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<title>SLEEF - Benchmark Results</title>
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<h1>SLEEF - Benchmark Results</h1>
<h2>Table of contents</h2>
<ul class="none" style="font-family: arial, sansserif; padding-left: 0.5cm;">
<li><a class="underlined" href="index.xhtml">Introduction</a></li>
<li><a class="underlined" href="compile.xhtml">Compiling and installing the library</a></li>
<li><a class="underlined" href="purec.xhtml">Math library reference</a></li>
<li><a class="underlined" href="quad.xhtml"> Quad-precision math library reference</a></li>
<li><a class="underlined" href="dft.xhtml">DFT library reference</a></li>
<li><a class="underlined" href="misc.xhtml">Other tools included in the package</a></li>
<li> </li>
<li><a class="underlined" href="benchmark.xhtml">Benchmark results</a></li>
<ul class="disc">
<li><a href="benchmark.xhtml#libm">Vectorized math library</a></li>
<li><a href="benchmark.xhtml#dft">Discrete Fourier transform</a></li>
</ul>
<li> </li>
<li><a class="underlined" href="additional.xhtml">Additional notes</a></li>
</ul>
<h2 id="libm">Vectorized math library</h2>
<p class="noindent" style="font-size:1em; margin-top:0.5cm;">
The graphs below show comparison of the execution time between
<a class="undecorated"
href="https://github.com/shibatch/sleef">SLEEF</a>-3.2 compiled
with GCC-7.2 and Intel SVML included in Intel C Compiler 18.0.1.
</p>
<p style="font-size:1em;">
The execution time of each function is measured by executing each
function 10^8 times and taking the average time. Each time a
function is executed, a uniformly distributed random number is set
to each element of the argument vector(each element is set a
different value.) The ranges of the random number for each
function are shown below. Argument vectors are generated before
the measurement, and the time to generate random argument vectors
is not included in the execution time.
</p>
<br/>
<ul>
<li>Trigonometric functions : [0, 6.28] and [0, 10^6] for
double-precision functions. [0, 6.28] and [0, 30000] for
single-precision functions.</li>
<li>Log : [0, 10^300] and [0, 10^38] for double-precision
functions and single-precision functions, respectively.</li>
<li>Exp : [-700, 700] and [-100, 100] for double-precision
functions and single-precision functions, respectively.</li>
<li>Pow : [-30, 30] for both the first and the second
arguments.</li>
<li>Asin : [-1, 1]</li>
<li>Atan : [-10, 10]</li>
<li>Atan2 : [-10, 10] for both the first and the second
arguments.</li>
</ul>
<br/>
<p style="font-size:1em;">
The accuracy of SVML functions can be chosen by compiler options,
not the function names. "-fimf-max-error=1.0" option is specified
to icc to obtain the 1-ulp-accuracy results, and
"-fimf-max-error=5.0" option is used for the 5-ulp-accuracy
results.
</p>
<p style="font-size:1em;">
Those results are measured on a PC with Intel Core i7-6700 CPU @
3.40GHz with Turbo Boost turned off. The CPU should be always
running at 3.4GHz during the measurement.
</p>
<p style="font-size:1.2em; margin-top:1.0cm;">
<b style="color:#0050a0;">Click graphs to magnify</b>.
