Constraint Graph-Based Macro Placement for Modern Mixed-Size Circuit Designs

1. Constraint Graph-Based Macro Placement for Modern Mixed-Size Circuit Designs Hisn-Chen Chen Yi-Lin Chuang Yao-Wen Chang Yung-Chung Chang ICCAD’08 Speaker: siang-ting

2. Outline • Introduction • TCG • Problem formulation • Our macro placement alogrithm • Experimental results • Conclusions

3. Introduction • Modern circuit designs usually contain large macros with areas more than 10,000 times greater than that of a standard cell. • Adopt the two-stage mixed-size placement - consist of macro placement followed by standard-cell placement. • Based on the TCG floorplan representation, this paper’s algorithm search for macro position through a new adaptive simulated annealing(SA).

4. TCG • Transitive Closure Graph (TCG) • Based on two graph - a horizontal transitive closure graph Ch - a vertical transitive closure graph Cv

5. biis horizontalto bj (bibj): if bi is on the left side of bj and their projection on the y axis overlap. • biis vertical to bj (bibj): if bi is on the bottom side of bj and their projection on the x axis overlap. • biis diagonal to bj : if bi is on the left side of bj and their projection on the x and y axis do not overlap.

6. If biis diagonal to bj , we set bi bi,unless there exist a chain of vertical relation,for which we make bi bi (bj bi ). • An edge (ni,nj) is said to be a reduction edge if there does not exits another path from ni and nj ,except the edge itself (ni,nj).

7. Augmented TCG: add the source node ns and the sink node nt ,and their width and height are zero.

8. *Generated by wirelength-drvien mixed- size global placement *may contain macro overlaps Problem Formulation • The Mixed-sized Flow

9. Macro placement problem: • goal: find legalized macro positions that minimize some cost metric(e.g., macro displacement from their original position)

10. Our Macro Placement Algorithm-Macro Placement Using TCG • Definition 1: A TCG isfeasible if there exists a legalized macro placement that can fit into the chip outline under the geometric relation defined by the TCG.

11. For a given TCG, we first add to pseudo macros ms and mt in Ch, and let C’h denote the modified graph. • lviand uvi denote the leftmost and rightmost coordinates that the macro mi can place. • The slack svifor each vertex vi in C’hbe calculated:

13. Our Macro Placement Algorithm-Linear Programming Formulation • goal: minimize the macro displacement and preserve a better standard-cell placement region. • idea : expand the displacement reference position linearly w.r.t. the gravity center of standard cells. • the expanded reference position

14. determine legalized macro positions with displacement minimization and standard-cell placement region. • Linear constraints based on the edges derived in

15. Our Macro Placement Algorithm-Macro Placement Evaluation • define the cost function Φ to evaluate the quality of a macro placement:

17. Our Macro Placement Algorithm-The Macro Placement Flow • Four operations of adaptive SA: 1) rotation: rotate a module. 2) swap : swap two nodes in both of Ch and Cv . 3) reverse: reverse a reduction edge in Ch or Cv . 4) move : move a reduction edge from TCG to another.

18. Corner packing:

20. Experimental Results

23. Conclusion • Using a TCG to represent the macro placement. • The results show that this placer is very flexible. • Four operations to perturb of TCG can be found in refernce[14].