Across Time and Space: Senju's Approach for Scaling Iterative Stencil Loop Accelerators on Single and Multiple FPGAs

Stencil-based applications play an essential role in high-performance systems as they occur in numerous computational areas, such as partial differential equation solving. In this context, Iterative Stencil Loops (ISLs) represent a prominent and well-known algorithmic class within the stencil domain. Specifically, ISL-based calculations iteratively apply the same stencil to a multi-dimensional point grid multiple times or until convergence. However, due to their iterative and intensive nature, ISLs are highly performance-hungry, demanding specialized solutions. Here, Field Programmable Gate Arrays (FPGAs) represent a valid architectural choice as they enable the design of custom, parallel, and scalable ISL accelerators. Besides, the regular structure of ISLs makes them an ideal candidate for automatic optimization and generation flows. For these reasons, this paper introduces Senju, an automation framework for the design of highly parallel ISL accelerators targeting single-/multi-FPGA systems. Given an input description, Senju automates the entire design process and provides accurate performance estimations. The experimental evaluation shows remarkable and scalable results, outperforming single- and multi-FPGA literature approaches under different metrics. Finally, we present a new analysis of temporal and spatial parallelism trade-offs in a real-case scenario and discuss our performance through a single- and novel specialized multi-FPGA formulation of the Roofline Model.