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//  (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_SPHERICAL_HARMONIC_HPP
#define BOOST_MATH_SPECIAL_SPHERICAL_HARMONIC_HPP

#ifdef _MSC_VER
#pragma once
#endif

#include <boost/math/special_functions/legendre.hpp>
#include <boost/math/tools/workaround.hpp>
#include <complex>

namespace boost{
namespace math{

namespace detail{

//
// Calculates the prefix term that's common to the real
// and imaginary parts.  Does *not* fix up the sign of the result
// though.
//
template <class T, class Policy>
inline T spherical_harmonic_prefix(unsigned n, unsigned m, T theta, const Policy& pol)
{
   BOOST_MATH_STD_USING

   if(m > n)
      return 0;

   T sin_theta = sin(theta);
   T x = cos(theta);

   T leg = detail::legendre_p_imp(n, m, x, static_cast<T>(pow(fabs(sin_theta), T(m))), pol);
   
   T prefix = boost::math::tgamma_delta_ratio(static_cast<T>(n - m + 1), static_cast<T>(2 * m), pol);
   prefix *= (2 * n + 1) / (4 * constants::pi<T>());
   prefix = sqrt(prefix);
   return prefix * leg;
}
//
// Real Part:
//
template <class T, class Policy>
T spherical_harmonic_r(unsigned n, int m, T theta, T phi, const Policy& pol)
{
   BOOST_MATH_STD_USING  // ADL of std functions

   bool sign = false;
   if(m < 0)
   {
      // Reflect and adjust sign if m < 0:
      sign = m&1;
      m = abs(m);
   }
   if(m&1)
   {
      // Check phase if theta is outside [0, PI]:
      T mod = boost::math::tools::fmod_workaround(theta, T(2 * constants::pi<T>()));
      if(mod < 0)
         mod += 2 * constants::pi<T>();
      if(mod > constants::pi<T>())
         sign = !sign;
   }
   // Get the value and adjust sign as required:
   T prefix = spherical_harmonic_prefix(n, m, theta, pol);
   prefix *= cos(m * phi);
   return sign ? T(-prefix) : prefix;
}

template <class T, class Policy>
T spherical_harmonic_i(unsigned n, int m, T theta, T phi, const Policy& pol)
{
   BOOST_MATH_STD_USING  // ADL of std functions

   bool sign = false;
   if(m < 0)
   {
      // Reflect and adjust sign if m < 0:
      sign = !(m&1);
      m = abs(m);
   }
   if(m&1)
   {
      // Check phase if theta is outside [0, PI]:
      T mod = boost::math::tools::fmod_workaround(theta, T(2 * constants::pi<T>()));
      if(mod < 0)
         mod += 2 * constants::pi<T>();
      if(mod > constants::pi<T>())
         sign = !sign;
   }
   // Get the value and adjust sign as required:
   T prefix = spherical_harmonic_prefix(n, m, theta, pol);
   prefix *= sin(m * phi);