Implement a faster sort algorithm #38192

ghost · 2016-12-06T12:19:30Z

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 fewer 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:

Merge sort
Block sort (famous implementations are WikiSort and GrailSort)
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) 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, C++, and D. The results were a bit disappointing. It seems bad performance is due to complex galloping procedures in hot loops. Galloping noticeably improves performance on partially sorted inputs, but worsens it on random ones.

The new algorithm

Choosing the best algorithm is not easy. Plain merge sort is bad on partially sorted inputs. TimSort is bad on random inputs and block sort is even worse. However, if we take the main ideas from TimSort (intelligent merging strategy of sorted runs) and drop galloping, then we'll have great performance on random inputs and it won't be bad on partially sorted inputs either.

That is exactly what this new algorithm does. I can't call it TimSort, since it steals just a few of it's ideas. Complete TimSort would be a much more complex and elaborate implementation. In case we in the future figure out how to incorporate more of it's ideas into this implementation without crippling performance on random inputs, it's going to be very easy to extend. I also did several other minor improvements, like reworked insertion sort to make it faster.

There are also new, more thorough benchmarks and panic safety tests.

The final code is not terribly complex and has less unsafe code than I anticipated, but there's still plenty of it that should be carefully reviewed. I did my best at documenting non-obvious code.

I'd like to notify several people of this PR, since they might be interested and have useful insights:

@huonw because he wrote the original merge sort.
@alexcrichton because he was involved in multiple discussions of it.
@veddan because he wrote introsort in Rust.
@notriddle because he wrote TimSort in Rust.
@bluss because he had an attempt at writing WikiSort in Rust.
@gnzlbg, @rkruppe, and @mark-i-m because they were involved in discussion Overhaul std collections and algorithm documentation #36318.

P.S. quickersort describes itself as being universally faster than the standard sort, which is true. However, if this PR gets merged, things might change a bit. ;)

nagisa · 2016-12-06T12:45:34Z

Since it is quite a major rewrite of the sorting routine, and I see that we have no test guaranteeing stability, I would very much like a test that ensures this invariant.

Something along the lines of

let x = [0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3];
let y = // array/vector/slice of references to each element of x. References compare the underlying value
y.shuffle();
let z = y.clone();
y.sort();
// assert that the addresses in y and z are ordered in the same order for each block of values.

ghost · 2016-12-06T13:12:36Z

Actually, we do have a sort guaranteeing stability. It's called test_sort_stability. However, it tests sort on short arrays only, essentially verifying correctness of just insertion sort. I'll bump the lengths up a bit.

bluss

I loved reading this. The request for changes is mostly comments and the guard struct names, but also a look at the zero sized types case, that it doesn't panic.

bluss · 2016-12-06T13:12:37Z

src/libcollections/slice.rs

-            // that case, `i == j` so we don't copy. The
-            // `.offset(j)` is always in bounds.
+    // When dropped, copies from `src` into `dst`.
+    struct Guard<T> {


Since there are two struct Guard with slightly different jobs, they should have different names. (Sidenote: What it does with a hole here is exactly like Hole in the implementation of BinaryHeap).

How about InsertionHole and MergeHole? Or InsertionGuard and MergeGuard?

Anything that sets them apart is fine.

bluss · 2016-12-06T13:14:08Z

src/libcollections/slice.rs


-    let len = v.len();
+    // Increments the pointer and returns the old value.
+    unsafe fn forward<T>(ptr: &mut *mut T) -> *mut T {


forward is also known as ptr++ in C, that is "post increment".

In my opinion, this is in easier to read style with an extension method on raw pointers, so that it reads ptr.post_increment(). Not sure what others think?

Relatedly, the fact that forward does a post-increment and that backwards does a pre-increment is somewhat confusing. It'd be nice to have a comment explaining that when iterating backwards, the pointer points past the end of the array, while when iterating forwards, the pointer points directly to the beginning of the array.

Another option is to name the two functions get_incr and decr_get instead, but I'm not too happy with that solution either.

