aboutsummaryrefslogtreecommitdiff
path: root/src/slice/quicksort.rs
diff options
context:
space:
mode:
Diffstat (limited to 'src/slice/quicksort.rs')
-rw-r--r--src/slice/quicksort.rs800
1 files changed, 800 insertions, 0 deletions
diff --git a/src/slice/quicksort.rs b/src/slice/quicksort.rs
new file mode 100644
index 0000000..b985073
--- /dev/null
+++ b/src/slice/quicksort.rs
@@ -0,0 +1,800 @@
+//! 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::mem;
+use std::ptr;
+
+/// When dropped, takes the value out of `Option` and writes it into `dest`.
+///
+/// This allows us to safely read the pivot into a stack-allocated variable for efficiency, and
+/// write it back into the slice after partitioning. This way we ensure that the write happens
+/// even if `is_less` panics in the meantime.
+struct WriteOnDrop<T> {
+ value: Option<T>,
+ dest: *mut T,
+}
+
+impl<T> Drop for WriteOnDrop<T> {
+ fn drop(&mut self) {
+ unsafe {
+ ptr::write(self.dest, self.value.take().unwrap());
+ }
+ }
+}
+
+/// Holds a value, but never drops it.
+struct NoDrop<T> {
+ value: Option<T>,
+}
+
+impl<T> Drop for NoDrop<T> {
+ fn drop(&mut self) {
+ mem::forget(self.value.take());
+ }
+}
+
+/// When dropped, copies from `src` into `dest`.
+struct CopyOnDrop<T> {
+ src: *mut T,
+ dest: *mut T,
+}
+
+impl<T> Drop for CopyOnDrop<T> {
+ fn drop(&mut self) {
+ 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();
+ 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 mut tmp = NoDrop {
+ value: Some(ptr::read(v.get_unchecked(0))),
+ };
+ let mut hole = CopyOnDrop {
+ src: tmp.value.as_mut().unwrap(),
+ dest: v.get_unchecked_mut(1),
+ };
+ ptr::copy_nonoverlapping(v.get_unchecked(1), v.get_unchecked_mut(0), 1);
+
+ for i in 2..len {
+ if !is_less(v.get_unchecked(i), tmp.value.as_ref().unwrap()) {
+ break;
+ }
+
+ // Move `i`-th element one place to the left, thus shifting the hole to the right.
+ ptr::copy_nonoverlapping(v.get_unchecked(i), v.get_unchecked_mut(i - 1), 1);
+ hole.dest = v.get_unchecked_mut(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();
+ 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 mut tmp = NoDrop {
+ value: Some(ptr::read(v.get_unchecked(len - 1))),
+ };
+ let mut hole = CopyOnDrop {
+ src: tmp.value.as_mut().unwrap(),
+ dest: v.get_unchecked_mut(len - 2),
+ };
+ ptr::copy_nonoverlapping(v.get_unchecked(len - 2), v.get_unchecked_mut(len - 1), 1);
+
+ for i in (0..len - 2).rev() {
+ if !is_less(&tmp.value.as_ref().unwrap(), v.get_unchecked(i)) {
+ break;
+ }
+
+ // Move `i`-th element one place to the right, thus shifting the hole to the left.
+ ptr::copy_nonoverlapping(v.get_unchecked(i), v.get_unchecked_mut(i + 1), 1);
+ hole.dest = v.get_unchecked_mut(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 {
+ 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], 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 left = 2 * node + 1;
+ let right = 2 * node + 2;
+
+ // Choose the greater child.
+ let greater = if right < v.len() && is_less(&v[left], &v[right]) {
+ right
+ } else {
+ left
+ };
+
+ // Stop if the invariant holds at `node`.
+ if greater >= v.len() || !is_less(&v[node], &v[greater]) {
+ break;
+ }
+
+ // Swap `node` with the greater child, move one step down, and continue sifting.
+ v.swap(node, greater);
+ node = greater;
+ }
+ };
+
+ // 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]: http://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.offset(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 = [0u8; BLOCK];
+
+ // The current block on the right side (from `r.offset(-block_r)` to `r`).
+ 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 = [0u8; BLOCK];
+
+ // 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);
+ (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 {
+ 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.
+ start_l = offsets_l.as_mut_ptr();
+ end_l = offsets_l.as_mut_ptr();
+ let mut elem = l;
+
+ for i in 0..block_l {
+ 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.
+ start_r = offsets_r.as_mut_ptr();
+ end_r = offsets_r.as_mut_ptr();
+ let mut elem = r;
+
+ for i in 0..block_r {
+ 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.
+ 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.
+ 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.
+ r = unsafe { r.sub(block_r) };
+ }
+
+ 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 it's remaining out-of-order elements to the far right.
+ debug_assert_eq!(width(l, r), block_l);
+ while start_l < end_l {
+ 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 it's remaining out-of-order elements to the far left.
+ debug_assert_eq!(width(l, r), block_r);
+ while start_r < end_r {
+ 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.
+ let write_on_drop = WriteOnDrop {
+ value: unsafe { Some(ptr::read(pivot)) },
+ dest: pivot,
+ };
+ let pivot = write_on_drop.value.as_ref().unwrap();
+
+ // Find the first pair of out-of-order elements.
+ let mut l = 0;
+ let mut r = v.len();
+ unsafe {
+ // Find the first element greater then 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,
+ )
+
+ // `write_on_drop` 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.
+ let write_on_drop = WriteOnDrop {
+ value: unsafe { Some(ptr::read(pivot)) },
+ dest: pivot,
+ };
+ let pivot = write_on_drop.value.as_ref().unwrap();
+
+ // Now partition the slice.
+ let mut l = 0;
+ let mut r = v.len();
+ loop {
+ unsafe {
+ // Find the first element greater that 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;
+ ptr::swap(v.get_unchecked_mut(l), v.get_unchecked_mut(r));
+ l += 1;
+ }
+ }
+
+ // We found `l` elements equal to the pivot. Add 1 to account for the pivot itself.
+ l + 1
+
+ // `write_on_drop` 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 mem::size_of::<usize>() <= 4 {
+ gen_u32() as usize
+ } else {
+ ((u64::from(gen_u32()) << 32) | u64::from(gen_u32())) 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.
+ 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]`.
+ 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: usize)
+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 = mem::size_of::<usize>() * 8 - v.len().leading_zeros() as usize;
+
+ 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 = 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 in 0..v.len() {
+ assert_eq!(v[i], i);
+ }
+ }
+}
generated by cgit v1.2.3 (git 2.25.1) at 2024-07-05 22:53:04 +0000