Abstract
In this paper, we propose an implementation of a parallel three-dimensional fast Fourier transform (FFT) using short vector SIMD instructions on clusters of PCs. We vectorized FFT kernels using Intel’s Streaming SIMD Extensions 2 (SSE2) instructions. We show that a combination of the vectorization and block three-dimensional FFT algorithm improves performance effectively. Performance results of three-dimensional FFTs on a dual Xeon 2.8 GHz PC SMP cluster are reported. We successfully achieved performance of over 5 GFLOPS on a 16-node dual Xeon 2.8 GHz PC SMP cluster.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Cooley, J.W., Tukey, J.W.: An algorithmfor themachine calculation of complex Fourier series. Math. Comput. 19, 297–301 (1965)
Brass, A., Pawley, G.S.: Two and three dimensional FFTs on highly parallel computers. Parallel Computing 3, 167–184 (1986)
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)
Hegland, M.: Real and complex fast Fourier transforms on the Fujitsu VPP 500. Parallel Computing 22, 539–553 (1996)
Calvin, C.: Implementation of parallel FFT algorithms on distributed memory machines with a minimum overhead of communication. Parallel Computing 22, 1255–1279 (1996)
Takahashi, D.: Efficient implementation of parallel three-dimensional FFT on clusters of PCs. Computer Physics Communications 152, 144–150 (2003)
Nadehara, K., Miyazaki, T., Kuroda, I.: Radix-4 FFT implementation using SIMDmultimedia instructions. In: Proc. 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 1999), vol. 4, pp. 2131–2134 (1999)
Franchetti, F., Karner, H., Kral, S., Ueberhuber, C.W.: Architecture independent short vector FFTs. In: Proc. 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2001), vol. 2, pp. 1109–1112 (2001)
Rodriguez, V.P.: A radix-2 FFT algorithm for modern single instruction multiple data (SIMD) architectures. In: Proc. 2002 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2002), vol. 3, pp. 3220–3223 (2002)
Kral, S., Franchetti, F., Lorenz, J., Ueberhuber, C.W.: SIMD vectorization of straight line FFT code. In: Kosch, H., Böszörményi, L., Hellwagner, H. (eds.) Euro-Par 2003. LNCS, vol. 2790, pp. 251–260. Springer, Heidelberg (2003)
Frigo, M., Johnson, S.G.: The design and implementation of FFTW3. Proc. IEEE 93, 216–231 (2005)
Franchetti, F., Kral, S., Lorenz, J., Ueberhuber, C.W.: Efficient utilization of SIMD extensions. Proc. IEEE 93, 409–425 (2005)
Bailey, D.H.: FFTs in external or hierarchical memory. The Journal of Supercomputing 4, 23–35 (1990)
Van Loan, C.: Computational Frameworks for the Fast Fourier Transform. SIAM Press, Philadelphia (1992)
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)
Intel Corporation: IA-32 Intel Architecture Software Developer’s Manual Volume 1: Basic Architecture (2004)
Intel Corporation: Intel C++ Compiler for Linux Systems User’s Guide (2004)
Swarztrauber, P.N.: FFT algorithms for vector computers. Parallel Computing 1, 45–63 (1984)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Takahashi, D., Boku, T., Sato, M. (2006). An Implementation of Parallel 3-D FFT Using Short Vector SIMD Instructions on Clusters of PCs. In: Dongarra, J., Madsen, K., Waśniewski, J. (eds) Applied Parallel Computing. State of the Art in Scientific Computing. PARA 2004. Lecture Notes in Computer Science, vol 3732. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11558958_139
Download citation
DOI: https://doi.org/10.1007/11558958_139
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29067-4
Online ISBN: 978-3-540-33498-9
eBook Packages: Computer ScienceComputer Science (R0)