Using the word order for ordering of operations is too subtle for me. Depends on what one is used to, maybe.

bluss · 2016-12-06T13:14:26Z

src/libcollections/slice.rs

-        insertion_sort(v, compare);
-        return;
+    // Decrements the pointer and returns the new value.
+    unsafe fn backward<T>(ptr: &mut *mut T) -> *mut T {


This is known as --ptr in C, that is "pre-decrement".

bluss · 2016-12-06T13:18:07Z

src/libcollections/slice.rs

-                // rather than <=, to maintain stability.
+    impl<T> Drop for Guard<T> {
+        fn drop(&mut self) {
+            let len = (self.end as usize - self.start as usize) / mem::size_of::<T>();


If T is a zero sized type (ZST), this is a division by zero.

Now I know — the old sort code also does this! The division by size of turns out to be unreachable for ZSTs in that implementation. We can't require much of anything in this case, but maybe a test that ensures that it finishes without panic.

Would it make sense to make the entire sort algorithm on ZSTs simply a no-op (i.e. return immediately from merge_sort)? Can one meaningfully sort an array of ZSTs at all?

I think it's fine to make it a noop. We could discuss the finer points of that another time. I don't think the current sort has any meaningful behaviour for sorting ZST.

bluss · 2016-12-06T13:19:28Z

src/libcollections/slice.rs

+    if len <= insertion {
+        if len >= 2 {
+            for i in (0..len-1).rev() {
+                insert_head(&mut v[i..len], &mut compare);


The len on the end of the range here seems redundant. Is it needed for some reason?

No, I'll remove it.

bluss · 2016-12-06T13:20:10Z

src/libcollections/slice.rs

+                len: left.len + right.len,
+            };
+            runs.remove(r + 1);
+        }
    }


There should be exactly one Run in the runs vector here, is that right? Maybe a debug assertion for that (so that tests exercise it)?

Added a debug assertion.

bluss · 2016-12-06T13:41:46Z

src/libcollections/slice.rs

+                    break;
+                }
+                ptr::copy_nonoverlapping(&v[i], &mut v[i - 1], 1);
+                guard.dst = &mut v[i];
            }


Can you put a comment after the } here that indicates that the guard fills the hole as part of normal execution.

bluss · 2016-12-06T13:43:36Z

src/libcollections/slice.rs

+            };
+            ptr::copy_nonoverlapping(to_copy, backward(&mut out), 1);
+        }
+    }



The same here: a comment reminding that guard is dropped and it copies the range into place.

bluss · 2016-12-06T13:48:56Z

src/libcollections/slice.rs

+    // http://envisage-project.eu/timsort-specification-and-verification/
+    //
+    // The gist of the story is: we must enforce the invariants on the top four runs on the stack.
+    // Enforcing them on just top three is not enough.


The invariants must be enforced, else .. what? Just that it will not be O(n log n) otherwise, if I understand correctly?

That and it eats too much memory for the runs stack.

I'll write a better comment to clarify.

apasel422 · 2016-12-06T15:14:19Z

src/libcollections/slice.rs

-            while j > 0 && compare(&*read_ptr, &*buf_v.offset(j - 1)) == Less {
-                j -= 1;
+            // A common method of doing insertion sort is swapping adjacent elements until the
+            // first one gets to it's destination. Swapping is slow whenever elements are big


s/it's/its/

gereeter · 2016-12-06T16:27:17Z

src/libcollections/slice.rs

+                src: &mut tmp.value,
+                dst: &mut v[1],
+            };
+            ptr::copy_nonoverlapping(&v[1], &mut v[0], 1);


What is the advantage of copying individual elements, overlapped with the comparisons? Is it slower to just search for the correct insertion location and do a single bulk ptr::copy? If so, could you add a comment explaining that?

