| <!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="Source of the Rust file `/root/.cargo/git/checkouts/rayon-3b3b152053499ede/a07ce2e/src/slice/quicksort.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>quicksort.rs - source</title><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../SourceSerif4-Regular.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../FiraSans-Regular.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../FiraSans-Medium.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../SourceCodePro-Regular.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../SourceSerif4-Bold.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../SourceCodePro-Semibold.ttf.woff2"><link rel="stylesheet" href="../../../normalize.css"><link rel="stylesheet" href="../../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" href="../../../ayu.css" disabled><link rel="stylesheet" href="../../../dark.css" disabled><link rel="stylesheet" href="../../../light.css" id="themeStyle"><script id="default-settings" ></script><script src="../../../storage.js"></script><script defer src="../../../source-script.js"></script><script defer src="../../../source-files.js"></script><script defer src="../../../main.js"></script><noscript><link rel="stylesheet" href="../../../noscript.css"></noscript><link rel="alternate icon" type="image/png" href="../../../favicon-16x16.png"><link rel="alternate icon" type="image/png" href="../../../favicon-32x32.png"><link rel="icon" type="image/svg+xml" href="../../../favicon.svg"></head><body class="rustdoc source"><!--[if lte IE 11]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><a class="sidebar-logo" href="../../../rayon/index.html"><div class="logo-container"><img class="rust-logo" src="../../../rust-logo.svg" alt="logo"></div></a></nav><main><div class="width-limiter"><nav class="sub"><a class="sub-logo-container" href="../../../rayon/index.html"><img class="rust-logo" src="../../../rust-logo.svg" alt="logo"></a><form class="search-form"><div class="search-container"><span></span><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"><div id="help-button" title="help" tabindex="-1"><a href="../../../help.html">?</a></div><div id="settings-menu" tabindex="-1"><a href="../../../settings.html" title="settings"><img width="22" height="22" alt="Change settings" src="../../../wheel.svg"></a></div></div></form></nav><section id="main-content" class="content"><div class="example-wrap"><pre class="src-line-numbers"><span id="1">1</span> |
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| <span id="903">903</span> |
| </pre><pre class="rust"><code><span class="doccomment">//! 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`. |
| |
| </span><span class="kw">use </span>std::cmp; |
| <span class="kw">use </span>std::marker::PhantomData; |
| <span class="kw">use </span>std::mem::{<span class="self">self</span>, MaybeUninit}; |
| <span class="kw">use </span>std::ptr; |
| |
| <span class="doccomment">/// When dropped, copies from `src` into `dest`. |
| </span><span class="attribute">#[must_use] |
| </span><span class="kw">struct </span>CopyOnDrop<<span class="lifetime">'a</span>, T> { |
| src: <span class="kw-2">*const </span>T, |
| dest: <span class="kw-2">*mut </span>T, |
| <span class="doccomment">/// `src` is often a local pointer here, make sure we have appropriate |
| /// PhantomData so that dropck can protect us. |
| </span>marker: PhantomData<<span class="kw-2">&</span><span class="lifetime">'a </span><span class="kw-2">mut </span>T>, |
| } |
| |
| <span class="kw">impl</span><<span class="lifetime">'a</span>, T> CopyOnDrop<<span class="lifetime">'a</span>, T> { |
| <span class="doccomment">/// Construct from a source pointer and a destination |
| /// Assumes dest lives longer than src, since there is no easy way to |
| /// copy down lifetime information from another pointer |
| </span><span class="kw">unsafe fn </span>new(src: <span class="kw-2">&</span><span class="lifetime">'a </span>T, dest: <span class="kw-2">*mut </span>T) -> <span class="self">Self </span>{ |
| CopyOnDrop { |
| src, |
| dest, |
| marker: PhantomData, |
| } |
| } |
| } |
| |
| <span class="kw">impl</span><T> Drop <span class="kw">for </span>CopyOnDrop<<span class="lifetime">'_</span>, T> { |
| <span class="kw">fn </span>drop(<span class="kw-2">&mut </span><span class="self">self</span>) { |
| <span class="comment">// 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`. |
| </span><span class="kw">unsafe </span>{ |
| ptr::copy_nonoverlapping(<span class="self">self</span>.src, <span class="self">self</span>.dest, <span class="number">1</span>); |
| } |
| } |
| } |
| |
| <span class="doccomment">/// Shifts the first element to the right until it encounters a greater or equal element. |
| </span><span class="kw">fn </span>shift_head<T, F>(v: <span class="kw-2">&mut </span>[T], is_less: <span class="kw-2">&</span>F) |
| <span class="kw">where |
| </span>F: Fn(<span class="kw-2">&</span>T, <span class="kw-2">&</span>T) -> bool, |
| { |
| <span class="kw">let </span>len = v.len(); |
| <span class="comment">// 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. |
| </span><span class="kw">unsafe </span>{ |
| <span class="comment">// If the first two elements are out-of-order... |
| </span><span class="kw">if </span>len >= <span class="number">2 </span>&& is_less(v.get_unchecked(<span class="number">1</span>), v.get_unchecked(<span class="number">0</span>)) { |
