Added boost header

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

@@ -0,0 +1,194 @@
+
+//  (C) 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_SPECIAL_LEGENDRE_HPP
+#define BOOST_MATH_SPECIAL_LEGENDRE_HPP
+
+#ifdef _MSC_VER
+#pragma once
+#endif
+
+#include <boost/math/special_functions/math_fwd.hpp>
+#include <boost/math/special_functions/factorials.hpp>
+#include <boost/math/tools/config.hpp>
+
+namespace boost{
+namespace math{
+
+// Recurrance relation for legendre P and Q polynomials:
+template <class T1, class T2, class T3>
+inline typename tools::promote_args<T1, T2, T3>::type
+   legendre_next(unsigned l, T1 x, T2 Pl, T3 Plm1)
+{
+   typedef typename tools::promote_args<T1, T2, T3>::type result_type;
+   return ((2 * l + 1) * result_type(x) * result_type(Pl) - l * result_type(Plm1)) / (l + 1);
+}
+
+namespace detail{
+
+// Implement Legendre P and Q polynomials via recurrance:
+template <class T, class Policy>
+T legendre_imp(unsigned l, T x, const Policy& pol, bool second = false)
+{
+   static const char* function = "boost::math::legrendre_p<%1%>(unsigned, %1%)";
+   // Error handling:
+   if((x < -1) || (x > 1))
+      return policies::raise_domain_error<T>(
+         function,
+         "The Legendre Polynomial is defined for"
+         " -1 <= x <= 1, but got x = %1%.", x, pol);
+
+   T p0, p1;
+   if(second)
+   {
+      // A solution of the second kind (Q):
+      p0 = (boost::math::log1p(x, pol) - boost::math::log1p(-x, pol)) / 2;
+      p1 = x * p0 - 1;
+   }
+   else
+   {
+      // A solution of the first kind (P):
+      p0 = 1;
+      p1 = x;
+   }
+   if(l == 0)
+      return p0;
+
+   unsigned n = 1;
+
+   while(n < l)
+   {
+      std::swap(p0, p1);
+      p1 = boost::math::legendre_next(n, x, p0, p1);
+      ++n;
+   }
+   return p1;
+}
+
+} // namespace detail
+
+template <class T, class Policy>
+inline typename tools::promote_args<T>::type 
+   legendre_p(int l, T x, const Policy& pol)
+{
+   typedef typename tools::promote_args<T>::type result_type;
+   typedef typename policies::evaluation<result_type, Policy>::type value_type;
+   static const char* function = "boost::math::legendre_p<%1%>(unsigned, %1%)";
+   if(l < 0)
+      return policies::checked_narrowing_cast<result_type, Policy>(detail::legendre_imp(-l-1, static_cast<value_type>(x), pol, false), function);
+   return policies::checked_narrowing_cast<result_type, Policy>(detail::legendre_imp(l, static_cast<value_type>(x), pol, false), function);
+}
+
+template <class T>
+inline typename tools::promote_args<T>::type 
+   legendre_p(int l, T x)
+{
+   return boost::math::legendre_p(l, x, policies::policy<>());
+}
+
+template <class T, class Policy>
+inline typename tools::promote_args<T>::type 
+   legendre_q(unsigned l, T x, const Policy& pol)
+{
+   typedef typename tools::promote_args<T>::type result_type;
+   typedef typename policies::evaluation<result_type, Policy>::type value_type;
+   return policies::checked_narrowing_cast<result_type, Policy>(detail::legendre_imp(l, static_cast<value_type>(x), pol, true), "boost::math::legendre_q<%1%>(unsigned, %1%)");
+}
+
+template <class T>
+inline typename tools::promote_args<T>::type 
+   legendre_q(unsigned l, T x)
+{
+   return boost::math::legendre_q(l, x, policies::policy<>());
+}
+
+// Recurrence for associated polynomials:
+template <class T1, class T2, class T3>
+inline typename tools::promote_args<T1, T2, T3>::type 
+   legendre_next(unsigned l, unsigned m, T1 x, T2 Pl, T3 Plm1)
+{
+   typedef typename tools::promote_args<T1, T2, T3>::type result_type;
+   return ((2 * l + 1) * result_type(x) * result_type(Pl) - (l + m) * result_type(Plm1)) / (l + 1 - m);
+}
+
+namespace detail{
+// Legendre P associated polynomial:
+template <class T, class Policy>
+T legendre_p_imp(int l, int m, T x, T sin_theta_power, const Policy& pol)
+{
+   // Error handling:
+   if((x < -1) || (x > 1))
+      return policies::raise_domain_error<T>(
+      "boost::math::legendre_p<%1%>(int, int, %1%)",
+         "The associated Legendre Polynomial is defined for"
+         " -1 <= x <= 1, but got x = %1%.", x, pol);
+   // Handle negative arguments first:
+   if(l < 0)
+      return legendre_p_imp(-l-1, m, x, sin_theta_power, pol);
+   if(m < 0)
+   {
+      int sign = (m&1) ? -1 : 1;
+      return sign * boost::math::tgamma_ratio(static_cast<T>(l+m+1), static_cast<T>(l+1-m), pol) * legendre_p_imp(l, -m, x, sin_theta_power, pol);
+   }
+   // Special cases:
+   if(m > l)
+      return 0;
+   if(m == 0)
+      return boost::math::legendre_p(l, x, pol);
+
+   T p0 = boost::math::double_factorial<T>(2 * m - 1, pol) * sin_theta_power;
+
+   if(m&1)
+      p0 *= -1;
+   if(m == l)
+      return p0;
+
+   T p1 = x * (2 * m + 1) * p0;
+
+   int n = m + 1;
+
+   while(n < l)
+   {
+      std::swap(p0, p1);
+      p1 = boost::math::legendre_next(n, m, x, p0, p1);
+      ++n;
+   }
+   return p1;
+}
+
+template <class T, class Policy>
+inline T legendre_p_imp(int l, int m, T x, const Policy& pol)
+{
+   BOOST_MATH_STD_USING
+   // TODO: we really could use that mythical "pow1p" function here:
+   return legendre_p_imp(l, m, x, static_cast<T>(pow(1 - x*x, T(abs(m))/2)), pol);
+}
+
+}
+
+template <class T, class Policy>
+inline typename tools::promote_args<T>::type
+   legendre_p(int l, int m, T x, const Policy& pol)
+{
+   typedef typename tools::promote_args<T>::type result_type;
+   typedef typename policies::evaluation<result_type, Policy>::type value_type;
+   return policies::checked_narrowing_cast<result_type, Policy>(detail::legendre_p_imp(l, m, static_cast<value_type>(x), pol), "bost::math::legendre_p<%1%>(int, int, %1%)");
+}
+
+template <class T>
+inline typename tools::promote_args<T>::type
+   legendre_p(int l, int m, T x)
+{
+   return boost::math::legendre_p(l, m, x, policies::policy<>());
+}
+
+} // namespace math
+} // namespace boost
+
+#endif // BOOST_MATH_SPECIAL_LEGENDRE_HPP
+
+
+