1. Mixed-Size Placement with Fixed Macrocells using Grid-Warping Zhong Xiu*, Rob Rutenbar * Advanced Micro Devices Inc., Department of Electrical and Computer Engineering, Carnegie Mellon University

2. Slide 2 Placement by Grid-Warping In [Zhong et al, DAC04], we showed first grid-warping placer In [Zhong et al, DAC05], we showed our timing-driven placer Fundamentally new idea for placement improvement  Imagine we place the gates on the surface of a flexible elastic sheet  We stretch the sheet to improve the placement Quadratic Initial placement Warp Placement surface Improved warped result Recurse & descend to continue

3. Slide 3 Grid Warping: Attractive Features Novel paradigm for placement: optimize the grid, not the gates  Think of “gravity” – we reshape curvature of space to move the mass Flexibly nonlinear  Free to warp anyway we like; not driven primarily by linear solves Low-dimensional optimization problem  We only need to control the sheet, we don’t move gates individually Early prototypes – WARP1, WARP2 – perform well  Competitive on wirelength with other published placers  As fast – or faster – than many other analytical placers

4. Slide 4 Organization of this Talk What’s missing? To handle Mixed-Size Placement  Wirelength/Timing optimization is necessary but not sufficient  We must be able to handle mixed-size placement with fixed macrocells First, we review basic mechanics of grid-warping Second, we show how to extend grid-warping for mixed-size placement with fixed macrocells Finally, we show our results and future directions

5. Slide 5 Review: Mechanics of Grid-Warping It’s conceptually useful to think of warping as distorting a regular mesh placed on the elastic placement surface…..but this is not actually how we implement warping Quadratic Initial placement Warp Placement surface Improved warped result Recurse & descend to continue

6. Slide 6 Warp grids and acquire gates We Formulate Warping in an “Inverse” Way We warp to “acquire” a new set of gates in each unit grid area… … then “pull” gates back to the undistorted grid, to move them Restore grids and pull gates back Initial placement mass and grids

7. Slide 7 And We Do Not Use a Regular Warping Grid 2x2 Warping grid4x4 Warping grid Instead, we use a grid defined by a set of slicing cuts  It turns out this allows a greater range of motion for the gates Yes—a lot like quadrisection or partitioning, but more general  The cuts need not be axis parallel  Because gates are fully placed in each region, we get real wirelength

8. Slide 8 Improvement Pre-Warping Decompose/Recurse Nonlinear Grid-Warping Loop Quadratic Placement Legalize (Domino) Complete Grid Warping Flow Complete flow has several steps We review them briefly here

9. Slide 9 Improvement Pre-Warping Decompose/Recurse Nonlinear Grid-Warping Loop Quadratic Placement Legalize (Domino) Complete Grid Warping Flow Quadratic place onto elastic sheet Note: pure quadratic wirelength No reweighting steps

10. Slide 10 Improvement Pre-Warping Decompose/Recurse Nonlinear Grid-Warping Loop Quadratic Placement Legalize (Domino) Complete Grid Warping Flow Geometric pre-conditioning step Spreads gates out quickly, uniformly, to improve final wirelen

11. Slide 11 Improvement Pre-Warping Decompose/Recurse Nonlinear Grid-Warping Loop Quadratic Placement Legalize (Domino) Complete Grid Warping Flow Nonlinear optimizer iteratively perturbs warping grid on sheet

12. Slide 12 Complete Grid Warping Flow Improvement Pre-Warping Decompose/Recurse Nonlinear Grid-Warping Loop Quadratic Placement Legalize (Domino) Nonlinear optimizer iteratively perturbs warping grid on sheet..each new warping is quickly “stretched” back to a full placement Use this to eval cost function, which tracks ‘rectilinear wirelen + capacity’ stretched

13. Slide 13 Improvement Pre-Warping Decompose/Recurse Nonlinear Grid-Warping Loop Quadratic Placement Legalize (Domino) Complete Grid Warping Flow Nonlinear optimizer delivers a final warped placement Standard improvement step runs hMetis to optimize location of gates placed near partition cuts

14. Slide 14 Improvement Pre-Warping Decompose/Recurse Nonlinear Grid-Warping Loop Quadratic Placement Legalize (Domino) Complete Grid Warping Flow Recurse: in this case, 4 new placements inside 4 regions Continue until ~few gates/region

15. Slide 15 Improvement Pre-Warping Decompose/Recurse Nonlinear Grid-Warping Loop Quadratic Placement Legalize (Domino) Complete Grid Warping Flow Warping flow delivers a final, but still slightly illegal, placement Use Domino (T.U. Munich) to legalize to final detailed placement