| <span class="comment">// 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. |
| </span><span class="kw">let </span>tmp = mem::ManuallyDrop::new(ptr::read(v.get_unchecked(<span class="number">0</span>))); |
| <span class="kw">let </span>v = v.as_mut_ptr(); |
| <span class="kw">let </span><span class="kw-2">mut </span>hole = CopyOnDrop::new(<span class="kw-2">&*</span>tmp, v.add(<span class="number">1</span>)); |
| ptr::copy_nonoverlapping(v.add(<span class="number">1</span>), v.add(<span class="number">0</span>), <span class="number">1</span>); |
| |
| <span class="kw">for </span>i <span class="kw">in </span><span class="number">2</span>..len { |
| <span class="kw">if </span>!is_less(<span class="kw-2">&*</span>v.add(i), <span class="kw-2">&*</span>tmp) { |
| <span class="kw">break</span>; |
| } |
| |
| <span class="comment">// Move `i`-th element one place to the left, thus shifting the hole to the right. |
| </span>ptr::copy_nonoverlapping(v.add(i), v.add(i - <span class="number">1</span>), <span class="number">1</span>); |
| hole.dest = v.add(i); |
| } |
| <span class="comment">// `hole` gets dropped and thus copies `tmp` into the remaining hole in `v`. |
| </span>} |
| } |
| } |
| |
| <span class="doccomment">/// Shifts the last element to the left until it encounters a smaller or equal element. |
| </span><span class="kw">fn </span>shift_tail<T, F>(v: <span class="kw-2">&mut </span>[T], is_less: <span class="kw-2">&</span>F) |
| <span class="kw">where |
| </span>F: Fn(<span class="kw-2">&</span>T, <span class="kw-2">&</span>T) -> bool, |
| { |
| <span class="kw">let </span>len = v.len(); |
| <span class="comment">// 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. |
| </span><span class="kw">unsafe </span>{ |
| <span class="comment">// If the last two elements are out-of-order... |
| </span><span class="kw">if </span>len >= <span class="number">2 </span>&& is_less(v.get_unchecked(len - <span class="number">1</span>), v.get_unchecked(len - <span class="number">2</span>)) { |
| <span class="comment">// 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. |
| </span><span class="kw">let </span>tmp = mem::ManuallyDrop::new(ptr::read(v.get_unchecked(len - <span class="number">1</span>))); |
| <span class="kw">let </span>v = v.as_mut_ptr(); |
| <span class="kw">let </span><span class="kw-2">mut </span>hole = CopyOnDrop::new(<span class="kw-2">&*</span>tmp, v.add(len - <span class="number">2</span>)); |
| ptr::copy_nonoverlapping(v.add(len - <span class="number">2</span>), v.add(len - <span class="number">1</span>), <span class="number">1</span>); |
| |
| <span class="kw">for </span>i <span class="kw">in </span>(<span class="number">0</span>..len - <span class="number">2</span>).rev() { |
| <span class="kw">if </span>!is_less(<span class="kw-2">&*</span>tmp, <span class="kw-2">&*</span>v.add(i)) { |
| <span class="kw">break</span>; |
| } |
| |
| <span class="comment">// Move `i`-th element one place to the right, thus shifting the hole to the left. |
| </span>ptr::copy_nonoverlapping(v.add(i), v.add(i + <span class="number">1</span>), <span class="number">1</span>); |
| hole.dest = v.add(i); |
| } |
| <span class="comment">// `hole` gets dropped and thus copies `tmp` into the remaining hole in `v`. |
| </span>} |
| } |
| } |
| |
| <span class="doccomment">/// 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. |
| </span><span class="attribute">#[cold] |
| </span><span class="kw">fn </span>partial_insertion_sort<T, F>(v: <span class="kw-2">&mut </span>[T], is_less: <span class="kw-2">&</span>F) -> bool |
| <span class="kw">where |
| </span>F: Fn(<span class="kw-2">&</span>T, <span class="kw-2">&</span>T) -> bool, |
| { |
| <span class="comment">// Maximum number of adjacent out-of-order pairs that will get shifted. |
| </span><span class="kw">const </span>MAX_STEPS: usize = <span class="number">5</span>; |
| <span class="comment">// If the slice is shorter than this, don't shift any elements. |
| </span><span class="kw">const </span>SHORTEST_SHIFTING: usize = <span class="number">50</span>; |
| |
| <span class="kw">let </span>len = v.len(); |
| <span class="kw">let </span><span class="kw-2">mut </span>i = <span class="number">1</span>; |
| |
| <span class="kw">for _ in </span><span class="number">0</span>..MAX_STEPS { |
| <span class="comment">// SAFETY: We already explicitly did the bound checking with `i < len`. |
| // All our subsequent indexing is only in the range `0 <= index < len` |
| </span><span class="kw">unsafe </span>{ |
| <span class="comment">// Find the next pair of adjacent out-of-order elements. |
| </span><span class="kw">while </span>i < len && !is_less(v.get_unchecked(i), v.get_unchecked(i - <span class="number">1</span>)) { |
| i += <span class="number">1</span>; |
| } |
| } |
| |
| <span class="comment">// Are we done? |
| </span><span class="kw">if </span>i == len { |
| <span class="kw">return </span><span class="bool-val">true</span>; |
| } |
| |
| <span class="comment">// Don't shift elements on short arrays, that has a performance cost. |
| </span><span class="kw">if </span>len < SHORTEST_SHIFTING { |
| <span class="kw">return </span><span class="bool-val">false</span>; |
| } |
| |
| <span class="comment">// Swap the found pair of elements. This puts them in correct order. |
| </span>v.swap(i - <span class="number">1</span>, i); |
| |
| <span class="comment">// Shift the smaller element to the left. |
| </span>shift_tail(<span class="kw-2">&mut </span>v[..i], is_less); |
