calculates an approximate value for the integral
where x ≥ 0 and y ≠ 0.
This function, which is related to the logarithm or inverse hyperbolic functions for y < x and to inverse circular functions if x < y, arises as a degenerate form of the elliptic integral of the first kind. If y < 0, the result computed is the Cauchy principal value of the integral.
For more information please review the s21bac function in the NAG document