import Data.Ratio

-- ignoring the task-given pi sequence: sucky convergence
-- pie = zip (3:repeat 6) (map (^2) [1,3..])

pie    = zip (0:[1,3..]) (4:map (^2) [1..])
sqrt2  = zip (1:repeat 2) (repeat 1)
napier = zip (2:[1..]) (1:[1..])

-- truncate after n terms
cf2rat n = foldr (\(a,b) f -> (a%1) + ((b%1) / f)) (1%1) . take n

-- truncate after error is at most 1/p
cf2rat_p p s = f $ map (\i -> (cf2rat i s, cf2rat (1+i) s)) $ map (2^) [0..]
	where f ((x,y):ys) = if abs (x-y) < (1/fromIntegral p) then x else f ys

-- returns a decimal string of n digits after the dot; all digits should
-- be correct (doesn't mean it's the best approximation! the decimal
-- string is simply truncated to given digits: pi=3.141 instead of 3.142)
cf2dec n = (ratstr n) . cf2rat_p (10^n) where
	ratstr l a = (show t) ++ '.':fracstr l n d where
		d = denominator a
		(t, n) = quotRem (numerator a) d
		fracstr 0 _ _ = []
		fracstr l n d = (show t)++ fracstr (l-1) n1 d where (t,n1) = quotRem (10 * n) d

main = do
	putStrLn $ cf2dec 200 sqrt2
	putStrLn $ cf2dec 200 napier
	putStrLn $ cf2dec 200 pie