Fibonacci in logarithmic time

fib.hs

fib :: Int -> Integer
fib n = 
    let fibTriplet k
          | k <= 0 = (0, 0, 1)
          | k == 1 = (0, 1, 1)
          | even k = let (a, b, c) = fibTriplet (k `div` 2)
                      in (a^2 + b^2, b * (a + c), b^2 + c^2)
          | odd  k = let (a, b, c) = fibTriplet (k - 1)
                      in (b, c, b + c)
        snd3 (_, y, _) = y 
     in snd3 $ fibTriplet n