A simple reform for treating the loss of accuracy of Humlicek's W4 algorithm near the real axis

We present a simple reform for treating the reported problem of loss-of-accuracy near the real axis of Humlicek’s w4 algorithm, widely used for the calculation of the Faddeyeva or complex probability function. The reformed routine maintains the claimed accuracy of the algorithm over a wide and fine grid that covers all the domain of the real part, x, of the complex input variable, z=x+iy, and values for the imaginary part in the range y=[10-30, 10+30]