using System;
using Complex = System.Numerics.Complex;

namespace IStation.Numerics
{
    /// <summary>
    /// This partial implementation of the SpecialFunctions class contains all methods related to the spherical Bessel functions.
    /// </summary>
    public static partial class SpecialFunctions
    {
        /// <summary>
        /// Returns the spherical Bessel function of the first kind.
        /// <para>SphericalBesselJ(n, z) is given by Sqrt(pi/2) / Sqrt(z) * BesselJ(n + 1/2, z).</para>
        /// </summary>
        /// <param name="n">The order of the spherical Bessel function.</param>
        /// <param name="z">The value to compute the spherical Bessel function of.</param>
        /// <returns>The spherical Bessel function of the first kind.</returns>
        public static Complex SphericalBesselJ(double n, Complex z)
        {
            if (double.IsNaN(n) || double.IsNaN(z.Real) || double.IsNaN(z.Imaginary))
            {
                return new Complex(double.NaN, double.NaN);
            }
            
            if (double.IsInfinity(z.Real))
            {
                return (z.Imaginary == 0) ? Complex.Zero : new Complex(double.PositiveInfinity, double.PositiveInfinity);
            }

            if (z.Real == 0 && z.Imaginary == 0)
            {
                return (n == 0) ? 1 : 0;
            }

            return Constants.SqrtPiOver2 * BesselJ(n + 0.5, z) / Complex.Sqrt(z);
        }

        /// <summary>
        /// Returns the spherical Bessel function of the first kind.
        /// <para>SphericalBesselJ(n, z) is given by Sqrt(pi/2) / Sqrt(z) * BesselJ(n + 1/2, z).</para>
        /// </summary>
        /// <param name="n">The order of the spherical Bessel function.</param>
        /// <param name="z">The value to compute the spherical Bessel function of.</param>
        /// <returns>The spherical Bessel function of the first kind.</returns>
        public static double SphericalBesselJ(double n, double z)
        {
            if (double.IsNaN(n) || double.IsNaN(z))
            {
                return double.NaN;
            }

            if (n < 0)
            {
                return double.NaN;
            }

            if (double.IsInfinity(z))
            {
                return 0;
            }

            if (z == 0)
            {
                return (n == 0) ? 1 : 0;
            }

            return Constants.SqrtPiOver2 * BesselJ(n + 0.5, z) / Math.Sqrt(z);
        }

        /// <summary>
        /// Returns the spherical Bessel function of the second kind.
        /// <para>SphericalBesselY(n, z) is given by Sqrt(pi/2) / Sqrt(z) * BesselY(n + 1/2, z).</para>
        /// </summary>
        /// <param name="n">The order of the spherical Bessel function.</param>
        /// <param name="z">The value to compute the spherical Bessel function of.</param>
        /// <returns>The spherical Bessel function of the second kind.</returns>
        public static Complex SphericalBesselY(double n, Complex z)
        {
            if (double.IsNaN(n) || double.IsNaN(z.Real) || double.IsNaN(z.Imaginary))
            {
                return new Complex(double.NaN, double.NaN);
            }

            if (double.IsInfinity(z.Real))
            {
                return (z.Imaginary == 0) ? Complex.Zero : new Complex(double.PositiveInfinity, double.PositiveInfinity);
            }

            if (z.Real == 0 && z.Imaginary == 0)
            {
                return new Complex(double.NaN, double.NaN);
            }

            return Constants.SqrtPiOver2 * BesselY(n + 0.5, z) / Complex.Sqrt(z);
        }

        /// <summary>
        /// Returns the spherical Bessel function of the second kind.
        /// <para>SphericalBesselY(n, z) is given by Sqrt(pi/2) / Sqrt(z) * BesselY(n + 1/2, z).</para>
        /// </summary>
        /// <param name="n">The order of the spherical Bessel function.</param>
        /// <param name="z">The value to compute the spherical Bessel function of.</param>
        /// <returns>The spherical Bessel function of the second kind.</returns>
        public static double SphericalBesselY(double n, double z)
        {
            if (double.IsNaN(n) || double.IsNaN(z))
            {
                return double.NaN;
            }

            if (n < 0)
            {
                return double.NaN;
            }

            if (double.IsInfinity(z))
            {
                return 0;
            }

            if (z == 0)
            {
                return double.NegativeInfinity;
            }

            return Constants.SqrtPiOver2 * BesselY(n + 0.5, z) / Math.Sqrt(z);
        }
    }
}