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About: Computing the fast Fourier transform on SIMD microprocessors

Collection type: Ph.D. thesis

Thesis by: Anthony Blake. E-mail the author

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Name: Computing the fast Fourier transform on SIMD microprocessors
ID: col11438
Language: English (en)
Summary: This thesis describes how to compute the fast Fourier transform (FFT) of a power-of-two length signal on single-instruction, multiple-data (SIMD) microprocessors faster than or very close to the speed of state of the art libraries such as FFTW (``Fastest Fourier Transform in the West''), SPIRAL and Intel Integrated Performance Primitives (IPP). The conjugate-pair algorithm has advantages in terms of memory bandwidth, and three implementations of this algorithm, which incorporate latency and spatial locality optimizations, are automatically vectorized at the algorithm level of abstraction. Performance results on 2-way, 4-way and 8-way SIMD machines show that the performance scales much better than FFTW or SPIRAL. The implementations presented in this thesis are compiled into a high-performance FFT library called SFFT (``Streaming Fast Fourier Transform''), and benchmarked against FFTW, SPIRAL, Intel IPP and Apple Accelerate on sixteen x86 machines and two ARM NEON machines, and shown to be, in many cases, faster than these state of the art libraries, but without having to perform extensive machine specific calibration, thus demonstrating that there are good heuristics for predicting the performance of the FFT on SIMD microprocessors (i.e., the need for empirical optimization may be overstated).
Collection Subtype: Ph.D. thesis
Subject: Mathematics and Statistics, Science and Technology
Keywords: DFT, FFT, SIMD
License: Creative Commons Attribution License CC-BY 3.0

Authors: Anthony Blake (amb33@cs.waikato.ac.nz)
Copyright Holders: Anthony Blake (amb33@cs.waikato.ac.nz)
Maintainers: Anthony Blake (amb33@cs.waikato.ac.nz)

Latest version: 1.2 (history)
First publication date: Jun 20, 2012 9:02 pm GMT-5
Last revision to collection: Jul 15, 2012 8:36 pm GMT-5

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Version History

Version: 1.2 Jul 15, 2012 8:36 pm GMT-5 by Anthony Blake
Changes:
Added appendices

Version: 1.1 Jul 15, 2012 5:28 pm GMT-5 by Anthony Blake
Changes:
Initial commit

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Blake, A. Computing the fast Fourier transform on SIMD microprocessors, OpenStax_CNX Web site. http://cnx.org/content/col11438/1.2/, Jul 15, 2012.

American Medical Assocation (AMA) Manual of Style:

Blake A. Computing the fast Fourier transform on SIMD microprocessors [OpenStax_CNX Web site]. July 15, 2012. Available at: http://cnx.org/content/col11438/1.2/.

American Psychological Assocation (APA) Publication Manual:

Blake, A. (2012, July 15). Computing the fast Fourier transform on SIMD microprocessors. Retrieved from the OpenStax_CNX Web site: http://cnx.org/content/col11438/1.2/

Chicago Manual of Style (Bibliography):

Blake, Anthony. "Computing the fast Fourier transform on SIMD microprocessors." OpenStax_CNX. July 15, 2012. http://cnx.org/content/col11438/1.2/.

Chicago Manual of Style (Note):

Anthony Blake, "Computing the fast Fourier transform on SIMD microprocessors," OpenStax_CNX, July 15, 2012, http://cnx.org/content/col11438/1.2/.

Chicago Manual of Style (Reference, in Author-Date style):

Blake, A. 2012. Computing the fast Fourier transform on SIMD microprocessors. OpenStax_CNX, July 15, 2012. http://cnx.org/content/col11438/1.2/.

Modern Languages Association (MLA) Style Manual:

Blake, Anthony. Computing the fast Fourier transform on SIMD microprocessors. OpenStax_CNX. 15 July 2012 <http://cnx.org/content/col11438/1.2/>.