asksign(asin(x)) asks whether x is p/n/z. But it doesn't ask whether abs(x)<=1.
So apparently it is assuming that the result is real.
This is fine if we assume that asksign works like sign and assumes everything (arguments and values) are real, but that isn't documented.
I do not suggest that it ask whether abs(x)<1. I suggest that its current behavior be documented clearly.