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src/boost/math/special_functions/detail/bessel_y0.hpp  view on Meta::CPAN

                   x12 =  static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.9519662791675215849e-03)),
                   x21 =  static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0130e+03)),
                   x22 =  static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 6.4716931485786837568e-04)),
                   x31 =  static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.8140e+03)),
                   x32 =  static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.1356030177269762362e-04))
    ;
    T value, factor, r, rc, rs;

    BOOST_MATH_STD_USING
    using namespace boost::math::tools;
    using namespace boost::math::constants;

    static const char* function = "boost::math::bessel_y0<%1%>(%1%,%1%)";

    if (x < 0)
    {
       return policies::raise_domain_error<T>(function,
            "Got x = %1% but x must be non-negative, complex result not supported.", x, pol);
    }
    if (x == 0)
    {
       return -policies::raise_overflow_error<T>(function, 0, pol);
    }
    if (x <= 3)                       // x in (0, 3]
    {
        T y = x * x;
        T z = 2 * log(x/x1) * bessel_j0(x) / pi<T>();
        r = evaluate_rational(P1, Q1, y);
        factor = (x + x1) * ((x - x11/256) - x12);
        value = z + factor * r;
    }
    else if (x <= 5.5f)                  // x in (3, 5.5]
    {
        T y = x * x;
        T z = 2 * log(x/x2) * bessel_j0(x) / pi<T>();
        r = evaluate_rational(P2, Q2, y);
        factor = (x + x2) * ((x - x21/256) - x22);
        value = z + factor * r;
    }
    else if (x <= 8)                  // x in (5.5, 8]
    {
        T y = x * x;
        T z = 2 * log(x/x3) * bessel_j0(x) / pi<T>();
        r = evaluate_rational(P3, Q3, y);
        factor = (x + x3) * ((x - x31/256) - x32);
        value = z + factor * r;
    }
    else                                // x in (8, \infty)
    {
        T y = 8 / x;
        T y2 = y * y;
        rc = evaluate_rational(PC, QC, y2);
        rs = evaluate_rational(PS, QS, y2);
        factor = sqrt(2 / (x * pi<T>()));
        //
        // The following code is really just:
        //
        // T z = x - 0.25f * pi<T>();
        // value = factor * (rc * sin(z) + y * rs * cos(z));
        //
        // But using the sin/cos addition formulae and constant values for
        // sin/cos of PI/4:
        //
        T sx = sin(x);
        T cx = cos(x);
        value = factor * (rc * (sx * constants::one_div_root_two<T>() - cx * constants::half_root_two<T>()) 
           + y * rs * (cx * constants::one_div_root_two<T>() + sx * constants::half_root_two<T>()));
    }

    return value;
}

}}} // namespaces

#endif // BOOST_MATH_BESSEL_Y0_HPP