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Diffstat (limited to 'library/core/src/slice/sort.rs')
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diff --git a/library/core/src/slice/sort.rs b/library/core/src/slice/sort.rs new file mode 100644 index 000000000..6a201834b --- /dev/null +++ b/library/core/src/slice/sort.rs @@ -0,0 +1,929 @@ +//! Slice sorting +//! +//! This module contains a sorting 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: *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: &mut F) +where + F: FnMut(&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: &mut F) +where + F: FnMut(&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: &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 { + // 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: &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] +#[unstable(feature = "sort_internals", reason = "internal to sort module", issue = "none")] +pub fn heapsort<T, F>(v: &mut [T], mut is_less: 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 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: &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>::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). + (r.addr() - l.addr()) / 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. + start_l = MaybeUninit::slice_as_mut_ptr(&mut offsets_l); + 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. + start_r = MaybeUninit::slice_as_mut_ptr(&mut offsets_r); + 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.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. + + // 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: &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. + + // 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: &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. + // 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: &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]`. + // 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: &mut F, mut pred: Option<&'a T>, mut limit: u32) +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 = usize::BITS - v.len().leading_zeros(); + + 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::Greater; + use cmp::Ordering::Less; + + 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) +} |