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authorValentin Popov <valentin@popov.link>2024-07-19 15:37:58 +0300
committerValentin Popov <valentin@popov.link>2024-07-19 15:37:58 +0300
commita990de90fe41456a23e58bd087d2f107d321f3a1 (patch)
tree15afc392522a9e85dc3332235e311b7d39352ea9 /vendor/rayon/src/slice/quicksort.rs
parent3d48cd3f81164bbfc1a755dc1d4a9a02f98c8ddd (diff)
downloadfparkan-a990de90fe41456a23e58bd087d2f107d321f3a1.tar.xz
fparkan-a990de90fe41456a23e58bd087d2f107d321f3a1.zip
Deleted vendor folder
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-rw-r--r--vendor/rayon/src/slice/quicksort.rs903
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diff --git a/vendor/rayon/src/slice/quicksort.rs b/vendor/rayon/src/slice/quicksort.rs
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--- a/vendor/rayon/src/slice/quicksort.rs
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-//! Parallel quicksort.
-//!
-//! This implementation is copied verbatim from `std::slice::sort_unstable` and then parallelized.
-//! The only difference from the original is that calls to `recurse` are executed in parallel using
-//! `rayon_core::join`.
-
-use std::cmp;
-use std::marker::PhantomData;
-use std::mem::{self, MaybeUninit};
-use std::ptr;
-
-/// When dropped, copies from `src` into `dest`.
-#[must_use]
-struct CopyOnDrop<'a, T> {
- src: *const T,
- dest: *mut T,
- /// `src` is often a local pointer here, make sure we have appropriate
- /// PhantomData so that dropck can protect us.
- marker: PhantomData<&'a mut T>,
-}
-
-impl<'a, T> CopyOnDrop<'a, T> {
- /// Construct from a source pointer and a destination
- /// Assumes dest lives longer than src, since there is no easy way to
- /// copy down lifetime information from another pointer
- unsafe fn new(src: &'a T, dest: *mut T) -> Self {
- CopyOnDrop {
- src,
- dest,
- marker: PhantomData,
- }
- }
-}
-
-impl<T> Drop for CopyOnDrop<'_, T> {
- fn drop(&mut self) {
- // SAFETY: This is a helper class.
- // Please refer to its usage for correctness.
- // Namely, one must be sure that `src` and `dst` does not overlap as required by `ptr::copy_nonoverlapping`.
- unsafe {
- ptr::copy_nonoverlapping(self.src, self.dest, 1);
- }
- }
-}
-
-/// Shifts the first element to the right until it encounters a greater or equal element.
-fn shift_head<T, F>(v: &mut [T], is_less: &F)
-where
- F: Fn(&T, &T) -> bool,
-{
- let len = v.len();
- // SAFETY: The unsafe operations below involves indexing without a bounds check (by offsetting a
- // pointer) and copying memory (`ptr::copy_nonoverlapping`).
- //
- // a. Indexing:
- // 1. We checked the size of the array to >=2.
- // 2. All the indexing that we will do is always between {0 <= index < len} at most.
- //
- // b. Memory copying
- // 1. We are obtaining pointers to references which are guaranteed to be valid.
- // 2. They cannot overlap because we obtain pointers to difference indices of the slice.
- // Namely, `i` and `i-1`.
- // 3. If the slice is properly aligned, the elements are properly aligned.
- // It is the caller's responsibility to make sure the slice is properly aligned.
- //
- // See comments below for further detail.
- unsafe {
- // If the first two elements are out-of-order...
- if len >= 2 && is_less(v.get_unchecked(1), v.get_unchecked(0)) {
- // Read the first element into a stack-allocated variable. If a following comparison
- // operation panics, `hole` will get dropped and automatically write the element back
- // into the slice.
- let tmp = mem::ManuallyDrop::new(ptr::read(v.get_unchecked(0)));
- let v = v.as_mut_ptr();
- let mut hole = CopyOnDrop::new(&*tmp, v.add(1));
- ptr::copy_nonoverlapping(v.add(1), v.add(0), 1);
-
- for i in 2..len {
- if !is_less(&*v.add(i), &*tmp) {
- break;
- }
-
- // Move `i`-th element one place to the left, thus shifting the hole to the right.
- ptr::copy_nonoverlapping(v.add(i), v.add(i - 1), 1);
- hole.dest = v.add(i);
- }
- // `hole` gets dropped and thus copies `tmp` into the remaining hole in `v`.
