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  26 <div class="titlepage"><div><div><h3 class="title">
  27 <a name="math_toolkit.powers.powm1"></a><a class="link" href="powm1.html" title="powm1">powm1</a>
  28 </h3></div></div></div>
  29 <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</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">&gt;</span>
  30 </pre>
  31 <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>
  32
  33 <span class="keyword">template</span> <span class="special">&lt;</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">&gt;</span>
  34 <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>
  35
  36 <span class="keyword">template</span> <span class="special">&lt;</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&#160;15.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&gt;</span>
  37 <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&#160;15.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&amp;);</span>
  38
  39 <span class="special">}}</span> <span class="comment">// namespaces</span>
  40 </pre>
  41 <p>
  42         Returns x<sup>y </sup> - 1.
  43       </p>
  44 <p>
  45         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
  46         type calculation rules</em></span></a> when T1 and T2 are dufferent types.
  47       </p>
  48 <p>
  49         The final <a class="link" href="../../policy.html" title="Chapter&#160;15.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
  50         be used to control the behaviour of the function: how it handles errors,
  51         what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Chapter&#160;15.&#160;Policies: Controlling Precision, Error Handling etc">policy
  52         documentation for more details</a>.
  53       </p>
  54 <p>
  55         There are two domains where this is useful: when y is very small, or when
  56         x is close to 1.
  57       </p>
  58 <p>
  59         Implemented in terms of <code class="computeroutput"><span class="identifier">expm1</span></code>.
  60       </p>
  61 <p>
  62         The following graph illustrates the behaviour of powm1:
  63       </p>
  64 <p>
  65         <span class="inlinemediaobject"><img src="../../../graphs/powm1.svg" align="middle"></span>
  66       </p>
  67 <h5>
  68 <a name="math_toolkit.powers.powm1.h0"></a>
  69         <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>
  70       </h5>
  71 <p>
  72         Should have approximately 2-3 epsilon accuracy.
  73       </p>
  74 <div class="table">
  75 <a name="math_toolkit.powers.powm1.table_powm1"></a><p class="title"><b>Table&#160;6.82.&#160;Error rates for powm1</b></p>
  76 <div class="table-contents"><table class="table" summary="Error rates for powm1">
  77 <colgroup>
  78 <col>
  79 <col>
  80 <col>
  81 <col>
  82 <col>
  83 </colgroup>
  84 <thead><tr>
  85 <th>
  86               </th>
  87 <th>
  88                 <p>
  89                   Microsoft Visual C++ version 12.0<br> Win32<br> double
  90                 </p>
  91               </th>
  92 <th>
  93                 <p>
  94                   GNU C++ version 5.1.0<br> linux<br> double
  95                 </p>
  96               </th>
  97 <th>
  98                 <p>
  99                   GNU C++ version 5.1.0<br> linux<br> long double
 100                 </p>
 101               </th>
 102 <th>
 103                 <p>
 104                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
 105                 </p>
 106               </th>
 107 </tr></thead>
 108 <tbody><tr>
 109 <td>
 110                 <p>
 111                   powm1
 112                 </p>
 113               </td>
 114 <td>
 115                 <p>
 116                   <span class="blue">Max = 1.99&#949; (Mean = 0.461&#949;)</span>
 117                 </p>
 118               </td>
 119 <td>
 120                 <p>
 121                   <span class="blue">Max = 1.26&#949; (Mean = 0.428&#949;)</span>
 122                 </p>
 123               </td>
 124 <td>
 125                 <p>
 126                   <span class="blue">Max = 2.04&#949; (Mean = 0.521&#949;)</span>
 127                 </p>
 128               </td>
 129 <td>
 130                 <p>
 131                   <span class="blue">Max = 2.14&#949; (Mean = 0.498&#949;)</span>
 132                 </p>
 133               </td>
 134 </tr></tbody>
 135 </table></div>
 136 </div>
 137 <br class="table-break"><h5>
 138 <a name="math_toolkit.powers.powm1.h1"></a>
 139         <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>
 140       </h5>
 141 <p>
 142         A selection of random high precision test values calculated using NTL::RR
 143         at 1000-bit precision.
 144       </p>
 145 </div>
 146 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 147 <td align="left"></td>
 148 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014 Nikhar Agrawal,
 149       Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
 150       Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam Sewani,
 151       Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
 152         Distributed under the Boost Software License, Version 1.0. (See accompanying
 153         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>)
 154       </p>
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