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  25 <div class="section">
  26 <div class="titlepage"><div><div><h3 class="title">
  27 <a name="math_toolkit.factorials.sf_factorial"></a><a class="link" href="sf_factorial.html" title="Factorial">Factorial</a>
  28 </h3></div></div></div>
  29 <h5>
  30 <a name="math_toolkit.factorials.sf_factorial.h0"></a>
  31         <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>
  32       </h5>
  33 <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">special_functions</span><span class="special">/</span><span class="identifier">factorials</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
  34 </pre>
  35 <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>
  36
  37 <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>
  38 <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>
  39
  40 <span class="keyword">template</span> <span class="special">&lt;</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&#160;20.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&gt;</span>
  41 <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&#160;20.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&amp;);</span>
  42
  43 <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>
  44 <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>
  45
  46 <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>
  47 <span class="keyword">struct</span> <span class="identifier">max_factorial</span><span class="special">;</span>
  48
  49 <span class="special">}}</span> <span class="comment">// namespaces</span>
  50 </pre>
  51 <h5>
  52 <a name="math_toolkit.factorials.sf_factorial.h1"></a>
  53         <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>
  54       </h5>
  55 <div class="important"><table border="0" summary="Important">
  56 <tr>
  57 <td rowspan="2" align="center" valign="top" width="25"><img alt="[Important]" src="../../../../../../doc/src/images/important.png"></td>
  58 <th align="left">Important</th>
  59 </tr>
  60 <tr><td align="left" valign="top">
  61 <p>
  62           The functions described below are templates where the template argument
  63           T CANNOT be deduced from the arguments passed to the function. Therefore
  64           if you write something like:
  65         </p>
  66 <p>
  67           <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>
  68         </p>
  69 <p>
  70           You will get a (perhaps perplexing) compiler error, ususally indicating
  71           that there is no such function to be found. Instead you need to specify
  72           the return type explicity and write:
  73         </p>
  74 <p>
  75           <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">&lt;</span><span class="keyword">double</span><span class="special">&gt;(</span><span class="number">2</span><span class="special">);</span></code>
  76         </p>
  77 <p>
  78           So that the return type is known.
  79         </p>
  80 <p>
  81           Furthermore, the template argument must be a real-valued type such as
  82           <code class="computeroutput"><span class="keyword">float</span></code> or <code class="computeroutput"><span class="keyword">double</span></code>
  83           and not an integer type - that would overflow far too easily for quite
  84           small values of parameter <code class="computeroutput"><span class="identifier">i</span></code>!
  85         </p>
  86 <p>
  87           The source code <code class="computeroutput"><span class="keyword">static_assert</span></code>
  88           and comment just after the will be:
  89         </p>
  90 <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">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">value</span><span class="special">);</span>
  91 <span class="comment">// factorial&lt;unsigned int&gt;(n) is not implemented</span>
  92 <span class="comment">// because it would overflow integral type T for too small n</span>
  93 <span class="comment">// to be useful. Use instead a floating-point type,</span>
  94 <span class="comment">// and convert to an unsigned type if essential, for example:</span>
  95 <span class="comment">// unsigned int nfac = static_cast&lt;unsigned int&gt;(factorial&lt;double&gt;(n));</span>
  96 <span class="comment">// See factorial documentation for more detail.</span>
  97 </pre>
  98 </td></tr>
  99 </table></div>
 100 <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>
 101 <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>
 102
 103 <span class="keyword">template</span> <span class="special">&lt;</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&#160;20.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&gt;</span>
 104 <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&#160;20.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&amp;);</span>
 105 </pre>
 106 <p>
 107         Returns <code class="literal">i!</code>.
 108       </p>
 109 <p>
 110         The final <a class="link" href="../../policy.html" title="Chapter&#160;20.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
 111         be used to control the behaviour of the function: how it handles errors,
 112         what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Chapter&#160;20.&#160;Policies: Controlling Precision, Error Handling etc">policy
 113         documentation for more details</a>.
 114       </p>
 115 <p>
 116         For <code class="literal">i &lt;= max_factorial&lt;T&gt;::value</code> this is implemented
 117         by table lookup, for larger values of <code class="literal">i</code>, this function
 118         is implemented in terms of <a class="link" href="../sf_gamma/tgamma.html" title="Gamma">tgamma</a>.
 119       </p>
 120 <p>
 121         If <code class="literal">i</code> is so large that the result can not be represented
 122         in type T, then calls <a class="link" href="../error_handling.html#math_toolkit.error_handling.overflow_error">overflow_error</a>.
 123       </p>
 124 <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>
 125 <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>
 126 </pre>
 127 <p>
 128         Returns <code class="literal">i!</code>.
 129       </p>
 130 <p>
 131         Internally this function performs table lookup of the result. Further it
 132         performs no range checking on the value of i: it is up to the caller to ensure
 133         that <code class="literal">i &lt;= max_factorial&lt;T&gt;::value</code>. This function
 134         is intended to be used inside inner loops that require fast table lookup
 135         of factorials, but requires care to ensure that argument <code class="literal">i</code>
 136         never grows too large.
 137       </p>
 138 <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>
 139 <span class="keyword">struct</span> <span class="identifier">max_factorial</span>
 140 <span class="special">{</span>
 141    <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>
 142 <span class="special">};</span>
 143 </pre>
 144 <p>
 145         This traits class defines the largest value that can be passed to <code class="literal">unchecked_factorial</code>.
 146         The member <code class="computeroutput"><span class="identifier">value</span></code> can be used
 147         where integral constant expressions are required: for example to define the
 148         size of further tables that depend on the factorials.
 149       </p>
 150 <p>
 151         This function is <code class="computeroutput"><span class="keyword">constexpr</span></code> only
 152         if the compiler supports C++14 constexpr functions.
 153       </p>
 154 <h5>
 155 <a name="math_toolkit.factorials.sf_factorial.h2"></a>
 156         <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>
 157       </h5>
 158 <p>
 159         For arguments smaller than <code class="computeroutput"><span class="identifier">max_factorial</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">value</span></code> the result should be correctly rounded.
 160         For larger arguments the accuracy will be the same as for <a class="link" href="../sf_gamma/tgamma.html" title="Gamma">tgamma</a>.
 161       </p>
 162 <h5>
 163 <a name="math_toolkit.factorials.sf_factorial.h3"></a>
 164         <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>
 165       </h5>
 166 <p>
 167         Basic sanity checks and spot values to verify the data tables: the main tests
 168         for the <a class="link" href="../sf_gamma/tgamma.html" title="Gamma">tgamma</a> function
 169         handle those cases already.
 170       </p>
 171 <h5>
 172 <a name="math_toolkit.factorials.sf_factorial.h4"></a>
 173         <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>
 174       </h5>
 175 <p>
 176         The factorial function is table driven for small arguments, and is implemented
 177         in terms of <a class="link" href="../sf_gamma/tgamma.html" title="Gamma">tgamma</a> for
 178         larger arguments.
 179       </p>
 180 </div>
 181 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 182 <td align="left"></td>
 183 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
 184       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
 185       Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
 186       R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
 187       Daryle Walker and Xiaogang Zhang<p>
 188         Distributed under the Boost Software License, Version 1.0. (See accompanying
 189         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>)
 190       </p>
 191 </div></td>
 192 </tr></table>
 193 <hr>
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