[Haskell-cafe] Effective function representation.

Hello! I need to deal with functions of type (Double -> Double). I need Fourier transform, integration, + - * / operations, value of a function in a point, probably composition. However it is not very effective to use straightforwardly this type. Since functions in question are rather smooth (if not analytical), the best option would be to use some kind of pointwise representation (e.g. lists, arrays). But in this case the code wouldn't be so easy to understand and implement, compact and so on. Is there some libraries which allow me to work with functions as if their type was (Double -> Double), but indeed it was something faster?