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   4 <title>The Overhead in the Number Class Wrapper</title>
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  26 <div class="titlepage"><div><div><h3 class="title">
  27 <a name="boost_multiprecision.perf.overhead"></a><a class="link" href="overhead.html" title="The Overhead in the Number Class Wrapper">The Overhead in the
  28       Number Class Wrapper</a>
  29 </h3></div></div></div>
  30 <p>
  31         Using a simple <a href="../../../../performance/arithmetic_backend.hpp" target="_top">backend
  32         class</a> that wraps any built in arithmetic type we can measure the
  33         overhead involved in wrapping a type inside the <code class="computeroutput"><span class="identifier">number</span></code>
  34         frontend, and the effect that turning on expression templates has. The following
  35         table compares the performance between <code class="computeroutput"><span class="keyword">double</span></code>
  36         and a <code class="computeroutput"><span class="keyword">double</span></code> wrapped inside
  37         class <code class="computeroutput"><span class="identifier">number</span></code>:
  38       </p>
  39 <div class="informaltable"><table class="table">
  40 <colgroup>
  41 <col>
  42 <col>
  43 <col>
  44 </colgroup>
  45 <thead><tr>
  46 <th>
  47                 <p>
  48                   Type
  49                 </p>
  50               </th>
  51 <th>
  52                 <p>
  53                   Bessel Function Evaluation
  54                 </p>
  55               </th>
  56 <th>
  57                 <p>
  58                   Non-Central T Evaluation
  59                 </p>
  60               </th>
  61 </tr></thead>
  62 <tbody>
  63 <tr>
  64 <td>
  65                 <p>
  66                   <code class="computeroutput"><span class="keyword">double</span></code>
  67                 </p>
  68               </td>
  69 <td>
  70                 <p>
  71                   <span class="bold"><strong>1.0 (0.016s)</strong></span>
  72                 </p>
  73               </td>
  74 <td>
  75                 <p>
  76                   <span class="bold"><strong>1.0</strong></span> (0.46s)
  77                 </p>
  78               </td>
  79 </tr>
  80 <tr>
  81 <td>
  82                 <p>
  83                   <code class="computeroutput"><span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">arithmetic_backend</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;,</span>
  84                   <span class="identifier">et_off</span><span class="special">&gt;</span></code>
  85                 </p>
  86               </td>
  87 <td>
  88                 <p>
  89                   1.2 (0.019s)
  90                 </p>
  91               </td>
  92 <td>
  93                 <p>
  94                   <span class="bold"><strong>1.0</strong></span>(0.46s)
  95                 </p>
  96               </td>
  97 </tr>
  98 <tr>
  99 <td>
 100                 <p>
 101                   <code class="computeroutput"><span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">arithmetic_backend</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;,</span>
 102                   <span class="identifier">et_on</span><span class="special">&gt;</span></code>
 103                 </p>
 104               </td>
 105 <td>
 106                 <p>
 107                   1.2 (0.019s)
 108                 </p>
 109               </td>
 110 <td>
 111                 <p>
 112                   1.7 (0.79s)
 113                 </p>
 114               </td>
 115 </tr>
 116 </tbody>
 117 </table></div>
 118 <p>
 119         As you can see whether or not there is an overhead, and how large it is depends
 120         on the actual situation, but the overhead is in any cases small. Expression
 121         templates generally add a greater overhead the more complex the expression
 122         becomes due to the logic of figuring out how to best unpack and evaluate
 123         the expression, but of course this is also the situation where you save more
 124         temporaries. For a "trivial" backend like this, saving temporaries
 125         has no benefit, but for larger types it becomes a bigger win.
 126       </p>
 127 <p>
 128         The following table compares arithmetic using either <code class="computeroutput"><span class="keyword">long</span>
 129         <span class="keyword">long</span></code> or <code class="computeroutput"><span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">arithmetic_backend</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">long</span><span class="special">&gt;</span> <span class="special">&gt;</span></code> for the <a href="../../../../performance/voronoi_performance.cpp" target="_top">voronoi-diagram
 130         builder test</a>:
 131       </p>
 132 <div class="informaltable"><table class="table">
 133 <colgroup>
 134 <col>
 135 <col>
 136 </colgroup>
 137 <thead><tr>
 138 <th>
 139                 <p>
 140                   Type
 141                 </p>
 142               </th>
 143 <th>
 144                 <p>
 145                   Relative time
 146                 </p>
 147               </th>
 148 </tr></thead>
 149 <tbody>
 150 <tr>
 151 <td>
 152                 <p>
 153                   <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">long</span></code>
 154                 </p>
 155               </td>
 156 <td>
 157                 <p>
 158                   <span class="bold"><strong>1.0</strong></span>(0.0823s)
 159                 </p>
 160               </td>
 161 </tr>
 162 <tr>
 163 <td>
 164                 <p>
 165                   <code class="computeroutput"><span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">arithmetic_backend</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">long</span><span class="special">&gt;,</span> <span class="identifier">et_off</span><span class="special">&gt;</span></code>
 166                 </p>
 167               </td>
 168 <td>
 169                 <p>
 170                   1.05 (0.0875s)
 171                 </p>
 172               </td>
 173 </tr>
 174 </tbody>
 175 </table></div>
 176 <p>
 177         This test involves mainly creating a lot of temporaries and performing a
 178         small amount of arithmetic on them, with very little difference in performance
 179         between the native and "wrapped" types.
 180       </p>
 181 <p>
 182         The test code was compiled with Microsoft Visual Studio 2010 with all optimisations
 183         turned on (/Ox), and used MPIR-2.3.0 and <a href="http://libtom.net" target="_top">libtommath</a>-0.42.0.
 184         The tests were run on 32-bit Windows Vista machine.
 185       </p>
 186 </div>
 187 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 188 <td align="left"></td>
 189 <td align="right"><div class="copyright-footer">Copyright &#169; 2002-2019 John Maddock
 190       and Christopher Kormanyos<p>
 191         Distributed under the Boost Software License, Version 1.0. (See accompanying
 192         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>)
 193       </p>
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