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<div class="titlepage"><div><div><h4 class="title">
<a name="math_toolkit.special.factorials.sf_factorial"></a><a class="link" href="sf_factorial.html" title="Factorial"> Factorial</a>
</h4></div></div></div>
<a name="math_toolkit.special.factorials.sf_factorial.synopsis"></a><h5>
<a name="id1088076"></a>
<a class="link" href="sf_factorial.html#math_toolkit.special.factorials.sf_factorial.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">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">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">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="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">unchecked_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">struct</span> <span class="identifier">max_factorial</span><span class="special">;</span>
<span class="special">}}</span> <span class="comment">// namespaces
</span></pre>
<a name="math_toolkit.special.factorials.sf_factorial.description"></a><h5>
<a name="id1088384"></a>
<a class="link" href="sf_factorial.html#math_toolkit.special.factorials.sf_factorial.description">Description</a>
</h5>
<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">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">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>
</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>
For <code class="literal">i <= max_factorial<T>::value</code> this is implemented
by table lookup, for larger values of <code class="literal">i</code>, this function
is implemented in terms of <a class="link" href="../sf_gamma/tgamma.html" title="Gamma">tgamma</a>.
</p>
<p>
If <code class="literal">i</code> is so large that the result can not be represented
in type T, then calls <a class="link" href="../../main_overview/error_handling.html#overflow_error">overflow_error</a>.
</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">unchecked_factorial</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">i</span><span class="special">);</span>
</pre>
<p>
Returns <code class="literal">i!</code>.
</p>
<p>
Internally this function performs table lookup of the result. Further it
performs no range checking on the value of i: it is up to the caller to
ensure that <code class="literal">i <= max_factorial<T>::value</code>. This
function is intended to be used inside inner loops that require fast table
lookup of factorials, but requires care to ensure that argument <code class="literal">i</code>
never grows too large.
</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="keyword">struct</span> <span class="identifier">max_factorial</span>
<span class="special">{</span>
<span class="keyword">static</span> <span class="keyword">const</span> <span class="keyword">unsigned</span> <span class="identifier">value</span> <span class="special">=</span> <span class="identifier">X</span><span class="special">;</span>
<span class="special">};</span>
</pre>
<p>
This traits class defines the largest value that can be passed to <code class="literal">unchecked_factorial</code>.
The member <code class="computeroutput"><span class="identifier">value</span></code> can be
used where integral constant expressions are required: for example to define
the size of further tables that depend on the factorials.
</p>
<a name="math_toolkit.special.factorials.sf_factorial.accuracy"></a><h5>
<a name="id1088744"></a>
<a class="link" href="sf_factorial.html#math_toolkit.special.factorials.sf_factorial.accuracy">Accuracy</a>
</h5>
<p>
For arguments smaller than <code class="computeroutput"><span class="identifier">max_factorial</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">value</span></code>
the result should be correctly rounded. For larger arguments the accuracy
will be the same as for <a class="link" href="../sf_gamma/tgamma.html" title="Gamma">tgamma</a>.
</p>
<a name="math_toolkit.special.factorials.sf_factorial.testing"></a><h5>
<a name="id1088787"></a>
<a class="link" href="sf_factorial.html#math_toolkit.special.factorials.sf_factorial.testing">Testing</a>
</h5>
<p>
Basic sanity checks and spot values to verify the data tables: the main
tests for the <a class="link" href="../sf_gamma/tgamma.html" title="Gamma">tgamma</a>
function handle those cases already.
</p>
<a name="math_toolkit.special.factorials.sf_factorial.implementation"></a><h5>
<a name="id1088812"></a>
<a class="link" href="sf_factorial.html#math_toolkit.special.factorials.sf_factorial.implementation">Implementation</a>
</h5>
<p>
The factorial function is table driven for small arguments, and is implemented
in terms of <a class="link" href="../sf_gamma/tgamma.html" title="Gamma">tgamma</a>
for larger arguments.
</p>
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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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