ka2m.hs

module Main where

derivation :: (Fractional a) => (a -> a) -> a -> a
derivation f = \ x -> ( f (x + dx) - f x ) / dx where dx = 0.1

evalA ::  (Fractional a) => Int -> (a -> a) -> a -> a
evalA 0 _ = id
evalA k f = \x -> derivation (evalA (k-1) f) x / derivation f x

evalA2 :: (Fractional a) => Int -> (a -> a) -> a -> a
evalA2 k f = iterate (\prev x -> derivation prev x / derivation f x) id !! k

inverseFun :: (Ord a, Fractional a) => (a -> a) -> a -> a
inverseFun f x = iter 0 1.0 0.0
    where
        x0 = 3.0
        eps = 0.001
        iter k prev sum' =
            let elemB = prev * (x - f x0) / fromIntegral (if k == 0 then 1 :: Int else k)
                newItem = evalA k f x0 * elemB
            in  if abs newItem < eps
                    then sum'
                    else iter (k + 1) elemB (sum' + newItem)

inverseFun2 :: (Ord a, Fractional a) => (a -> a) -> a -> a
inverseFun2 f x = iter 0 1.0 0.0
    where
        x0 = 3.0
        eps = 0.001
        iter k prev sum' =
            let elemB = prev * (x - f x0) / fromIntegral (if k == 0 then 1 :: Int else k)
                newItem = evalA2 k f x0 * elemB
            in  if abs newItem < eps
                    then sum'
                    else iter (k + 1) elemB (sum' + newItem)


f1 :: Fractional a => a -> a
f1 x = 1.0 * x * x

main :: IO ()
main = print (inverseFun f1 2.5 :: Double)