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<h1>SLEEF Documentation - Other tools included in the package</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="dft.xhtml">DFT library reference</a></li>
<li> </li>
<li><a class="underlined" href="misc.xhtml">Other tools included in the package</a></li>
<ul class="disc">
<li><a href="misc.xhtml#testerlibm">Testers for libm</a></li>
<li><a href="misc.xhtml#testerdft">Testers for DFT</a></li>
<li><a href="misc.xhtml#gencoef">Tool for generating coefficients</a></li>
<li><a href="misc.xhtml#benchmark">Benchmarking tool</a></li>
</ul>
<li> </li>
<li><a class="underlined" href="benchmark.xhtml">Benchmark results</a></li>
<li><a class="underlined" href="additional.xhtml">Additional notes</a></li>
</ul>
<h2 id="testerlibm">Libm tester</h2>
<p class="noindent">
SLEEF libm has two kinds of testers, and each kind of testers has
its own role.
</p>
<p>
The first kind of testers consist of a tester and an IUT (which
stands for Implementation Under Test.) Those two are built as
separate executables, and communicate with each other using a
pipe. The role for this tester is to perform a perfunctory set of
tests to check if the build is correct. It is also performs
regression tests. Since the tester executable and the iut executable
are separated, the iut can be implemented with an exotic
languages. It is also possible to perform a test over the network.
</p>
<p>
The second kind of testers are designed to run continuously. It
repeats randomly generating arguments for each function, and
comparing the results of each function to the results calculated
with the corresponding function in libmpfr. This tester is expected
to find bugs if it is run for sufficiently long time.
</p>
<h2 id="testerdft">DFT tester</h2>
<p class="noindent">
SLEEF DFT has three kinds of testers. The first ones, named
naivetest, compare the results computed by SLEEF DFT with that from
a naive DFT implementation. These testers cannot be built with MSVC
since complex data types are not supported. The second testers,
named fftwtest, compare the results of computation between SLEEF DFT
and FFTW. Rigorous testing is possible with the second testers, but
obviously it requires FFTW to run. The third testers, named
roundtriptest, executes a forward transform followed by a backward
transform. Then, it compares the results with the original data. An
advantage of the third testers is that it does not require external
library and it runs on all environment, but there could be many
cases that this testing does not find flaw. The third testers are
used only if FFTW is not available.
</p>
<h2 id="gencoef">Gencoef</h2>
<p class="noindent">
Gencoef is a small tool for generating the coefficients for
polynomial approximation used in the kernels.
</p>
<p>
In order to change the configurations, please edit gencoefdp.c. In
the beginning of the file, specifications of the parameters for
generating coefficients are listed. Enable one of them by changing
#if. Then, run make to compile the source code. Run the gencoef, and
it will show the generated coefficients in a few minutes. It may
take longer time depending on the settings.
</p>
<p>
There are two phases of the program. The first phase is the
regression for minimizing the maximum relative error. This problem
can be reduced to a linear programming problem, and the Simplex
method is used in this implementation. This requires multi-precision
calculation, and the implementation uses the MPFR library to do
this. In this phase, it uses only a small number of values
(specified by macro S, usually less than 100) within the input
domain of the kernel function to approximate the function. The
function to approximate is given by FRFUNC function. Specifying
higher values for S does not always give better results.
</p>
<p>
The second phase is to optimize the coefficients so that it gives
good accuracy with double precision calculation. In this phase, it
checks 10000 points (specified by macro Q) within the specified
argument range to see if the polynomial gives good error bounds. In
some cases, the last few terms have to be calculated in higher
precision in order to achieve 1 ULP or less overall accuracy, and
this implementation can take care of that. The L parameter specifies
the number of high precision coefficients.
</p>
<p>
In some cases, it is desirable to fix the last few coefficients to
values like 1 or 0.5. This can be specified if you define FIXCOEF0
macro.
</p>
<p>
Finding a set of good parameters is not a straightforward process.
</p>
<h2 id="benchmark">Benchmarking tool</h2>
<p class="noindent">
SLEEF has a tool for measuring and plotting execution time of each
function in the library. It consists of an executable for
measurements, a makefile for driving measurement and plotting, and a
couple of scripts.
</p>
<p>
In order to start a measurement, you need to first build the
executable for measurement. CMake builds the executable along with
the library. Please refer to <a class="underlined"
href="compile.xhtml">compiling and installing the library</a> for
this.
</p>
<p>
Then, change directory to sleef-3.X/src/libm-benchmarks/. You also
need to set the build directory to BUILDDIR environment variable.
</p>
<pre class="command">$ export BUILDDIR=$PATH:`pwd`/../../build</pre>
<p>
Type "make measure". After compiling the tools, it will prompt a
label for measurement. After you input a label, measurement
begins. After a measurement finishes, you can repeat measurements
under different configurations. If you want to measure on a
different computer, please copy the entire directory on to that
computer and continue measurements. If you have Intel Compiler
installed on your computer, you can type "make measureSVML" to
measure the computation time of SVML functions.
</p>
<pre class="command">$ make measure
./measure.sh benchsleef
...
Enter label of measurement(e.g. My desktop PC) : Skylake
Measurement in progress. This may take several minutes.
Sleef_sind2_u10
Sleef_cosd2_u10
Sleef_tand2_u10
Sleef_sincosd2_u10
...
Sleef_atanf8_u10
Sleef_atan2f8_u10
Sleef_atanf8_u35
Sleef_atan2f8_u35
Now, you can plot the results of measurement by 'make plot'.
You can do another measurement by 'make measure'.
You can start over by 'make restart'.
$ make plot
javac ProcessData.java
java ProcessData *dptrig*.out
gnuplot script.out
mv output.png trigdp.png
java ProcessData *dpnontrig*.out
gnuplot script.out
mv output.png nontrigdp.png
java ProcessData *sptrig*.out
gnuplot script.out
mv output.png trigsp.png
java ProcessData *spnontrig*.out
gnuplot script.out
mv output.png nontrigsp.png
$ █</pre>
<p>
Then type "make plot" to generate graphs. You need to have JDK and
gnuplot installed on your computer. Four graphs are generated :
trigdp.png, nontrigdp.png, trigsp.png and nontrigsp.png. Please see our
<a class="underlined" href="benchmark.xhtml">benchmark results</a>
for an example of generated graphs by this tool.
</p>
<p class="footer">
Copyright © 2018 SLEEF Project.<br/>
SLEEF is open-source software and is distributed under the Boost Software License, Version 1.0.
</p>
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