Software - Math - Fast Mod

There is a technique for quickly calculating mod which makes use of the fact that, for example:

(256 * HI + LO) mod 255 = (255 * HI + HI + LO) mod 255

The first term (on the right side) can be discarded since it is a multiple of 255, leaving:

(HI + LO) mod 255

The modulus 255 yields a very short and fast implementation:

CLC
LDA LO
ADC HI
ADC #1
SBC #0

The HI+LO sum is a 9 bit number from $000 to $1FE inclusive (accumulator and carry), so the ADC #1 performs a second HI+LO calculation. By also adding 1, it leaves the carry set if the second HI+LO = 255. When the carry is clear, the addition of 1 must be undone, and the SBC #0 does just that, leaving a result from $00 to $FE inclusive.