1//! Parallel quicksort.
2//!
3//! This implementation is copied verbatim from `std::slice::sort_unstable` and then parallelized.
4//! The only difference from the original is that calls to `recurse` are executed in parallel using
5//! `rayon_core::join`.
6
7use std::marker::PhantomData;
8use std::mem::{self, MaybeUninit};
9use std::ptr;
10
11/// When dropped, copies from `src` into `dest`.
12#[must_use]
13struct CopyOnDrop<'a, T> {
14 src: *const T,
15 dest: *mut T,
16 /// `src` is often a local pointer here, make sure we have appropriate
17 /// PhantomData so that dropck can protect us.
18 marker: PhantomData<&'a mut T>,
19}
20
21impl<'a, T> CopyOnDrop<'a, T> {
22 /// Construct from a source pointer and a destination
23 /// Assumes dest lives longer than src, since there is no easy way to
24 /// copy down lifetime information from another pointer
25 unsafe fn new(src: &'a T, dest: *mut T) -> Self {
26 CopyOnDrop {
27 src,
28 dest,
29 marker: PhantomData,
30 }
31 }
32}
33
34impl<T> Drop for CopyOnDrop<'_, T> {
35 fn drop(&mut self) {
36 // SAFETY: This is a helper class.
37 // Please refer to its usage for correctness.
38 // Namely, one must be sure that `src` and `dst` does not overlap as required by `ptr::copy_nonoverlapping`.
39 unsafe {
40 ptr::copy_nonoverlapping(self.src, self.dest, count:1);
41 }
42 }
43}
44
45/// Shifts the first element to the right until it encounters a greater or equal element.
46fn shift_head<T, F>(v: &mut [T], is_less: &F)
47where
48 F: Fn(&T, &T) -> bool,
49{
50 let len = v.len();
51 // SAFETY: The unsafe operations below involves indexing without a bounds check (by offsetting a
52 // pointer) and copying memory (`ptr::copy_nonoverlapping`).
53 //
54 // a. Indexing:
55 // 1. We checked the size of the array to >=2.
56 // 2. All the indexing that we will do is always between {0 <= index < len} at most.
57 //
58 // b. Memory copying
59 // 1. We are obtaining pointers to references which are guaranteed to be valid.
60 // 2. They cannot overlap because we obtain pointers to difference indices of the slice.
61 // Namely, `i` and `i-1`.
62 // 3. If the slice is properly aligned, the elements are properly aligned.
63 // It is the caller's responsibility to make sure the slice is properly aligned.
64 //
65 // See comments below for further detail.
66 unsafe {
67 // If the first two elements are out-of-order...
68 if len >= 2 && is_less(v.get_unchecked(1), v.get_unchecked(0)) {
69 // Read the first element into a stack-allocated variable. If a following comparison
70 // operation panics, `hole` will get dropped and automatically write the element back
71 // into the slice.
72 let tmp = mem::ManuallyDrop::new(ptr::read(v.get_unchecked(0)));
73 let v = v.as_mut_ptr();
74 let mut hole = CopyOnDrop::new(&*tmp, v.add(1));
75 ptr::copy_nonoverlapping(v.add(1), v.add(0), 1);
76
77 for i in 2..len {
78 if !is_less(&*v.add(i), &*tmp) {
79 break;
80 }
81
82 // Move `i`-th element one place to the left, thus shifting the hole to the right.
83 ptr::copy_nonoverlapping(v.add(i), v.add(i - 1), 1);
84 hole.dest = v.add(i);
85 }
86 // `hole` gets dropped and thus copies `tmp` into the remaining hole in `v`.
87 }
88 }
89}
90
91/// Shifts the last element to the left until it encounters a smaller or equal element.
92fn shift_tail<T, F>(v: &mut [T], is_less: &F)
93where
94 F: Fn(&T, &T) -> bool,
95{
96 let len = v.len();
97 // SAFETY: The unsafe operations below involves indexing without a bound check (by offsetting a
98 // pointer) and copying memory (`ptr::copy_nonoverlapping`).
99 //
100 // a. Indexing:
101 // 1. We checked the size of the array to >= 2.
102 // 2. All the indexing that we will do is always between `0 <= index < len-1` at most.
103 //
104 // b. Memory copying
105 // 1. We are obtaining pointers to references which are guaranteed to be valid.
106 // 2. They cannot overlap because we obtain pointers to difference indices of the slice.
107 // Namely, `i` and `i+1`.
108 // 3. If the slice is properly aligned, the elements are properly aligned.
109 // It is the caller's responsibility to make sure the slice is properly aligned.
