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<div class="titlepage"><div><div><h4 class="title">
<a name="math_toolkit.special.factorials.sf_double_factorial"></a><a class="link" href="sf_double_factorial.html" title="Double Factorial">
Double Factorial</a>
</h4></div></div></div>
<p>
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<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">factorials</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">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">double_factorial</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">i</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="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">></span>
<span class="identifier">T</span> <span class="identifier">double_factorial</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">i</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&);</span>
<span class="special">}}</span> <span class="comment">// namespaces
</span></pre>
<p>
Returns <code class="literal">i!!</code>.
</p>
<p>
</p>
<p>
The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
is optional and can be used to control the behaviour of the function:
how it handles errors, what level of precision to use etc. Refer to the
<a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
</p>
<p>
</p>
<p>
May return the result of <a class="link" href="../../main_overview/error_handling.html#overflow_error">overflow_error</a>
if the result is too large to represent in type T. The implementation is
designed to be optimised for small <span class="emphasis"><em>i</em></span> where table lookup
of i! is possible.
</p>
<a name="math_toolkit.special.factorials.sf_double_factorial.accuracy"></a><h5>
<a name="id1091306"></a>
<a class="link" href="sf_double_factorial.html#math_toolkit.special.factorials.sf_double_factorial.accuracy">Accuracy</a>
</h5>
<p>
The implementation uses a trivial adaptation of the factorial function,
so error rates should be no more than a couple of epsilon higher.
</p>
<a name="math_toolkit.special.factorials.sf_double_factorial.testing"></a><h5>
<a name="id1091328"></a>
<a class="link" href="sf_double_factorial.html#math_toolkit.special.factorials.sf_double_factorial.testing">Testing</a>
</h5>
<p>
The spot tests for the double factorial use data generated by functions.wolfram.com.
</p>
<a name="math_toolkit.special.factorials.sf_double_factorial.implementation"></a><h5>
<a name="id1091347"></a>
<a class="link" href="sf_double_factorial.html#math_toolkit.special.factorials.sf_double_factorial.implementation">Implementation</a>
</h5>
<p>
The double factorial is implemented in terms of the factorial and gamma
functions using the relations:
</p>
<p>
(2n)!! = 2<sup>n </sup> * n!
</p>
<p>
(2n+1)!! = (2n+1)! / (2<sup>n </sup> n!)
</p>
<p>
and
</p>
<p>
(2n-1)!! = Γ((2n+1)/2) * 2<sup>n </sup> / sqrt(pi)
</p>
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<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>)
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