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It's not just time zones and leap seconds. SI seconds on Earth are slower because of relativity, so there are time standards for space stuff (TCB, TGC) that use faster SI seconds than UTC/Unix time. T2 - T1 = [God doesn't know and the Devil isn't telling.]
If your system hasn’t been upgraded to 64-bit types by 2038, you’d deserve your overflow bug
Let's just nake it 128-Bit so it's not our problem anymore.
Hell, let's make it 256-Bit because it sounds like AES256
64 bits is already enough not to overflow for 292 billion years. That’s 21 times longer than the estimated age of the universe.
With a 128 bit integer you can represent 340 undecillion (or sextillion if you use the long scale notation) seconds, which is equivalent to 10 nonillion (or quintillion, long scale) years. The universe will long have have stopped being able to support life by then because stars stopped forming (enough time would have passed it could have happened a hundred quadrillion (a hundred thousand billion, long form) times over assuming we start counting from the birth of the universe).