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diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_double_factorial.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_double_factorial.html new file mode 100644 index 0000000000..ddd30492a4 --- /dev/null +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_double_factorial.html @@ -0,0 +1,156 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Double Factorial</title> +<link rel="stylesheet" href="../../../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.76.1"> +<link rel="home" href="../../../index.html" title="Math Toolkit"> +<link rel="up" href="../factorials.html" title="Factorials and Binomial Coefficients"> +<link rel="prev" href="sf_factorial.html" title="Factorial"> +<link rel="next" href="sf_rising_factorial.html" title="Rising Factorial"> +</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 href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="sf_factorial.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../factorials.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="sf_rising_factorial.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section math_toolkit_special_factorials_sf_double_factorial"> +<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> +</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">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> + 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> + 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> +<div class="important"><table border="0" summary="Important"> +<tr> +<td rowspan="2" align="center" valign="top" width="25"><img alt="[Important]" src="../../../../../../../../doc/src/images/important.png"></td> +<th align="left">Important</th> +</tr> +<tr><td align="left" valign="top"> +<p> + The functions described above are templates where the template argument + T can not be deduced from the arguments passed to the function. Therefore + if you write something like: + </p> +<p> + <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">double_factorial</span><span class="special">(</span><span class="number">2</span><span class="special">);</span></code> + </p> +<p> + You will get a (possibly perplexing) compiler error, ususally indicating + that there is no such function to be found. Instead you need to specifiy + the return type explicity and write: + </p> +<p> + <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">double_factorial</span><span class="special"><</span><span class="keyword">double</span><span class="special">>(</span><span class="number">2</span><span class="special">);</span></code> + </p> +<p> + So that the return type is known. Further, the template argument must + be a real-valued type such as <code class="computeroutput"><span class="keyword">float</span></code> + or <code class="computeroutput"><span class="keyword">double</span></code> and not an integer + type - that would overflow far too easily! + </p> +<p> + The source code <code class="computeroutput"><span class="identifier">static_assert</span></code> + and comment just after the will be: + </p> +<p> +</p> +<pre class="programlisting"><span class="identifier">BOOST_STATIC_ASSERT</span><span class="special">(!</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">is_integral</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">value</span><span class="special">);</span> +<span class="comment">// factorial<unsigned int>(n) is not implemented</span> +<span class="comment">// because it would overflow integral type T for too small n</span> +<span class="comment">// to be useful. Use instead a floating-point type,</span> +<span class="comment">// and convert to an unsigned type if essential, for example:</span> +<span class="comment">// unsigned int nfac = static_cast<unsigned int>(factorial<double>(n));</span> +<span class="comment">// See factorial documentation for more detail.</span> +</pre> +<p> + </p> +</td></tr> +</table></div> +<h5> +<a name="math_toolkit.special.factorials.sf_double_factorial.h0"></a> + <span><a name="math_toolkit.special.factorials.sf_double_factorial.accuracy"></a></span><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> +<h5> +<a name="math_toolkit.special.factorials.sf_double_factorial.h1"></a> + <span><a name="math_toolkit.special.factorials.sf_double_factorial.testing"></a></span><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> +<h5> +<a name="math_toolkit.special.factorials.sf_double_factorial.h2"></a> + <span><a name="math_toolkit.special.factorials.sf_double_factorial.implementation"></a></span><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> +</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 © 2006-2010 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> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="sf_factorial.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../factorials.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="sf_rising_factorial.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> |