Mixed-Size Placement with Fixed Macrocells using Grid-Warping

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. 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& descendto continue

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. 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. 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& descendto continue

6. Restore grids and pull gates back Initial placement mass and grids 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

7. And We Do Not Use a Regular Warping Grid 2x2 Warping grid 4x4 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. Quadratic Placement Pre-Warping Nonlinear Grid-Warping Loop Improvement Decompose/Recurse Legalize (Domino) Complete Grid Warping Flow • Complete flow has several steps • We review them briefly here

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

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

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

12. Quadratic Placement Pre-Warping Nonlinear Grid-Warping Loop Improvement Decompose/Recurse Legalize (Domino) Complete Grid Warping Flow stretched • 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’

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

15. Quadratic Placement Pre-Warping Nonlinear Grid-Warping Loop Improvement Decompose/Recurse 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. 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. Handling Fixed Macrocells • 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) Quadratic Placement Pre-Warping Nonlinear Grid-Warping Loop Improvement Re-Warping Decompose/Recurse Legalize (FastPlace)

18. 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 (1) Geometric Hashing During Warping M M M M

19. 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. If a column (row) contains only one cell, star model is used and no additional variables is introduced. (2) New Net Models • 1st 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) • 2nd 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

20. (3) Better Consideration of Capacity • 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 Quadratic Placement Pre-Warping Nonlinear Grid-Warping Loop Improvement Re-Warping Decompose/Recurse Legalize (FastPlace)

21. 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 (4) New Backend

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.

23. ISPD’02 Layouts ibm01 ibm04

24. More Macrocell Results – ISPD’05 • 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. ISPD’05 Layouts adaptec2 adaptec4

26. ISPD’05 Layouts bigblue2 bigblue3

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)