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26 <div class=
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"title">
27 <a name=
"math_toolkit.factorials.sf_falling_factorial"></a><a class=
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"sf_falling_factorial.html" title=
"Falling Factorial">Falling
29 </h3></div></div></div>
30 <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>
32 <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>
34 <span class=
"keyword">template
</span> <span class=
"special"><</span><span class=
"keyword">class
</span> <span class=
"identifier">T
</span><span class=
"special">></span>
35 <a class=
"link" href=
"../result_type.html" title=
"Calculation of the Type of the Result"><span class=
"emphasis"><em>calculated-result-type
</em></span></a> <span class=
"identifier">falling_factorial
</span><span class=
"special">(
</span><span class=
"identifier">T
</span> <span class=
"identifier">x
</span><span class=
"special">,
</span> <span class=
"keyword">unsigned
</span> <span class=
"identifier">i
</span><span class=
"special">);
</span>
37 <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 15. Policies: Controlling Precision, Error Handling etc">Policy
</a><span class=
"special">></span>
38 <a class=
"link" href=
"../result_type.html" title=
"Calculation of the Type of the Result"><span class=
"emphasis"><em>calculated-result-type
</em></span></a> <span class=
"identifier">falling_factorial
</span><span class=
"special">(
</span><span class=
"identifier">T
</span> <span class=
"identifier">x
</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 15. Policies: Controlling Precision, Error Handling etc">Policy
</a><span class=
"special">&);
</span>
40 <span class=
"special">}}
</span> <span class=
"comment">// namespaces
</span>
43 Returns the falling factorial of
<span class=
"emphasis"><em>x
</em></span> and
<span class=
"emphasis"><em>i
</em></span>:
46 falling_factorial(x, i) = x(x-
1)(x-
2)(x-
3)...(x-i+
1)
49 Note that this function is only defined for positive
<span class=
"emphasis"><em>i
</em></span>,
50 hence the
<code class=
"computeroutput"><span class=
"keyword">unsigned
</span></code> second argument.
51 Argument
<span class=
"emphasis"><em>x
</em></span> can be either positive or negative however.
54 The final
<a class=
"link" href=
"../../policy.html" title=
"Chapter 15. Policies: Controlling Precision, Error Handling etc">Policy
</a> argument is optional and can
55 be used to control the behaviour of the function: how it handles errors,
56 what level of precision to use etc. Refer to the
<a class=
"link" href=
"../../policy.html" title=
"Chapter 15. Policies: Controlling Precision, Error Handling etc">policy
57 documentation for more details
</a>.
60 May return the result of
<a class=
"link" href=
"../error_handling.html#math_toolkit.error_handling.overflow_error">overflow_error
</a>
61 if the result is too large to represent in type T.
64 The return type of these functions is computed using the
<a class=
"link" href=
"../result_type.html" title=
"Calculation of the Type of the Result"><span class=
"emphasis"><em>result
65 type calculation rules
</em></span></a>: the type of the result is
<code class=
"computeroutput"><span class=
"keyword">double
</span></code> if T is an integer type, otherwise
66 the type of the result is T.
69 <a name=
"math_toolkit.factorials.sf_falling_factorial.h0"></a>
70 <span class=
"phrase"><a name=
"math_toolkit.factorials.sf_falling_factorial.accuracy"></a></span><a class=
"link" href=
"sf_falling_factorial.html#math_toolkit.factorials.sf_falling_factorial.accuracy">Accuracy
</a>
73 The accuracy will be the same as the
<a class=
"link" href=
"../sf_gamma/gamma_ratios.html" title=
"Ratios of Gamma Functions">tgamma_delta_ratio
</a>
77 <a name=
"math_toolkit.factorials.sf_falling_factorial.h1"></a>
78 <span class=
"phrase"><a name=
"math_toolkit.factorials.sf_falling_factorial.testing"></a></span><a class=
"link" href=
"sf_falling_factorial.html#math_toolkit.factorials.sf_falling_factorial.testing">Testing
</a>
81 The spot tests for the falling factorials use data generated by functions.wolfram.com.
84 <a name=
"math_toolkit.factorials.sf_falling_factorial.h2"></a>
85 <span class=
"phrase"><a name=
"math_toolkit.factorials.sf_falling_factorial.implementation"></a></span><a class=
"link" href=
"sf_falling_factorial.html#math_toolkit.factorials.sf_falling_factorial.implementation">Implementation
</a>
88 Rising and falling factorials are implemented as ratios of gamma functions
89 using
<a class=
"link" href=
"../sf_gamma/gamma_ratios.html" title=
"Ratios of Gamma Functions">tgamma_delta_ratio
</a>.
90 Optimisations for small integer arguments are handled internally by that
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96 <td align=
"right"><div class=
"copyright-footer">Copyright
© 2006-
2010,
2012-
2014 Nikhar Agrawal,
97 Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
98 Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R
åde, Gautam Sewani,
99 Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang
<p>
100 Distributed under the Boost Software License, Version
1.0. (See accompanying
101 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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