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P3DFFT: a framework for parallel computations of Fourier transforms in three dimensions (1905.02803v1)

Published 7 May 2019 in cs.DC and cs.MS

Abstract: Fourier and related transforms is a family of algorithms widely employed in diverse areas of computational science, notoriously difficult to scale on high-performance parallel computers with large number of processing elements (cores). This paper introduces a popular software package called P3DFFT implementing Fast Fourier Transforms (FFT) in three dimensions (3D) in a highly efficient and scalable way. It overcomes a well-known scalability bottleneck of 3D FFT implementations by using two-dimensional domain decomposition. Designed for portable performance, P3DFFT achieves excellent timings for a number of systems and problem sizes. On Cray XT5 system P3DFFT attains 45% efficiency in weak scaling from 128 to 65,536 computational cores. Library features include Fourier and Chebyshev transforms, Fortran and C interfaces, in- and out-of-place transforms, uneven data grids, single and double precision. P3DFFT is available as open source at http://code.google.com/p/p3dfft/. This paper discusses P3DFFT implementation and performance in a way that helps guide the user in making optimal choices for parameters of their runs.

Citations (236)

Summary

  • The paper presents P3DFFT as a scalable parallel 3D FFT implementation using a 2D pencil decomposition strategy to optimize communication overhead.
  • It achieved 45% weak scaling efficiency on the Cray XT5 when scaling cores from 128 to 65,536, demonstrating robust performance on high-end systems.
  • The framework supports multiple transform types, precision modes, and both Fortran and C interfaces, offering flexibility for varied scientific applications.

Overview of P3DFFT: A Framework for Parallel 3D Fourier Transforms

The paper "P3DFFT: a framework for parallel computations of Fourier transforms in three dimensions," authored by Dmitry Pekurovsky from the San Diego Supercomputer Center, presents a robust software package designed to perform three-dimensional Fast Fourier Transforms (FFTs) on high-performance computing systems. Given the substantial computational and communication loads associated with 3D FFTs, this paper addresses scalability challenges by employing a two-dimensional domain decomposition strategy.

Technical Highlights

P3DFFT is a comprehensive software solution that provides parallel implementations of 3D FFTs with scalability far exceeding traditional one-dimensional decomposition methods. It supports two-dimensional (2D) "pencil" decompositions and can achieve high levels of efficiency across a variety of computational platforms, indicating interoperable design and architecture. The Cray XT5 system, a key benchmark in this paper, demonstrated a weak scaling efficiency of 45% when the number of computational cores scaled from 128 to 65,536.

Similarly, P3DFFT accommodates various transform types, including Fourier and Chebyshev, and supports both Fortran and C interfaces. The package's feature set is broad, allowing for single and double precision, uneven data grids, and both in-place and out-of-place transformations.

Performance Analysis

The performance results of P3DFFT showcased its scalability on several platforms, including the Cray XT5 (Jaguar) and Ranger systems. Significant emphasis was placed on the two transposes during parallel computations, underscoring the library's reliance on an optimized implementation of MPI_Alltoall(v). Notably, on architectures with 3D torus interconnects like Cray's SeaStar, optimal processor grid configurations were explored for minimizing communication overhead, with results showing variations in processor grid dimensions impacting performance.

The paper provided an asymptotic model demonstrating that the principal execution time for 3D FFTs can be approximated by computational workload and data exchange volumes, impacted by the bisection bandwidth of the system's network.

Implications and Future Directions

The development of P3DFFT aligns with the increasing demands for scalable computational approaches in sectors dealing with three-dimensional grid problems, such as turbulence simulations, molecular dynamics, and astrophysics. Its open-source availability aids a broad range of scientific computations, offering flexibility and adaptability for various applications.

The paper's findings highlight crucial areas for future research, including further optimization of task placements across varying network topologies, a potential hybrid MPI/OpenMP model to mitigate messaging overhead, and exploration into communication-computation overlap strategies in CUDA-capable architectures.

Conclusion

Dmitry Pekurovsky's paper introduces P3DFFT as a significant step forward in reliable, scalable computing for 3D transforms. Its two-dimensional domain decomposition method notably enhances scalability, facilitating high-performance calculations on modern supercomputers. Through rigorous benchmarking and well-documented software design choices, P3DFFT emerges as a crucial tool for scientific computing disciplines reliant on large-scale, three-dimensional FFT computations. Future research and development may explore further refinements in scalability and optimization aligned with evolving supercomputing architectures.