Yes, it's slightly slower to do a single bulk ptr::copy after search. I'll explain that in a comment.

gereeter · 2016-12-06T16:34:36Z

src/libcollections/slice.rs

+    struct Guard<T> {
+        start: *mut T,
+        end: *mut T,
+        dst: *mut T,


Nit: could this be called dest instead of dst? At least for me, the first thing I think of with dst is dynamically sized types.

ptr::copy has arguments src and dst (link).
Good point about dynamically sized types. I agree that dest is clearer, so I'll rename this field.

gereeter · 2016-12-06T16:48:52Z

src/libcollections/slice.rs

-        mem::swap(&mut buf_dat, &mut buf_tmp);
+        // Insert some more elements into the run if it's too short. Insertion sort is faster than
+        // merge sort on short sequences, so this significantly improves performance.
+        while start > 0 && end - start < insertion {


Possible micro-optimization (I don't know if LLVM does this already or how much it matters): instead of using two conditionals here, the final start position could be calculated once (if end > insertion { end - insertion } else { 0 }), and then start could be compared against that final start position.

I did a bit of benchmarking, and it seems this micro-optimization is totally irrelevant. I'll keep the code as is to keep clarity.

gereeter · 2016-12-06T17:09:01Z

src/libcollections/slice.rs

+
+    let mut runs = vec![];
+    let mut end = len;
+    while end > 0 {


Is there any particular reason that this implementation goes back-to-front through the array? This isn't a problem, just a bit surprising - almost every piece of array-handling code I've seen, when given the choice, goes front-to-back.

Yeah, the fact that you're asking this tells me I should explain this decision in comments. Will do so. :)

gereeter · 2016-12-06T17:12:52Z

src/libcollections/slice.rs

+///
+/// The invariants ensure that the total running time is `O(n log n)` worst-case.
+fn merge_sort<T, F>(v: &mut [T], mut compare: F)
+    where F: FnMut(&T, &T) -> Ordering


As far as I can tell, this implementation of merge sort only ever compares the result of compare to Greater. It might be more efficient to just pass around a function greater: FnMut(&T, &T) -> bool, since I think that some types can implement binary comparisons slightly more efficiently than trinary comparisons.

How would we expose the ability to pass a function greater instead of compare in the public API, if at all?

It would probably only matter for sort, where we can call a.gt(b) rather than a.cmp(b) == Greater.

How about adding greater (and the others - less, less_eq, ...) to std::cmp::Ord trait with a default implementation using cmp? That will allow anyone to write specializations for any type. It's the same we are doing for std::iter::Iterator.

gt is already that (PartialOrd and Ord must be in sync).

Oh, missed it because I foolishly looked at Ord.

gereeter · 2016-12-06T17:29:22Z

src/libcollections/slice.rs


-    let len = v.len();
+    // Increments the pointer and returns the old value.
+    unsafe fn forward<T>(ptr: &mut *mut T) -> *mut T {


Relatedly, the fact that forward does a post-increment and that backwards does a pre-increment is somewhat confusing. It'd be nice to have a comment explaining that when iterating backwards, the pointer points past the end of the array, while when iterating forwards, the pointer points directly to the beginning of the array.

gereeter · 2016-12-06T17:33:50Z

src/libcollections/slice.rs

-                ptr::copy(&*buf_dat.offset(j), buf_dat.offset(j + 1), i - j as usize);
-                ptr::copy_nonoverlapping(read_ptr, buf_dat.offset(j), 1);
+    // Short arrays get sorted in-place via insertion sort to avoid allocations.
+    if len <= insertion {


It occurs to me that this threshold might want to be higher than the threshold for sorting runs, since it might be worth some time penalty to avoid the allocation.

You're absolutely right. I did some benchmarking and will separate the two threshold into two different variables.

Stebalien · 2016-12-06T22:50:32Z

src/libcollections/lib.rs

 #![feature(trusted_len)]
 #![feature(unicode)]
 #![feature(unique)]
-#![feature(slice_get_slice)]
+#![feature(untagged_unions)]


Maybe I'm missing something obvious but I don't see where you use this feature (or why you changed these).

Three changes to feature list are in this file:

Removed step_by. Old sort used it, but the new one doesn't.

Simply moved slice_get_slice a few line up to make the feature list sorted alphabetically.

Added untagged_unions. This feature is used in function insert_head above struct NoDrop<T>.

