Add midpoint function for all integers and floating numbers
This pull-request adds the `midpoint` function to `{u,i}{8,16,32,64,128,size}`, `NonZeroU{8,16,32,64,size}` and `f{32,64}`.
This new function is analog to the [C++ midpoint](https://en.cppreference.com/w/cpp/numeric/midpoint) function, and basically compute `(a + b) / 2` with a rounding towards ~~`a`~~ negative infinity in the case of integers. Or simply said: `midpoint(a, b)` is `(a + b) >> 1` as if it were performed in a sufficiently-large signed integral type.
Note that unlike the C++ function this pull-request does not implement this function on pointers (`*const T` or `*mut T`). This could be implemented in a future pull-request if desire.
### Implementation
For `f32` and `f64` the implementation in based on the `libcxx` [one](18ab892ff7/libcxx/include/__numeric/midpoint.h (L65-L77)). I originally tried many different approach but all of them failed or lead me with a poor version of the `libcxx`. Note that `libstdc++` has a very similar one; Microsoft STL implementation is also basically the same as `libcxx`. It unfortunately doesn't seems like a better way exist.
For unsigned integers I created the macro `midpoint_impl!`, this macro has two branches:
- The first one take `$SelfT` and is used when there is no unsigned integer with at least the double of bits. The code simply use this formula `a + (b - a) / 2` with the arguments in the correct order and signs to have the good rounding.
- The second branch is used when a `$WideT` (at least double of bits as `$SelfT`) is provided, using a wider number means that no overflow can occur, this greatly improve the codegen (no branch and less instructions).
For signed integers the code basically forwards the signed numbers to the unsigned version of midpoint by mapping the signed numbers to their unsigned numbers (`ex: i8 [-128; 127] to [0; 255]`) and vice versa.
I originally created a version that worked directly on the signed numbers but the code was "ugly" and not understandable. Despite this mapping "overhead" the codegen is better than my most optimized version on signed integers.
~~Note that in the case of unsigned numbers I tried to be smart and used `#[cfg(target_pointer_width = "64")]` to determine if using the wide version was better or not by looking at the assembly on godbolt. This was applied to `u32`, `u64` and `usize` and doesn't change the behavior only the assembly code generated.~~
Spelling library
Split per https://github.com/rust-lang/rust/pull/110392
I can squash once people are happy w/ the changes. It's really uncommon for large sets of changes to be perfectly acceptable w/o at least some changes.
I probably won't have time to respond until tomorrow or the next day
Fix inconsistent rounding of 0.5 when formatted to 0 decimal places
As described in #70336, when displaying values to zero decimal places the value of 0.5 is rounded to 1, which is inconsistent with the display of other half-integer values which round to even.
From testing the flt2dec implementation, it looks like this comes down to the condition in the fixed-width Dragon implementation where an empty buffer is treated as a case to apply rounding up. I believe the change below fixes it and updates only the relevant tests.
Nevertheless I am aware this is very much a core piece of functionality, so please take a very careful look to make sure I haven't missed anything. I hope this change does not break anything in the wider ecosystem as having a consistent rounding behaviour in floating point formatting is in my opinion a useful feature to have.
Resolves#70336
Reimplement `carrying_add` and `borrowing_sub` for signed integers.
As per the discussion in #85532, this PR reimplements `carrying_add` and `borrowing_sub` for signed integers.
It also adds unit tests for both unsigned and signed integers, emphasing on the behaviours of the methods.
Faster parsing for lower numbers for radix up to 16 (cont.)
( Continuation of https://github.com/rust-lang/rust/pull/83371 )
With LingMan's change I think this is potentially ready.
This updates the standard library's documentation to use the new syntax. The
documentation is worthwhile to update as it should be more idiomatic
(particularly for features like this, which are nice for users to get acquainted
with). The general codebase is likely more hassle than benefit to update: it'll
hurt git blame, and generally updates can be done by folks updating the code if
(and when) that makes things more readable with the new format.
A few places in the compiler and library code are updated (mostly just due to
already having been done when this commit was first authored).
As indicated in the comment, the BigNum::bit_length function could be
optimized by using CLZ, which is often a single instruction instead a
loop.
I think the code is also simpler now without the loop.
