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

Routability-Driven and Fence-Aware Legalization for Mixed-Cell-Height Circuits Haocheng Li 1 , Wing Kai Chow 2 , Gengjie Chen 1 , Evangeline F. Y. Young 1 , Bei Yu 1 1 The Chinese University of Hong Kong 2 Cadence 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] ◮ Cells like multi-bit flip-flops (MBFFs) occupy 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] Figure 2: Multi-Row Cell [Baek et al. 2008] 3 / 17

Legalization Objective function a : H S am = 1 1 � � δ i , (1) H | C h | c i ∈ C h h = 1 where δ i = δ xi + δ yi = | x i − x ′ i | + | y i − y ′ i | , satisfying b : ◮ Cells are overlap-free; Figure 3: Power/ground alignment. ◮ 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. Cell Pin Access M1 Cell Pin ◮ Signal pins of cells should not be short or inaccessible due M2 Cell Pin to the P/G grids and IO pins c . Pin Short M1 Rail M2 Rail a [Darav, Bustany, et al. 2017] b [Chow, Pui, and Young 2016] Figure 4: Pin access and pin short. 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. Max Displacement Fixed Row & Fixed Legalization Optimization Order Optimization MGL Bipartite Matching 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] ◮ Define local region b a ◮ Enumerate insertion points blockage d c c e e ◮ Evaluate cost f f g g h i i k ◮ Spread overlapping cells j Figure 6: Local Region 𝑒 𝑗 𝑦 𝑢 𝑒 𝑑 𝑦 𝑢 𝑒 𝑐 𝑦 𝑢 4 𝑒 𝑢 𝑦 𝑢 𝑒 𝑏 𝑦 𝑢 3 𝑐 4 2 𝑏 3 1 L R 𝑢 𝑑 𝑒 2 𝑓 1 0 1 2 3 4 5 6 𝑦 𝑢 Figure 7: Insertion Point Figure 8: Cost Evaluation 6 / 17

Difference between MLL & MGL c 1 c 1 c 1 c 1 c t c t c t c 3 c 3 c 3 c 3 c 2 c 2 c 2 c 2 c 4 c 4 c 4 c 4 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 (a) Global Placement (b) Local Region (c) MLL (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 Type A Type B 4 4 2 2 c 1 c 1 Disp. 0 0 x t x t c t − 2 − 2 c 3 c 3 a b c 2 c 2 Type C Type D c 4 c 4 4 4 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 2 2 Disp. (a) Global Placement (b) Local Region 0 0 x t x t Figure 10: c 2 and c 4 form a cluster. − 2 − 2 c a d b 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: � n i ( x − i − x + i ) (2) max x i , x − i , x + i i s.t. x − i ≤ x i − x ′ i ≤ x + ∀ c i ∈ C , (2a) i , x − i ≤ 0 ≤ x + ∀ c i ∈ C , (2b) i , x i − x j ≤ − w i , ∀ ( i , j ) ∈ E , (2c) l i ≤ x i ≤ r i , ∀ c i ∈ C . (2d) x 0 be the absolute position of the origin , then the absolute positions { ˜ x − i } of { x i , x − Let ˜ x + i , x + i } are x i , ˜ i , ˜ x 0 , ˜ x − i = x − x 0 , ˜ x 0 . Thus, x + i = x + ˜ x i = x i + ˜ i + ˜ i + ˜ � x − x + max n i ( ˜ i − ˜ i ) (3) x − x 0 x i , ˜ ˜ i , ˜ x + i , ˜ i x − x i − x ′ x + s.t. ˜ i ≤ ˜ i ≤ ˜ ∀ c i ∈ C , (3a) i , x 0 ≤ 0 ≤ ˜ x − x 0 , x + i − ˜ i − ˜ ∀ c i ∈ C , (3b) ˜ x i − ˜ x j ≤ − w i , ∀ ( i , j ) ∈ E , (3c) ˜ x 0 ≤ r i , l i ≤ ˜ x i − ˜ ∀ c i ∈ C , (3d) whose dual linear programming is a min-cost flow problem. 11 / 17

Example of Min-Cost Flow f n f n 1 1 N f n f 13 f l f − 2 1 1 f n 3 f − 3 f + 1 1 f r 3 Z 3 3 2 f − 2 f + f p 3 3 f 23 f p f l Figure 13: GP. f + 1 2 2 f p 2 2 P f p 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 Avg. Disp. Normalized Avg. des_perf_1 des_perf_a_md1 1st 1 . 18 Avg. Disp. des_perf_a_md2 1 Ours des_perf_b_md1 des_perf_b_md2 edit_dist_1_md1 1 . 12 Max. Disp. edit_dist_a_md2 1 edit_dist_a_md3 fft_2_md2 fft_a_md2 1 . 26 fft_a_md3 Score S 1 pci_bridge32_a_md1 pci_bridge32_a_md2 pci_bridge32_b_md1 1st pci_bridge32_b_md2 0 . 72 Ours Runtime (s) pci_bridge32_b_md3 1 0 . 5 1 1 . 5 2 2 . 5 3 3 . 5 0 . 5 1 1 . 5 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