[bonzini]

That's just because the power series would take ages to converge for large arguments, so you take advantage of periodicity. But the implementation in a floating point world is a different thing than the definition in an infinite series world.

For example, e^x can be implemented by handling the integer and fractional parts separately, for similar reasons. But no one really cares about the functions e^floor(y) and e^(y-floor(y)). They are only useful as part of an implementation trick.

[wnoise]

That's really not the only thing going on. Yes, it allows you to take advantage of periodicity. But many common function approximations work best (i.e. not requiring any transform of the argument) over the interval [-1, 1].