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</pre><pre class="rust ">
<span class="comment">// Copyright 2017 The Rust Project Developers. See the COPYRIGHT</span>
<span class="comment">// file at the top-level directory of this distribution and at</span>
<span class="comment">// http://rust-lang.org/COPYRIGHT.</span>
<span class="comment">//</span>
<span class="comment">// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or</span>
<span class="comment">// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license</span>
<span class="comment">// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your</span>
<span class="comment">// option. This file may not be copied, modified, or distributed</span>
<span class="comment">// except according to those terms.</span>
<span class="doccomment">//! Slice sorting</span>
<span class="doccomment">//!</span>
<span class="doccomment">//! This module contains an sort algorithm based on Orson Peters' pattern-defeating quicksort,</span>
<span class="doccomment">//! published at: https://github.com/orlp/pdqsort</span>
<span class="doccomment">//!</span>
<span class="doccomment">//! Unstable sorting is compatible with libcore because it doesn't allocate memory, unlike our</span>
<span class="doccomment">//! stable sorting implementation.</span>
<span class="kw">use</span> <span class="ident">cmp</span>;
<span class="kw">use</span> <span class="ident">mem</span>;
<span class="kw">use</span> <span class="ident">ptr</span>;
<span class="doccomment">/// When dropped, copies from `src` into `dest`.</span>
<span class="kw">struct</span> <span class="ident">CopyOnDrop</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="ident">src</span>: <span class="kw-2">*</span><span class="kw-2">mut</span> <span class="ident">T</span>,
<span class="ident">dest</span>: <span class="kw-2">*</span><span class="kw-2">mut</span> <span class="ident">T</span>,
}
<span class="kw">impl</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> <span class="ident">Drop</span> <span class="kw">for</span> <span class="ident">CopyOnDrop</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="kw">fn</span> <span class="ident">drop</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="self">self</span>) {
<span class="kw">unsafe</span> { <span class="ident">ptr</span>::<span class="ident">copy_nonoverlapping</span>(<span class="self">self</span>.<span class="ident">src</span>, <span class="self">self</span>.<span class="ident">dest</span>, <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> <span class="ident">shift_head</span><span class="op"><</span><span class="ident">T</span>, <span class="ident">F</span><span class="op">></span>(<span class="ident">v</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> [<span class="ident">T</span>], <span class="ident">is_less</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">F</span>)
<span class="kw">where</span> <span class="ident">F</span>: <span class="ident">FnMut</span>(<span class="kw-2">&</span><span class="ident">T</span>, <span class="kw-2">&</span><span class="ident">T</span>) <span class="op">-></span> <span class="ident">bool</span>
{
<span class="kw">let</span> <span class="ident">len</span> <span class="op">=</span> <span class="ident">v</span>.<span class="ident">len</span>();
<span class="kw">unsafe</span> {
<span class="comment">// If the first two elements are out-of-order...</span>
<span class="kw">if</span> <span class="ident">len</span> <span class="op">>=</span> <span class="number">2</span> <span class="op">&&</span> <span class="ident">is_less</span>(<span class="ident">v</span>.<span class="ident">get_unchecked</span>(<span class="number">1</span>), <span class="ident">v</span>.<span class="ident">get_unchecked</span>(<span class="number">0</span>)) {
<span class="comment">// Read the first element into a stack-allocated variable. If a following comparison</span>
<span class="comment">// operation panics, `hole` will get dropped and automatically write the element back</span>
<span class="comment">// into the slice.</span>
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">tmp</span> <span class="op">=</span> <span class="ident">mem</span>::<span class="ident">ManuallyDrop</span>::<span class="ident">new</span>(<span class="ident">ptr</span>::<span class="ident">read</span>(<span class="ident">v</span>.<span class="ident">get_unchecked</span>(<span class="number">0</span>)));
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">hole</span> <span class="op">=</span> <span class="ident">CopyOnDrop</span> {
<span class="ident">src</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="kw-2">*</span><span class="ident">tmp</span>,
<span class="ident">dest</span>: <span class="ident">v</span>.<span class="ident">get_unchecked_mut</span>(<span class="number">1</span>),
};
<span class="ident">ptr</span>::<span class="ident">copy_nonoverlapping</span>(<span class="ident">v</span>.<span class="ident">get_unchecked</span>(<span class="number">1</span>), <span class="ident">v</span>.<span class="ident">get_unchecked_mut</span>(<span class="number">0</span>), <span class="number">1</span>);
<span class="kw">for</span> <span class="ident">i</span> <span class="kw">in</span> <span class="number">2</span>..<span class="ident">len</span> {
<span class="kw">if</span> <span class="op">!</span><span class="ident">is_less</span>(<span class="ident">v</span>.<span class="ident">get_unchecked</span>(<span class="ident">i</span>), <span class="kw-2">&</span><span class="kw-2">*</span><span class="ident">tmp</span>) {
<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>
<span class="ident">ptr</span>::<span class="ident">copy_nonoverlapping</span>(<span class="ident">v</span>.<span class="ident">get_unchecked</span>(<span class="ident">i</span>), <span class="ident">v</span>.<span class="ident">get_unchecked_mut</span>(<span class="ident">i</span> <span class="op">-</span> <span class="number">1</span>), <span class="number">1</span>);
<span class="ident">hole</span>.<span class="ident">dest</span> <span class="op">=</span> <span class="ident">v</span>.<span class="ident">get_unchecked_mut</span>(<span class="ident">i</span>);
}
<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> <span class="ident">shift_tail</span><span class="op"><</span><span class="ident">T</span>, <span class="ident">F</span><span class="op">></span>(<span class="ident">v</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> [<span class="ident">T</span>], <span class="ident">is_less</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">F</span>)
<span class="kw">where</span> <span class="ident">F</span>: <span class="ident">FnMut</span>(<span class="kw-2">&</span><span class="ident">T</span>, <span class="kw-2">&</span><span class="ident">T</span>) <span class="op">-></span> <span class="ident">bool</span>
{
<span class="kw">let</span> <span class="ident">len</span> <span class="op">=</span> <span class="ident">v</span>.<span class="ident">len</span>();
<span class="kw">unsafe</span> {
<span class="comment">// If the last two elements are out-of-order...</span>
<span class="kw">if</span> <span class="ident">len</span> <span class="op">>=</span> <span class="number">2</span> <span class="op">&&</span> <span class="ident">is_less</span>(<span class="ident">v</span>.<span class="ident">get_unchecked</span>(<span class="ident">len</span> <span class="op">-</span> <span class="number">1</span>), <span class="ident">v</span>.<span class="ident">get_unchecked</span>(<span class="ident">len</span> <span class="op">-</span> <span class="number">2</span>)) {
<span class="comment">// Read the last element into a stack-allocated variable. If a following comparison</span>
<span class="comment">// operation panics, `hole` will get dropped and automatically write the element back</span>
<span class="comment">// into the slice.</span>
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">tmp</span> <span class="op">=</span> <span class="ident">mem</span>::<span class="ident">ManuallyDrop</span>::<span class="ident">new</span>(<span class="ident">ptr</span>::<span class="ident">read</span>(<span class="ident">v</span>.<span class="ident">get_unchecked</span>(<span class="ident">len</span> <span class="op">-</span> <span class="number">1</span>)));
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">hole</span> <span class="op">=</span> <span class="ident">CopyOnDrop</span> {
<span class="ident">src</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="kw-2">*</span><span class="ident">tmp</span>,
<span class="ident">dest</span>: <span class="ident">v</span>.<span class="ident">get_unchecked_mut</span>(<span class="ident">len</span> <span class="op">-</span> <span class="number">2</span>),
};
