[sf.cmath.general]

If any argument value to any of the functions specified in [sf.cmath] is a NaN (Not a Number), the function shall return a NaN but it shall not report a domain error.

Otherwise, the function shall report a domain error for just those argument values for which:

(1.1)
the function description's Returns: element explicitly specifies a domain and those argument values fall outside the specified domain, or
(1.2)
the corresponding mathematical function value has a nonzero imaginary component, or
(1.3)
the corresponding mathematical function is not mathematically defined.245

Unless otherwise specified, each function is defined for all finite values, for negative infinity, and for positive infinity.

245)245)

A mathematical function is mathematically defined for a given set of argument values (a) if it is explicitly defined for that set of argument values, or (b) if its limiting value exists and does not depend on the direction of approach.