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+// Pattern-defeating quicksort
+
+// Copyright Orson Peters 2017.
+// Distributed under the Boost Software License, Version 1.0.
+// (See accompanying file LICENSE_1_0.txt or copy at
+// http://www.boost.org/LICENSE_1_0.txt)
+
+// See http://www.boost.org/libs/sort/ for library home page.
+
+
+#ifndef BOOST_SORT_PDQSORT_HPP
+#define BOOST_SORT_PDQSORT_HPP
+
+#include <algorithm>
+#include <cstddef>
+#include <functional>
+#include <iterator>
+#include <utility>
+#include <boost/type_traits.hpp>
+
+#if __cplusplus >= 201103L
+ #include <cstdint>
+ #define BOOST_PDQSORT_PREFER_MOVE(x) std::move(x)
+#else
+ #define BOOST_PDQSORT_PREFER_MOVE(x) (x)
+#endif
+
+namespace boost {
+namespace sort {
+
+namespace pdqsort_detail {
+ enum {
+ // Partitions below this size are sorted using insertion sort.
+ insertion_sort_threshold = 24,
+
+ // Partitions above this size use Tukey's ninther to select the pivot.
+ ninther_threshold = 128,
+
+ // When we detect an already sorted partition, attempt an insertion sort that allows this
+ // amount of element moves before giving up.
+ partial_insertion_sort_limit = 8,
+
+ // Must be multiple of 8 due to loop unrolling, and < 256 to fit in unsigned char.
+ block_size = 64,
+
+ // Cacheline size, assumes power of two.
+ cacheline_size = 64
+ };
+
+ template<class T> struct is_default_compare : boost::false_type { };
+ template<class T> struct is_default_compare<std::less<T> > : boost::true_type { };
+ template<class T> struct is_default_compare<std::greater<T> > : boost::true_type { };
+
+ // Returns floor(log2(n)), assumes n > 0.
+ template<class T>
+ inline int log2(T n) {
+ int log = 0;
+ while (n >>= 1) ++log;
+ return log;
+ }
+
+ // Sorts [begin, end) using insertion sort with the given comparison function.
+ template<class Iter, class Compare>
+ inline void insertion_sort(Iter begin, Iter end, Compare comp) {
+ typedef typename std::iterator_traits<Iter>::value_type T;
+ if (begin == end) return;
+
+ for (Iter cur = begin + 1; cur != end; ++cur) {
+ Iter sift = cur;
+ Iter sift_1 = cur - 1;
+
+ // Compare first so we can avoid 2 moves for an element already positioned correctly.
+ if (comp(*sift, *sift_1)) {
+ T tmp = BOOST_PDQSORT_PREFER_MOVE(*sift);
+
+ do { *sift-- = BOOST_PDQSORT_PREFER_MOVE(*sift_1); }
+ while (sift != begin && comp(tmp, *--sift_1));
+
+ *sift = BOOST_PDQSORT_PREFER_MOVE(tmp);
+ }
+ }
+ }
+
+ // Sorts [begin, end) using insertion sort with the given comparison function. Assumes
+ // *(begin - 1) is an element smaller than or equal to any element in [begin, end).
+ template<class Iter, class Compare>
+ inline void unguarded_insertion_sort(Iter begin, Iter end, Compare comp) {
+ typedef typename std::iterator_traits<Iter>::value_type T;
+ if (begin == end) return;
+
+ for (Iter cur = begin + 1; cur != end; ++cur) {
+ Iter sift = cur;
+ Iter sift_1 = cur - 1;
+
+ // Compare first so we can avoid 2 moves for an element already positioned correctly.
+ if (comp(*sift, *sift_1)) {
+ T tmp = BOOST_PDQSORT_PREFER_MOVE(*sift);
+
+ do { *sift-- = BOOST_PDQSORT_PREFER_MOVE(*sift_1); }
+ while (comp(tmp, *--sift_1));
+
+ *sift = BOOST_PDQSORT_PREFER_MOVE(tmp);
+ }
+ }
+ }
+
+ // Attempts to use insertion sort on [begin, end). Will return false if more than
+ // partial_insertion_sort_limit elements were moved, and abort sorting. Otherwise it will
+ // successfully sort and return true.
