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