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//! Slice sorting
//!
//! This module contains an sort algorithm based on Orson Peters' pattern-defeating quicksort,
//! published at: https://github.com/orlp/pdqsort
//!
//! Unstable sorting is compatible with libcore because it doesn't allocate memory, unlike our
//! stable sorting implementation.
use crate::cmp;
use crate::mem::{self, MaybeUninit};
use crate::ptr;
/// 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: &mut F)
where F: FnMut(&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 = mem::ManuallyDrop::new(ptr::read(v.get_unchecked(0)));
let mut hole = CopyOnDrop {
src: &mut *tmp,
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) {
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: &mut F)
where F: FnMut(&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 = mem::ManuallyDrop::new(ptr::read(v.get_unchecked(len - 1)));
let mut hole = CopyOnDrop {
src: &mut *tmp,
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, 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: &mut F) -> bool
where F: FnMut(&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: &mut F)
where F: FnMut(&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]
pub fn heapsort<T, F>(v: &mut [T], is_less: &mut F)
where F: FnMut(&T, &T) -> bool
{
// This binary heap respects the invariant `parent >= child`.
let mut 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: &mut F) -> usize
where F: FnMut(&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>; BLOCK] = uninitialized_array![u8; BLOCK];
// The current block on the right side (from `r.sub(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: [MaybeUninit<u8>; BLOCK] = uninitialized_array![u8; 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);
(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 = MaybeUninit::first_ptr_mut(&mut offsets_l);
end_l = MaybeUninit::first_ptr_mut(&mut offsets_l);
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 = MaybeUninit::first_ptr_mut(&mut offsets_r);
end_r = MaybeUninit::first_ptr_mut(&mut offsets_r);
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.offset(block_l as isize) };
}
if start_r == end_r {
// All out-of-order elements in the right block were moved. Move to the previous block.
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 {
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 {
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: &mut F) -> (usize, bool)
where F: FnMut(&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 mut tmp = mem::ManuallyDrop::new(unsafe { ptr::read(pivot) });
let _pivot_guard = CopyOnDrop {
src: &mut *tmp,
dest: pivot,
};
let pivot = &*tmp;
// 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)
// `_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: &mut F) -> usize
where F: FnMut(&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 mut tmp = mem::ManuallyDrop::new(unsafe { ptr::read(pivot) });
let _pivot_guard = CopyOnDrop {
src: &mut *tmp,
dest: pivot,
};
let pivot = &*tmp;
// 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
// `_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 mem::size_of::<usize>() <= 4 {
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: &mut F) -> (usize, bool)
where F: FnMut(&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: &mut F, mut pred: Option<&'a T>, mut limit: usize)
where F: FnMut(&T, &T) -> bool
{
// Slices of up to this length get sorted using insertion sort.
const MAX_INSERTION: usize = 20;
// 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(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 = &pivot[0];
// 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;
}
}
}
/// Sorts `v` using pattern-defeating quicksort, which is `O(n log n)` worst-case.
pub fn quicksort<T, F>(v: &mut [T], mut is_less: F)
where F: FnMut(&T, &T) -> bool
{
// 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, &mut is_less, None, limit);
}
fn partition_at_index_loop<'a, T, F>( mut v: &'a mut [T], mut index: usize, is_less: &mut F
, mut pred: Option<&'a T>) where F: FnMut(&T, &T) -> bool
{
loop {
// For slices of up to this length it's probably faster to simply sort them.
const MAX_INSERTION: usize = 10;
if v.len() <= MAX_INSERTION {
insertion_sort(v, is_less);
return;
}
// Choose a pivot
let (pivot, _) = choose_pivot(v, is_less);
// 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(p) = pred {
if !is_less(p, &v[pivot]) {
let mid = partition_equal(v, pivot, is_less);
// If we've passed our index, then we're good.
if mid > index {
return;
}
// Otherwise, continue sorting elements greater than the pivot.
v = &mut v[mid..];
index = index - mid;
pred = None;
continue;
}
}
let (mid, _) = partition(v, pivot, is_less);
// 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 = &pivot[0];
if mid < index {
v = right;
index = index - mid - 1;
pred = Some(pivot);
} else if mid > index {
v = left;
} else {
// If mid == index, then we're done, since partition() guaranteed that all elements
// after mid are greater than or equal to mid.
return;
}
}
}
pub fn partition_at_index<T, F>(v: &mut [T], index: usize, mut is_less: F)
-> (&mut [T], &mut T, &mut [T]) where F: FnMut(&T, &T) -> bool
{
use cmp::Ordering::Less;
use cmp::Ordering::Greater;
if index >= v.len() {
panic!("partition_at_index index {} greater than length of slice {}", index, v.len());
}
if mem::size_of::<T>() == 0 {
// Sorting has no meaningful behavior on zero-sized types. Do nothing.
} else if index == v.len() - 1 {
// Find max element and place it in the last position of the array. We're free to use
// `unwrap()` here because we know v must not be empty.
let (max_index, _) = v.iter().enumerate().max_by(
|&(_, x), &(_, y)| if is_less(x, y) { Less } else { Greater }).unwrap();
v.swap(max_index, index);
} else if index == 0 {
// Find min element and place it in the first position of the array. We're free to use
// `unwrap()` here because we know v must not be empty.
let (min_index, _) = v.iter().enumerate().min_by(
|&(_, x), &(_, y)| if is_less(x, y) { Less } else { Greater }).unwrap();
v.swap(min_index, index);
} else {
partition_at_index_loop(v, index, &mut is_less, None);
}
let (left, right) = v.split_at_mut(index);
let (pivot, right) = right.split_at_mut(1);
let pivot = &mut pivot[0];
(left, pivot, right)
}
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