GitHub wasn't loading all the diffs... sigh (sorry). I was excited to see a non-ffi usecase for unions and got a bit confused when searching didn't pick up any.

ghost · 2016-12-07T02:38:53Z

I addressed all requests for changes and improved comments in the code.

mark-i-m · 2016-12-07T09:24:50Z

Re: #38192 (comment), sorting a collection of ZSTs

For what its worth, I think the only correct answer is to make it a nop. ZSTs are types with exactly one value. Thus, given a collection x of values of type T, for some ZST T, and two arbitrary values in the collection x[i] and x[j], we know that x[i] == x[j], so the only correct behavior (for a stable sort) is to preserve the exact order of the input collection, right?

mark-i-m · 2016-12-07T09:50:41Z

src/libcollections/slice.rs

@@ -1087,7 +1086,7 @@ impl<T> [T] {
    /// elements.
    ///
    /// This sort is stable and `O(n log n)` worst-case but allocates
-    /// approximately `2 * n`, where `n` is the length of `self`.
+    /// approximately `n / 2`, where `n` is the length of `self`.


I haven't gotten a chance to read all of the code yet, but I was wondering why big-O notation is used for the time complexity, but not for space? Is "approximately n / 2" not asymptotic behavior (e.g. is it an empirical number)? If not, then, I think it would be good to explicitly mention this.

Saying "allocates O(n / 2)" is equivalent to "allocates less than n / 2 * K, for some constant K".

Saying "allocates approximately n / 2" is equivalent to "allocates between n / 2 - K and n / 2 + K, for some constant K".

The latter is more precise and therefore a better description of memory usage.

There's still a constant factor hidden in this wording, because it doesn't contain any units. n / 2 what? Bytes? Words? size_of::<T>()?

The old version also has this problem, but while you're updating it and have the details fresh in mind, could you add this detail?

Fair point. I've updated the wording.

mark-i-m · 2016-12-07T10:15:27Z

Ah, I see. Thanks

…

On Dec 7, 2016 4:10 AM, "Stjepan Glavina" ***@***.***> wrote: ***@***.**** commented on this pull request. ------------------------------ In src/libcollections/slice.rs <#38192>: > @@ -1087,7 +1086,7 @@ impl<T> [T] { /// elements. /// /// This sort is stable and `O(n log n)` worst-case but allocates - /// approximately `2 * n`, where `n` is the length of `self`. + /// approximately `n / 2`, where `n` is the length of `self`. Saying "allocates O(n / 2)" is equivalent to "allocates less than n / 2 * K, for some constant K". Saying "allocates approximately n / 2" is equivalent to "allocates between n / 2 - K and n / 2 + K", for some constant K". The latter is more precise and therefore a better description of memory usage. — You are receiving this because you were mentioned. Reply to this email directly, view it on GitHub <#38192>, or mute the thread <https://github.com/notifications/unsubscribe-auth/AIazwFQoAPKJio1ylmgBO8x7imia05Txks5rFoYYgaJpZM4LFWL1> .

gnzlbg · 2016-12-07T11:29:56Z

Is there a case for which this implementation performs worse than the old one?

ghost · 2016-12-07T11:59:14Z

@gnzlbg I don't think so. Let's discuss a few cases:

Small arrays (below the insertion sort threshold). I tried sorting big & small structures on ascending & descending & random inputs. The sorts are always either tied, or the new sort wins.
Medium sized arrays (just above the insertion sort threshold). One might think that additional allocation caused by runs is troubling, but turns out it isn't. I tried poking at various cases. Again, the new sort wins in all of them, except a few in which they are tied.
Large arrays. The new sort destroys it on partially sorted arrays, so such cases are no contest. The old sort is strongest on random inputs, and even then it's consistently behind the new sort. There is a test called sort_large_random_expensive, which sorts a random array using a very costly comparison function. I've examined the total number of comparisons required using the old vs new algorithm, and it turns out the new one performs a slightly smaller number of comparisons. It's no wonder it wins with a slight edge in that test, too.