- }
- }
-}
-
-/// Shifts the last element to the left until it encounters a smaller or equal element.
-fn shift_tail<T, F>(v: &mut [T], is_less: &F)
-where
- F: Fn(&T, &T) -> bool,
-{
- let len = v.len();
- // SAFETY: The unsafe operations below involves indexing without a bound check (by offsetting a
- // pointer) and copying memory (`ptr::copy_nonoverlapping`).
- //
- // a. Indexing:
- // 1. We checked the size of the array to >= 2.
- // 2. All the indexing that we will do is always between `0 <= index < len-1` at most.
- //
- // b. Memory copying
- // 1. We are obtaining pointers to references which are guaranteed to be valid.
- // 2. They cannot overlap because we obtain pointers to difference indices of the slice.
- // Namely, `i` and `i+1`.
- // 3. If the slice is properly aligned, the elements are properly aligned.
- // It is the caller's responsibility to make sure the slice is properly aligned.
- //
- // See comments below for further detail.
- unsafe {
- // If the last two elements are out-of-order...
- if len >= 2 && is_less(v.get_unchecked(len - 1), v.get_unchecked(len - 2)) {
- // Read the last element into a stack-allocated variable. If a following comparison
- // operation panics, `hole` will get dropped and automatically write the element back
- // into the slice.
- let tmp = mem::ManuallyDrop::new(ptr::read(v.get_unchecked(len - 1)));
- let v = v.as_mut_ptr();
- let mut hole = CopyOnDrop::new(&*tmp, v.add(len - 2));
- ptr::copy_nonoverlapping(v.add(len - 2), v.add(len - 1), 1);
-
- for i in (0..len - 2).rev() {
- if !is_less(&*tmp, &*v.add(i)) {
- break;
- }
-
- // Move `i`-th element one place to the right, thus shifting the hole to the left.
- ptr::copy_nonoverlapping(v.add(i), v.add(i + 1), 1);
- hole.dest = v.add(i);
- }
- // `hole` gets dropped and thus copies `tmp` into the remaining hole in `v`.
- }
- }
-}
-
-/// Partially sorts a slice by shifting several out-of-order elements around.
-///
-/// Returns `true` if the slice is sorted at the end. This function is *O*(*n*) worst-case.
-#[cold]
-fn partial_insertion_sort<T, F>(v: &mut [T], is_less: &F) -> bool
-where
- F: Fn(&T, &T) -> bool,
-{
- // Maximum number of adjacent out-of-order pairs that will get shifted.
- const MAX_STEPS: usize = 5;
- // If the slice is shorter than this, don't shift any elements.
- const SHORTEST_SHIFTING: usize = 50;
-
- let len = v.len();
- let mut i = 1;
-
- for _ in 0..MAX_STEPS {
- // SAFETY: We already explicitly did the bound checking with `i < len`.
- // All our subsequent indexing is only in the range `0 <= index < len`
- unsafe {
- // Find the next pair of adjacent out-of-order elements.
- while i < len && !is_less(v.get_unchecked(i), v.get_unchecked(i - 1)) {
- i += 1;
- }
- }
-
- // Are we done?
- if i == len {
- return true;
- }
-
- // Don't shift elements on short arrays, that has a performance cost.
- if len < SHORTEST_SHIFTING {
- return false;
- }
-
- // Swap the found pair of elements. This puts them in correct order.
- v.swap(i - 1, i);
-
- // Shift the smaller element to the left.
- shift_tail(&mut v[..i], is_less);
- // Shift the greater element to the right.
- shift_head(&mut v[i..], is_less);
- }
-
- // Didn't manage to sort the slice in the limited number of steps.
- false
-}
-
-/// Sorts a slice using insertion sort, which is *O*(*n*^2) worst-case.
-fn insertion_sort<T, F>(v: &mut [T], is_less: &F)
-where
- F: Fn(&T, &T) -> bool,
-{
- for i in 1..v.len() {
- shift_tail(&mut v[..i + 1], is_less);
- }
-}
-
-/// Sorts `v` using heapsort, which guarantees *O*(*n* \* log(*n*)) worst-case.
-#[cold]
-fn heapsort<T, F>(v: &mut [T], is_less: &F)
-where
- F: Fn(&T, &T) -> bool,
-{
- // This binary heap respects the invariant `parent >= child`.
- let sift_down = |v: &mut [T], mut node| {
- loop {
- // Children of `node`.
- let mut child = 2 * node + 1;
- if child >= v.len() {
- break;
- }
-
- // Choose the greater child.
