boost/move/algo/detail/adaptive_sort_merge.hpp
////////////////////////////////////////////////////////////////////////////// // // (C) Copyright Ion Gaztanaga 2015-2016. // 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/move for documentation. // ////////////////////////////////////////////////////////////////////////////// // // Stable sorting that works in O(N*log(N)) worst time // and uses O(1) extra memory // ////////////////////////////////////////////////////////////////////////////// // // The main idea of the adaptive_sort algorithm was developed by Andrey Astrelin // and explained in the article from the russian collaborative blog // Habrahabr (http://habrahabr.ru/post/205290/). The algorithm is based on // ideas from B-C. Huang and M. A. Langston explained in their article // "Fast Stable Merging and Sorting in Constant Extra Space (1989-1992)" // (http://comjnl.oxfordjournals.org/content/35/6/643.full.pdf). // // This implementation by Ion Gaztanaga uses previous ideas with additional changes: // // - Use of GCD-based rotation. // - Non power of two buffer-sizes. // - Tries to find sqrt(len)*2 unique keys, so that the merge sort // phase can form up to sqrt(len)*4 segments if enough keys are found. // - The merge-sort phase can take advantage of external memory to // save some additional combination steps. // - Optimized comparisons when selection-sorting blocks as A and B blocks // are already sorted. // - The combination phase is performed alternating merge to left and merge // to right phases minimizing swaps due to internal buffer repositioning. // - When merging blocks special optimizations are made to avoid moving some // elements twice. // // The adaptive_merge algorithm was developed by Ion Gaztanaga reusing some parts // from the sorting algorithm and implementing an additional block merge algorithm // without moving elements to left or right, which is used when external memory // is available. ////////////////////////////////////////////////////////////////////////////// #ifndef BOOST_MOVE_ADAPTIVE_SORT_MERGE_HPP #define BOOST_MOVE_ADAPTIVE_SORT_MERGE_HPP #include <boost/move/detail/config_begin.hpp> #include <boost/move/detail/reverse_iterator.hpp> #include <boost/move/algo/move.hpp> #include <boost/move/algo/detail/merge.hpp> #include <boost/move/adl_move_swap.hpp> #include <boost/move/algo/detail/insertion_sort.hpp> #include <boost/move/algo/detail/merge_sort.hpp> #include <boost/move/algo/detail/merge.hpp> #include <boost/assert.hpp> #include <boost/cstdint.hpp> #ifdef BOOST_MOVE_ADAPTIVE_SORT_STATS #define BOOST_MOVE_ADAPTIVE_SORT_PRINT(STR, L) \ print_stats(STR, L)\ // #else #define BOOST_MOVE_ADAPTIVE_SORT_PRINT(STR, L) #endif namespace boost { namespace movelib { namespace detail_adaptive { static const std::size_t AdaptiveSortInsertionSortThreshold = 16; //static const std::size_t AdaptiveSortInsertionSortThreshold = 4; BOOST_STATIC_ASSERT((AdaptiveSortInsertionSortThreshold&(AdaptiveSortInsertionSortThreshold-1)) == 0); #if defined BOOST_HAS_INTPTR_T typedef ::boost::uintptr_t uintptr_t; #else typedef std::size_t uintptr_t; #endif template<class T> const T &min_value(const T &a, const T &b) { return a < b ? a : b; } template<class T> const T &max_value(const T &a, const T &b) { return a > b ? a : b; } template<class T> class adaptive_xbuf { adaptive_xbuf(const adaptive_xbuf &); adaptive_xbuf & operator=(const adaptive_xbuf &); public: typedef T* iterator; adaptive_xbuf() : m_ptr(0), m_size(0), m_capacity(0) {} adaptive_xbuf(T *raw_memory, std::size_t capacity) : m_ptr(raw_memory), m_size(0), m_capacity(capacity) {} template<class RandIt> void move_assign(RandIt first, std::size_t n) { if(n <= m_size){ boost::move(first, first+n, m_ptr); std::size_t size = m_size; while(size-- != n){ m_ptr[size].~T(); } m_size = n; } else{ T *result = boost::move(first, first+m_size, m_ptr); boost::uninitialized_move(first+m_size, first+n, result); m_size = n; } } template<class RandIt> void push_back(RandIt first, std::size_t n) { BOOST_ASSERT(m_capacity - m_size >= n); boost::uninitialized_move(first, first+n, m_ptr+m_size); m_size += n; } template<class RandIt> iterator add(RandIt it) { BOOST_ASSERT(m_size < m_capacity); T * p_ret = m_ptr + m_size; ::new(p_ret) T(::boost::move(*it)); ++m_size; return p_ret; } template<class RandIt> void insert(iterator pos, RandIt it) { if(pos == (m_ptr + m_size)){ this->add(it); } else{ this->add(m_ptr+m_size-1); //m_size updated boost::move_backward(pos, m_ptr+m_size-2, m_ptr+m_size-1); *pos = boost::move(*it); } } void set_size(std::size_t size) { m_size = size; } void shrink_to_fit(std::size_t const size) { if(m_size > size){ for(std::size_t szt_i = size; szt_i != m_size; ++szt_i){ m_ptr[szt_i].