Bitwise overflow checking in c

Question

I am trying to write two functions that will check/prevent overflow in c (using only ! ~ | & ^ +) but cant get it. The first is will a certain twos compliment/signed int will fit in a certatin amount of bits: fitsB(int x, int n) where is the int and n is the size of bits to use. Also a function that will check to see if two ints will not overflow when added together: overflowInt(int x, int y). I can get it if they are unsigned ints but the negatives just make things harder for me. Anyone know how to?

There also is no casting and ints are always 32 bit

Answer 1

/* 
 * addOK - Determine if can compute x+y without overflow
 *   Example: addOK(0x80000000,0x80000000) = 0,
 *            addOK(0x80000000,0x70000000) = 1, 
 *   Legal ops: ! ~ & ^ | + << >>
 *   Max ops: 20
 *   Rating: 3
 */
 int addOK(int x, int y) {
  // Find the sign bit in each word
  //if a and b have different signs, you cannot get overflow.
  //if they are the same, check that a is different from c and b is different from c, 
  // if they are the same, then there was no overflow.
  int z=x+y;
  int a=x>>31;
  int b=y>>31;
  int c=z>>31;
  return !!(a^b)|(!(a^c)&!(b^c));
}