Is this converting from or to premultiplied alpha?

Question

I found this code buried under some rocks:

var divAlpha = 0xff00/color.A;
var r = (byte) (color.R*divAlpha >> 8);
var g = (byte) (color.G*divAlpha >> 8);
var b = (byte) (color.B*divAlpha >> 8);

The fields on color are bytes, of course. My guess would be it's avoiding using floating point operations to handle premultiplied alpha, but is it converting from or to? How does this work out?

Example output:

0x44112233 -> a: 0x44, r: 0x3f, g: 0x7f, b: 0xbf

Answer 1

This code is converting from premultiplied alpha:

Expanding one of the assignments by substituting for divAlpha:

var r = (byte) (color.R*(0xff00/color.A) >> 8);

which on rearrangement of the multiplicative terms becomes

var r = (byte) ((color.R*(0xff00) >> 8)/color.A);

which in turn simplifies to:

var r = (byte) (color.R*0xff /color.A);

or

var r = (byte) (color.R * (0xff /color.A) );

which is clearly seen to be a division by the (fractional) alpha channel value.

This can be verified by computing the reverse operation:

R: (0x3F * 0x44 + 0x80) >> 8 = 0x113C >> 8 = 0x11
G: (0x7F * 0x44 + 0x80) >> 8 = 0x223C >> 8 = 0x22
B: (0xBF * 0x44 + 0x80) >> 8 = 0x333C >> 8 = 0x33