Just a quick addition here regarding the singularities to these
functions.  The atanh(x) is only defined for |x| < 1, so atanh(1) or
atanh(-1) isn't singular there so much as simply isn't defined.  So,
even though the function approaches infinite as x -> 1, it wouldn't
really be correct to return a value at |x| = 1.  I think raising an
exception at those points would be more correct.