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<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.powers.powm1"></a><a class="link" href="powm1.html" title="powm1">powm1</a>
</h3></div></div></div>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">powm1</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span>
</pre>
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">></span>
<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">powm1</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">y</span><span class="special">);</span>
<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Chapter 15. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">></span>
<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">powm1</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">y</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter 15. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&);</span>
<span class="special">}}</span> <span class="comment">// namespaces</span>
</pre>
<p>
Returns x<sup>y </sup> - 1.
</p>
<p>
The return type of this function is computed using the <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
type calculation rules</em></span></a> when T1 and T2 are dufferent types.
</p>
<p>
The final <a class="link" href="../../policy.html" title="Chapter 15. Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
be used to control the behaviour of the function: how it handles errors,
what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Chapter 15. Policies: Controlling Precision, Error Handling etc">policy
documentation for more details</a>.
</p>
<p>
There are two domains where this is useful: when y is very small, or when
x is close to 1.
</p>
<p>
Implemented in terms of <code class="computeroutput"><span class="identifier">expm1</span></code>.
</p>
<p>
The following graph illustrates the behaviour of powm1:
</p>
<p>
<span class="inlinemediaobject"><img src="../../../graphs/powm1.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.powers.powm1.h0"></a>
<span class="phrase"><a name="math_toolkit.powers.powm1.accuracy"></a></span><a class="link" href="powm1.html#math_toolkit.powers.powm1.accuracy">Accuracy</a>
</h5>
<p>
Should have approximately 2-3 epsilon accuracy.
</p>
<div class="table">
<a name="math_toolkit.powers.powm1.table_powm1"></a><p class="title"><b>Table 6.82. Error rates for powm1</b></p>
<div class="table-contents"><table class="table" summary="Error rates for powm1">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
</th>
<th>
<p>
Microsoft Visual C++ version 12.0<br> Win32<br> double
</p>
</th>
<th>
<p>
GNU C++ version 5.1.0<br> linux<br> double
</p>
</th>
<th>
<p>
GNU C++ version 5.1.0<br> linux<br> long double
</p>
</th>
<th>
<p>
Sun compiler version 0x5130<br> Sun Solaris<br> long double
</p>
</th>
</tr></thead>
<tbody><tr>
<td>
<p>
powm1
</p>
</td>
<td>
<p>
<span class="blue">Max = 1.99ε (Mean = 0.461ε)</span>
</p>
</td>
<td>
<p>
<span class="blue">Max = 1.26ε (Mean = 0.428ε)</span>
</p>
</td>
<td>
<p>
<span class="blue">Max = 2.04ε (Mean = 0.521ε)</span>
</p>
</td>
<td>
<p>
<span class="blue">Max = 2.14ε (Mean = 0.498ε)</span>
</p>
</td>
</tr></tbody>
</table></div>
</div>
<br class="table-break"><h5>
<a name="math_toolkit.powers.powm1.h1"></a>
<span class="phrase"><a name="math_toolkit.powers.powm1.testing"></a></span><a class="link" href="powm1.html#math_toolkit.powers.powm1.testing">Testing</a>
</h5>
<p>
A selection of random high precision test values calculated using NTL::RR
at 1000-bit precision.
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<td align="right"><div class="copyright-footer">Copyright © 2006-2010, 2012-2014 Nikhar Agrawal,
Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan Råde, Gautam Sewani,
Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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