> The integers mod 2*64 are a ring even though not a field, if that helps. Oh, ugh: I actually usually say "modular ring", but I'm not even sure that's a techn

> The integers mod 2*64 are a ring even though not a field, if that helps. Oh, ugh: I actually usually say "modular ring", but I'm not even sure that's a technical term, so for this comment I tried to get all fancy (as I thought I remembered that all rings are fields but not all fields are rings) and failed :(. > We do in fact normally use integer datatypes to represent integers rather than elements of a cyclic group. I assume our core disagreement comes because I believe that fundamentally everything representable on a Von Neumann computer is cyclic due to how memory works. I continue to 100% appreciate that this is an incredibly controversial opinion and that very few people are going to agree with me on this. > If your program experiences uint64 overflow it's likely to be a genuine error condition unless the program is doing bit twiddling rather than arithmetic. In the case where it is an error condition, of course I'd want to trap it. However, here I want to claim you are just wrong: you simply shouldn't be using that type for this... you should be using a big integer type; and the core solution here should NOT be to make overflow of this type trap, but to figure out why you are using this type in the first place and fix the language until you stop. > In (say) Python, the int type is bigint, sometimes informally called "infinite precision" though their size is actually bounded by the size of the computer's memory. If your integers get too big, your program runs out of memory and weird things can happen, such as crashing, the OOM killer clobbering the process, or whatever. This is fundamentally different, though: this isn't your program being wrong, but the system executing your program being wrong. Your program should strive to be correct, and insisting that "no one is ever going to need more than X-bits worth of Y" as an assertion in your program--as opposed to it merely being a limitation of the machine running your program--is a mistake.