| //! Parallel quicksort. |
| //! |
| //! This implementation is copied verbatim from `std::slice::sort_unstable` and then parallelized. |
| //! The only difference from the original is that calls to `recurse` are executed in parallel using |
| //! `rayon_core::join`. |
| |
| use std::cmp; |
| use std::mem; |
| use std::ptr; |
| |
| /// When dropped, takes the value out of `Option` and writes it into `dest`. |
| /// |
| /// This allows us to safely read the pivot into a stack-allocated variable for efficiency, and |
| /// write it back into the slice after partitioning. This way we ensure that the write happens |
| /// even if `is_less` panics in the meantime. |
| struct WriteOnDrop<T> { |
| value: Option<T>, |
| dest: *mut T, |
| } |
| |
| impl<T> Drop for WriteOnDrop<T> { |
| fn drop(&mut self) { |
| unsafe { |
| ptr::write(self.dest, self.value.take().unwrap()); |
| } |
| } |
| } |
| |
| /// Holds a value, but never drops it. |
| struct NoDrop<T> { |
| value: Option<T>, |
| } |
| |
| impl<T> Drop for NoDrop<T> { |
| fn drop(&mut self) { |
| mem::forget(self.value.take()); |
| } |
| } |
| |
| /// When dropped, copies from `src` into `dest`. |
| struct CopyOnDrop<T> { |
| src: *mut T, |
| dest: *mut T, |
| } |
| |
| impl<T> Drop for CopyOnDrop<T> { |
| fn drop(&mut self) { |
| unsafe { |
| ptr::copy_nonoverlapping(self.src, self.dest, 1); |
| } |
| } |
| } |
| |
| /// Shifts the first element to the right until it encounters a greater or equal element. |
| fn shift_head<T, F>(v: &mut [T], is_less: &F) |
| where |
| F: Fn(&T, &T) -> bool, |
| { |
| let len = v.len(); |
| unsafe { |
| // If the first two elements are out-of-order... |
| if len >= 2 && is_less(v.get_unchecked(1), v.get_unchecked(0)) { |
| // Read the first element into a stack-allocated variable. If a following comparison |
| // operation panics, `hole` will get dropped and automatically write the element back |
| // into the slice. |
| let mut tmp = NoDrop { |
| value: Some(ptr::read(v.get_unchecked(0))), |
| }; |
| let mut hole = CopyOnDrop { |
| src: tmp.value.as_mut().unwrap(), |
| dest: v.get_unchecked_mut(1), |
| }; |
| ptr::copy_nonoverlapping(v.get_unchecked(1), v.get_unchecked_mut(0), 1); |
| |
| for i in 2..len { |
| if !is_less(v.get_unchecked(i), tmp.value.as_ref().unwrap()) { |
| break; |
| } |
| |
| // Move `i`-th element one place to the left, thus shifting the hole to the right. |
| ptr::copy_nonoverlapping(v.get_unchecked(i), v.get_unchecked_mut(i - 1), 1); |
| hole.dest = v.get_unchecked_mut(i); |
| } |
| // `hole` gets dropped and thus copies `tmp` into the remaining hole in `v`. |
| } |
| } |
| } |
| |
| /// Shifts the last element to the left until it encounters a smaller or equal element. |
| fn shift_tail<T, F>(v: &mut [T], is_less: &F) |
| where |
| F: Fn(&T, &T) -> bool, |
| { |
| let len = v.len(); |
| unsafe { |
| // If the last two elements are out-of-order... |
| if len >= 2 && is_less(v.get_unchecked(len - 1), v.get_unchecked(len - 2)) { |
| // Read the last element into a stack-allocated variable. If a following comparison |
| // operation panics, `hole` will get dropped and automatically write the element back |
| // into the slice. |
| let mut tmp = NoDrop { |
| value: Some(ptr::read(v.get_unchecked(len - 1))), |
| }; |
| let mut hole = CopyOnDrop { |
| src: tmp.value.as_mut().unwrap(), |
| dest: v.get_unchecked_mut(len - 2), |
| }; |
| ptr::copy_nonoverlapping(v.get_unchecked(len - 2), v.get_unchecked_mut(len - 1), 1); |
| |
| for i in (0..len - 2).rev() { |
| if !is_less(&tmp.value.as_ref().unwrap(), v.get_unchecked(i)) { |
