A decomposition method with minimum communication amount for parallelization of multi-dimensional FFTs

TL;DR

This paper introduces an adaptive decomposition method for multi-dimensional FFTs that minimizes communication costs across various process counts by intelligently choosing transpose orders and data partitioning strategies.

Contribution

The proposed method adaptively decomposes multi-dimensional FFT data and optimizes transpose order to reduce communication, outperforming previous fixed-dimension approaches.

Findings

Achieves minimal communication for all process ranges

Identifies optimal transpose orders for 3D, 4D, and 5D FFTs

Enhances scalability and efficiency of parallel FFT implementations

Abstract

The fast Fourier transform (FFT) is undoubtedly an essential primitive that has been applied in various fields of science and engineering. In this paper, we present a decomposition method for parallelization of multi-dimensional FFTs with smallest communication amount for all ranges of the number of processes compared to previously proposed methods. This is achieved by two distinguishing features: adaptive decomposition and transpose order awareness. In the proposed method, the FFT data are decomposed based on a row-wise basis that maps the multi-dimensional data into one-dimensional data, and translates the corresponding coordinates from multi-dimensions into one-dimension so that the resultant one-dimensional data can be divided and allocated equally to the processes. As a result, differently from previous works that have the dimensions of decomposition pre-defined, our method can adaptively decompose the FFT data on the lowest possible dimensions depending on the number of processes. In addition, this row-wise decomposition provides plenty of alternatives in data transpose, and different transpose order results in different amount of communication. We identify the best transpose orders with smallest communication amounts for the 3-D, 4-D, and 5-D FFTs by analyzing all possible cases. Given both communication efficiency and scalability, our method is promising in development of highly efficient parallel packages for the FFT.