Reproducible, Accurately Rounded and Efficient BLAS
Reproducible, Accurately Rounded and Efficient BLAS
复制标题
可重复、精确舍入且高效的 BLAS
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
David Parello
中科院分区：
文献类型：
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作者：
Chemseddine Chohra;P. Langlois;David Parello
在平行计算中，数值可重复性失败会增加，因为浮点求和是非缔合性的。大规模平行和优化的执行会动态修改浮点操作顺序。因此，数值结果可能会从一个运行变为另一种运行。我们建议通过尽可能扩展IEEE-754正确的圆形属性到更大的操作序列来确保可重复性。我们介绍了稀有的 - 可重现的，准确的，圆形的，有效的布拉），从最近的准确有效的求和算法中受益。提出了1级（ASUM，DOT和NRM2）和2级（GEMV）例程的解决方案。与英特尔MKL库和其他现有可重复的算法相比，研究了它们的性能。对于共享和分布式存储器并行系统，我们在最坏的情况下表现出2（IME）的额外成本为2（IME），这对于广泛的应用程序令人满意。对于Intel Xeon Phi加速器，观察到更大的外部成本（4（IME）至6（IMES）），至少对调试和验证步骤至少有帮助。
Numerical reproducibility failures rise in parallel computation because floating-point summation is non-associative. Massively parallel and optimized executions dynamically modify the floating-point operation order. Hence, numerical results may change from one run to another. We propose to ensure reproducibility by extending as far as possible the IEEE-754 correct rounding property to larger operation sequences. We introduce our RARE-BLAS (Reproducible, Accurately Rounded and Efficient BLAS) that benefits from recent accurate and efficient summation algorithms. Solutions for level 1 (asum, dot and nrm2) and level 2 (gemv) routines are presented. Their performance is studied compared to the Intel MKL library and other existing reproducible algorithms. For both shared and distributed memory parallel systems, we exhibit an extra-cost of 2( imes ) in the worst case scenario, which is satisfying for a wide range of applications. For Intel Xeon Phi accelerator a larger extra-cost (4( imes ) to 6( imes )) is observed, which is still helpful at least for debugging and validation steps.