:import std/Pair .
:import std/Combinator .
:import std/Number/Unary .

qadd &[[&[[p : q]]]] ⧗ Rational → Rational → Rational
	p (3 ⋅ ++0) + (1 ⋅ ++2)
	q (2 ⋅ 0) + (2 + 0)

fac [[1 [[0 (1 [[2 1 (1 0)]])]] [1] i]] ⧗ Unary → Unary

# challenge: smallest, yet fastest converging, π ratio calculation

# naive
v1-pi/2 [0 &[[op]] start [[1]]]
	start ((+0u) : (+0u)) : (+0u)
	op (qadd 1 (enum : --denom)) : ++0
		enum (0 (+2u)) ⋅ ((+2u) (fac 0))
		denom fac ++((+2u) ⋅ 0)

dfac [[1 [[0 (1 [[2 1 (1 (1 0))]])]] [1] i]] ⧗ Unary → Unary

# double factorial
# dfac and fac could be shared!
v2-pi/2 [0 &[[op]] start [[1]]]
	start ((+0u) : (+0u)) : (+0u)
	op (qadd 1 (enum : --denom)) : ++0
		enum fac 0
		denom dfac ++0