Christian Heimes added the comment:

I've added your complex patch and its tests to my patch. The tests are
showing some flaws in the atanh (or log1p) function on Windows:

AssertionError: atanh0022:atanh(-1.000000) returned -18.36840028483855,
expected -18.714973875118524

On Linux the tests are passing just fine.

Added file: 
http://bugs.python.org/file9250/trunk_pymath_hyberbolic_complex.patch

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