I added some additional tests for Big8x3 and Big32x40 to ensure that
there were no regressions.
Speedup int log10 branchless
This is achieved with a branchless bit-twiddling implementation of the case x < 100_000, and using this as building block.
Benchmark on an Intel i7-8700K (Coffee Lake):
```
name old ns/iter new ns/iter diff ns/iter diff % speedup
num::int_log::u8_log10_predictable 165 169 4 2.42% x 0.98
num::int_log::u8_log10_random 438 423 -15 -3.42% x 1.04
num::int_log::u8_log10_random_small 438 423 -15 -3.42% x 1.04
num::int_log::u16_log10_predictable 633 417 -216 -34.12% x 1.52
num::int_log::u16_log10_random 908 471 -437 -48.13% x 1.93
num::int_log::u16_log10_random_small 945 471 -474 -50.16% x 2.01
num::int_log::u32_log10_predictable 1,496 1,340 -156 -10.43% x 1.12
num::int_log::u32_log10_random 1,076 873 -203 -18.87% x 1.23
num::int_log::u32_log10_random_small 1,145 874 -271 -23.67% x 1.31
num::int_log::u64_log10_predictable 4,005 3,171 -834 -20.82% x 1.26
num::int_log::u64_log10_random 1,247 1,021 -226 -18.12% x 1.22
num::int_log::u64_log10_random_small 1,265 921 -344 -27.19% x 1.37
num::int_log::u128_log10_predictable 39,667 39,579 -88 -0.22% x 1.00
num::int_log::u128_log10_random 6,456 6,696 240 3.72% x 0.96
num::int_log::u128_log10_random_small 4,108 3,903 -205 -4.99% x 1.05
```
Benchmark on an M1 Mac Mini:
```
name old ns/iter new ns/iter diff ns/iter diff % speedup
num::int_log::u8_log10_predictable 143 130 -13 -9.09% x 1.10
num::int_log::u8_log10_random 375 325 -50 -13.33% x 1.15
num::int_log::u8_log10_random_small 376 325 -51 -13.56% x 1.16
num::int_log::u16_log10_predictable 500 322 -178 -35.60% x 1.55
num::int_log::u16_log10_random 794 405 -389 -48.99% x 1.96
num::int_log::u16_log10_random_small 1,035 405 -630 -60.87% x 2.56
num::int_log::u32_log10_predictable 1,144 894 -250 -21.85% x 1.28
num::int_log::u32_log10_random 832 786 -46 -5.53% x 1.06
num::int_log::u32_log10_random_small 832 787 -45 -5.41% x 1.06
num::int_log::u64_log10_predictable 2,681 2,057 -624 -23.27% x 1.30
num::int_log::u64_log10_random 1,015 806 -209 -20.59% x 1.26
num::int_log::u64_log10_random_small 1,004 795 -209 -20.82% x 1.26
num::int_log::u128_log10_predictable 56,825 56,526 -299 -0.53% x 1.01
num::int_log::u128_log10_random 9,056 8,861 -195 -2.15% x 1.02
num::int_log::u128_log10_random_small 1,528 1,527 -1 -0.07% x 1.00
```
The 128 bit case remains ridiculously slow because llvm fails to optimize division by a constant 128-bit value to multiplications. This could be worked around but it seems preferable to fix this in llvm.
From u32 up, table lookup (like suggested [here](https://github.com/rust-lang/rust/issues/70887#issuecomment-881099813)) is still faster, but requires a hardware `leading_zeros` to be viable, and might clog up the cache.
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.
This is achieved with a branchless bit-twiddling implementation of the
case x < 100_000, and using this as building block.