110 //
111 // See comments below for further detail.
112 unsafe {
113 // If the last two elements are out-of-order...
114 if len >= 2 && is_less(v.get_unchecked(len - 1), v.get_unchecked(len - 2)) {
115 // Read the last element into a stack-allocated variable. If a following comparison
116 // operation panics, `hole` will get dropped and automatically write the element back
117 // into the slice.
118 let tmp = mem::ManuallyDrop::new(ptr::read(v.get_unchecked(len - 1)));
119 let v = v.as_mut_ptr();
120 let mut hole = CopyOnDrop::new(&*tmp, v.add(len - 2));
121 ptr::copy_nonoverlapping(v.add(len - 2), v.add(len - 1), 1);
122
123 for i in (0..len - 2).rev() {
124 if !is_less(&*tmp, &*v.add(i)) {
125 break;
126 }
127
128 // Move `i`-th element one place to the right, thus shifting the hole to the left.
129 ptr::copy_nonoverlapping(v.add(i), v.add(i + 1), 1);
130 hole.dest = v.add(i);
131 }
132 // `hole` gets dropped and thus copies `tmp` into the remaining hole in `v`.
133 }
134 }
135}
136
137/// Partially sorts a slice by shifting several out-of-order elements around.
138///
139/// Returns `true` if the slice is sorted at the end. This function is *O*(*n*) worst-case.
140#[cold]
141fn partial_insertion_sort<T, F>(v: &mut [T], is_less: &F) -> bool
142where
143 F: Fn(&T, &T) -> bool,
144{
145 // Maximum number of adjacent out-of-order pairs that will get shifted.
146 const MAX_STEPS: usize = 5;
147 // If the slice is shorter than this, don't shift any elements.
148 const SHORTEST_SHIFTING: usize = 50;
149
150 let len = v.len();
151 let mut i = 1;
152
153 for _ in 0..MAX_STEPS {
154 // SAFETY: We already explicitly did the bound checking with `i < len`.
155 // All our subsequent indexing is only in the range `0 <= index < len`
156 unsafe {
157 // Find the next pair of adjacent out-of-order elements.
158 while i < len && !is_less(v.get_unchecked(i), v.get_unchecked(i - 1)) {
159 i += 1;
160 }
161 }
162
163 // Are we done?
164 if i == len {
165 return true;
166 }
167
168 // Don't shift elements on short arrays, that has a performance cost.
169 if len < SHORTEST_SHIFTING {
170 return false;
171 }
172
173 // Swap the found pair of elements. This puts them in correct order.
174 v.swap(i - 1, i);
175
176 // Shift the smaller element to the left.
177 shift_tail(&mut v[..i], is_less);
178 // Shift the greater element to the right.
179 shift_head(&mut v[i..], is_less);
180 }
181
182 // Didn't manage to sort the slice in the limited number of steps.
183 false
184}
185
186/// Sorts a slice using insertion sort, which is *O*(*n*^2) worst-case.
187fn insertion_sort<T, F>(v: &mut [T], is_less: &F)
188where
189 F: Fn(&T, &T) -> bool,
190{
191 for i: usize in 1..v.len() {
192 shift_tail(&mut v[..i + 1], is_less);
193 }
194}
195
196/// Sorts `v` using heapsort, which guarantees *O*(*n* \* log(*n*)) worst-case.
197#[cold]
198fn heapsort<T, F>(v: &mut [T], is_less: &F)
199where
200 F: Fn(&T, &T) -> bool,
201{
202 // This binary heap respects the invariant `parent >= child`.
203 let sift_down = |v: &mut [T], mut node| {
204 loop {
205 // Children of `node`.
206 let mut child = 2 * node + 1;
207 if child >= v.len() {
208 break;
209 }
210
211 // Choose the greater child.
212 if child + 1 < v.len() && is_less(&v[child], &v[child + 1]) {
213 child += 1;
214 }
215
216 // Stop if the invariant holds at `node`.
217 if !is_less(&v[node], &v[child]) {
218 break;
219 }
220
221 // Swap `node` with the greater child, move one step down, and continue sifting.
222 v.swap(node, child);
223 node = child;
224 }
225 };
226
227 // Build the heap in linear time.
228 for i in (0..v.len() / 2).rev() {
229 sift_down(v, i);
230 }
231
232 // Pop maximal elements from the heap.
233 for i in (1..v.len()).rev() {
234 v.swap(0, i);
235 sift_down(&mut v[..i], 0);
236 }
237}
238
239/// Partitions `v` into elements smaller than `pivot`, followed by elements greater than or equal
240/// to `pivot`.
