//////////////////////////////////////////////////////////////////////////////
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//
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// (C) Copyright Orson Peters 2017.
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// (C) Copyright Ion Gaztanaga 2017-2018.
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// Distributed under the Boost Software License, Version 1.0.
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// (See accompanying file LICENSE_1_0.txt or copy at
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// http://www.boost.org/LICENSE_1_0.txt)
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//
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// See http://www.boost.org/libs/move for documentation.
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//
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//////////////////////////////////////////////////////////////////////////////
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//
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// This implementation of Pattern-defeating quicksort (pdqsort) was written
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// by Orson Peters, and discussed in the Boost mailing list:
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// http://boost.2283326.n4.nabble.com/sort-pdqsort-td4691031.html
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//
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// This implementation is the adaptation by Ion Gaztanaga of code originally in GitHub
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// with permission from the author to relicense it under the Boost Software License
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// (see the Boost mailing list for details).
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//
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// The original copyright statement is pasted here for completeness:
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//
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// pdqsort.h - Pattern-defeating quicksort.
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// Copyright (c) 2015 Orson Peters
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// This software is provided 'as-is', without any express or implied warranty. In no event will the
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// authors be held liable for any damages arising from the use of this software.
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// Permission is granted to anyone to use this software for any purpose, including commercial
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// applications, and to alter it and redistribute it freely, subject to the following restrictions:
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// 1. The origin of this software must not be misrepresented; you must not claim that you wrote the
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// original software. If you use this software in a product, an acknowledgment in the product
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// documentation would be appreciated but is not required.
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// 2. Altered source versions must be plainly marked as such, and must not be misrepresented as
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// being the original software.
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// 3. This notice may not be removed or altered from any source distribution.
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//
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//////////////////////////////////////////////////////////////////////////////
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#ifndef BOOST_MOVE_ALGO_PDQSORT_HPP
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#define BOOST_MOVE_ALGO_PDQSORT_HPP
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#ifndef BOOST_CONFIG_HPP
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# include <boost/config.hpp>
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#endif
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#
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#if defined(BOOST_HAS_PRAGMA_ONCE)
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# pragma once
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#endif
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#include <boost/move/detail/config_begin.hpp>
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#include <boost/move/detail/workaround.hpp>
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#include <boost/move/utility_core.hpp>
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#include <boost/move/algo/detail/insertion_sort.hpp>
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#include <boost/move/algo/detail/heap_sort.hpp>
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#include <boost/move/detail/iterator_traits.hpp>
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#include <boost/move/adl_move_swap.hpp>
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#include <cstddef>
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namespace boost {
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namespace movelib {
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namespace pdqsort_detail {
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//A simple pair implementation to avoid including <utility>
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template<class T1, class T2>
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struct pair
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{
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pair()
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{}
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pair(const T1 &t1, const T2 &t2)
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: first(t1), second(t2)
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{}
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T1 first;
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T2 second;
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};
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enum {
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// Partitions below this size are sorted using insertion sort.
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insertion_sort_threshold = 24,
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// Partitions above this size use Tukey's ninther to select the pivot.
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ninther_threshold = 128,
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// When we detect an already sorted partition, attempt an insertion sort that allows this
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// amount of element moves before giving up.
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partial_insertion_sort_limit = 8,
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// Must be multiple of 8 due to loop unrolling, and < 256 to fit in unsigned char.
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block_size = 64,
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// Cacheline size, assumes power of two.
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cacheline_size = 64
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};
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// Returns floor(log2(n)), assumes n > 0.
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template<class Unsigned>
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Unsigned log2(Unsigned n) {
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Unsigned log = 0;
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while (n >>= 1) ++log;
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return log;
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}
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// Attempts to use insertion sort on [begin, end). Will return false if more than
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// partial_insertion_sort_limit elements were moved, and abort sorting. Otherwise it will
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// successfully sort and return true.
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template<class Iter, class Compare>
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inline bool partial_insertion_sort(Iter begin, Iter end, Compare comp) {
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typedef typename boost::movelib::iterator_traits<Iter>::value_type T;
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typedef typename boost::movelib::iterator_traits<Iter>::size_type size_type;
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if (begin == end) return true;
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size_type limit = 0;
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for (Iter cur = begin + 1; cur != end; ++cur) {
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if (limit > partial_insertion_sort_limit) return false;
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Iter sift = cur;
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Iter sift_1 = cur - 1;
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// Compare first so we can avoid 2 moves for an element already positioned correctly.
