A Flexible Framework For Multidimensional Dfts

Multidimensional discrete Fourier transforms (DFTs) are typically decomposed into multiple one-dimensional (1D) transforms. Hence, parallel implementations of any multidimentional DFT focus on parallelizing within or across the 1D DFT. Existing DFT packages exploit the inherent parallelism across the 1D DFTs and offer rigid frameworks, that cannot be extended to incorporate both forms of parallelism and various data layouts to enable some of the parallelism. However, in the era of exascale, where systems have thousand of nodes and intricate network topologies, flexibility and parallel efficiency are key aspects all multidimentional DFT frameworks need to have in order to map and scale the computation appropriately. In this work, we show the need for a versatile parallel framework that facilitates the development of a family of parallel multidimentional DFT algorithms by (1) using different data layouts to distribute the data across the compute nodes, (2) exploiting the two different parallelization schemes to different degrees, and (3) unifying the two parallelization schemes within a single framework. We show that the flexibility of selecting different parallel multidimentional DFT algorithms allows for almost linear strong scaling results for problem sizes of 1024(3) on two supercomputers, namely, RIKEN's K-Computer and Oakridge's Summit.