module std::math::complex<Real>;

union Complex
{
	struct
    {
    	Real r, c;
    }
	Real[<2>] v;
}


macro Complex identity() = { 1, 0 };
macro Complex Complex.add(Complex a, Complex b) = Complex { .v = a.v + b.v };
macro Complex Complex.add_each(Complex a, Real b) = Complex { .v = a.v + b };
macro Complex Complex.sub(Complex a, Complex b) = Complex { .v = a.v - b.v };
macro Complex Complex.sub_each(Complex a, Real b) = Complex { .v = a.v - b };
macro Complex Complex.scale(Complex a, Real s) = Complex { .v = a.v * s };
macro Complex Complex.mul(Complex a, Complex b)
{
	return { .r = a.r * b.r - a.c * b.c, .c = a.r * b.c + b.r * a.c };
}
macro Complex Complex.div(Complex a, Complex b)
{
	Real div = b.r * b.r + b.c * b.c;
	return Complex { .r = (a.r * b.r + a.c * b.c) / div, .c = (a.c * b.r - a.r * b.c) / div };
}