some simple recursive function

Recursive.hs

module Recursive where

g :: Int -> Int -> Int
g 0 _ = 0
g m n = g (m - 1) (2 * n) + n

f :: Int -> Int
f 0 = 1
f n = n * f (div n 2)

-- tail recursive
f' :: Int -> Int
f' n = fi n 1
  where
    fi i acc =
        case i of
          0 -> acc
          i1 -> fi (div i1 2) (i1 * acc)


testF :: Bool
testF = and $ map test [0..1000]
  where test n = f' n == f' n

-- tail recursive
mySqrt :: (Fractional a, Ord a) => a -> a -> a -> a
mySqrt x guess e =
    if goodEnough
       then guess
       else mySqrt x nextGuess e
  where
    goodEnough = abs (guess ^ (2::Int) - x) < e
    nextGuess = (1/2*(guess + x / guess))

akm 0 n = n + 1
akm m 0 = akm (m - 1) 1
akm m n = akm (m - 1) (akm m (n - 1))