| break; |
| } |
| |
| // Move `i`-th element one place to the right, thus shifting the hole to the left. |
| ptr::copy_nonoverlapping(v.get_unchecked(i), v.get_unchecked_mut(i + 1), 1); |
| hole.dest = v.get_unchecked_mut(i); |
| } |
| // `hole` gets dropped and thus copies `tmp` into the remaining hole in `v`. |
| } |
| } |
| } |
| |
| /// Partially sorts a slice by shifting several out-of-order elements around. |
| /// |
| /// Returns `true` if the slice is sorted at the end. This function is `O(n)` worst-case. |
| #[cold] |
| fn partial_insertion_sort<T, F>(v: &mut [T], is_less: &F) -> bool |
| where |
| F: Fn(&T, &T) -> bool, |
| { |
| // Maximum number of adjacent out-of-order pairs that will get shifted. |
| const MAX_STEPS: usize = 5; |
| // If the slice is shorter than this, don't shift any elements. |
| const SHORTEST_SHIFTING: usize = 50; |
| |
| let len = v.len(); |
| let mut i = 1; |
| |
| for _ in 0..MAX_STEPS { |
| unsafe { |
| // Find the next pair of adjacent out-of-order elements. |
| while i < len && !is_less(v.get_unchecked(i), v.get_unchecked(i - 1)) { |
| i += 1; |
| } |
| } |
| |
| // Are we done? |
| if i == len { |
| return true; |
| } |
| |
| // Don't shift elements on short arrays, that has a performance cost. |
| if len < SHORTEST_SHIFTING { |
| return false; |
| } |
| |
| // Swap the found pair of elements. This puts them in correct order. |
| v.swap(i - 1, i); |
| |
| // Shift the smaller element to the left. |
| shift_tail(&mut v[..i], is_less); |
| // Shift the greater element to the right. |
| shift_head(&mut v[i..], is_less); |
| } |
| |
| // Didn't manage to sort the slice in the limited number of steps. |
| false |
| } |
| |
| /// Sorts a slice using insertion sort, which is `O(n^2)` worst-case. |
| fn insertion_sort<T, F>(v: &mut [T], is_less: &F) |
| where |
| F: Fn(&T, &T) -> bool, |
| { |
| for i in 1..v.len() { |
| shift_tail(&mut v[..=i], is_less); |
| } |
| } |
| |
| /// Sorts `v` using heapsort, which guarantees `O(n log n)` worst-case. |
| #[cold] |
| fn heapsort<T, F>(v: &mut [T], is_less: &F) |
| where |
| F: Fn(&T, &T) -> bool, |
| { |
| // This binary heap respects the invariant `parent >= child`. |
| let sift_down = |v: &mut [T], mut node| { |
| loop { |
| // Children of `node`: |
| let left = 2 * node + 1; |
| let right = 2 * node + 2; |
| |
| // Choose the greater child. |
| let greater = if right < v.len() && is_less(&v[left], &v[right]) { |
| right |
| } else { |
| left |
| }; |
| |
| // Stop if the invariant holds at `node`. |
| if greater >= v.len() || !is_less(&v[node], &v[greater]) { |
| break; |
| } |
| |
| // Swap `node` with the greater child, move one step down, and continue sifting. |
| v.swap(node, greater); |
| node = greater; |
| } |
| }; |
| |
| // Build the heap in linear time. |
| for i in (0..v.len() / 2).rev() { |
| sift_down(v, i); |
| } |
| |
| // Pop maximal elements from the heap. |
| for i in (1..v.len()).rev() { |
| v.swap(0, i); |
| sift_down(&mut v[..i], 0); |
| } |
| } |
| |
| /// Partitions `v` into elements smaller than `pivot`, followed by elements greater than or equal |
| /// to `pivot`. |
| /// |
| /// Returns the number of elements smaller than `pivot`. |
| /// |
| /// Partitioning is performed block-by-block in order to minimize the cost of branching operations. |
| /// This idea is presented in the [BlockQuicksort][pdf] paper. |
| /// |
| /// [pdf]: 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: &F) -> usize |
| where |
| F: Fn(&T, &T) -> bool, |
| { |
| // Number of elements in a typical block. |
| const BLOCK: usize = 128; |
