FAR: Fixed Points Addition & Relaxation Based Placement Bo Hu and Malgorzata Marek-Sadowska University of California, Santa Barbara
Outline • Introduction • Previous works • Fixed points Addition & Relaxation(FAR) • Experimental results • Conclusion
Simulated Annealing Quadratic Partitioning Partitioning Constant force FAR AR model Introduction Placement Methodology
Introduction cont. Placement Category Global Placement Detailed Placement Incremental 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)
Controlling Fixed point Category-I: controlling fixed points • Controlling fixed points are used to maintain force equilibrium state.
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 CF initial FAR
FAR based incremental placement • Buffer Site Generation(BSG)
Apply FAR in BSG Controlling Fixed point Perturbing fixed point Constraining fixed point
Experimental results for global placement – CPU time for one transformation
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.