<span class="ident">ptr</span>::<span class="ident">copy_nonoverlapping</span>(<span class="ident">v</span>.<span class="ident">get_unchecked</span>(<span class="ident">len</span> <span class="op">-</span> <span class="number">2</span>), <span class="ident">v</span>.<span class="ident">get_unchecked_mut</span>(<span class="ident">len</span> <span class="op">-</span> <span class="number">1</span>), <span class="number">1</span>);
<span class="kw">for</span> <span class="ident">i</span> <span class="kw">in</span> (<span class="number">0</span>..<span class="ident">len</span><span class="op">-</span><span class="number">2</span>).<span class="ident">rev</span>() {
<span class="kw">if</span> <span class="op">!</span><span class="ident">is_less</span>(<span class="kw-2">&</span><span class="kw-2">*</span><span class="ident">tmp</span>, <span class="ident">v</span>.<span class="ident">get_unchecked</span>(<span class="ident">i</span>)) {
<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>
<span class="ident">ptr</span>::<span class="ident">copy_nonoverlapping</span>(<span class="ident">v</span>.<span class="ident">get_unchecked</span>(<span class="ident">i</span>), <span class="ident">v</span>.<span class="ident">get_unchecked_mut</span>(<span class="ident">i</span> <span class="op">+</span> <span class="number">1</span>), <span class="number">1</span>);
<span class="ident">hole</span>.<span class="ident">dest</span> <span class="op">=</span> <span class="ident">v</span>.<span class="ident">get_unchecked_mut</span>(<span class="ident">i</span>);
}
<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.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// Returns `true` if the slice is sorted at the end. This function is `O(n)` worst-case.</span>
<span class="attribute">#[<span class="ident">cold</span>]</span>
<span class="kw">fn</span> <span class="ident">partial_insertion_sort</span><span class="op"><</span><span class="ident">T</span>, <span class="ident">F</span><span class="op">></span>(<span class="ident">v</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> [<span class="ident">T</span>], <span class="ident">is_less</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">F</span>) <span class="op">-></span> <span class="ident">bool</span>
<span class="kw">where</span> <span class="ident">F</span>: <span class="ident">FnMut</span>(<span class="kw-2">&</span><span class="ident">T</span>, <span class="kw-2">&</span><span class="ident">T</span>) <span class="op">-></span> <span class="ident">bool</span>
{
<span class="comment">// Maximum number of adjacent out-of-order pairs that will get shifted.</span>
<span class="kw">const</span> <span class="ident">MAX_STEPS</span>: <span class="ident">usize</span> <span class="op">=</span> <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> <span class="ident">SHORTEST_SHIFTING</span>: <span class="ident">usize</span> <span class="op">=</span> <span class="number">50</span>;
<span class="kw">let</span> <span class="ident">len</span> <span class="op">=</span> <span class="ident">v</span>.<span class="ident">len</span>();
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">i</span> <span class="op">=</span> <span class="number">1</span>;
<span class="kw">for</span> _ <span class="kw">in</span> <span class="number">0</span>..<span class="ident">MAX_STEPS</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> <span class="ident">i</span> <span class="op"><</span> <span class="ident">len</span> <span class="op">&&</span> <span class="op">!</span><span class="ident">is_less</span>(<span class="ident">v</span>.<span class="ident">get_unchecked</span>(<span class="ident">i</span>), <span class="ident">v</span>.<span class="ident">get_unchecked</span>(<span class="ident">i</span> <span class="op">-</span> <span class="number">1</span>)) {
<span class="ident">i</span> <span class="op">+=</span> <span class="number">1</span>;
}
}
<span class="comment">// Are we done?</span>
<span class="kw">if</span> <span class="ident">i</span> <span class="op">==</span> <span class="ident">len</span> {
<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> <span class="ident">len</span> <span class="op"><</span> <span class="ident">SHORTEST_SHIFTING</span> {
<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>
<span class="ident">v</span>.<span class="ident">swap</span>(<span class="ident">i</span> <span class="op">-</span> <span class="number">1</span>, <span class="ident">i</span>);
<span class="comment">// Shift the smaller element to the left.</span>
<span class="ident">shift_tail</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">v</span>[..<span class="ident">i</span>], <span class="ident">is_less</span>);
<span class="comment">// Shift the greater element to the right.</span>
<span class="ident">shift_head</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">v</span>[<span class="ident">i</span>..], <span class="ident">is_less</span>);
}
<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> <span class="ident">insertion_sort</span><span class="op"><</span><span class="ident">T</span>, <span class="ident">F</span><span class="op">></span>(<span class="ident">v</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> [<span class="ident">T</span>], <span class="ident">is_less</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">F</span>)
<span class="kw">where</span> <span class="ident">F</span>: <span class="ident">FnMut</span>(<span class="kw-2">&</span><span class="ident">T</span>, <span class="kw-2">&</span><span class="ident">T</span>) <span class="op">-></span> <span class="ident">bool</span>
{
<span class="kw">for</span> <span class="ident">i</span> <span class="kw">in</span> <span class="number">1</span>..<span class="ident">v</span>.<span class="ident">len</span>() {
<span class="ident">shift_tail</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">v</span>[..<span class="ident">i</span><span class="op">+</span><span class="number">1</span>], <span class="ident">is_less</span>);
}
}
<span class="doccomment">/// Sorts `v` using heapsort, which guarantees `O(n log n)` worst-case.</span>
<span class="attribute">#[<span class="ident">cold</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">heapsort</span><span class="op"><</span><span class="ident">T</span>, <span class="ident">F</span><span class="op">></span>(<span class="ident">v</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> [<span class="ident">T</span>], <span class="ident">is_less</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">F</span>)
<span class="kw">where</span> <span class="ident">F</span>: <span class="ident">FnMut</span>(<span class="kw-2">&</span><span class="ident">T</span>, <span class="kw-2">&</span><span class="ident">T</span>) <span class="op">-></span> <span class="ident">bool</span>
{
<span class="comment">// This binary heap respects the invariant `parent >= child`.</span>
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">sift_down</span> <span class="op">=</span> <span class="op">|</span><span class="ident">v</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> [<span class="ident">T</span>], <span class="kw-2">mut</span> <span class="ident">node</span><span class="op">|</span> {
<span class="kw">loop</span> {
<span class="comment">// Children of `node`:</span>
<span class="kw">let</span> <span class="ident">left</span> <span class="op">=</span> <span class="number">2</span> <span class="op">*</span> <span class="ident">node</span> <span class="op">+</span> <span class="number">1</span>;
<span class="kw">let</span> <span class="ident">right</span> <span class="op">=</span> <span class="number">2</span> <span class="op">*</span> <span class="ident">node</span> <span class="op">+</span> <span class="number">2</span>;
<span class="comment">// Choose the greater child.</span>
<span class="kw">let</span> <span class="ident">greater</span> <span class="op">=</span> <span class="kw">if</span> <span class="ident">right</span> <span class="op"><</span> <span class="ident">v</span>.<span class="ident">len</span>() <span class="op">&&</span> <span class="ident">is_less</span>(<span class="kw-2">&</span><span class="ident">v</span>[<span class="ident">left</span>], <span class="kw-2">&</span><span class="ident">v</span>[<span class="ident">right</span>]) {
<span class="ident">right</span>
} <span class="kw">else</span> {
<span class="ident">left</span>
};
<span class="comment">// Stop if the invariant holds at `node`.</span>
<span class="kw">if</span> <span class="ident">greater</span> <span class="op">>=</span> <span class="ident">v</span>.<span class="ident">len</span>() <span class="op">||</span> <span class="op">!</span><span class="ident">is_less</span>(<span class="kw-2">&</span><span class="ident">v</span>[<span class="ident">node</span>], <span class="kw-2">&</span><span class="ident">v</span>[<span class="ident">greater</span>]) {
