A Fast, Robust Network Flow-based Standard-Cell Legalization Method - - PowerPoint PPT Presentation

A Fast, Robust Network Flow-based Standard-Cell Legalization Method for Minimizing Maximum Movement

Nima Karimpour Darav Laleh Behjat Ismail Bustany Andrew Kennings

Outline

• Standard Cell Legalization Problem
• Problem Analogy
• Challenges
• The Proposed Network Flow Based Algorithm
• Illustrative Example
• Empirical Results
• Conclusion

2

Standard Cell Legalization Problem

3

Movable cells Blocked area

C 1 C 2 C 3 C 4 C 5 C 6 C 7

C2 C3 C6

C 1 C 2 C 3 C 4 C 5 C 6 C 7

Problem Analogy

4

Problem Analogy

5

The legalization process is similar to the process of flattening humps

How To Flatten A Hump?

6

How To Flatten A Hump Using Traditional Approaches?

7

How To Flatten A Hump Using Traditional Approaches?

8

How To Flatten A Hump Using Traditional Approaches?

9

How To Flatten A Hump Using Traditional Approaches?

10

How To Flatten A Hump Using Traditional Approaches?

11

How To Flatten A Hump Using Traditional Approaches?

12

How To Flatten A Hump Using Traditional Approaches?

13

How To Flatten A Hump Using Traditional Approaches?

14

Proposed Network Flow Based Approach

15

Proposed Network Flow Based Approach

16

Proposed Network Flow Based Approach

17

Proposed Network Flow Based Approach

18

Proposed Network Flow Based Approach

19

Proposed Network Flow Based Approach

20

Proposed Network Flow Based Approach

21

Proposed Network Flow Based Approach

22

Proposed Network Flow Based Approach

23

Proposed Network Flow Based Approach

24

1

3 8 2 4 6 7 5

Proposed Method vs. Traditional Methods

25 1 3 8 2 4 6 7 5 6 1 3 8 2 4 7 5

• Network Flow:
• minimizes maximum movement.
• better preserves the order.

Traditional Methods Example Max movement = 3 Proposed Method Example Max movement = 1.5 The order is based on x positions.

1 2 3 4 5 7 6 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8

Legalization Challenges

26

Challenges

27

Legalization

Routability Wire Length Timing closure Robust Runtime Complicated Design Rules Multi-Deck Cells

Challenges

28

Legalization

Routability Wire Length Timing closure Robust Runtime Complicated Design Rules Multi-Deck Cells

Challenges

29

Legalization

Routability Wire Length Timing closure Robust Runtime Complicated Design Rules Multi-Deck Cells

Challenges

30

Legalization

Routability Wire Length Timing closure Robust Runtime Edge Spacing Rules Multi- Deck Cells

Challenges – Edge Spacing Constraint

31 Two cells are too close to each other

Prone to pin access and short problems

Objectives

• Minimize
• Maximum Cell Movement
• Average Cell movement

But it is not easy to minimize the above objectives because these are two NP hard problems.

32

Our Network-Flow Based Approach

33

Our Network-Flow Based Approach

• Inspired by the path augmentation algorithm, reference [8] (Brenner 2012).
• Objective is to flatten humps subject to the constraints.
• Set maximum movement as a constraint.
• Uses BFS to identify multiple paths subject to the maximum movement

constraint.

34

Our Network-Flow Based Approach

35 Preparation Step Initial solution Build a grid of connected bins Set an initial upper bound for displacement Assign cells to bins

Our Network-Flow Based Approach

36 Preparation Step Initial solution Build a grid of connected bins Set an initial upper bound for displacement Assign cells to bins Resolving Overflow Step Relax max displacement Identify overflowed bins B |B| > 0 Find paths for bin 𝑐𝑗 ∈ 𝐶 Move cells over the paths i = i +1 i < |B| i = 0

