How would you check signed overflow after adding two 32-bit integers in x86-64?

ADD updates arithmetic flags. For signed 32-bit addition, JO branches when the overflow flag is set, meaning the mathematical result is outside the representable signed 32-bit range. Carry indicates a different condition relevant to unsigned arithmetic, so JC is not a substitute. Check the flag before another flag-changing instruction overwrites it. The destination still contains the wrapped low 32 bits, and writing EAX clears the upper half of RAX. Decide what the surrounding function should retu or report on overflow.