shoki

    fibonacci = fib 1 0 0 1
      where
        fib a b p q n
          | n == 0 = b
          | even n = fib a b p' q' (n `div` 2)
          | otherwise = fib a' b' p q (n - 1)
            where
              p' = p*p + q*q
              q' = 2*p*q + q*q
              a' = a*q + b*q + a*p
              b' = b*p + a*q