Very cool, I'll definitely be playing around with this some more! Two questions:

- How difficult would it be to add many-valued functions to this? It would be really nice to be able to get the full set of [pi/2, pi/2] + n[2pi, 2pi] from asin(1) without needing to break out Mathematica.

- And:

> Numbers input by the user are interpreted as the smallest interval that contains the IEEE 754 value closest to the input decimal representation but where neither bounds are equal to it

Am I missing something obvious, or should this be the other way round, i.e. the output bounds are the closest two IEEE 754 numbers that contain the input number?

The way it's written I'd interpret the smallest interval to be IEEE754(input)+[-epsilon, epsilon] for infinitesimally small epsilon.