Performance-driven Analog Placement Considering Boundary Constraint

1. Performance-driven Analog Placement Considering Boundary Constraint C. Lin, J. Lin, C. Huang and S. Chang Department of EE, NCKU, Taiwan DAC 2010

2. Outline • Introduction • Problem Formulation • In-Out Modules in a Symmetry Island • Symmetry Island Considering Boundary Constraint • Maintaining a Feasible ASF-B*-tree • Experimental Results • Conclusions

3. Introduction • To improve circuit performances in analog design, designers would place matched devices symmetrically in layouts • Place the matched devices belonging to the same sub-circuit close to each other, in which a symmetry group is formed • Symmetry-island boundary constraint: To further reduce the routing parasitics, designers should be better to place in-out modules on the boundaries of symmetry islands

4. Introduction • A symmetry island consists of one symmetry pair (b1, b1’) and three self-symmetry modules b0, b2, b3 • The in-out module b2 is placed inside the island, the routing wires would be longer than that when it is placed on the boundary of the island

5. Problem Formulation • Given a set of device modules and symmetry-constrained matching groups • The objective is to obtain a placement P that satisfies the proposed symmetry-island boundary constraint and minimizes the cost function: • Ap: area of the placement • Wp: total wirelength measured by HPWL

6. In-Out Modules in a Symmetry Island • Show the impact on circuit performance due to the in-out module locations in a symmetry island • Implement two placements for an op-amp, and then compare their performances

7. In-Out Modules in a Symmetry Island

8. In-Out Modules in a Symmetry Island

9. Symmetry Island Considering Boundary Constraint • Review of ASF-B*-tree • Three major symmetry types: 1D vertical symmetry, 1D horizontal symmetry, and 2D symmetry 1D vertical symmetry 2D symmetry

10. 1D Symmetry Island with Boundary Constraint • An in-out module can only be placed on the bottom, or the right, or the top boundary of the right-half plane • If an in-out module is a symmetry pair: • In the leftmost branch: thebottom boundary • In the bottom-left branch: theright boundary • In the bottom-right branch: thetop boundary

11. 1D Symmetry Island with Boundary Constraint • If the in-out module is a self-symmetry module: • Being the root node or the bottom node in the rightmost branch:bottom-left corner or top-left corner

12. 1D Symmetry Island with Boundary Constraint • Being the node between two hierarchy nodes, these nodes being arranged in a right-skewed branch:left boundary and no module could be placed at its right side HB*-tree

13. 2D Symmetry Island with Boundary Constraint • For 2D symmetry island, the in-out module needs to be placed on the right or top boundary • If an in-out module is a symmetry pair: • Being the bottom node in the rightmost branch or in the leftmost branch:the top-left corner or the bottom-right corner

14. 2D Symmetry Island with Boundary Constraint • If the in-out module is a self-symmetry module: • Being the root node in a left-skewed branch or in a right-skewed branch:the bottom-left corner and no module could be placed at either its top side or right side

15. Maintaining a Feasible ASF-B*-tree • After an initial HB*-tree is given, perturbs the HB*-tree to get a new solution • Check the feasible conditions of each ASF-B*-tree • If any boundary constraint is violated, transform the infeasible ASF-B*-tree into a feasible one • The algorithm repeats until predefined termination conditions are satisfied

16. Maintaining a Feasible ASF-B*-tree

17. Maintaining a Feasible ASF-B*-tree • For the in-out module nodes corresponding to the self-symmetry modules in 1D symmetry island • If the in-out module node is not on the boundary, delete the node from its current position and insert it into the rightmost branch bottom node

18. Experimental Results • Implemented in C++ and run on a 2.8GHz Intel Pentium4 PC with 1GB RAM • Two circuits • Biasynth_2p4g, Inamixbias_2p4g • Combine some symmetry groups in the two circuits and the MCNC benchmarks • apte, hp, ami33 and ami49

19. Experimental Results

20. Experimental Results

21. Experimental Results

22. Experimental Results

23. Conclusions • Based on ASF-B*-tree, this paper has explored the feasible conditions with boundary constraint and developed an algorithm to meet this property in each perturbation