| |
| // The partitioning algorithm repeats the following steps until completion: |
| // |
| // 1. Trace a block from the left side to identify elements greater than or equal to the pivot. |
| // 2. Trace a block from the right side to identify elements smaller than the pivot. |
| // 3. Exchange the identified elements between the left and right side. |
| // |
| // We keep the following variables for a block of elements: |
| // |
| // 1. `block` - Number of elements in the block. |
| // 2. `start` - Start pointer into the `offsets` array. |
| // 3. `end` - End pointer into the `offsets` array. |
| // 4. `offsets - Indices of out-of-order elements within the block. |
| |
| // The current block on the left side (from `l` to `l.offset(block_l)`). |
| let mut l = v.as_mut_ptr(); |
| let mut block_l = BLOCK; |
| let mut start_l = ptr::null_mut(); |
| let mut end_l = ptr::null_mut(); |
| let mut offsets_l = [0u8; BLOCK]; |
| |
| // The current block on the right side (from `r.offset(-block_r)` to `r`). |
| let mut r = unsafe { l.add(v.len()) }; |
| let mut block_r = BLOCK; |
| let mut start_r = ptr::null_mut(); |
| let mut end_r = ptr::null_mut(); |
| let mut offsets_r = [0u8; BLOCK]; |
| |
| // Returns the number of elements between pointers `l` (inclusive) and `r` (exclusive). |
| fn width<T>(l: *mut T, r: *mut T) -> usize { |
| assert!(mem::size_of::<T>() > 0); |
| (r as usize - l as usize) / mem::size_of::<T>() |
| } |
| |
| loop { |
| // We are done with partitioning block-by-block when `l` and `r` get very close. Then we do |
| // some patch-up work in order to partition the remaining elements in between. |
| let is_done = width(l, r) <= 2 * BLOCK; |
| |
| if is_done { |
| // Number of remaining elements (still not compared to the pivot). |
| let mut rem = width(l, r); |
| if start_l < end_l || start_r < end_r { |
| rem -= BLOCK; |
| } |
| |
| // Adjust block sizes so that the left and right block don't overlap, but get perfectly |
| // aligned to cover the whole remaining gap. |
| if start_l < end_l { |
| block_r = rem; |
| } else if start_r < end_r { |
| block_l = rem; |
| } else { |
| block_l = rem / 2; |
| block_r = rem - block_l; |
| } |
| debug_assert!(block_l <= BLOCK && block_r <= BLOCK); |
| debug_assert!(width(l, r) == block_l + block_r); |
| } |
| |
| if start_l == end_l { |
| // Trace `block_l` elements from the left side. |
| start_l = offsets_l.as_mut_ptr(); |
| end_l = offsets_l.as_mut_ptr(); |
| let mut elem = l; |
| |
| for i in 0..block_l { |
| unsafe { |
| // Branchless comparison. |
| *end_l = i as u8; |
| end_l = end_l.offset(!is_less(&*elem, pivot) as isize); |
| elem = elem.offset(1); |
| } |
| } |
| } |
| |
| if start_r == end_r { |
| // Trace `block_r` elements from the right side. |
| start_r = offsets_r.as_mut_ptr(); |
| end_r = offsets_r.as_mut_ptr(); |
| let mut elem = r; |
| |
| for i in 0..block_r { |
| unsafe { |
| // Branchless comparison. |
| elem = elem.offset(-1); |
| *end_r = i as u8; |
| end_r = end_r.offset(is_less(&*elem, pivot) as isize); |
| } |
| } |
| } |
| |
| // Number of out-of-order elements to swap between the left and right side. |
| let count = cmp::min(width(start_l, end_l), width(start_r, end_r)); |
| |
| if count > 0 { |
| macro_rules! left { |
| () => { |
| l.offset(*start_l as isize) |
| }; |
| } |
| macro_rules! right { |
| () => { |
| r.offset(-(*start_r as isize) - 1) |
| }; |
| } |
| |
| // Instead of swapping one pair at the time, it is more efficient to perform a cyclic |
| // permutation. This is not strictly equivalent to swapping, but produces a similar |