241///
242/// Returns the number of elements smaller than `pivot`.
243///
244/// Partitioning is performed block-by-block in order to minimize the cost of branching operations.
245/// This idea is presented in the [BlockQuicksort][pdf] paper.
246///
247/// [pdf]: https://drops.dagstuhl.de/opus/volltexte/2016/6389/pdf/LIPIcs-ESA-2016-38.pdf
248fn partition_in_blocks<T, F>(v: &mut [T], pivot: &T, is_less: &F) -> usize
249where
250 F: Fn(&T, &T) -> bool,
251{
252 // Number of elements in a typical block.
253 const BLOCK: usize = 128;
254
255 // The partitioning algorithm repeats the following steps until completion:
256 //
257 // 1. Trace a block from the left side to identify elements greater than or equal to the pivot.
258 // 2. Trace a block from the right side to identify elements smaller than the pivot.
259 // 3. Exchange the identified elements between the left and right side.
260 //
261 // We keep the following variables for a block of elements:
262 //
263 // 1. `block` - Number of elements in the block.
264 // 2. `start` - Start pointer into the `offsets` array.
265 // 3. `end` - End pointer into the `offsets` array.
266 // 4. `offsets - Indices of out-of-order elements within the block.
267
268 // The current block on the left side (from `l` to `l.add(block_l)`).
269 let mut l = v.as_mut_ptr();
270 let mut block_l = BLOCK;
271 let mut start_l = ptr::null_mut();
272 let mut end_l = ptr::null_mut();
273 let mut offsets_l = [MaybeUninit::<u8>::uninit(); BLOCK];
274
275 // The current block on the right side (from `r.sub(block_r)` to `r`).
276 // SAFETY: The documentation for .add() specifically mention that `vec.as_ptr().add(vec.len())` is always safe`
277 let mut r = unsafe { l.add(v.len()) };
278 let mut block_r = BLOCK;
279 let mut start_r = ptr::null_mut();
280 let mut end_r = ptr::null_mut();
281 let mut offsets_r = [MaybeUninit::<u8>::uninit(); BLOCK];
282
283 // FIXME: When we get VLAs, try creating one array of length `min(v.len(), 2 * BLOCK)` rather
284 // than two fixed-size arrays of length `BLOCK`. VLAs might be more cache-efficient.
285
286 // Returns the number of elements between pointers `l` (inclusive) and `r` (exclusive).
287 fn width<T>(l: *mut T, r: *mut T) -> usize {
288 assert!(mem::size_of::<T>() > 0);
289 // FIXME: this should *likely* use `offset_from`, but more
290 // investigation is needed (including running tests in miri).
291 // TODO unstable: (r.addr() - l.addr()) / mem::size_of::<T>()
292 (r as usize - l as usize) / mem::size_of::<T>()
293 }
294
295 loop {
296 // We are done with partitioning block-by-block when `l` and `r` get very close. Then we do
297 // some patch-up work in order to partition the remaining elements in between.
298 let is_done = width(l, r) <= 2 * BLOCK;
299
300 if is_done {
301 // Number of remaining elements (still not compared to the pivot).
302 let mut rem = width(l, r);
303 if start_l < end_l || start_r < end_r {
304 rem -= BLOCK;
305 }
306
307 // Adjust block sizes so that the left and right block don't overlap, but get perfectly
308 // aligned to cover the whole remaining gap.
309 if start_l < end_l {
310 block_r = rem;
311 } else if start_r < end_r {
312 block_l = rem;
313 } else {
314 // There were the same number of elements to switch on both blocks during the last
315 // iteration, so there are no remaining elements on either block. Cover the remaining
316 // items with roughly equally-sized blocks.
317 block_l = rem / 2;
318 block_r = rem - block_l;
319 }
320 debug_assert!(block_l <= BLOCK && block_r <= BLOCK);
321 debug_assert!(width(l, r) == block_l + block_r);
322 }
323
324 if start_l == end_l {
325 // Trace `block_l` elements from the left side.
326 // TODO unstable: start_l = MaybeUninit::slice_as_mut_ptr(&mut offsets_l);
327 start_l = offsets_l.as_mut_ptr() as *mut u8;
328 end_l = start_l;
329 let mut elem = l;
330
331 for i in 0..block_l {
332 // SAFETY: The unsafety operations below involve the usage of the `offset`.
333 // According to the conditions required by the function, we satisfy them because:
334 // 1. `offsets_l` is stack-allocated, and thus considered separate allocated object.
335 // 2. The function `is_less` returns a `bool`.
336 // Casting a `bool` will never overflow `isize`.
