Ultrafast CPU/GPU Kernels for Density Accumulation in Placement

Density accumulation is a widely-used primitive operation in physical design, especially for placement. Iterative invocation in the optimization flow makes it one of the runtime bottlenecks. Accelerating density accumulation is challenging due to data dependency and workload imbalance. In this paper, we propose efficient CPU/GPU kernels for density accumulation by decomposing the problem into two phases: constant-time density collection for each instance and a linear-time prefix sum. We develop CPU and GPU dedicated implementations, and demonstrate promising efficiency benefits on tasks from large-scale placement problems.