With increasing sizes of distributed systems, there comes an increased risk of communication bottlenecks. In the past decade there has been a growing interest in communication-avoiding algorithms. The distributed memory Fast Fourier Transform is an important algorithm which suffers from major communication bottlenecks. In this work, we take a look at an existing communication-avoiding algorithm FMM-FFT, an alternative to FFT which utilizes the Fast Multipole Method (FMM) to reduce communications to a single all-to-all communication. We present a detailed implementation of FMM-FFT relying on modern libraries and demonstrate it on two distinct distributed memory architectures notably a traditional Intel Xeon based HPC cluster and then a Beowulf cluster. We show that while the FMM-FFT is significantly slower than FFT on the traditional HPC cluster, on the Beowulf cluster it outperforms standard FFT, consistently getting speedups of 1.5x or more against FFTW. We then proceed to show how the communication to computation cost metric is important and useful in explaining the performance results of FMM-FFT against standard FFT. The source code pertaining to this work is being made publicly available under a permissive open source licence at Github.

随着分布式系统规模的增加，通信瓶颈的风险也随之增加。在过去的十年中，人们对避免通信的算法越来越感兴趣。分布式内存快速傅立叶变换是一种重要的算法，它存在主要的通信瓶颈。在这项工作中，我们看一下现有的避免通信算法FMM-FFT，它是FFT的替代方法，它利用快速多极子方法（FMM）将通信减少为单一的全部通信。我们介绍了依赖于现代库的FMM-FFT的详细实现，并在两种不同的分布式内存体系结构上进行了演示，特别是传统的基于Intel Xeon的HPC集群，然后是Beowulf集群。我们显示，虽然FMM-FFT的速度明显比传统HPC群集上的FFT慢，在Beowulf集群上，它的性能优于标准FFT，与FFTW相比，始终保持1.5倍甚至更高的速度。然后，我们将继续展示与计算成本度量的通信在解释FMM-FFT与标准FFT的性能结果方面如何重要和有用。与这项工作相关的源代码已在Github上以允许的开源许可证公开提供。