Added boost header

test/external/boost/math/special_functions/factorials.hpp

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