x = x >> 1;

x = x / 2;

-5 / 2  = -2
-5 >> 1 = -3

x = x / 2 + 5;
x = x >> 1 + 5;  // not the same as above

int div2signed(int a) {
  return a / 2;
}

movl    %edi, %eax
    shrl    $31, %eax
    addl    %edi, %eax
    sarl    %eax
    ret

int shr2signed(int a) {
  return a >> 1;
}

sarl    %edi
    movl    %edi, %eax
    ret

q = i >> n; is the same as: q = i / 2**n;