Yes No Yes No

Our Network-Flow Based Approach

37 Removing Overlap Step Remove overlaps inside bins Remove overlaps inside placement segments Legalized Solution Preparation Step Initial solution Build a grid of connected bins Set an initial upper bound for displacement Assign cells to bins Resolving Overflow Step Relax max displacement Identify overflowed bins B |B| > 0 Find paths for bin 𝑐𝑗 ∈ 𝐶 Move cells over the paths i = i +1 i < |B| i = 0

Yes No Yes No

Our Network-Flow Based Approach

38 Removing Overlap Step Remove overlaps inside bins Remove overlaps inside placement segments Legalized Solution Preparation Step Initial solution Build a grid of connected bins Set an initial upper bound for displacement Assign cells to bins Resolving Overflow Step Relax max displacement Identify overflowed bins B |B| > 0 Find paths for bin 𝑐𝑗 ∈ 𝐶 Move cells over the paths i = i +1 i < |B| i = 0

Yes No Yes No

Illustrative Example

39 Initial illegal placement: off rows and overlapping cells

Illustrative Example (The Capacity Map)

40 2

• 2

1

• 1

1

• 1
• 4

1

• 1
• 1
• 2

1 1 1 1 2 0 1 2 3 4

Illustrative Example (Finding Paths)

41 2

• 2

1

• 1

1

• 1
• 4

1

• 1
• 1
• 2

1 1 1 0 1 2 3 4 1 2 1,2 1,1 The proposed BFS-based method for finding paths for an overflowed bin.

Illustrative Example (Finding Paths)

42 2

• 2

1

• 1

1

• 1
• 4

1

• 1
• 1
• 2

1 1 1 0 1 2 3 4 1 2 1,2 1,1 1,3 The proposed BFS-based method for finding paths for an overflowed bin.

Illustrative Example (Finding Paths)

43 2

• 2

1

• 1

1

• 1
• 4

1

• 1
• 1
• 2

1 1 1 0 1 2 3 4 1 2 1,2 1,1 1,3 2,2 The proposed BFS-based method for finding paths for an overflowed bin.

Illustrative Example (Finding Paths)

44 2

• 2

1

• 1

1

• 1
• 4

1

• 1
• 1
• 2

1 1 1 0 1 2 3 4 1 2 1,2 1,1 1,3 2,2 0,2 The proposed BFS-based method for finding paths for an overflowed bin.

Illustrative Example (Finding Paths)

45 2

• 2

1

• 1

1

• 1
• 4

1

• 1
• 1
• 2

1 1 1 0 1 2 3 4 1 2 1,2 1,1 1,3 2,2 0,2 1,0 The proposed BFS-based method for finding paths for an overflowed bin.

Illustrative Example (Finding Paths)

46 2

• 2

1

• 1

1

• 1
• 4

1

• 1
• 1
• 2

1 1 1 0 1 2 3 4 1 2 1,2 1,1 1,3 2,2 0,2 1,0 2,1 The proposed BFS-based method for finding paths for an overflowed bin.

Illustrative Example (Finding Paths)

47 2

• 2

1

• 1

1

• 1
• 4

1

• 1
• 1
• 2

1 1 1 0 1 2 3 4 1 2 1,2 1,1 1,3 2,2 0,2 1,0 2,1 0,1 The proposed BFS-based method for finding paths for an overflowed bin.

Illustrative Example (Finding Paths)

48 2

• 2

1

• 1

1

• 1
• 4

1

• 1
• 1
• 2

1 1 1 0 1 2 3 4 1 2 1,2 1,1 1,3 2,2 0,2 1,0 2,1 0,1 1,4 The proposed BFS-based method for finding paths for an overflowed bin.

Illustrative Example (Finding Paths)

49 2

• 2

1

• 1

1

• 1
• 4

1

• 1
• 1
• 2

1 1 1 0 1 2 3 4 1 2 1,2 1,1 1,3 2,2 0,2 1,0 2,1 0,1 1,4 The proposed BFS-based method for finding paths for an overflowed bin.

