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  26 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
  27 <a name="math_toolkit.tradoffs"></a><a class="link" href="tradoffs.html" title="Trading Accuracy for Performance">Trading Accuracy for Performance</a>
  28 </h2></div></div></div>
  29 <p>
  30       There are a number of <a class="link" href="../policy.html" title="Chapter&#160;15.&#160;Policies: Controlling Precision, Error Handling etc">Policies</a> that can be used
  31       to trade accuracy for performance:
  32     </p>
  33 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
  34 <li class="listitem">
  35           Internal promotion: by default functions with <code class="computeroutput"><span class="keyword">float</span></code>
  36           arguments are evaluated at <code class="computeroutput"><span class="keyword">double</span></code>
  37           precision internally to ensure full precision in the result. Similarly
  38           <code class="computeroutput"><span class="keyword">double</span></code> precision functions
  39           are evaluated at <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>
  40           precision internally by default. Changing these defaults can have a significant
  41           speed advantage at the expense of accuracy, note also that evaluating using
  42           <code class="computeroutput"><span class="keyword">float</span></code> internally may result
  43           in numerical instability for some of the more complex algorithms, we suggest
  44           you use this option with care.
  45         </li>
  46 <li class="listitem">
  47           Target accuracy: just because you choose to evaluate at <code class="computeroutput"><span class="keyword">double</span></code>
  48           precision doesn't mean you necessarily want to target full 16-digit accuracy,
  49           if you wish you can change the default (full machine precision) to whatever
  50           is "good enough" for your particular use case.
  51         </li>
  52 </ul></div>
  53 <p>
  54       For example, suppose you want to evaluate <code class="computeroutput"><span class="keyword">double</span></code>
  55       precision functions at <code class="computeroutput"><span class="keyword">double</span></code>
  56       precision internally, you can change the global default by passing <code class="computeroutput"><span class="special">-</span><span class="identifier">DBOOST_MATH_PROMOTE_DOUBLE_POLICY</span><span class="special">=</span><span class="keyword">false</span></code> on the
  57       command line, or at the point of call via something like this:
  58     </p>
  59 <pre class="programlisting"><span class="keyword">double</span> <span class="identifier">val</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">erf</span><span class="special">(</span><span class="identifier">my_argument</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">policies</span><span class="special">::</span><span class="identifier">make_policy</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">policies</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>
  60 </pre>
  61 <p>
  62       However, an easier option might be:
  63     </p>
  64 <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">hpp</span><span class="special">&gt;</span> <span class="comment">// Or any individual special function header</span>
  65
  66 <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
  67
  68 <span class="keyword">namespace</span> <span class="identifier">precise</span><span class="special">{</span>
  69 <span class="comment">//</span>
  70 <span class="comment">// Define a Policy for accurate evaluation - this is the same as the default, unless</span>
  71 <span class="comment">// someone has changed the global defaults.</span>
  72 <span class="comment">//</span>
  73 <span class="keyword">typedef</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><span class="identifier">policy</span><span class="special">&lt;&gt;</span> <span class="identifier">accurate_policy</span><span class="special">;</span>
  74 <span class="comment">//</span>
  75 <span class="comment">// Invoke BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS to declare</span>
  76 <span class="comment">// functions that use the above policy.  Note no trailing</span>
  77 <span class="comment">// ";" required on the macro call:</span>
  78 <span class="comment">//</span>
  79 <span class="identifier">BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS</span><span class="special">(</span><span class="identifier">accurate_policy</span><span class="special">)</span>
  80
  81
  82 <span class="special">}</span>
  83
  84 <span class="keyword">namespace</span> <span class="identifier">fast</span><span class="special">{</span>
  85 <span class="comment">//</span>
  86 <span class="comment">// Define a Policy for fast evaluation:</span>
  87 <span class="comment">//</span>
  88 <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">polcies</span><span class="special">;</span>
  89 <span class="keyword">typedef</span> <span class="identifier">policy</span><span class="special">&lt;</span><span class="identifier">promote_double</span><span class="special">&lt;</span><span class="keyword">false</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="identifier">fast_policy</span><span class="special">;</span>
  90 <span class="comment">//</span>
  91 <span class="comment">// Invoke BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS:</span>
  92 <span class="comment">//</span>
  93 <span class="identifier">BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS</span><span class="special">(</span><span class="identifier">fast_policy</span><span class="special">)</span>
  94
  95 <span class="special">}</span>
  96
  97 <span class="special">}</span>
  98 </pre>
  99 <p>
 100       And now one can call:
 101     </p>
 102 <pre class="programlisting"><span class="identifier">math</span><span class="special">::</span><span class="identifier">accurate</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">x</span><span class="special">);</span>
 103 </pre>
 104 <p>
 105       For the "accurate" version of tgamma, and:
 106     </p>
 107 <pre class="programlisting"><span class="identifier">math</span><span class="special">::</span><span class="identifier">fast</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">x</span><span class="special">);</span>