| <span class="comment">// Shift the greater element to the right. |
| </span>shift_head(<span class="kw-2">&mut </span>v[i..], is_less); |
| } |
| |
| <span class="comment">// Didn't manage to sort the slice in the limited number of steps. |
| </span><span class="bool-val">false |
| </span>} |
| |
| <span class="doccomment">/// Sorts a slice using insertion sort, which is *O*(*n*^2) worst-case. |
| </span><span class="kw">fn </span>insertion_sort<T, F>(v: <span class="kw-2">&mut </span>[T], is_less: <span class="kw-2">&</span>F) |
| <span class="kw">where |
| </span>F: Fn(<span class="kw-2">&</span>T, <span class="kw-2">&</span>T) -> bool, |
| { |
| <span class="kw">for </span>i <span class="kw">in </span><span class="number">1</span>..v.len() { |
| shift_tail(<span class="kw-2">&mut </span>v[..i + <span class="number">1</span>], is_less); |
| } |
| } |
| |
| <span class="doccomment">/// Sorts `v` using heapsort, which guarantees *O*(*n* \* log(*n*)) worst-case. |
| </span><span class="attribute">#[cold] |
| </span><span class="kw">fn </span>heapsort<T, F>(v: <span class="kw-2">&mut </span>[T], is_less: <span class="kw-2">&</span>F) |
| <span class="kw">where |
| </span>F: Fn(<span class="kw-2">&</span>T, <span class="kw-2">&</span>T) -> bool, |
| { |
| <span class="comment">// This binary heap respects the invariant `parent >= child`. |
| </span><span class="kw">let </span>sift_down = |v: <span class="kw-2">&mut </span>[T], <span class="kw-2">mut </span>node| { |
| <span class="kw">loop </span>{ |
| <span class="comment">// Children of `node`. |
| </span><span class="kw">let </span><span class="kw-2">mut </span>child = <span class="number">2 </span>* node + <span class="number">1</span>; |
| <span class="kw">if </span>child >= v.len() { |
| <span class="kw">break</span>; |
| } |
| |
| <span class="comment">// Choose the greater child. |
| </span><span class="kw">if </span>child + <span class="number">1 </span>< v.len() && is_less(<span class="kw-2">&</span>v[child], <span class="kw-2">&</span>v[child + <span class="number">1</span>]) { |
| child += <span class="number">1</span>; |
| } |
| |
| <span class="comment">// Stop if the invariant holds at `node`. |
| </span><span class="kw">if </span>!is_less(<span class="kw-2">&</span>v[node], <span class="kw-2">&</span>v[child]) { |
| <span class="kw">break</span>; |
| } |
| |
| <span class="comment">// Swap `node` with the greater child, move one step down, and continue sifting. |
| </span>v.swap(node, child); |
| node = child; |
| } |
| }; |
| |
| <span class="comment">// Build the heap in linear time. |
| </span><span class="kw">for </span>i <span class="kw">in </span>(<span class="number">0</span>..v.len() / <span class="number">2</span>).rev() { |
| sift_down(v, i); |
| } |
| |
| <span class="comment">// Pop maximal elements from the heap. |
| </span><span class="kw">for </span>i <span class="kw">in </span>(<span class="number">1</span>..v.len()).rev() { |
| v.swap(<span class="number">0</span>, i); |
| sift_down(<span class="kw-2">&mut </span>v[..i], <span class="number">0</span>); |
| } |
| } |
| |
| <span class="doccomment">/// 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 |
| </span><span class="kw">fn </span>partition_in_blocks<T, F>(v: <span class="kw-2">&mut </span>[T], pivot: <span class="kw-2">&</span>T, is_less: <span class="kw-2">&</span>F) -> usize |
| <span class="kw">where |
| </span>F: Fn(<span class="kw-2">&</span>T, <span class="kw-2">&</span>T) -> bool, |
| { |
| <span class="comment">// Number of elements in a typical block. |
| </span><span class="kw">const </span>BLOCK: usize = <span class="number">128</span>; |
| |
| <span class="comment">// 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)`). |
| </span><span class="kw">let </span><span class="kw-2">mut </span>l = v.as_mut_ptr(); |
| <span class="kw">let </span><span class="kw-2">mut </span>block_l = BLOCK; |
| <span class="kw">let </span><span class="kw-2">mut </span>start_l = ptr::null_mut(); |
| <span class="kw">let </span><span class="kw-2">mut </span>end_l = ptr::null_mut(); |
| <span class="kw">let </span><span class="kw-2">mut </span>offsets_l = [MaybeUninit::<u8>::uninit(); BLOCK]; |
| |
| <span class="comment">// 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` |
| </span><span class="kw">let </span><span class="kw-2">mut </span>r = <span class="kw">unsafe </span>{ l.add(v.len()) }; |
| <span class="kw">let </span><span class="kw-2">mut </span>block_r = BLOCK; |
| <span class="kw">let </span><span class="kw-2">mut </span>start_r = ptr::null_mut(); |
| <span class="kw">let </span><span class="kw-2">mut </span>end_r = ptr::null_mut(); |
| <span class="kw">let </span><span class="kw-2">mut </span>offsets_r = [MaybeUninit::<u8>::uninit(); BLOCK]; |
| |
| <span class="comment">// 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). |
| </span><span class="kw">fn </span>width<T>(l: <span class="kw-2">*mut </span>T, r: <span class="kw-2">*mut </span>T) -> usize { |
| <span class="macro">assert!</span>(mem::size_of::<T>() > <span class="number">0</span>); |
| <span class="comment">// FIXME: this should *likely* use `offset_from`, but more |
| // investigation is needed (including running tests in miri). |
| // TODO unstable: (r.addr() - l.addr()) / mem::size_of::<T>() |
| </span>(r <span class="kw">as </span>usize - l <span class="kw">as </span>usize) / mem::size_of::<T>() |
| } |
| |
| <span class="kw">loop </span>{ |
| <span class="comment">// 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. |
