Discrete fourier transform on multicore

Franz Franchetti, Markus Puschel, Yevgen Voronenko, Srinivas Chellappa, Jose M. F. Moura
Electr. & Comput. Eng. (ECE) Dept., Carnegie Mellon Univ., Pittsburgh, PA, USA
IEEE Signal Processing Magazine, 2009


   title={Discrete Fourier transform on multicore},

   author={Franchetti, F. and Puschel, M. and Voronenko, Y. and Chellappa, S. and Moura, J.M.F.},

   journal={Signal Processing Magazine, IEEE},







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This article gives an overview on the techniques needed to implement the discrete Fourier transform (DFT) efficiently on current multicore systems. The focus is on Intel-compatible multicores, but we also discuss the IBM Cell and, briefly, graphics processing units (GPUs). The performance optimization is broken down into three key challenges: parallelization, vectorization, and memory hierarchy optimization. In each case, we use the Kronecker product formalism to formally derive the necessary algorithmic transformations based on a few hardware parameters. Further code-level optimizations are discussed. The rigorous nature of this framework enables the complete automation of the implementation task as shown by the program generator Spiral. Finally, we show and analyze DFT benchmarks of the fastest libraries available for the considered platforms.
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