Multi-Bend Bus-Driven Floorplanning

1. Multi-Bend Bus-Driven Floorplanning Jill H.Y.Law & Evangeline F.Y.Young The Chinese University of Hong Kong

2. Outline • Introduction • Background • Sequence Pair • Methodology • Shape Validation • Bus Ordering • Floorplan Realization • Experimental Results • Conclusion

3. Introduction

4. Background • Why is bus-driven floorplanning important? • Previous work: • Hua Xiang, Xiaoping Tang and Martin D.F. Wong “Bus-Driven Floorplanning” ICCAD 2003 • 0-bend is not enough for buses going through many blocks

5. Problem Formulation • A set of n blocks B = {b0, b1, …, bn-1} • A set of m buses U = {u0, u1, …, um-1}, where each bus is associated with a width ti • Decide the position of blocks, such that • Buses go through their blocks • Chip area minimized • Bus area minimized • Buses can have at most 2-bends

6. Problem Formulation • What is meant by “going through” ? • Assume block height > bus width

7. Problem Formulation

8. Sequence Pair (SP) • A pair of sequences of n elements • (…a…b…, …a…b…), a is on the left of b • (…a…b…, …b…a…), a is on top of b • Example: (acbde, daceb)

9. Methodology

10. Overview • While Temp > threshold • Apply a move to obtain a new SP • Evaluate the floorplan • Shape Validation • Bus Ordering • Floorplan Realization • Accept or reject according to Cost and Temp

11. Steps • Assumption • 2 layers for bus routing • Evaluation • Shape Validation • 0-bend • 1-bend • 2-bend • Bus Ordering • Floorplan Realization

12. Shape Validation • Check the bus one by one • From the relative position of the blocks, check if a bus of at most 2 bends can go through all blocks

13. Shape Validation – 0 bend • Step 1: Extract the related blocks from the sequence pair • Example: For a bus ABE • Given a SP (ABCDE, ABCED)  (ABE, ABE) • Step 2: Check relative position between blocks • Example: For a bus ABC • Horizontal bus: (ABCDE, ADEBC)  (ABC, ABC) • Vertical bus: (CDBEA , ABCDE)  (CBA, ABC)

14. Shape Validation – 1 bend • L-shape bus • 1 horizontal component • 1 vertical component • How to recognize them? • Step 1: Extract the related blocks (X, Y) • Step 2: Find the Longest Common Subsequence (LCS) of (X, Y)  Horizontal component

15. Shape Validation – 1 bend • Step 3: Check if the remaining blocks in reverse order • Example: (ABCDEF, ABCFED) • LCSABCD, remaining blocks (DEF, FED) • Step 4: Check if T-shape • T-shape also contains one horizontal component and one vertical component • T-shape is kept for later 2-bend checking

16. Shape Validation – 1 bend • When will a T-shape be formed?

17. Shape Validation – 1 bend • Example: (ABCDE, ADCBE) • Horizontal Component: ABE • Vertical Component: CD

18. Shape Validation – 2 bend • C-Shapes, Z-Shapes, mirrored Z-Shapes … • HVH or VHV • Assume HVH (VHV is similar) • How to recognize them? • Step 1: Extract the related blocks (X, Y) • Step 2: Find the LCS of (X, YR)  vertical • Example: (ABCDE, ADCBE) • Find the LCS of (ABCDE, EBCDA): BCD

19. E A B C D Shape Validation – 2 bend • Step 3: Put the remaining blocks in different relationships with the vertical component

20. Shape Validation – 2 bend • 8 possible relationships • Step 4: Put the blocks into 2 horizontal components

21. Shape Validation – 2 bend • Example: (GHABCEFD, EFDCBGHA) • (GHABCEFD, AHGBCDFE)  vertical component • Upper = {A, H, G}, Lower = {D, E, F} • A C-shape can be formed

22. Shape Validation – 2 bend • Example: (AEBCDF, EDCBFA) • (AEBCDF, AFBCDE)  vertical component • Upper = {A}, Lower = {D}, LowerLeft = {E}, LowerRight = {F} • No valid 2-bend shape can be formed

23. Shape Validation • Extract the related blocks • Check if 0-bend • Check if 1-bend • Assume HVH • Check if 2-bend • Assume VHV • Check if 2-bend • Mark it invalid if all “no”

24. Steps • Evaluation • Shape Validation • Bus Ordering • Floorplan Realization

25. Determine Bus Ordering

26. Bus Ordering • Step 1: Split all the buses into 0-bend bus components • Step 2: Build vertical graph and horizontal graph by looking at each pair of bus components • Use a node to represent each bus component • If bus component a has to be on top of bus component b, add an edge from node a to node b • If there is cycle, at least one bus component in the cycle has to be removed • Horizontal graph can be built in a similar fashion

27. Bus Ordering • Step 3: If there are cycles, remove nodes (bus components) to make the graph acyclic • Aim at removing the least number of nodes • NP-complete • Maximum degree heuristic • Step 4: Remove the corresponding bus components in the other graph as well

28. Steps • Evaluation • Shape Validation • Bus Ordering • Floorplan Realization

29. Floorplan Realization • Realization = obtaining the positions of the blocks and buses • This step is the same as that in Xiang’s work

30. Simulated Annealing • Simulated Annealing Framework • Moves: • Swap • Rotation • Cost Function • Cost = ‧A + ‧B + ‧I • A: chip area, B: total bus area, I: number of invalid bus • Can consider other aspects by adding more terms in the cost function • Total wire length • Routing congestion

31. Summary • While Temp > threshold • Apply a move to obtain a new floorplan • Evaluate the floorplan • Shape Validation • Bus Ordering • Floorplan Realization • Accept or reject according to Cost and Temp

32. Experimental Results

33. Platform • Language • Implemented using C ++ • Machine • Intel Xeon (2.2 GHz) with 1 G memory • MCNC benchmarks

34. Experimental Results • The data set used in Xiang’s work * calculated by [(y1 – y0) / y0]*100%

35. Experimental Results • In this data set, each bus has to go through 10 – 15 blocks * calculated by [(y1 – y0) / y0]*100%

36. Experimental Results • ami49 – 2

37. Experimental Results • ami49 – 3

38. Experimental Results • ami49 – 6

39. Conclusion • Solve the bus-driven floorplanning problem for 0-bend, 1-bend, 2-bend buses • The presence of 1-bend and 2-bend buses is important, especially when the number of blocks that a bus goes through is large