Sparse Matrix-dense Vector Multiplication Research Articles

A Streaming Dataflow Engine for Sparse Matrix-Vector Multiplication Using High-Level Synthesis

Using high-level synthesis techniques, this paper proposes an adaptable high-performance streaming dataflow engine for sparse matrix dense vector multiplication (SpMV) suitable for embedded FPGAs. As the SpMV is a memory-bound algorithm, this engine combines the three concepts of loop pipelining , dataflow graph , and data streaming to utilize most of the memory bandwidth available to the FPGA. The main goal of this paper is to show that FPGAs can provide comparable performance for memory-bound applications to that of the corresponding CPUs and GPUs but with significantly less energy consumption. The experimental results indicate that the FPGA provides higher performance compared to that of embedded GPUs for small and medium-size matrices by an average factor of 3.25 whereas the embedded GPU is faster for larger size matrices by an average factor of 1.58. In addition, the FPGA implementation is more energy efficient for the range of considered matrices by an average factor of 8.9 compared to the embedded CPU and GPU. A case study based on adapting the proposed SpMV optimization to accelerate the support vector machine (SVM) algorithm, one of the successful classification techniques in the machine learning literature, justifies the benefits of utilizing the proposed FPGA-based SpMV compared to that of the embedded CPU and GPU. The experimental results show that the FPGA is faster by an average factor of 1.7 and consumes less energy by an average factor of 6.8 compared to the GPU.

Optimization by runtime specialization for sparse matrix-vector multiplication

Runtime specialization optimizes programs based on partial information available only at run time. It is applicable when some input data is used repeatedly while other input data varies. This technique has the potential of generating highly efficient codes. In this paper, we explore the potential for obtaining speedups for sparse matrix-dense vector multiplication using runtime specialization, in the case where a single matrix is to be multiplied by many vectors. We experiment with five methods involving runtime specialization, comparing them to methods that do not (including Intel's MKL library). For this work, our focus is the evaluation of the speedups that can be obtained with runtime specialization without considering the overheads of the code generation. Our experiments use 23 matrices from the Matrix Market and Florida collections, and run on five different machines. In 94 of those 115 cases, the specialized code runs faster than any version without specialization. If we only use specialization, the average speedup with respect to Intel's MKL library ranges from 1.44x to 1.77x, depending on the machine. We have also found that the best method depends on the matrix and machine; no method is best for all matrices and machines.