In high-performance computing on distributed-memory systems, communication often represents a significant part of the overall execution time. The relative cost of communication will certainly continue to rise as compute-density growth follows the current technology and industry trends. Design of lower-communication alternatives to fundamental computational algorithms has become an important field of research. For distributed 1-D FFT, communication cost has hitherto remained high as all industry-standard implementations perform three all-to-all internode data exchanges (also called global transposes). These communication steps indeed dominate execution time. In this paper, we present a mathematical framework from which many single-all-to-all and easy-to-implement 1-D FFT algorithms can be derived. For large-scale problems, our implementation can be twice as fast as leading FFT libraries on state-of-the-art computer clusters. Moreover, our framework allows tradeoff between accuracy and performance, further boosting performance if reduced accuracy is acceptable.

中文翻译：

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低通信一维FFT框架

在分布式内存系统上的高性能计算中，通信通常占整个执行时间的重要部分。随着计算密度的增长遵循当前的技术和行业趋势，通信的相对成本肯定会继续上升。低通信替代基本计算算法的设计已成为重要的研究领域。迄今为止，对于分布式一维FFT，由于所有行业标准实现都执行三个所有节点间数据交换（也称为全局转置），因此通信成本一直很高。这些通信步骤确实控制了执行时间。在本文中，我们提供了一个数学框架，从中可以导出许多单对所有和易于实现的一维FFT算法。对于大规模问题，我们的实现速度可以是最新计算机集群上领先的FFT库的两倍。此外，我们的框架允许在精度和性能之间进行权衡，如果可以接受降低的精度，则可以进一步提高性能。