FPGA-Accelerated Spreading for Global Placement

Abstract

Placement takes a large part of the runtime in an Electronic Design Automation design implementation flow. In modern industrial and academic physical design impementation tools, global placement consumes a significant part of the overall placement runtime. Many of these global placers decouple the placement problem into two main parts - numerical optimization and spreading. In this paper, we propose a new and massively parallel spreading algorithm and also accelerate a part of this algorithm on FPGA. Our algorithm produces placements with comparable quality when integrated into a state-of-the-art academic placer. We formulate the spreading problem as a system of fluid flows across reservoirs and mathematically prove that this formulation produces flows without cycles when solved as a continuous-time system. We also propose a flow correction algorithm to make the flows monotonic, reduce total cell displacement and remove cycles which may arise during the discretization process. Our new flow correction algorithm has a better time complexity for cycle removal than previous algorithms for finding cycles in a generic graph. When compared to our previously published linear programming based spreading algorithm [1], our new fluid-flow based multi-threaded spreading algorithm is 3.44x faster, and the corresponding FPGA-accelerated version is 5.15x faster.