Sorting depends on structure size, type of input, comparison function, your platform, etc. I can't guarantee the new sort always wins, but haven't found a case where it wouldn't. If it ever loses, I'm sure that would be a race lost by a very small margin.

gnzlbg · 2016-12-07T15:30:17Z

@stjepang In practice, most data to be sorted has some structure and is rarely truly random. I think it would be worth it to check the benchmarking patterns of Boost.Sort, libc++ algorithm benchmarks, Morwenn/cpp-sort, ... (the licenses are permissive). For example, libc++-std::sort is benchmarked using the following patterns:

This makes libc++'s std::sort slower than libstdc++'s for truly random data, but much better when the data isn't truly random. Besides these patterns, the following patterns are also common:

A brief description of what perf.txt is showing you

size is exactly what it sounds like it means. At size = 10, we're comparing the insertion sort implementations of quickersort and Implement a faster sort algorithm #38192
m is the "constant factor" used by the list generator and transformation.
pattern describes what kind of list should be generated at first. For examples where size = 20 and m = 5:
- sawtooth: A repeating, incrementing list with period m: [ 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4 ]
- rand: A series of random numbers (note that m is not used): [ 174485772, 204021123, 71605603, 334131482, 785758972, 574747816, 150801346, 844973720, 876360420, 210798088, 688904552, 975251835, 835778151, 935999844, 786148954, 779096211, 338255767, 826878933, 563001734, 315096245 ]
- stagger: A classic, terrible pseduo-RNG with a short period: [ 0, 6, 12, 18, 4, 10, 16, 2, 8, 14, 0, 6, 12, 18, 4, 10, 16, 2, 8, 14 ]
- plateau: A list that starts out incrementing but becomes repeating at m: [ 0, 1, 2, 3, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5 ]
- shuffle: The result of applying a single pass of "bridge" shuffling to two incrementing lists (note that this is a lopsided shuffle unless m is 2): [ 0, 0, 2, 4, 4, 4, 6, 8, 12, 8, 14, 8, 12, 16, 14, 16, 18, 18, 20, 20 ]
After generating the pattern, we then generate a variant by applying a transformation to the list:
- ident: Don't do any transformation. Note that rand / ident completely ignores m.
- reverse: Turn it backwards. Note that this is semantically a no-op for rand, and ignores m.
- reverse_front: Turn the first len / 2 items backwards. Note that this is semantically a no-op for rand, and ignores m.
- reverse_back: Turn the last len / 2 items backwards. Note that this is semantically a no-op for rand, and ignores m.
- sorted: Sort the list. Note that this is a no-op for plateau.
- dither: Take all the items modulus m, thus increasing the number of duplicates. For example, this will turn plateau into [ 0, 1, 2, 3, 4, 0, 0, 0, 0, ... ].
After the two-step process of generating the list, the list is copied, and the copies are sorted with both sorting algorithms. The time is recorded, and the "throughput" is computed using the formula size / ( time / trial_count ). Larger throughput is better.
Finally, the ratio of throughputs is taken. A larger ratio means quickersort did better than standard sort, while a ratio smaller than 1 means standard sort did better.

gnzlbg · 2016-12-07T17:33:08Z

@notriddle Where are the benchmarks for the patterns: organ pipe and sawtooth? I cannot find them.

EDIT: the benchmarks are there (at least for sawtooth, can't still find organ pipe), but the results for those don't seem to have been posted in the OP?

notriddle · 2016-12-07T17:38:25Z

Sawtooth is literally the first one shown.

Organ pipe is actually not there. I'd be happy to add it, though.

bluss · 2016-12-07T17:42:59Z

Thanks for the explanation.

ghost · 2016-12-07T19:10:13Z

@gnzlbg Some of the patterns displayed in the picture you posted are already benchmarked as part of this PR. I get what you're saying about sorting structured data, and agree with you.

The new implementation is better than the old one on all of those benchmarks. That is undisputable even without any further benchmarking, really. And it won't blow up by design either. :) It's O(n log n) worst-case and finds natural runs in input data before sorting, so there's not much to worry.

It is certainly possible to harness more speed on structured data at the expense of speed on random data (and code complexity, too!). However, note that speed on structured data is already very good (look at the benchmarks we have).

