Before revision:  We show that the present code compares favorably with Mathematica's function, point to further improvements, and discuss the issue of singularities.
After revision:  We show that the present code compares favorably with Mathematica's HeunG and with an Octave/Matlab code of Motygin, in particular when the Heun function is to be evaluated at a large number of points if less accuracy is sufficient. We suggest further improvements concerning the accuracy and discuss the issue of singularities.