You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and dots ('.'), can be up to 35 characters long. Letters must be lowercase.
81 lines
2.4 KiB
81 lines
2.4 KiB
// Copyright John Maddock 2006. |
|
// Use, modification and distribution are subject to the |
|
// Boost Software License, Version 1.0. (See accompanying file |
|
// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) |
|
|
|
#ifndef BOOST_MATH_SF_BINOMIAL_HPP |
|
#define BOOST_MATH_SF_BINOMIAL_HPP |
|
|
|
#ifdef _MSC_VER |
|
#pragma once |
|
#endif |
|
|
|
#include <boost/math/special_functions/factorials.hpp> |
|
#include <boost/math/special_functions/beta.hpp> |
|
#include <boost/math/policies/error_handling.hpp> |
|
|
|
namespace boost{ namespace math{ |
|
|
|
template <class T, class Policy> |
|
T binomial_coefficient(unsigned n, unsigned k, const Policy& pol) |
|
{ |
|
BOOST_STATIC_ASSERT(!boost::is_integral<T>::value); |
|
BOOST_MATH_STD_USING |
|
static const char* function = "boost::math::binomial_coefficient<%1%>(unsigned, unsigned)"; |
|
if(k > n) |
|
return policies::raise_domain_error<T>( |
|
function, |
|
"The binomial coefficient is undefined for k > n, but got k = %1%.", |
|
k, pol); |
|
T result; |
|
if((k == 0) || (k == n)) |
|
return 1; |
|
if((k == 1) || (k == n-1)) |
|
return n; |
|
|
|
if(n <= max_factorial<T>::value) |
|
{ |
|
// Use fast table lookup: |
|
result = unchecked_factorial<T>(n); |
|
result /= unchecked_factorial<T>(n-k); |
|
result /= unchecked_factorial<T>(k); |
|
} |
|
else |
|
{ |
|
// Use the beta function: |
|
if(k < n - k) |
|
result = k * beta(static_cast<T>(k), static_cast<T>(n-k+1), pol); |
|
else |
|
result = (n - k) * beta(static_cast<T>(k+1), static_cast<T>(n-k), pol); |
|
if(result == 0) |
|
return policies::raise_overflow_error<T>(function, 0, pol); |
|
result = 1 / result; |
|
} |
|
// convert to nearest integer: |
|
return ceil(result - 0.5f); |
|
} |
|
// |
|
// Type float can only store the first 35 factorials, in order to |
|
// increase the chance that we can use a table driven implementation |
|
// we'll promote to double: |
|
// |
|
template <> |
|
inline float binomial_coefficient<float, policies::policy<> >(unsigned n, unsigned k, const policies::policy<>& pol) |
|
{ |
|
return policies::checked_narrowing_cast<float, policies::policy<> >(binomial_coefficient<double>(n, k, pol), "boost::math::binomial_coefficient<%1%>(unsigned,unsigned)"); |
|
} |
|
|
|
template <class T> |
|
inline T binomial_coefficient(unsigned n, unsigned k) |
|
{ |
|
return binomial_coefficient<T>(n, k, policies::policy<>()); |
|
} |
|
|
|
} // namespace math |
|
} // namespace boost |
|
|
|
|
|
#endif // BOOST_MATH_SF_BINOMIAL_HPP |
|
|
|
|
|
|
|
|