Fixed Outline Multi-Bend Bus Driven Floorplanning

1. Fixed Outline Multi-Bend Bus Driven Floorplanning W. Sheng, S. Dong, Y. Wu and S. Goto Tsinghua University, Beijing ISQED 2010

2. Outline • Introduction • Problem Formulation • Placement Constraints for Bus • Algorithm • Experimental Results • Conclusion

3. Introduction • Modern Hierarchical SOC design flows need to deal with fixed-outline floorplanning under the interconnect constraints • This paper integrates the bus routing issue into the floorplanning process, which handles hard blocks in a fixed-outline area for SOC designing

4. Introduction • By far, all the existed methods that were adopted to address the BDF problem are based on SA framework • With the help of a certain kind of topological representations • SA is a non-deterministic method, it always needs a great number of iterations to get the result • This paper re-visits the BDF problem and adopts a deterministic algorithm named Less Flexibility First • Without any topological representations

5. Problem Formulation • Input: • A set of rectangle blocks B={bi | i=0,1,…,n-1} • A set of m buses U={ui | i=0,1,…,m-1} and goes through a set of blocks BiB • The width W and height H of the chip, as the fixed-outline constraint • Output: • The position information of the n blocks and the m buses • The objective is to minimize the chip area and the total bus area

6. Problem Formulation • Assumptions: • All the blocks are hard ones • All the blocks in the test cases can be rotated or reflected during the packing process • All the bus bendings should occur at the blocks that are in the corresponding bus nets • There is no restriction on the shape of the bus and the number of bendings in the bus

7. Basic Concepts for LFF • Less Flexibility First (LFF) is a deterministic algorithm for block placement • It packs the blocks one by one during the floorplanning process • The most suitable block from the unpacked blocks is chosen and packed in every step • Which block is chosen in a step depends on its “flexibilities”

8. Basic Concepts for LFF

9. Basic Concepts for LFF • The basic idea of the LFF algorithm is packing the blocks from corners of the die gradually to the center • Choosing and packing one block is called a Packing Step • In every step, each unpacked block will be pseudo-placed at each existed corner, called Corner Packing Step (CPS) • If the placing is feasible, then it is a Candidate Corner Packing Step (CCPS) • The block pseudo-placed at the corner will not cause the overlap between this block and those already packed blocks

10. Basic Concepts for LFF • Each step has some CCPSs • The task of the LFF is to choose the best CCPS in every step • The quality of the CCPS is measured by flexibility • The flexibility of the empty space • (a) The flexibility of a corner packing is 3/8 • (b) The flexibility of a side packing is 5/8 • (c) The flexibility of a hollow space packing is 1

11. Basic Concepts for LFF • The flexibility of the to-be packed blocks • Ai, wi, hi are block i’s area, width and height • A, W, H are the given outline’s area, width and height

12. Basic Concepts for LFF • The flexibility of the packing position • ( x0 , y0 ) denotes the coordination of the center of the work space • ( xc , yc ) denotes the corresponding corner coordination of the CCPS

13. Basic Concepts for LFF • The flexibility of the buses • k is the number of the bus components that can be packed • li is the length of each bus component

14. Basic Concepts for LFF • The flexibility of the CCPS

15. Placement Constraints For Bus • Position Constraint

16. Placement Constraints For Bus • All the bus bendings should occur at the blocks that are in the corresponding bus nets • No-Overlapping Constraint • In a feasible BDF solution, no horizontal/vertical bus component overlaps any other horizontal/vertical bus components

17. Algorithm • Flexibility Modification • Redefine the flexibility of the to-be-packed blocks • TL is the total initial length of all the buses • Li is the initial length of the buses that pass through the block bi

18. Algorithm • Update the flexibility of the to-be-packed blocks after every packing step

19. Algorithm Implementation • Get All CCPSs In A Packing Step • In every packing step, each unpacked block will be pseudo-placed at each existed corner • (a) The block pseudo-placed at the corner will not cause the overlapping between this block and those already packed blocks • (b) There exist can-be-packed bus components that will connect this block to the corresponding buses

20. Algorithm Implementation • Get All CCPSs In A Packing Step • For (b), there are three cases: • Case 1. bi is the first to-be-packed block of the blocks in Bi • Case 2. bi is the second to-be-packed block of the blocks in Bi • Case 3. There are more than one blocks in Bi have been packed before bi

21. Algorithm Implementation

22. Algorithm Implementation • For case 3, suppose there are two blocks bj , bk in Bi have already been packed and the bus component between them is ui1, then this case can be divided into two cases: • Case 3.1 bi is connected to bj (bk) by bus ui2 , and ui1 and ui2 are both horizontal/vertical • Case 3.2 bi is connected to bj (bk) by bus ui2 , but the direction of ui2 is not the same as the direction of ui1

23. Algorithm Implementation • In case 3.1, ui1 and ui2 should be merged • Case 3.2 is the same as case 2, except that it will form a bending in the bus ui

24. Algorithm Implementation • Bus Overlapping Removal • If the to-be-packed bus component overlaps any packed bus component, adjust the position of the to-be-packed bus component until there is no overlapping • If the position adjustment doesn’t work, this CCPS will be discarded

25. Algorithm Implementation • Get The Best CCPS • According to the principle of Less Flexibility First, the best CCPS is from all the CCPSs with the smallest flexibility value • In every packing step, the best CCPS is selected, and the corresponding block and bus components are packed

26. Experimental Results

27. Experimental Results

28. Experimental Results

29. Experimental Results • n100-c, dead space=5.72%, aspect ratio=1.0

30. Conclusion • This paper addresses the BDF problem in a fixed-outline area • By adding the placement constraints for buses to the LFF algorithm, their approach can generate a good BDF solution with small dead space percentage and short run time