genRoot x0 root = Just (search 0 (x0+1))
  where
  search from to = let x = from + div (to - from) 2
                       a = x ^ root
                   in case compare a x0 of
                        EQ              -> (x, True)
                        LT | x /= from  -> search x to
                           | otherwise  -> (from, False)
                        GT | x /= to    -> search from x
                           | otherwise  -> (from, False)

{- | Compute the logarithm of a number in the given base, rounded down to the
closest integer.  The boolean indicates if we the result is exact
(i.e., True means no rounding happened, False means we rounded down).
The logarithm base is the second argument. -}
genRoot x0 root = Just (search 0 (x0+1))
  where
  search from to = let x = from + div (to - from) 2
                       a = x ^ root
                   in case compare a x0 of
                        EQ              -> (x, True)
                        LT | x /= from  -> search x to
                           | otherwise  -> (from, False)
                        GT | x /= to    -> search from x
                           | otherwise  -> (from, False)

{- | Compute the logarithm of a number in the given base, rounded down to the
closest integer.  The boolean indicates if we the result is exact
(i.e., True means no rounding happened, False means we rounded down).
The logarithm base is the second argument. -}
genRoot x0 root = Just (search 0 (x0+1))
  where
  search from to = let x = from + div (to - from) 2
                       a = x ^ root
                   in case compare a x0 of
                        EQ              -> (x, True)
                        LT | x /= from  -> search x to
                           | otherwise  -> (from, False)
                        GT | x /= to    -> search from x
                           | otherwise  -> (from, False)

{- | Compute the logarithm of a number in the given base, rounded down to the
closest integer.  The boolean indicates if we the result is exact
(i.e., True means no rounding happened, False means we rounded down).
The logarithm base is the second argument. -}