namespace AP
{
    /********************************************************************
    Class defining a complex number with double precision.
    ********************************************************************/
    public struct Complex
    {
        public double x;
        public double y;

        public Complex(double _x)
        {
            x = _x;
            y = 0;
        }
        public Complex(double _x, double _y)
        {
            x = _x;
            y = _y;
        }
        public static implicit operator Complex(double _x)
        {
            return new Complex(_x);
        }
        public static bool operator==(Complex lhs, Complex rhs)
        {
            return (lhs.x==rhs.x) & (lhs.y==rhs.y);
        }
        public static bool operator!=(Complex lhs, Complex rhs)
        {
            return (lhs.x!=rhs.x) | (lhs.y!=rhs.y);
        }
        public static Complex operator+(Complex lhs)
        {
            return lhs;
        }
        public static Complex operator-(Complex lhs)
        {
            return new Complex(-lhs.x,-lhs.y);
        }
        public static Complex operator+(Complex lhs, Complex rhs)
        {
            return new Complex(lhs.x+rhs.x,lhs.y+rhs.y);
        }
        public static Complex operator-(Complex lhs, Complex rhs)
        {
            return new Complex(lhs.x-rhs.x,lhs.y-rhs.y);
        }
        public static Complex operator*(Complex lhs, Complex rhs)
        { 
            return new Complex(lhs.x*rhs.x-lhs.y*rhs.y, lhs.x*rhs.y+lhs.y*rhs.x);
        }
        public static Complex operator/(Complex lhs, Complex rhs)
        {
            Complex result;
            double e;
            double f;
            if( System.Math.Abs(rhs.y)<System.Math.Abs(rhs.x) )
            {
                e = rhs.y/rhs.x;
                f = rhs.x+rhs.y*e;
                result.x = (lhs.x+lhs.y*e)/f;
                result.y = (lhs.y-lhs.x*e)/f;
            }
            else
            {
                e = rhs.x/rhs.y;
                f = rhs.y+rhs.x*e;
                result.x = (lhs.y+lhs.x*e)/f;
                result.y = (-lhs.x+lhs.y*e)/f;
            }
            return result;
        }
    }    
    
	/********************************************************************
	AP math namespace
	********************************************************************/
	public struct rcommstate
	{
		public int stage;
		public int[] ia;
		public bool[] ba;
		public double[] ra;
		public AP.Complex[] ca;
	};

	/********************************************************************
    AP math namespace
    ********************************************************************/
    public class Math
    {
        public static System.Random RndObject = new System.Random(System.DateTime.Now.Millisecond);

        public const double MachineEpsilon = 5E-16;
        public const double MaxRealNumber = 1E300;
        public const double MinRealNumber = 1E-300;
        
        public static double RandomReal()
        {
            double r = 0;
            lock(RndObject){ r = RndObject.NextDouble(); }
            return r;
        }
        public static int RandomInteger(int N)
        {
            int r = 0;
            lock(RndObject){ r = RndObject.Next(N); }
            return r;
        }
        public static double Sqr(double X)
        {
            return X*X;
        }        
        public static double AbsComplex(Complex z)
        {
            double w;
            double xabs;
            double yabs;
            double v;
    
            xabs = System.Math.Abs(z.x);
            yabs = System.Math.Abs(z.y);
            w = xabs>yabs ? xabs : yabs;
            v = xabs<yabs ? xabs : yabs; 
            if( v==0 )
                return w;
            else
            {
                double t = v/w;
                return w*System.Math.Sqrt(1+t*t);
            }
        }
        public static Complex Conj(Complex z)
        {
            return new Complex(z.x, -z.y); 
        }    
        public static Complex CSqr(Complex z)
        {
            return new Complex(z.x*z.x-z.y*z.y, 2*z.x*z.y); 
        }

    }
}