0.6 Results and discussion

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.

[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

[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.