337 // 3. We have guaranteed that `block_l` will be `<= BLOCK`.
338 // Plus, `end_l` was initially set to the begin pointer of `offsets_` which was declared on the stack.
339 // Thus, we know that even in the worst case (all invocations of `is_less` returns false) we will only be at most 1 byte pass the end.
340 // Another unsafety operation here is dereferencing `elem`.
341 // However, `elem` was initially the begin pointer to the slice which is always valid.
342 unsafe {
343 // Branchless comparison.
344 *end_l = i as u8;
345 end_l = end_l.offset(!is_less(&*elem, pivot) as isize);
346 elem = elem.offset(1);
347 }
348 }
349 }
350
351 if start_r == end_r {
352 // Trace `block_r` elements from the right side.
353 // TODO unstable: start_r = MaybeUninit::slice_as_mut_ptr(&mut offsets_r);
354 start_r = offsets_r.as_mut_ptr() as *mut u8;
355 end_r = start_r;
356 let mut elem = r;
357
358 for i in 0..block_r {
359 // SAFETY: The unsafety operations below involve the usage of the `offset`.
360 // According to the conditions required by the function, we satisfy them because:
361 // 1. `offsets_r` is stack-allocated, and thus considered separate allocated object.
362 // 2. The function `is_less` returns a `bool`.
363 // Casting a `bool` will never overflow `isize`.
364 // 3. We have guaranteed that `block_r` will be `<= BLOCK`.
365 // Plus, `end_r` was initially set to the begin pointer of `offsets_` which was declared on the stack.
366 // Thus, we know that even in the worst case (all invocations of `is_less` returns true) we will only be at most 1 byte pass the end.
367 // Another unsafety operation here is dereferencing `elem`.
368 // However, `elem` was initially `1 * sizeof(T)` past the end and we decrement it by `1 * sizeof(T)` before accessing it.
369 // Plus, `block_r` was asserted to be less than `BLOCK` and `elem` will therefore at most be pointing to the beginning of the slice.
370 unsafe {
371 // Branchless comparison.
372 elem = elem.offset(-1);
373 *end_r = i as u8;
374 end_r = end_r.offset(is_less(&*elem, pivot) as isize);
375 }
376 }
377 }
378
379 // Number of out-of-order elements to swap between the left and right side.
380 let count = Ord::min(width(start_l, end_l), width(start_r, end_r));
381
382 if count > 0 {
383 macro_rules! left {
384 () => {
385 l.offset(*start_l as isize)
386 };
387 }
388 macro_rules! right {
389 () => {
390 r.offset(-(*start_r as isize) - 1)
391 };
392 }
393
394 // Instead of swapping one pair at the time, it is more efficient to perform a cyclic
395 // permutation. This is not strictly equivalent to swapping, but produces a similar
396 // result using fewer memory operations.
397
398 // SAFETY: The use of `ptr::read` is valid because there is at least one element in
399 // both `offsets_l` and `offsets_r`, so `left!` is a valid pointer to read from.
400 //
401 // The uses of `left!` involve calls to `offset` on `l`, which points to the
402 // beginning of `v`. All the offsets pointed-to by `start_l` are at most `block_l`, so
403 // these `offset` calls are safe as all reads are within the block. The same argument
404 // applies for the uses of `right!`.
405 //
406 // The calls to `start_l.offset` are valid because there are at most `count-1` of them,
407 // plus the final one at the end of the unsafe block, where `count` is the minimum number
408 // of collected offsets in `offsets_l` and `offsets_r`, so there is no risk of there not
409 // being enough elements. The same reasoning applies to the calls to `start_r.offset`.
410 //
411 // The calls to `copy_nonoverlapping` are safe because `left!` and `right!` are guaranteed
412 // not to overlap, and are valid because of the reasoning above.
413 unsafe {
414 let tmp = ptr::read(left!());
415 ptr::copy_nonoverlapping(right!(), left!(), 1);
416
417 for _ in 1..count {
418 start_l = start_l.offset(1);
419 ptr::copy_nonoverlapping(left!(), right!(), 1);
420 start_r = start_r.offset(1);
421 ptr::copy_nonoverlapping(right!(), left!(), 1);
422 }
423
424 ptr::copy_nonoverlapping(&tmp, right!(), 1);
425 mem::forget(tmp);
426 start_l = start_l.offset(1);
427 start_r = start_r.offset(1);
428 }
429 }
430
431 if start_l == end_l {
432 // All out-of-order elements in the left block were moved. Move to the next block.