- if child + 1 < v.len() && is_less(&v[child], &v[child + 1]) {
- child += 1;
- }
-
- // Stop if the invariant holds at `node`.
- if !is_less(&v[node], &v[child]) {
- break;
- }
-
- // Swap `node` with the greater child, move one step down, and continue sifting.
- v.swap(node, child);
- node = child;
- }
- };
-
- // Build the heap in linear time.
- for i in (0..v.len() / 2).rev() {
- sift_down(v, i);
- }
-
- // Pop maximal elements from the heap.
- for i in (1..v.len()).rev() {
- v.swap(0, i);
- sift_down(&mut v[..i], 0);
- }
-}
-
-/// Partitions `v` into elements smaller than `pivot`, followed by elements greater than or equal
-/// to `pivot`.
-///
-/// Returns the number of elements smaller than `pivot`.
-///
-/// Partitioning is performed block-by-block in order to minimize the cost of branching operations.
-/// This idea is presented in the [BlockQuicksort][pdf] paper.
-///
-/// [pdf]: https://drops.dagstuhl.de/opus/volltexte/2016/6389/pdf/LIPIcs-ESA-2016-38.pdf
-fn partition_in_blocks<T, F>(v: &mut [T], pivot: &T, is_less: &F) -> usize
-where
- F: Fn(&T, &T) -> bool,
-{
- // Number of elements in a typical block.
- const BLOCK: usize = 128;
-
- // The partitioning algorithm repeats the following steps until completion:
- //
- // 1. Trace a block from the left side to identify elements greater than or equal to the pivot.
- // 2. Trace a block from the right side to identify elements smaller than the pivot.
- // 3. Exchange the identified elements between the left and right side.
- //
- // We keep the following variables for a block of elements:
- //
- // 1. `block` - Number of elements in the block.
- // 2. `start` - Start pointer into the `offsets` array.
- // 3. `end` - End pointer into the `offsets` array.
- // 4. `offsets - Indices of out-of-order elements within the block.
-
- // The current block on the left side (from `l` to `l.add(block_l)`).
- let mut l = v.as_mut_ptr();
- let mut block_l = BLOCK;
- let mut start_l = ptr::null_mut();
- let mut end_l = ptr::null_mut();
- let mut offsets_l = [MaybeUninit::<u8>::uninit(); BLOCK];
-
- // The current block on the right side (from `r.sub(block_r)` to `r`).
- // SAFETY: The documentation for .add() specifically mention that `vec.as_ptr().add(vec.len())` is always safe`
- let mut r = unsafe { l.add(v.len()) };
- let mut block_r = BLOCK;
- let mut start_r = ptr::null_mut();
- let mut end_r = ptr::null_mut();
- let mut offsets_r = [MaybeUninit::<u8>::uninit(); BLOCK];
-
- // FIXME: When we get VLAs, try creating one array of length `min(v.len(), 2 * BLOCK)` rather
- // than two fixed-size arrays of length `BLOCK`. VLAs might be more cache-efficient.
-
- // Returns the number of elements between pointers `l` (inclusive) and `r` (exclusive).
- fn width<T>(l: *mut T, r: *mut T) -> usize {
- assert!(mem::size_of::<T>() > 0);
- // FIXME: this should *likely* use `offset_from`, but more
- // investigation is needed (including running tests in miri).
- // TODO unstable: (r.addr() - l.addr()) / mem::size_of::<T>()
- (r as usize - l as usize) / mem::size_of::<T>()
- }
-
- loop {
- // We are done with partitioning block-by-block when `l` and `r` get very close. Then we do
- // some patch-up work in order to partition the remaining elements in between.
- let is_done = width(l, r) <= 2 * BLOCK;
-
- if is_done {
- // Number of remaining elements (still not compared to the pivot).
- let mut rem = width(l, r);
- if start_l < end_l || start_r < end_r {
- rem -= BLOCK;
- }
-
- // Adjust block sizes so that the left and right block don't overlap, but get perfectly
- // aligned to cover the whole remaining gap.
- if start_l < end_l {
- block_r = rem;
- } else if start_r < end_r {
- block_l = rem;
- } else {
- // There were the same number of elements to switch on both blocks during the last
- // iteration, so there are no remaining elements on either block. Cover the remaining
- // items with roughly equally-sized blocks.