+ template<class Iter, class Compare>
+ inline bool partial_insertion_sort(Iter begin, Iter end, Compare comp) {
+ typedef typename std::iterator_traits<Iter>::value_type T;
+ if (begin == end) return true;
+
+ int limit = 0;
+ for (Iter cur = begin + 1; cur != end; ++cur) {
+ if (limit > partial_insertion_sort_limit) return false;
+
+ Iter sift = cur;
+ Iter sift_1 = cur - 1;
+
+ // Compare first so we can avoid 2 moves for an element already positioned correctly.
+ if (comp(*sift, *sift_1)) {
+ T tmp = BOOST_PDQSORT_PREFER_MOVE(*sift);
+
+ do { *sift-- = BOOST_PDQSORT_PREFER_MOVE(*sift_1); }
+ while (sift != begin && comp(tmp, *--sift_1));
+
+ *sift = BOOST_PDQSORT_PREFER_MOVE(tmp);
+ limit += cur - sift;
+ }
+ }
+
+ return true;
+ }
+
+ template<class Iter, class Compare>
+ inline void sort2(Iter a, Iter b, Compare comp) {
+ if (comp(*b, *a)) std::iter_swap(a, b);
+ }
+
+ // Sorts the elements *a, *b and *c using comparison function comp.
+ template<class Iter, class Compare>
+ inline void sort3(Iter a, Iter b, Iter c, Compare comp) {
+ sort2(a, b, comp);
+ sort2(b, c, comp);
+ sort2(a, b, comp);
+ }
+
+ template<class T>
+ inline T* align_cacheline(T* p) {
+#if defined(UINTPTR_MAX) && __cplusplus >= 201103L
+ std::uintptr_t ip = reinterpret_cast<std::uintptr_t>(p);
+#else
+ std::size_t ip = reinterpret_cast<std::size_t>(p);
+#endif
+ ip = (ip + cacheline_size - 1) & -cacheline_size;
+ return reinterpret_cast<T*>(ip);
+ }
+
+ template<class Iter>
+ inline void swap_offsets(Iter first, Iter last,
+ unsigned char* offsets_l, unsigned char* offsets_r,
+ int num, bool use_swaps) {
+ typedef typename std::iterator_traits<Iter>::value_type T;
+ if (use_swaps) {
+ // This case is needed for the descending distribution, where we need
+ // to have proper swapping for pdqsort to remain O(n).
+ for (int i = 0; i < num; ++i) {
+ std::iter_swap(first + offsets_l[i], last - offsets_r[i]);
+ }
+ } else if (num > 0) {
+ Iter l = first + offsets_l[0]; Iter r = last - offsets_r[0];
+ T tmp(BOOST_PDQSORT_PREFER_MOVE(*l)); *l = BOOST_PDQSORT_PREFER_MOVE(*r);
+ for (int i = 1; i < num; ++i) {
+ l = first + offsets_l[i]; *r = BOOST_PDQSORT_PREFER_MOVE(*l);
+ r = last - offsets_r[i]; *l = BOOST_PDQSORT_PREFER_MOVE(*r);
+ }
+ *r = BOOST_PDQSORT_PREFER_MOVE(tmp);
+ }
+ }
+
+ // Partitions [begin, end) around pivot *begin using comparison function comp. Elements equal
+ // to the pivot are put in the right-hand partition. Returns the position of the pivot after
+ // partitioning and whether the passed sequence already was correctly partitioned. Assumes the
+ // pivot is a median of at least 3 elements and that [begin, end) is at least
+ // insertion_sort_threshold long. Uses branchless partitioning.
+ template<class Iter, class Compare>
+ inline std::pair<Iter, bool> partition_right_branchless(Iter begin, Iter end, Compare comp) {
+ typedef typename std::iterator_traits<Iter>::value_type T;
+
+ // Move pivot into local for speed.
+ T pivot(BOOST_PDQSORT_PREFER_MOVE(*begin));
+ Iter first = begin;
+ Iter last = end;
+
+ // Find the first element greater than or equal than the pivot (the median of 3 guarantees
+ // this exists).
+ while (comp(*++first, pivot));
+
+ // Find the first element strictly smaller than the pivot. We have to guard this search if
+ // there was no element before *first.
+ if (first - 1 == begin) while (first < last && !comp(*--last, pivot));
+ else while ( !comp(*--last, pivot));
+
+ // If the first pair of elements that should be swapped to partition are the same element,
+ // the passed in sequence already was correctly partitioned.
