module Approx where

approxGolden :: Int -> Double
approxGolden n = approx n 1 1
  where
    approx 0 p q = q / p
    approx n p q = approx (n - 1) q (p + q)

golden :: Double
golden = approxGolden 64

approxEuler :: Int -> Double
approxEuler n = approx 0 1 0 where
  approx m a r = if m == n
    then r
    else approx (m + 1) a' r'
    where
      a' = (fromInteger . toInteger) (m + 1) * a
      r' = r + (1 / a)

euler :: Double
euler = approxEuler 64