Scalable Parallelization Strategies to Accelerate NuFFT Data Translation on Multicores

  • Yuanrui Zhang
  • Jun Liu
  • Emre Kultursay
  • Mahmut Kandemir
  • Nikos Pitsianis
  • Xiaobai Sun
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6272)


The non-uniform FFT (NuFFT) has been widely used in many applications. In this paper, we propose two new scalable parallelization strategies to accelerate the data translation step of the NuFFT on multicore machines. Both schemes employ geometric tiling and binning to exploit data locality, and use recursive partitioning and scheduling with dynamic task allocation to achieve load balancing. The experimental results collected from a commercial multicore machine show that, with the help of our parallelization strategies, the data translation step is no longer the bottleneck in the NuFFT computation, even for large data set sizes, with any input sample distribution.


Fast Fourier Transform Conventional Tiling Mutual Exclusion Cartesian Grid Cache Size 
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  1. 1.
  2. 2.
    Beylkin, G.: On the fast Fourier transform of functions with singularities. Applied and Computational Harmonic Analysis 2, 363–381 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Chen, G., Xue, L., et al.: Geometric tiling for reducing power consumption in structured matrix operations. In: Proceedings of IEEE International SOC Conference, pp. 113–114 (September 2006)Google Scholar
  4. 4.
    Cooley, J., Tukey, J.: An algorithm for the machine computation of complex Fourier series. Mathematics of Computation 19, 297–301 (1965)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Debroy, N., Pitsianis, N., Sun, X.: Accelerating nonuniform fast Fourier transform via reduction in memory access latency. In: SPIE, vol. 7074, p. 707404 (2008)Google Scholar
  6. 6.
    Duijndam, A., Schonewille, M.: Nonunifrom fast Fourier transform. Geophysics 64, 539 (1999)CrossRefGoogle Scholar
  7. 7.
    Dutt, A., Rokhlin, V.: Fast Fourier transforms for nonequispaced data. SIAM Journal on Scientific Computing 14, 1368–1393 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Fessler, J.A., Sutton, B.P.: Nonuniform fast Fourier transforms using min-max interpolation. IEEE Transactions on Signal Processing 51, 560–574 (2003)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Finkel, R., Bentley, J.: Quad trees: A data structure for retrieval on composite keys. Acta Informatica 4, 1–9 (1974)CrossRefzbMATHGoogle Scholar
  10. 10.
    Frigo, M.: A fast Fourier transform compiler. ACM SIGPLAN Notices 34, 169–180 (1999)CrossRefGoogle Scholar
  11. 11.
    Frigo, M., Johnson, S.: FFTW: An adaptive software architecture for the FFT. In: Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing, vol. 3, pp. 1381–1384 (May 1998)Google Scholar
  12. 12.
    Greengard, L., Lee, J.Y.: Accelerating the nonuniform fast Fourier transform. SIAM Review 46, 443–454 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Knopp, T., Kunis, S., Potts, D.: A note on the iterative MRI reconstruction from nonuniform k-space data. International Journal of Biomedical Imaging 6, 4089–4091 (2007)Google Scholar
  14. 14.
    Liu, Q., Nguyen, N.: An accurate algorithm for nonuniform fast Fourier transforms (NUFFTs). IEEE Microwaves and Guided Wave Letters 8, 18–20 (1998)CrossRefGoogle Scholar
  15. 15.
    Liu, Q., Tang, X.: Iterative algorithm for nonuniform inverse fast Fourier transform (NU-IFFT). Electronics Letters 34, 1913–1914 (1998)CrossRefGoogle Scholar
  16. 16.
    Renganarayana, L., Rajopadhye, S.: An approach to SAR imaging by means of non-uniform FFTs. In: Proceedings of IEEE International Geoscience and Remote Sensing Symposium, vol. 6, pp. 4089–4091 (July 2003)Google Scholar
  17. 17.
    Renganarayana, L., Rajopadhye, S.: A geometric programming framework for optimal multi-level tiling. In: Proceedings of ACM/IEEE Conference on Supercomputing, May 2004, p. 18 (2004)Google Scholar
  18. 18.
    Sorensen, T., Schaeffter, T., Noe, K., Hansen, M.: Accelerating the nonequispaced fast Fourier transform on commodity graphics hardware. IEEE Transactions on Medical Imaging 27, 538–547 (2008)CrossRefGoogle Scholar
  19. 19.
    Ying, S., Kuo, J.: Application of two-dimensional nonuniform fast Fourier transform (2-d NuFFT) technique to analysis of shielded microstrip circuits. IEEE Transactions on Microwave Theory and Techniques 53, 993–999 (2005)CrossRefGoogle Scholar
  20. 20.
    Zhang, Y., Kandemir, M., Pitsianis, N., Sun, X.: Exploring parallelization strategies for NUFFT data translation. In: Proceedings of Esweek, EMSOFT (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Yuanrui Zhang
    • 1
  • Jun Liu
    • 1
  • Emre Kultursay
    • 1
  • Mahmut Kandemir
    • 1
  • Nikos Pitsianis
    • 2
    • 3
  • Xiaobai Sun
    • 3
  1. 1.Pennsylvania State UniversityUniversity ParkUSA
  2. 2.Aristotle UniversityThessalonikiGreece
  3. 3.Duke UniversityDurhamU.S.A.

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