I agree with adding '(absolute value)'. I think the following covers the NaN behavior. "NaN acts as a positive value that cannot be negated." This should be added to both doc and docstring.

I do not think we generally specify the nan behavior for each function, but it usually follows general rules. The copysign(x,nan) behavior is not obvious as nan, like int 0, does not really have a sign. One might expect copysign(-1.0,nan) to be -1.