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<h1>SLEEF Vectorized Math Library<img src="sleeflogo3.png" alt="logo" width="25%" height="25%" style="float: right" /></h1>
<ul class="none" style="font-family: arial, sansserif; margin-top: 1.0cm;">
<li><a class="underlined" style="color:#a00000;" href="https://github.com/shibatch/sleef/releases">Download the latest version</a></li>
<li><a class="underlined" href="https://sleef.org/">Latest documentation on the web</a></li>
<li><a class="underlined" href="https://github.com/shibatch/sleef">GitHub repository</a></li>
<li><a class="underlined" href="https://github.com/shibatch/sleef/discussions">Discussions</a></li>
<li><a class="underlined" href="https://github.com/shibatch/sleef/wiki">Wiki pages</a></li>
</ul>
<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>
<ul class="disc">
<li><a href="index.xhtml#overview">Overview</a></li>
<li><a href="index.xhtml#environment">Supported environments</a></li>
<li><a href="index.xhtml#credit">Credit</a></li>
<li><a href="index.xhtml#license">License</a></li>
<li><a href="index.xhtml#history">History</a></li>
<li><a href="index.xhtml#related">Related projects</a></li>
<li><a href="index.xhtml#publication">Publication</a></li>
</ul>
</li>
<li> </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><a class="underlined" href="benchmark.xhtml">Benchmark results</a></li>
<li><a class="underlined" href="additional.xhtml">Additional notes</a></li>
</ul>
<h2 id="overview">Overview</h2>
<p class="noindent">
SLEEF stands for SIMD Library for Evaluating Elementary
Functions. It implements manually <a class="underlined"
href="https://en.wikipedia.org/wiki/Automatic_vectorization">vectorized</a>
versions of all C99 real floating point math functions. It can
utilize SIMD instructions that are available on modern
processors. SLEEF is designed to effciently perform computation with
SIMD instructions by reducing the use of conditional branches and
scatter/gather memory access. Our <a class="underlined"
href="benchmark.xhtml">benchmarks</a> show that the performance of
SLEEF is comparable to that of the best commercial library.
</p>
<p>
Unlike closed-source commercial libraries, which are often
assembly-optimized, SLEEF is designed to work with various
architectures, operating systems and compilers. It is distributed
under <a class="underlined"
href="http://www.boost.org/users/license.html">the Boost Software
License</a>, which is a permissive open source license. SLEEF can be
easily ported to other architectures by writing a helper file, which
is a thin abstraction layer of SIMD intrinsics. SLEEF also
provides <a class="underlined"
href="additional.xhtml#dispatcher">dispatchers</a> that
automatically choose the best subroutines for the computer on which
the library is executed. In order to further optimize the
application code that calls SLEEF functions,
<a class="underlined" href="additional.xhtml#lto">link time
optimization(LTO)</a> can be used to reduce the overhead of
functions calls, and the build system of SLEEF supports usage of
LTO. The library also has a functionality to generate
<a class="underlined" href="additional.xhtml#inline">header
files</a> in which the library functions are all defined as inline
functions. SLEEF can be used for <a class="underlined"
href="cuda.xhtml">GPGPU</a> and <a class="underlined"
href="additional.xhtml#wasm">WebAssembly</a> with these header
files. In addition to the vectorized functions, SLEEF provides
scalar functions. Calls to these scalar SLEEF functions can be
<a class="underlined"
href="additional.xhtml#vectorizing">auto-vectorized</a> by GCC and
Clang.
</p>
<p>
The library contains implementations of all C99 real FP math
functions in double precision and single precision. Different
accuracy of the results can be chosen for a subset of the elementary
functions; for this subset there are versions with up to
1 <a class="underlined" href="additional.xhtml#ulp">ULP</a> error
(which is the maximum error, not the average) and even faster
versions with a few ULPs of error bounds. For non-finite inputs and
outputs, the functions return correct results as specified in the
C99 standard. All the functions in the library
are <a class="underlined" href="misc.xhtml#testerlibm">thoroughly
tested</a> and confirmed that the evaluation error is within the
designed limit by comparing the returned values against
high-precision evaluation using the GNU MPFR Library.
</p>
<p>
SLEEF also includes a <a class="underlined"
href="quad.xhtml">quad-precision math library</a>. This library
includes fully vectorized IEEE 754 quadruple-precision (QP)
functions that correspond to the standard C math functions. I/O
functions for converting between QP numbers and strings are also
available.
</p>
<br/>
<p>
SLEEF includes a library of <a class="underlined"
href="dft.xhtml">discrete Fourier transform(DFT)</a>. It is fully
vectorized, heavily unrolled, and parallelized in such a way that
modern SIMD instructions and multiple cores can be utilized, and it
can utilize long vectors up to 2048 bits. It has an API similar to
that of FFTW for easy migration. The helper files for abstracting
SIMD intrinsics are shared with SLEEF libm, and thus it is easy to
port the DFT library to other architectures. <a class="underlined"
href="benchmark.xhtml#dft">Benchmark results of the DFT library</a>
are now available.
