| //! 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, SizedTypeProperties}; |
| 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.add(!is_less(&*elem, pivot) as usize); |
| elem = elem.add(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.sub(1); |
| *end_r = i as u8; |
| end_r = end_r.add(is_less(&*elem, pivot) as usize); |
| } |
| } |
| } |
| |
| // 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.add(usize::from(*start_l)) |
| }; |
| } |
| macro_rules! right { |
| () => { |
| r.sub(usize::from(*start_r) + 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.add(1); |
| ptr::copy_nonoverlapping(left!(), right!(), 1); |
| start_r = start_r.add(1); |
| ptr::copy_nonoverlapping(right!(), left!(), 1); |
| } |
| |
| ptr::copy_nonoverlapping(&tmp, right!(), 1); |
| mem::forget(tmp); |
| start_l = start_l.add(1); |
| start_r = start_r.add(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.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 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.sub(1); |
| ptr::swap(l.add(usize::from(*end_l)), r.sub(1)); |
| r = r.sub(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.sub(1); |
| ptr::swap(l, r.sub(usize::from(*end_r) + 1)); |
| l = l.add(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 T::IS_ZST { |
| 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 T::IS_ZST { |
| // 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) |
| } |