| // result using fewer memory operations. |
| unsafe { |
| let tmp = ptr::read(left!()); |
| ptr::copy_nonoverlapping(right!(), left!(), 1); |
| |
| for _ in 1..count { |
| start_l = start_l.offset(1); |
| ptr::copy_nonoverlapping(left!(), right!(), 1); |
| start_r = start_r.offset(1); |
| ptr::copy_nonoverlapping(right!(), left!(), 1); |
| } |
| |
| ptr::copy_nonoverlapping(&tmp, right!(), 1); |
| mem::forget(tmp); |
| start_l = start_l.offset(1); |
| start_r = start_r.offset(1); |
| } |
| } |
| |
| if start_l == end_l { |
| // All out-of-order elements in the left block were moved. Move to the next block. |
| l = unsafe { l.add(block_l) }; |
| } |
| |
| if start_r == end_r { |
| // All out-of-order elements in the right block were moved. Move to the previous block. |
| r = unsafe { r.sub(block_r) }; |
| } |
| |
| if is_done { |
| break; |
| } |
| } |
| |
| // All that remains now is at most one block (either the left or the right) with out-of-order |
| // elements that need to be moved. Such remaining elements can be simply shifted to the end |
| // within their block. |
| |
| if start_l < end_l { |
| // The left block remains. |
| // Move it's remaining out-of-order elements to the far right. |
| debug_assert_eq!(width(l, r), block_l); |
| while start_l < end_l { |
| unsafe { |
| end_l = end_l.offset(-1); |
| ptr::swap(l.offset(*end_l as isize), r.offset(-1)); |
| r = r.offset(-1); |
| } |
| } |
| width(v.as_mut_ptr(), r) |
| } else if start_r < end_r { |
| // The right block remains. |
| // Move it's remaining out-of-order elements to the far left. |
| debug_assert_eq!(width(l, r), block_r); |
| while start_r < end_r { |
| unsafe { |
| end_r = end_r.offset(-1); |
| ptr::swap(l, r.offset(-(*end_r as isize) - 1)); |
| l = l.offset(1); |
| } |
| } |
| width(v.as_mut_ptr(), l) |
| } else { |
| // Nothing else to do, we're done. |
| width(v.as_mut_ptr(), l) |
| } |
| } |
| |
| /// Partitions `v` into elements smaller than `v[pivot]`, followed by elements greater than or |
| /// equal to `v[pivot]`. |
| /// |
| /// Returns a tuple of: |
| /// |
| /// 1. Number of elements smaller than `v[pivot]`. |
| /// 2. True if `v` was already partitioned. |
| fn partition<T, F>(v: &mut [T], pivot: usize, is_less: &F) -> (usize, bool) |
| where |
| F: Fn(&T, &T) -> bool, |
| { |
| let (mid, was_partitioned) = { |
| // Place the pivot at the beginning of slice. |
| v.swap(0, pivot); |
| let (pivot, v) = v.split_at_mut(1); |
| let pivot = &mut pivot[0]; |
| |
| // Read the pivot into a stack-allocated variable for efficiency. If a following comparison |
| // operation panics, the pivot will be automatically written back into the slice. |
| let write_on_drop = WriteOnDrop { |
| value: unsafe { Some(ptr::read(pivot)) }, |
| dest: pivot, |
| }; |
| let pivot = write_on_drop.value.as_ref().unwrap(); |
| |
| // Find the first pair of out-of-order elements. |
| let mut l = 0; |
| let mut r = v.len(); |
| unsafe { |
| // Find the first element greater then or equal to the pivot. |
| while l < r && is_less(v.get_unchecked(l), pivot) { |
| l += 1; |
| } |
| |
| // Find the last element smaller that the pivot. |
| while l < r && !is_less(v.get_unchecked(r - 1), pivot) { |
| r -= 1; |
| } |
| } |
| |
| ( |
| l + partition_in_blocks(&mut v[l..r], pivot, is_less), |
| l >= r, |
| ) |
| |
| // `write_on_drop` goes out of scope and writes the pivot (which is a stack-allocated |
| // variable) back into the slice where it originally was. This step is critical in ensuring |
| // safety! |
| }; |
| |
| // Place the pivot between the two partitions. |
| v.swap(0, mid); |
