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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 <p>
  32         namespace boost{ namespace math{
  33       </p>
  34 <pre class="programlisting"><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>
  35 <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>
  36
  37 <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;20.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&gt;</span>
  38 <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;20.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&amp;);</span>
  39
  40 <span class="special">}}</span> <span class="comment">// namespaces</span>
  41 </pre>
  42 <p>
  43         Returns x<sup>y </sup> - 1.
  44       </p>
  45 <p>
  46         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
  47         type calculation rules</em></span></a> when T1 and T2 are different types.
  48       </p>
  49 <p>
  50         The final <a class="link" href="../../policy.html" title="Chapter&#160;20.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
  51         be used to control the behaviour of the function: how it handles errors,
  52         what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Chapter&#160;20.&#160;Policies: Controlling Precision, Error Handling etc">policy
  53         documentation for more details</a>.
  54       </p>
  55 <p>
  56         There are two domains where this is useful: when <span class="emphasis"><em>y</em></span> is
  57         very small, or when <span class="emphasis"><em>x</em></span> is close to 1.
  58       </p>
  59 <p>
  60         Implemented in terms of <code class="computeroutput"><span class="identifier">expm1</span></code>.
  61       </p>
  62 <p>
  63         The following graph illustrates the behaviour of powm1:
  64       </p>
  65 <div class="blockquote"><blockquote class="blockquote"><p>
  66           <span class="inlinemediaobject"><img src="../../../graphs/powm1.svg" align="middle"></span>
  67
  68         </p></blockquote></div>
  69 <h5>
  70 <a name="math_toolkit.powers.powm1.h0"></a>
  71         <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>
  72       </h5>
  73 <p>
  74         Should have approximately 2-3 epsilon accuracy.
  75       </p>
  76 <div class="table">
  77 <a name="math_toolkit.powers.powm1.table_powm1"></a><p class="title"><b>Table&#160;8.85.&#160;Error rates for powm1</b></p>
  78 <div class="table-contents"><table class="table" summary="Error rates for powm1">
  79 <colgroup>
  80 <col>
  81 <col>
  82 <col>
  83 <col>
  84 <col>
  85 </colgroup>
  86 <thead><tr>
  87 <th>
  88               </th>
  89 <th>
  90                 <p>
  91                   GNU C++ version 7.1.0<br> linux<br> double
  92                 </p>
  93               </th>
  94 <th>
  95                 <p>
  96                   GNU C++ version 7.1.0<br> linux<br> long double
  97                 </p>
  98               </th>
  99 <th>
 100                 <p>
 101                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
 102                 </p>
 103               </th>
 104 <th>
 105                 <p>
 106                   Microsoft Visual C++ version 14.1<br> Win32<br> double
 107                 </p>
 108               </th>
 109 </tr></thead>
 110 <tbody><tr>
 111 <td>
 112                 <p>
 113                   powm1
 114                 </p>
 115               </td>
 116 <td>
 117                 <p>
 118                   <span class="blue">Max = 1.06&#949; (Mean = 0.425&#949;)</span>
 119                 </p>
 120               </td>
 121 <td>
 122                 <p>
 123                   <span class="blue">Max = 2.04&#949; (Mean = 0.493&#949;)</span>
 124                 </p>
 125               </td>
 126 <td>
 127                 <p>
 128                   <span class="blue">Max = 1.88&#949; (Mean = 0.49&#949;)</span>
 129                 </p>
 130               </td>
 131 <td>
 132                 <p>
 133                   <span class="blue">Max = 1.84&#949; (Mean = 0.486&#949;)</span>
 134                 </p>
 135               </td>
 136 </tr></tbody>
 137 </table></div>
 138 </div>
 139 <br class="table-break"><h5>
 140 <a name="math_toolkit.powers.powm1.h1"></a>
 141         <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>
 142       </h5>
 143 <p>
 144         A selection of random high precision test values calculated using NTL::RR
 145         at 1000-bit precision.
 146       </p>
 147 </div>
 148 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 149 <td align="left"></td>
 150 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
 151       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
 152       Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
 153       R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
 154       Daryle Walker and Xiaogang Zhang<p>
 155         Distributed under the Boost Software License, Version 1.0. (See accompanying
 156         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>)
 157       </p>
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