+ bool already_partitioned = first >= last;
+ if (!already_partitioned) {
+ std::iter_swap(first, last);
+ ++first;
+ }
+
+ // The following branchless partitioning is derived from "BlockQuicksort: How Branch
+ // Mispredictions don't affect Quicksort" by Stefan Edelkamp and Armin Weiss.
+ unsigned char offsets_l_storage[block_size + cacheline_size];
+ unsigned char offsets_r_storage[block_size + cacheline_size];
+ unsigned char* offsets_l = align_cacheline(offsets_l_storage);
+ unsigned char* offsets_r = align_cacheline(offsets_r_storage);
+ int num_l, num_r, start_l, start_r;
+ num_l = num_r = start_l = start_r = 0;
+
+ while (last - first > 2 * block_size) {
+ // Fill up offset blocks with elements that are on the wrong side.
+ if (num_l == 0) {
+ start_l = 0;
+ Iter it = first;
+ for (unsigned char i = 0; i < block_size;) {
+ offsets_l[num_l] = i++; num_l += !comp(*it, pivot); ++it;
+ offsets_l[num_l] = i++; num_l += !comp(*it, pivot); ++it;
+ offsets_l[num_l] = i++; num_l += !comp(*it, pivot); ++it;
+ offsets_l[num_l] = i++; num_l += !comp(*it, pivot); ++it;
+ offsets_l[num_l] = i++; num_l += !comp(*it, pivot); ++it;
+ offsets_l[num_l] = i++; num_l += !comp(*it, pivot); ++it;
+ offsets_l[num_l] = i++; num_l += !comp(*it, pivot); ++it;
+ offsets_l[num_l] = i++; num_l += !comp(*it, pivot); ++it;
+ }
+ }
+ if (num_r == 0) {
+ start_r = 0;
+ Iter it = last;
+ for (unsigned char i = 0; i < block_size;) {
+ offsets_r[num_r] = ++i; num_r += comp(*--it, pivot);
+ offsets_r[num_r] = ++i; num_r += comp(*--it, pivot);
+ offsets_r[num_r] = ++i; num_r += comp(*--it, pivot);
+ offsets_r[num_r] = ++i; num_r += comp(*--it, pivot);
+ offsets_r[num_r] = ++i; num_r += comp(*--it, pivot);
+ offsets_r[num_r] = ++i; num_r += comp(*--it, pivot);
+ offsets_r[num_r] = ++i; num_r += comp(*--it, pivot);
+ offsets_r[num_r] = ++i; num_r += comp(*--it, pivot);
+ }
+ }
+
+ // Swap elements and update block sizes and first/last boundaries.
+ int num = (std::min)(num_l, num_r);
+ swap_offsets(first, last, offsets_l + start_l, offsets_r + start_r,
+ num, num_l == num_r);
+ num_l -= num; num_r -= num;
+ start_l += num; start_r += num;
+ if (num_l == 0) first += block_size;
+ if (num_r == 0) last -= block_size;
+ }
+
+ int l_size = 0, r_size = 0;
+ int unknown_left = (last - first) - ((num_r || num_l) ? block_size : 0);
+ if (num_r) {
+ // Handle leftover block by assigning the unknown elements to the other block.
+ l_size = unknown_left;
+ r_size = block_size;
+ } else if (num_l) {
+ l_size = block_size;
+ r_size = unknown_left;
+ } else {
+ // No leftover block, split the unknown elements in two blocks.
+ l_size = unknown_left/2;
+ r_size = unknown_left - l_size;
+ }
+
+ // Fill offset buffers if needed.
+ if (unknown_left && !num_l) {
+ start_l = 0;
+ Iter it = first;
+ for (unsigned char i = 0; i < l_size;) {
+ offsets_l[num_l] = i++; num_l += !comp(*it, pivot); ++it;
+ }
+ }
+ if (unknown_left && !num_r) {
+ start_r = 0;
+ Iter it = last;
+ for (unsigned char i = 0; i < r_size;) {
+ offsets_r[num_r] = ++i; num_r += comp(*--it, pivot);
+ }
+ }
+
+ int num = (std::min)(num_l, num_r);
+ swap_offsets(first, last, offsets_l + start_l, offsets_r + start_r, num, num_l == num_r);
+ num_l -= num; num_r -= num;
+ start_l += num; start_r += num;
+ if (num_l == 0) first += l_size;
+ if (num_r == 0) last -= r_size;
+
+ // We have now fully identified [first, last)'s proper position. Swap the last elements.
