Since the wrapped remainder is going to be 0 for all cases when the rhs is -1,
there is no need to divide in this case. Comparing the lhs with MIN is only done
for the overflow bool. In particular, this results in better code generation for
wrapping remainder, which discards the overflow bool completely.
Mark unsafe methods NonZero*::unchecked_(add|mul) as const.
Now that https://github.com/rust-lang/rfcs/pull/3016 has landed, these two unstable `std` function can be marked `const`, according to this detail of #84186.
For `self == Self::MIN && rhs == -1`, LLVM does not realize that this is the
same check made by `self / rhs`, so the code generated may have some unnecessary
duplication. For `(self == Self::MIN) & (rhs == -1)`, LLVM realizes it is the
same check.
These functions are unstable, but because they're inherent they still
introduce conflicts with stable trait functions in crates. Temporarily
rename them to fix these conflicts, until we can resolve those conflicts
in a better way.
Add carrying_add, borrowing_sub, widening_mul, carrying_mul methods to integers
This comes in part from my own attempts to make (crude) big integer implementations, and also due to the stalled discussion in [RFC 2417](https://github.com/rust-lang/rfcs/pull/2417). My understanding is that changes like these are best offered directly as code and then an RFC can be opened if there needs to be more discussion before stabilisation. Since all of these methods are unstable from the start, I figured I might as well offer them now.
I tried looking into intrinsics, messed around with a few different implementations, and ultimately concluded that these are "good enough" implementations for now to at least put up some code and maybe start bikeshedding on a proper API for these.
For the `carrying_add` and `borrowing_sub`, I tried looking into potential architecture-specific code and realised that even using the LLVM intrinsics for `addcarry` and `subborrow` on x86 specifically, I was getting exactly the same assembly as the naive implementation using `overflowing_add` and `overflowing_sub`, although the LLVM IR did differ because of the architecture-specific code. Longer-term I think that they would be best suited to specific intrinsics as that would make optimisations easier (instructions like add-carry tend to use implicit flags, and thus can only be optimised if they're done one-after-another, and thus it would make the most sense to have compact intrinsics that can be merged together easily).
For `widening_mul` and `carrying_mul`, for now at least, I simply cast to the larger type and perform arithmetic that way, since we currently have no intrinsic that would work better for 128-bit integers. In the future, I also think that some form of intrinsic would work best to cover that case, but for now at least, I think that they're "good enough" for now.
The main reasoning for offering these directly to the standard library even though they're relatively niche optimisations is to help ensure that the code generated for them is optimal. Plus, these operations alone aren't enough to create big integer implementations, although they could help simplify the code required to do so and make it a bit more accessible for the average implementor.
That said, I 100% understand if any or all of these methods are not desired simply because of how niche they are. Up to you. 🤷🏻
Add Saturating type (based on Wrapping type)
Tracking #87920
### Unresolved Questions
<!--
Include any open questions that need to be answered before the feature can be
stabilised.
-->
- [x] ~`impl Div for Saturating<T>` falls back on inner integer division - which seems alright?~
- [x] add `saturating_div`? (to respect division by `-1`)
- [x] There is no `::saturating_shl` and `::saturating_shr`. (How to) implement `Shl`, `ShlAssign`, `Shr` and `ShrAssign`?
- [naively](3f7d2ce28f8cf4dec56bf65fa2e6da0cf329ec55)
- [x] ~`saturating_neg` is only implemented on [signed integer types](https://doc.rust-lang.org/std/?search=saturating_n)~
- [x] Is the implementation copied over from the `Wrapping`-type correct for `Saturating`?
- [x] `Saturating::rotate_left`
- [x] `Saturating::rotate_right`
- [x] `Not`
- [x] `BitXorOr` and `BitXorOrAssign`
- [x] `BitOr` and `BitOrAssign`
- [x] `BitAnd` and `BitAndAssign`
- [x] `Saturating::swap_bytes`
- [x] `Saturating::reverse_bits`
Make wrapping_neg() use wrapping_sub(), #[inline(always)]
This is a follow-up change to the fix for #75598. It simplifies the implementation of wrapping_neg() for all integer types by just calling 0.wrapping_sub(self) and always inlines it. This leads to much less assembly code being emitted for opt-level≤1 and thus much better performance for debug-compiled code.
Background is [this discussion on the internals forum](https://internals.rust-lang.org/t/why-does-rust-generate-10x-as-much-unoptimized-assembly-as-gcc/14930).
Document math behind MIN/MAX consts on integers
Currently the documentation for `[integer]::{MIN, MAX}` doesn't explain where the constants come from. This documents how the values of those constants are related to powers of 2.
