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<a name="mpfr"></a>
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<hr size="1">
<a name="mpfr-1"></a>
<h2 class="section">D.14 <code>mpfr</code></h2>

<p>The <code>mpfr</code> library provides a rich assortment of floating point
operations on arbitrary precision numbers
(<a href="http://www.mpfr.org">http://www.mpfr.org</a>). These numbers are represented in a format
that is not binary compatible with the standard IEEE floating point
number format used by other libraries, but they offer superior
numerical stability suitable for many ill conditioned problems.
</p>
<p>The virtual code interface to the <code>mpfr</code> library follows the
native API to the extent of using the same names for most operations,
but excludes features pertaining to i/o, mutable storage, and memory
management.
</p>
<p>The <code>mpfr</code> library functions are invoked by an expression of the
form
</p>
<table><tr><td>&nbsp;</td><td><pre class="example">library('mpfr',f)
</pre></td></tr></table>

<p>Aside from a few exceptions as noted, <code>f</code> is a character string
derived from the name of the related function from the <code>mpfr</code> C
library as documented at the above address, but without the
<code>mpfr_</code> prefix.
</p>
<p>The full complement of available functions is documented in the
remainder of this section.
</p>
<ul>
<li>
References to natural numbers pertain to the list representation
described in <a href="Representation-of-Numeric-and-Textual-Data.html#Representation-of-Numeric-and-Textual-Data">Representation of Numeric and Textual Data</a>.
</li><li>
All functions that perform rounding use a mode of <code>GMP_RNDN</code> for
<a name="index-rounding"></a>
rounding to nearest, which is not explicitly specified on the virtual
side.
</li></ul>

<table class="menu" border="0" cellspacing="0">
<tr><td align="left" valign="top"><a href="mpfr-binary-operators.html#mpfr-binary-operators">D.14.1 <code>mpfr</code> binary operators</a></td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top"><a href="mpfr-unary-operators.html#mpfr-unary-operators">D.14.2 <code>mpfr</code> unary operators</a></td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top"><a href="mpfr-binary-operators-with-a-natural-operand.html#mpfr-binary-operators-with-a-natural-operand">D.14.3 <code>mpfr</code> binary operators with a natural operand</a></td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top"><a href="mpfr-binary-predicates.html#mpfr-binary-predicates">D.14.4 <code>mpfr</code> binary predicates</a></td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top"><a href="mpfr-unary-predicates.html#mpfr-unary-predicates">D.14.5 <code>mpfr</code> unary predicates</a></td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top"><a href="mpfr-constants.html#mpfr-constants">D.14.6 <code>mpfr</code> constants</a></td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top"><a href="mpfr-functions-with-miscellaneous-calling-conventions.html#mpfr-functions-with-miscellaneous-calling-conventions">D.14.7 <code>mpfr</code> functions with miscellaneous calling conventions</a></td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top"><a href="mpfr-conversion-functions.html#mpfr-conversion-functions">D.14.8 <code>mpfr</code> conversion functions</a></td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top"><a href="mpfr-exceptions.html#mpfr-exceptions">D.14.9 <code>mpfr</code> exceptions</a></td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top"><a href="Additional-mpfr-notes.html#Additional-mpfr-notes">D.14.10 Additional <code>mpfr</code> notes</a></td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
</table>

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