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In order to test the hypotheses set out in Introduction , SFFT was benchmarked alongside FFTW and other libraries on a wide range of machines, as per the methods set out in Benchmark methods . The majority of the data was collected on Linux machines populated with SSE capable Intel microprocessors, with some additionaldata collected on small set of AVX and ARM NEON machines. The results are divided into three sections: speed, accuracy and setup time, with an additional section detailing a model that predicts SFFT's performance for different configurations. Finally, the chapter concludes by relating the results to other work.

Linux benchmark machines, listed with the size of each level of cache (in kilobytes)
Modelstring L1d L2 L3
Intel(R) Pentium(R) 4 CPU 2.80GHz 16 512 -
Intel(R) Pentium(R) D CPU 3.00GHz 16 1024 -
Intel(R) Pentium(R) M processor 1000MHz 32 1024 -
Intel(R) Xeon(TM) CPU 2.40GHz 16 2048 -
Intel(R) Xeon(R) CPU E5335 @ 2.00GHz 32 4096 -
Intel(R) Xeon(R) CPU X5355 @ 2.66GHz 32 8192 -
Intel(R) Xeon(R) CPU E5430 @ 2.66GHz 32 6144 -
Intel(R) Xeon(R) CPU X5560 @ 2.80GHz 32 256 8192
Intel(R) Core(TM)2 CPU 6600 @ 2.40GHz 32 4096 -
Intel(R) Core(TM)2 Quad CPU Q6600 @ 2.40GHz 32 4096 -
Intel(R) Core(TM)2 Duo CPU E6850 @ 3.00GHz 32 4096 -
Intel(R) Core(TM)2 Duo CPU E8400 @ 3.00GHz 32 6144 -
Intel(R) Core(TM)2 Duo CPU P8600 @ 2.40GHz 32 3072 -
Intel(R) Core(TM) i5 CPU 660 @ 3.33GHz 32 256 4096
Intel(R) Core(TM) i7-2600 CPU @ 3.40GHz 32 256 8192

[link] presents a summary of the Linux machines that were used to run benchmarks. The majority of the machines were functioning as either lab workstations or servers in a University environment. The benchmarks took approximately 12 hours to run, and while efforts were made to reduce each machine's load to a minimum, there were still transient system processes, such as log rotations and backups during the night that have introduced noise into the results.

For the Linux benchmarks, both 32-bit and 64-bit statically-linked binaries for SFFT, FFTW 3.3 and SPIRAL were compiled with icc 12.0.5, gcc 4.4.5 and clang 1.1. For the OS X benchmarks, 32-bit and 64-bit binaries for SFFT, FFTW 3.3 and SPIRAL were compiled with icc 12.1.0, llvm-gcc 4.2.1 and clang 3.0. The builds of SFFT and FFTW 3.3.1 for iOS 5 on ARM NEON were compiled with Apple clang 3.0.

Several binary libraries were also benchmarked: Intel IPP 7 and Apple Accelerate. Because these libraries are only available in binary form, they are compared against the icc builds of SFFT, FFTW 3.3 and SPIRAL, because icc generally produced the fastest code.

Speed

The speed results are presented in subsections according to the SIMD extensions: SSE, AVX and ARM NEON.

Sse

Performance comparison between SFFT and FFTW 3.3 in estimate mode on SSE machines
Performance comparison between SFFT and FFTW 3.3 in patient mode on SSE machines
Performance comparison between SFFT and SPIRAL on SSE machines. Although SPIRAL is faster when compiled with clang 1.1, [link] shows that SFFT is faster than SPIRAL when compiled with clang 3.0

[link] summarizes the speed performance of SFFT against FFTW 3.3 running in estimate mode on Linux machines with SSE. Twelve heatmaps are used to present data from different configurations. The three rows in the grid correspond to the three different compilers used, while the four columns correspond to the four different architecture and floating-point precision pairs. Within each heatmap, the rows correspond to different machines, and the columns correspond to different sizes of transform ( 2 1 through to 2 18 ). Shades of green indicate that SFFT is faster for a particular point of data, while shades of yellow through to red indicate that FFTW is faster; lighter shades indicate a small difference, while darker shades indicate a bigger difference in performance. The scale for the colour map is computed separately for each of the 12 heatmaps in the grid, so a particular colour in one heatmap is not directly comparable to the same colour in another heatmap; the colours are only meant to indicate differences within each heatmap.

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Source:  OpenStax, Computing the fast fourier transform on simd microprocessors. OpenStax CNX. Jul 15, 2012 Download for free at http://cnx.org/content/col11438/1.2
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