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240 lines
6.8 KiB
240 lines
6.8 KiB
// Copyright John Maddock 2006, 2010. |
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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_SP_FACTORIALS_HPP |
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#define BOOST_MATH_SP_FACTORIALS_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/gamma.hpp> |
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#include <boost/math/special_functions/math_fwd.hpp> |
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#include <boost/math/special_functions/detail/unchecked_factorial.hpp> |
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#include <boost/array.hpp> |
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#ifdef BOOST_MSVC |
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#pragma warning(push) // Temporary until lexical cast fixed. |
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#pragma warning(disable: 4127 4701) |
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#endif |
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#include <boost/lexical_cast.hpp> |
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#ifdef BOOST_MSVC |
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#pragma warning(pop) |
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#endif |
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#include <boost/config/no_tr1/cmath.hpp> |
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namespace boost { namespace math |
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{ |
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template <class T, class Policy> |
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inline T factorial(unsigned i, const Policy& pol) |
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{ |
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BOOST_STATIC_ASSERT(!boost::is_integral<T>::value); |
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// factorial<unsigned int>(n) is not implemented |
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// because it would overflow integral type T for too small n |
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// to be useful. Use instead a floating-point type, |
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// and convert to an unsigned type if essential, for example: |
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// unsigned int nfac = static_cast<unsigned int>(factorial<double>(n)); |
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// See factorial documentation for more detail. |
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BOOST_MATH_STD_USING // Aid ADL for floor. |
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if(i <= max_factorial<T>::value) |
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return unchecked_factorial<T>(i); |
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T result = boost::math::tgamma(static_cast<T>(i+1), pol); |
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if(result > tools::max_value<T>()) |
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return result; // Overflowed value! (But tgamma will have signalled the error already). |
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return floor(result + 0.5f); |
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} |
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template <class T> |
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inline T factorial(unsigned i) |
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{ |
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return factorial<T>(i, policies::policy<>()); |
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} |
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/* |
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// Can't have these in a policy enabled world? |
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template<> |
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inline float factorial<float>(unsigned i) |
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{ |
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if(i <= max_factorial<float>::value) |
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return unchecked_factorial<float>(i); |
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return tools::overflow_error<float>(BOOST_CURRENT_FUNCTION); |
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} |
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template<> |
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inline double factorial<double>(unsigned i) |
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{ |
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if(i <= max_factorial<double>::value) |
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return unchecked_factorial<double>(i); |
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return tools::overflow_error<double>(BOOST_CURRENT_FUNCTION); |
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} |
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*/ |
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template <class T, class Policy> |
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T double_factorial(unsigned i, 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 // ADL lookup of std names |
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if(i & 1) |
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{ |
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// odd i: |
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if(i < max_factorial<T>::value) |
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{ |
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unsigned n = (i - 1) / 2; |
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return ceil(unchecked_factorial<T>(i) / (ldexp(T(1), (int)n) * unchecked_factorial<T>(n)) - 0.5f); |
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} |
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// |
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// Fallthrough: i is too large to use table lookup, try the |
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// gamma function instead. |
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// |
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T result = boost::math::tgamma(static_cast<T>(i) / 2 + 1, pol) / sqrt(constants::pi<T>()); |
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if(ldexp(tools::max_value<T>(), -static_cast<int>(i+1) / 2) > result) |
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return ceil(result * ldexp(T(1), static_cast<int>(i+1) / 2) - 0.5f); |
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} |
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else |
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{ |
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// even i: |
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unsigned n = i / 2; |
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T result = factorial<T>(n, pol); |
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if(ldexp(tools::max_value<T>(), -(int)n) > result) |
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return result * ldexp(T(1), (int)n); |
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} |
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// |
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// If we fall through to here then the result is infinite: |
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// |
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return policies::raise_overflow_error<T>("boost::math::double_factorial<%1%>(unsigned)", 0, pol); |
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} |
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template <class T> |
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inline T double_factorial(unsigned i) |
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{ |
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return double_factorial<T>(i, policies::policy<>()); |
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} |
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namespace detail{ |
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template <class T, class Policy> |
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T rising_factorial_imp(T x, int n, const Policy& pol) |
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{ |
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BOOST_STATIC_ASSERT(!boost::is_integral<T>::value); |
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if(x < 0) |
