Sparse Matrix-Vector multiplication (SpMV) is an important computational kernel in scientific applications. Its performance highly depends on the nonzero distribution of sparse matrices. In this paper, we propose a new storage format for diagonal sparse matrices, defined as Compressed Row Segment with Diagonal-pattern (CRSD). In CRSD, we design diagonal patterns to represent the diagonal distribution. As the Graphics Processing Units (GPUs) have tremendous computation power and OpenCL makes them more suitable for the scientific computing, we implement the SpMV for CRSD format on the GPUs using OpenCL. Since the OpenCL kernels are complied at runtime, we design the code generator to produce the codelets for all diagonal patterns after storing matrices into CRSD format. Specifically, the generated codelets already contain the index information of nonzeros, which reduces the memory pressure during the SpMV operation. Furthermore, the code generator also utilizes property of memory architecture and thread schedule on the GPUs to improve the performance. In the evaluation, we select four storage formats from prior state-of-the-art implementations (Bell and Garland, 2009) on GPU. Experimental results demonstrate that the speedups reach up to 1.52 and 1.94 in comparison with the optimal implementation of the four formats for the double and single precision respectively. We also evaluate on a two-socket quad-core Intel Xeon system. The speedups reach up to 11.93 and 12.79 in comparison with CSR format under 8 threads for the double and single precision respectively.
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