- block_l = rem / 2;
- block_r = rem - block_l;
- }
- debug_assert!(block_l <= BLOCK && block_r <= BLOCK);
- debug_assert!(width(l, r) == block_l + block_r);
- }
-
- if start_l == end_l {
- // Trace `block_l` elements from the left side.
- // TODO unstable: start_l = MaybeUninit::slice_as_mut_ptr(&mut offsets_l);
- start_l = offsets_l.as_mut_ptr() as *mut u8;
- end_l = start_l;
- let mut elem = l;
-
- for i in 0..block_l {
- // SAFETY: The unsafety operations below involve the usage of the `offset`.
- // According to the conditions required by the function, we satisfy them because:
- // 1. `offsets_l` is stack-allocated, and thus considered separate allocated object.
- // 2. The function `is_less` returns a `bool`.
- // Casting a `bool` will never overflow `isize`.
- // 3. We have guaranteed that `block_l` will be `<= BLOCK`.
- // Plus, `end_l` was initially set to the begin pointer of `offsets_` which was declared on the stack.
- // 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.
- // Another unsafety operation here is dereferencing `elem`.
- // However, `elem` was initially the begin pointer to the slice which is always valid.
- unsafe {
- // Branchless comparison.
- *end_l = i as u8;
- end_l = end_l.offset(!is_less(&*elem, pivot) as isize);
- elem = elem.offset(1);
- }
- }
- }
-
- if start_r == end_r {
- // Trace `block_r` elements from the right side.
- // TODO unstable: start_r = MaybeUninit::slice_as_mut_ptr(&mut offsets_r);
- start_r = offsets_r.as_mut_ptr() as *mut u8;
- end_r = start_r;
- let mut elem = r;
-
- for i in 0..block_r {
- // SAFETY: The unsafety operations below involve the usage of the `offset`.
- // According to the conditions required by the function, we satisfy them because:
- // 1. `offsets_r` is stack-allocated, and thus considered separate allocated object.
- // 2. The function `is_less` returns a `bool`.
- // Casting a `bool` will never overflow `isize`.
- // 3. We have guaranteed that `block_r` will be `<= BLOCK`.
- // Plus, `end_r` was initially set to the begin pointer of `offsets_` which was declared on the stack.
- // 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.
- // Another unsafety operation here is dereferencing `elem`.
- // However, `elem` was initially `1 * sizeof(T)` past the end and we decrement it by `1 * sizeof(T)` before accessing it.
- // Plus, `block_r` was asserted to be less than `BLOCK` and `elem` will therefore at most be pointing to the beginning of the slice.
- unsafe {
- // Branchless comparison.
- elem = elem.offset(-1);
- *end_r = i as u8;
- end_r = end_r.offset(is_less(&*elem, pivot) as isize);
- }
- }
- }
-
- // Number of out-of-order elements to swap between the left and right side.
- let count = cmp::min(width(start_l, end_l), width(start_r, end_r));
-
- if count > 0 {
- macro_rules! left {
- () => {
- l.offset(*start_l as isize)
- };
- }
- macro_rules! right {
- () => {
- r.offset(-(*start_r as isize) - 1)
- };
- }
-
- // Instead of swapping one pair at the time, it is more efficient to perform a cyclic
- // permutation. This is not strictly equivalent to swapping, but produces a similar
- // result using fewer memory operations.
-
- // SAFETY: The use of `ptr::read` is valid because there is at least one element in
- // both `offsets_l` and `offsets_r`, so `left!` is a valid pointer to read from.
- //
- // The uses of `left!` involve calls to `offset` on `l`, which points to the
- // beginning of `v`. All the offsets pointed-to by `start_l` are at most `block_l`, so
- // these `offset` calls are safe as all reads are within the block. The same argument
- // applies for the uses of `right!`.
- //
- // The calls to `start_l.offset` are valid because there are at most `count-1` of them,
- // plus the final one at the end of the unsafe block, where `count` is the minimum number
- // of collected offsets in `offsets_l` and `offsets_r`, so there is no risk of there not
- // being enough elements. The same reasoning applies to the calls to `start_r.offset`.
- //
- // The calls to `copy_nonoverlapping` are safe because `left!` and `right!` are guaranteed
- // not to overlap, and are valid because of the reasoning above.
