Accelerating the SpMV kernel on standard CPUs by exploiting the partially diagonal structures

Abstract: Sparse Matrix Vector multiplication (SpMV) is one of basic building blocks in scientific computing, and acceleration of SpMV has been continuously required. In this research, we aim for accelerating SpMV on recent CPUs for sparse matrices that have a specific sparsity structure, namely a diagonally structured sparsity pattern. We focus a hybrid storage format that combines the DIA and CSR formats, so-called the HDC format. First, we recall the importance of introducing cache blocking techniques into HDC-based SpMV kernels. Next, based on the observation of the cache blocked kernel, we present a modified version of the HDC formats, which we call the M-HDC format, in which partial diagonal structures are expected to be more efficiently picked up. For these SpMV kernels, we theoretically analyze the expected performance improvement based on performance models. Then, we conduct comprehensive experiments on state-of-the-art multi-core CPUs. By the experiments using typical matrices, we clarify the detailed performance characteristics of each SpMV kernel. We also evaluate the performance for matrices appearing in practical applications and demonstrate that our approach can accelerate SpMV for some of them. Through the present paper, we demonstrate the effectiveness of exploiting partial diagonal structures by the M-HDC format as a promising approach to accelerating SpMV on CPUs for a certain kind of practical sparse matrices.