| </span><span class="kw">let </span>is_done = width(l, r) <= <span class="number">2 </span>* BLOCK; |
| |
| <span class="kw">if </span>is_done { |
| <span class="comment">// Number of remaining elements (still not compared to the pivot). |
| </span><span class="kw">let </span><span class="kw-2">mut </span>rem = width(l, r); |
| <span class="kw">if </span>start_l < end_l || start_r < end_r { |
| rem -= BLOCK; |
| } |
| |
| <span class="comment">// Adjust block sizes so that the left and right block don't overlap, but get perfectly |
| // aligned to cover the whole remaining gap. |
| </span><span class="kw">if </span>start_l < end_l { |
| block_r = rem; |
| } <span class="kw">else if </span>start_r < end_r { |
| block_l = rem; |
| } <span class="kw">else </span>{ |
| <span class="comment">// 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. |
| </span>block_l = rem / <span class="number">2</span>; |
| block_r = rem - block_l; |
| } |
| <span class="macro">debug_assert!</span>(block_l <= BLOCK && block_r <= BLOCK); |
| <span class="macro">debug_assert!</span>(width(l, r) == block_l + block_r); |
| } |
| |
| <span class="kw">if </span>start_l == end_l { |
| <span class="comment">// Trace `block_l` elements from the left side. |
| // TODO unstable: start_l = MaybeUninit::slice_as_mut_ptr(&mut offsets_l); |
| </span>start_l = offsets_l.as_mut_ptr() <span class="kw">as </span><span class="kw-2">*mut </span>u8; |
| end_l = start_l; |
| <span class="kw">let </span><span class="kw-2">mut </span>elem = l; |
| |
| <span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..block_l { |
| <span class="comment">// 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. |
| </span><span class="kw">unsafe </span>{ |
| <span class="comment">// Branchless comparison. |
| </span><span class="kw-2">*</span>end_l = i <span class="kw">as </span>u8; |
| end_l = end_l.offset(!is_less(<span class="kw-2">&*</span>elem, pivot) <span class="kw">as </span>isize); |
| elem = elem.offset(<span class="number">1</span>); |
| } |
| } |
| } |
| |
| <span class="kw">if </span>start_r == end_r { |
| <span class="comment">// Trace `block_r` elements from the right side. |
| // TODO unstable: start_r = MaybeUninit::slice_as_mut_ptr(&mut offsets_r); |
| </span>start_r = offsets_r.as_mut_ptr() <span class="kw">as </span><span class="kw-2">*mut </span>u8; |
| end_r = start_r; |
| <span class="kw">let </span><span class="kw-2">mut </span>elem = r; |
| |
| <span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..block_r { |
| <span class="comment">// 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. |
| </span><span class="kw">unsafe </span>{ |
| <span class="comment">// Branchless comparison. |
| </span>elem = elem.offset(-<span class="number">1</span>); |
| <span class="kw-2">*</span>end_r = i <span class="kw">as </span>u8; |
| end_r = end_r.offset(is_less(<span class="kw-2">&*</span>elem, pivot) <span class="kw">as </span>isize); |
| } |
| } |
| } |
| |
| <span class="comment">// Number of out-of-order elements to swap between the left and right side. |
| </span><span class="kw">let </span>count = cmp::min(width(start_l, end_l), width(start_r, end_r)); |
| |
| <span class="kw">if </span>count > <span class="number">0 </span>{ |
| <span class="macro">macro_rules! </span>left { |
| () => { |
| l.offset(<span class="kw-2">*</span>start_l <span class="kw">as </span>isize) |
| }; |
| } |
| <span class="macro">macro_rules! </span>right { |
| () => { |
| r.offset(-(<span class="kw-2">*</span>start_r <span class="kw">as </span>isize) - <span class="number">1</span>) |
| }; |
| } |
| |
| <span class="comment">// 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. |
| </span><span class="kw">unsafe </span>{ |
| <span class="kw">let </span>tmp = ptr::read(<span class="macro">left!</span>()); |
| ptr::copy_nonoverlapping(<span class="macro">right!</span>(), <span class="macro">left!</span>(), <span class="number">1</span>); |
| |
| <span class="kw">for _ in </span><span class="number">1</span>..count { |
| start_l = start_l.offset(<span class="number">1</span>); |
| ptr::copy_nonoverlapping(<span class="macro">left!</span>(), <span class="macro">right!</span>(), <span class="number">1</span>); |
| start_r = start_r.offset(<span class="number">1</span>); |
| ptr::copy_nonoverlapping(<span class="macro">right!</span>(), <span class="macro">left!</span>(), <span class="number">1</span>); |
| } |
| |
| ptr::copy_nonoverlapping(<span class="kw-2">&</span>tmp, <span class="macro">right!</span>(), <span class="number">1</span>); |
| mem::forget(tmp); |
| start_l = start_l.offset(<span class="number">1</span>); |
| start_r = start_r.offset(<span class="number">1</span>); |
| } |
| } |
| |
| <span class="kw">if </span>start_l == end_l { |
| <span class="comment">// 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. |
| </span>l = <span class="kw">unsafe </span>{ l.add(block_l) }; |
| } |
| |
| <span class="kw">if </span>start_r == end_r { |
| <span class="comment">// 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. |
| </span>r = <span class="kw">unsafe </span>{ r.offset(-(block_r <span class="kw">as </span>isize)) }; |
| } |
| |
| <span class="kw">if </span>is_done { |
| <span class="kw">break</span>; |
| } |
| } |
| |
| <span class="comment">// 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. |
| |
| </span><span class="kw">if </span>start_l < end_l { |
| <span class="comment">// The left block remains. |
