo 9.0 Rel. WL = 1.28 UCLA VLSICAD LAB

  21. Results on PEKO Benchmarks UCLA VLSICAD LAB

  22. mPL5 placement on ICCAD2004 Mixed-size IBM02 UCLA VLSICAD LAB

  23. Conclusions • mPL5 is a highly scalable multilevel placer based on bin-density constrained optimization formulation • Provides a mathematically sound foundation for force-directed methods • mPL5 produces the best wirelength with competitive runtime on both standard cell and mixed-size designs. • 3% to 9% shorter WL on standard cell designs • 9% to 18% shorter WL on mixed size designs compared the best-known academic placers UCLA VLSICAD LAB

  24. Acknowledgement • Financially supported by SRC, NSF, and ONR. • Thank Min Xie for implementation of detailed placement • Thank Joseph Shinnerl and Min Xie for valuable discussions • Thank Chris Chu and Natarajan Viswanathan for providing ISPD04 FastPlace IBM benchmarks. UCLA VLSICAD LAB

  25. End of the Presentation Thank you! UCLA VLSICAD LAB

More Related