Saturated signed addition

So this a exercise from the book COMPUTERS SYSTEMS A PROGRAMMERS PERSPECTIVE
I need to add two signed numbers and in case it overflows or underflows return TMAX (011..1b) or TMIN (100..0b) respectively. In this case we can assumed two's complement representation.

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The book imposes a set of rules that the solution must follow :
Forbidden:

1. Conditionals, loops, function calls and macros.
2. Division, modulus and multiplication.
3. Relative comparison operators (<, >, <= and >=).

Allowed operations:

1. All bit level and logic operations.
2. Left and right shifts, but only with shift amounts between 0 and w - 1
3. Addition and subtraction.
4. Equality (==) and inequality (!=) tests.
5. Casting between int and unsigned.

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My code

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int saturating_add(int x, int y) { int sum = (unsigned int)x + y; int w = (sizeof(int) << 3) - 1; int mask = (~(x ^ y) & (x ^ sum)) >> w; int max_min = (1 << w) ^ (sum >> w); return (~mask & sum) + (mask & max_min); }