<html> <head> <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Numeric Constants</title> <link rel="stylesheet" href="../../../../../../../../doc/src/boostbook.css" type="text/css"> <meta name="generator" content="DocBook XSL Stylesheets V1.74.0"> <link rel="home" href="../../../index.html" title="Math Toolkit"> <link rel="up" href="../internals1.html" title="Reused Utilities"> <link rel="prev" href="../internals1.html" title="Reused Utilities"> <link rel="next" href="series_evaluation.html" title="Series Evaluation"> </head> <body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> <table cellpadding="2" width="100%"><tr> <td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../../boost.png"></td> <td align="center"><a href="../../../../../../../../index.html">Home</a></td> <td align="center"><a href="../../../../../../../../libs/libraries.htm">Libraries</a></td> <td align="center"><a 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name="math_toolkit.toolkit.internals1.constants.synopsis"></a><h5> <a name="id1193188"></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="id1193827"></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 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> </div></td> </tr></table> <hr> <div class="spirit-nav"> <a accesskey="p" href="../internals1.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../internals1.html"><img src="../../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="series_evaluation.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a> </div> </body> </html>