- unsafe {
- let tmp = ptr::read(left!());
- ptr::copy_nonoverlapping(right!(), left!(), 1);
-
- for _ in 1..count {
- start_l = start_l.offset(1);
- ptr::copy_nonoverlapping(left!(), right!(), 1);
- start_r = start_r.offset(1);
- ptr::copy_nonoverlapping(right!(), left!(), 1);
- }
-
- ptr::copy_nonoverlapping(&tmp, right!(), 1);
- mem::forget(tmp);
- start_l = start_l.offset(1);
- start_r = start_r.offset(1);
- }
- }
-
- if start_l == end_l {
- // All out-of-order elements in the left block were moved. Move to the next block.
-
- // block-width-guarantee
- // SAFETY: if `!is_done` then the slice width is guaranteed to be at least `2*BLOCK` wide. There
- // are at most `BLOCK` elements in `offsets_l` because of its size, so the `offset` operation is
- // safe. Otherwise, the debug assertions in the `is_done` case guarantee that
- // `width(l, r) == block_l + block_r`, namely, that the block sizes have been adjusted to account
- // for the smaller number of remaining elements.
- l = unsafe { l.add(block_l) };
- }
-
- if start_r == end_r {
- // All out-of-order elements in the right block were moved. Move to the previous block.
-
- // SAFETY: Same argument as [block-width-guarantee]. Either this is a full block `2*BLOCK`-wide,
- // or `block_r` has been adjusted for the last handful of elements.
- r = unsafe { r.offset(-(block_r as isize)) };
- }
-
- if is_done {
- break;
- }
- }
-
- // All that remains now is at most one block (either the left or the right) with out-of-order
- // elements that need to be moved. Such remaining elements can be simply shifted to the end
- // within their block.
-
- if start_l < end_l {
- // The left block remains.
- // Move its remaining out-of-order elements to the far right.
- debug_assert_eq!(width(l, r), block_l);
- while start_l < end_l {
- // remaining-elements-safety
- // SAFETY: while the loop condition holds there are still elements in `offsets_l`, so it
- // is safe to point `end_l` to the previous element.
- //
- // The `ptr::swap` is safe if both its arguments are valid for reads and writes:
- // - Per the debug assert above, the distance between `l` and `r` is `block_l`
- // elements, so there can be at most `block_l` remaining offsets between `start_l`
- // and `end_l`. This means `r` will be moved at most `block_l` steps back, which
- // makes the `r.offset` calls valid (at that point `l == r`).
- // - `offsets_l` contains valid offsets into `v` collected during the partitioning of
- // the last block, so the `l.offset` calls are valid.
- unsafe {
- end_l = end_l.offset(-1);
- ptr::swap(l.offset(*end_l as isize), r.offset(-1));
- r = r.offset(-1);
- }
- }
- width(v.as_mut_ptr(), r)
- } else if start_r < end_r {
- // The right block remains.
- // Move its remaining out-of-order elements to the far left.
- debug_assert_eq!(width(l, r), block_r);
- while start_r < end_r {
- // SAFETY: See the reasoning in [remaining-elements-safety].
- unsafe {
- end_r = end_r.offset(-1);
- ptr::swap(l, r.offset(-(*end_r as isize) - 1));
- l = l.offset(1);
- }
- }
- width(v.as_mut_ptr(), l)
- } else {
- // Nothing else to do, we're done.
- width(v.as_mut_ptr(), l)
- }
-}
-
-/// Partitions `v` into elements smaller than `v[pivot]`, followed by elements greater than or
-/// equal to `v[pivot]`.
-///
-/// Returns a tuple of:
-///
-/// 1. Number of elements smaller than `v[pivot]`.
-/// 2. True if `v` was already partitioned.
-fn partition<T, F>(v: &mut [T], pivot: usize, is_less: &F) -> (usize, bool)
-where
- F: Fn(&T, &T) -> bool,
-{
- let (mid, was_partitioned) = {
- // Place the pivot at the beginning of slice.
- v.swap(0, pivot);
- let (pivot, v) = v.split_at_mut(1);
- let pivot = &mut pivot[0];
-
- // Read the pivot into a stack-allocated variable for efficiency. If a following comparison
- // operation panics, the pivot will be automatically written back into the slice.
-
- // SAFETY: `pivot` is a reference to the first element of `v`, so `ptr::read` is safe.
- let tmp = mem::ManuallyDrop::new(unsafe { ptr::read(pivot) });
- let _pivot_guard = unsafe { CopyOnDrop::new(&*tmp, pivot) };
- let pivot = &*tmp;
-
- // Find the first pair of out-of-order elements.
- let mut l = 0;
- let mut r = v.len();
-
- // SAFETY: The unsafety below involves indexing an array.
- // For the first one: We already do the bounds checking here with `l < r`.
