Chris@16: //  Copyright (c) 2006 Xiaogang Zhang
Chris@16: //  Use, modification and distribution are subject to the
Chris@16: //  Boost Software License, Version 1.0. (See accompanying file
Chris@16: //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
Chris@16: 
Chris@16: #ifndef BOOST_MATH_BESSEL_YN_HPP
Chris@16: #define BOOST_MATH_BESSEL_YN_HPP
Chris@16: 
Chris@16: #ifdef _MSC_VER
Chris@16: #pragma once
Chris@16: #endif
Chris@16: 
Chris@16: #include <boost/math/special_functions/detail/bessel_y0.hpp>
Chris@16: #include <boost/math/special_functions/detail/bessel_y1.hpp>
Chris@16: #include <boost/math/special_functions/detail/bessel_jy_series.hpp>
Chris@16: #include <boost/math/policies/error_handling.hpp>
Chris@16: 
Chris@16: // Bessel function of the second kind of integer order
Chris@16: // Y_n(z) is the dominant solution, forward recurrence always OK (though unstable)
Chris@16: 
Chris@16: namespace boost { namespace math { namespace detail{
Chris@16: 
Chris@16: template <typename T, typename Policy>
Chris@16: T bessel_yn(int n, T x, const Policy& pol)
Chris@16: {
Chris@16:     BOOST_MATH_STD_USING
Chris@16:     T value, factor, current, prev;
Chris@16: 
Chris@16:     using namespace boost::math::tools;
Chris@16: 
Chris@16:     static const char* function = "boost::math::bessel_yn<%1%>(%1%,%1%)";
Chris@16: 
Chris@16:     if ((x == 0) && (n == 0))
Chris@16:     {
Chris@16:        return -policies::raise_overflow_error<T>(function, 0, pol);
Chris@16:     }
Chris@16:     if (x <= 0)
Chris@16:     {
Chris@16:        return policies::raise_domain_error<T>(function,
Chris@16:             "Got x = %1%, but x must be > 0, complex result not supported.", x, pol);
Chris@16:     }
Chris@16: 
Chris@16:     //
Chris@16:     // Reflection comes first:
Chris@16:     //
Chris@16:     if (n < 0)
Chris@16:     {
Chris@16:         factor = (n & 0x1) ? -1 : 1;  // Y_{-n}(z) = (-1)^n Y_n(z)
Chris@16:         n = -n;
Chris@16:     }
Chris@16:     else
Chris@16:     {
Chris@16:         factor = 1;
Chris@16:     }
Chris@16: 
Chris@16:     if(x < policies::get_epsilon<T, Policy>())
Chris@16:     {
Chris@16:        T scale = 1;
Chris@16:        value = bessel_yn_small_z(n, x, &scale, pol);
Chris@16:        if(tools::max_value<T>() * fabs(scale) < fabs(value))
Chris@16:           return boost::math::sign(scale) * boost::math::sign(value) * policies::raise_overflow_error<T>(function, 0, pol);
Chris@16:        value /= scale;
Chris@16:     }
Chris@16:     else if (n == 0)
Chris@16:     {
Chris@16:         value = bessel_y0(x, pol);
Chris@16:     }
Chris@16:     else if (n == 1)
Chris@16:     {
Chris@16:         value = factor * bessel_y1(x, pol);
Chris@16:     }
Chris@16:     else
Chris@16:     {
Chris@16:        prev = bessel_y0(x, pol);
Chris@16:        current = bessel_y1(x, pol);
Chris@16:        int k = 1;
Chris@16:        BOOST_ASSERT(k < n);
Chris@16:        policies::check_series_iterations<T>("boost::math::bessel_y_n<%1%>(%1%,%1%)", n, pol);
Chris@16:        do
Chris@16:        {
Chris@16:            T fact = 2 * k / x;
Chris@16:            if((fact > 1) && ((tools::max_value<T>() - fabs(prev)) / fact < fabs(current)))
Chris@16:            {
Chris@16:               prev /= current;
Chris@16:               factor /= current;
Chris@16:               current = 1;
Chris@16:            }
Chris@16:            value = fact * current - prev;
Chris@16:            prev = current;
Chris@16:            current = value;
Chris@16:            ++k;
Chris@16:        }
Chris@16:        while(k < n);
Chris@16:        if(fabs(tools::max_value<T>() * factor) < fabs(value))
Chris@16:           return sign(value) * sign(value) * policies::raise_overflow_error<T>(function, 0, pol);
Chris@16:        value /= factor;
Chris@16:     }
Chris@16:     return value;
Chris@16: }
Chris@16: 
Chris@16: }}} // namespaces
Chris@16: 
Chris@16: #endif // BOOST_MATH_BESSEL_YN_HPP
Chris@16: