A Hybrid MPI/OpenMP Implementation of a Parallel 3-D FFT on SMP Clusters

  • Daisuke Takahashi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3911)


In the present paper, we propose a hybrid MPI/OpenMP implementation of a parallel three-dimensional fast Fourier transform (FFT) algorithm on SMP clusters. The three-dimensional FFT algorithm can be altered to create a block three-dimensional FFT algorithm in order to reduce the number of cache misses. We then use the obtained block three-dimensional FFT algorithm to implement the parallel three-dimensional FFT. We succeeded in obtaining a performance of over 14 GFLOPS on the AIST Super Cluster M-64 (using 32 nodes out of 132 available, Itanium2 1.3 GHz, 4-way SMP).


Fast Fourier Transform Fast Fourier Transform Algorithm Twiddle Factor Hybrid Implementation Compiler Option 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Cooley, J.W., Tukey, J.W.: An algorithm for the machine calculation of complex Fourier series. Math. Comput. 19, 297–301 (1965)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Agarwal, R.C., Gustavson, F.G., Zubair, M.: An efficient parallel algorithm for the 3-D FFT NAS parallel benchmark. In: Proceedings of the Scalable High-Performance Computing Conference, pp. 129–133 (1994)Google Scholar
  3. 3.
    Hegland, M.: Real and complex fast Fourier transforms on the Fujitsu VPP 500. Parallel Computing 22, 539–553 (1996)CrossRefMATHGoogle Scholar
  4. 4.
    Calvin, C.: Implementation of parallel FFT algorithms on distributed memory machines with a minimum overhead of communication. Parallel Computing 22, 1255–1279 (1996)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Takahashi, D.: Efficient implementation of parallel three-dimensional FFT on clusters of PCs. Computer Physics Communications 152, 144–150 (2003)CrossRefGoogle Scholar
  6. 6.
    Bailey, D.H.: FFTs in external or hierarchical memory. The Journal of Supercomputing 4, 23–35 (1990)CrossRefGoogle Scholar
  7. 7.
    Van Loan, C.: Computational Frameworks for the Fast Fourier Transform. SIAM Press, Philadelphia (1992)CrossRefMATHGoogle Scholar
  8. 8.
    Swarztrauber, P.N.: FFT algorithms for vector computers. Parallel Computing 1, 45–63 (1984)CrossRefMATHGoogle Scholar
  9. 9.
    Frigo, M., Johnson, S.G.: FFTW: An adaptive software architecture for the FFT. In: Proc. 1998 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 1998), pp. 1381–1384 (1998)Google Scholar
  10. 10.
    Sumimoto, S., Tezuka, H., Hori, A., Harada, H., Takahashi, T., Ishikawa, Y.: High performance communication using a commodity network for cluster systems. In: Proc. Ninth International Symposium on High Performance Distributed Computing (HPDC-9), pp. 139–146 (2000)Google Scholar
  11. 11.
    Cappello, F.R., Richard, O., Etiemble, D.: MPI versus MPI+OpenMP on IBM SP for the NAS benchmarks. In: Proc. 2000 ACM/IEEE Conference on Supercompuring (SC 2000) (2000)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Daisuke Takahashi
    • 1
  1. 1.Graduate School of Systems and Information EngineeringUniversity of TsukubaTsukuba, IbarakiJapan

Personalised recommendations