- // For the second one: We initially have `l == 0` and `r == v.len()` and we checked that `l < r` at every indexing operation.
- // From here we know that `r` must be at least `r == l` which was shown to be valid from the first one.
- unsafe {
- // Find the first element greater than or equal to the pivot.
- while l < r && is_less(v.get_unchecked(l), pivot) {
- l += 1;
- }
-
- // Find the last element smaller that the pivot.
- while l < r && !is_less(v.get_unchecked(r - 1), pivot) {
- r -= 1;
- }
- }
-
- (
- l + partition_in_blocks(&mut v[l..r], pivot, is_less),
- l >= r,
- )
-
- // `_pivot_guard` goes out of scope and writes the pivot (which is a stack-allocated
- // variable) back into the slice where it originally was. This step is critical in ensuring
- // safety!
- };
-
- // Place the pivot between the two partitions.
- v.swap(0, mid);
-
- (mid, was_partitioned)
-}
-
-/// Partitions `v` into elements equal to `v[pivot]` followed by elements greater than `v[pivot]`.
-///
-/// Returns the number of elements equal to the pivot. It is assumed that `v` does not contain
-/// elements smaller than the pivot.
-fn partition_equal<T, F>(v: &mut [T], pivot: usize, is_less: &F) -> usize
-where
- F: Fn(&T, &T) -> bool,
-{
- // Place the pivot at the beginning of slice.
- v.swap(0, pivot);
- let (pivot, v) = v.split_at_mut(1);
- let pivot = &mut pivot[0];
-
- // Read the pivot into a stack-allocated variable for efficiency. If a following comparison
- // operation panics, the pivot will be automatically written back into the slice.
- // SAFETY: The pointer here is valid because it is obtained from a reference to a slice.
- let tmp = mem::ManuallyDrop::new(unsafe { ptr::read(pivot) });
- let _pivot_guard = unsafe { CopyOnDrop::new(&*tmp, pivot) };
- let pivot = &*tmp;
-
- // Now partition the slice.
- let mut l = 0;
- let mut r = v.len();
- loop {
- // SAFETY: The unsafety below involves indexing an array.
- // For the first one: We already do the bounds checking here with `l < r`.
- // For the second one: We initially have `l == 0` and `r == v.len()` and we checked that `l < r` at every indexing operation.
- // From here we know that `r` must be at least `r == l` which was shown to be valid from the first one.
- unsafe {
- // Find the first element greater than the pivot.
- while l < r && !is_less(pivot, v.get_unchecked(l)) {
- l += 1;
- }
-
- // Find the last element equal to the pivot.
- while l < r && is_less(pivot, v.get_unchecked(r - 1)) {
- r -= 1;
- }
-
- // Are we done?
- if l >= r {
- break;
- }
-
- // Swap the found pair of out-of-order elements.
- r -= 1;
- let ptr = v.as_mut_ptr();
- ptr::swap(ptr.add(l), ptr.add(r));
- l += 1;
- }
- }
-
- // We found `l` elements equal to the pivot. Add 1 to account for the pivot itself.
- l + 1
-
- // `_pivot_guard` goes out of scope and writes the pivot (which is a stack-allocated variable)
- // back into the slice where it originally was. This step is critical in ensuring safety!
-}
-
-/// Scatters some elements around in an attempt to break patterns that might cause imbalanced
-/// partitions in quicksort.
-#[cold]
-fn break_patterns<T>(v: &mut [T]) {
- let len = v.len();
- if len >= 8 {
- // Pseudorandom number generator from the "Xorshift RNGs" paper by George Marsaglia.
- let mut random = len as u32;
- let mut gen_u32 = || {
- random ^= random << 13;
- random ^= random >> 17;
- random ^= random << 5;
- random
- };
- let mut gen_usize = || {
- if usize::BITS <= 32 {
- gen_u32() as usize
- } else {
- (((gen_u32() as u64) << 32) | (gen_u32() as u64)) as usize
- }
- };
-
- // Take random numbers modulo this number.
- // The number fits into `usize` because `len` is not greater than `isize::MAX`.
- let modulus = len.next_power_of_two();
-
- // Some pivot candidates will be in the nearby of this index. Let's randomize them.
- let pos = len / 4 * 2;
-
- for i in 0..3 {
- // Generate a random number modulo `len`. However, in order to avoid costly operations
- // we first take it modulo a power of two, and then decrease by `len` until it fits
- // into the range `[0, len - 1]`.
