一种加速稀疏矩阵-向量乘法的新方法

P. Tvrdík, I. Šimeček
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引用次数: 7

摘要

稀疏矩阵向量乘法(简称SpMtimesV)是数值线性代数中最常见的子例程之一。问题是SpMtimesV期间的内存访问模式是不规则的,缓存的利用率可能受到低空间或时间局部性的影响。本文介绍了一种加速SpMtimesV的新方法。这个方法包括3个步骤。第一步是将整个矩阵分成更小的部分(区域),这些部分可以放入缓存中。由于更好地利用了远程引用,第二步提高了乘法期间的局部性。最后一步是最大化每个区域的部分乘法的机器计算性能。在本文中,我们更详细地描述了这3个步骤的各个方面(包括所有步骤的快速和节省时间的算法)。我们的测量证明,我们的方法对来自不同技术领域的几乎所有矩阵都有显著的加速
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A New Approach for Accelerating the Sparse Matrix-Vector Multiplication
Sparse matrix-vector multiplication (shortly SpMtimesV) is one of most common subroutines in the numerical linear algebra. The problem is that the memory access patterns during the SpMtimesV are irregular and the utilization of cache can suffer from low spatial or temporal locality. This paper introduces new approach for the acceleration the SpMtimesV. This approach consists of 3 steps. The first step divides the whole matrix into smaller parts (regions) those can fit in the cache. The second step improves locality during the multiplication due to better utilization of distant references. The last step maximizes machine computation performance of the partial multiplication for each region. In this paper, we describe aspects of these 3 steps in more detail (including fast and time-inexpensive algorithms for all steps). Our measurements proved that our approach gives a significant speedup for almost all matrices arising from various technical areas
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