 108 </pre>
 109 <p>
 110       For the faster version.
 111     </p>
 112 <p>
 113       Had we wished to change the target precision (to 9 decimal places) as well
 114       as the evaluation type used, we might have done:
 115     </p>
 116 <pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
 117 <span class="keyword">namespace</span> <span class="identifier">fast</span><span class="special">{</span>
 118 <span class="comment">//</span>
 119 <span class="comment">// Define a Policy for fast evaluation:</span>
 120 <span class="comment">//</span>
 121 <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">polcies</span><span class="special">;</span>
 122 <span class="keyword">typedef</span> <span class="identifier">policy</span><span class="special">&lt;</span><span class="identifier">promote_double</span><span class="special">&lt;</span><span class="keyword">false</span><span class="special">&gt;,</span> <span class="identifier">digits10</span><span class="special">&lt;</span><span class="number">9</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="identifier">fast_policy</span><span class="special">;</span>
 123 <span class="comment">//</span>
 124 <span class="comment">// Invoke BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS:</span>
 125 <span class="comment">//</span>
 126 <span class="identifier">BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS</span><span class="special">(</span><span class="identifier">fast_policy</span><span class="special">)</span>
 127
 128 <span class="special">}</span>
 129 <span class="special">}</span>
 130 </pre>
 131 <p>
 132       One can do a similar thing with the distribution classes:
 133     </p>
 134 <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">hpp</span><span class="special">&gt;</span> <span class="comment">// or any individual distribution header</span>
 135
 136 <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">fast</span><span class="special">{</span>
 137 <span class="comment">//</span>
 138 <span class="comment">// Define a policy for fastest possible evaluation:</span>
 139 <span class="comment">//</span>
 140 <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">polcies</span><span class="special">;</span>
 141 <span class="keyword">typedef</span> <span class="identifier">policy</span><span class="special">&lt;</span><span class="identifier">promote_float</span><span class="special">&lt;</span><span class="keyword">false</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="identifier">fast_float_policy</span><span class="special">;</span>
 142 <span class="comment">//</span>
 143 <span class="comment">// Invoke BOOST_MATH_DECLARE_DISTRIBUTIONS</span>
 144 <span class="comment">//</span>
 145 <span class="identifier">BOOST_MATH_DECLARE_DISTRIBUTIONS</span><span class="special">(</span><span class="keyword">float</span><span class="special">,</span> <span class="identifier">fast_float_policy</span><span class="special">)</span>
 146
 147 <span class="special">}}</span> <span class="comment">// namespaces</span>
 148
 149 <span class="comment">//</span>
 150 <span class="comment">// And use:</span>
 151 <span class="comment">//</span>
 152 <span class="keyword">float</span> <span class="identifier">p_val</span> <span class="special">=</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">fast</span><span class="special">::</span><span class="identifier">normal</span><span class="special">(</span><span class="number">1.0f</span><span class="special">,</span> <span class="number">3.0f</span><span class="special">),</span> <span class="number">0.25f</span><span class="special">);</span>
 153 </pre>
 154 <p>
 155       Here's how these options change the relative performance of the distributions
 156       on Linux:
 157     </p>
 158 <p>
 159       [table_Distribution_performance_comparison_for_different_performance_options_with_GNU_C_version_5_1_0_on_linux]
 160     </p>
 161 </div>
 162 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 163 <td align="left"></td>
 164 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014 Nikhar Agrawal,
 165       Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
 166       Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam Sewani,
 167       Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
 168         Distributed under the Boost Software License, Version 1.0. (See accompanying
 169         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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