The documentation for the cmath module is misleading on the behaviour near branch cuts. For example, the documentation for cmath.acos says:

   Return the arc cosine of x. There are two branch cuts: One
   extends right from 1 along the real axis to ∞, continuous
   from below. The other extends left from -1 along the real
   axis to -∞, continuous from above.

That "continuous from below" and "continuous from above" language is misleading; in fact what happens on the vast majority of systems (those for which the floating-point format used is IEEE 754 binary64), if the imaginary part of x is zero, the sign of x is used to determine which side of the branch cut x lies.