Problems with "normal" blending of two images with alpha

Answer 1

If t_a is not a floating point value, then calculations such as (255 - t_a) / 255 are done as integers too. You need to cast one of your inputs to a float beforehand, e.g ((255 - t_a) / 255f).

Answer 2

You need to change a lot of this.

t_r, t_a etc must all be floats from 0 to 1. Do all your calculations in floating point, then multiply by 255 and then cast to int.