Routability-Driven and Fence-Aware Legalization for - - PowerPoint PPT Presentation

Routability-Driven and Fence-Aware Legalization for Mixed-Cell-Height Circuits

Haocheng Li1, Wing Kai Chow2, Gengjie Chen1, Evangeline F. Y. Young1, Bei Yu1

1The Chinese University of Hong Kong 2Cadence Design System Inc. 1 / 17

Outline

Introduction Multi-row Global Legalization Max Displacement Optimization Fixed-Row-and-Order Optimization Experimental Results Conclusion

2 / 17

Outline

Introduction Multi-row Global Legalization Max Displacement Optimization Fixed-Row-and-Order Optimization Experimental Results Conclusion

3 / 17

Motivation

Figure 1: Large Single-Row Cell [Baek et al. 2008] Figure 2: Multi-Row Cell [Baek et al. 2008]

◮ Cells like multi-bit flip-flops (MBFFs)

• ccupy multiple rows a.

◮ Cells are much more accessible by being modified to be multi-row height b.

a[Lin, Hsu, and Chang 2011] b[Raghavan et al. 2016]

3 / 17

Legalization

Figure 3: Power/ground alignment.

Cell M1 Cell Pin M2 Cell Pin M1 Rail M2 Rail Pin Access Pin Short

Figure 4: Pin access and pin short.

Objective function a: Sam = 1 H

H

• h=1

1 |Ch|

• ci ∈Ch

δi, (1) where δi = δxi + δyi = |xi − x′

i | + |yi − y′ i |, satisfying b:

◮ Cells are overlap-free; ◮ Cells are aligned to placement sites. ◮ Cells with height of even multiples of site height must be placed in alternate rows with matching power and ground alignment. ◮ Signal pins of cells should not be short or inaccessible due to the P/G grids and IO pins c.

a[Darav, Bustany, et al. 2017] b[Chow, Pui, and Young 2016] c[Darav, Kennings, et al. 2016]

4 / 17

Detailed Placement Flow

The detailed placement consists of three stages. ◮ Inserts the cells sequentially into the placement region. ◮ Optimize the maximum displacement by swapping cells. ◮ Further optimize the average and maximum displacement.

Legalization MGL

Max Displacement Optimization Bipartite Matching Fixed Row & Fixed Order Optimization Dual Min Cost Flow

Figure 5: Detailed placement flow.

5 / 17

Outline

Introduction Multi-row Global Legalization Max Displacement Optimization Fixed-Row-and-Order Optimization Experimental Results Conclusion

6 / 17

[Chow, Pui, and Young 2016]

f i j g k e c a b d h blockage f g e i c

Figure 6: Local Region

𝑏 𝑓 𝑑 𝑒 𝑐 𝑢

4 3 2 1 L R

Figure 7: Insertion Point

◮ Define local region ◮ Enumerate insertion points ◮ Evaluate cost ◮ Spread overlapping cells

3 2 4 6 5 1 1 2 3 4

𝑒𝑗 𝑦𝑢

𝑦𝑢

𝑒𝑑 𝑦𝑢 𝑒𝑢 𝑦𝑢 𝑒𝑏 𝑦𝑢 𝑒𝑐 𝑦𝑢 Figure 8: Cost Evaluation

6 / 17

Difference between MLL & MGL

0 1 2 3 4 5 6 7 8

ct c1 c2 c3 c4 (a) Global Placement

0 1 2 3 4 5 6 7 8

c1 c2 c3 c4 (b) Local Region

0 1 2 3 4 5 6 7 8

ct c1 c2 c3 c4 (c) MLL

0 1 2 3 4 5 6 7 8

ct c1 c2 c3 c4 (d) MGL

Figure 9: Comparison between MLL and MGL.

MLL optimizes the total displacement from the initial positions of the cells in the window before calling MLL. MGL minimizes the displacement from the respective positions of cells obtained afer global placement.

7 / 17

Clustered Cells

0 1 2 3 4 5 6 7 8

ct c1 c2 c3 c4 (a) Global Placement

0 1 2 3 4 5 6 7 8

c1 c2 c3 c4 (b) Local Region

Figure 10: c2 and c4 form a cluster.

−2 2 4 a xt Disp. Type A −2 2 4 b xt Type B −2 2 4 a c xt Disp. Type C −2 2 4 d b xt Type D

Figure 11: Cost Curve Types A – D.

8 / 17

Outline

Introduction Multi-row Global Legalization Max Displacement Optimization Fixed-Row-and-Order Optimization Experimental Results Conclusion

9 / 17

Bipartite Matching

(a) Before (b) Afer

Figure 12: Bipartite matching.

9 / 17

Outline

Introduction Multi-row Global Legalization Max Displacement Optimization Fixed-Row-and-Order Optimization Experimental Results Conclusion

10 / 17

[Vygen 1998]

◮ Fixed-row and fixed-order. ◮ Minimizes the half-perimeter wire length (HPWL). ◮ A dual of min-cost flow problem.