<span class="kw">break</span>;
}
<span class="comment">// Swap `node` with the greater child, move one step down, and continue sifting.</span>
<span class="ident">v</span>.<span class="ident">swap</span>(<span class="ident">node</span>, <span class="ident">greater</span>);
<span class="ident">node</span> <span class="op">=</span> <span class="ident">greater</span>;
}
};
<span class="comment">// Build the heap in linear time.</span>
<span class="kw">for</span> <span class="ident">i</span> <span class="kw">in</span> (<span class="number">0</span> .. <span class="ident">v</span>.<span class="ident">len</span>() <span class="op">/</span> <span class="number">2</span>).<span class="ident">rev</span>() {
<span class="ident">sift_down</span>(<span class="ident">v</span>, <span class="ident">i</span>);
}
<span class="comment">// Pop maximal elements from the heap.</span>
<span class="kw">for</span> <span class="ident">i</span> <span class="kw">in</span> (<span class="number">1</span> .. <span class="ident">v</span>.<span class="ident">len</span>()).<span class="ident">rev</span>() {
<span class="ident">v</span>.<span class="ident">swap</span>(<span class="number">0</span>, <span class="ident">i</span>);
<span class="ident">sift_down</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">v</span>[..<span class="ident">i</span>], <span class="number">0</span>);
}
}
<span class="doccomment">/// Partitions `v` into elements smaller than `pivot`, followed by elements greater than or equal</span>
<span class="doccomment">/// to `pivot`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// Returns the number of elements smaller than `pivot`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// Partitioning is performed block-by-block in order to minimize the cost of branching operations.</span>
<span class="doccomment">/// This idea is presented in the [BlockQuicksort][pdf] paper.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// [pdf]: http://drops.dagstuhl.de/opus/volltexte/2016/6389/pdf/LIPIcs-ESA-2016-38.pdf</span>
<span class="kw">fn</span> <span class="ident">partition_in_blocks</span><span class="op"><</span><span class="ident">T</span>, <span class="ident">F</span><span class="op">></span>(<span class="ident">v</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> [<span class="ident">T</span>], <span class="ident">pivot</span>: <span class="kw-2">&</span><span class="ident">T</span>, <span class="ident">is_less</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">F</span>) <span class="op">-></span> <span class="ident">usize</span>
<span class="kw">where</span> <span class="ident">F</span>: <span class="ident">FnMut</span>(<span class="kw-2">&</span><span class="ident">T</span>, <span class="kw-2">&</span><span class="ident">T</span>) <span class="op">-></span> <span class="ident">bool</span>
{
<span class="comment">// Number of elements in a typical block.</span>
<span class="kw">const</span> <span class="ident">BLOCK</span>: <span class="ident">usize</span> <span class="op">=</span> <span class="number">128</span>;
<span class="comment">// The partitioning algorithm repeats the following steps until completion:</span>
<span class="comment">//</span>
<span class="comment">// 1. Trace a block from the left side to identify elements greater than or equal to the pivot.</span>
<span class="comment">// 2. Trace a block from the right side to identify elements smaller than the pivot.</span>
<span class="comment">// 3. Exchange the identified elements between the left and right side.</span>
<span class="comment">//</span>
<span class="comment">// We keep the following variables for a block of elements:</span>
<span class="comment">//</span>
<span class="comment">// 1. `block` - Number of elements in the block.</span>
<span class="comment">// 2. `start` - Start pointer into the `offsets` array.</span>
<span class="comment">// 3. `end` - End pointer into the `offsets` array.</span>
<span class="comment">// 4. `offsets - Indices of out-of-order elements within the block.</span>
<span class="comment">// The current block on the left side (from `l` to `l.offset(block_l)`).</span>
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">l</span> <span class="op">=</span> <span class="ident">v</span>.<span class="ident">as_mut_ptr</span>();
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">block_l</span> <span class="op">=</span> <span class="ident">BLOCK</span>;
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">start_l</span> <span class="op">=</span> <span class="ident">ptr</span>::<span class="ident">null_mut</span>();
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">end_l</span> <span class="op">=</span> <span class="ident">ptr</span>::<span class="ident">null_mut</span>();
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">offsets_l</span>: [<span class="ident">u8</span>; <span class="ident">BLOCK</span>] <span class="op">=</span> <span class="kw">unsafe</span> { <span class="ident">mem</span>::<span class="ident">uninitialized</span>() };
<span class="comment">// The current block on the right side (from `r.offset(-block_r)` to `r`).</span>
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">r</span> <span class="op">=</span> <span class="kw">unsafe</span> { <span class="ident">l</span>.<span class="ident">offset</span>(<span class="ident">v</span>.<span class="ident">len</span>() <span class="kw">as</span> <span class="ident">isize</span>) };
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">block_r</span> <span class="op">=</span> <span class="ident">BLOCK</span>;
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">start_r</span> <span class="op">=</span> <span class="ident">ptr</span>::<span class="ident">null_mut</span>();
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">end_r</span> <span class="op">=</span> <span class="ident">ptr</span>::<span class="ident">null_mut</span>();
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">offsets_r</span>: [<span class="ident">u8</span>; <span class="ident">BLOCK</span>] <span class="op">=</span> <span class="kw">unsafe</span> { <span class="ident">mem</span>::<span class="ident">uninitialized</span>() };
<span class="comment">// FIXME: When we get VLAs, try creating one array of length `min(v.len(), 2 * BLOCK)` rather</span>
<span class="comment">// than two fixed-size arrays of length `BLOCK`. VLAs might be more cache-efficient.</span>
<span class="comment">// Returns the number of elements between pointers `l` (inclusive) and `r` (exclusive).</span>
<span class="kw">fn</span> <span class="ident">width</span><span class="op"><</span><span class="ident">T</span><span class="op">></span>(<span class="ident">l</span>: <span class="kw-2">*</span><span class="kw-2">mut</span> <span class="ident">T</span>, <span class="ident">r</span>: <span class="kw-2">*</span><span class="kw-2">mut</span> <span class="ident">T</span>) <span class="op">-></span> <span class="ident">usize</span> {
<span class="macro">assert</span><span class="macro">!</span>(<span class="ident">mem</span>::<span class="ident">size_of</span>::<span class="op"><</span><span class="ident">T</span><span class="op">></span>() <span class="op">></span> <span class="number">0</span>);
(<span class="ident">r</span> <span class="kw">as</span> <span class="ident">usize</span> <span class="op">-</span> <span class="ident">l</span> <span class="kw">as</span> <span class="ident">usize</span>) <span class="op">/</span> <span class="ident">mem</span>::<span class="ident">size_of</span>::<span class="op"><</span><span class="ident">T</span><span class="op">></span>()
}
<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</span>
<span class="comment">// some patch-up work in order to partition the remaining elements in between.</span>
<span class="kw">let</span> <span class="ident">is_done</span> <span class="op">=</span> <span class="ident">width</span>(<span class="ident">l</span>, <span class="ident">r</span>) <span class="op"><=</span> <span class="number">2</span> <span class="op">*</span> <span class="ident">BLOCK</span>;
<span class="kw">if</span> <span class="ident">is_done</span> {
<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> <span class="ident">rem</span> <span class="op">=</span> <span class="ident">width</span>(<span class="ident">l</span>, <span class="ident">r</span>);
<span class="kw">if</span> <span class="ident">start_l</span> <span class="op"><</span> <span class="ident">end_l</span> <span class="op">||</span> <span class="ident">start_r</span> <span class="op"><</span> <span class="ident">end_r</span> {
<span class="ident">rem</span> <span class="op">-=</span> <span class="ident">BLOCK</span>;
}
<span class="comment">// Adjust block sizes so that the left and right block don't overlap, but get perfectly</span>
