Flexible Development of Dense Linear Algebra Algorithms on Massively Parallel Architectures with DPLASMA
Flexible Development of Dense Linear Algebra Algorithms on Massively Parallel Architectures with DPLASMA
复制标题
使用 DPLASMA 在大规模并行架构上灵活开发密集线性代数算法
DOI：
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发表时间：
2011
期刊：
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通讯作者：
J. Dongarra
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作者：
G. Bosilca;A. Bouteiller;Anthony Danalis;Mathieu Faverge;A. Haidar;T. Hérault;J. Kurzak;J. Langou;Pierre Lemarinier;H. Ltaief;P. Luszczek;A. YarKhan;J. Dongarra
我们提出了一种开发密集线性代数算法的方法，可以无缝扩展到数千个核心。这可以通过我们的DPLASMA（分布式PLASMA）项目来完成，该项目使用了一种新的通用分布式直接无环图引擎（DAGuE）。该引擎是为高性能计算而设计的，因此它能够在大型分布式存储器系统上扩展源自PLASMA的瓦片算法。当考虑具有异构多核节点的分布式内存平台时，底层DAGuE框架具有许多吸引人的功能：独立于问题大小的DAG表示，从依赖关系中自动提取通信，通信和计算的重叠，任务优先级，以及任务的架构感知调度和管理。该引擎的独创性在于它能够将嵌套循环的顺序代码转换为简洁和合成的格式，然后可以在分布式环境中解释和执行。本文介绍了PLASMA~（Parallel Linear Algebra for Scalable Multi-core Architectures）中三种常见的稠密线性代数算法：Cholesky分解、LU分解和QR分解，并研究了它们在分布式系统中的数据驱动表达和执行。我们通过Cray XT5 Kraken系统上的实验结果证明，我们基于DAG的方法有可能实现相当大比例的峰值性能，这是当前和新兴架构上最先进的分布式数值软件的特征。
We present a method for developing dense linear algebra algorithms that seamlessly scales to thousands of cores. It can be done with our project called DPLASMA (Distributed PLASMA) that uses a novel generic distributed Direct Acyclic Graph Engine (DAGuE). The engine has been designed for high performance computing and thus it enables scaling of tile algorithms, originating in PLASMA, on large distributed memory systems. The underlying DAGuE framework has many appealing features when considering distributed-memory platforms with heterogeneous multicore nodes: DAG representation that is independent of the problem-size, automatic extraction of the communication from the dependencies, overlapping of communication and computation, task prioritization, and architecture-aware scheduling and management of tasks. The originality of this engine lies in its capacity to translate a sequential code with nested-loops into a concise and synthetic format which can then be interpreted and executed in a distributed environment. We present three common dense linear algebra algorithms from PLASMA~(Parallel Linear Algebra for Scalable Multi-core Architectures), namely: Cholesky, LU, and QR factorizations, to investigate their data driven expression and execution in a distributed system. We demonstrate through experimental results on the Cray XT5 Kraken system that our DAG-based approach has the potential to achieve sizable fraction of peak performance which is characteristic of the state-of-the-art distributed numerical software on current and emerging architectures.