1// Copyright John Maddock 2006.
2// Use, modification and distribution are subject to the
3// Boost Software License, Version 1.0. (See accompanying file
4// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
5
6#ifndef BOOST_MATH_SF_BINOMIAL_HPP
7#define BOOST_MATH_SF_BINOMIAL_HPP
8
9#ifdef _MSC_VER
10#pragma once
11#endif
12
13#include <boost/math/special_functions/math_fwd.hpp>
14#include <boost/math/special_functions/factorials.hpp>
15#include <boost/math/special_functions/beta.hpp>
16#include <boost/math/policies/error_handling.hpp>
17#include <type_traits>
18
19namespace boost{ namespace math{
20
21template <class T, class Policy>
22T binomial_coefficient(unsigned n, unsigned k, const Policy& pol)
23{
24 static_assert(!std::is_integral<T>::value, "Type T must not be an integral type");
25 BOOST_MATH_STD_USING
26 static const char* function = "boost::math::binomial_coefficient<%1%>(unsigned, unsigned)";
27 if(k > n)
28 return policies::raise_domain_error<T>(
29 function,
30 "The binomial coefficient is undefined for k > n, but got k = %1%.",
31 static_cast<T>(k), pol);
32 T result;
33 if((k == 0) || (k == n))
34 return static_cast<T>(1);
35 if((k == 1) || (k == n-1))
36 return static_cast<T>(n);
37
38 if(n <= max_factorial<T>::value)
39 {
40 // Use fast table lookup:
41 result = unchecked_factorial<T>(n);
42 result /= unchecked_factorial<T>(n-k);
43 result /= unchecked_factorial<T>(k);
44 }
45 else
46 {
47 // Use the beta function:
48 if(k < n - k)
49 result = static_cast<T>(k * beta(static_cast<T>(k), static_cast<T>(n-k+1), pol));
50 else
51 result = static_cast<T>((n - k) * beta(static_cast<T>(k+1), static_cast<T>(n-k), pol));
52 if(result == 0)
53 return policies::raise_overflow_error<T>(function, nullptr, pol);
54 result = 1 / result;
55 }
56 // convert to nearest integer:
57 return ceil(result - 0.5f);
58}
59//
60// Type float can only store the first 35 factorials, in order to
61// increase the chance that we can use a table driven implementation
62// we'll promote to double:
63//
64template <>
65inline float binomial_coefficient<float, policies::policy<> >(unsigned n, unsigned k, const policies::policy<>&)
66{
67 typedef policies::normalise<
68 policies::policy<>,
69 policies::promote_float<true>,
70 policies::promote_double<false>,
71 policies::discrete_quantile<>,
72 policies::assert_undefined<> >::type forwarding_policy;
73 return policies::checked_narrowing_cast<float, forwarding_policy>(val: binomial_coefficient<double>(n, k, pol: forwarding_policy()), function: "boost::math::binomial_coefficient<%1%>(unsigned,unsigned)");
74}
75
76template <class T>
77inline T binomial_coefficient(unsigned n, unsigned k)
78{
79 return binomial_coefficient<T>(n, k, policies::policy<>());
80}
81
82} // namespace math
83} // namespace boost
84
85
86#endif // BOOST_MATH_SF_BINOMIAL_HPP
87
88
89
90

source code of include/boost/math/special_functions/binomial.hpp