Ultrafast Density Gradient Accumulation in 3D Analytical Placement with Divergence Theorem

Peiyu Liao, Yuxuan Zhao, Siting Liu, Bei Yu

Abstract: Density gradient accumulation plays a pivotal role in 3D analytical placement. Analytical placers rely on this fundamental operation during the backward step of each iteration to compute the gradient of the density penalty for every node. This primitive operation thus constitutes a significant runtime bottleneck, especially for mixed-size designs with large macros. Furthermore, this bottleneck becomes increasingly critical as the grid size in 3D placement is considerably larger than that in conventional 2D placement. In this paper, we propose an algorithm inspired by the divergence theorem to reduce the time complexity of density gradient accumulation. We also present our implementations of this algorithm for both CPU and GPU versions. Experimental results demonstrate that our method achieves more than 3× end-to-end runtime speedup on CPU and GPU compared to the SOTA analytical 3D placer.

External IDs:dblp:conf/iccad/LiaoZLY25