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| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="math_toolkit.toolkit.internals1.constants"></a><a class="link" href="constants.html" title="Numeric Constants"> Numeric |
| Constants</a> |
| </h4></div></div></div> |
| <a name="math_toolkit.toolkit.internals1.constants.synopsis"></a><h5> |
| <a name="id1189569"></a> |
| <a class="link" href="constants.html#math_toolkit.toolkit.internals1.constants.synopsis">Synopsis</a> |
| </h5> |
| <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">constants</span><span class="special">/</span><span class="identifier">constants</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> |
| </pre> |
| <p> |
| </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">constants</span><span class="special">{</span> |
| |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <span class="identifier">pi</span><span class="special">();</span> |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <span class="identifier">root_pi</span><span class="special">();</span> |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <span class="identifier">root_half_pi</span><span class="special">();</span> |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <span class="identifier">root_two_pi</span><span class="special">();</span> |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <span class="identifier">root_ln_four</span><span class="special">();</span> |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <span class="identifier">e</span><span class="special">();</span> |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <span class="identifier">half</span><span class="special">();</span> |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <span class="identifier">euler</span><span class="special">();</span> |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <span class="identifier">root_two</span><span class="special">();</span> |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <span class="identifier">ln_two</span><span class="special">();</span> |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <span class="identifier">ln_ln_two</span><span class="special">();</span> |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <span class="identifier">third</span><span class="special">();</span> |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <span class="identifier">twothirds</span><span class="special">();</span> |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <span class="identifier">pi_minus_three</span><span class="special">();</span> |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <span class="identifier">four_minus_pi</span><span class="special">();</span> |
| |
| <span class="special">}}}</span> <span class="comment">// namespaces |
| </span></pre> |
| <a name="math_toolkit.toolkit.internals1.constants.description"></a><h5> |
| <a name="id1190209"></a> |
| <a class="link" href="constants.html#math_toolkit.toolkit.internals1.constants.description">Description</a> |
| </h5> |
| <p> |
| The header <code class="computeroutput"><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">constants</span><span class="special">/</span><span class="identifier">constants</span><span class="special">.</span><span class="identifier">hpp</span></code> contains some numeric constants that |
| we have found useful in the development of this library. New constants |
| are added on an ad-hoc basis based on need. |
| </p> |
| <p> |
| Usage is like this: |
| </p> |
| <pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> |
| <span class="identifier">T</span> <span class="identifier">circumference</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">r</span><span class="special">)</span> |
| <span class="special">{</span> |
| <span class="keyword">return</span> <span class="number">2</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">constants</span><span class="special">::</span><span class="identifier">pi</span><span class="special"><</span><span class="identifier">T</span><span class="special">>()</span> <span class="special">*</span> <span class="identifier">r</span><span class="special">;</span> |
| <span class="special">}</span> |
| </pre> |
| <p> |
| All the constants are accurate to at least the 34 decimal digits required |
| for 128-bit long doubles, and most are accurate to 100 digits or more when |
| used with a suitable arbitrary precision type. |
| </p> |
| <p> |
| The following table summarises the constants we have at present: |
| </p> |
| <div class="informaltable"><table class="table"> |
| <colgroup> |
| <col> |
| <col> |
| <col> |
| </colgroup> |
| <thead><tr> |
| <th> |
| <p> |
| Constant |
| </p> |
| </th> |
| <th> |
| <p> |
| Meaning |
| </p> |
| </th> |
| <th> |
| <p> |
| Value |
| </p> |
| </th> |
| </tr></thead> |
| <tbody> |
| <tr> |
| <td> |
| <p> |
| pi |
| </p> |
| </td> |
| <td> |
| <p> |
| π |
| </p> |
| </td> |
| <td> |
| <p> |
| 3.1415926535897932384... |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| root_pi |
| </p> |
| </td> |
| <td> |
| <p> |
| √π |
| </p> |
| </td> |
| <td> |
| <p> |
| 1.772453850905516027... |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| root_half_pi |
| </p> |
| </td> |
| <td> |
| <p> |
| √(π/2) |
| </p> |
| </td> |
| <td> |
| <p> |
| 1.253314137315500251... |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| root_two_pi |
| </p> |
| </td> |
| <td> |
| <p> |
| √(2*π) |
| </p> |
| </td> |
| <td> |
| <p> |
| 2.506628274631000502... |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| root_ln_four |
| </p> |
| </td> |
| <td> |
| <p> |
| √(ln(4)) |
| </p> |
| </td> |
| <td> |
| <p> |
| 1.17741002251547469... |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| e |
| </p> |
| </td> |
| <td> |
| <p> |
| <span class="emphasis"><em>e</em></span> |
| </p> |
| </td> |
| <td> |
| <p> |
| 2.71828182845904523536... |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| half |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.5 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.5 |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| euler |
| </p> |
| </td> |
| <td> |
| <p> |
| Euler's constant |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.577215664901532860606 |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| root_two |
| </p> |
| </td> |
| <td> |
| <p> |
| √2 |
| </p> |
| </td> |
| <td> |
| <p> |
| 1.4142135623730950488... |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| ln_two |
| </p> |
| </td> |
| <td> |
| <p> |
| ln(2) |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.6931471805599453094... |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| ln_ln_two |
| </p> |
| </td> |
| <td> |
| <p> |
| ln(ln(2)) |
| </p> |
| </td> |
| <td> |
| <p> |
| -0.3665129205816643... |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| third |
| </p> |
| </td> |
| <td> |
| <p> |
| 1/3 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.333333333333333333... |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| twothirds |
| </p> |
| </td> |
| <td> |
| <p> |
| 2/3 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.666666666666666666... |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| pi_minus_three |
| </p> |
| </td> |
| <td> |
| <p> |
| π-3 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.14159265358979323846... |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| four_minus_pi |
| </p> |
| </td> |
| <td> |
| <p> |
| 4-π |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.85840734641020676153735... |
| </p> |
| </td> |
| </tr> |
| </tbody> |
| </table></div> |
| </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 , 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>) |
| </p> |
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