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if (comp(*sift, *sift_1)) {
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T tmp = boost::move(*sift);
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do { *sift-- = boost::move(*sift_1); }
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while (sift != begin && comp(tmp, *--sift_1));
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*sift = boost::move(tmp);
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limit += size_type(cur - sift);
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}
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}
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return true;
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}
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template<class Iter, class Compare>
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inline void sort2(Iter a, Iter b, Compare comp) {
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if (comp(*b, *a)) boost::adl_move_iter_swap(a, b);
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}
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// Sorts the elements *a, *b and *c using comparison function comp.
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template<class Iter, class Compare>
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inline void sort3(Iter a, Iter b, Iter c, Compare comp) {
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sort2(a, b, comp);
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sort2(b, c, comp);
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sort2(a, b, comp);
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}
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// Partitions [begin, end) around pivot *begin using comparison function comp. Elements equal
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// to the pivot are put in the right-hand partition. Returns the position of the pivot after
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// partitioning and whether the passed sequence already was correctly partitioned. Assumes the
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// pivot is a median of at least 3 elements and that [begin, end) is at least
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// insertion_sort_threshold long.
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template<class Iter, class Compare>
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pdqsort_detail::pair<Iter, bool> partition_right(Iter begin, Iter end, Compare comp) {
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typedef typename boost::movelib::iterator_traits<Iter>::value_type T;
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// Move pivot into local for speed.
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T pivot(boost::move(*begin));
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Iter first = begin;
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Iter last = end;
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// Find the first element greater than or equal than the pivot (the median of 3 guarantees
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// this exists).
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while (comp(*++first, pivot));
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// Find the first element strictly smaller than the pivot. We have to guard this search if
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// there was no element before *first.
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if (first - 1 == begin) while (first < last && !comp(*--last, pivot));
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else while ( !comp(*--last, pivot));
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// If the first pair of elements that should be swapped to partition are the same element,
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// the passed in sequence already was correctly partitioned.
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bool already_partitioned = first >= last;
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// Keep swapping pairs of elements that are on the wrong side of the pivot. Previously
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// swapped pairs guard the searches, which is why the first iteration is special-cased
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// above.
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while (first < last) {
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boost::adl_move_iter_swap(first, last);
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while (comp(*++first, pivot));
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while (!comp(*--last, pivot));
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}
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// Put the pivot in the right place.
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Iter pivot_pos = first - 1;
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*begin = boost::move(*pivot_pos);
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*pivot_pos = boost::move(pivot);
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return pdqsort_detail::pair<Iter, bool>(pivot_pos, already_partitioned);
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}
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// Similar function to the one above, except elements equal to the pivot are put to the left of
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// the pivot and it doesn't check or return if the passed sequence already was partitioned.
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// Since this is rarely used (the many equal case), and in that case pdqsort already has O(n)
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// performance, no block quicksort is applied here for simplicity.
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template<class Iter, class Compare>
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inline Iter partition_left(Iter begin, Iter end, Compare comp) {
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typedef typename boost::movelib::iterator_traits<Iter>::value_type T;
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T pivot(boost::move(*begin));
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Iter first = begin;
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Iter last = end;
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while (comp(pivot, *--last));
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if (last + 1 == end) while (first < last && !comp(pivot, *++first));
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else while ( !comp(pivot, *++first));
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while (first < last) {
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boost::adl_move_iter_swap(first, last);
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while (comp(pivot, *--last));
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while (!comp(pivot, *++first));
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}
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Iter pivot_pos = last;
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*begin = boost::move(*pivot_pos);
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*pivot_pos = boost::move(pivot);
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return pivot_pos;
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}
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template<class Iter, class Compare>
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void pdqsort_loop( Iter begin, Iter end, Compare comp
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, typename boost::movelib::iterator_traits<Iter>::size_type bad_allowed
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, bool leftmost = true)
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{
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typedef typename boost::movelib::iterator_traits<Iter>::size_type size_type;
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// Use a while loop for tail recursion elimination.
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while (true) {
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size_type size = size_type(end - begin);
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// Insertion sort is faster for small arrays.
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if (size < insertion_sort_threshold) {
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insertion_sort(begin, end, comp);
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return;
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}
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// Choose pivot as median of 3 or pseudomedian of 9.