433
434 // block-width-guarantee
435 // SAFETY: if `!is_done` then the slice width is guaranteed to be at least `2*BLOCK` wide. There
436 // are at most `BLOCK` elements in `offsets_l` because of its size, so the `offset` operation is
437 // safe. Otherwise, the debug assertions in the `is_done` case guarantee that
438 // `width(l, r) == block_l + block_r`, namely, that the block sizes have been adjusted to account
439 // for the smaller number of remaining elements.
440 l = unsafe { l.add(block_l) };
441 }
442
443 if start_r == end_r {
444 // All out-of-order elements in the right block were moved. Move to the previous block.
445
446 // SAFETY: Same argument as [block-width-guarantee]. Either this is a full block `2*BLOCK`-wide,
447 // or `block_r` has been adjusted for the last handful of elements.
448 r = unsafe { r.offset(-(block_r as isize)) };
449 }
450
451 if is_done {
452 break;
453 }
454 }
455
456 // All that remains now is at most one block (either the left or the right) with out-of-order
457 // elements that need to be moved. Such remaining elements can be simply shifted to the end
458 // within their block.
459
460 if start_l < end_l {
461 // The left block remains.
462 // Move its remaining out-of-order elements to the far right.
463 debug_assert_eq!(width(l, r), block_l);
464 while start_l < end_l {
465 // remaining-elements-safety
466 // SAFETY: while the loop condition holds there are still elements in `offsets_l`, so it
467 // is safe to point `end_l` to the previous element.
468 //
469 // The `ptr::swap` is safe if both its arguments are valid for reads and writes:
470 // - Per the debug assert above, the distance between `l` and `r` is `block_l`
471 // elements, so there can be at most `block_l` remaining offsets between `start_l`
472 // and `end_l`. This means `r` will be moved at most `block_l` steps back, which
473 // makes the `r.offset` calls valid (at that point `l == r`).
474 // - `offsets_l` contains valid offsets into `v` collected during the partitioning of
475 // the last block, so the `l.offset` calls are valid.
476 unsafe {
477 end_l = end_l.offset(-1);
478 ptr::swap(l.offset(*end_l as isize), r.offset(-1));
479 r = r.offset(-1);
480 }
481 }
482 width(v.as_mut_ptr(), r)
483 } else if start_r < end_r {
484 // The right block remains.
485 // Move its remaining out-of-order elements to the far left.
486 debug_assert_eq!(width(l, r), block_r);
487 while start_r < end_r {
488 // SAFETY: See the reasoning in [remaining-elements-safety].
489 unsafe {
490 end_r = end_r.offset(-1);
491 ptr::swap(l, r.offset(-(*end_r as isize) - 1));
492 l = l.offset(1);
493 }
494 }
495 width(v.as_mut_ptr(), l)
496 } else {
497 // Nothing else to do, we're done.
498 width(v.as_mut_ptr(), l)
499 }
500}
501
502/// Partitions `v` into elements smaller than `v[pivot]`, followed by elements greater than or
503/// equal to `v[pivot]`.
504///
505/// Returns a tuple of:
506///
507/// 1. Number of elements smaller than `v[pivot]`.
508/// 2. True if `v` was already partitioned.
509fn partition<T, F>(v: &mut [T], pivot: usize, is_less: &F) -> (usize, bool)
510where
511 F: Fn(&T, &T) -> bool,
512{
513 let (mid, was_partitioned) = {
514 // Place the pivot at the beginning of slice.
515 v.swap(0, pivot);
516 let (pivot, v) = v.split_at_mut(1);
517 let pivot = &mut pivot[0];
518
519 // Read the pivot into a stack-allocated variable for efficiency. If a following comparison
520 // operation panics, the pivot will be automatically written back into the slice.
521
522 // SAFETY: `pivot` is a reference to the first element of `v`, so `ptr::read` is safe.
523 let tmp = mem::ManuallyDrop::new(unsafe { ptr::read(pivot) });
524 let _pivot_guard = unsafe { CopyOnDrop::new(&*tmp, pivot) };
525 let pivot = &*tmp;
526
527 // Find the first pair of out-of-order elements.
528 let mut l = 0;
529 let mut r = v.len();
530
531 // SAFETY: The unsafety below involves indexing an array.
532 // For the first one: We already do the bounds checking here with `l < r`.
533 // For the second one: We initially have `l == 0` and `r == v.len()` and we checked that `l < r` at every indexing operation.
534 // From here we know that `r` must be at least `r == l` which was shown to be valid from the first one.
535 unsafe {
536 // Find the first element greater than or equal to the pivot.
537 while l < r && is_less(v.get_unchecked(l), pivot) {
538 l += 1;
539 }
540
541 // Find the last element smaller that the pivot.
