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<h1>Floating-point numbers</h1>

<p>Version 1.0.9</p>

<p>26/08/2025</p>

</div>
<p>
    Integration of mpfr, mpfi, mpc, fplll and cxsc in GAP
  </p>
<p><b>Laurent Bartholdi
           
   
  </b>
<br />Email: <span class="URL"><a href="mailto:laurent.bartholdi@gmail.com ">laurent.bartholdi@gmail.com </a></span>
<br />Homepage: <span class="URL"><a href="https://www.math.uni-sb.de/ag/bartholdi/">https://www.math.uni-sb.de/ag/bartholdi/</a></span>
</p>

<p><b>Address:</b><br />
FR Mathematik<br /> D-66041 Saarbrücken<br /> Germany</p>
<p><a id="X7AA6C5737B711C89" name="X7AA6C5737B711C89"></a></p>
<h3>Abstract</h3>
<p>This document describes the package <strong class="pkg">Float</strong>, which implements in <strong class="pkg">GAP</strong> arbitrary-precision floating-point numbers.</p>

<p>The computer algebra system <strong class="pkg">GAP</strong> is available at <span class="URL"><a href="https://www.gap-system.org">https://www.gap-system.org</a></span>.</p>

<p>This documentation for <strong class="pkg">Float</strong> is available at <span class="URL"><a href="https://docs.gap-system.org/pkg/float/doc/manual.pdf">https://docs.gap-system.org/pkg/float/doc/manual.pdf</a></span> in PDF format, and may be accessed online at <span class="URL"><a href="https://gap-packages.github.io/float/">https://gap-packages.github.io/float/</a></span>.</p>

<p>The latest release of the package may be downloaded as <span class="URL"><a href="https://github.com/gap-packages/float/releases/download/v1.0.9/float-1.0.9.tar.gz">https://github.com/gap-packages/float/releases/download/v1.0.9/float-1.0.9.tar.gz</a></span> (tar, gzipped). The latest repository version (possibly unstable) may be downloaded as <span class="URL"><a href="https://github.com/gap-packages/float/tarball/master">https://github.com/gap-packages/float/tarball/master</a></span> (tar, gzipped), <span class="URL"><a href="https://github.com/gap-packages/float.git">https://github.com/gap-packages/float.git</a></span> (git repository), <span class="URL"><a href="https://packages.debian.org/search?keywords=gap-float&searchon=names&suite=all§ion=all">https://packages.debian.org/search?keywords=gap-float&searchon=names&suite=all&section=all</a></span> (debian package), or explored at <span class="URL"><a href="https://github.com/gap-packages/float/tree/master/">https://github.com/gap-packages/float/tree/master/</a></span>.</p>

<p>For comments or questions on <strong class="pkg">Float</strong> please contact the author.</p>

<p><a id="X81488B807F2A1CF1" name="X81488B807F2A1CF1"></a></p>
<h3>Copyright</h3>
<p>© 2011-2021 by Laurent Bartholdi</p>

<p><a id="X82A988D47DFAFCFA" name="X82A988D47DFAFCFA"></a></p>
<h3>Acknowledgements</h3>
<p>Part of this work was supported by the "Swiss National Fund for Scientific Research (SNF)", the "German National Science Foundation (DFG)", and the Courant Research Centre "Higher Order Structures" of the University of Göttingen.</p>

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<div class="contents">
<h3>Contents<a id="contents" name="contents"></a></h3>

<div class="ContChap"><a href="chap1.html#X86DB23CC834ABD71">1 <span class="Heading">Licensing</span></a>
</div>
<div class="ContChap"><a href="chap2.html#X7E12358984CA3111">2 <span class="Heading">Float package</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X7B4092CA7ABB93B0">2.1 <span class="Heading">A sample run</span></a>
</span>
</div>
</div>
<div class="ContChap"><a href="chap3.html#X826D8334845549EC">3 <span class="Heading">Polynomials</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X7BDA2E7C85ECC18C">3.1 <span class="Heading">The Floats pseudo-field</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7AB8BC957952B662">3.1-1 FLOAT_PSEUDOFIELD</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X788CDC24834012D7">3.2 <span class="Heading">Roots of polynomials</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X7C9EF7E27EFA3288">3.3 <span class="Heading">Finding integer relations</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X85DEB4B584870F67">3.3-1 PSLQ</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X83445BFB7901B88F">3.4 <span class="Heading">LLL lattice reduction</span></a>
</span>
</div>
</div>
<div class="ContChap"><a href="chap4.html#X82DC33E982C4D157">4 <span class="Heading">Implemented packages</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X79E38C3781F79E35">4.1 <span class="Heading">MPFR</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X82B38FFE86A5A0B5">4.1-1 IsMPFRFloat</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X8145D0A97986133C">4.2 <span class="Heading">MPFI</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X842290DB8034BF90">4.2-1 IsMPFIFloat</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X82C3C26F7C11A26F">4.3 <span class="Heading">MPC</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7D7AD4C67FF04E38">4.3-1 IsMPCFloat</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X82DF12317C250153">4.4 <span class="Heading">CXSC</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X794C3A0F7925BDA1">4.4-1 IsCXSCReal</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X7CD9EDF079B439BC">4.5 <span class="Heading">FPLLL</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X832DFC257C5C4D32">4.5-1 FPLLLReducedBasis</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7C759DED84B77805">4.5-2 FPLLLShortestVector</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chapBib.html"><span class="Heading">References</span></a></div>
<div class="ContChap"><a href="chapInd.html"><span class="Heading">Index</span></a></div>
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