+ if (num_l) {
+ offsets_l += start_l;
+ while (num_l--) std::iter_swap(first + offsets_l[num_l], --last);
+ first = last;
+ }
+ if (num_r) {
+ offsets_r += start_r;
+ while (num_r--) std::iter_swap(last - offsets_r[num_r], first), ++first;
+ last = first;
+ }
+
+ // Put the pivot in the right place.
+ Iter pivot_pos = first - 1;
+ *begin = BOOST_PDQSORT_PREFER_MOVE(*pivot_pos);
+ *pivot_pos = BOOST_PDQSORT_PREFER_MOVE(pivot);
+
+ return std::make_pair(pivot_pos, already_partitioned);
+ }
+
+ // Partitions [begin, end) around pivot *begin using comparison function comp. Elements equal
+ // to the pivot are put in the right-hand partition. Returns the position of the pivot after
+ // partitioning and whether the passed sequence already was correctly partitioned. Assumes the
+ // pivot is a median of at least 3 elements and that [begin, end) is at least
+ // insertion_sort_threshold long.
+ template<class Iter, class Compare>
+ inline std::pair<Iter, bool> partition_right(Iter begin, Iter end, Compare comp) {
+ typedef typename std::iterator_traits<Iter>::value_type T;
+
+ // Move pivot into local for speed.
+ T pivot(BOOST_PDQSORT_PREFER_MOVE(*begin));
+
+ Iter first = begin;
+ Iter last = end;
+
+ // Find the first element greater than or equal than the pivot (the median of 3 guarantees
+ // this exists).
+ while (comp(*++first, pivot));
+
+ // Find the first element strictly smaller than the pivot. We have to guard this search if
+ // there was no element before *first.
+ if (first - 1 == begin) while (first < last && !comp(*--last, pivot));
+ else while ( !comp(*--last, pivot));
+
+ // If the first pair of elements that should be swapped to partition are the same element,
+ // the passed in sequence already was correctly partitioned.
+ bool already_partitioned = first >= last;
+
+ // Keep swapping pairs of elements that are on the wrong side of the pivot. Previously
+ // swapped pairs guard the searches, which is why the first iteration is special-cased
+ // above.
+ while (first < last) {
+ std::iter_swap(first, last);
+ while (comp(*++first, pivot));
+ while (!comp(*--last, pivot));
+ }
+
+ // Put the pivot in the right place.
+ Iter pivot_pos = first - 1;
+ *begin = BOOST_PDQSORT_PREFER_MOVE(*pivot_pos);
+ *pivot_pos = BOOST_PDQSORT_PREFER_MOVE(pivot);
+
+ return std::make_pair(pivot_pos, already_partitioned);
+ }
+
+ // Similar function to the one above, except elements equal to the pivot are put to the left of
+ // the pivot and it doesn't check or return if the passed sequence already was partitioned.
+ // Since this is rarely used (the many equal case), and in that case pdqsort already has O(n)
+ // performance, no block quicksort is applied here for simplicity.
+ template<class Iter, class Compare>
+ inline Iter partition_left(Iter begin, Iter end, Compare comp) {
+ typedef typename std::iterator_traits<Iter>::value_type T;
+
+ T pivot(BOOST_PDQSORT_PREFER_MOVE(*begin));
+ Iter first = begin;
+ Iter last = end;
+
+ while (comp(pivot, *--last));
+
+ if (last + 1 == end) while (first < last && !comp(pivot, *++first));
+ else while ( !comp(pivot, *++first));
+
+ while (first < last) {
+ std::iter_swap(first, last);
+ while (comp(pivot, *--last));
+ while (!comp(pivot, *++first));
+ }
+
+ Iter pivot_pos = last;
+ *begin = BOOST_PDQSORT_PREFER_MOVE(*pivot_pos);
+ *pivot_pos = BOOST_PDQSORT_PREFER_MOVE(pivot);
+
+ return pivot_pos;
+ }
+
+
+ template<class Iter, class Compare, bool Branchless>
+ inline void pdqsort_loop(Iter begin, Iter end, Compare comp, int bad_allowed, bool leftmost = true) {
+ typedef typename std::iterator_traits<Iter>::difference_type diff_t;
+
+ // Use a while loop for tail recursion elimination.