Benchmark on an Intel i7-8700K (Coffee Lake):
name old ns/iter new ns/iter diff ns/iter diff % speedup
num::int_log::u8_log10_predictable 165 169 4 2.42% x 0.98
num::int_log::u8_log10_random 438 423 -15 -3.42% x 1.04
num::int_log::u8_log10_random_small 438 423 -15 -3.42% x 1.04
num::int_log::u16_log10_predictable 633 417 -216 -34.12% x 1.52
num::int_log::u16_log10_random 908 471 -437 -48.13% x 1.93
num::int_log::u16_log10_random_small 945 471 -474 -50.16% x 2.01
num::int_log::u32_log10_predictable 1,496 1,340 -156 -10.43% x 1.12
num::int_log::u32_log10_random 1,076 873 -203 -18.87% x 1.23
num::int_log::u32_log10_random_small 1,145 874 -271 -23.67% x 1.31
num::int_log::u64_log10_predictable 4,005 3,171 -834 -20.82% x 1.26
num::int_log::u64_log10_random 1,247 1,021 -226 -18.12% x 1.22
num::int_log::u64_log10_random_small 1,265 921 -344 -27.19% x 1.37
num::int_log::u128_log10_predictable 39,667 39,579 -88 -0.22% x 1.00
num::int_log::u128_log10_random 6,456 6,696 240 3.72% x 0.96
num::int_log::u128_log10_random_small 4,108 3,903 -205 -4.99% x 1.05
Benchmark on an M1 Mac Mini:
name old ns/iter new ns/iter diff ns/iter diff % speedup
num::int_log::u8_log10_predictable 143 130 -13 -9.09% x 1.10
num::int_log::u8_log10_random 375 325 -50 -13.33% x 1.15
num::int_log::u8_log10_random_small 376 325 -51 -13.56% x 1.16
num::int_log::u16_log10_predictable 500 322 -178 -35.60% x 1.55
num::int_log::u16_log10_random 794 405 -389 -48.99% x 1.96
num::int_log::u16_log10_random_small 1,035 405 -630 -60.87% x 2.56
num::int_log::u32_log10_predictable 1,144 894 -250 -21.85% x 1.28
num::int_log::u32_log10_random 832 786 -46 -5.53% x 1.06
num::int_log::u32_log10_random_small 832 787 -45 -5.41% x 1.06
num::int_log::u64_log10_predictable 2,681 2,057 -624 -23.27% x 1.30
num::int_log::u64_log10_random 1,015 806 -209 -20.59% x 1.26
num::int_log::u64_log10_random_small 1,004 795 -209 -20.82% x 1.26
num::int_log::u128_log10_predictable 56,825 56,526 -299 -0.53% x 1.01
num::int_log::u128_log10_random 9,056 8,861 -195 -2.15% x 1.02
num::int_log::u128_log10_random_small 1,528 1,527 -1 -0.07% x 1.00
The 128 bit case remains ridiculously slow because llvm fails to optimize division by
a constant 128-bit value to multiplications. This could be worked around but it seems
preferable to fix this in llvm.
From u32 up, table lookup (like suggested here
https://github.com/rust-lang/rust/issues/70887#issuecomment-881099813) is still
faster, but requires a hardware leading_zero to be viable, and might clog up the
cache.
Update Rust Float-Parsing Algorithms to use the Eisel-Lemire algorithm.
# Summary
Rust, although it implements a correct float parser, has major performance issues in float parsing. Even for common floats, the performance can be 3-10x [slower](https://arxiv.org/pdf/2101.11408.pdf) than external libraries such as [lexical](https://github.com/Alexhuszagh/rust-lexical) and [fast-float-rust](https://github.com/aldanor/fast-float-rust).
Recently, major advances in float-parsing algorithms have been developed by Daniel Lemire, along with others, and implement a fast, performant, and correct float parser, with speeds up to 1200 MiB/s on Apple's M1 architecture for the [canada](0e2b5d163d/data/canada.txt) dataset, 10x faster than Rust's 130 MiB/s.
In addition, [edge-cases](https://github.com/rust-lang/rust/issues/85234) in Rust's [dec2flt](868c702d0c/library/core/src/num/dec2flt) algorithm can lead to over a 1600x slowdown relative to efficient algorithms. This is due to the use of Clinger's correct, but slow [AlgorithmM and Bellepheron](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.45.4152&rep=rep1&type=pdf), which have been improved by faster big-integer algorithms and the Eisel-Lemire algorithm, respectively.
Finally, this algorithm provides substantial improvements in the number of floats the Rust core library can parse. Denormal floats with a large number of digits cannot be parsed, due to use of the `Big32x40`, which simply does not have enough digits to round a float correctly. Using a custom decimal class, with much simpler logic, we can parse all valid decimal strings of any digit count.