Also, keep in mind that we really don't have much choice with stable sorts. TimSort is basically the only reasonably fast and versatile stable sort, and it was designed to be fast on structured data in the first place. Our choices boil down to: how far do we go with it, and how do we adapt TimSort (designed for Python) to Rust (a vastly different language)?

bluss · 2016-12-07T20:28:40Z

The PR is a great improvement on several fronts (:tada: @stjepang!!) and I believe it to be correct and memory safe so it's r=me when the fixup commits have been squashed together like the author indicated they wanted to do.

There's a lot of interesting things that can follow here. We can create a meta issue to track the different ideas for those that are interested.

This is a complete rewrite of the standard sort algorithm. The new algorithm is a simplified variant of TimSort. In summary, the changes are: * 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.

ghost · 2016-12-07T20:36:35Z

The fixup commits are squashed now.

bluss · 2016-12-07T20:39:51Z

@bors r+

bors · 2016-12-07T20:39:52Z

📌 Commit c8d73ea has been approved by bluss

bors · 2016-12-08T19:08:50Z

⌛ Testing commit c8d73ea with merge 7d4c55a...

notriddle · 2016-12-08T19:37:01Z

Why did the Travis build fail?

ghost · 2016-12-08T19:43:51Z

@notriddle Due to an unrelated problem. Looks like all builds have been failing for the past day or two.
https://travis-ci.org/rust-lang/rust/builds

bors · 2016-12-08T20:21:58Z

💔 Test failed - auto-linux-64-x-android-t

Since merge_sort is generic and collapse isn't, that means calls to collapse won't be inlined. inlined. Therefore, we must stick an `#[inline]` above `fn collapse`.

bluss · 2016-12-08T21:41:42Z

@bors r+

bors · 2016-12-08T21:41:44Z

📌 Commit c0e150a has been approved by bluss

bors · 2016-12-09T09:55:25Z

⌛ Testing commit c0e150a with merge dedd985...

@huonw

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](https://github.com/dlang/phobos/blob/fd518eb310a9494cccf28c54892542b052c49669/std/algorithm/sorting.d#L2062). The results were a bit disappointing. It seems bad performance is due to complex galloping procedures in hot loops. Galloping noticeably improves performance on partially sorted inputs, but worsens it on random ones. #### The new algorithm Choosing the best algorithm is not easy. Plain merge sort is bad on partially sorted inputs. TimSort is bad on random inputs and block sort is even worse. However, if we take the main ideas from TimSort (intelligent merging strategy of sorted runs) and drop galloping, then we'll have great performance on random inputs and it won't be bad on partially sorted inputs either. That is exactly what this new algorithm does. I can't call it TimSort, since it steals just a few of it's ideas. Complete TimSort would be a much more complex and elaborate implementation. In case we in the future figure out how to incorporate more of it's ideas into this implementation without crippling performance on random inputs, it's going to be very easy to extend. I also did several other minor improvements, like reworked insertion sort to make it faster. There are also new, more thorough benchmarks and panic safety tests. The final code is not terribly complex and has less unsafe code than I anticipated, but there's still plenty of it that should be carefully reviewed. I did my best at documenting non-obvious code. I'd like to notify several people of this PR, since they might be interested and have useful insights: 1. @huonw because he wrote the [original merge sort](#11064). 2. @alexcrichton because he was involved in multiple discussions of it. 3. @veddan because he wrote [introsort](https://github.com/veddan/rust-introsort) in Rust. 4. @notriddle because he wrote [TimSort](https://github.com/notriddle/rust-timsort) in Rust. 5. @bluss because he had an attempt at writing WikiSort in Rust. 6. @gnzlbg, @rkruppe, and @mark-i-m because they were involved in discussion #36318. **P.S.** [quickersort](https://github.com/notriddle/quickersort) describes itself as being universally [faster](https://github.com/notriddle/quickersort/blob/master/perf.txt) than the standard sort, which is true. However, if this PR gets merged, things might [change](https://gist.github.com/stjepang/b9f0c3eaa0e1f1280b61b963dae19a30) a bit. ;)

bors · 2016-12-09T12:47:32Z

tbelaire · 2016-12-14T19:24:17Z

src/libcollections/slice.rs

+/// satisfied, for every `i` in `0 .. runs.len() - 2`:
+///
+/// 1. `runs[i].len > runs[i + 1].len`
+/// 2. `runs[i].len > runs[i + 1].len + runs[i + 2].len`


Uh, I think there's a typo in your invariant?
From the timsort post

What turned out to be a good compromise maintains two invariants on the
stack entries, where A, B and C are the lengths of the three righmost not-yet
merged slices:

A > B+C

B > C

But here you have

A > B

A > B + C
which seems incorrect.