</p>
<p style="margin-bottom:1cm;"> </p>
<p style="text-align:center; margin-bottom:2cm;">
<a class="nothing" href="trigdp.png">
<img src="trigdp.png" alt="Performance graph for DP trigonometric functions" width="50%" height="50%"/>
</a>
<br />
Fig. 6.1: Execution time of double precision trigonometric functions
</p>
<p style="text-align:center; margin-bottom:2cm;">
<a class="nothing" href="trigsp.png">
<img src="trigsp.png" alt="Performance graph for SP trigonometric functions" width="50%" height="50%"/>
</a>
<br />
Fig. 6.2: Execution time of single precision trigonometric functions
</p>
<p style="text-align:center; margin-bottom:2cm;">
<a class="nothing" href="nontrigdp.png">
<img src="nontrigdp.png" alt="Performance graph for other DP functions" width="50%" height="50%"/>
</a>
<br />
Fig. 6.3: Execution time of double precision log, exp, pow and inverse trigonometric functions
</p>
<p style="text-align:center; margin-bottom:2cm;">
<a class="nothing" href="nontrigsp.png">
<img src="nontrigsp.png" alt="Performance graph for other SP functions" width="50%" height="50%"/>
</a>
<br />
Fig. 6.4: Execution time of single precision log, exp, pow and inverse trigonometric functions
</p>
<p class="footer">
Copyright © 2010-2025 SLEEF Project, Naoki Shibata and contributors.<br/>
SLEEF is open-source software and is distributed under the Boost Software License, Version 1.0.
</p>
<h2 id="dft">Discrete Fourier transform</h2>
<p>
Below is the result of performance comparison between SleefDFT and
FFTW3. The graphs show the performance of complex transform by both
libraries, with the following settings.
</p>
<br/>
<ul>
<li>Compiler : gcc version 14.2.0 (Ubuntu 14.2.0-4ubuntu2~24.04)</li>
<li>CPU : Ryzen 9 7950X (clock frequency fixed at 4.5GHz)</li>
<li>SLEEF build option : -DSLEEF_BUILD_DFT=True -DSLEEFDFT_ENABLE_STREAM=True -DSLEEFDFT_MAXBUTWIDTH=7</li>
<li>FFTW version 3.3.10-1ubuntu3</li>
</ul>
<br/>
<p>
The vertical axis represents the performance in Mflops calculated in
the way indicated in the FFTW web site. The horizontal axis represents
log2 of the size of transform. Execution plans were made with
SLEEF_MODE_MEASURE mode and FFTW_MEASURE mode, respectively.
</p>
<br/><br/>
<p style="text-align:center; margin-bottom:2cm;">
<a class="nothing" href="dftzen4dp.png">
<img src="dftzen4dp.png" alt="Performance of transform in double precision on Ryzen 9 7950X" width="60%" height="60%"/>
</a>
<br />
Fig. 6.5: Performance of transform in double precision on Ryzen 9 7950X
</p>
<p style="text-align:center; margin-bottom:2cm;">
<a class="nothing" href="dftzen4sp.png">
<img src="dftzen4sp.png" alt="Performance of transform in single precision on Ryzen 9 7950X" width="60%" height="60%"/>
</a>
<br />
Fig. 6.6: Performance of transform in single precision on Ryzen 9 7950X
</p>
<p>
Below is the result of comparison on M1 MacBook Pro 16-inch with the following settings.
</p>
<br/>
<ul>
<li>OS : Ubuntu 24.04, Linux 6.8.0-1011-asahi-arm</li>
<li>Compiler : Clang version 19.1.1 (1ubuntu1~24.04.2)</li>
<li>FFTW version 3.3.10-1ubuntu3</li>
</ul>
<br/><br/>
<p style="text-align:center; margin-bottom:2cm;">
<a class="nothing" href="dftm1dp.png">
<img src="dftm1dp.png" alt="Performance of transform in double precision on M1 Pro" width="60%" height="60%"/>
</a>
<br />
Fig. 6.7: Performance of transform in double precision on M1 MacBook Pro
</p>
<p style="text-align:center; margin-bottom:2cm;">
<a class="nothing" href="dftm1sp.png">
<img src="dftm1sp.png" alt="Performance of transform in single precision on M1 Pro" width="60%" height="60%"/>
</a>
<br />
Fig. 6.8: Performance of transform in single precision on M1 MacBook Pro
</p>
<br/>
<p>
When benchmarking on your own, please keep in mind that the <b style="color:#ff0000;">CPU clock must be fixed</b>.
</p>
<p class="footer">
Copyright © 2010-2025 SLEEF Project, Naoki Shibata and contributors.<br/>
SLEEF is open-source software and is distributed under the Boost Software License, Version 1.0.
</p>
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