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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.
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