542 while l < r && !is_less(v.get_unchecked(r - 1), pivot) {
543 r -= 1;
544 }
545 }
546
547 (
548 l + partition_in_blocks(&mut v[l..r], pivot, is_less),
549 l >= r,
550 )
551
552 // `_pivot_guard` goes out of scope and writes the pivot (which is a stack-allocated
553 // variable) back into the slice where it originally was. This step is critical in ensuring
554 // safety!
555 };
556
557 // Place the pivot between the two partitions.
558 v.swap(0, mid);
559
560 (mid, was_partitioned)
561}
562
563/// Partitions `v` into elements equal to `v[pivot]` followed by elements greater than `v[pivot]`.
564///
565/// Returns the number of elements equal to the pivot. It is assumed that `v` does not contain
566/// elements smaller than the pivot.
567fn partition_equal<T, F>(v: &mut [T], pivot: usize, is_less: &F) -> usize
568where
569 F: Fn(&T, &T) -> bool,
570{
571 // Place the pivot at the beginning of slice.
572 v.swap(0, pivot);
573 let (pivot, v) = v.split_at_mut(1);
574 let pivot = &mut pivot[0];
575
576 // Read the pivot into a stack-allocated variable for efficiency. If a following comparison
577 // operation panics, the pivot will be automatically written back into the slice.
578 // SAFETY: The pointer here is valid because it is obtained from a reference to a slice.
579 let tmp = mem::ManuallyDrop::new(unsafe { ptr::read(pivot) });
580 let _pivot_guard = unsafe { CopyOnDrop::new(&*tmp, pivot) };
581 let pivot = &*tmp;
582
583 // Now partition the slice.
584 let mut l = 0;
585 let mut r = v.len();
586 loop {
587 // SAFETY: The unsafety below involves indexing an array.
588 // For the first one: We already do the bounds checking here with `l < r`.
589 // For the second one: We initially have `l == 0` and `r == v.len()` and we checked that `l < r` at every indexing operation.
590 // From here we know that `r` must be at least `r == l` which was shown to be valid from the first one.
591 unsafe {
592 // Find the first element greater than the pivot.
593 while l < r && !is_less(pivot, v.get_unchecked(l)) {
594 l += 1;
595 }
596
597 // Find the last element equal to the pivot.
598 while l < r && is_less(pivot, v.get_unchecked(r - 1)) {
599 r -= 1;
600 }
601
602 // Are we done?
603 if l >= r {
604 break;
605 }
606
607 // Swap the found pair of out-of-order elements.
608 r -= 1;
609 let ptr = v.as_mut_ptr();
610 ptr::swap(ptr.add(l), ptr.add(r));
611 l += 1;
612 }
613 }
614
615 // We found `l` elements equal to the pivot. Add 1 to account for the pivot itself.
616 l + 1
617
618 // `_pivot_guard` goes out of scope and writes the pivot (which is a stack-allocated variable)
619 // back into the slice where it originally was. This step is critical in ensuring safety!
620}
621
622/// Scatters some elements around in an attempt to break patterns that might cause imbalanced
623/// partitions in quicksort.
624#[cold]
625fn break_patterns<T>(v: &mut [T]) {
626 let len = v.len();
627 if len >= 8 {
628 // Pseudorandom number generator from the "Xorshift RNGs" paper by George Marsaglia.
629 let mut random = len as u32;
630 let mut gen_u32 = || {
631 random ^= random << 13;
632 random ^= random >> 17;
633 random ^= random << 5;
634 random
635 };
636 let mut gen_usize = || {
637 if usize::BITS <= 32 {
638 gen_u32() as usize
639 } else {
640 (((gen_u32() as u64) << 32) | (gen_u32() as u64)) as usize
641 }
642 };
643
644 // Take random numbers modulo this number.
645 // The number fits into `usize` because `len` is not greater than `isize::MAX`.
646 let modulus = len.next_power_of_two();
647
648 // Some pivot candidates will be in the nearby of this index. Let's randomize them.
649 let pos = len / 4 * 2;
650
651 for i in 0..3 {
652 // Generate a random number modulo `len`. However, in order to avoid costly operations
653 // we first take it modulo a power of two, and then decrease by `len` until it fits
654 // into the range `[0, len - 1]`.
655 let mut other = gen_usize() & (modulus - 1);
656
657 // `other` is guaranteed to be less than `2 * len`.
658 if other >= len {
659 other -= len;
660 }
661
662 v.swap(pos - 1 + i, other);
663 }
664 }
665}
666
667/// Chooses a pivot in `v` and returns the index and `true` if the slice is likely already sorted.
