HCL color to RGB and backward

Question

I need an algorithm to convert the HCL color to RGB and backward RGB to HCL keeping in mind that these color spaces have different gamuts (I need to constrain the HCL colors

Answer 1

I think

if (rg <  0) {
    if (gb >= 0) H = 90 + H;
    else { H = H - 90; }
} //works

is not really necessary because of atan2(,) instead of atan(/) from paper (but dont now anything about java atan2(,) especially