Callipepla: Stream Centric Instruction Set and Mixed Precision for Accelerating Conjugate Gradient Solver

The continued growth in the processing power of FPGAs coupled with high bandwidth memories (HBM), makes systems like the Xilinx U280 credible platforms for the linear solvers which often dominate the run time of scientific and engineering applications. In this paper we present Callipepla, an accelerator for a preconditioned conjugate gradient linear solver (CG). FPGA acceleration of CG faces three challenges: (1) how to support an arbitrary problem and terminate acceleration processing on the fly, (2) how to coordinate long-vector data flow among processing modules, and (3) how to save off-chip memory bandwidth and maintain double (FP64) precision accuracy. To tackle the three challenges, we present (1) a stream-centric instruction set for efficient streaming processing and control, (2) decentralized vector flow scheduling to coordinate vector data flow among modules and further reduce off-chip memory accesses with a double memory channel design, and (3) a mixed precision scheme to save bandwidth yet still achieve effective double precision quality solutions. We prototype the accelerator on a Xilinx U280 HBM FPGA. Our evaluation shows that compared to the Xilinx HPC product, the XcgSolver, Callipepla archives a speedup of 3.94x, 3.36x higher throughput, and 2.94x better energy efficiency. Compared to an NVIDIA A100 GPU which has 4x the memory bandwidth of Callipepla, we still achieve 77% of its throughput with 3.34x higher the energy efficiency.