```rust
// Issue in Rust's dec2fly.
"2.47032822920623272088284396434110686182e-324".parse::<f64>(); // Err(ParseFloatError { kind: Invalid })
```
# Solution
This pull request implements the Eisel-Lemire algorithm, modified from [fast-float-rust](https://github.com/aldanor/fast-float-rust) (which is licensed under Apache 2.0/MIT), along with numerous modifications to make it more amenable to inclusion in the Rust core library. The following describes both features in fast-float-rust and improvements in fast-float-rust for inclusion in core.
**Documentation**
Extensive documentation has been added to ensure the code base may be maintained by others, which explains the algorithms as well as various associated constants and routines. For example, two seemingly magical constants include documentation to describe how they were derived as follows:
```rust
// Round-to-even only happens for negative values of q
// when q ≥ −4 in the 64-bit case and when q ≥ −17 in
// the 32-bitcase.
//
// When q ≥ 0,we have that 5^q ≤ 2m+1. In the 64-bit case,we
// have 5^q ≤ 2m+1 ≤ 2^54 or q ≤ 23. In the 32-bit case,we have
// 5^q ≤ 2m+1 ≤ 2^25 or q ≤ 10.
//
// When q < 0, we have w ≥ (2m+1)×5^−q. We must have that w < 2^64
// so (2m+1)×5^−q < 2^64. We have that 2m+1 > 2^53 (64-bit case)
// or 2m+1 > 2^24 (32-bit case). Hence,we must have 2^53×5^−q < 2^64
// (64-bit) and 2^24×5^−q < 2^64 (32-bit). Hence we have 5^−q < 2^11
// or q ≥ −4 (64-bit case) and 5^−q < 2^40 or q ≥ −17 (32-bitcase).
//
// Thus we have that we only need to round ties to even when
// we have that q ∈ [−4,23](in the 64-bit case) or q∈[−17,10]
// (in the 32-bit case). In both cases,the power of five(5^|q|)
// fits in a 64-bit word.
const MIN_EXPONENT_ROUND_TO_EVEN: i32;
const MAX_EXPONENT_ROUND_TO_EVEN: i32;
```
This ensures maintainability of the code base.
**Improvements for Disguised Fast-Path Cases**
The fast path in float parsing algorithms attempts to use native, machine floats to represent both the significant digits and the exponent, which is only possible if both can be exactly represented without rounding. In practice, this means that the significant digits must be 53-bits or less and the then exponent must be in the range `[-22, 22]` (for an f64). This is similar to the existing dec2flt implementation.
However, disguised fast-path cases exist, where there are few significant digits and an exponent above the valid range, such as `1.23e25`. In this case, powers-of-10 may be shifted from the exponent to the significant digits, discussed at length in https://github.com/rust-lang/rust/issues/85198.
**Digit Parsing Improvements**
Typically, integers are parsed from string 1-at-a-time, requiring unnecessary multiplications which can slow down parsing. An approach to parse 8 digits at a time using only 3 multiplications is described in length [here](https://johnnylee-sde.github.io/Fast-numeric-string-to-int/). This leads to significant performance improvements, and is implemented for both big and little-endian systems.
**Unsafe Changes**
Relative to fast-float-rust, this library makes less use of unsafe functionality and clearly documents it. This includes the refactoring and documentation of numerous unsafe methods undesirably marked as safe. The original code would look something like this, which is deceptively marked as safe for unsafe functionality.
```rust
impl AsciiStr {
#[inline]
pub fn step_by(&mut self, n: usize) -> &mut Self {
unsafe { self.ptr = self.ptr.add(n) };
self
}
}
...
#[inline]
fn parse_scientific(s: &mut AsciiStr<'_>) -> i64 {
// the first character is 'e'/'E' and scientific mode is enabled
let start = *s;
s.step();
...
}
```
The new code clearly documents safety concerns, and does not mark unsafe functionality as safe, leading to better safety guarantees.
```rust
impl AsciiStr {
/// Advance the view by n, advancing it in-place to (n..).
pub unsafe fn step_by(&mut self, n: usize) -> &mut Self {
// SAFETY: same as step_by, safe as long n is less than the buffer length
self.ptr = unsafe { self.ptr.add(n) };
self
}
}
...
