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<a accesskey="p" href="../factorials.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_double_factorial.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
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<div class="titlepage"><div><div><h3 class="title">
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<a name="math_toolkit.factorials.sf_factorial"></a><a class="link" href="sf_factorial.html" title="Factorial">Factorial</a>
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</h3></div></div></div>
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<h5>
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<a name="math_toolkit.factorials.sf_factorial.h0"></a>
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<span class="phrase"><a name="math_toolkit.factorials.sf_factorial.synopsis"></a></span><a class="link" href="sf_factorial.html#math_toolkit.factorials.sf_factorial.synopsis">Synopsis</a>
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</h5>
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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>
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</pre>
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<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>
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<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span>
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<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>
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<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="Chapter 21. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">></span>
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<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="Chapter 21. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&);</span>
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<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span>
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<span class="keyword">constexpr</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>
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<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span>
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<span class="keyword">struct</span> <span class="identifier">max_factorial</span><span class="special">;</span>
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<span class="special">}}</span> <span class="comment">// namespaces</span>
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</pre>
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<h5>
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<a name="math_toolkit.factorials.sf_factorial.h1"></a>
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<span class="phrase"><a name="math_toolkit.factorials.sf_factorial.description"></a></span><a class="link" href="sf_factorial.html#math_toolkit.factorials.sf_factorial.description">Description</a>
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</h5>
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<div class="important"><table border="0" summary="Important">
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<tr>
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<td rowspan="2" align="center" valign="top" width="25"><img alt="[Important]" src="../../../../../../doc/src/images/important.png"></td>
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<th align="left">Important</th>
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</tr>
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<tr><td align="left" valign="top">
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<p>
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The functions described below are templates where the template argument
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T CANNOT be deduced from the arguments passed to the function. Therefore
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if you write something like:
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</p>
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<p>
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<code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">factorial</span><span class="special">(</span><span class="number">2</span><span class="special">);</span></code>
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</p>
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<p>
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You will get a (perhaps perplexing) compiler error, usually indicating
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that there is no such function to be found. Instead you need to specify
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the return type explicitly and write:
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</p>
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<p>
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<code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">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>
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</p>
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<p>
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So that the return type is known.
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</p>
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<p>
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Furthermore, the template argument must be a real-valued type such as
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<code class="computeroutput"><span class="keyword">float</span></code> or <code class="computeroutput"><span class="keyword">double</span></code>
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and not an integer type - that would overflow far too easily for quite
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small values of parameter <code class="computeroutput"><span class="identifier">i</span></code>!
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</p>
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<p>
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The source code <code class="computeroutput"><span class="keyword">static_assert</span></code>
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and comment just after the will be:
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</p>
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<pre class="programlisting"><span class="keyword">static_assert</span><span class="special">(!</span><span class="identifier">std</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="string">"Type T must not be an integral type"</span><span class="special">);</span>
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<span class="comment">// factorial<unsigned int>(n) is not implemented</span>
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<span class="comment">// because it would overflow integral type T for too small n</span>
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<span class="comment">// to be useful. Use instead a floating-point type,</span>
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<span class="comment">// and convert to an unsigned type if essential, for example:</span>
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<span class="comment">// unsigned int nfac = static_cast<unsigned int>(factorial<double>(n));</span>
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<span class="comment">// See factorial documentation for more detail.</span>
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</pre>
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</td></tr>
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</table></div>
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<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>
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<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>
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<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="Chapter 21. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">></span>
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<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="Chapter 21. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&);</span>
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</pre>
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<p>
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Returns <code class="literal">i!</code>.
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</p>
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<p>
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The final <a class="link" href="../../policy.html" title="Chapter 21. Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
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be used to control the behaviour of the function: how it handles errors,
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what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Chapter 21. Policies: Controlling Precision, Error Handling etc">policy
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documentation for more details</a>.
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</p>
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<p>
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For <code class="literal">i <= max_factorial<T>::value</code> this is implemented
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by table lookup, for larger values of <code class="literal">i</code>, this function
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is implemented in terms of <a class="link" href="../sf_gamma/tgamma.html" title="Gamma">tgamma</a>.
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</p>
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<p>
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If <code class="literal">i</code> is so large that the result can not be represented
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in type T, then calls <a class="link" href="../error_handling.html#math_toolkit.error_handling.overflow_error">overflow_error</a>.
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</p>
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<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>
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<span class="keyword">constexpr</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>
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</pre>
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<p>
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Returns <code class="literal">i!</code>.
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</p>
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<p>
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Internally this function performs table lookup of the result. Further it
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performs no range checking on the value of i: it is up to the caller to ensure
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that <code class="literal">i <= max_factorial<T>::value</code>. This function
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is intended to be used inside inner loops that require fast table lookup
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of factorials, but requires care to ensure that argument <code class="literal">i</code>
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never grows too large.
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</p>
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<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>
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<span class="keyword">struct</span> <span class="identifier">max_factorial</span>
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<span class="special">{</span>
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<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>
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<span class="special">};</span>
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</pre>
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<p>
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This traits class defines the largest value that can be passed to <code class="literal">unchecked_factorial</code>.
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The member <code class="computeroutput"><span class="identifier">value</span></code> can be used
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where integral constant expressions are required: for example to define the
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size of further tables that depend on the factorials.
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</p>
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<p>
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This function is <code class="computeroutput"><span class="keyword">constexpr</span></code> only
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if the compiler supports C++14 constexpr functions.
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</p>
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<h5>
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<a name="math_toolkit.factorials.sf_factorial.h2"></a>
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<span class="phrase"><a name="math_toolkit.factorials.sf_factorial.accuracy"></a></span><a class="link" href="sf_factorial.html#math_toolkit.factorials.sf_factorial.accuracy">Accuracy</a>
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</h5>
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<p>
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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.
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For larger arguments the accuracy will be the same as for <a class="link" href="../sf_gamma/tgamma.html" title="Gamma">tgamma</a>.
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</p>
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<h5>
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<a name="math_toolkit.factorials.sf_factorial.h3"></a>
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<span class="phrase"><a name="math_toolkit.factorials.sf_factorial.testing"></a></span><a class="link" href="sf_factorial.html#math_toolkit.factorials.sf_factorial.testing">Testing</a>
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</h5>
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<p>
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Basic sanity checks and spot values to verify the data tables: the main tests
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for the <a class="link" href="../sf_gamma/tgamma.html" title="Gamma">tgamma</a> function
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handle those cases already.
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</p>
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<h5>
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<a name="math_toolkit.factorials.sf_factorial.h4"></a>
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<span class="phrase"><a name="math_toolkit.factorials.sf_factorial.implementation"></a></span><a class="link" href="sf_factorial.html#math_toolkit.factorials.sf_factorial.implementation">Implementation</a>
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</h5>
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<p>
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The factorial function is table driven for small arguments, and is implemented
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in terms of <a class="link" href="../sf_gamma/tgamma.html" title="Gamma">tgamma</a> for
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larger arguments.
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</p>
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</div>
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<td align="left"></td>
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<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
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Walker and Xiaogang Zhang<p>
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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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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