| |
| (mid, was_partitioned) |
| } |
| |
| /// Partitions `v` into elements equal to `v[pivot]` followed by elements greater than `v[pivot]`. |
| /// |
| /// Returns the number of elements equal to the pivot. It is assumed that `v` does not contain |
| /// elements smaller than the pivot. |
| fn partition_equal<T, F>(v: &mut [T], pivot: usize, is_less: &F) -> usize |
| where |
| F: Fn(&T, &T) -> bool, |
| { |
| // Place the pivot at the beginning of slice. |
| v.swap(0, pivot); |
| let (pivot, v) = v.split_at_mut(1); |
| let pivot = &mut pivot[0]; |
| |
| // Read the pivot into a stack-allocated variable for efficiency. If a following comparison |
| // operation panics, the pivot will be automatically written back into the slice. |
| let write_on_drop = WriteOnDrop { |
| value: unsafe { Some(ptr::read(pivot)) }, |
| dest: pivot, |
| }; |
| let pivot = write_on_drop.value.as_ref().unwrap(); |
| |
| // Now partition the slice. |
| let mut l = 0; |
| let mut r = v.len(); |
| loop { |
| unsafe { |
| // Find the first element greater that the pivot. |
| while l < r && !is_less(pivot, v.get_unchecked(l)) { |
| l += 1; |
| } |
| |
| // Find the last element equal to the pivot. |
| while l < r && is_less(pivot, v.get_unchecked(r - 1)) { |
| r -= 1; |
| } |
| |
| // Are we done? |
| if l >= r { |
| break; |
| } |
| |
| // Swap the found pair of out-of-order elements. |
| r -= 1; |
| ptr::swap(v.get_unchecked_mut(l), v.get_unchecked_mut(r)); |
| l += 1; |
| } |
| } |
| |
| // We found `l` elements equal to the pivot. Add 1 to account for the pivot itself. |
| l + 1 |
| |
| // `write_on_drop` goes out of scope and writes the pivot (which is a stack-allocated variable) |
| // back into the slice where it originally was. This step is critical in ensuring safety! |
| } |
| |
| /// Scatters some elements around in an attempt to break patterns that might cause imbalanced |
| /// partitions in quicksort. |
| #[cold] |
| fn break_patterns<T>(v: &mut [T]) { |
| let len = v.len(); |
| if len >= 8 { |
| // Pseudorandom number generator from the "Xorshift RNGs" paper by George Marsaglia. |
| let mut random = len as u32; |
| let mut gen_u32 = || { |
| random ^= random << 13; |
| random ^= random >> 17; |
| random ^= random << 5; |
| random |
| }; |
| let mut gen_usize = || { |
| if mem::size_of::<usize>() <= 4 { |
| gen_u32() as usize |
| } else { |
| ((u64::from(gen_u32()) << 32) | u64::from(gen_u32())) as usize |
| } |
| }; |
| |
| // Take random numbers modulo this number. |
| // The number fits into `usize` because `len` is not greater than `isize::MAX`. |
| let modulus = len.next_power_of_two(); |
| |
| // Some pivot candidates will be in the nearby of this index. Let's randomize them. |
| let pos = len / 4 * 2; |
| |
| for i in 0..3 { |
| // Generate a random number modulo `len`. However, in order to avoid costly operations |
| // we first take it modulo a power of two, and then decrease by `len` until it fits |
| // into the range `[0, len - 1]`. |
| let mut other = gen_usize() & (modulus - 1); |
| |
| // `other` is guaranteed to be less than `2 * len`. |
| if other >= len { |
| other -= len; |
| } |
| |
| v.swap(pos - 1 + i, other); |
| } |
| } |
| } |
| |
| /// Chooses a pivot in `v` and returns the index and `true` if the slice is likely already sorted. |
| /// |
| /// Elements in `v` might be reordered in the process. |
| fn choose_pivot<T, F>(v: &mut [T], is_less: &F) -> (usize, bool) |
| where |
| F: Fn(&T, &T) -> bool, |
| { |
| // Minimum length to choose the median-of-medians method. |
| // Shorter slices use the simple median-of-three method. |
