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- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="math_toolkit.tradoffs"></a><a class="link" href="tradoffs.html" title="Trading Accuracy for Performance">Trading Accuracy for Performance</a>
- </h2></div></div></div>
- <p>
- There are a number of <a class="link" href="../policy.html" title="Chapter 20. Policies: Controlling Precision, Error Handling etc">Policies</a> that can be used
- to trade accuracy for performance:
- </p>
- <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
- <li class="listitem">
- Internal promotion: by default functions with <code class="computeroutput"><span class="keyword">float</span></code>
- arguments are evaluated at <code class="computeroutput"><span class="keyword">double</span></code>
- precision internally to ensure full precision in the result. Similarly
- <code class="computeroutput"><span class="keyword">double</span></code> precision functions
- are evaluated at <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>
- precision internally by default. Changing these defaults can have a significant
- speed advantage at the expense of accuracy, note also that evaluating using
- <code class="computeroutput"><span class="keyword">float</span></code> internally may result
- in numerical instability for some of the more complex algorithms, we suggest
- you use this option with care.
- </li>
- <li class="listitem">
- Target accuracy: just because you choose to evaluate at <code class="computeroutput"><span class="keyword">double</span></code>
- precision doesn't mean you necessarily want to target full 16-digit accuracy,
- if you wish you can change the default (full machine precision) to whatever
- is "good enough" for your particular use case.
- </li>
- </ul></div>
- <p>
- For example, suppose you want to evaluate <code class="computeroutput"><span class="keyword">double</span></code>
- precision functions at <code class="computeroutput"><span class="keyword">double</span></code>
- 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
- command line, or at the point of call via something like this:
- </p>
- <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>
- </pre>
- <p>
- However, an easier option might be:
- </p>
- <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>
- <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
- <span class="keyword">namespace</span> <span class="identifier">precise</span><span class="special">{</span>
- <span class="comment">//</span>
- <span class="comment">// Define a Policy for accurate evaluation - this is the same as the default, unless</span>
- <span class="comment">// someone has changed the global defaults.</span>
- <span class="comment">//</span>
- <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>
- <span class="comment">//</span>
- <span class="comment">// Invoke BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS to declare</span>
- <span class="comment">// functions that use the above policy. Note no trailing</span>
- <span class="comment">// ";" required on the macro call:</span>
- <span class="comment">//</span>
- <span class="identifier">BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS</span><span class="special">(</span><span class="identifier">accurate_policy</span><span class="special">)</span>
- <span class="special">}</span>
- <span class="keyword">namespace</span> <span class="identifier">fast</span><span class="special">{</span>
- <span class="comment">//</span>
- <span class="comment">// Define a Policy for fast evaluation:</span>
- <span class="comment">//</span>
- <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>
- <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>
- <span class="comment">//</span>
- <span class="comment">// Invoke BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS:</span>
- <span class="comment">//</span>
- <span class="identifier">BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS</span><span class="special">(</span><span class="identifier">fast_policy</span><span class="special">)</span>
- <span class="special">}</span>
- <span class="special">}</span>
- </pre>
- <p>
- And now one can call:
- </p>
- <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>
- </pre>
- <p>
- For the "accurate" version of tgamma, and:
- </p>
- <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>
- </pre>
- <p>
- For the faster version.
- </p>
- <p>
- Had we wished to change the target precision (to 9 decimal places) as well
- as the evaluation type used, we might have done:
- </p>
- <pre class="programlisting"><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>
- <span class="comment">//</span>
- <span class="comment">// Define a Policy for fast evaluation:</span>
- <span class="comment">//</span>
- <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>
- <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>
- <span class="comment">//</span>
- <span class="comment">// Invoke BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS:</span>
- <span class="comment">//</span>
- <span class="identifier">BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS</span><span class="special">(</span><span class="identifier">fast_policy</span><span class="special">)</span>
- <span class="special">}</span>
- <span class="special">}</span>
- </pre>
- <p>
- One can do a similar thing with the distribution classes:
- </p>
- <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>
- <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>
- <span class="comment">//</span>
- <span class="comment">// Define a policy for fastest possible evaluation:</span>
- <span class="comment">//</span>
- <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>
- <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>
- <span class="comment">//</span>
- <span class="comment">// Invoke BOOST_MATH_DECLARE_DISTRIBUTIONS</span>
- <span class="comment">//</span>
- <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>
- <span class="special">}}</span> <span class="comment">// namespaces</span>
- <span class="comment">//</span>
- <span class="comment">// And use:</span>
- <span class="comment">//</span>
- <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>
- </pre>
- <p>
- Here's how these options change the relative performance of the distributions
- on Linux:
- </p>
- <p>
- [table_Distribution_performance_comparison_for_different_performance_options_with_GNU_C_version_5_1_0_on_linux]
- </p>
- </div>
- <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
- <td align="left"></td>
- <td align="right"><div class="copyright-footer">Copyright © 2006-2019 Nikhar
- Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
- Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
- Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
- Daryle Walker and Xiaogang Zhang<p>
- Distributed under the Boost Software License, Version 1.0. (See accompanying
- 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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