</p>
<h2 id="environment">Supported environments</h2>
<p class="noindent">
This library supports the following architectures :
</p>
<div><br/></div>
<ul class="disc">
<li><a class="underlined" href="x86.xhtml">x86</a> - SSE2, AVX2, AVX512F</li>
<li>RISC-V - RVV1, RVV2</li>
<li><a class="underlined" href="ppc64.xhtml">PowerPC64</a> - VSX (POWER8), VSX-3 (POWER9)</li>
<li><a class="underlined" href="s390x.xhtml">System/390</a> - VXE (z14), VXE2 (z15)</li>
<li><a class="underlined" href="cuda.xhtml">CUDA</a></li>
<li><a class="underlined" href="aarch64.xhtml">AArch64</a> - Advanced SIMD, SVE</li>
<li><a class="underlined" href="additional.xhtml#wasm">WebAssembly</a> - SSE2</li>
</ul>
<div><br/></div>
<p>
The supported combinations of the architecture, operating system and
compiler are shown in Table 1.1.
</p>
<div style="margin-top: 1.0cm;"></div>
<table style="text-align:center;" align="center">
<tr align="center">
<td class="caption">Table 1.1: Environment support matrix</td>
</tr>
<tr align="center">
<td>
<table class="lt">
<tr>
<td class="lt-hl"></td>
<td class="lt-hl"></td>
<td class="lt-hl"></td>
<td class="lt-hl"></td>
<td class="lt-hl"></td>
</tr>
<tr>
<td class="lt-br"></td>
<td class="lt-hl"></td>
<td class="lt-blr" align="center">GCC</td>
<td class="lt-br" align="center">Clang</td>
<td class="lt-b" align="center">MSVC</td>
</tr>
<tr>
<td class="lt-hl"></td>
<td class="lt-hl"></td>
<td class="lt-hl"></td>
<td class="lt-hl"></td>
<td class="lt-hl"></td>
</tr>
<tr>
<td class="lt-r" align="left">x86_64, Linux</td>
<td></td>
<td class="lt-lr" align="center">Supported</td>
<td class="lt-r" align="center">Experimental</td>
<td class="lt-" align="center">N/A</td>
</tr>
<tr>
<td class="lt-r" align="left">x86_64, Windows</td>
<td></td>
<td class="lt-lr" align="center">Experimental(Cygwin)</td>
<td class="lt-r" align="center">Experimental</td>
<td class="lt-" align="center">Supported</td>
</tr>
<tr>
<td class="lt-r" align="left">RISC-V (64-bit), Linux</td>
<td></td>
<td class="lt-lr" align="center">Supported</td>
<td class="lt-r" align="center">Experimental</td>
<td class="lt-" align="center">N/A</td>
</tr>
<tr>
<td class="lt-r" align="left">PowerPC (64 bit), Linux</td>
<td></td>
<td class="lt-lr" align="center">Supported</td>
<td class="lt-r" align="center">Experimental</td>
<td class="lt-" align="center">N/A</td>
</tr>
<tr>
<td class="lt-r" align="left">System/390 (64 bit), Linux</td>
<td></td>
<td class="lt-lr" align="center">Supported</td>
<td class="lt-r" align="center">Experimental</td>
<td class="lt-" align="center">N/A</td>
</tr>
<tr>
<td class="lt-r" align="left">AArch64, Linux</td>
<td></td>
<td class="lt-lr" align="center">Supported</td>
<td class="lt-r" align="center">Experimental</td>
<td class="lt-" align="center">N/A</td>
</tr>
<tr>
<td class="lt-br" align="left">AArch64, macOS</td>
<td class="lt-hl"></td>
<td class="lt-blr" align="center">Experimental</td>
<td class="lt-br" align="center">Supported</td>
<td class="lt-b" align="center">N/A</td>
</tr>
</table>
</td>
</tr>
</table>
<div style="margin-top: 2.0cm;"></div>
<p>
Supported compilers are only the latest versions of compilers
officially used on the OSes. All functions in the library are thread
safe unless otherwise noted.
</p>
<h2 id="credit">Credit</h2>
<ul class="disc">
<li>The main developer is <a class="underlined"
href="https://github.com/shibatch">Naoki Shibata</a>
( <a href="mailto:shibatch@users.sourceforge.net">shibatch@users.sourceforge.net</a> ).</li>
<li><a class="underlined"
href="https://github.com/shibatch/sleef/graphs/contributors">
And many more contributors you can find listed on GitHub.</a></li>
</ul>
<h2 id="license">License</h2>
<p class="noindent">
SLEEF is distributed under <a class="underlined"
href="http://www.boost.org/LICENSE_1_0.txt">Boost Software License
Version 1.0</a>.
</p>
<p class="noindent" style="margin-top: 0.8cm;">
<a class="nothing" href="https://opensource.org/">
<img src="osi_logo.png" width="90" height="103" alt="open source logo" style="position:relative; top:3px;"/>
</a>
Boost Software License is <a class="underlined"
href="https://opensource.org/licenses/BSL-1.0">OSI-certified</a>.
See <a class="underlined"
href="http://www.boost.org/users/license.html">this page</a> for more
information about Boost Software License.
</p>
<h2 id="history">History</h2>
<p class="noindent" style="margin-top: 1.0cm;">
See <a class="underlined"
href="https://github.com/shibatch/sleef/blob/master/CHANGELOG.md">Changelog</a>
for a full history of changes to SLEEF.</p>
<h2 id="publication">Publication</h2>
<ul class="disc">
<li>Naoki Shibata and Francesco Petrogalli : <B>SLEEF: A Portable Vectorized Library of C Standard Mathematical Functions,</B> <I>in IEEE Transactions on Parallel and Distributed Systems,</I> <a class="underlined" href="https://doi.org/10.1109/TPDS.2019.2960333">DOI:10.1109/TPDS.2019.2960333</a> (Dec. 2019). [<a class="underlined" href="https://arxiv.org/pdf/2001.09258">PDF</a>]</li>
</ul>
<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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