国产异构系统上的HPCG并行算法及高效实现

Parallel Algorithm and Efficient Implementation of HPCG on Domestic Heterogeneous Systems

HPCG基准测试程序是一种新的超级计算机排名度量标准.该测试基准主要用于衡量超级计算机解决大规模稀疏线性系统的能力,更贴近实际应用,近年来广受关注.基于国产超级计算机研究异构众核并行HPCG软件具有非常重要的意义,其不仅可以提升国产超级计算机HPCG的排名,还对很多应用提供了并行算法、优化技术等方面的参考.面向某国产复杂异构超级计算机开展研究,首先采用了分块图着色算法对HPCG进行并行,并提出一种适用于结构化网格的图着色算法.该算法并行性能高于传统的JPL、CC等算法,且着色质量高,运用于HPCG后,迭代次数减少了3次,整体性能提升了6%.分析了复杂异构系统各个部件传输的开销,提出一套更适用于HPCG的任务划分方法,并从稀疏矩阵存储格式、稀疏矩阵重排、访存等角度开展了细粒度的优化.在多进程计算时,还采用内外区划分算法将核心函数SpMV、SymGS中的邻居通信操作进行了隐藏.最终整机测试时,性能达到了国产超级计算机峰值性能的1.67%,与单节点相比,整机弱可扩展性并行效率达到了92%.

HPCG benchmark is a new standard for supercomputer ranking.This benchmark is used mainly for evaluating how fast a supercomputer is able to solve a large scale sparse linear system,which is closer to real applications,and has attracted extensive attention recently.Research of parallel HPCG on domestic heterogeneous many-core supercomputers is very important,not only to improve the HPCG ranking of Chinese supercomputers,but also to provide reference of parallel algorithm and optimization techniques for many applications.This work studies parallelization and optimization of HPCG on a domestically produced complex heterogeneous supercomputer,leveraging blocked graph coloring algorithm for parallelism exploration for the first time on this system,and proposes a graph coloring algorithm for structured grids.The parallelism produced by this algorithm is higher than the traditional JPL and CC algorithm,with better coloring quality.With this algorithm,successfully reduced the iteration number of HPCG by 3 times,and the total performance is improved by 6%.This study also analyzes the data transfer cost of each component in the complex heterogeneous system,providing a task partitioning method,which is more suitable for HPCG,and the neighbor communication cost in SpMV and SymGS is hidden by inner-outer region partitioning.In the whole-system test,an HPCG performance of 1.67% of the peek GFLOPS of the system is achieved,compared to single-node performance,the weak-scaling efficiency on the whole system has reached 92%.