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: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
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