Optimized Data Reuse via Reordering for Sparse Matrix-Vector Multiplication on FPGAs

Abstract

Sparse matrix-vector multiplication (SpMV) is of paramount importance in both scientific and engineering applications. The main workload of SpMV is multiplications between randomly distributed nonzero elements in sparse matrices and their corresponding vector elements. Due to irregular data access patterns of vector elements and the limited memory bandwidth, the computational throughput of CPUs and GPUs is lower than the peak performance offered by FPGAs. FPGA's large on-chip memory allows the input vector to be buffered on-chip and hence the off-chip memory bandwidth is only utilized to transfer the nonzero elements' values, column indices, and row indices. Multiple nonzero elements are transmitted to FPGA and then their corresponding vector elements are accessed per cycle. However, typical on-chip block RAMs (BRAM) in FPGAs only have two access ports. The mismatch between off-chip memory bandwidth and on-chip memory ports stalls the whole engine, resulting in inefficient utilization of off-chip memory bandwidth. In this work, we reorder the nonzero elements to optimize data reuse for SpMV on FPGAs. The key observation is that since the vector elements can be reused for nonzero elements with the same column index, memory requests of these elements can be omitted by reusing the fetched data. Based on this observation, a novel compressed format is proposed to optimize data reuse by reordering the matrix's nonzero elements. Further, to support the compressed format, we design a scalable hardware accelerator and implement it on the Xilinx UltraScale ZCU106 platform. We evaluate the proposed design with a set of matrices from the University of Florida sparse matrix collection. The experimental results show that the proposed design achieves an average 1.22x performance speedup w.r.t. the state-of-the-art work.