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   4 <title>Internal Floating-point Promotion Policies</title>
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  26 <div class="titlepage"><div><div><h3 class="title">
  27 <a name="math_toolkit.pol_ref.internal_promotion"></a><a class="link" href="internal_promotion.html" title="Internal Floating-point Promotion Policies">Internal Floating-point
  28       Promotion Policies</a>
  29 </h3></div></div></div>
  30 <p>
  31         Normally when evaluating a function at say <code class="computeroutput"><span class="keyword">float</span></code>
  32         precision, maximal accuracy is assured by conducting the calculation at
  33         <code class="computeroutput"><span class="keyword">double</span></code> precision internally,
  34         and then rounding the result. There are two policies that control whether
  35         internal promotion to a higher precision floating-point type takes place,
  36         or not:
  37       </p>
  38 <div class="informaltable"><table class="table">
  39 <colgroup>
  40 <col>
  41 <col>
  42 </colgroup>
  43 <thead><tr>
  44 <th>
  45                 <p>
  46                   Policy
  47                 </p>
  48               </th>
  49 <th>
  50                 <p>
  51                   Meaning
  52                 </p>
  53               </th>
  54 </tr></thead>
  55 <tbody>
  56 <tr>
  57 <td>
  58                 <p>
  59                   <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">promote_float</span><span class="special">&lt;</span><span class="identifier">B</span><span class="special">&gt;</span></code>
  60                 </p>
  61               </td>
  62 <td>
  63                 <p>
  64                   Indicates whether <code class="computeroutput"><span class="keyword">float</span></code>
  65                   arguments should be promoted to <code class="computeroutput"><span class="keyword">double</span></code>
  66                   precision internally: defaults to <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">promote_float</span><span class="special">&lt;</span><span class="keyword">true</span><span class="special">&gt;</span></code>
  67                 </p>
  68               </td>
  69 </tr>
  70 <tr>
  71 <td>
  72                 <p>
  73                   <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">promote_double</span><span class="special">&lt;</span><span class="identifier">B</span><span class="special">&gt;</span></code>
  74                 </p>
  75               </td>
  76 <td>
  77                 <p>
  78                   Indicates whether <code class="computeroutput"><span class="keyword">double</span></code>
  79                   arguments should be promoted to <code class="computeroutput"><span class="keyword">long</span>
  80                   <span class="keyword">double</span></code> precision internally:
  81                   defaults to <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">promote_double</span><span class="special">&lt;</span><span class="keyword">true</span><span class="special">&gt;</span></code>
  82                 </p>
  83               </td>
  84 </tr>
  85 </tbody>
  86 </table></div>
  87 <h5>
  88 <a name="math_toolkit.pol_ref.internal_promotion.h0"></a>
  89         <span class="phrase"><a name="math_toolkit.pol_ref.internal_promotion.examples"></a></span><a class="link" href="internal_promotion.html#math_toolkit.pol_ref.internal_promotion.examples">Examples</a>
  90       </h5>
  91 <p>
  92         Suppose we want <code class="computeroutput"><span class="identifier">tgamma</span></code> to
  93         be evaluated without internal promotion to <code class="computeroutput"><span class="keyword">long</span>
  94         <span class="keyword">double</span></code>, then we could use:
  95       </p>
  96 <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">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
  97
  98 <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">;</span>
  99 <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">;</span>
 100
 101 <span class="comment">// Define a new policy *not* internally promoting RealType to double:</span>
 102 <span class="keyword">typedef</span> <span class="identifier">policy</span><span class="special">&lt;</span>
 103       <span class="identifier">promote_double</span><span class="special">&lt;</span><span class="keyword">false</span><span class="special">&gt;</span>
 104       <span class="special">&gt;</span> <span class="identifier">my_policy</span><span class="special">;</span>
 105
 106 <span class="comment">// Call the function, applying the new policy:</span>
 107 <span class="keyword">double</span> <span class="identifier">t1</span> <span class="special">=</span> <span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">some_value</span><span class="special">,</span> <span class="identifier">my_policy</span><span class="special">());</span>
 108
 109 <span class="comment">// Alternatively we could use helper function make_policy,</span>
 110 <span class="comment">// and concisely define everything at the call site:</span>
 111 <span class="keyword">double</span> <span class="identifier">t2</span> <span class="special">=</span> <span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">some_value</span><span class="special">,</span> <span class="identifier">make_policy</span><span class="special">(</span><span class="identifier">promote_double</span><span class="special">&lt;</span><span class="keyword">false</span><span class="special">&gt;()));</span>
 112 </pre>
 113 <p>
 114         Alternatively, suppose we want a distribution to perform calculations without
 115         promoting <code class="computeroutput"><span class="keyword">float</span></code> to <code class="computeroutput"><span class="keyword">double</span></code>, then we could use:
 116       </p>
 117 <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">distributions</span><span class="special">/</span><span class="identifier">normal</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
 118 <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">normal_distribution</span><span class="special">;</span>
 119
 120 <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">;</span>
 121
 122 <span class="comment">// Define a policy:</span>
 123 <span class="keyword">typedef</span> <span class="identifier">policy</span><span class="special">&lt;</span>
 124       <span class="identifier">promote_float</span><span class="special">&lt;</span><span class="keyword">false</span><span class="special">&gt;</span>
 125       <span class="special">&gt;</span> <span class="identifier">my_policy</span><span class="special">;</span>
 126
 127 <span class="comment">// Define the new normal distribution using my_policy:</span>
 128 <span class="keyword">typedef</span> <span class="identifier">normal_distribution</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">,</span> <span class="identifier">my_policy</span><span class="special">&gt;</span> <span class="identifier">my_norm</span><span class="special">;</span>
 129
 130 <span class="comment">// Get a quantile:</span>
 131 <span class="keyword">float</span> <span class="identifier">q</span> <span class="special">=</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">my_norm</span><span class="special">(),</span> <span class="number">0.05f</span><span class="special">);</span>
 132 </pre>
 133 </div>
 134 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 135 <td align="left"></td>
 136 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014 Nikhar Agrawal,
 137       Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
 138       Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam Sewani,
 139       Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
 140         Distributed under the Boost Software License, Version 1.0. (See accompanying
 141         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>)
 142       </p>
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