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size_type s2 = size / 2;
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if (size > ninther_threshold) {
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sort3(begin, begin + s2, end - 1, comp);
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sort3(begin + 1, begin + (s2 - 1), end - 2, comp);
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sort3(begin + 2, begin + (s2 + 1), end - 3, comp);
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sort3(begin + (s2 - 1), begin + s2, begin + (s2 + 1), comp);
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boost::adl_move_iter_swap(begin, begin + s2);
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} else sort3(begin + s2, begin, end - 1, comp);
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// If *(begin - 1) is the end of the right partition of a previous partition operation
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// there is no element in [begin, end) that is smaller than *(begin - 1). Then if our
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// pivot compares equal to *(begin - 1) we change strategy, putting equal elements in
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// the left partition, greater elements in the right partition. We do not have to
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// recurse on the left partition, since it's sorted (all equal).
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if (!leftmost && !comp(*(begin - 1), *begin)) {
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begin = partition_left(begin, end, comp) + 1;
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continue;
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}
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// Partition and get results.
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pdqsort_detail::pair<Iter, bool> part_result = partition_right(begin, end, comp);
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Iter pivot_pos = part_result.first;
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bool already_partitioned = part_result.second;
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// Check for a highly unbalanced partition.
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size_type l_size = size_type(pivot_pos - begin);
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size_type r_size = size_type(end - (pivot_pos + 1));
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bool highly_unbalanced = l_size < size / 8 || r_size < size / 8;
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// If we got a highly unbalanced partition we shuffle elements to break many patterns.
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if (highly_unbalanced) {
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// If we had too many bad partitions, switch to heapsort to guarantee O(n log n).
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if (--bad_allowed == 0) {
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boost::movelib::heap_sort(begin, end, comp);
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return;
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}
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if (l_size >= insertion_sort_threshold) {
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boost::adl_move_iter_swap(begin, begin + l_size / 4);
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boost::adl_move_iter_swap(pivot_pos - 1, pivot_pos - l_size / 4);
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if (l_size > ninther_threshold) {
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boost::adl_move_iter_swap(begin + 1, begin + (l_size / 4 + 1));
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boost::adl_move_iter_swap(begin + 2, begin + (l_size / 4 + 2));
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boost::adl_move_iter_swap(pivot_pos - 2, pivot_pos - (l_size / 4 + 1));
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boost::adl_move_iter_swap(pivot_pos - 3, pivot_pos - (l_size / 4 + 2));
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}
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}
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if (r_size >= insertion_sort_threshold) {
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boost::adl_move_iter_swap(pivot_pos + 1, pivot_pos + (1 + r_size / 4));
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boost::adl_move_iter_swap(end - 1, end - r_size / 4);
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if (r_size > ninther_threshold) {
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boost::adl_move_iter_swap(pivot_pos + 2, pivot_pos + (2 + r_size / 4));
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boost::adl_move_iter_swap(pivot_pos + 3, pivot_pos + (3 + r_size / 4));
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boost::adl_move_iter_swap(end - 2, end - (1 + r_size / 4));
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boost::adl_move_iter_swap(end - 3, end - (2 + r_size / 4));
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}
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}
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} else {
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// If we were decently balanced and we tried to sort an already partitioned
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// sequence try to use insertion sort.
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if (already_partitioned && partial_insertion_sort(begin, pivot_pos, comp)
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&& partial_insertion_sort(pivot_pos + 1, end, comp)) return;
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}
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// Sort the left partition first using recursion and do tail recursion elimination for
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// the right-hand partition.
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pdqsort_loop<Iter, Compare>(begin, pivot_pos, comp, bad_allowed, leftmost);
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begin = pivot_pos + 1;
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leftmost = false;
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}
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}
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}
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template<class Iter, class Compare>
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void pdqsort(Iter begin, Iter end, Compare comp)
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{
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if (begin == end) return;
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typedef typename boost::movelib::iterator_traits<Iter>::size_type size_type;
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pdqsort_detail::pdqsort_loop<Iter, Compare>(begin, end, comp, pdqsort_detail::log2(size_type(end - begin)));
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}
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} //namespace movelib {
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} //namespace boost {
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#include <boost/move/detail/config_end.hpp>
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#endif //BOOST_MOVE_ALGO_PDQSORT_HPP
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