Abacus: Fast Legalization of Standard Cell Circuits with Minimal Movement

Transcription

1 EDA Institute for Electronic Design Automation Prof. Ulf Schlichtmann Abacus: Fast Legalization of Standard Cell Circuits with Minimal Movement Peter Spindler, Ulf Schlichtmann and Frank M. Johannes Technische Universitaet Muenchen ISPD, April 008

2 Outline Background State-of-the-Art Abacus, PlaceRow Experimental Results Conclusion Slide

3 Background Standard cell circuits: Millions of cells: inverter, NAND, NOR Physical representation: Rectangles, all have the same height, but different widths Placement: Align cells overlap-free to row structure. Global Placement Legalization. Legal Placement Legal placement: No overlap Cells aligned to rows Preserve global placement: minimal cell movement Slide 3

4 State-of-the-Art in Legalization State-of-the-Art: Flow based: assign cells to places Domino [Doll et al., TCAD 994] BonnPlace [Vygen et al., TCAD 004] Two stage: first assign cells to rows, then place the rows [Madden et al., ICCAD 003, Kahng et al., GLS-VLSI 004] Diffusion based [Alpert et al., DAC 005] Computational Geometry based [Alpert et al., DAC 007] Greedy: legalize one cell at a time: Tetris [Hill, Patent, 00] Slide 4

5 Abacus: Overview Abacus: Similar to Tetris: sort cells, legalize one cell at a time Legalization of one cell: move cell over the rows, place cell to best/nearest row Difference to Tetris: PlaceRow: move already legalized cells within one row, minimize total movement Because of PlaceRow: lower total movement Slide 5

6 Step : Sorting Sort cells according to x-pos in global placement Process order:,, 3, 4, 5, 6, 7, 8, 9 x Slide 6

7 Legalize Cell Cell to be legalized Row Row Insert to row Insert to row Insert to row 3 Best row: Row 3 Slide 7

8 Legalize Cell Cell to be legalized Row Row Row 3 Insert to row Insert to row PlaceRow : Minimize quadratic movement in Cell x-dir already of cells legalized to row Insert to row 3 Best row: 3 Slide 8

9 Legalize Cell 3 Row Row Row 3 Cell 3 to be legalized Cell already legalized to row 3 Insert to row Insert to row PlaceRow : Minimize quadratic movement in Cell x-dir already of cells legalized to row Insert to row 3 PlaceRow 3: Minimize quadratic movement in x-dir of cells Best row: Slide 9

10 Legalize Cell 4 Row Row Row 3 Cell 4 to be legalized Insert to row PlaceRow Insert to row PlaceRow Insert to row 3 PlaceRow 3 Best row: Already legalized cell is moved within the row Slide 0

11 Final Result Global Placement Abacus Tetris: No PlaceRow higher movement (about 50% more for a large circuit) Slide

12 Input: one row with N cells, x-pos of cells: global placement ( x i ) w w PlaceRow Output: new (legal) x-pos of cells ( x i ) such that the overlap is removed and the total quadratic movement is minimized Input: Output: QP: x x x x x 3 x 3 min N i= e i weight ( ) x i xi s.t. xi xi + wi global x-pos legal x-pos no overlap x width Slide

13 PlaceRow: Dynamic Programming PlaceRow: Solve QP by dynamic programming approach: solve sub problems optimally to obtain final solution Process cells from left to right Cell : first cell do not move Slide 3

14 PlaceRow, Cell w Cell : overlap with previous cell? yes cluster with previous cell Clustering process: x = x + w x ( x x ) + e ( x x ) min e Update x, e, and w : e x + e ( x w ) min ( e + e ) e e + e w w + w e + e ( x x ) min e Result: = x x x ex + e e + e new e new x ( x w ) Slide 4

15 PlaceRow, Cell (Cont d) Animation: Result: () Global: Cluster cell and Move cluster to new global x-pos Slide 5

16 PlaceRow, Cell 3 Cell 3: w w 3 3 Overlap with previous cell? yes cluster with previous cell Update x, e, and w : e x + e ( x w ) 3 3 x w w + w3 e + e3 e e + e3 x x = x ( x ) min e Move cell : Result: 3 (3) Prev: 3 Slide 6

17 PlaceRow, Cell 4 Cell 4: 4 Overlap with previous cell? no no clustering, no movement Slide 7

18 PlaceRow, Cell 5 Cell 5: 4 5 Overlap with previous cell? yes cluster with previous cell 4 Update x e4x 4 + e5 ( x 5 w4 4, e 4, and w 4 : ) x 4 e 4 e4 + e5 e4 + e5 w 4 w4 + w5 Move cell 4: min e ( ) 4 x4 x 4 x 4 = x Overlap with previous cell? yes cluster with previous cell (5) Result: 4 (4) (5) Prev: 4 5 Slide 8

19 PlaceRow, Cell 6 Cell 6: 6 Overlap with previous cell? no no clustering, no movement Last cell done, PlaceRow finished Slide 9

20 PlaceRow: Summary PlaceRow: Called several times for legalizing one cell Places cells aligned to one row: minimize quadratic movement quadratic program (QP) Solves QP by dynamic programming: Process cells from left to right If cell overlaps with previous cell: clustering movement further checks with left cells Clustering: update width, weight, and global x-pos of cell constant execution time Linear worst-case complexity: O(N) N: number of cells in the row At most N- clustering operations for N cells Slide 0

21 Complexity Worst-case for a complete circuit with N cells: Average-case (experimental results): O( N ) Θ( N. ) Slide

22 Movement Experimental results of one circuit: Abacus (this work) Abacus: more cells are moved less Tetris Tetris: more cells are moved farther Lower movement with Abacus Slide

23 Results IBM-Place.0 benchmark suite: Routability-driven placement Global placement: Kraftwerk (with routability optimization) Legalization: preserve global placement, minimal movement Results of Abacus (normalized to Tetris): Avg. movement Routed wirelength -3% -.% (negative: better positive: worse) Total CPU time place. +7% Slide 3

24 Conclusion Abacus: Greedy legalization approach, legalizes one cell at a time, similar to Tetris Already legalized cells are moved within the row: PlaceRow PlaceRow: minimize total quadratic movement, dynamic programming, linear worst-case complexity Results: lower movement than Tetris better results in routability-driven placement Slide 4

25 The End Thanks for the attention! Questions? Slide 5