10 / 17

Fixed Row & Fixed Order Optimization

Formulate linear displacement: max

xi,x−

i ,x+ i

• i

ni(x−

i − x+ i )

(2) s.t. x−

i ≤ xi − x′ i ≤ x+ i ,

∀ci ∈ C, (2a) x−

i ≤ 0 ≤ x+ i ,

∀ci ∈ C, (2b) xi − xj ≤ −wi, ∀(i, j) ∈ E, (2c) li ≤ xi ≤ ri, ∀ci ∈ C. (2d) Let ˜ x0 be the absolute position of the origin, then the absolute positions {˜ xi, ˜ x−

i , ˜

x+

i } of {xi, x− i , x+ i } are

˜ xi = xi + ˜ x0, ˜ x−

i = x− i + ˜

x0, ˜ x+

i = x+ i + ˜

• x0. Thus,

max

˜ xi,˜ x−

i ,˜

x+

i ,˜

x0

• i

ni(˜ x−

i − ˜

x+

i )

(3) s.t. ˜ x−

i ≤ ˜

xi − x′

i ≤ ˜

x+

i ,

∀ci ∈ C, (3a) ˜ x−

i − ˜

x0 ≤ 0 ≤ ˜ x+

i − ˜

x0, ∀ci ∈ C, (3b) ˜ xi − ˜ xj ≤ −wi, ∀(i, j) ∈ E, (3c) li ≤ ˜ xi − ˜ x0 ≤ ri, ∀ci ∈ C, (3d) whose dual linear programming is a min-cost flow problem.

11 / 17

Example of Min-Cost Flow

3 1 2

Figure 13: GP.

1 3 2 N P Z

f p

2

f n f n

1

f n

2

f p

1

f p

3

f n

3

f13 f23 f −

3

f +

3

f r

3

f p f +

1

f −

2

f l

2

f −

1

f +

2

f l

1

Figure 14: Flow network.

12 / 17

Outline

Introduction Multi-row Global Legalization Max Displacement Optimization Fixed-Row-and-Order Optimization Experimental Results Conclusion

13 / 17

Experimental Results

0.5 1 1.5

• Avg. Disp.
• Max. Disp.

Score S Runtime (s) 1 1 1 1 1.18 1.12 1.26 0.72 Normalized Avg. 1st Ours 0.5 1 1.5 2 2.5 3 3.5

des_perf_1 des_perf_a_md1 des_perf_a_md2 des_perf_b_md1 des_perf_b_md2 edit_dist_1_md1 edit_dist_a_md2 edit_dist_a_md3 fft_2_md2 fft_a_md2 fft_a_md3 pci_bridge32_a_md1 pci_bridge32_a_md2 pci_bridge32_b_md1 pci_bridge32_b_md2 pci_bridge32_b_md3

• Avg. Disp.

1st Ours

13 / 17

Outline

Introduction Multi-row Global Legalization Max Displacement Optimization Fixed-Row-and-Order Optimization Experimental Results Conclusion

14 / 17

Conclusion

◮ Propose multi-row global legalization. ◮ Adjust the maximum displacement by bipartite matching. ◮ Formulate the fix-row-and-order legalization into a minimum-cost flow problem. ◮ Comparing with the champion of the ICCAD 2017 Contest, we achieved 18% less average displacement, 12% less maximum displacement, and much fewer routability-driven violations.

14 / 17

Thanks! Qestions?

15 / 17

References I

Baek, Sang-Hoon, Ha-Young Kim, Young-Keun Lee, Duck-Yang Jin, Se-Chang Park, and Jun-Dong Cho (2008). “Ultra-high density standard cell library using multi-height cell structure”. In: Proceedings of SPIE. Vol. 7268. Chow, Wing Kai, Chak Wa Pui, and Evangeline F. Y. Young (2016). “Legalization Algorithm for Multiple-Row Height Standard Cell Design”. In: ACM/IEEE Design Automation Conference (DAC), 83:1–83:6. Darav, Nima Karimpour, Ismail S. Bustany, Andrew Kennings, and Ravi Mamidi (2017). “ICCAD-2017 CAD Contest in Multi-Deck Standard Cell Legalization and Benchmarks”. In: IEEE/ACM International Conference on Computer-Aided Design (ICCAD), pp. 867–871. Darav, Nima Karimpour, Andrew Kennings, Aysa Fakheri Tabrizi, David Westwick, and Laleh Behjat (2016). “Eh? Placer: a high-performance modern technology-driven placer”. In: ACM Transactions on Design Automation of Electronic Systems (TODAES) 21.3, p. 37.

16 / 17

References II

Lin, Mark Po-Hung, Chih-Cheng Hsu, and Yao-Tsung Chang (2011). “Recent research in clock power saving with multi-bit flip-flops”. In: IEEE International Midwest Symposium on Circuits and Systems (MWSCAS), pp. 1–4. Raghavan, Praveen, F Firouzi, L Mati, P Debacker, R Baert, SMY Sherazi, D Trivkovic, V Gerousis, M Dusa, J Ryckaert, et al. (2016). “Metal stack optimization for low-power and high-density for N7-N5”. In: Design-Process-Technology Co-optimization for Manufacturability X. Vol. 9781. International Society for Optics and Photonics, 97810Q. Vygen, Jens (1998). “Algorithms for detailed placement of standard cells”. In: IEEE/ACM Proceedings Design, Automation and Test in Europe (DATE), pp. 321–324.

17 / 17