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{ |
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// |
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// For x less than zero, we really have a falling |
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// factorial, modulo a possible change of sign. |
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// |
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// Note that the falling factorial isn't defined |
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// for negative n, so we'll get rid of that case |
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// first: |
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// |
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bool inv = false; |
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if(n < 0) |
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{ |
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x += n; |
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n = -n; |
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inv = true; |
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} |
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T result = ((n&1) ? -1 : 1) * falling_factorial(-x, n, pol); |
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if(inv) |
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result = 1 / result; |
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return result; |
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} |
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if(n == 0) |
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return 1; |
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// |
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// We don't optimise this for small n, because |
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// tgamma_delta_ratio is alreay optimised for that |
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// use case: |
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// |
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return 1 / boost::math::tgamma_delta_ratio(x, static_cast<T>(n), pol); |
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} |
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template <class T, class Policy> |
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inline T falling_factorial_imp(T x, unsigned n, 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 // ADL of std names |
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if(x == 0) |
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return 0; |
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if(x < 0) |
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{ |
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// |
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// For x < 0 we really have a rising factorial |
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// modulo a possible change of sign: |
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// |
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return (n&1 ? -1 : 1) * rising_factorial(-x, n, pol); |
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} |
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if(n == 0) |
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return 1; |
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if(x < n-1) |
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{ |
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// |
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// x+1-n will be negative and tgamma_delta_ratio won't |
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// handle it, split the product up into three parts: |
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// |
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T xp1 = x + 1; |
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unsigned n2 = itrunc((T)floor(xp1), pol); |
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if(n2 == xp1) |
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return 0; |
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T result = boost::math::tgamma_delta_ratio(xp1, -static_cast<T>(n2), pol); |
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x -= n2; |
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result *= x; |
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++n2; |
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if(n2 < n) |
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result *= falling_factorial(x - 1, n - n2, pol); |
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return result; |
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} |
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// |
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// Simple case: just the ratio of two |
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// (positive argument) gamma functions. |
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// Note that we don't optimise this for small n, |
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// because tgamma_delta_ratio is alreay optimised |
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// for that use case: |
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// |
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return boost::math::tgamma_delta_ratio(x + 1, -static_cast<T>(n), pol); |
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} |
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} // namespace detail |
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template <class RT> |
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inline typename tools::promote_args<RT>::type |
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falling_factorial(RT x, unsigned n) |
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{ |
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typedef typename tools::promote_args<RT>::type result_type; |
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return detail::falling_factorial_imp( |
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static_cast<result_type>(x), n, policies::policy<>()); |
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} |
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template <class RT, class Policy> |
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inline typename tools::promote_args<RT>::type |
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falling_factorial(RT x, unsigned n, const Policy& pol) |
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{ |
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typedef typename tools::promote_args<RT>::type result_type; |
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return detail::falling_factorial_imp( |
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static_cast<result_type>(x), n, pol); |
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} |
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template <class RT> |
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inline typename tools::promote_args<RT>::type |
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rising_factorial(RT x, int n) |
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{ |
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typedef typename tools::promote_args<RT>::type result_type; |
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return detail::rising_factorial_imp( |
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static_cast<result_type>(x), n, policies::policy<>()); |
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} |
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template <class RT, class Policy> |
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inline typename tools::promote_args<RT>::type |
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rising_factorial(RT x, int n, const Policy& pol) |
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{ |
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typedef typename tools::promote_args<RT>::type result_type; |
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return detail::rising_factorial_imp( |
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static_cast<result_type>(x), n, pol); |
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} |
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} // namespace math |
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} // namespace boost |
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#endif // BOOST_MATH_SP_FACTORIALS_HPP |
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