# ideas by u/DaVinci103
# MIT License, Copyright (c) 2024 Marvin Borner

:import std/Combinator .
:import std/Pair .
:import std/Math/Real R

ι (+0.0r) : (+1.0r)

# adds two complex numbers
add &[[&[[(R.add 3 1) : (R.add 2 0)]]]] ⧗ Complex → Complex → Complex

# subtracts two complex numbers
sub &[[&[[(R.sub 3 1) : (R.sub 2 0)]]]] ⧗ Complex → Complex → Complex

# multiplies two complex numbers
mul &[[&[[p : q]]]] ⧗ Complex → Complex → Complex
	p R.sub (R.mul 3 1) (R.mul 2 0)
	q R.add (R.mul 3 0) (R.mul 2 1)

# divides two complex numbers
div &[[&[[p : q]]]] ⧗ Complex → Complex → Complex
	p R.div (R.add (R.mul 3 1) (R.mul 2 0)) (R.add (R.mul 1 1) (R.mul 0 0))
	q R.div (R.sub (R.mul 2 1) (R.mul 1 0)) (R.add (R.mul 1 1) (R.mul 0 0))

# negates a complex number
negate &[[(R.negate 1) : (R.negate 0)]] ⧗ Complex → Complex

# inverts a complex number
invert &[[p : q]]
	p R.div 1 (R.add (R.mul 1 1) (R.mul 0 0))
	q R.div 0 (R.add (R.mul 1 1) (R.mul 0 0))