<span class="comment">// aligned to cover the whole remaining gap.</span>
<span class="kw">if</span> <span class="ident">start_l</span> <span class="op"><</span> <span class="ident">end_l</span> {
<span class="ident">block_r</span> <span class="op">=</span> <span class="ident">rem</span>;
} <span class="kw">else</span> <span class="kw">if</span> <span class="ident">start_r</span> <span class="op"><</span> <span class="ident">end_r</span> {
<span class="ident">block_l</span> <span class="op">=</span> <span class="ident">rem</span>;
} <span class="kw">else</span> {
<span class="ident">block_l</span> <span class="op">=</span> <span class="ident">rem</span> <span class="op">/</span> <span class="number">2</span>;
<span class="ident">block_r</span> <span class="op">=</span> <span class="ident">rem</span> <span class="op">-</span> <span class="ident">block_l</span>;
}
<span class="macro">debug_assert</span><span class="macro">!</span>(<span class="ident">block_l</span> <span class="op"><=</span> <span class="ident">BLOCK</span> <span class="op">&&</span> <span class="ident">block_r</span> <span class="op"><=</span> <span class="ident">BLOCK</span>);
<span class="macro">debug_assert</span><span class="macro">!</span>(<span class="ident">width</span>(<span class="ident">l</span>, <span class="ident">r</span>) <span class="op">==</span> <span class="ident">block_l</span> <span class="op">+</span> <span class="ident">block_r</span>);
}
<span class="kw">if</span> <span class="ident">start_l</span> <span class="op">==</span> <span class="ident">end_l</span> {
<span class="comment">// Trace `block_l` elements from the left side.</span>
<span class="ident">start_l</span> <span class="op">=</span> <span class="ident">offsets_l</span>.<span class="ident">as_mut_ptr</span>();
<span class="ident">end_l</span> <span class="op">=</span> <span class="ident">offsets_l</span>.<span class="ident">as_mut_ptr</span>();
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">elem</span> <span class="op">=</span> <span class="ident">l</span>;
<span class="kw">for</span> <span class="ident">i</span> <span class="kw">in</span> <span class="number">0</span>..<span class="ident">block_l</span> {
<span class="kw">unsafe</span> {
<span class="comment">// Branchless comparison.</span>
<span class="kw-2">*</span><span class="ident">end_l</span> <span class="op">=</span> <span class="ident">i</span> <span class="kw">as</span> <span class="ident">u8</span>;
<span class="ident">end_l</span> <span class="op">=</span> <span class="ident">end_l</span>.<span class="ident">offset</span>(<span class="op">!</span><span class="ident">is_less</span>(<span class="kw-2">&</span><span class="kw-2">*</span><span class="ident">elem</span>, <span class="ident">pivot</span>) <span class="kw">as</span> <span class="ident">isize</span>);
<span class="ident">elem</span> <span class="op">=</span> <span class="ident">elem</span>.<span class="ident">offset</span>(<span class="number">1</span>);
}
}
}
<span class="kw">if</span> <span class="ident">start_r</span> <span class="op">==</span> <span class="ident">end_r</span> {
<span class="comment">// Trace `block_r` elements from the right side.</span>
<span class="ident">start_r</span> <span class="op">=</span> <span class="ident">offsets_r</span>.<span class="ident">as_mut_ptr</span>();
<span class="ident">end_r</span> <span class="op">=</span> <span class="ident">offsets_r</span>.<span class="ident">as_mut_ptr</span>();
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">elem</span> <span class="op">=</span> <span class="ident">r</span>;
<span class="kw">for</span> <span class="ident">i</span> <span class="kw">in</span> <span class="number">0</span>..<span class="ident">block_r</span> {
<span class="kw">unsafe</span> {
<span class="comment">// Branchless comparison.</span>
<span class="ident">elem</span> <span class="op">=</span> <span class="ident">elem</span>.<span class="ident">offset</span>(<span class="op">-</span><span class="number">1</span>);
<span class="kw-2">*</span><span class="ident">end_r</span> <span class="op">=</span> <span class="ident">i</span> <span class="kw">as</span> <span class="ident">u8</span>;
<span class="ident">end_r</span> <span class="op">=</span> <span class="ident">end_r</span>.<span class="ident">offset</span>(<span class="ident">is_less</span>(<span class="kw-2">&</span><span class="kw-2">*</span><span class="ident">elem</span>, <span class="ident">pivot</span>) <span class="kw">as</span> <span class="ident">isize</span>);
}
}
}
<span class="comment">// Number of out-of-order elements to swap between the left and right side.</span>
<span class="kw">let</span> <span class="ident">count</span> <span class="op">=</span> <span class="ident">cmp</span>::<span class="ident">min</span>(<span class="ident">width</span>(<span class="ident">start_l</span>, <span class="ident">end_l</span>), <span class="ident">width</span>(<span class="ident">start_r</span>, <span class="ident">end_r</span>));
<span class="kw">if</span> <span class="ident">count</span> <span class="op">></span> <span class="number">0</span> {
<span class="macro">macro_rules</span><span class="macro">!</span> <span class="ident">left</span> { () <span class="op">=></span> { <span class="ident">l</span>.<span class="ident">offset</span>(<span class="kw-2">*</span><span class="ident">start_l</span> <span class="kw">as</span> <span class="ident">isize</span>) } }
<span class="macro">macro_rules</span><span class="macro">!</span> <span class="ident">right</span> { () <span class="op">=></span> { <span class="ident">r</span>.<span class="ident">offset</span>(<span class="op">-</span>(<span class="kw-2">*</span><span class="ident">start_r</span> <span class="kw">as</span> <span class="ident">isize</span>) <span class="op">-</span> <span class="number">1</span>) } }
<span class="comment">// Instead of swapping one pair at the time, it is more efficient to perform a cyclic</span>
<span class="comment">// permutation. This is not strictly equivalent to swapping, but produces a similar</span>
<span class="comment">// result using fewer memory operations.</span>
<span class="kw">unsafe</span> {
<span class="kw">let</span> <span class="ident">tmp</span> <span class="op">=</span> <span class="ident">ptr</span>::<span class="ident">read</span>(<span class="macro">left</span><span class="macro">!</span>());
<span class="ident">ptr</span>::<span class="ident">copy_nonoverlapping</span>(<span class="macro">right</span><span class="macro">!</span>(), <span class="macro">left</span><span class="macro">!</span>(), <span class="number">1</span>);
<span class="kw">for</span> _ <span class="kw">in</span> <span class="number">1</span>..<span class="ident">count</span> {
<span class="ident">start_l</span> <span class="op">=</span> <span class="ident">start_l</span>.<span class="ident">offset</span>(<span class="number">1</span>);
<span class="ident">ptr</span>::<span class="ident">copy_nonoverlapping</span>(<span class="macro">left</span><span class="macro">!</span>(), <span class="macro">right</span><span class="macro">!</span>(), <span class="number">1</span>);
<span class="ident">start_r</span> <span class="op">=</span> <span class="ident">start_r</span>.<span class="ident">offset</span>(<span class="number">1</span>);
<span class="ident">ptr</span>::<span class="ident">copy_nonoverlapping</span>(<span class="macro">right</span><span class="macro">!</span>(), <span class="macro">left</span><span class="macro">!</span>(), <span class="number">1</span>);
}
<span class="ident">ptr</span>::<span class="ident">copy_nonoverlapping</span>(<span class="kw-2">&</span><span class="ident">tmp</span>, <span class="macro">right</span><span class="macro">!</span>(), <span class="number">1</span>);
<span class="ident">mem</span>::<span class="ident">forget</span>(<span class="ident">tmp</span>);
<span class="ident">start_l</span> <span class="op">=</span> <span class="ident">start_l</span>.<span class="ident">offset</span>(<span class="number">1</span>);
<span class="ident">start_r</span> <span class="op">=</span> <span class="ident">start_r</span>.<span class="ident">offset</span>(<span class="number">1</span>);
}
}
<span class="kw">if</span> <span class="ident">start_l</span> <span class="op">==</span> <span class="ident">end_l</span> {
<span class="comment">// All out-of-order elements in the left block were moved. Move to the next block.</span>
<span class="ident">l</span> <span class="op">=</span> <span class="kw">unsafe</span> { <span class="ident">l</span>.<span class="ident">offset</span>(<span class="ident">block_l</span> <span class="kw">as</span> <span class="ident">isize</span>) };
}
<span class="kw">if</span> <span class="ident">start_r</span> <span class="op">==</span> <span class="ident">end_r</span> {
<span class="comment">// All out-of-order elements in the right block were moved. Move to the previous block.</span>