+ while (true) {
+ diff_t size = end - begin;
+
+ // Insertion sort is faster for small arrays.
+ if (size < insertion_sort_threshold) {
+ if (leftmost) insertion_sort(begin, end, comp);
+ else unguarded_insertion_sort(begin, end, comp);
+ return;
+ }
+
+ // Choose pivot as median of 3 or pseudomedian of 9.
+ diff_t s2 = size / 2;
+ if (size > ninther_threshold) {
+ sort3(begin, begin + s2, end - 1, comp);
+ sort3(begin + 1, begin + (s2 - 1), end - 2, comp);
+ sort3(begin + 2, begin + (s2 + 1), end - 3, comp);
+ sort3(begin + (s2 - 1), begin + s2, begin + (s2 + 1), comp);
+ std::iter_swap(begin, begin + s2);
+ } else sort3(begin + s2, begin, end - 1, comp);
+
+ // If *(begin - 1) is the end of the right partition of a previous partition operation
+ // there is no element in [begin, end) that is smaller than *(begin - 1). Then if our
+ // pivot compares equal to *(begin - 1) we change strategy, putting equal elements in
+ // the left partition, greater elements in the right partition. We do not have to
+ // recurse on the left partition, since it's sorted (all equal).
+ if (!leftmost && !comp(*(begin - 1), *begin)) {
+ begin = partition_left(begin, end, comp) + 1;
+ continue;
+ }
+
+ // Partition and get results.
+ std::pair<Iter, bool> part_result =
+ Branchless ? partition_right_branchless(begin, end, comp)
+ : partition_right(begin, end, comp);
+ Iter pivot_pos = part_result.first;
+ bool already_partitioned = part_result.second;
+
+ // Check for a highly unbalanced partition.
+ diff_t l_size = pivot_pos - begin;
+ diff_t r_size = end - (pivot_pos + 1);
+ bool highly_unbalanced = l_size < size / 8 || r_size < size / 8;
+
+ // If we got a highly unbalanced partition we shuffle elements to break many patterns.
+ if (highly_unbalanced) {
+ // If we had too many bad partitions, switch to heapsort to guarantee O(n log n).
+ if (--bad_allowed == 0) {
+ std::make_heap(begin, end, comp);
+ std::sort_heap(begin, end, comp);
+ return;
+ }
+
+ if (l_size >= insertion_sort_threshold) {
+ std::iter_swap(begin, begin + l_size / 4);
+ std::iter_swap(pivot_pos - 1, pivot_pos - l_size / 4);
+
+ if (l_size > ninther_threshold) {
+ std::iter_swap(begin + 1, begin + (l_size / 4 + 1));
+ std::iter_swap(begin + 2, begin + (l_size / 4 + 2));
+ std::iter_swap(pivot_pos - 2, pivot_pos - (l_size / 4 + 1));
+ std::iter_swap(pivot_pos - 3, pivot_pos - (l_size / 4 + 2));
+ }
+ }
+
+ if (r_size >= insertion_sort_threshold) {
+ std::iter_swap(pivot_pos + 1, pivot_pos + (1 + r_size / 4));
+ std::iter_swap(end - 1, end - r_size / 4);
+
+ if (r_size > ninther_threshold) {
+ std::iter_swap(pivot_pos + 2, pivot_pos + (2 + r_size / 4));
+ std::iter_swap(pivot_pos + 3, pivot_pos + (3 + r_size / 4));
+ std::iter_swap(end - 2, end - (1 + r_size / 4));
+ std::iter_swap(end - 3, end - (2 + r_size / 4));
+ }
+ }
+ } else {
+ // If we were decently balanced and we tried to sort an already partitioned
+ // sequence try to use insertion sort.
+ if (already_partitioned && partial_insertion_sort(begin, pivot_pos, comp)
+ && partial_insertion_sort(pivot_pos + 1, end, comp)) return;
+ }
+
+ // Sort the left partition first using recursion and do tail recursion elimination for
+ // the right-hand partition.
