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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::mem::{self, MaybeUninit};
use std::ptr;
/// When dropped, copies from `src` into `dest`.
struct CopyOnDrop<T> {
src: *const T,
dest: *mut T,
}
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 {
src: &*tmp,
dest: 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 {
src: &*tmp,
dest: 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.
///
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 = CopyOnDrop {
src: &*tmp,
dest: 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 = CopyOnDrop {
src: &*tmp,
dest: 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);
}
}
}