- let mut other = gen_usize() & (modulus - 1);
-
- // `other` is guaranteed to be less than `2 * len`.
- if other >= len {
- other -= len;
- }
-
- v.swap(pos - 1 + i, other);
- }
- }
-}
-
-/// Chooses a pivot in `v` and returns the index and `true` if the slice is likely already sorted.
-///
-/// Elements in `v` might be reordered in the process.
-fn choose_pivot<T, F>(v: &mut [T], is_less: &F) -> (usize, bool)
-where
- F: Fn(&T, &T) -> bool,
-{
- // Minimum length to choose the median-of-medians method.
- // Shorter slices use the simple median-of-three method.
- const SHORTEST_MEDIAN_OF_MEDIANS: usize = 50;
- // Maximum number of swaps that can be performed in this function.
- const MAX_SWAPS: usize = 4 * 3;
-
- let len = v.len();
-
- // Three indices near which we are going to choose a pivot.
- #[allow(clippy::identity_op)]
- let mut a = len / 4 * 1;
- let mut b = len / 4 * 2;
- let mut c = len / 4 * 3;
-
- // Counts the total number of swaps we are about to perform while sorting indices.
- let mut swaps = 0;
-
- if len >= 8 {
- // Swaps indices so that `v[a] <= v[b]`.
- // SAFETY: `len >= 8` so there are at least two elements in the neighborhoods of
- // `a`, `b` and `c`. This means the three calls to `sort_adjacent` result in
- // corresponding calls to `sort3` with valid 3-item neighborhoods around each
- // pointer, which in turn means the calls to `sort2` are done with valid
- // references. Thus the `v.get_unchecked` calls are safe, as is the `ptr::swap`
- // call.
- let mut sort2 = |a: &mut usize, b: &mut usize| unsafe {
- if is_less(v.get_unchecked(*b), v.get_unchecked(*a)) {
- ptr::swap(a, b);
- swaps += 1;
- }
- };
-
- // Swaps indices so that `v[a] <= v[b] <= v[c]`.
- let mut sort3 = |a: &mut usize, b: &mut usize, c: &mut usize| {
- sort2(a, b);
- sort2(b, c);
- sort2(a, b);
- };
-
- if len >= SHORTEST_MEDIAN_OF_MEDIANS {
- // Finds the median of `v[a - 1], v[a], v[a + 1]` and stores the index into `a`.
- let mut sort_adjacent = |a: &mut usize| {
- let tmp = *a;
- sort3(&mut (tmp - 1), a, &mut (tmp + 1));
- };
-
- // Find medians in the neighborhoods of `a`, `b`, and `c`.
- sort_adjacent(&mut a);
- sort_adjacent(&mut b);
- sort_adjacent(&mut c);
- }
-
- // Find the median among `a`, `b`, and `c`.
- sort3(&mut a, &mut b, &mut c);
- }
-
- if swaps < MAX_SWAPS {
- (b, swaps == 0)
- } else {
- // The maximum number of swaps was performed. Chances are the slice is descending or mostly
- // descending, so reversing will probably help sort it faster.
- v.reverse();
- (len - 1 - b, true)
- }
-}
-
-/// Sorts `v` recursively.
-///
-/// If the slice had a predecessor in the original array, it is specified as `pred`.
-///
-/// `limit` is the number of allowed imbalanced partitions before switching to `heapsort`. If zero,
-/// this function will immediately switch to heapsort.
-fn recurse<'a, T, F>(mut v: &'a mut [T], is_less: &F, mut pred: Option<&'a mut T>, mut limit: u32)
-where
- T: Send,
- F: Fn(&T, &T) -> bool + Sync,
-{
- // Slices of up to this length get sorted using insertion sort.
- const MAX_INSERTION: usize = 20;
- // If both partitions are up to this length, we continue sequentially. This number is as small
- // as possible but so that the overhead of Rayon's task scheduling is still negligible.
- const MAX_SEQUENTIAL: usize = 2000;
-
- // True if the last partitioning was reasonably balanced.
- let mut was_balanced = true;
- // True if the last partitioning didn't shuffle elements (the slice was already partitioned).
- let mut was_partitioned = true;
-
- loop {
- let len = v.len();
-
- // Very short slices get sorted using insertion sort.
- if len <= MAX_INSERTION {
- insertion_sort(v, is_less);
- return;
- }
-
- // If too many bad pivot choices were made, simply fall back to heapsort in order to
- // guarantee `O(n * log(n))` worst-case.
