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.
Add a check for ASCII characters in to_upper and to_lower
This extra check has better performance. See discussion here:
https://internals.rust-lang.org/t/to-upper-speed/13896
Thanks to `@gilescope` for helping discover and test this.
Improve slice.binary_search_by()'s best-case performance to O(1)
This PR aimed to improve the [slice.binary_search_by()](https://doc.rust-lang.org/std/primitive.slice.html#method.binary_search_by)'s best-case performance to O(1).
# Noticed
I don't know why the docs of `binary_search_by` said `"If there are multiple matches, then any one of the matches could be returned."`, but the implementation isn't the same thing. Actually, it returns the **last one** if multiple matches found.
Then we got two options:
## If returns the last one is the correct or desired result
Then I can rectify the docs and revert my changes.
## If the docs are correct or desired result
Then my changes can be merged after fully reviewed.
However, if my PR gets merged, another issue raised: this could be a **breaking change** since if multiple matches found, the returning order no longer the last one instead of it could be any one.
For example:
```rust
let mut s = vec![0, 1, 1, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55];
let num = 1;
let idx = s.binary_search(&num);
s.insert(idx, 2);
// Old implementations
assert_eq!(s, [0, 1, 1, 1, 1, 2, 2, 3, 5, 8, 13, 21, 34, 42, 55]);
// New implementations
assert_eq!(s, [0, 1, 1, 1, 2, 1, 2, 3, 5, 8, 13, 21, 34, 42, 55]);
```
# Benchmarking
**Old implementations**
```sh
$ ./x.py bench --stage 1 library/libcore
test slice::binary_search_l1 ... bench: 59 ns/iter (+/- 4)
test slice::binary_search_l1_with_dups ... bench: 59 ns/iter (+/- 3)
test slice::binary_search_l2 ... bench: 76 ns/iter (+/- 5)
test slice::binary_search_l2_with_dups ... bench: 77 ns/iter (+/- 17)
test slice::binary_search_l3 ... bench: 183 ns/iter (+/- 23)
test slice::binary_search_l3_with_dups ... bench: 185 ns/iter (+/- 19)
```
**New implementations (1)**
Implemented by this PR.
```rust
if cmp == Equal {
return Ok(mid);
} else if cmp == Less {
base = mid
}
```
```sh
$ ./x.py bench --stage 1 library/libcore
test slice::binary_search_l1 ... bench: 58 ns/iter (+/- 2)
test slice::binary_search_l1_with_dups ... bench: 37 ns/iter (+/- 4)
test slice::binary_search_l2 ... bench: 76 ns/iter (+/- 3)
test slice::binary_search_l2_with_dups ... bench: 57 ns/iter (+/- 6)
test slice::binary_search_l3 ... bench: 200 ns/iter (+/- 30)
test slice::binary_search_l3_with_dups ... bench: 157 ns/iter (+/- 6)
$ ./x.py bench --stage 1 library/libcore
test slice::binary_search_l1 ... bench: 59 ns/iter (+/- 8)
test slice::binary_search_l1_with_dups ... bench: 37 ns/iter (+/- 2)
test slice::binary_search_l2 ... bench: 77 ns/iter (+/- 2)
test slice::binary_search_l2_with_dups ... bench: 57 ns/iter (+/- 2)
test slice::binary_search_l3 ... bench: 198 ns/iter (+/- 21)
test slice::binary_search_l3_with_dups ... bench: 158 ns/iter (+/- 11)
```
**New implementations (2)**
Suggested by `@nbdd0121` in [comment](https://github.com/rust-lang/rust/pull/74024#issuecomment-665430239).
```rust
base = if cmp == Greater { base } else { mid };
if cmp == Equal { break }
```
```sh
$ ./x.py bench --stage 1 library/libcore
test slice::binary_search_l1 ... bench: 59 ns/iter (+/- 7)
test slice::binary_search_l1_with_dups ... bench: 37 ns/iter (+/- 5)
test slice::binary_search_l2 ... bench: 75 ns/iter (+/- 3)
test slice::binary_search_l2_with_dups ... bench: 56 ns/iter (+/- 3)
test slice::binary_search_l3 ... bench: 195 ns/iter (+/- 15)
test slice::binary_search_l3_with_dups ... bench: 151 ns/iter (+/- 7)
$ ./x.py bench --stage 1 library/libcore
test slice::binary_search_l1 ... bench: 57 ns/iter (+/- 2)
test slice::binary_search_l1_with_dups ... bench: 38 ns/iter (+/- 2)
test slice::binary_search_l2 ... bench: 77 ns/iter (+/- 11)
test slice::binary_search_l2_with_dups ... bench: 57 ns/iter (+/- 4)
test slice::binary_search_l3 ... bench: 194 ns/iter (+/- 15)
test slice::binary_search_l3_with_dups ... bench: 151 ns/iter (+/- 18)
```
I run some benchmarking testings against on two implementations. The new implementation has a lot of improvement in duplicates cases, while in `binary_search_l3` case, it's a little bit slower than the old one.
Add zero padding
Add benchmarks for fmt u128
This tests both when there is the max amount of work(all characters used)
And least amount of work(1 character used)
