Avoiding overflow in integer multiplication followed by division

Question

I have two integral variables a and b and a constant s resp. d. I need to calculate the value of (a*b)>>s

Answer 1

I haven't exhaustively tested this, but could you do the division first, then account for the remainder, at the expense of extra operations? Since d is a power of two, all the divisions can be reduced to bitwise operations.

For example, always assume a > b (you want to divide the larger number first). Then a * b / d = ((a / d) * b) + (((a % d) * b) / d)