Illustrative Example (Moving Cells)

50 1,2 1,1 1,3 2,2 0,2 1,0 2,1 0,1 1,4 0 1 2 3 4 1 2

Illustrative Example (Moving Cells)

51 1,2 1,1 1,3 2,2 0,2 1,0 2,1 0,1 1,4 0 1 2 3 4 1 2

Illustrative Example (Moving Cells)

52 1,2 1,1 1,3 2,2 0,2 1,0 2,1 0,1 1,4 0 1 2 3 4 1 2

Illustrative Example (Moving Cells)

53 1,2 1,1 1,3 2,2 0,2 1,0 2,1 0,1 1,4 0 1 2 3 4 1 2

Illustrative Example (Moving Cells)

54 1,2 1,1 1,3 2,2 0,2 1,0 2,1 0,1 1,4 0 1 2 3 4 1 2

Illustrative Example (Moving Cells)

55 1,2 1,1 1,3 2,2 0,2 1,0 2,1 0,1 1,4 0 1 2 3 4 1 2

Illustrative Example (Moving Cells)

56 1,2 1,1 1,3 2,2 0,2 1,0 2,1 0,1 1,4 0 1 2 3 4 1 2

Illustrative Example (Moving Cells)

57 1,2 1,1 1,3 2,2 0,2 1,0 2,1 0,1 1,4 0 1 2 3 4 1 2

Illustrative Example (Moving Cells)

58 1,2 1,1 1,3 2,2 0,2 1,0 2,1 0,1 1,4 0 1 2 3 4 1 2

Illustrative Example (Moving Cells)

59 1,2 1,1 1,3 2,2 0,2 1,0 2,1 0,1 1,4 0 1 2 3 4 1 2

Illustrative Example (Moving Cells)

60 1,2 1,1 1,3 2,2 0,2 1,0 2,1 0,1 1,4 0 1 2 3 4 1 2

Illustrative Example (The Capacity Map)

61 2

• 2
• 1
• 1
• 1
• 1
• 2

1 1 0 1 2 3 4 1 2

Experimental Results

62

First Set

• ISPD 2014 benchmarks.
• GP generated by Eh?Placer.
• LEF/DEF format.
• All DR rules removed.

Second Set

• ISPD 2014 benchmarks.
• The same GPs.
• Edge spacing rules enabled.
• LEF/DEF format.

Third Set

• ISPD 2006 benchmarks with

movable single deck cells.

• GP generated by POLAR.
• Bookshelf format.

Experimental Results

63

First Set

• ISPD 2014 benchmarks.
• GP generated by Eh?Placer.
• LEF/DEF format.
• All DR rules removed.

Second Set

• ISPD 2014 benchmarks.
• GP generated by Eh?Placer.
• LEF/DEF format.
• Edge spacing rules enabled.

Third Set

• ISPD 2006 benchmarks with

movable single deck cells.

• GP generated by POLAR.
• Bookshelf format.

Experimental Results

64

First Set

• ISPD 2014 benchmarks.
• GP generated by Eh?Placer.
• LEF/DEF format.
• All DR rules removed.

Second Set

• ISPD 2014 benchmarks.
• The same GPs.
• LEF/DEF format.
• Edge spacing rules enabled.

Third Set

• ISPD 2006 benchmarks with

movable single deck cells.

• GP generated by POLAR.
• Bookshelf format.

Experimental Results

65

First Set

• ISPD 2014 benchmarks.
• GP generated by Eh?Placer.
• LEF/DEF format.
• All DR rules removed.

Second Set

• ISPD 2014 benchmarks.
• The same GPs.
• LEF/DEF format.
• Edge spacing rules enabled.

Third Set

• ISPD 2006 benchmarks with

movable single deck cells.

• GP generated by POLAR.
• Bookshelf format.

