mPL 5 Overview ISPD 2005 Placement Contest Entry Tony Chan2, Jason Cong1, Joe Shinnerl1, Kenton Sze2, Michalis Romesis1, Min Xie1 1VLSI CAD Lab, Computer Science Department 2Mathematics Department University of California, Los Angeles http://cadlab.cs.ucla.edu/~cong cong@cs.ucla.edu

Multiscale Optimization Framework Given problem Coarsening (Clustering) Problem size decreases Interpolation & Relaxation (optimization) Explores different scales of the solution space at different levels Supports VERY FAST and SCALABLE methods Supports inclusion of complicated objectives and constraints Successful across MANY DIVERSE applications 12/9/2018 UCLA VLSICAD LAB

Multiscale Placement Vocabulary Coarsening: build a hierarchy of problem approximations by generalized recursive clustering (or partitioning) Relaxation: improve the placement at each level by iterative optimization Interpolation: transfer coarse-level solution to adjacent, finer level (generalized declustering) Multilevel Flow: multiple traversals over multiple hierarchies (V-cycle variations) 12/9/2018 UCLA VLSICAD LAB

A Brief History of mPL UNIFORM CELL SIZE NON-UNIFORM CELL SIZE 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 2000 2001 2002 2003 2004 year 12/9/2018 UCLA VLSICAD LAB

Coarsening by Recursive Aggregation First-Choice Clustering (hMetis [Karypis 1999]). Merged Nets Merge each vertex with its “best” neighbor 12/9/2018 UCLA VLSICAD LAB

Weighted Interpolation (Generalized Declustering) Transfer a partial solution from a coarser level to its adjacent finer level Place a component ( ) at the weighted average of the positions of the clusters containing its neighbors Place representative components Place others by weighted interpolation 12/9/2018 UCLA VLSICAD LAB

mPL5 Generalized Force-Directed Placement Smooth the density constraints by solving a Helmholtz Equation: Assume Neumann boundary conditions: forces pointing outside the chip boundary are zero: Log-sum-exp smooth approximation to half-perimeter wirelength [Naylor 2001; Kahng and Wang 2004]: 12/9/2018 UCLA VLSICAD LAB

mPL5 Nonlinear-Programing Solution Using the Uzawa algorithm to solve the above nonlinear constrained minimization problem, we iteratively solve No matrix storage and no second derivatives are computed. Separate updates for separate lagrange multipliers; the bin-density constraints are NOT lumped together Use multilevel approach to speed-up computation and better quality 12/9/2018 UCLA VLSICAD LAB

Iterated Multilevel Flow Make use of placement solution from 1st V-cycle Geometric based FC clustering First Choice (FC) clustering 12/9/2018 UCLA VLSICAD LAB

Legalization The Patoma flow for guaranteed legalizability (ASPDAC 2005) is not needed for the ISPD05 contest benchmarks… …because they have so much white space. Work on Patoma-enabled mPL (“mPL6”) for large-scale, high-utilization cases ( even above 99%!) continues. In the presence of many fixed macros, we sometimes reduce HPWL more than 30% (!) simply by assigning cells to obstacle-free subregions before placing them. Can apply LP/network-flow techniques. Preserve the global placement as much as possible (tetris-like) 12/9/2018 UCLA VLSICAD LAB

Important command-line options for ISPD 2005 suite -shrinkRegion, -shrinkRatio Usually get shorter wirelength by packing cells Can pack cells to left, right, or center to a user-specified level of utilization -addDummyCells The best configuration may be highly nonuniform Adding unconnected “dummy” filler cells enables mPL to find good nonuniform placements -legalRegion Divide the chip into rectangular regions defined by fixed-block boundaries. Assign cells to subregions first, then legalize separately within the subregions. -GFD::Gamma Can fine tune the rate at which the weight of spreading forces is increased relative to wirelength forces 12/9/2018 UCLA VLSICAD LAB

Improvements by parameter tuning 12/9/2018 UCLA VLSICAD LAB

Acknowledgments Collaborators Sponsors Chin-Chih Chang, Cadence Tim Kong, Magma Yuchun (Clara) Ma, UCLA CS Xin Yuan, IBM Sponsors SRC Contracts 99-TJ-686 and 2003-TJ-1091 NSF Awards CCF-0430077 & CCR-9901153 ONR Contract N00014-03-1-0888 12/9/2018 UCLA VLSICAD LAB