Spare-Cell-Aware Multilevel Analytical Placement

1. Zhe-Wei Jiang, Meng-Kai Hsu, Yao-Wen Chang and Kai-Yuan Chao From DAC2009 Spare-Cell-Aware Multilevel Analytical Placement

2. Outline • Background • Problem formulation • Analytical placement framework • Integrate spare-cell consideration to AP • Multilevel spare-cell-aware insertion • Experimental result

3. Placement

4. Spare Cell

5. Introduction • There are two common ways to performing post-silicon debugging. • Metal fix : reuse the transistor masks and change only the metal layer masks. • FIB(Focus Ion Beam): cut unwanted electrical connections, or to deposit conductive material to make a connection after chip is manufactured Both of them require spare cells insertion

6. Outline • Background • Problem formulation • Analytical placement framework • Integrate spare-cell consideration to AP • Multilevel spare-cell-aware insertion • Experimental result

7. Problem formulation • Given a hypergraph H = (V,E) • Let V= be blocks E= be nets We intend to determine the optimal positions of movable blocks such that the wirelength is minimized, and there is no overlap among blocks.

8. Previous Work • PostSpare[26][22] : inserting spare cells after design placement. • UniSpare[10]: place spare cells among the chip uniformly before placement.

9. Outline • Background • Problem formulation • Analytical placement framework • Integrate spare-cell consideration to AP • Multilevel spare-cell-aware insertion • Experimental result

10. Multi-level framwork

11. Flow chart Upper-level Uncoarsening stage Lower-level uncoarsening stage

12. Analytical Placement Framework(global placement)

13. Log-sum-exp wirelength Smooth the function When is small, log-sum-exp wirelength is close to the HPWL.

14. Potential function Bell-shaped smooth function

17. Solve Unconstraint programming Solve by conjugate gradient Apply quadratic penalty method. We solve a sequence of unconstrained minimization problem with increasing

19. Outline • Background • Problem formulation • Analytical placement framework • Integrate spare-cell consideration to AP • Multilevel spare-cell-aware insertion • Experimental result

20. Cluster Expansion • In most cases, the spare cell requirement is determined by designer’s experience. Designer need to set this parameter

21. Density-Constraint Determination

22. Outline • Background • Problem formulation • Analytical placement framework • Integrate spare-cell consideration to AP • Multilevel spare-cell-aware insertion • Experimental result

23. Multilevel Spare Cell Insertion Top-down partition & spare cell allocation Partition according to block distribution 35:15 15:20 10:5 bottom-up spare cell position computation

24. Determination of Optimal Spare Cell Positions • The optimal positions that minimize the avg distance form blocks to spare cells.

25. Determination of Optimal Spare Cell Positions The sub-region usually contain less than 5 spare cell.

26. Outline • Background • Problem formulation • Analytical placement framework • Integrate spare-cell consideration to AP • Multilevel spare-cell-aware insertion • Experimental result

27. Experimental Result • Quality Comparison of Spare Cell Insertion IWLS 2005 benchmark

28. Experimental Result • HPWL Comparison after Spare Cell Insertion

29. Conclusions • The paper proposed the first spare-cell-aware analytical placement framework. • Experimental result have shown that this algorithm can achieve a much better solution quality of spare cell insertion than existing algorithms with only slight quality overhead.