| const SHORTEST_MEDIAN_OF_MEDIANS: usize = 50; |
| // Maximum number of swaps that can be performed in this function. |
| const MAX_SWAPS: usize = 4 * 3; |
| |
| let len = v.len(); |
| |
| // Three indices near which we are going to choose a pivot. |
| let mut a = len / 4 * 1; |
| let mut b = len / 4 * 2; |
| let mut c = len / 4 * 3; |
| |
| // Counts the total number of swaps we are about to perform while sorting indices. |
| let mut swaps = 0; |
| |
| if len >= 8 { |
| // Swaps indices so that `v[a] <= v[b]`. |
| let mut sort2 = |a: &mut usize, b: &mut usize| unsafe { |
| if is_less(v.get_unchecked(*b), v.get_unchecked(*a)) { |
| ptr::swap(a, b); |
| swaps += 1; |
| } |
| }; |
| |
| // Swaps indices so that `v[a] <= v[b] <= v[c]`. |
| let mut sort3 = |a: &mut usize, b: &mut usize, c: &mut usize| { |
| sort2(a, b); |
| sort2(b, c); |
| sort2(a, b); |
| }; |
| |
| if len >= SHORTEST_MEDIAN_OF_MEDIANS { |
| // Finds the median of `v[a - 1], v[a], v[a + 1]` and stores the index into `a`. |
| let mut sort_adjacent = |a: &mut usize| { |
| let tmp = *a; |
| sort3(&mut (tmp - 1), a, &mut (tmp + 1)); |
| }; |
| |
| // Find medians in the neighborhoods of `a`, `b`, and `c`. |
| sort_adjacent(&mut a); |
| sort_adjacent(&mut b); |
| sort_adjacent(&mut c); |
| } |
| |
| // Find the median among `a`, `b`, and `c`. |
| sort3(&mut a, &mut b, &mut c); |
| } |
| |
| if swaps < MAX_SWAPS { |
| (b, swaps == 0) |
| } else { |
| // The maximum number of swaps was performed. Chances are the slice is descending or mostly |
| // descending, so reversing will probably help sort it faster. |
| v.reverse(); |
| (len - 1 - b, true) |
| } |
| } |
| |
| /// Sorts `v` recursively. |
| /// |
| /// If the slice had a predecessor in the original array, it is specified as `pred`. |
| /// |
| /// `limit` is the number of allowed imbalanced partitions before switching to `heapsort`. If zero, |
| /// this function will immediately switch to heapsort. |
| fn recurse<'a, T, F>(mut v: &'a mut [T], is_less: &F, mut pred: Option<&'a mut T>, mut limit: usize) |
| where |
| T: Send, |
| F: Fn(&T, &T) -> bool + Sync, |
| { |
| // Slices of up to this length get sorted using insertion sort. |
| const MAX_INSERTION: usize = 20; |
| // If both partitions are up to this length, we continue sequentially. This number is as small |
| // as possible but so that the overhead of Rayon's task scheduling is still negligible. |
| const MAX_SEQUENTIAL: usize = 2000; |
| |
| // True if the last partitioning was reasonably balanced. |
| let mut was_balanced = true; |
| // True if the last partitioning didn't shuffle elements (the slice was already partitioned). |
| let mut was_partitioned = true; |
| |
| loop { |
| let len = v.len(); |
| |
| // Very short slices get sorted using insertion sort. |
| if len <= MAX_INSERTION { |
| insertion_sort(v, is_less); |
| return; |
| } |
| |
| // If too many bad pivot choices were made, simply fall back to heapsort in order to |
| // guarantee `O(n log n)` worst-case. |
| if limit == 0 { |
| heapsort(v, is_less); |
| return; |
| } |
| |
| // If the last partitioning was imbalanced, try breaking patterns in the slice by shuffling |
| // some elements around. Hopefully we'll choose a better pivot this time. |
| if !was_balanced { |
| break_patterns(v); |
| limit -= 1; |
| } |
| |
| // Choose a pivot and try guessing whether the slice is already sorted. |
| let (pivot, likely_sorted) = choose_pivot(v, is_less); |
| |
| // If the last partitioning was decently balanced and didn't shuffle elements, and if pivot |
