Add Integer::log variants
_This is another attempt at landing https://github.com/rust-lang/rust/pull/70835, which was approved by the libs team but failed on Android tests through Bors. The text copied here is from the original issue. The only change made so far is the addition of non-`checked_` variants of the log methods._
_Tracking issue: #70887_
---
This implements `{log,log2,log10}` methods for all integer types. The implementation was provided by `@substack` for use in the stdlib.
_Note: I'm not big on math, so this PR is a best effort written with limited knowledge. It's likely I'll be getting things wrong, but happy to learn and correct. Please bare with me._
## Motivation
Calculating the logarithm of a number is a generally useful operation. Currently the stdlib only provides implementations for floats, which means that if we want to calculate the logarithm for an integer we have to cast it to a float and then back to an int.
> would be nice if there was an integer log2 instead of having to either use the f32 version or leading_zeros() which i have to verify the results of every time to be sure
_— [`@substack,` 2020-03-08](https://twitter.com/substack/status/1236445105197727744)_
At higher numbers converting from an integer to a float we also risk overflows. This means that Rust currently only provides log operations for a limited set of integers.
The process of doing log operations by converting between floats and integers is also prone to rounding errors. In the following example we're trying to calculate `base10` for an integer. We might try and calculate the `base2` for the values, and attempt [a base swap](https://www.rapidtables.com/math/algebra/Logarithm.html#log-rules) to arrive at `base10`. However because we're performing intermediate rounding we arrive at the wrong result:
```rust
// log10(900) = ~2.95 = 2
dbg!(900f32.log10() as u64);
// log base change rule: logb(x) = logc(x) / logc(b)
// log2(900) / log2(10) = 9/3 = 3
dbg!((900f32.log2() as u64) / (10f32.log2() as u64));
```
_[playground](https://play.rust-lang.org/?version=stable&mode=debug&edition=2018&gist=6bd6c68b3539e400f9ca4fdc6fc2eed0)_
This is somewhat nuanced as a lot of the time it'll work well, but in real world code this could lead to some hard to track bugs. By providing correct log implementations directly on integers we can help prevent errors around this.
## Implementation notes
I checked whether LLVM intrinsics existed before implementing this, and none exist yet. ~~Also I couldn't really find a better way to write the `ilog` function. One option would be to make it a private method on the number, but I didn't see any precedent for that. I also didn't know where to best place the tests, so I added them to the bottom of the file. Even though they might seem like quite a lot they take no time to execute.~~
## References
- [Log rules](https://www.rapidtables.com/math/algebra/Logarithm.html#log-rules)
- [Rounding error playground](https://play.rust-lang.org/?version=stable&mode=debug&edition=2018&gist=6bd6c68b3539e400f9ca4fdc6fc2eed0)
- [substack's tweet asking about integer log2 in the stdlib](https://twitter.com/substack/status/1236445105197727744)
- [Integer Logarithm, A. Jaffer 2008](https://people.csail.mit.edu/jaffer/III/ilog.pdf)
This commit removes the previous mechanism of differentiating
between "Debug" and "Display" formattings for the sign of -0 so as
to comply with the IEEE 754 standard's requirements on external
character sequences preserving various attributes of a floating
point representation.
In addition, numerous tests are fixed.
These tests invoke the various op traits using all accepted types they
are implemented for as well as for references to those types.
This fixes#49660 and ensures the following implementations exist:
* `Add`, `Sub`, `Mul`, `Div`, `Rem`
* `T op T`, `T op &T`, `&T op T` and `&T op &T`
* for all integer and floating point types
* `AddAssign`, `SubAssign`, `MulAssign`, `DivAssign`, `RemAssign`
* `&mut T op T` and `&mut T op &T`
* for all integer and floating point types
* `Neg`
* `op T` and `op &T`
* for all signed integer and floating point types
* `Not`
* `op T` and `op &T`
* for `bool`
* `BitAnd`, `BitOr`, `BitXor`
* `T op T`, `T op &T`, `&T op T` and `&T op &T`
* for all integer types and bool
* `BitAndAssign`, `BitOrAssign`, `BitXorAssign`
* `&mut T op T` and `&mut T op &T`
* for all integer types and bool
* `Shl`, `Shr`
* `L op R`, `L op &R`, `&L op R` and `&L op &R`
* for all pairs of integer types
* `ShlAssign`, `ShrAssign`
* `&mut L op R`, `&mut L op &R`
* for all pairs of integer types
Part of #68490.
Care has been taken to leave the old consts where appropriate, for testing backcompat regressions, module shadowing, etc. The intrinsics docs were accidentally referring to some methods on f64 as std::f64, which I changed due to being contrary with how we normally disambiguate the shadow module from the primitive. In one other place I changed std::u8 to std::ops since it was just testing path handling in macros.
For places which have legitimate uses of the old consts, deprecated attributes have been optimistically inserted. Although currently unnecessary, they exist to emphasize to any future deprecation effort the necessity of these specific symbols and prevent them from being accidentally removed.
Refactor IntErrorKind to avoid "underflow" terminology
This PR is a continuation of #76455
# Changes
- `Overflow` renamed to `PosOverflow` and `Underflow` renamed to `NegOverflow` after discussion in #76455
- Changed some of the parsing code to return `InvalidDigit` rather than `Empty` for strings "+" and "-". https://users.rust-lang.org/t/misleading-error-in-str-parse-for-int-types/49178
- Carry the problem `char` with the `InvalidDigit` variant.
- Necessary changes were made to the compiler as it depends on `int_error_matching`.
- Redid tests to match on specific errors.
r? ```@KodrAus```