<span class="ident">r</span> <span class="op">=</span> <span class="kw">unsafe</span> { <span class="ident">r</span>.<span class="ident">offset</span>(<span class="op">-</span>(<span class="ident">block_r</span> <span class="kw">as</span> <span class="ident">isize</span>)) };
}
<span class="kw">if</span> <span class="ident">is_done</span> {
<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</span>
<span class="comment">// elements that need to be moved. Such remaining elements can be simply shifted to the end</span>
<span class="comment">// within their block.</span>
<span class="kw">if</span> <span class="ident">start_l</span> <span class="op"><</span> <span class="ident">end_l</span> {
<span class="comment">// The left block remains.</span>
<span class="comment">// Move it's remaining out-of-order elements to the far right.</span>
<span class="macro">debug_assert_eq</span><span class="macro">!</span>(<span class="ident">width</span>(<span class="ident">l</span>, <span class="ident">r</span>), <span class="ident">block_l</span>);
<span class="kw">while</span> <span class="ident">start_l</span> <span class="op"><</span> <span class="ident">end_l</span> {
<span class="kw">unsafe</span> {
<span class="ident">end_l</span> <span class="op">=</span> <span class="ident">end_l</span>.<span class="ident">offset</span>(<span class="op">-</span><span class="number">1</span>);
<span class="ident">ptr</span>::<span class="ident">swap</span>(<span class="ident">l</span>.<span class="ident">offset</span>(<span class="kw-2">*</span><span class="ident">end_l</span> <span class="kw">as</span> <span class="ident">isize</span>), <span class="ident">r</span>.<span class="ident">offset</span>(<span class="op">-</span><span class="number">1</span>));
<span class="ident">r</span> <span class="op">=</span> <span class="ident">r</span>.<span class="ident">offset</span>(<span class="op">-</span><span class="number">1</span>);
}
}
<span class="ident">width</span>(<span class="ident">v</span>.<span class="ident">as_mut_ptr</span>(), <span class="ident">r</span>)
} <span class="kw">else</span> <span class="kw">if</span> <span class="ident">start_r</span> <span class="op"><</span> <span class="ident">end_r</span> {
<span class="comment">// The right block remains.</span>
<span class="comment">// Move it's remaining out-of-order elements to the far left.</span>
<span class="macro">debug_assert_eq</span><span class="macro">!</span>(<span class="ident">width</span>(<span class="ident">l</span>, <span class="ident">r</span>), <span class="ident">block_r</span>);
<span class="kw">while</span> <span class="ident">start_r</span> <span class="op"><</span> <span class="ident">end_r</span> {
<span class="kw">unsafe</span> {
<span class="ident">end_r</span> <span class="op">=</span> <span class="ident">end_r</span>.<span class="ident">offset</span>(<span class="op">-</span><span class="number">1</span>);
<span class="ident">ptr</span>::<span class="ident">swap</span>(<span class="ident">l</span>, <span class="ident">r</span>.<span class="ident">offset</span>(<span class="op">-</span>(<span class="kw-2">*</span><span class="ident">end_r</span> <span class="kw">as</span> <span class="ident">isize</span>) <span class="op">-</span> <span class="number">1</span>));
<span class="ident">l</span> <span class="op">=</span> <span class="ident">l</span>.<span class="ident">offset</span>(<span class="number">1</span>);
}
}
<span class="ident">width</span>(<span class="ident">v</span>.<span class="ident">as_mut_ptr</span>(), <span class="ident">l</span>)
} <span class="kw">else</span> {
<span class="comment">// Nothing else to do, we're done.</span>
<span class="ident">width</span>(<span class="ident">v</span>.<span class="ident">as_mut_ptr</span>(), <span class="ident">l</span>)
}
}
<span class="doccomment">/// Partitions `v` into elements smaller than `v[pivot]`, followed by elements greater than or</span>
<span class="doccomment">/// equal to `v[pivot]`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// Returns a tuple of:</span>
<span class="doccomment">///</span>
<span class="doccomment">/// 1. Number of elements smaller than `v[pivot]`.</span>
<span class="doccomment">/// 2. True if `v` was already partitioned.</span>
<span class="kw">fn</span> <span class="ident">partition</span><span class="op"><</span><span class="ident">T</span>, <span class="ident">F</span><span class="op">></span>(<span class="ident">v</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> [<span class="ident">T</span>], <span class="ident">pivot</span>: <span class="ident">usize</span>, <span class="ident">is_less</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">F</span>) <span class="op">-></span> (<span class="ident">usize</span>, <span class="ident">bool</span>)
<span class="kw">where</span> <span class="ident">F</span>: <span class="ident">FnMut</span>(<span class="kw-2">&</span><span class="ident">T</span>, <span class="kw-2">&</span><span class="ident">T</span>) <span class="op">-></span> <span class="ident">bool</span>
{
<span class="kw">let</span> (<span class="ident">mid</span>, <span class="ident">was_partitioned</span>) <span class="op">=</span> {
<span class="comment">// Place the pivot at the beginning of slice.</span>
<span class="ident">v</span>.<span class="ident">swap</span>(<span class="number">0</span>, <span class="ident">pivot</span>);
<span class="kw">let</span> (<span class="ident">pivot</span>, <span class="ident">v</span>) <span class="op">=</span> <span class="ident">v</span>.<span class="ident">split_at_mut</span>(<span class="number">1</span>);
<span class="kw">let</span> <span class="ident">pivot</span> <span class="op">=</span> <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">pivot</span>[<span class="number">0</span>];
<span class="comment">// Read the pivot into a stack-allocated variable for efficiency. If a following comparison</span>
<span class="comment">// operation panics, the pivot will be automatically written back into the slice.</span>
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">tmp</span> <span class="op">=</span> <span class="ident">mem</span>::<span class="ident">ManuallyDrop</span>::<span class="ident">new</span>(<span class="kw">unsafe</span> { <span class="ident">ptr</span>::<span class="ident">read</span>(<span class="ident">pivot</span>) });
<span class="kw">let</span> <span class="ident">_pivot_guard</span> <span class="op">=</span> <span class="ident">CopyOnDrop</span> {
<span class="ident">src</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="kw-2">*</span><span class="ident">tmp</span>,
<span class="ident">dest</span>: <span class="ident">pivot</span>,
};
<span class="kw">let</span> <span class="ident">pivot</span> <span class="op">=</span> <span class="kw-2">&</span><span class="kw-2">*</span><span class="ident">tmp</span>;
<span class="comment">// Find the first pair of out-of-order elements.</span>
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">l</span> <span class="op">=</span> <span class="number">0</span>;
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">r</span> <span class="op">=</span> <span class="ident">v</span>.<span class="ident">len</span>();
<span class="kw">unsafe</span> {
<span class="comment">// Find the first element greater then or equal to the pivot.</span>
<span class="kw">while</span> <span class="ident">l</span> <span class="op"><</span> <span class="ident">r</span> <span class="op">&&</span> <span class="ident">is_less</span>(<span class="ident">v</span>.<span class="ident">get_unchecked</span>(<span class="ident">l</span>), <span class="ident">pivot</span>) {
<span class="ident">l</span> <span class="op">+=</span> <span class="number">1</span>;
}
<span class="comment">// Find the last element smaller that the pivot.</span>
<span class="kw">while</span> <span class="ident">l</span> <span class="op"><</span> <span class="ident">r</span> <span class="op">&&</span> <span class="op">!</span><span class="ident">is_less</span>(<span class="ident">v</span>.<span class="ident">get_unchecked</span>(<span class="ident">r</span> <span class="op">-</span> <span class="number">1</span>), <span class="ident">pivot</span>) {
<span class="ident">r</span> <span class="op">-=</span> <span class="number">1</span>;
}
}
(<span class="ident">l</span> <span class="op">+</span> <span class="ident">partition_in_blocks</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">v</span>[<span class="ident">l</span>..<span class="ident">r</span>], <span class="ident">pivot</span>, <span class="ident">is_less</span>), <span class="ident">l</span> <span class="op">>=</span> <span class="ident">r</span>)
<span class="comment">// `_pivot_guard` goes out of scope and writes the pivot (which is a stack-allocated</span>
