judgement on whether or not there is an overflow

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Sum is just an intermediate variable for the calculation, and the final output has the same number of bits as input. Besides, there is also an output (a flag) indicating whether there is an overflow in the final result. Then, how to make a judgement on whether or not there is an overflow, and why?

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in general if your internal bitwidth is say 20 bits and you want only 16 LSBs out then you check bit(18:15) if it is different from sign bit then you clip output to either +32767 or -32767 and raise the flag, otherwise you pass the 16 bits direct out.

if data_int(19 downto 15) = "00000" or data_int(19 downto 15) = "11111" then
    dout <= data_int(15 downto 0);
    clip <= '0';
elsif if data_int(19) = '0' then
     dout <= 32767;
     clip <= '1';
else
     dout <= -32767;
     clip <= '1';
end if;