+ pdqsort_loop<Iter, Compare, Branchless>(begin, pivot_pos, comp, bad_allowed, leftmost);
+ begin = pivot_pos + 1;
+ leftmost = false;
+ }
+ }
+}
+
+
+/*! \brief Generic sort algorithm using random access iterators and a user-defined comparison operator.
+
+ \details @c pdqsort is a fast generic sorting algorithm that is similar in concept to introsort
+but runs faster on certain patterns. @c pdqsort is in-place, unstable, deterministic, has a worst
+case runtime of <em>O(N * lg(N))</em> and a best case of <em>O(N)</em>. Even without patterns, the
+quicksort has been very efficiently implemented, and @c pdqsort runs 1-5% faster than GCC 6.2's
+@c std::sort. If the type being sorted is @c std::is_arithmetic and Compare is @c std::less or
+@c std::greater this function will automatically use @c pdqsort_branchless for far greater speedups.
+
+ \param[in] first Iterator pointer to first element.
+ \param[in] last Iterator pointing to one beyond the end of data.
+ \param[in] comp A binary functor that returns whether the first element passed to it should go before the second in order.
+ \pre [@c first, @c last) is a valid range.
+ \pre @c RandomAccessIter @c value_type is <a href="http://en.cppreference.com/w/cpp/concept/MoveAssignable">MoveAssignable</a>
+ \pre @c RandomAccessIter @c value_type is <a href="http://en.cppreference.com/w/cpp/concept/MoveConstructible">MoveConstructible</a>
+ \pre @c RandomAccessIter @c value_type is <a href="http://en.cppreference.com/w/cpp/concept/LessThanComparable">LessThanComparable</a>
+ \post The elements in the range [@c first, @c last) are sorted in ascending order.
+
+ \return @c void.
+
+ \throws std::exception Propagates exceptions if any of the element comparisons, the element swaps
+ (or moves), functors, or any operations on iterators throw.
+ \warning Invalid arguments cause undefined behaviour.
+ \warning Throwing an exception may cause data loss.
+*/
+template<class Iter, class Compare>
+inline void pdqsort(Iter first, Iter last, Compare comp) {
+ if (first == last) return;
+ pdqsort_detail::pdqsort_loop<Iter, Compare,
+ pdqsort_detail::is_default_compare<typename boost::decay<Compare>::type>::value &&
+ boost::is_arithmetic<typename std::iterator_traits<Iter>::value_type>::value>(
+ first, last, comp, pdqsort_detail::log2(last - first));
+}
+
+
+/*! \brief Generic sort algorithm using random access iterators and a user-defined comparison operator.
+
+ \details @c pdqsort_branchless is a fast generic sorting algorithm that is similar in concept to
+introsort but runs faster on certain patterns. @c pdqsort_branchless is in-place, unstable,
+deterministic, has a worst case runtime of <em>O(N * lg(N))</em> and a best case of <em>O(N)</em>.
+Even without patterns, the quicksort has been very efficiently implemented with block based
+partitioning, and @c pdqsort_branchless runs 80-90% faster than GCC 6.2's @c std::sort when sorting
+small data such as integers. However, this speedup is gained by totally bypassing the branch
+predictor, if your comparison operator or iterator contains branches you will most likely see little
+gain or a small loss in performance.
+
+ \param[in] first Iterator pointer to first element.
+ \param[in] last Iterator pointing to one beyond the end of data.
+ \param[in] comp A binary functor that returns whether the first element passed to it should go before the second in order.
+ \pre [@c first, @c last) is a valid range.
+ \pre @c RandomAccessIter @c value_type is <a href="http://en.cppreference.com/w/cpp/concept/MoveAssignable">MoveAssignable</a>
+ \pre @c RandomAccessIter @c value_type is <a href="http://en.cppreference.com/w/cpp/concept/MoveConstructible">MoveConstructible</a>
+ \pre @c RandomAccessIter @c value_type is <a href="http://en.cppreference.com/w/cpp/concept/LessThanComparable">LessThanComparable</a>
+ \post The elements in the range [@c first, @c last) are sorted in ascending order.
+
+ \return @c void.
+
+ \throws std::exception Propagates exceptions if any of the element comparisons, the element swaps
+ (or moves), functors, or any operations on iterators throw.
+ \warning Invalid arguments cause undefined behaviour.
