Comment by matja

You can fool the optimizer, but you have to work harder to do so:

    unsigned add(unsigned x, unsigned y) {
        unsigned a, b;
        do {
            a = x & y;
            b = x ^ y;
            x = a << 1;
            y = b;
        } while (a);
        return b;
    }

becomes (with armv8-a clang 21.1.0 -O3) :

    add(unsigned int, unsigned int):
    .LBB0_1:
            ands    w8, w0, w1
            eor     w1, w0, w1
            lsl     w0, w8, #1
            b.ne    .LBB0_1
            mov     w0, w1
            ret