Create method which checks if x + y will overflow using bitwise operations

Question

I need to create a method in C using bitwise operations which checks if x + y will overflow or not. I can only use a maximum of 20 of the following operations; ! ~ & ^ | + << >> Keep in mind I have to test for both negative and positive numbers.

I've tried several times to make it work. Is my logic sound? I'm going by: if (x + y) is less than x, then it has overflowed. Based on that logic, I wrote this;

int addOK(int x, int y)
{
  int sum = x + y;
  int nx = ((~x) + 1);
  int check = (sum + nx)>>31;
  return !check;
}

Thank you!

Answer 1

This should work, but it doesn't use only bitwise operator, but it work for signed :

int addOK(int x, int y)
{
  int check;
  if (greaterThan(0, x^y)) 
    check = 0; 
  else if (greaterThan(x, 0)) 
    check = greaterThan(y, INT_MAX -x);
  else 
    check = greaterThan(INT_MIN -x, y);

  return check;
}

int greaterThan(int first, int second) {
   /* first > second means second - first is less than 0
      shift the sign bit and then compare it to 1 */
   return (second + (~first +1)) >> ((sizeof(int) * 8) -1) & 1;
}

If the two numbers are both positive should be enough :

int addOK(int x, int y) {
 if(x^y < 0)
   return 0;

 return 1;
}