- if limit == 0 {
- heapsort(v, is_less);
- return;
- }
-
- // If the last partitioning was imbalanced, try breaking patterns in the slice by shuffling
- // some elements around. Hopefully we'll choose a better pivot this time.
- if !was_balanced {
- break_patterns(v);
- limit -= 1;
- }
-
- // Choose a pivot and try guessing whether the slice is already sorted.
- let (pivot, likely_sorted) = choose_pivot(v, is_less);
-
- // If the last partitioning was decently balanced and didn't shuffle elements, and if pivot
- // selection predicts the slice is likely already sorted...
- if was_balanced && was_partitioned && likely_sorted {
- // Try identifying several out-of-order elements and shifting them to correct
- // positions. If the slice ends up being completely sorted, we're done.
- if partial_insertion_sort(v, is_less) {
- return;
- }
- }
-
- // If the chosen pivot is equal to the predecessor, then it's the smallest element in the
- // slice. Partition the slice into elements equal to and elements greater than the pivot.
- // This case is usually hit when the slice contains many duplicate elements.
- if let Some(ref p) = pred {
- if !is_less(p, &v[pivot]) {
- let mid = partition_equal(v, pivot, is_less);
-
- // Continue sorting elements greater than the pivot.
- v = &mut v[mid..];
- continue;
- }
- }
-
- // Partition the slice.
- let (mid, was_p) = partition(v, pivot, is_less);
- was_balanced = cmp::min(mid, len - mid) >= len / 8;
- was_partitioned = was_p;
-
- // Split the slice into `left`, `pivot`, and `right`.
- let (left, right) = v.split_at_mut(mid);
- let (pivot, right) = right.split_at_mut(1);
- let pivot = &mut pivot[0];
-
- if cmp::max(left.len(), right.len()) <= MAX_SEQUENTIAL {
- // Recurse into the shorter side only in order to minimize the total number of recursive
- // calls and consume less stack space. Then just continue with the longer side (this is
- // akin to tail recursion).
- if left.len() < right.len() {
- recurse(left, is_less, pred, limit);
- v = right;
- pred = Some(pivot);
- } else {
- recurse(right, is_less, Some(pivot), limit);
- v = left;
- }
- } else {
- // Sort the left and right half in parallel.
- rayon_core::join(
- || recurse(left, is_less, pred, limit),
- || recurse(right, is_less, Some(pivot), limit),
- );
- break;
- }
- }
-}
-
-/// Sorts `v` using pattern-defeating quicksort in parallel.
-///
-/// The algorithm is unstable, in-place, and *O*(*n* \* log(*n*)) worst-case.
-pub(super) fn par_quicksort<T, F>(v: &mut [T], is_less: F)
-where
- T: Send,
- F: Fn(&T, &T) -> bool + Sync,
-{
- // Sorting has no meaningful behavior on zero-sized types.
- if mem::size_of::<T>() == 0 {
- return;
- }
-
- // Limit the number of imbalanced partitions to `floor(log2(len)) + 1`.
- let limit = usize::BITS - v.len().leading_zeros();
-
- recurse(v, &is_less, None, limit);
-}
-
-#[cfg(test)]
-mod tests {
- use super::heapsort;
- use rand::distributions::Uniform;
- use rand::{thread_rng, Rng};
-
- #[test]
- fn test_heapsort() {
- let rng = &mut thread_rng();
-
- for len in (0..25).chain(500..501) {
- for &modulus in &[5, 10, 100] {
- let dist = Uniform::new(0, modulus);
- for _ in 0..100 {
- let v: Vec<i32> = rng.sample_iter(&dist).take(len).collect();
-
- // Test heapsort using `<` operator.
- let mut tmp = v.clone();
- heapsort(&mut tmp, &|a, b| a < b);
- assert!(tmp.windows(2).all(|w| w[0] <= w[1]));
-
- // Test heapsort using `>` operator.
- let mut tmp = v.clone();
- heapsort(&mut tmp, &|a, b| a > b);
- assert!(tmp.windows(2).all(|w| w[0] >= w[1]));
- }
- }
- }
-
- // Sort using a completely random comparison function.
- // This will reorder the elements *somehow*, but won't panic.
- let mut v: Vec<_> = (0..100).collect();
- heapsort(&mut v, &|_, _| thread_rng().gen());
- heapsort(&mut v, &|a, b| a < b);
-
- for (i, &entry) in v.iter().enumerate() {
- assert_eq!(entry, i);
- }
- }
-}