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<a name="Introduction-to-MPFR"></a>
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Next: <a href="Installing-MPFR.html#Installing-MPFR" accesskey="n" rel="next">Installing MPFR</a>, Previous: <a href="Copying.html#Copying" accesskey="p" rel="previous">Copying</a>, Up: <a href="index.html#Top" accesskey="u" rel="up">Top</a> &nbsp; [<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
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<a name="Introduction-to-MPFR-1"></a>
<h2 class="chapter">1 Introduction to MPFR</h2>


<p>MPFR is a portable library written in C for arbitrary precision arithmetic
on floating-point numbers. It is based on the GNU MP library.
It aims to provide a class of floating-point numbers with
precise semantics. The main characteristics of MPFR, which make it differ
from most arbitrary precision floating-point software tools, are:
</p>
<ul>
<li> the MPFR code is portable, i.e., the result of any operation
does not depend on the machine word size
<code>mp_bits_per_limb</code> (64 on most current processors);
</li><li> the precision in bits can be set <em>exactly</em> to any valid value
for each variable (including very small precision);
</li><li> MPFR provides the four rounding modes from the IEEE 754-1985
standard, plus away-from-zero, as well as for basic operations as for other
mathematical functions.
</li></ul>

<p>In particular, with a precision of 53 bits, MPFR is able to
exactly reproduce all computations with double-precision machine
floating-point numbers (e.g., <code>double</code> type in C, with a C
implementation that rigorously follows Annex F of the ISO C99 standard
and <code>FP_CONTRACT</code> pragma set to <code>OFF</code>) on the four arithmetic
operations and the square root, except the default exponent range is much
wider and subnormal numbers are not implemented (but can be emulated).
</p>
<p>This version of MPFR is released under the GNU Lesser General Public
License, version 3 or any later version.
It is permitted to link MPFR to most non-free programs, as long as when
distributing them the MPFR source code and a means to re-link with a
modified MPFR library is provided.
</p>
<a name="How-to-Use-This-Manual"></a>
<h3 class="section">1.1 How to Use This Manual</h3>

<p>Everyone should read <a href="MPFR-Basics.html#MPFR-Basics">MPFR Basics</a>.  If you need to install the library
yourself, you need to read <a href="Installing-MPFR.html#Installing-MPFR">Installing MPFR</a>, too.
To use the library you will need to refer to <a href="MPFR-Interface.html#MPFR-Interface">MPFR Interface</a>.
</p>
<p>The rest of the manual can be used for later reference, although it is
probably a good idea to glance through it.
</p>
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