<span class="comment">// variable) back into the slice where it originally was. This step is critical in ensuring</span>
<span class="comment">// safety!</span>
};
<span class="comment">// Place the pivot between the two partitions.</span>
<span class="ident">v</span>.<span class="ident">swap</span>(<span class="number">0</span>, <span class="ident">mid</span>);
(<span class="ident">mid</span>, <span class="ident">was_partitioned</span>)
}
<span class="doccomment">/// Partitions `v` into elements equal to `v[pivot]` followed by elements greater than `v[pivot]`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// Returns the number of elements equal to the pivot. It is assumed that `v` does not contain</span>
<span class="doccomment">/// elements smaller than the pivot.</span>
<span class="kw">fn</span> <span class="ident">partition_equal</span><span class="op"><</span><span class="ident">T</span>, <span class="ident">F</span><span class="op">></span>(<span class="ident">v</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> [<span class="ident">T</span>], <span class="ident">pivot</span>: <span class="ident">usize</span>, <span class="ident">is_less</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">F</span>) <span class="op">-></span> <span class="ident">usize</span>
<span class="kw">where</span> <span class="ident">F</span>: <span class="ident">FnMut</span>(<span class="kw-2">&</span><span class="ident">T</span>, <span class="kw-2">&</span><span class="ident">T</span>) <span class="op">-></span> <span class="ident">bool</span>
{
<span class="comment">// Place the pivot at the beginning of slice.</span>
<span class="ident">v</span>.<span class="ident">swap</span>(<span class="number">0</span>, <span class="ident">pivot</span>);
<span class="kw">let</span> (<span class="ident">pivot</span>, <span class="ident">v</span>) <span class="op">=</span> <span class="ident">v</span>.<span class="ident">split_at_mut</span>(<span class="number">1</span>);
<span class="kw">let</span> <span class="ident">pivot</span> <span class="op">=</span> <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">pivot</span>[<span class="number">0</span>];
<span class="comment">// Read the pivot into a stack-allocated variable for efficiency. If a following comparison</span>
<span class="comment">// operation panics, the pivot will be automatically written back into the slice.</span>
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">tmp</span> <span class="op">=</span> <span class="ident">mem</span>::<span class="ident">ManuallyDrop</span>::<span class="ident">new</span>(<span class="kw">unsafe</span> { <span class="ident">ptr</span>::<span class="ident">read</span>(<span class="ident">pivot</span>) });
<span class="kw">let</span> <span class="ident">_pivot_guard</span> <span class="op">=</span> <span class="ident">CopyOnDrop</span> {
<span class="ident">src</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="kw-2">*</span><span class="ident">tmp</span>,
<span class="ident">dest</span>: <span class="ident">pivot</span>,
};
<span class="kw">let</span> <span class="ident">pivot</span> <span class="op">=</span> <span class="kw-2">&</span><span class="kw-2">*</span><span class="ident">tmp</span>;
<span class="comment">// Now partition the slice.</span>
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">l</span> <span class="op">=</span> <span class="number">0</span>;
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">r</span> <span class="op">=</span> <span class="ident">v</span>.<span class="ident">len</span>();
<span class="kw">loop</span> {
<span class="kw">unsafe</span> {
<span class="comment">// Find the first element greater that the pivot.</span>
<span class="kw">while</span> <span class="ident">l</span> <span class="op"><</span> <span class="ident">r</span> <span class="op">&&</span> <span class="op">!</span><span class="ident">is_less</span>(<span class="ident">pivot</span>, <span class="ident">v</span>.<span class="ident">get_unchecked</span>(<span class="ident">l</span>)) {
<span class="ident">l</span> <span class="op">+=</span> <span class="number">1</span>;
}
<span class="comment">// Find the last element equal to the pivot.</span>
<span class="kw">while</span> <span class="ident">l</span> <span class="op"><</span> <span class="ident">r</span> <span class="op">&&</span> <span class="ident">is_less</span>(<span class="ident">pivot</span>, <span class="ident">v</span>.<span class="ident">get_unchecked</span>(<span class="ident">r</span> <span class="op">-</span> <span class="number">1</span>)) {
<span class="ident">r</span> <span class="op">-=</span> <span class="number">1</span>;
}
<span class="comment">// Are we done?</span>
<span class="kw">if</span> <span class="ident">l</span> <span class="op">>=</span> <span class="ident">r</span> {
<span class="kw">break</span>;
}
<span class="comment">// Swap the found pair of out-of-order elements.</span>
<span class="ident">r</span> <span class="op">-=</span> <span class="number">1</span>;
<span class="ident">ptr</span>::<span class="ident">swap</span>(<span class="ident">v</span>.<span class="ident">get_unchecked_mut</span>(<span class="ident">l</span>), <span class="ident">v</span>.<span class="ident">get_unchecked_mut</span>(<span class="ident">r</span>));
<span class="ident">l</span> <span class="op">+=</span> <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>
<span class="ident">l</span> <span class="op">+</span> <span class="number">1</span>
<span class="comment">// `_pivot_guard` goes out of scope and writes the pivot (which is a stack-allocated variable)</span>
<span class="comment">// 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</span>
<span class="doccomment">/// partitions in quicksort.</span>
<span class="attribute">#[<span class="ident">cold</span>]</span>
<span class="kw">fn</span> <span class="ident">break_patterns</span><span class="op"><</span><span class="ident">T</span><span class="op">></span>(<span class="ident">v</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> [<span class="ident">T</span>]) {
<span class="kw">let</span> <span class="ident">len</span> <span class="op">=</span> <span class="ident">v</span>.<span class="ident">len</span>();
<span class="kw">if</span> <span class="ident">len</span> <span class="op">>=</span> <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> <span class="ident">random</span> <span class="op">=</span> <span class="ident">len</span> <span class="kw">as</span> <span class="ident">u32</span>;
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">gen_u32</span> <span class="op">=</span> <span class="op">||</span> {
<span class="ident">random</span> <span class="op">^=</span> <span class="ident">random</span> <span class="op"><<</span> <span class="number">13</span>;
<span class="ident">random</span> <span class="op">^=</span> <span class="ident">random</span> <span class="op">>></span> <span class="number">17</span>;
<span class="ident">random</span> <span class="op">^=</span> <span class="ident">random</span> <span class="op"><<</span> <span class="number">5</span>;
<span class="ident">random</span>
};
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">gen_usize</span> <span class="op">=</span> <span class="op">||</span> {
<span class="kw">if</span> <span class="ident">mem</span>::<span class="ident">size_of</span>::<span class="op"><</span><span class="ident">usize</span><span class="op">></span>() <span class="op"><=</span> <span class="number">4</span> {
<span class="ident">gen_u32</span>() <span class="kw">as</span> <span class="ident">usize</span>
} <span class="kw">else</span> {
(((<span class="ident">gen_u32</span>() <span class="kw">as</span> <span class="ident">u64</span>) <span class="op"><<</span> <span class="number">32</span>) <span class="op">|</span> (<span class="ident">gen_u32</span>() <span class="kw">as</span> <span class="ident">u64</span>)) <span class="kw">as</span> <span class="ident">usize</span>
}
};
<span class="comment">// Take random numbers modulo this number.</span>
<span class="comment">// The number fits into `usize` because `len` is not greater than `isize::MAX`.</span>
<span class="kw">let</span> <span class="ident">modulus</span> <span class="op">=</span> <span class="ident">len</span>.<span class="ident">next_power_of_two</span>();
<span class="comment">// Some pivot candidates will be in the nearby of this index. Let's randomize them.</span>
<span class="kw">let</span> <span class="ident">pos</span> <span class="op">=</span> <span class="ident">len</span> <span class="op">/</span> <span class="number">4</span> <span class="op">*</span> <span class="number">2</span>;
<span class="kw">for</span> <span class="ident">i</span> <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</span>
<span class="comment">// we first take it modulo a power of two, and then decrease by `len` until it fits</span>
