/* add the swapped two 16-bit halves of sum,
a possible carry from adding the two 16-bit halves,
will carry from the lower half into the upper half,
giving us the correct sum in the upper half. */
sum += (sum << 16) + (sum >> 16);
/* add the swapped two 16-bit halves of sum,
a possible carry from adding the two 16-bit halves,
will carry from the lower half into the upper half,
giving us the correct sum in the upper half. */
sum += (sum << 16) + (sum >> 16);