Color depth reduction without floating point math

gistfile1.txt

The bit reduction formulas converts the colors to give a minimal error after converting back to 8 bit. The sum of the signed errors is 0 and the sum of absolute diffs are as small as possible.

The formulas that convert back to 8 bit are done using bit shifting which introduces a rounding error for some color values. However bit shifting creates nice symmetric patterns and seems to be how hardware does it.

8 bit -> 4 bit -> 8 bit
c4 = (c8 + 8) / 17
c8 = c4 << 4 | c4

8 bit -> 5 bit -> 8 bit
c5 = (31 * c8 + 127) / 255
c8 = c5 << 3 | c5 >> 2

8 bit -> 6 bit -> 8 bit
c6 = (63 * c8 + 127) / 255
c8 = c6 << 2 | c6 >> 4;