| // Move its remaining out-of-order elements to the far right. |
| </span><span class="macro">debug_assert_eq!</span>(width(l, r), block_l); |
| <span class="kw">while </span>start_l < end_l { |
| <span class="comment">// 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. |
| </span><span class="kw">unsafe </span>{ |
| end_l = end_l.offset(-<span class="number">1</span>); |
| ptr::swap(l.offset(<span class="kw-2">*</span>end_l <span class="kw">as </span>isize), r.offset(-<span class="number">1</span>)); |
| r = r.offset(-<span class="number">1</span>); |
| } |
| } |
| width(v.as_mut_ptr(), r) |
| } <span class="kw">else if </span>start_r < end_r { |
| <span class="comment">// The right block remains. |
| // Move its remaining out-of-order elements to the far left. |
| </span><span class="macro">debug_assert_eq!</span>(width(l, r), block_r); |
| <span class="kw">while </span>start_r < end_r { |
| <span class="comment">// SAFETY: See the reasoning in [remaining-elements-safety]. |
| </span><span class="kw">unsafe </span>{ |
| end_r = end_r.offset(-<span class="number">1</span>); |
| ptr::swap(l, r.offset(-(<span class="kw-2">*</span>end_r <span class="kw">as </span>isize) - <span class="number">1</span>)); |
| l = l.offset(<span class="number">1</span>); |
| } |
| } |
| width(v.as_mut_ptr(), l) |
| } <span class="kw">else </span>{ |
| <span class="comment">// Nothing else to do, we're done. |
| </span>width(v.as_mut_ptr(), l) |
| } |
| } |
| |
| <span class="doccomment">/// 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. |
| </span><span class="kw">fn </span>partition<T, F>(v: <span class="kw-2">&mut </span>[T], pivot: usize, is_less: <span class="kw-2">&</span>F) -> (usize, bool) |
| <span class="kw">where |
| </span>F: Fn(<span class="kw-2">&</span>T, <span class="kw-2">&</span>T) -> bool, |
| { |
| <span class="kw">let </span>(mid, was_partitioned) = { |
| <span class="comment">// Place the pivot at the beginning of slice. |
| </span>v.swap(<span class="number">0</span>, pivot); |
| <span class="kw">let </span>(pivot, v) = v.split_at_mut(<span class="number">1</span>); |
| <span class="kw">let </span>pivot = <span class="kw-2">&mut </span>pivot[<span class="number">0</span>]; |
| |
| <span class="comment">// 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. |
| </span><span class="kw">let </span>tmp = mem::ManuallyDrop::new(<span class="kw">unsafe </span>{ ptr::read(pivot) }); |
| <span class="kw">let </span>_pivot_guard = <span class="kw">unsafe </span>{ CopyOnDrop::new(<span class="kw-2">&*</span>tmp, pivot) }; |
| <span class="kw">let </span>pivot = <span class="kw-2">&*</span>tmp; |
| |
| <span class="comment">// Find the first pair of out-of-order elements. |
| </span><span class="kw">let </span><span class="kw-2">mut </span>l = <span class="number">0</span>; |
| <span class="kw">let </span><span class="kw-2">mut </span>r = v.len(); |
| |
| <span class="comment">// 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. |
| </span><span class="kw">unsafe </span>{ |
| <span class="comment">// Find the first element greater than or equal to the pivot. |
| </span><span class="kw">while </span>l < r && is_less(v.get_unchecked(l), pivot) { |
| l += <span class="number">1</span>; |
| } |
| |
| <span class="comment">// Find the last element smaller that the pivot. |
| </span><span class="kw">while </span>l < r && !is_less(v.get_unchecked(r - <span class="number">1</span>), pivot) { |
| r -= <span class="number">1</span>; |
| } |
| } |
| |
| ( |
| l + partition_in_blocks(<span class="kw-2">&mut </span>v[l..r], pivot, is_less), |
| l >= r, |
| ) |
| |
| <span class="comment">// `_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! |
| </span>}; |
| |
| <span class="comment">// Place the pivot between the two partitions. |
| </span>v.swap(<span class="number">0</span>, mid); |
| |
| (mid, was_partitioned) |
| } |
| |
| <span class="doccomment">/// 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. |
| </span><span class="kw">fn </span>partition_equal<T, F>(v: <span class="kw-2">&mut </span>[T], pivot: usize, is_less: <span class="kw-2">&</span>F) -> usize |
| <span class="kw">where |
| </span>F: Fn(<span class="kw-2">&</span>T, <span class="kw-2">&</span>T) -> bool, |
| { |
| <span class="comment">// Place the pivot at the beginning of slice. |
| </span>v.swap(<span class="number">0</span>, pivot); |
| <span class="kw">let </span>(pivot, v) = v.split_at_mut(<span class="number">1</span>); |
| <span class="kw">let </span>pivot = <span class="kw-2">&mut </span>pivot[<span class="number">0</span>]; |
| |
| <span class="comment">// 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. |
| </span><span class="kw">let </span>tmp = mem::ManuallyDrop::new(<span class="kw">unsafe </span>{ ptr::read(pivot) }); |
| <span class="kw">let </span>_pivot_guard = <span class="kw">unsafe </span>{ CopyOnDrop::new(<span class="kw-2">&*</span>tmp, pivot) }; |
| <span class="kw">let </span>pivot = <span class="kw-2">&*</span>tmp; |
| |
| <span class="comment">// Now partition the slice. |
| </span><span class="kw">let </span><span class="kw-2">mut </span>l = <span class="number">0</span>; |
| <span class="kw">let </span><span class="kw-2">mut </span>r = v.len(); |
| <span class="kw">loop </span>{ |
| <span class="comment">// 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. |
| </span><span class="kw">unsafe </span>{ |
| <span class="comment">// Find the first element greater than the pivot. |
