(Data.Fixed.mod' n d) not less than d

If one encounters the expression mod' n d, one might reasonably assume that the result of the expression is less than d. However, this is not true:

$ ghci
>>=mod' 3.154831645792668e16 (2 * pi)
8.0

The definition of mod' reveals the problem (when a is an IEEE float):

mod' :: (Real a) => a -> a -> a
mod' n d = n - (fromInteger f) * d where
    f = div' n d

Substituting:

mod' 3.154831645792668e16 (2 * pi)
->
3.154831645792668e16 - (fromIntegral 5021070510506425) * (2 * pi)
->
3.154831645792668e16 - 3.1548316457926672e16
->
8.0

We can repair mod' if we're willing to add a Fractional constraint:

mod' :: (Fractional a, Real a) => a -> a -> a
mod' n d =
    let dr = toRational d
        nr = toRational n
        qt = toRational $ floor (nr / dr)
    in fromRational (nr - (qt * dr))

>>= mod' 3.154831645792668e16 (2 * pi)
6.177334810858532

The advantage of a definition like this is that it yields a correct result. The disadvantages are worse performance and the additional Fractional constraint. Perhaps it would be easier to define div'', mod'', and divMod'' or similar?