<span class="comment">// into the range `[0, len - 1]`.</span>
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">other</span> <span class="op">=</span> <span class="ident">gen_usize</span>() <span class="op">&</span> (<span class="ident">modulus</span> <span class="op">-</span> <span class="number">1</span>);
<span class="comment">// `other` is guaranteed to be less than `2 * len`.</span>
<span class="kw">if</span> <span class="ident">other</span> <span class="op">>=</span> <span class="ident">len</span> {
<span class="ident">other</span> <span class="op">-=</span> <span class="ident">len</span>;
}
<span class="ident">v</span>.<span class="ident">swap</span>(<span class="ident">pos</span> <span class="op">-</span> <span class="number">1</span> <span class="op">+</span> <span class="ident">i</span>, <span class="ident">other</span>);
}
}
}
<span class="doccomment">/// Chooses a pivot in `v` and returns the index and `true` if the slice is likely already sorted.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// Elements in `v` might be reordered in the process.</span>
<span class="kw">fn</span> <span class="ident">choose_pivot</span><span class="op"><</span><span class="ident">T</span>, <span class="ident">F</span><span class="op">></span>(<span class="ident">v</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> [<span class="ident">T</span>], <span class="ident">is_less</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">F</span>) <span class="op">-></span> (<span class="ident">usize</span>, <span class="ident">bool</span>)
<span class="kw">where</span> <span class="ident">F</span>: <span class="ident">FnMut</span>(<span class="kw-2">&</span><span class="ident">T</span>, <span class="kw-2">&</span><span class="ident">T</span>) <span class="op">-></span> <span class="ident">bool</span>
{
<span class="comment">// Minimum length to choose the median-of-medians method.</span>
<span class="comment">// Shorter slices use the simple median-of-three method.</span>
<span class="kw">const</span> <span class="ident">SHORTEST_MEDIAN_OF_MEDIANS</span>: <span class="ident">usize</span> <span class="op">=</span> <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> <span class="ident">MAX_SWAPS</span>: <span class="ident">usize</span> <span class="op">=</span> <span class="number">4</span> <span class="op">*</span> <span class="number">3</span>;
<span class="kw">let</span> <span class="ident">len</span> <span class="op">=</span> <span class="ident">v</span>.<span class="ident">len</span>();
<span class="comment">// Three indices near which we are going to choose a pivot.</span>
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">a</span> <span class="op">=</span> <span class="ident">len</span> <span class="op">/</span> <span class="number">4</span> <span class="op">*</span> <span class="number">1</span>;
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">b</span> <span class="op">=</span> <span class="ident">len</span> <span class="op">/</span> <span class="number">4</span> <span class="op">*</span> <span class="number">2</span>;
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">c</span> <span class="op">=</span> <span class="ident">len</span> <span class="op">/</span> <span class="number">4</span> <span class="op">*</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> <span class="ident">swaps</span> <span class="op">=</span> <span class="number">0</span>;
<span class="kw">if</span> <span class="ident">len</span> <span class="op">>=</span> <span class="number">8</span> {
<span class="comment">// Swaps indices so that `v[a] <= v[b]`.</span>
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">sort2</span> <span class="op">=</span> <span class="op">|</span><span class="ident">a</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">usize</span>, <span class="ident">b</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">usize</span><span class="op">|</span> <span class="kw">unsafe</span> {
<span class="kw">if</span> <span class="ident">is_less</span>(<span class="ident">v</span>.<span class="ident">get_unchecked</span>(<span class="kw-2">*</span><span class="ident">b</span>), <span class="ident">v</span>.<span class="ident">get_unchecked</span>(<span class="kw-2">*</span><span class="ident">a</span>)) {
<span class="ident">ptr</span>::<span class="ident">swap</span>(<span class="ident">a</span>, <span class="ident">b</span>);
<span class="ident">swaps</span> <span class="op">+=</span> <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> <span class="ident">sort3</span> <span class="op">=</span> <span class="op">|</span><span class="ident">a</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">usize</span>, <span class="ident">b</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">usize</span>, <span class="ident">c</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">usize</span><span class="op">|</span> {
<span class="ident">sort2</span>(<span class="ident">a</span>, <span class="ident">b</span>);
<span class="ident">sort2</span>(<span class="ident">b</span>, <span class="ident">c</span>);
<span class="ident">sort2</span>(<span class="ident">a</span>, <span class="ident">b</span>);
};
<span class="kw">if</span> <span class="ident">len</span> <span class="op">>=</span> <span class="ident">SHORTEST_MEDIAN_OF_MEDIANS</span> {
<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> <span class="ident">sort_adjacent</span> <span class="op">=</span> <span class="op">|</span><span class="ident">a</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">usize</span><span class="op">|</span> {
<span class="kw">let</span> <span class="ident">tmp</span> <span class="op">=</span> <span class="kw-2">*</span><span class="ident">a</span>;
<span class="ident">sort3</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> (<span class="ident">tmp</span> <span class="op">-</span> <span class="number">1</span>), <span class="ident">a</span>, <span class="kw-2">&</span><span class="kw-2">mut</span> (<span class="ident">tmp</span> <span class="op">+</span> <span class="number">1</span>));
};
<span class="comment">// Find medians in the neighborhoods of `a`, `b`, and `c`.</span>
<span class="ident">sort_adjacent</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">a</span>);
<span class="ident">sort_adjacent</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">b</span>);
<span class="ident">sort_adjacent</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">c</span>);
}
<span class="comment">// Find the median among `a`, `b`, and `c`.</span>
<span class="ident">sort3</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">a</span>, <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">b</span>, <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">c</span>);
}
<span class="kw">if</span> <span class="ident">swaps</span> <span class="op"><</span> <span class="ident">MAX_SWAPS</span> {
(<span class="ident">b</span>, <span class="ident">swaps</span> <span class="op">==</span> <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</span>
<span class="comment">// descending, so reversing will probably help sort it faster.</span>
<span class="ident">v</span>.<span class="ident">reverse</span>();
(<span class="ident">len</span> <span class="op">-</span> <span class="number">1</span> <span class="op">-</span> <span class="ident">b</span>, <span class="bool-val">true</span>)
}
}
<span class="doccomment">/// Sorts `v` recursively.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// If the slice had a predecessor in the original array, it is specified as `pred`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// `limit` is the number of allowed imbalanced partitions before switching to `heapsort`. If zero,</span>
<span class="doccomment">/// this function will immediately switch to heapsort.</span>
<span class="kw">fn</span> <span class="ident">recurse</span><span class="op"><</span><span class="lifetime">'a</span>, <span class="ident">T</span>, <span class="ident">F</span><span class="op">></span>(<span class="kw-2">mut</span> <span class="ident">v</span>: <span class="kw-2">&</span><span class="lifetime">'a</span> <span class="kw-2">mut</span> [<span class="ident">T</span>], <span class="ident">is_less</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">F</span>, <span class="kw-2">mut</span> <span class="ident">pred</span>: <span class="prelude-ty">Option</span><span class="op"><</span><span class="kw-2">&</span><span class="lifetime">'a</span> <span class="ident">T</span><span class="op">></span>, <span class="kw-2">mut</span> <span class="ident">limit</span>: <span class="ident">usize</span>)
<span class="kw">where</span> <span class="ident">F</span>: <span class="ident">FnMut</span>(<span class="kw-2">&</span><span class="ident">T</span>, <span class="kw-2">&</span><span class="ident">T</span>) <span class="op">-></span> <span class="ident">bool</span>