Good catch, there's a minor off-by-one error in the comment. However, probably not for the reason you have in mind :)

Take a look at fn collapse - it's equivalent to the corrected and formally verified mergeCollapse presented in the paper (link). Let's trust that one instead of the original TimSort post from 2002.

I suggest rewriting the comment like this:

/// satisfied: /// /// 1. for every `i` in `1..runs.len()`: `runs[i - 1].len > runs[i].len` /// 2. for every `i` in `2..runs.len()`: `runs[i - 2].len > runs[i - 1].len + runs[i].len`

These invariants are exactly what fn collapse is enforcing.
What do you think - does that look good to you?

TomOnTime · 2016-12-15T00:12:33Z

I'm not usually this particular about English grammar, but the sentence "Performs less comparisons on both random and partially sorted inputs." should be changed s/less/fewer/g. Less refers to non-countable items (I'm less happy today than yesterday). Fewer refers to countable items ("Mary has fewer apples than John.").

mark-i-m · 2016-12-15T00:15:58Z

Lol, grammar makes me fewer happy :P

ghost · 2016-12-15T00:49:33Z

Heh, fixed :) Feel free to point out any grammar mistakes in comments within the code.

alexcrichton · 2017-03-17T20:56:05Z

For those interested, the pdqsort implementation is here: #40601

bluss suggested changes Dec 6, 2016

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bluss reviewed Dec 6, 2016

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apasel422 reviewed Dec 6, 2016

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gereeter reviewed Dec 6, 2016

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Stebalien reviewed Dec 6, 2016

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bluss approved these changes Dec 7, 2016

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mark-i-m reviewed Dec 7, 2016

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bluss added the relnotes Marks issues that should be documented in the release notes of the next release. label Dec 7, 2016

ghost mentioned this pull request Dec 8, 2016

Buildbot failing due to a link error on arm-linux-androideabi #38248

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Inline nested fn collapse

c0e150a

Since merge_sort is generic and collapse isn't, that means calls to collapse won't be inlined. inlined. Therefore, we must stick an `#[inline]` above `fn collapse`.

bors merged commit c0e150a into rust-lang:master Dec 9, 2016

ghost deleted the faster-sort-algorithm branch December 9, 2016 13:01

tbelaire reviewed Dec 14, 2016

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ysbaddaden mentioned this pull request Dec 14, 2016

Add intro sort to Array crystal-lang/crystal#3514

Merged

ghost mentioned this pull request Dec 21, 2016

Reconsidering the recent changes in sort guarantees #38524

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alexcrichton mentioned this pull request Dec 29, 2016

iwls-0.0.2 fails its test suite in Rust 1.15 beta #38685

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mgattozzi mentioned this pull request Jan 17, 2018

slice::sort_by and slice::unstable_sort_by have bad performance when targeting wasm rustwasm/team#27

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dralley mentioned this pull request Sep 26, 2019

Current sorting algorithm isn't stable RustPython/RustPython#578

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leeoniya mentioned this pull request Apr 2, 2020

Use in-place radix sort instead of quicksort mourner/flatbush#31

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coderb mentioned this pull request Apr 4, 2022

Please add a stable sorting algorithm to the base library (eg timsort or rust-style) dotnet/runtime#67546

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ghost mentioned this pull request May 30, 2022

Implement a faster stable sort algorithm #90545

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Implement a faster sort algorithm #38192

Implement a faster sort algorithm #38192

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ghost commented Dec 6, 2016 • edited by ghost Loading

Summary

Background

The new algorithm

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A brief description of what perf.txt is showing you

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