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| 4 | <title>Trading Accuracy for Performance</title> | |
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| 24 | </div> | |
| 25 | <div class="section"> | |
| 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 15. 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"><</span><span class="keyword">false</span><span class="special">>()));</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"><</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">></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"><></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"><</span><span class="identifier">promote_double</span><span class="special"><</span><span class="keyword">false</span><span class="special">></span> <span class="special">></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"><</span><span class="identifier">promote_double</span><span class="special"><</span><span class="keyword">false</span><span class="special">>,</span> <span class="identifier">digits10</span><span class="special"><</span><span class="number">9</span><span class="special">></span> <span class="special">></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"><</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">></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"><</span><span class="identifier">promote_float</span><span class="special"><</span><span class="keyword">false</span><span class="special">></span> <span class="special">></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 © 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 Råde, 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>) | |
| 170 | </p> | |
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