| </span><span class="kw">while </span>l < r && !is_less(pivot, v.get_unchecked(l)) { |
| l += <span class="number">1</span>; |
| } |
| |
| <span class="comment">// Find the last element equal to the pivot. |
| </span><span class="kw">while </span>l < r && is_less(pivot, v.get_unchecked(r - <span class="number">1</span>)) { |
| r -= <span class="number">1</span>; |
| } |
| |
| <span class="comment">// Are we done? |
| </span><span class="kw">if </span>l >= r { |
| <span class="kw">break</span>; |
| } |
| |
| <span class="comment">// Swap the found pair of out-of-order elements. |
| </span>r -= <span class="number">1</span>; |
| <span class="kw">let </span>ptr = v.as_mut_ptr(); |
| ptr::swap(ptr.add(l), ptr.add(r)); |
| l += <span class="number">1</span>; |
| } |
| } |
| |
| <span class="comment">// We found `l` elements equal to the pivot. Add 1 to account for the pivot itself. |
| </span>l + <span class="number">1 |
| |
| </span><span class="comment">// `_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! |
| </span>} |
| |
| <span class="doccomment">/// Scatters some elements around in an attempt to break patterns that might cause imbalanced |
| /// partitions in quicksort. |
| </span><span class="attribute">#[cold] |
| </span><span class="kw">fn </span>break_patterns<T>(v: <span class="kw-2">&mut </span>[T]) { |
| <span class="kw">let </span>len = v.len(); |
| <span class="kw">if </span>len >= <span class="number">8 </span>{ |
| <span class="comment">// Pseudorandom number generator from the "Xorshift RNGs" paper by George Marsaglia. |
| </span><span class="kw">let </span><span class="kw-2">mut </span>random = len <span class="kw">as </span>u32; |
| <span class="kw">let </span><span class="kw-2">mut </span>gen_u32 = || { |
| random ^= random << <span class="number">13</span>; |
| random ^= random >> <span class="number">17</span>; |
| random ^= random << <span class="number">5</span>; |
| random |
| }; |
| <span class="kw">let </span><span class="kw-2">mut </span>gen_usize = || { |
| <span class="kw">if </span>usize::BITS <= <span class="number">32 </span>{ |
| gen_u32() <span class="kw">as </span>usize |
| } <span class="kw">else </span>{ |
| (((gen_u32() <span class="kw">as </span>u64) << <span class="number">32</span>) | (gen_u32() <span class="kw">as </span>u64)) <span class="kw">as </span>usize |
| } |
| }; |
| |
| <span class="comment">// Take random numbers modulo this number. |
| // The number fits into `usize` because `len` is not greater than `isize::MAX`. |
| </span><span class="kw">let </span>modulus = len.next_power_of_two(); |
| |
| <span class="comment">// Some pivot candidates will be in the nearby of this index. Let's randomize them. |
| </span><span class="kw">let </span>pos = len / <span class="number">4 </span>* <span class="number">2</span>; |
| |
| <span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..<span class="number">3 </span>{ |
| <span class="comment">// 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]`. |
| </span><span class="kw">let </span><span class="kw-2">mut </span>other = gen_usize() & (modulus - <span class="number">1</span>); |
| |
| <span class="comment">// `other` is guaranteed to be less than `2 * len`. |
| </span><span class="kw">if </span>other >= len { |
| other -= len; |
| } |
| |
| v.swap(pos - <span class="number">1 </span>+ i, other); |
| } |
| } |
| } |
| |
| <span class="doccomment">/// 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. |
| </span><span class="kw">fn </span>choose_pivot<T, F>(v: <span class="kw-2">&mut </span>[T], is_less: <span class="kw-2">&</span>F) -> (usize, bool) |
| <span class="kw">where |
| </span>F: Fn(<span class="kw-2">&</span>T, <span class="kw-2">&</span>T) -> bool, |
| { |
| <span class="comment">// Minimum length to choose the median-of-medians method. |
| // Shorter slices use the simple median-of-three method. |
| </span><span class="kw">const </span>SHORTEST_MEDIAN_OF_MEDIANS: usize = <span class="number">50</span>; |
| <span class="comment">// Maximum number of swaps that can be performed in this function. |
| </span><span class="kw">const </span>MAX_SWAPS: usize = <span class="number">4 </span>* <span class="number">3</span>; |
| |
| <span class="kw">let </span>len = v.len(); |
| |
| <span class="comment">// Three indices near which we are going to choose a pivot. |
| </span><span class="attribute">#[allow(clippy::identity_op)] |
| </span><span class="kw">let </span><span class="kw-2">mut </span>a = len / <span class="number">4 </span>* <span class="number">1</span>; |
| <span class="kw">let </span><span class="kw-2">mut </span>b = len / <span class="number">4 </span>* <span class="number">2</span>; |
| <span class="kw">let </span><span class="kw-2">mut </span>c = len / <span class="number">4 </span>* <span class="number">3</span>; |
| |
| <span class="comment">// Counts the total number of swaps we are about to perform while sorting indices. |
| </span><span class="kw">let </span><span class="kw-2">mut </span>swaps = <span class="number">0</span>; |
| |
| <span class="kw">if </span>len >= <span class="number">8 </span>{ |
| <span class="comment">// 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. |
| </span><span class="kw">let </span><span class="kw-2">mut </span>sort2 = |a: <span class="kw-2">&mut </span>usize, b: <span class="kw-2">&mut </span>usize| <span class="kw">unsafe </span>{ |
| <span class="kw">if </span>is_less(v.get_unchecked(<span class="kw-2">*</span>b), v.get_unchecked(<span class="kw-2">*</span>a)) { |