+ \warning Throwing an exception may cause data loss.
+*/
+template<class Iter, class Compare>
+inline void pdqsort_branchless(Iter first, Iter last, Compare comp) {
+ if (first == last) return;
+ pdqsort_detail::pdqsort_loop<Iter, Compare, true>(
+ first, last, comp, pdqsort_detail::log2(last - first));
+}
+
+
+/*! \brief Generic sort algorithm using random access iterators.
+
+ \details @c pdqsort is a fast generic sorting algorithm that is similar in concept to introsort
+but runs faster on certain patterns. @c pdqsort is in-place, unstable, deterministic, has a worst
+case runtime of <em>O(N * lg(N))</em> and a best case of <em>O(N)</em>. Even without patterns, the
+quicksort partitioning has been very efficiently implemented, and @c pdqsort runs 80-90% faster than
+GCC 6.2's @c std::sort. If the type being sorted is @c std::is_arithmetic this function will
+automatically use @c pdqsort_branchless.
+
+ \param[in] first Iterator pointer to first element.
+ \param[in] last Iterator pointing to one beyond the end of data.
+ \pre [@c first, @c last) is a valid range.
+ \pre @c RandomAccessIter @c value_type is <a href="http://en.cppreference.com/w/cpp/concept/MoveAssignable">MoveAssignable</a>
+ \pre @c RandomAccessIter @c value_type is <a href="http://en.cppreference.com/w/cpp/concept/MoveConstructible">MoveConstructible</a>
+ \pre @c RandomAccessIter @c value_type is <a href="http://en.cppreference.com/w/cpp/concept/LessThanComparable">LessThanComparable</a>
+ \post The elements in the range [@c first, @c last) are sorted in ascending order.
+
+ \return @c void.
+
+ \throws std::exception Propagates exceptions if any of the element comparisons, the element swaps
+ (or moves), functors, or any operations on iterators throw.
+ \warning Invalid arguments cause undefined behaviour.
+ \warning Throwing an exception may cause data loss.
+*/
+template<class Iter>
+inline void pdqsort(Iter first, Iter last) {
+ typedef typename std::iterator_traits<Iter>::value_type T;
+ pdqsort(first, last, std::less<T>());
+}
+
+
+/*! \brief Generic sort algorithm using random access iterators.
+
+ \details @c pdqsort_branchless is a fast generic sorting algorithm that is similar in concept to
+introsort but runs faster on certain patterns. @c pdqsort_branchless is in-place, unstable,
+deterministic, has a worst case runtime of <em>O(N * lg(N))</em> and a best case of <em>O(N)</em>.
+Even without patterns, the quicksort has been very efficiently implemented with block based
+partitioning, and @c pdqsort_branchless runs 80-90% faster than GCC 6.2's @c std::sort when sorting
+small data such as integers. However, this speedup is gained by totally bypassing the branch
+predictor, if your comparison operator or iterator contains branches you will most likely see little
+gain or a small loss in performance.
+
+ \param[in] first Iterator pointer to first element.
+ \param[in] last Iterator pointing to one beyond the end of data.
+ \pre [@c first, @c last) is a valid range.
+ \pre @c RandomAccessIter @c value_type is <a href="http://en.cppreference.com/w/cpp/concept/MoveAssignable">MoveAssignable</a>
+ \pre @c RandomAccessIter @c value_type is <a href="http://en.cppreference.com/w/cpp/concept/MoveConstructible">MoveConstructible</a>
+ \pre @c RandomAccessIter @c value_type is <a href="http://en.cppreference.com/w/cpp/concept/LessThanComparable">LessThanComparable</a>
+ \post The elements in the range [@c first, @c last) are sorted in ascending order.
+
+ \return @c void.
+
+ \throws std::exception Propagates exceptions if any of the element comparisons, the element swaps
+ (or moves), functors, or any operations on iterators throw.
+ \warning Invalid arguments cause undefined behaviour.
+ \warning Throwing an exception may cause data loss.
+*/
+template<class Iter>
+inline void pdqsort_branchless(Iter first, Iter last) {
+ typedef typename std::iterator_traits<Iter>::value_type T;
+ pdqsort_branchless(first, last, std::less<T>());
+}
+
+}
+}
+
+#undef BOOST_PDQSORT_PREFER_MOVE
+
+#endif
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