There are times when you want to know how much overflow occurred -- think of the way you learn to do multi-digit addition. There is a checked_add that returns an Option<T> if you only care about success/failure.
> If A happened to be larger than C, and therefore the result of the subtraction underflowed, then we can correct for this by adding p to the result. [...] we can multiply B by 2^32 using a binary shift and a subtraction, and then add it to the result. We might encounter an overflow, but we can correct for that by subtracting p.
(Highlighting the parts that relate to reacting to overflow.)
https://cp4space.hatsya.com/2021/09/01/an-efficient-prime-fo...
> If A happened to be larger than C, and therefore the result of the subtraction underflowed, then we can correct for this by adding p to the result. [...] we can multiply B by 2^32 using a binary shift and a subtraction, and then add it to the result. We might encounter an overflow, but we can correct for that by subtracting p.
(Highlighting the parts that relate to reacting to overflow.)