| // selection predicts the slice is likely already sorted... |
| if was_balanced && was_partitioned && likely_sorted { |
| // Try identifying several out-of-order elements and shifting them to correct |
| // positions. If the slice ends up being completely sorted, we're done. |
| if partial_insertion_sort(v, is_less) { |
| return; |
| } |
| } |
| |
| // If the chosen pivot is equal to the predecessor, then it's the smallest element in the |
| // slice. Partition the slice into elements equal to and elements greater than the pivot. |
| // This case is usually hit when the slice contains many duplicate elements. |
| if let Some(ref p) = pred { |
| if !is_less(p, &v[pivot]) { |
| let mid = partition_equal(v, pivot, is_less); |
| |
| // Continue sorting elements greater than the pivot. |
| v = &mut { v }[mid..]; |
| continue; |
| } |
| } |
| |
| // Partition the slice. |
| let (mid, was_p) = partition(v, pivot, is_less); |
| was_balanced = cmp::min(mid, len - mid) >= len / 8; |
| was_partitioned = was_p; |
| |
| // Split the slice into `left`, `pivot`, and `right`. |
| let (left, right) = { v }.split_at_mut(mid); |
| let (pivot, right) = right.split_at_mut(1); |
| let pivot = &mut pivot[0]; |
| |
| if cmp::max(left.len(), right.len()) <= MAX_SEQUENTIAL { |
| // Recurse into the shorter side only in order to minimize the total number of recursive |
| // calls and consume less stack space. Then just continue with the longer side (this is |
| // akin to tail recursion). |
| if left.len() < right.len() { |
| recurse(left, is_less, pred, limit); |
| v = right; |
| pred = Some(pivot); |
| } else { |
| recurse(right, is_less, Some(pivot), limit); |
| v = left; |
| } |
| } else { |
| // Sort the left and right half in parallel. |
| rayon_core::join( |
| || recurse(left, is_less, pred, limit), |
| || recurse(right, is_less, Some(pivot), limit), |
| ); |
| break; |
| } |
| } |
| } |
| |
| /// Sorts `v` using pattern-defeating quicksort in parallel. |
| /// |
| /// The algorithm is unstable, in-place, and `O(n log n)` worst-case. |
| pub(super) fn par_quicksort<T, F>(v: &mut [T], is_less: F) |
| where |
| T: Send, |
| F: Fn(&T, &T) -> bool + Sync, |
| { |
| // Sorting has no meaningful behavior on zero-sized types. |
| if mem::size_of::<T>() == 0 { |
| return; |
| } |
| |
| // Limit the number of imbalanced partitions to `floor(log2(len)) + 1`. |
| let limit = mem::size_of::<usize>() * 8 - v.len().leading_zeros() as usize; |
| |
| recurse(v, &is_less, None, limit); |
| } |
| |
| #[cfg(test)] |
| mod tests { |
| use super::heapsort; |
| use rand::distributions::Uniform; |
| use rand::{thread_rng, Rng}; |
| |
| #[test] |
| fn test_heapsort() { |
| let ref mut rng = thread_rng(); |
| |
| for len in (0..25).chain(500..501) { |
| for &modulus in &[5, 10, 100] { |
| let dist = Uniform::new(0, modulus); |
| for _ in 0..100 { |
| let v: Vec<i32> = rng.sample_iter(&dist).take(len).collect(); |
| |
| // Test heapsort using `<` operator. |
| let mut tmp = v.clone(); |
| heapsort(&mut tmp, &|a, b| a < b); |
| assert!(tmp.windows(2).all(|w| w[0] <= w[1])); |
| |
| // Test heapsort using `>` operator. |
| let mut tmp = v.clone(); |
| heapsort(&mut tmp, &|a, b| a > b); |
| assert!(tmp.windows(2).all(|w| w[0] >= w[1])); |
| } |
| } |
| } |
| |
| // Sort using a completely random comparison function. |
| // This will reorder the elements *somehow*, but won't panic. |
| let mut v: Vec<_> = (0..100).collect(); |
| heapsort(&mut v, &|_, _| thread_rng().gen()); |
| heapsort(&mut v, &|a, b| a < b); |
| |
| for i in 0..v.len() { |
| assert_eq!(v[i], i); |
| } |
| } |
| } |