| ptr::swap(a, b); |
| swaps += <span class="number">1</span>; |
| } |
| }; |
| |
| <span class="comment">// Swaps indices so that `v[a] <= v[b] <= v[c]`. |
| </span><span class="kw">let </span><span class="kw-2">mut </span>sort3 = |a: <span class="kw-2">&mut </span>usize, b: <span class="kw-2">&mut </span>usize, c: <span class="kw-2">&mut </span>usize| { |
| sort2(a, b); |
| sort2(b, c); |
| sort2(a, b); |
| }; |
| |
| <span class="kw">if </span>len >= SHORTEST_MEDIAN_OF_MEDIANS { |
| <span class="comment">// Finds the median of `v[a - 1], v[a], v[a + 1]` and stores the index into `a`. |
| </span><span class="kw">let </span><span class="kw-2">mut </span>sort_adjacent = |a: <span class="kw-2">&mut </span>usize| { |
| <span class="kw">let </span>tmp = <span class="kw-2">*</span>a; |
| sort3(<span class="kw-2">&mut </span>(tmp - <span class="number">1</span>), a, <span class="kw-2">&mut </span>(tmp + <span class="number">1</span>)); |
| }; |
| |
| <span class="comment">// Find medians in the neighborhoods of `a`, `b`, and `c`. |
| </span>sort_adjacent(<span class="kw-2">&mut </span>a); |
| sort_adjacent(<span class="kw-2">&mut </span>b); |
| sort_adjacent(<span class="kw-2">&mut </span>c); |
| } |
| |
| <span class="comment">// Find the median among `a`, `b`, and `c`. |
| </span>sort3(<span class="kw-2">&mut </span>a, <span class="kw-2">&mut </span>b, <span class="kw-2">&mut </span>c); |
| } |
| |
| <span class="kw">if </span>swaps < MAX_SWAPS { |
| (b, swaps == <span class="number">0</span>) |
| } <span class="kw">else </span>{ |
| <span class="comment">// The maximum number of swaps was performed. Chances are the slice is descending or mostly |
| // descending, so reversing will probably help sort it faster. |
| </span>v.reverse(); |
| (len - <span class="number">1 </span>- b, <span class="bool-val">true</span>) |
| } |
| } |
| |
| <span class="doccomment">/// 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. |
| </span><span class="kw">fn </span>recurse<<span class="lifetime">'a</span>, T, F>(<span class="kw-2">mut </span>v: <span class="kw-2">&</span><span class="lifetime">'a </span><span class="kw-2">mut </span>[T], is_less: <span class="kw-2">&</span>F, <span class="kw-2">mut </span>pred: <span class="prelude-ty">Option</span><<span class="kw-2">&</span><span class="lifetime">'a </span><span class="kw-2">mut </span>T>, <span class="kw-2">mut </span>limit: u32) |
| <span class="kw">where |
| </span>T: Send, |
| F: Fn(<span class="kw-2">&</span>T, <span class="kw-2">&</span>T) -> bool + Sync, |
| { |
| <span class="comment">// Slices of up to this length get sorted using insertion sort. |
| </span><span class="kw">const </span>MAX_INSERTION: usize = <span class="number">20</span>; |
| <span class="comment">// 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. |
| </span><span class="kw">const </span>MAX_SEQUENTIAL: usize = <span class="number">2000</span>; |
| |
| <span class="comment">// True if the last partitioning was reasonably balanced. |
| </span><span class="kw">let </span><span class="kw-2">mut </span>was_balanced = <span class="bool-val">true</span>; |
| <span class="comment">// True if the last partitioning didn't shuffle elements (the slice was already partitioned). |
| </span><span class="kw">let </span><span class="kw-2">mut </span>was_partitioned = <span class="bool-val">true</span>; |
| |
| <span class="kw">loop </span>{ |
| <span class="kw">let </span>len = v.len(); |
| |
| <span class="comment">// Very short slices get sorted using insertion sort. |
| </span><span class="kw">if </span>len <= MAX_INSERTION { |
| insertion_sort(v, is_less); |
| <span class="kw">return</span>; |
| } |
| |
| <span class="comment">// If too many bad pivot choices were made, simply fall back to heapsort in order to |
| // guarantee `O(n * log(n))` worst-case. |
| </span><span class="kw">if </span>limit == <span class="number">0 </span>{ |
| heapsort(v, is_less); |
| <span class="kw">return</span>; |
| } |
| |
| <span class="comment">// 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. |
| </span><span class="kw">if </span>!was_balanced { |
| break_patterns(v); |
| limit -= <span class="number">1</span>; |
| } |
| |
| <span class="comment">// Choose a pivot and try guessing whether the slice is already sorted. |
| </span><span class="kw">let </span>(pivot, likely_sorted) = choose_pivot(v, is_less); |
| |
| <span class="comment">// If the last partitioning was decently balanced and didn't shuffle elements, and if pivot |
| // selection predicts the slice is likely already sorted... |
| </span><span class="kw">if </span>was_balanced && was_partitioned && likely_sorted { |
| <span class="comment">// Try identifying several out-of-order elements and shifting them to correct |
| // positions. If the slice ends up being completely sorted, we're done. |
| </span><span class="kw">if </span>partial_insertion_sort(v, is_less) { |
| <span class="kw">return</span>; |
| } |
| } |
| |
| <span class="comment">// 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. |
| </span><span class="kw">if let </span><span class="prelude-val">Some</span>(<span class="kw-2">ref </span>p) = pred { |
| <span class="kw">if </span>!is_less(p, <span class="kw-2">&</span>v[pivot]) { |
| <span class="kw">let </span>mid = partition_equal(v, pivot, is_less); |
| |
| <span class="comment">// Continue sorting elements greater than the pivot. |
| </span>v = <span class="kw-2">&mut </span>v[mid..]; |