668///
669/// Elements in `v` might be reordered in the process.
670fn choose_pivot<T, F>(v: &mut [T], is_less: &F) -> (usize, bool)
671where
672 F: Fn(&T, &T) -> bool,
673{
674 // Minimum length to choose the median-of-medians method.
675 // Shorter slices use the simple median-of-three method.
676 const SHORTEST_MEDIAN_OF_MEDIANS: usize = 50;
677 // Maximum number of swaps that can be performed in this function.
678 const MAX_SWAPS: usize = 4 * 3;
679
680 let len = v.len();
681
682 // Three indices near which we are going to choose a pivot.
683 #[allow(clippy::identity_op)]
684 let mut a = len / 4 * 1;
685 let mut b = len / 4 * 2;
686 let mut c = len / 4 * 3;
687
688 // Counts the total number of swaps we are about to perform while sorting indices.
689 let mut swaps = 0;
690
691 if len >= 8 {
692 // Swaps indices so that `v[a] <= v[b]`.
693 // SAFETY: `len >= 8` so there are at least two elements in the neighborhoods of
694 // `a`, `b` and `c`. This means the three calls to `sort_adjacent` result in
695 // corresponding calls to `sort3` with valid 3-item neighborhoods around each
696 // pointer, which in turn means the calls to `sort2` are done with valid
697 // references. Thus the `v.get_unchecked` calls are safe, as is the `ptr::swap`
698 // call.
699 let mut sort2 = |a: &mut usize, b: &mut usize| unsafe {
700 if is_less(v.get_unchecked(*b), v.get_unchecked(*a)) {
701 ptr::swap(a, b);
702 swaps += 1;
703 }
704 };
705
706 // Swaps indices so that `v[a] <= v[b] <= v[c]`.
707 let mut sort3 = |a: &mut usize, b: &mut usize, c: &mut usize| {
708 sort2(a, b);
709 sort2(b, c);
710 sort2(a, b);
711 };
712
713 if len >= SHORTEST_MEDIAN_OF_MEDIANS {
714 // Finds the median of `v[a - 1], v[a], v[a + 1]` and stores the index into `a`.
715 let mut sort_adjacent = |a: &mut usize| {
716 let tmp = *a;
717 sort3(&mut (tmp - 1), a, &mut (tmp + 1));
718 };
719
720 // Find medians in the neighborhoods of `a`, `b`, and `c`.
721 sort_adjacent(&mut a);
722 sort_adjacent(&mut b);
723 sort_adjacent(&mut c);
724 }
725
726 // Find the median among `a`, `b`, and `c`.
727 sort3(&mut a, &mut b, &mut c);
728 }
729
730 if swaps < MAX_SWAPS {
731 (b, swaps == 0)
732 } else {
733 // The maximum number of swaps was performed. Chances are the slice is descending or mostly
734 // descending, so reversing will probably help sort it faster.
735 v.reverse();
736 (len - 1 - b, true)
737 }
738}
739
740/// Sorts `v` recursively.
741///
742/// If the slice had a predecessor in the original array, it is specified as `pred`.
743///
744/// `limit` is the number of allowed imbalanced partitions before switching to `heapsort`. If zero,
745/// this function will immediately switch to heapsort.
746fn recurse<'a, T, F>(mut v: &'a mut [T], is_less: &F, mut pred: Option<&'a mut T>, mut limit: u32)
747where
748 T: Send,
749 F: Fn(&T, &T) -> bool + Sync,
750{
751 // Slices of up to this length get sorted using insertion sort.
752 const MAX_INSERTION: usize = 20;
753 // If both partitions are up to this length, we continue sequentially. This number is as small
754 // as possible but so that the overhead of Rayon's task scheduling is still negligible.
755 const MAX_SEQUENTIAL: usize = 2000;
756
757 // True if the last partitioning was reasonably balanced.
758 let mut was_balanced = true;
759 // True if the last partitioning didn't shuffle elements (the slice was already partitioned).
760 let mut was_partitioned = true;
761
762 loop {
763 let len = v.len();
764
765 // Very short slices get sorted using insertion sort.
766 if len <= MAX_INSERTION {
767 insertion_sort(v, is_less);
768 return;
769 }
770
771 // If too many bad pivot choices were made, simply fall back to heapsort in order to
772 // guarantee `O(n * log(n))` worst-case.
773 if limit == 0 {
774 heapsort(v, is_less);
775 return;
776 }
777
778 // If the last partitioning was imbalanced, try breaking patterns in the slice by shuffling
779 // some elements around. Hopefully we'll choose a better pivot this time.
