Abstract
The Fast Fourier Transform is probably one of the most studied algorithms of all time. New techniques regarding hardware and software are often applied and tested on it, but the interest in FFT is still large because of its applications - signal and image processing, numerical computations, etc. In this paper, we start from a trivial recursive version of the algorithm and we speed it up using AVX-512 Single Instruction Multiple Data (SIMD) instructions on an Intel i7 CPU with native support to AVX-512. In particular, we study the impact of two different storage choices of vector of complex numbers: block interleaving and complex interleaving. Experimental results show that automatic vectorization provides a 10.65% (\(\sim 1.12\times \)) speedup, while with vectorization done by hand the speedup reaches 33.78% (\(\sim 1.51\times \)). We have made our code publicly available, which could be helpful for SIMD instructions teaching purposes.
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Notes
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The machine we used has an Intel® Xeon®, 15 GiB of RAM and Ubuntu 4.15.0-171 as OS.
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Acknowledgments
Work partially supported by H2020 project TEXTAROSSA (grant no. 956831), https://textarossa.eu/) and partially by the Italian Ministry of Education and Research (MUR), CrossLab project (Departments of Excellence). We also want to thank Prof. Carlo Vallati for providing the machine used to run the experiments and Emanuele Ruffaldi for interesting discussions on the topic.
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Sansone, G., Cococcioni, M. (2023). Experiments on Speeding Up the Recursive Fast Fourier Transform by Using AVX-512 SIMD Instructions. In: Berta, R., De Gloria, A. (eds) Applications in Electronics Pervading Industry, Environment and Society. ApplePies 2022. Lecture Notes in Electrical Engineering, vol 1036. Springer, Cham. https://doi.org/10.1007/978-3-031-30333-3_34
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DOI: https://doi.org/10.1007/978-3-031-30333-3_34
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