Is it possible to do interval arithmetic, simulate passing intervals as function arguments, like in Giac?

[Neven Sajko <nsajko@gmail.com>]

Hello,

In Giac if I do this, the result is pretty much the same as in Pari:
sin(i[0.01, 0.02])
But, consider this Giac command:
sin(i[0.01, 2 * Pi + 0.02])
The result is the entire interval [-1 .. +1].

Is there a way to do something like this (for any analytic function,
not just sin)?

BTW., I'm not actually satisfied with Giac, among other reasons
because this feature does not work for my user defined function, which
is a power series. Giac also seems to be quite buggy in general.

Thanks,
Neven