すごい乱暴な方法で小数を割かし正確な有理数にする

ExactNum.hs

--
-- Problem
-- > toRational 1.1 -- 2476979795053773 % 2251799813685248 I want `11 % 10`
-- > fromRational $ toRational 1.1 -- 1.1
-- > (toRational 1.1) == (11 % 10) -- False
--
import Numeric ( floatToDigit, fromRat )
import Data.Ratio ( (%), denominator )

-- | exact ratio number from Real `a`
-- example
-- > exact 1.1 -- 11 % 10
-- > (exact 1.1) == (11 % 10) -- True
-- > fromRational $ exact 1.1 -- 1.1
exactFromReal :: Real a => a -> Rational
exactFromReal x
  | asInt      = ratio
  | otherwise  = numer % denom
  where
  asInt  = denominator ratio == 1
  ratio  = toRational x
  numer  = round $ ratio * (denom % 1)
  denom  = 10 ^ (uN - iN)
  iN     = snd digits
  uN     = length $ fst digits
  digits = floatToDigits 10 $ fromRat ratio