FAR: Fixed Points Addition & Relaxation Based

PlacementBo Hu and Malgorzata Marek-

Sadowska

University of California,Santa Barbara

Outline Introduction Previous works Fixed points Addition &

Relaxation(FAR) Experimental results Conclusion

Introduction

Placement Methodology

Simulated Annealing Quadratic Partitioning

Partitioning Constant force AR modelFAR

Introduction cont.

Placement Category

Incremental Placement

Detailed Placement Global Placement

FAR

Previous Works Constant Force

“Generic Global Placement and Floorplanning”, Hans Eisenmann and Frank M. Johannes, DAC98.

Attractor-Repeller Model “Attractor-Repeller Approach for Global

Placement”, Hussein Etawil, Shawki Areibi, and Anthony Vannelli, ICCAD-99.

Constant Force(EQ1)

(EQ2)(EQ3)(EQ4)

Vector e is constant force based on density.

Fixed Point A fixed point p(x, y) is a

dimensionless pseudo cell positioned at (x,y) on the chip plane. Fixed point can be anywhere, not

necessarily within the chip boundary. Connectivity between fixed points and real

cells can be dynamically modified.(EQ5)

Category-I: controlling fixed points Controlling fixed points are used to

maintain force equilibrium state.

Controlling Fixed point

Category-II: Perturbing fixed points Perturbing fixed points are used to

transform the placement

Perturbing fixed point

Perturbing fixed point

Perturbing fixed point

Category-III: Constraining fixed points

Constraining fixed points are used to restrict the movement of cells.

constraining fixed point

constraining fixed point

constraining fixed point

Apply FAR in global placement – one transform

initial

CF

FAR

FAR based incremental placement Buffer Site Generation(BSG)

Apply FAR in BSG

Controlling Fixed pointPerturbing fixed pointConstraining fixed point

Experimental results for global placement – wire length

Experimental results for global placement – CPU time for one transformation

Experimental results for BSG – test cases

Experimental results for BSG – CF vs. FAR

Experimental results for BSG

Conclusion FAR based placement approach

can be applied in both global placement( overlapping elimination ) and incremental placement (Buffer Site Generation) contexts.

FAR is quadratic-solver friendly approach.