module math_tests @test;
import math_tests::complex;

def ComplexDouble = ComplexType{double} @local;
def ComplexInt = ComplexType{int} @local;

module math_tests::complex{ElementType} @test;
import std::math;

def ComplexType = Complex{ElementType};

fn void complex_mul_imaginary()
{
	ComplexType i = complex::IMAGINARY{ElementType};
	assert(i.mul(i).equals((ComplexType){-1, 0}));
	assert(i.mul(i).mul(i).equals((ComplexType){0, -1}));
}

fn void complex_add()
{
	ComplexType a = {3, 4};
	ComplexType b = {1, 2};
	assert(a.add(b).equals((ComplexType){4, 6}));
	assert(a.add_each(1).equals((ComplexType){4, 5}));
}

fn void complex_sub()
{
	ComplexType a = {3, 4};
	ComplexType b = {1, 2};
	assert(a.sub(b).equals((ComplexType){2, 2}));
	assert(a.sub_each(1).equals((ComplexType){2, 3}));
}

fn void complex_scale()
{
	ComplexType a = {2, 1};
	assert(a.scale(2).equals((ComplexType){4, 2}));
}

fn void complex_conjugate()
{
	ComplexType a = {3, 4};
	assert(a.conjugate().equals((ComplexType){3, -4}));
}

fn void complex_inverse() @if(types::is_float(ElementType))
{
	ComplexType a = {3, 4};
	assert(a.inverse().mul(a).equals(complex::IDENTITY{ElementType}));
}

fn void complex_div() @if(types::is_float(ElementType))
{
	ComplexType a = {2, 5};
	ComplexType b = {4, -1};
	assert(a.div(b).equals((ComplexType){3.0/17.0, 22.0/17.0}));
}