780 if !was_balanced {
781 break_patterns(v);
782 limit -= 1;
783 }
784
785 // Choose a pivot and try guessing whether the slice is already sorted.
786 let (pivot, likely_sorted) = choose_pivot(v, is_less);
787
788 // If the last partitioning was decently balanced and didn't shuffle elements, and if pivot
789 // selection predicts the slice is likely already sorted...
790 if was_balanced && was_partitioned && likely_sorted {
791 // Try identifying several out-of-order elements and shifting them to correct
792 // positions. If the slice ends up being completely sorted, we're done.
793 if partial_insertion_sort(v, is_less) {
794 return;
795 }
796 }
797
798 // If the chosen pivot is equal to the predecessor, then it's the smallest element in the
799 // slice. Partition the slice into elements equal to and elements greater than the pivot.
800 // This case is usually hit when the slice contains many duplicate elements.
801 if let Some(ref p) = pred {
802 if !is_less(p, &v[pivot]) {
803 let mid = partition_equal(v, pivot, is_less);
804
805 // Continue sorting elements greater than the pivot.
806 v = &mut v[mid..];
807 continue;
808 }
809 }
810
811 // Partition the slice.
812 let (mid, was_p) = partition(v, pivot, is_less);
813 was_balanced = Ord::min(mid, len - mid) >= len / 8;
814 was_partitioned = was_p;
815
816 // Split the slice into `left`, `pivot`, and `right`.
817 let (left, right) = v.split_at_mut(mid);
818 let (pivot, right) = right.split_at_mut(1);
819 let pivot = &mut pivot[0];
820
821 if Ord::max(left.len(), right.len()) <= MAX_SEQUENTIAL {
822 // Recurse into the shorter side only in order to minimize the total number of recursive
823 // calls and consume less stack space. Then just continue with the longer side (this is
824 // akin to tail recursion).
825 if left.len() < right.len() {
826 recurse(left, is_less, pred, limit);
827 v = right;
828 pred = Some(pivot);
829 } else {
830 recurse(right, is_less, Some(pivot), limit);
831 v = left;
832 }
833 } else {
834 // Sort the left and right half in parallel.
835 rayon_core::join(
836 || recurse(left, is_less, pred, limit),
837 || recurse(right, is_less, Some(pivot), limit),
838 );
839 break;
840 }
841 }
842}
843
844/// Sorts `v` using pattern-defeating quicksort in parallel.
845///
846/// The algorithm is unstable, in-place, and *O*(*n* \* log(*n*)) worst-case.
847pub(super) fn par_quicksort<T, F>(v: &mut [T], is_less: F)
848where
849 T: Send,
850 F: Fn(&T, &T) -> bool + Sync,
851{
852 // Sorting has no meaningful behavior on zero-sized types.
853 if mem::size_of::<T>() == 0 {
854 return;
855 }
856
857 // Limit the number of imbalanced partitions to `floor(log2(len)) + 1`.
858 let limit: u32 = usize::BITS - v.len().leading_zeros();
859
860 recurse(v, &is_less, pred:None, limit);
861}
862
863#[cfg(test)]
864mod tests {
865 use super::heapsort;
866 use rand::distributions::Uniform;
867 use rand::{thread_rng, Rng};
868
869 #[test]
870 fn test_heapsort() {
871 let rng = &mut thread_rng();
872
873 for len in (0..25).chain(500..501) {
874 for &modulus in &[5, 10, 100] {
875 let dist = Uniform::new(0, modulus);
876 for _ in 0..100 {
877 let v: Vec<i32> = rng.sample_iter(&dist).take(len).collect();
878
879 // Test heapsort using `<` operator.
880 let mut tmp = v.clone();
881 heapsort(&mut tmp, &|a, b| a < b);
882 assert!(tmp.windows(2).all(|w| w[0] <= w[1]));
883
884 // Test heapsort using `>` operator.
885 let mut tmp = v.clone();
886 heapsort(&mut tmp, &|a, b| a > b);
887 assert!(tmp.windows(2).all(|w| w[0] >= w[1]));
888 }
889 }
890 }
891
892 // Sort using a completely random comparison function.
893 // This will reorder the elements *somehow*, but won't panic.
894 let mut v: Vec<_> = (0..100).collect();
895 heapsort(&mut v, &|_, _| thread_rng().gen());
896 heapsort(&mut v, &|a, b| a < b);
897
898 for (i, &entry) in v.iter().enumerate() {
899 assert_eq!(entry, i);
900 }
901 }
902}
903