Abstract
This paper discuss an approach to implementing and optimizing fast signal transforms based on a domain-specific computer language, called SPL. SPL programs, which are essentially mathematical formulas, represent matrix factorizations, which provide fast algorithms for computing many important signal transforms. A special purpose compiler translates SPL programs into efficient FORTRAN programs. Since there are many formulas for a given transform, a fast implementation can be obtained by generating alternative formulas and searching for the one with the fastest execution time. This paper presents an application of this methodology to the implementation of the FFT.
This work was partially supported by DARPA through research grant DABT63-98- 1-0004 administered by the Army Directorate of Contracting.
Acknowledgements
The authors would like to thank the referees for their comments and suggestions.
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
L. Auslander, J. R. Johnson, and R. W. Johnson. Automatic implementation of FFT algorithms. Technical Report 96-01, Dept. of Math. and Computer Science, Drexel University, Philadelphia, PA, June 1996. Presented at the DARPA ACMP PI meeting.
J. W. Cooley and J. W. Tukey. An Algorithm for the Machine Calculation of Complex Fourier Series.Math. of Computation, 19:297–301, 1965.
M. Frigo. A fast fourier transform compiler. In PLDI’ 99, pages 169–180, 1999.
M. Frigo and S. G. Johnson. FFTW: An adaptive software architecture for the FFT. In ICASSP’ 98, volume 3, pages 1381–1384, 1998. http://www.fftw.org.
Johnson J., Johnson R., D Rodriguez, and R. Tolimieri. A Methodology for Designing, Modifying, and Implementing Fourier Transform Algorithms on Various Architectures. IEEE Trans. Circuits Sys., 9, 1990.
J. Johnson, R. Johnson, D. Padua, and J. Xiong. SPL: Signal Processing Language, 1999. http://www.ece.cmu.edu/~spiral/SPL.html.
J. R. Johnson and R. W. Johnson. Automatic generation and implementation of FFT algorithms. In SIAM Conference on Parallel Processing for Scientific Computing, March 1999.
J. R. Johnson and M. Püschel. In search of the optimal Walsh-Hadamard transform. In Proc. ICASSP 2000, 2000.
T. Kisuki, P.M.W. Knijnenberg, M.F.P. O’Boyle, and H.A.G. Wijshoff. Iterative compilation in program optimization. In Proc. CPC2000, pages 35–44, 2000.
H. Massalin. Superoptimizer-a look at the smallest program. In Proc. ASPLOS II, pages 122–126, 1987.
J. M. F. Moura, J. Johnson, R. Johnson, D. Padua, V. Prasanna, and M. M. Veloso. SPIRAL: Portable Library of Optimized SP Algorithms, 1998. http://www.ece.cmu.edu/~spiral/.
K. R. Rao and P. Yip. Discrete Cosine Transform. Academic Press, 1990.
R. Tolimieri, M. An, and C. Lu. Algorithms for Discrete Fourier Transforms and Convolution. Springer, 2nd edition, 1997.
C. Van Loan. Computational Framework of the Fast Fourier Transform. Siam, 1992.
R. Clint Whaley and Jack Dongarra. Automatically tuned linear algebra software (ATLAS), 1998.http://www.netlib.org/atlas/.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Johnson, J., Johnson, R.W., Padua, D.A., Xiong, J. (2001). searching for the Best FFT Formulas with the SPL Compiler. In: Midkiff, S.P., et al. Languages and Compilers for Parallel Computing. LCPC 2000. Lecture Notes in Computer Science, vol 2017. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45574-4_8
Download citation
DOI: https://doi.org/10.1007/3-540-45574-4_8
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42862-6
Online ISBN: 978-3-540-45574-5
eBook Packages: Springer Book Archive