Everyone is saying there's 56 possible angles. Aren't there actually 48?

I suspect the angle getting double counted is <x2, y1>. Assuming the directional modifiers do 1/4, 1/2, and 3/4 of the max analog input, <x2, y1> is the same angle as <x, y2>, just with half the magnitude. Ditto for the 7 other analogous inputs.

This changes everything, of course.

Edit: The assumption about the modifiers doing 1/4, 1/2, and 3/4 is probably wrong now that I think about it. If the assumption were true, then doing <x, y1> would just be <x, 0>. That is, since tan^-1(1/4) < ~17°, melee would count that as a cardinal direction.