This routine will take an 8 bit integer that corresponds to the numerator of a fraction whose denominator is 256 and find its arctangent. So the input ranges from 0 to 255 which corresponds to 0 to 255/256 = 0.996 . The output for an arctangent routine that returns a floating point number would be from 0 (atan(0)) to 0.783 (atan(255/256)) radians; or if you prefer, 0 to 44.89 degrees. However, this routine scales the output so that pi/4 radians (or 45 degrees) corresponds to 256. So for the input range of 0 to 255 you get an output of 0 to 255 ( atan(255/256) * 256 / (pi/4) is about 255). It's probably a little more interesting to see an intermediate data point or two:
The On-Line Encyclopedia of Integer Sequences (OEIS), also cited simply as Sloane's, is an extensive searchable database of integer sequences, freely available on the Web.
B. Rosenhahn. European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML-PKDD), Seite 1-17. (September 2022)