16. Slide 16 Problem: Warped Placement with Macrocells Assumptions  We focus on the fixed-macro case The core problem  Warping is intrinsically weak at separating large macros and small gates  All instances modeled as points; elastic “stretching” keeps nearby points close

17. Slide 17 Handling Fixed Macrocells Improvement Pre-Warping Decompose/Recurse Nonlinear Grid-Warping Loop Quadratic Placement Legalize (FastPlace) Re-Warping 4 new geometric solutions Inside warping, a geometric “hash” function that greedily re-locates gates that warp on top of macrocells …and a new net model (QP) During partition improvement, closer attention to size imbalances New backend (FastPlace)

18. Slide 18 (1) Geometric Hashing During Warping Problem: nonlinear warping drops gates on top of fixed macros Solution: “hash” them off, inside warping loop  Inside warping, inside each eval of global cost func, check if each cell overlaps macro  If so, we push it to the nearest boundary that has enough space for the cell  We chop chip up into small grids, store “nearest boundary” info in a hash table Note  No attempt to manage density or wirelength in this solution, just legality M M M M

19. Slide 19 (2) New Net Models 1 st QP & QPs in re-warping  For 2-pin nets, use the clique model, and set weight to 1.  For nets with 3 or more pins, use star model and introduce a new variable, each net has a weight: #Pins/(#Pins - 1). (FastPlace, ISPD’04) 2 nd QP and beyond  At 2nd layer of QP and beyond, use Jens Vygen’s net-split technique  Hybrid models, make QP faster and conserve quality If a column (row) contains only one cell, star model is used and no additional variables is introduced. If a column (row) contains two or more cells, a new cell is introduced and is connected to all the internal cells and all the propagated pins.

20. Slide 20 (3) Better Consideration of Capacity Improvement Pre-Warping Decompose/Recurse Nonlinear Grid-Warping Loop Quadratic Placement Legalize (FastPlace) Re-Warping Get rid of “Pre-Warping” Cost Function: use a single-sided cost function, under-filled regions receive no capacity penalty hMetis: the total area of all cells in each region does not exceed the capacity of that region Re-Warping: all of the above mentioned modifications are applied here

21. Slide 21 (4) New Backend Use ideas from FastPlace [ICCAD’05]  Swap based detail placement algorithm – greedy algorithm  Find the “optimal region” for a cell, if the cell is not in this region, try to swap it with a cell or space in that optimal region Detailed backend flow  First pass legalize  FengShui 5.1 from SUNY Binghm  Local repair for small macros/overlaps  Local greedy swaps  Wirelength minimization  Chu’s FastPlace legalizer ideas Our new overall flow  Run WARP as global placement  Sort all the cells and ~legalize them  Run the new detailed backend

22. Slide 22 Macrocell Results – ISPD’02 Wirelength  3-4% better than Feng Shui  Competitive with BonnPlace Run time  2X Fengshui  ~ Competitive with BonnPlace  Exact comparison difficult – BonnPlace is running on an 1.45GHz IBM 4- processor server and is explicitly parallelized software  We’re on a 2.0GHz Xeon. Feng Shui 5.1BonnPlaceWarp 3 WireCPUWireCPUWireCPU 1.0370.450.993--1.0001.00

23. Slide 23 ISPD’02 Layouts ibm01ibm04

24. Slide 24 More Macrocell Results – ISPD’05 Design WARP 3APlace GlobalLegalizationBackendWirelen adaptec1 1.02731.04470.97200.8731 adaptec4 2.12582.18922.04551.8731 bigblue1 1.06391.06591.01810.9464 bigblue2 1.77641.85261.69501.4382 bigblue3 3.68783.69593.57833.5789 bigblue4 8.94669.18968.59818.3321 Ratio1.0431.0631.0000.927 Versus APlace (Kahng@UCSD)  ~7% more wirelen  Total 41.75 hours for all 6 designs for Warp on 2.8GHz Xeon Aside: ISPD’05 contest results:  APlace 1.00  mFAR 1.06  Dragon 1.08  mPL 1.09  FastPlace 1.16  Capo 1.17  NTUP 1.21  Fengshui 1.50  Kraftwerk+Domino 1.84

25. Slide 25 ISPD’05 Layouts adaptec2 adaptec4

26. Slide 26 ISPD’05 Layouts bigblue2bigblue3

27. Slide 27 Conclusion and Future Work Placement with macrocells – WARP3 – competitive  New techniques such as geometric hashing, improved hybrid net model  Can produce very good quality mixed-size placements reasonably quickly Future Work  Improve both quality and runtime  Better handle macrocells and routing congestion  “Hybrid” layout strategies (warping, but a flatter, analytical style)