On the Need for Reproducible Numerical Accuracy through Intelligent Runtime Selection of Reduction Algorithms at the Extreme Scale
On the Need for Reproducible Numerical Accuracy through Intelligent Runtime Selection of Reduction Algorithms at the Extreme Scale
复制标题
通过智能运行时选择极端规模的缩减算法来实现可重复的数值精度的需求
DOI：
10.1109/cluster.2015.34
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
M. Taufer
中科院分区：
文献类型：
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作者：
Dylan Chapp;Travis Johnston;M. Taufer
在亿级系统上的归约运算中存在固有的不确定性，再加上浮点算术的非结合性，使得获得可重现的结果变得困难或不可能。研究不可重复性现象的工作通常沿着两条主线之一进行：(1)开发算法，产生可重现的数值结果，而不考虑约简树中的不确定性；(2)研究导致不确定性的系统级因素。我们的工作建立在后者的基础上，并揭示了数学方法的力量，以减少以艾级为单位的错误传播。我们专注于浮点误差累积，而不是全局求和，在这种情况下，执行任何归约顺序都是昂贵的或不可能的。我们用约简树对并行求和进行建模，并确定可用于估计约简对约简树中可变性的敏感度的参数。我们评估了这些参数对不同归约方法成功减少错误的能力的影响。我们的结果表明，迫切需要智能地选择简化运算符，以确保给定程度的可重复精度。
The inherent nondeterminism present in reduction operations on an exascale system, coupled with the nonassociativity of floating-point arithmetic, makes achieving reproducible results difficult or impossible. Work investigating the irreproducibility phenomenon has generally proceeded along one of two veins: (1) development of algorithms that produce reproducible numerical results irrespective of nondeterminism in the reduction tree and (2) study of the system-level factors that induce nondeterminism. Our work builds on the latter and unveils the power of mathematical methods to mitigate error propagation at the exascale. We focus on floating-point error accumulation over global summations where enforcing any reduction order is expensive or impossible. We model parallel summations with reduction trees and identify those parameters that can be used to estimate the reduction's sensitivity to variability in the reduction tree. We assess the impact of these parameters on the ability of different reduction methods to successfully mitigate errors. Our results illustrate the pressing need for intelligent runtime selection of reduction operators that ensure a given degree of reproducible accuracy.