| <span class="kw">continue</span>; |
| } |
| } |
| |
| <span class="comment">// Partition the slice. |
| </span><span class="kw">let </span>(mid, was_p) = partition(v, pivot, is_less); |
| was_balanced = cmp::min(mid, len - mid) >= len / <span class="number">8</span>; |
| was_partitioned = was_p; |
| |
| <span class="comment">// Split the slice into `left`, `pivot`, and `right`. |
| </span><span class="kw">let </span>(left, right) = v.split_at_mut(mid); |
| <span class="kw">let </span>(pivot, right) = right.split_at_mut(<span class="number">1</span>); |
| <span class="kw">let </span>pivot = <span class="kw-2">&mut </span>pivot[<span class="number">0</span>]; |
| |
| <span class="kw">if </span>cmp::max(left.len(), right.len()) <= MAX_SEQUENTIAL { |
| <span class="comment">// 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). |
| </span><span class="kw">if </span>left.len() < right.len() { |
| recurse(left, is_less, pred, limit); |
| v = right; |
| pred = <span class="prelude-val">Some</span>(pivot); |
| } <span class="kw">else </span>{ |
| recurse(right, is_less, <span class="prelude-val">Some</span>(pivot), limit); |
| v = left; |
| } |
| } <span class="kw">else </span>{ |
| <span class="comment">// Sort the left and right half in parallel. |
| </span>rayon_core::join( |
| || recurse(left, is_less, pred, limit), |
| || recurse(right, is_less, <span class="prelude-val">Some</span>(pivot), limit), |
| ); |
| <span class="kw">break</span>; |
| } |
| } |
| } |
| |
| <span class="doccomment">/// Sorts `v` using pattern-defeating quicksort in parallel. |
| /// |
| /// The algorithm is unstable, in-place, and *O*(*n* \* log(*n*)) worst-case. |
| </span><span class="kw">pub</span>(<span class="kw">super</span>) <span class="kw">fn </span>par_quicksort<T, F>(v: <span class="kw-2">&mut </span>[T], is_less: F) |
| <span class="kw">where |
| </span>T: Send, |
| F: Fn(<span class="kw-2">&</span>T, <span class="kw-2">&</span>T) -> bool + Sync, |
| { |
| <span class="comment">// Sorting has no meaningful behavior on zero-sized types. |
| </span><span class="kw">if </span>mem::size_of::<T>() == <span class="number">0 </span>{ |
| <span class="kw">return</span>; |
| } |
| |
| <span class="comment">// Limit the number of imbalanced partitions to `floor(log2(len)) + 1`. |
| </span><span class="kw">let </span>limit = usize::BITS - v.len().leading_zeros(); |
| |
| recurse(v, <span class="kw-2">&</span>is_less, <span class="prelude-val">None</span>, limit); |
| } |
| |
| <span class="attribute">#[cfg(test)] |
| </span><span class="kw">mod </span>tests { |
| <span class="kw">use </span><span class="kw">super</span>::heapsort; |
| <span class="kw">use </span>rand::distributions::Uniform; |
| <span class="kw">use </span>rand::{thread_rng, Rng}; |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_heapsort() { |
| <span class="kw">let </span>rng = <span class="kw-2">&mut </span>thread_rng(); |
| |
| <span class="kw">for </span>len <span class="kw">in </span>(<span class="number">0</span>..<span class="number">25</span>).chain(<span class="number">500</span>..<span class="number">501</span>) { |
| <span class="kw">for </span><span class="kw-2">&</span>modulus <span class="kw">in </span><span class="kw-2">&</span>[<span class="number">5</span>, <span class="number">10</span>, <span class="number">100</span>] { |
| <span class="kw">let </span>dist = Uniform::new(<span class="number">0</span>, modulus); |
| <span class="kw">for _ in </span><span class="number">0</span>..<span class="number">100 </span>{ |
| <span class="kw">let </span>v: Vec<i32> = rng.sample_iter(<span class="kw-2">&</span>dist).take(len).collect(); |
| |
| <span class="comment">// Test heapsort using `<` operator. |
| </span><span class="kw">let </span><span class="kw-2">mut </span>tmp = v.clone(); |
| heapsort(<span class="kw-2">&mut </span>tmp, <span class="kw-2">&</span>|a, b| a < b); |
| <span class="macro">assert!</span>(tmp.windows(<span class="number">2</span>).all(|w| w[<span class="number">0</span>] <= w[<span class="number">1</span>])); |
| |
| <span class="comment">// Test heapsort using `>` operator. |
| </span><span class="kw">let </span><span class="kw-2">mut </span>tmp = v.clone(); |
| heapsort(<span class="kw-2">&mut </span>tmp, <span class="kw-2">&</span>|a, b| a > b); |
| <span class="macro">assert!</span>(tmp.windows(<span class="number">2</span>).all(|w| w[<span class="number">0</span>] >= w[<span class="number">1</span>])); |
| } |
| } |
| } |
| |
| <span class="comment">// Sort using a completely random comparison function. |
| // This will reorder the elements *somehow*, but won't panic. |
| </span><span class="kw">let </span><span class="kw-2">mut </span>v: Vec<<span class="kw">_</span>> = (<span class="number">0</span>..<span class="number">100</span>).collect(); |
| heapsort(<span class="kw-2">&mut </span>v, <span class="kw-2">&</span>|<span class="kw">_</span>, <span class="kw">_</span>| thread_rng().gen()); |
| heapsort(<span class="kw-2">&mut </span>v, <span class="kw-2">&</span>|a, b| a < b); |
| |
| <span class="kw">for </span>(i, <span class="kw-2">&</span>entry) <span class="kw">in </span>v.iter().enumerate() { |
| <span class="macro">assert_eq!</span>(entry, i); |
| } |
| } |
| } |
| </code></pre></div> |
| </section></div></main><div id="rustdoc-vars" data-root-path="../../../" data-current-crate="rayon" data-themes="ayu,dark,light" data-resource-suffix="" data-rustdoc-version="1.66.0-nightly (5c8bff74b 2022-10-21)" ></div></body></html> |
