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<title>Numeric Constants</title>
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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>
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<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">&lt;</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">&gt;</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">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <span class="identifier">pi</span><span class="special">();</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <span class="identifier">root_pi</span><span class="special">();</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</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">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</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">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</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">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <span class="identifier">e</span><span class="special">();</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <span class="identifier">half</span><span class="special">();</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <span class="identifier">euler</span><span class="special">();</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <span class="identifier">root_two</span><span class="special">();</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <span class="identifier">ln_two</span><span class="special">();</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</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">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <span class="identifier">third</span><span class="special">();</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <span class="identifier">twothirds</span><span class="special">();</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</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">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</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">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</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">&lt;</span><span class="identifier">T</span><span class="special">&gt;()</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>
&#960;
</p>
</td>
<td>
<p>
3.1415926535897932384...
</p>
</td>
</tr>
<tr>
<td>
<p>
root_pi
</p>
</td>
<td>
<p>
&#8730;&#960;
</p>
</td>
<td>
<p>
1.772453850905516027...
</p>
</td>
</tr>
<tr>
<td>
<p>
root_half_pi
</p>
</td>
<td>
<p>
&#8730;(&#960;/2)
</p>
</td>
<td>
<p>
1.253314137315500251...
</p>
</td>
</tr>
<tr>
<td>
<p>
root_two_pi
</p>
</td>
<td>
<p>
&#8730;(2*&#960;)
</p>
</td>
<td>
<p>
2.506628274631000502...
</p>
</td>
</tr>
<tr>
<td>
<p>
root_ln_four
</p>
</td>
<td>
<p>
&#8730;(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>
&#8730;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>
&#960;-3
</p>
</td>
<td>
<p>
0.14159265358979323846...
</p>
</td>
</tr>
<tr>
<td>
<p>
four_minus_pi
</p>
</td>
<td>
<p>
4-&#960;
</p>
</td>
<td>
<p>
0.85840734641020676153735...
</p>
</td>
</tr>
</tbody>
</table></div>
</div>
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<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2006 , 2007, 2008, 2009, 2010 John Maddock, Paul A. Bristow,
Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan R&#229;de, 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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