SimPL: An Effective Placement Algorithm Myung-Chul Kim, Dong-Jin Lee and Igor L. Markov Dept. of EECS, University of Michigan 1ICCAD 2010, Myung-Chul Kim, University of Michigan

Global Placement: Motivation ■Interconnect lagging in performance while transistors continue scaling −Circuit delay, power dissipation and area dominated by interconnect −Routing quality highly controlled by placement ■Circuit size and complexity rapidly increasing −Scalable placement algorithm is critical −Simplicity, integration with other optimizations 2ICCAD 2010, Myung-Chul Kim, University of Michigan Unloaded Coupling IR drop RC delay

Placement Formulation ■Objective: Minimize estimated wirelength (half-perimeter wirelength) ■Subject to constraints: −Legality: Row-based placement with no overlaps −Routability: Limiting local interconnect congestion for successful routing −Timing: Meeting performance target of a design 3ICCAD 2010, Myung-Chul Kim, University of Michigan

Prior Work ■Ideal Placer −Fast runtime without sacrificing solution quality −Simplicity, integration with other optimization 4ICCAD 2010, Myung-Chul Kim, University of Michigan Speed Solution Quality Non-convex optimization mFAR, Kraftwerk2, FastPlace3 Ideal placer mPL6, APlace2, NTUPlace3 Quadratic and force-directed

Key features of SimPL ■Flat quadratic placement ■Primal dual optimization −Closing the gap between upper and lower bounds 5 Final Solution Lower-Bound Solution by Linear System Solver Wirelength Iteration Final Legal Solution Upper-Bound Solution by Look-ahead Legalization Initial WL Opt.

Common Analytical Placement Flow 6 Placement Instance Converge yes no Global Placement Initial WL Optimization Legalization and Detailed Placement ICCAD 2010, Myung-Chul Kim, University of Michigan

SimPL Flow 7 We delegate final legalization and detailed placement to FastPlace-DP [M. Pan, et al, “An Efficient and Effective Detailed Placement Algorithm”, ICCAD2005] Placement Instance Legalization and Detailed Placement B2B net model[P. Spindler, et al, “Kraftwerk2 - A Fast Force-Directed Quadratic Placement Approach Using an Accurate Net Model,” TCAD 2008] yes no Pseudonet Insertion Look-ahead Legalization (Upper-Bound) B2B Graph Building Linear System Solver (Lower-Bound) Converge Global Placement B2B Graph Building Linear System Solver WL Converge yes no Initial WL Optimization

SimPL: Look-ahead Legalization ■Purpose: Produces almost-legal placement (Upper-Bound) while preserving the relative cell ordering given by linear system solver (Lower-Bound) ■Identify target region −Find overflow bin b −Create a minimal wide enough bin cluster B around b ■Perform geometric top-down partitioning −Find cell area median (C c ) and whitespace median (C B ) −Assign cells (C c ) to corresponding partitions (C B ) ■Non-linear scaling −Form stripe regions −Move cells across stripe regions in-order based on whitespace 8

SimPL: Look-ahead Legalization (1) Performing geometric top-down partitioning Overfilled bin Cell-area median (C c ) B0 B0 B 1 whitespace median (C B ) Bin cluster (B) 9ICCAD 2010, Myung-Chul Kim, University of Michigan

SimPL: Look-ahead Legalization (2) 10ICCAD 2010, Myung-Chul Kim, University of Michigan Cell-area median (C c ) whitespace median (C B ) B0 B0

SimPL: Look-ahead Legalization (2) C B Obstacle borders Uniform cutlines Cell Ordering Per-stripe Linear Scaling C B ICCAD 2010, Myung-Chul Kim, University of Michigan

SimPL: Look-ahead Legalization (3) ■Example ( adaptec1 ) Look-ahead legalization stops when target regions become small enough

SimPL: Using legal locations as anchors ■Purpose: Gradually perturb the linear system to generate lower-bound solutions with less overlap ■Anchors and Pseudonets −Look-ahead locations used as fixed, zero-area anchors −Anchors and original cells connected with 2-pin pseudonets −Pseudonet weights grow linearly with iterations 13ICCAD 2010, Myung-Chul Kim, University of Michigan

Next illustration: Tug-of-war between low-wirelength and legalized placements 14ICCAD 2010, Myung-Chul Kim, University of Michigan

SimPL Iterations on Adaptec1 (1) Iteration=0 (Init WL Opt.)Iteration=1 (Upper Bound) Iteration=2 (Lower Bound)Iteration=3 (Upper Bound) 15

SimPL Iterations on Adaptec1 (2) Iteration=11 (Upper Bound) Iteration=20 (Lower Bound)Iteration=21 (Upper Bound) Iteration=11 (Upper Bound) Iteration=20 (Lower Bound)Iteration=21 (Upper Bound) Iteration=10 (Lower Bound) 16

SimPL Iterations on Adaptec1 (3) 17 Iteration=31 (Upper Bound)Iteration=30 (Lower Bound) Iteration=40 (Lower Bound)Iteration=41 (Upper Bound)

Convergence of SimPL ■Legal solution is formed between two bounds 18ICCAD 2010, Myung-Chul Kim, University of Michigan

Empirical Results: ISPD05 Benchmarks ■Experimental setup −Single threaded runs on a 3.2GHz Intel core i7 Quad CPU Q660 Linux workstation −HPWL is computed by GSRC Bookshelf Evaluator −< 5000 lines of code in C++, including CG-based solver for sparse linear systems with Jacobi preconditioner 19ICCAD 2010, Myung-Chul Kim, University of Michigan Improvements after ICCAD submission

Empirical Results: Scalability Study ■Take an existing design (ISPD 2005) and split each movable cell into two cells of smaller size −Each connection to the original cell is inherited by one of two split cells, which are connected by a 2-pin net Not in ICCAD paper

Parallelism in Conjugate Gradient Solver ■Runtime bottleneck in SimPL: Conjugate gradient linear system solver ■Coarse-grain row partitioning −Implemented using OpenMP3.0 compiler intrinsic ■SSE2 (Streaming SIMD Extensions) instructions −Process 4 multiple data with a single instruction −Marginal runtime improvement in SpMxV ■Reducing memory bandwidth demand of SpMxV −CSR (Compressed Sparse Row) format Y. Saad, “Iterative Methods for Sparse Linear Systems,” SIAM ICCAD 2010, Myung-Chul Kim, University of Michigan

On-going Research ■Integration with physical synthesis −Look-ahead placement offers opportunity for early estimation of circuit parameters –Timing look-ahead –Congestion look-ahead –Power-density look-ahead −Improving the speed and quality of physical synthesis ■Parallel look-ahead legalization −Run independently in separate sub-regions 22ICCAD 2010, Myung-Chul Kim, University of Michigan

Conclusions ■New flat quadratic placement algorithm: SimPL −Novel primal-dual approach −Amenable to integration with physical synthesis ■Self-contained, compact implementation −Fastest among available academic placers −Highly competitive solution quality 23ICCAD 2010, Myung-Chul Kim, University of Michigan

Questions and Answers Thank you! Time for Questions 24ICCAD 2010, Myung-Chul Kim, University of Michigan