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| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="math_toolkit.policy.pol_ref.precision_pol"></a><a class="link" href="precision_pol.html" title="Precision Policies"> Precision |
| Policies</a> |
| </h4></div></div></div> |
| <p> |
| There are two equivalent policies that effect the <span class="emphasis"><em>working precision</em></span> |
| used to calculate results, these policies both default to 0 - meaning calculate |
| to the maximum precision available in the type being used - but can be |
| set to other values to cause lower levels of precision to be used. One |
| might want to trade precision for evaluation speed. |
| </p> |
| <pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">policies</span><span class="special">{</span> |
| |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">int</span> <span class="identifier">N</span><span class="special">></span> |
| <span class="identifier">digits10</span><span class="special">;</span> |
| |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">int</span> <span class="identifier">N</span><span class="special">></span> |
| <span class="identifier">digits2</span><span class="special">;</span> |
| |
| <span class="special">}}}</span> <span class="comment">// namespaces |
| </span></pre> |
| <p> |
| As you would expect, <span class="emphasis"><em>digits10</em></span> specifies the number |
| of decimal digits to use, and <span class="emphasis"><em>digits2</em></span> the number of |
| binary digits. Internally, whichever is used, the precision is always converted |
| to <span class="emphasis"><em>binary digits</em></span>. |
| </p> |
| <p> |
| These policies are specified at compile-time, because many of the special |
| functions use compile-time-dispatch to select which approximation to use |
| based on the precision requested and the numeric type being used. |
| </p> |
| <p> |
| For example we could calculate <code class="computeroutput"><span class="identifier">tgamma</span></code> |
| to approximately 5 decimal digits using: |
| </p> |
| <p> |
| </p> |
| <p> |
| |
| </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">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> |
| <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> |
| <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">policies</span><span class="special">::</span><span class="identifier">policy</span><span class="special">;</span> |
| <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">policies</span><span class="special">::</span><span class="identifier">digits10</span><span class="special">;</span> |
| |
| <span class="keyword">typedef</span> <span class="identifier">policy</span><span class="special"><</span><span class="identifier">digits10</span><span class="special"><</span><span class="number">5</span><span class="special">></span> <span class="special">></span> <span class="identifier">my_pol_5</span><span class="special">;</span> <span class="comment">// Define a new, non-default, policy |
| </span><span class="comment">// to calculate tgamma to accuracy of approximately 5 decimal digits. |
| </span></pre> |
| <p> |
| </p> |
| <p> |
| </p> |
| <p> |
| Or again using helper function <code class="computeroutput"><span class="identifier">make_policy</span></code>: |
| </p> |
| <p> |
| </p> |
| <p> |
| |
| </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">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> |
| <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> |
| |
| <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> |
| |
| <span class="keyword">double</span> <span class="identifier">t</span> <span class="special">=</span> <span class="identifier">tgamma</span><span class="special">(</span><span class="number">12</span><span class="special">,</span> <span class="identifier">policy</span><span class="special"><</span><span class="identifier">digits10</span><span class="special"><</span><span class="number">5</span><span class="special">></span> <span class="special">>());</span> <span class="comment">// Concise make_policy. |
| </span> |
| </pre> |
| <p> |
| </p> |
| <p> |
| </p> |
| <p> |
| And for a quantile of a distribution to approximately 25-bit precision: |
| </p> |
| <p> |
| </p> |
| <p> |
| |
| </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">normal</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> |
| <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> |
| |
| <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> |
| |
| <span class="keyword">const</span> <span class="keyword">int</span> <span class="identifier">bits</span> <span class="special">=</span> <span class="number">25</span><span class="special">;</span> <span class="comment">// approximate precision. |
| </span> |
| <span class="keyword">double</span> <span class="identifier">q</span> <span class="special">=</span> <span class="identifier">quantile</span><span class="special">(</span> |
| <span class="identifier">normal_distribution</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">policy</span><span class="special"><</span><span class="identifier">digits2</span><span class="special"><</span><span class="identifier">bits</span><span class="special">></span> <span class="special">></span> <span class="special">>(),</span> |
| <span class="number">0.05</span><span class="special">);</span> <span class="comment">// 5% quantile. |
| </span> |
| </pre> |
| <p> |
| </p> |
| <p> |
| </p> |
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| <td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009, 2010 John Maddock, Paul A. Bristow, |
| Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani and |
| Thijs van den Berg<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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