dedd985084
Implement a faster sort algorithm
Hi everyone, this is my first PR.
I've made some changes to the standard sort algorithm, starting out with a few tweaks here and there, but in the end this endeavour became a complete rewrite of it.
#### Summary
Changes:
* Improved performance, especially on partially sorted inputs.
* Performs less comparisons on both random and partially sorted inputs.
* Decreased the size of temporary memory: the new sort allocates 4x less.
Benchmark:
```
name out1 ns/iter out2 ns/iter diff ns/iter diff %
slice::bench::sort_large_ascending 85,323 (937 MB/s) 8,970 (8918 MB/s) -76,353 -89.49%
slice::bench::sort_large_big_ascending 2,135,297 (599 MB/s) 355,955 (3595 MB/s) -1,779,342 -83.33%
slice::bench::sort_large_big_descending 2,266,402 (564 MB/s) 416,479 (3073 MB/s) -1,849,923 -81.62%
slice::bench::sort_large_big_random 3,053,031 (419 MB/s) 1,921,389 (666 MB/s) -1,131,642 -37.07%
slice::bench::sort_large_descending 313,181 (255 MB/s) 14,725 (5432 MB/s) -298,456 -95.30%
slice::bench::sort_large_mostly_ascending 287,706 (278 MB/s) 243,204 (328 MB/s) -44,502 -15.47%
slice::bench::sort_large_mostly_descending 415,078 (192 MB/s) 271,028 (295 MB/s) -144,050 -34.70%
slice::bench::sort_large_random 545,872 (146 MB/s) 521,559 (153 MB/s) -24,313 -4.45%
slice::bench::sort_large_random_expensive 30,321,770 (2 MB/s) 23,533,735 (3 MB/s) -6,788,035 -22.39%
slice::bench::sort_medium_ascending 616 (1298 MB/s) 155 (5161 MB/s) -461 -74.84%
slice::bench::sort_medium_descending 1,952 (409 MB/s) 202 (3960 MB/s) -1,750 -89.65%
slice::bench::sort_medium_random 3,646 (219 MB/s) 3,421 (233 MB/s) -225 -6.17%
slice::bench::sort_small_ascending 39 (2051 MB/s) 34 (2352 MB/s) -5 -12.82%
slice::bench::sort_small_big_ascending 96 (13333 MB/s) 96 (13333 MB/s) 0 0.00%
slice::bench::sort_small_big_descending 248 (5161 MB/s) 243 (5267 MB/s) -5 -2.02%
slice::bench::sort_small_big_random 501 (2554 MB/s) 490 (2612 MB/s) -11 -2.20%
slice::bench::sort_small_descending 95 (842 MB/s) 63 (1269 MB/s) -32 -33.68%
slice::bench::sort_small_random 372 (215 MB/s) 354 (225 MB/s) -18 -4.84%
```
#### Background
First, let me just do a quick brain dump to discuss what I learned along the way.
The official documentation says that the standard sort in Rust is a stable sort. This constraint is thus set in stone and immediately rules out many popular sorting algorithms. Essentially, the only algorithms we might even take into consideration are:
1. [Merge sort](https://en.wikipedia.org/wiki/Merge_sort)
2. [Block sort](https://en.wikipedia.org/wiki/Block_sort) (famous implementations are [WikiSort](https://github.com/BonzaiThePenguin/WikiSort) and [GrailSort](https://github.com/Mrrl/GrailSort))
3. [TimSort](https://en.wikipedia.org/wiki/Timsort)
Actually, all of those are just merge sort flavors. :) The current standard sort in Rust is a simple iterative merge sort. It has three problems. First, it's slow on partially sorted inputs (even though #29675 helped quite a bit). Second, it always makes around `log(n)` iterations copying the entire array between buffers, no matter what. Third, it allocates huge amounts of temporary memory (a buffer of size `2*n`, where `n` is the size of input).
The problem of auxilliary memory allocation is a tough one. Ideally, it would be best for our sort to allocate `O(1)` additional memory. This is what block sort (and it's variants) does. However, it's often very complicated (look at [this](https://github.com/BonzaiThePenguin/WikiSort/blob/master/WikiSort.cpp)) and even then performs rather poorly. The author of WikiSort claims good performance, but that must be taken with a grain of salt. It performs well in comparison to `std::stable_sort` in C++. It can even beat `std::sort` on partially sorted inputs, but on random inputs it's always far worse. My rule of thumb is: high performance, low memory overhead, stability - choose two.
TimSort is another option. It allocates a buffer of size `n/2`, which is not great, but acceptable. Performs extremelly well on partially sorted inputs. However, it seems pretty much all implementations suck on random inputs. I benchmarked implementations in [Rust](https://github.com/notriddle/rust-timsort), [C++](https://github.com/gfx/cpp-TimSort), and [D](
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| .travis.yml | ||
| appveyor.yml | ||
| COMPILER_TESTS.md | ||
| configure | ||
| CONTRIBUTING.md | ||
| COPYRIGHT | ||
| LICENSE-APACHE | ||
| LICENSE-MIT | ||
| Makefile.in | ||
| README.md | ||
| RELEASES.md | ||
| x.py | ||
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