bit manipulation - Saturating signed integer addition with only bitwise operators in C (HW) -

for homework assignment, have write function in c adds 2 signed integers, returns int_max if there positive overflow , int_min if there negative overflow. have follow strict restrictions in operators can use. integers in two's complement form, right shifts arithmetic, , integer size variable (i can find sizeof(int)<<3). can't use contitionals, loops, comparison operators, or casting. can use bitwise , logical operators, addition , subtraction, equality tests, , integer constants int_max , int_min.

i know overflow can detected if 2 inputs have same sign , result has different sign. i've gotten point have flag showing if equation did overflow. have no idea how there end product. have far:

int saturating_add(int x, int y){     int w = sizeof(int)<<3;     int result = x+y;     int signx = (x>>w-1)&0x01;//sign bit of x     int signy = (y>>w-1)&0x01;//sign bit of y     int resultsign = (result>>w-1)&0x01; //sign bit of result     int canoverflow = ~(signx ^ signy); //if they're same sign, can overflow     int didoverflow = (resultsign^signx)&canoverflow; //1 if input signs same , result sign different, 0 otherwise  } 

i'm trying follow answer shown @ bitwise saturated addition in c (hw), i'm stuck on part have fill integer same bit sign bit (1 goes 0111..11 , 0 goes 0000.00). have no idea "combination of shifts , ors" be.

i think misunderstood answer. should extend sign bit all of bits, including msb. can accomplished taking int holding sign bit, e.g. didoverflow, , add 1 complement.

then find overflow value should returned in case there overflow. can done xoring int_max extended signx (or signy, both work). let's call value overflow. finally, alter overflow , result this:

overflow := (extended didoverflow) , overflow result := (not (extended didoverflow)) , result 

now, after these assignments, if extended didoverflow 1...1, overflow remain unchanged. result, on other hand, equal 0.

but if didoverflow 0...0, opposite applies: overflow 0, while result remains unchanged.

in first case (where didoverflow 1...1, signaling there overflow), overflow or result equals overflow. in second case (where have no overflow), overflow or result equals result. either way, overflow or result give correct value.