[Asooka]

>Hardware addition is filled with edge cases that cause it to not work as expected

I am not aware of a single case where integer addition does not work as expected at the hardware level. Of course if you have a different expectation than what the hardware does it could be called "unexpected", but I would classify this more as "ignorance". I think we can reword it as "addition must be predictable and consistent".

This is not the case in standard C, because addition can produce a weird value that the compiler assumes obeys a set of axioms but in fact doesn't, due to hardware semantics. Most C compilers allow you to opt into hardware semantics for integer arithmetic, at which point you can safely use the result of addition of any two integer values. That is really the crux of the matter here - if I write "a = b + c", can I safely examine the value "a"? In C, you cannot. You must fist make sure that b and c fulfil the criteria for safe use with the "+" operator. Or, as is more usual, close your eyes and hope they do. Or just turn on hardware semantics and only turn them off for specific very hot regions of the code where you can actually prove that the input values obey the required criteria.