AMF-CSR:基于GPU的SpMV自适应多行折叠CSR

Jianhua Gao, Weixing Ji, Jie Liu, Senhao Shao, Yizhuo Wang, Feng Shi
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引用次数: 0

摘要

SpMV是一种成本优势运算,用于求解大规模稀疏线性系统的迭代方法中。然而,SpMV对乘向量的不规则内存访问导致数据局部性低,从而影响了性能。提出了一种适用于GPU上SpMV计算的自适应CSR多行折叠(AMF-CSR)格式。这种新的存储格式支持可变行数的折叠,以便在计算中实现更好的负载平衡。AMF-CSR不仅增加了折叠行中非零元素的密度,从而提高了相乘向量的访问局部性,而且在折叠行中合并了近似相等数量的非零元素,从而实现了负载均衡。基于28个稀疏矩阵的性能评价表明,与基于固定多行折叠的SpMV算法相比,基于AMF-CSR的SpMV算法在GTX 1080 Ti和Tesla V100上分别实现了4.11x和3.62x的最高加速。使用450个正则稀疏矩阵和450个不规则稀疏矩阵的评价结果也表明AMF-CSR优于其他SpMV实现。
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AMF-CSR: Adaptive Multi-Row Folding of CSR for SpMV on GPU
SpMV is a cost-dominant operation used in many iterative methods for solving large-scale sparse linear systems. However, irregular memory access of SpMV to the multiplied vector leads to low data locality and then harms the performance. This paper presents an adaptive multi-row folding of CSR (AMF-CSR) format for SpMV calculation on GPU. This new storage format supports the folding of the variable number of rows in order to achieve better load balancing in computation. AMF-CSR not only increases the density of non-zero elements in a folded row, thereby improving the access locality of the multiplied vector, but also merges an approximately equal number of nonzero elements in a folded row, hence achieving load balancing. The performance evaluation using 28 sparse matrices shows that the proposed SpMV algorithm based on AMF-CSR achieves the highest speedup of 4.11x and 3.62x on GTX 1080 Ti and Tesla V100 respectively against a fixed multi-row folding-based SpMV algorithm. Evaluation results using 450 regular sparse matrices and 450 irregular sparse matrices also show that AMF-CSR is superior to other SpMV implementations.
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