The ISPD 2014 Benchmarks

Global Placements generated by Eh?Placer ISPD 2014 Benchmark #Cells #Fixed Utilization mgc_des_perf_1 112,644 0.91 mgc_des_perf_2 112,644 0.85 mgc_edit_dist_1 130,661 0.40 mgc_edit_dist_2 130,661 0.43 mgc_fft 32,281 0.84 mgc_matrix_mult 155,325 0.80 mgc_pci_bridge32_1 30,675 0.84 mgc_superblue11 925616 1458 0.41 mgc_superblue12 1286948 89 0.44 mgc_superblue16 680450 419 0.46

66

The ISPD 2006 Benchmarks

67

ISPD 2006 Benchmark Global Placements generated by POLAR #Cells #Fixed Utilization newblue3 482833 11178 0.26 newblue4 642717 3422 0.46 newblue5 1228177 4881 0.50 newblue6 1248150 6889 0.39 newblue7 2481372 26582 0.49

Sample Illegal Placement from ISPD 2014

68 Areas as humps

Results on the ISPD 2014 (Set 1)

69

Benchmark HPWL Increase (%)

• Avg. Disp (rows)
• Max. Disp (rows)

Runtime (sec) RDP EP Ours RDP EP Ours RDP EP Ours RDP EP Ours des_perf_1 5.4 14.2 6.1 3.6 1.3 0.8 10.0 11.1 4.3 89.1 5.5 2.5 des_perf_2 4.5 12.7 5.9 3.6 1.2 0.8 10.0 13.2 3.7 80.1 5.1 2.1 edit_dist_1

• 5.8

3.3

• 1.2

1.1

• 17.8

8.3

• 5.9

1.0 edit_dist_2

• 5.7

3.4

• 1.2

1.1

• 12.2

7.8

• 6.1

1.1 fft 10.4 17.5 8.5 3.8 1.3 0.9 10.0 17.9 3.9 10.9 1.2 0.4 matrix_mult 9.2 15.0 7.9 3.8 1.2 0.8 10.0 12.5 3.8 52.8 7.8 3.0 pci_bridge32_1 12.3 25.2 12.7 4.0 1.2 0.8 10.0 8.7 3.0 17.8 0.9 0.3 pci_bridge32_2 10.4 23.9 12.5 4.1 1.1 0.8 10.0 8.2 3.8 17.1 0.8 0.3 superblue11

• 32.4

4.3

• 21.2

3.0

• 951.6

388.6

• - 3088.1

154.7 superblue12

• 26.6

4.8

• 6.6

1.9

• 428.0

180.6

• - 1537.5

112.1 superblue16

• 18.1

4.0

• 10.6

2.6

• 666.9

259.0

• - 2123.9

85.5

Norm

1.0 2.7 1.0 4.6 3.3 1.0 2.7 2.5 1.0 31.1 18.7 1.0

Ours vs Eh?Placer (EP) and RippleDP (RDP)

Results on the ISPD 2014 (Set 2)

70 Edge spacing rules were Enabled.

10 20 30 40 50 60 Rows

• Max. Displacement

Eh?Placer Ours 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 Rows

• Avg. Displacement

Eh?Placer Ours

Results on the ISPD 2014 (Set 2)

71 Edge spacing rules were Enabled.

0.0 5.0 10.0 15.0 20.0 25.0 30.0 %

HPWL Increase

Eh?Placer Ours 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 Sec

Runtime

Eh?Placer Ours

Results on the ISPD 2006 (Set 3)

72

0.0 200.0 400.0 600.0 800.0 1000.0 1200.0 1400.0 Rows

• Max. Displacement

FastPlace Ours 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Rows

• Avg. Displacement

FastDP Ours

Results on the ISPD 2006 (Set 3)

73

50 100 150 200 250 Sec

Runtime

FastPlace Ours 1 2 3 4 5 6 7 %

HPWL Increase

FastPlace Ours

Scalability and Robustness

74

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

Sec/(1000 cells)

FastPlace Ours

Our approach is scalable and robust with respect to design size and floorplan complexity

Conclusion

• The proposed legalizer results in
• less maximum cell movement.
• less average cell movement.
• The proposed legalizer is
• fast.
• scalable and robust (independent of the floorplan complexity).

75

A Fast, Robust Network Flow-based Standard-Cell Legalization Method for Minimizing Maximum Movement

Nima Karimpour Darav Laleh Behjat Ismail Bustany Andrew Kennings