[Haskell-cafe] Correct parsers for bounded integral values

[Brandon Allbery]

Mostly. One difference is that over/underflow is signaled in `CF` (carry
bit), and that's used to extend arithmetic: to add a pair of 128-bit
numbers you `ADD` the lower 64 bits, advance to the higher 64 bits, and
`ADC` those (the "C" means it uses the carry bit). And `CF` might again be
set afterward indicating that it overflowed 128 bits. (This is also why
Intel architecture orders bytes/words the way it does.) That it otherwise
behaves as modular is in support of this, not in support of a mathematical
law, and the behavior might differ on other architectures (e.g. PPC, or if
someone somewhere still has a processor using 1s- complement). Which is the
most important point: the Report specifies `Integral` types other than
`Integer` to behave like the machine type, and you're basically assuming
x86-64 (_probably_ also AArch64 but i haven't studied that one, just
assuming it's 2s-complement) if you assume either modular arithmetic or any
other behavior. The only promise you get is "matches the underlying
hardware".

On Sun, Jul 20, 2025 at 8:25 PM Jeff Clites via Haskell-Cafe <
haskell-cafe at haskell.org> wrote:

>
> > On Jul 20, 2025, at 9:43 AM, Brandon Allbery <allbery.b at gmail.com>
> wrote:
> >
> > I would like to point out that if you want correctness, you should use
> `Integer`. If you are using a bounded `Integral` it is expected that you
> are doing so because you value speed over correctness. They are _not_
> `Z/n`, they are hardware values that have little to do with formal
> mathematics.
>
> But aren't they de-facto modular integers?
>
> Jeff
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-- 
brandon s allbery kf8nh
allbery.b at gmail.com
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