{
<span class="comment">// Slices of up to this length get sorted using insertion sort.</span>
<span class="kw">const</span> <span class="ident">MAX_INSERTION</span>: <span class="ident">usize</span> <span class="op">=</span> <span class="number">20</span>;
<span class="comment">// True if the last partitioning was reasonably balanced.</span>
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">was_balanced</span> <span class="op">=</span> <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> <span class="ident">was_partitioned</span> <span class="op">=</span> <span class="bool-val">true</span>;
<span class="kw">loop</span> {
<span class="kw">let</span> <span class="ident">len</span> <span class="op">=</span> <span class="ident">v</span>.<span class="ident">len</span>();
<span class="comment">// Very short slices get sorted using insertion sort.</span>
<span class="kw">if</span> <span class="ident">len</span> <span class="op"><=</span> <span class="ident">MAX_INSERTION</span> {
<span class="ident">insertion_sort</span>(<span class="ident">v</span>, <span class="ident">is_less</span>);
<span class="kw">return</span>;
}
<span class="comment">// If too many bad pivot choices were made, simply fall back to heapsort in order to</span>
<span class="comment">// guarantee `O(n log n)` worst-case.</span>
<span class="kw">if</span> <span class="ident">limit</span> <span class="op">==</span> <span class="number">0</span> {
<span class="ident">heapsort</span>(<span class="ident">v</span>, <span class="ident">is_less</span>);
<span class="kw">return</span>;
}
<span class="comment">// If the last partitioning was imbalanced, try breaking patterns in the slice by shuffling</span>
<span class="comment">// some elements around. Hopefully we'll choose a better pivot this time.</span>
<span class="kw">if</span> <span class="op">!</span><span class="ident">was_balanced</span> {
<span class="ident">break_patterns</span>(<span class="ident">v</span>);
<span class="ident">limit</span> <span class="op">-=</span> <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> (<span class="ident">pivot</span>, <span class="ident">likely_sorted</span>) <span class="op">=</span> <span class="ident">choose_pivot</span>(<span class="ident">v</span>, <span class="ident">is_less</span>);
<span class="comment">// If the last partitioning was decently balanced and didn't shuffle elements, and if pivot</span>
<span class="comment">// selection predicts the slice is likely already sorted...</span>
<span class="kw">if</span> <span class="ident">was_balanced</span> <span class="op">&&</span> <span class="ident">was_partitioned</span> <span class="op">&&</span> <span class="ident">likely_sorted</span> {
<span class="comment">// Try identifying several out-of-order elements and shifting them to correct</span>
<span class="comment">// positions. If the slice ends up being completely sorted, we're done.</span>
<span class="kw">if</span> <span class="ident">partial_insertion_sort</span>(<span class="ident">v</span>, <span class="ident">is_less</span>) {
<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</span>
<span class="comment">// slice. Partition the slice into elements equal to and elements greater than the pivot.</span>
<span class="comment">// This case is usually hit when the slice contains many duplicate elements.</span>
<span class="kw">if</span> <span class="kw">let</span> <span class="prelude-val">Some</span>(<span class="ident">p</span>) <span class="op">=</span> <span class="ident">pred</span> {
<span class="kw">if</span> <span class="op">!</span><span class="ident">is_less</span>(<span class="ident">p</span>, <span class="kw-2">&</span><span class="ident">v</span>[<span class="ident">pivot</span>]) {
<span class="kw">let</span> <span class="ident">mid</span> <span class="op">=</span> <span class="ident">partition_equal</span>(<span class="ident">v</span>, <span class="ident">pivot</span>, <span class="ident">is_less</span>);
<span class="comment">// Continue sorting elements greater than the pivot.</span>
<span class="ident">v</span> <span class="op">=</span> <span class="kw-2">&</span><span class="kw-2">mut</span> {<span class="ident">v</span>}[<span class="ident">mid</span>..];
<span class="kw">continue</span>;
}
}
<span class="comment">// Partition the slice.</span>
<span class="kw">let</span> (<span class="ident">mid</span>, <span class="ident">was_p</span>) <span class="op">=</span> <span class="ident">partition</span>(<span class="ident">v</span>, <span class="ident">pivot</span>, <span class="ident">is_less</span>);
<span class="ident">was_balanced</span> <span class="op">=</span> <span class="ident">cmp</span>::<span class="ident">min</span>(<span class="ident">mid</span>, <span class="ident">len</span> <span class="op">-</span> <span class="ident">mid</span>) <span class="op">>=</span> <span class="ident">len</span> <span class="op">/</span> <span class="number">8</span>;
<span class="ident">was_partitioned</span> <span class="op">=</span> <span class="ident">was_p</span>;
<span class="comment">// Split the slice into `left`, `pivot`, and `right`.</span>
<span class="kw">let</span> (<span class="ident">left</span>, <span class="ident">right</span>) <span class="op">=</span> {<span class="ident">v</span>}.<span class="ident">split_at_mut</span>(<span class="ident">mid</span>);
<span class="kw">let</span> (<span class="ident">pivot</span>, <span class="ident">right</span>) <span class="op">=</span> <span class="ident">right</span>.<span class="ident">split_at_mut</span>(<span class="number">1</span>);
<span class="kw">let</span> <span class="ident">pivot</span> <span class="op">=</span> <span class="kw-2">&</span><span class="ident">pivot</span>[<span class="number">0</span>];
<span class="comment">// Recurse into the shorter side only in order to minimize the total number of recursive</span>
<span class="comment">// calls and consume less stack space. Then just continue with the longer side (this is</span>
<span class="comment">// akin to tail recursion).</span>
<span class="kw">if</span> <span class="ident">left</span>.<span class="ident">len</span>() <span class="op"><</span> <span class="ident">right</span>.<span class="ident">len</span>() {
<span class="ident">recurse</span>(<span class="ident">left</span>, <span class="ident">is_less</span>, <span class="ident">pred</span>, <span class="ident">limit</span>);
<span class="ident">v</span> <span class="op">=</span> <span class="ident">right</span>;
<span class="ident">pred</span> <span class="op">=</span> <span class="prelude-val">Some</span>(<span class="ident">pivot</span>);
} <span class="kw">else</span> {
<span class="ident">recurse</span>(<span class="ident">right</span>, <span class="ident">is_less</span>, <span class="prelude-val">Some</span>(<span class="ident">pivot</span>), <span class="ident">limit</span>);
<span class="ident">v</span> <span class="op">=</span> <span class="ident">left</span>;
}
}
}
<span class="doccomment">/// Sorts `v` using pattern-defeating quicksort, which is `O(n log n)` worst-case.</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">quicksort</span><span class="op"><</span><span class="ident">T</span>, <span class="ident">F</span><span class="op">></span>(<span class="ident">v</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> [<span class="ident">T</span>], <span class="kw-2">mut</span> <span class="ident">is_less</span>: <span class="ident">F</span>)
<span class="kw">where</span> <span class="ident">F</span>: <span class="ident">FnMut</span>(<span class="kw-2">&</span><span class="ident">T</span>, <span class="kw-2">&</span><span class="ident">T</span>) <span class="op">-></span> <span class="ident">bool</span>
{
<span class="comment">// Sorting has no meaningful behavior on zero-sized types.</span>
<span class="kw">if</span> <span class="ident">mem</span>::<span class="ident">size_of</span>::<span class="op"><</span><span class="ident">T</span><span class="op">></span>() <span class="op">==</span> <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> <span class="ident">limit</span> <span class="op">=</span> <span class="ident">mem</span>::<span class="ident">size_of</span>::<span class="op"><</span><span class="ident">usize</span><span class="op">></span>() <span class="op">*</span> <span class="number">8</span> <span class="op">-</span> <span class="ident">v</span>.<span class="ident">len</span>().<span class="ident">leading_zeros</span>() <span class="kw">as</span> <span class="ident">usize</span>;
<span class="ident">recurse</span>(<span class="ident">v</span>, <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">is_less</span>, <span class="prelude-val">None</span>, <span class="ident">limit</span>);
}
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