//	Spludlow Software
//	Copyright © Samuel P. Ludlow 2020 All Rights Reserved
//	Distributed under the terms of the GNU General Public License version 3
//	Distributed WITHOUT ANY WARRANTY; without implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE
//	https://www.spludlow.co.uk/LICENCE.TXT
//	The Spludlow logo is a registered trademark of Samuel P. Ludlow and may not be used without permission
//	v1.14

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

using System.Numerics;

namespace Spludlow
{
	public class Maths
	{
		public static UInt64 NextUInt64(Random random)
		{
			byte[] buffer = new byte[sizeof(UInt64)];
			random.NextBytes(buffer);
			return BitConverter.ToUInt64(buffer, 0);
		}

		public static Int64 NextInt64(Random random)
		{
			byte[] buffer = new byte[sizeof(Int64)];
			random.NextBytes(buffer);
			return BitConverter.ToInt64(buffer, 0);
		}

		public static double ModulusSquared(Complex complex)
		{
			return complex.Real * complex.Real + complex.Imaginary * complex.Imaginary;
		}

		public static bool IsCloseTo(Complex x, Complex y)
		{
			const double tiny = 0.001;
			return (Math.Abs(y.Real - x.Real) + Math.Abs(y.Imaginary - x.Imaginary) < tiny);
		}

		public static Complex Pow(Complex complex, double exponent)	//	Exponent power
		{
			double x = complex.Real;
			double y = complex.Imaginary;

			double modulus = Math.Pow(x * x + y * y, exponent * 0.5);
			double argument = Math.Atan2(y, x) * exponent;

			double real = modulus * Math.Cos(argument);
			double imaginary = modulus * Math.Sin(argument);

			return new Complex(real, imaginary);
		}


		public static Complex Power(Complex a, Complex b)		//	raise to the power
		{
			double r = Math.Sqrt(a.Real * a.Real + a.Imaginary * a.Imaginary);
			double theta = Math.Atan2(a.Imaginary, a.Real);
			double factor = Math.Pow(r, b.Real) * (Math.Pow(Math.E, -b.Imaginary * theta));
			double angle = b.Real * theta + b.Imaginary * Math.Log(r);

			return new Complex(factor * Math.Cos(angle), factor * Math.Sin(angle));
		}


	}
}