/// Parse the scientific notation component of a float.
fn parse_scientific(s: &mut AsciiStr<'_>) -> i64 {
let start = *s;
// SAFETY: the first character is 'e'/'E' and scientific mode is enabled
unsafe {
s.step();
}
...
}
```
This allows us to trivially demonstrate the new implementation of dec2flt is safe.
**Inline Annotations Have Been Removed**
In the previous implementation of dec2flt, inline annotations exist practically nowhere in the entire module. Therefore, these annotations have been removed, which mostly does not impact [performance](https://github.com/aldanor/fast-float-rust/issues/15#issuecomment-864485157).
**Fixed Correctness Tests**
Numerous compile errors in `src/etc/test-float-parse` were present, due to deprecation of `time.clock()`, as well as the crate dependencies with `rand`. The tests have therefore been reworked as a [crate](https://github.com/Alexhuszagh/rust/tree/master/src/etc/test-float-parse), and any errors in `runtests.py` have been patched.
**Undefined Behavior**
An implementation of `check_len` which relied on undefined behavior (in fast-float-rust) has been refactored, to ensure that the behavior is well-defined. The original code is as follows:
```rust
#[inline]
pub fn check_len(&self, n: usize) -> bool {
unsafe { self.ptr.add(n) <= self.end }
}
```
And the new implementation is as follows:
```rust
/// Check if the slice at least `n` length.
fn check_len(&self, n: usize) -> bool {
n <= self.as_ref().len()
}
```
Note that this has since been fixed in [fast-float-rust](https://github.com/aldanor/fast-float-rust/pull/29).
**Inferring Binary Exponents**
Rather than explicitly store binary exponents, this new implementation infers them from the decimal exponent, reducing the amount of static storage required. This removes the requirement to store [611 i16s](868c702d0c/library/core/src/num/dec2flt/table.rs (L8)).
# Code Size
The code size, for all optimizations, does not considerably change relative to before for stripped builds, however it is **significantly** smaller prior to stripping the resulting binaries. These binary sizes were calculated on x86_64-unknown-linux-gnu.
**new**
Using rustc version 1.55.0-dev.
opt-level|size|size(stripped)
|:-:|:-:|:-:|
0|400k|300K
1|396k|292K
2|392k|292K
3|392k|296K
s|396k|292K
z|396k|292K
**old**
Using rustc version 1.53.0-nightly.
opt-level|size|size(stripped)
|:-:|:-:|:-:|
0|3.2M|304K
1|3.2M|292K
2|3.1M|284K
3|3.1M|284K
s|3.1M|284K
z|3.1M|284K
# Correctness
The dec2flt implementation passes all of Rust's unittests and comprehensive float parsing tests, along with numerous other tests such as Nigel Toa's comprehensive float [tests](https://github.com/nigeltao/parse-number-fxx-test-data) and Hrvoje Abraham [strtod_tests](https://github.com/ahrvoje/numerics/blob/master/strtod/strtod_tests.toml). Therefore, it is unlikely that this algorithm will incorrectly round parsed floats.
# Issues Addressed
This will fix and close the following issues:
- resolves#85198
- resolves#85214
- resolves#85234
- fixes#31407
- fixes#31109
- fixes#53015
- resolves#68396
- closes https://github.com/aldanor/fast-float-rust/issues/15
Implementation is based off fast-float-rust, with a few notable changes.
- Some unsafe methods have been removed.
- Safe methods with inherently unsafe functionality have been removed.
- All unsafe functionality is documented and provably safe.
- Extensive documentation has been added for simpler maintenance.
- Inline annotations on internal routines has been removed.
- Fixed Python errors in src/etc/test-float-parse/runtests.py.
- Updated test-float-parse to be a library, to avoid missing rand dependency.
- Added regression tests for #31109 and #31407 in core tests.
- Added regression tests for #31109 and #31407 in ui tests.
- Use the existing slice primitive to simplify shared dec2flt methods
- Remove Miri ignores from dec2flt, due to faster parsing times.
- resolves#85198
- resolves#85214
- resolves#85234
- fixes#31407
- fixes#31109
- fixes#53015
- resolves#68396
- closes https://github.com/aldanor/fast-float-rust/issues/15
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