~T(); } m_size = size; } } void initialize_until(std::size_t const size, T &t) { BOOST_ASSERT(m_size < m_capacity); if(m_size < size){ ::new((void*)&m_ptr[m_size]) T(::boost::move(t)); ++m_size; for(; m_size != size; ++m_size){ ::new((void*)&m_ptr[m_size]) T(::boost::move(m_ptr[m_size-1])); } t = ::boost::move(m_ptr[m_size-1]); } } template<class U> bool supports_aligned_trailing(std::size_t size, std::size_t trail_count) const { if(this->data()){ uintptr_t u_addr_sz = uintptr_t(this->data()+size); uintptr_t u_addr_cp = uintptr_t(this->data()+this->capacity()); u_addr_sz = ((u_addr_sz + sizeof(U)-1)/sizeof(U))*sizeof(U); return (u_addr_cp >= u_addr_sz) && ((u_addr_cp - u_addr_sz)/sizeof(U) >= trail_count); } return false; } template<class U> U *aligned_trailing() const { return this->aligned_trailing<U>(this->size()); } template<class U> U *aligned_trailing(std::size_t pos) const { uintptr_t u_addr = uintptr_t(this->data()+pos); u_addr = ((u_addr + sizeof(U)-1)/sizeof(U))*sizeof(U); return (U*)u_addr; } ~adaptive_xbuf() { this->clear(); } std::size_t capacity() const { return m_capacity; } iterator data() const { return m_ptr; } iterator end() const { return m_ptr+m_size; } std::size_t size() const { return m_size; } bool empty() const { return !m_size; } void clear() { this->shrink_to_fit(0u); } private: T *m_ptr; std::size_t m_size; std::size_t m_capacity; }; template<class Iterator, class Op> class range_xbuf { range_xbuf(const range_xbuf &); range_xbuf & operator=(const range_xbuf &); public: typedef typename iterator_traits<Iterator>::size_type size_type; typedef Iterator iterator; range_xbuf(Iterator first, Iterator last) : m_first(first), m_last(first), m_cap(last) {} template<class RandIt> void move_assign(RandIt first, std::size_t n) { BOOST_ASSERT(size_type(n) <= size_type(m_cap-m_first)); m_last = Op()(forward_t(), first, first+n, m_first); } ~range_xbuf() {} std::size_t capacity() const { return m_cap-m_first; } Iterator data() const { return m_first; } Iterator end() const { return m_last; } std::size_t size() const { return m_last-m_first; } bool empty() const { return m_first == m_last; } void clear() { m_last = m_first; } template<class RandIt> iterator add(RandIt it) { Iterator pos(m_last); *pos = boost::move(*it); ++m_last; return pos; } void set_size(std::size_t size) { m_last = m_first; m_last += size; } private: Iterator const m_first; Iterator m_last; Iterator const m_cap; }; template<class RandIt, class Compare> RandIt skip_until_merge ( RandIt first1, RandIt const last1 , const typename iterator_traits<RandIt>::value_type &next_key, Compare comp) { while(first1 != last1 && !comp(next_key, *first1)){ ++first1; } return first1; } template<class InputIt1, class InputIt2, class OutputIt, class Compare, class Op> OutputIt op_partial_merge (InputIt1 &r_first1, InputIt1 const last1, InputIt2 &r_first2, InputIt2 const last2, OutputIt d_first, Compare comp, Op op) { InputIt1 first1(r_first1); InputIt2 first2(r_first2); if(first2 != last2 && last1 != first1) while(1){ if(comp(*first2, *first1)) { op(first2++, d_first++); if(first2 == last2){ break; } } else{ op(first1++, d_first++); if(first1 == last1){ break; } } } r_first1 = first1; r_first2 = first2; return d_first; } template<class RandIt1, class RandIt2, class RandItB, class Compare, class Op> RandItB op_buffered_partial_merge_to_left_placed ( RandIt1 first1, RandIt1 const last1 , RandIt2 &rfirst2, RandIt2 const last2 , RandItB &rfirstb, Compare comp, Op op ) { RandItB firstb = rfirstb; RandItB lastb = firstb; RandIt2 first2 = rfirst2; //Move to buffer while merging //Three way moves need less moves when op is swap_op so use it //when merging elements from range2 to the destination occupied by range1 if(first1 != last1 && first2 != last2){ op(three_way_t(), first2++, first1++, lastb++); while(true){ if(first1 == last1){ break; } if(first2 == last2){ lastb = op(forward_t(), first1, last1, firstb); break; } op(three_way_t(), comp(*first2, *firstb) ? first2++ : firstb++, first1++, lastb++); } } rfirst2 = first2; rfirstb = firstb; return lastb; } /////////////////////////////////////////////////////////////////////////////// // // PARTIAL MERGE BUF // /////////////////////////////////////////////////////////////////////////////// template<class Buf, class RandIt, class Compare, class Op> RandIt op_partial_merge_with_buf_impl ( RandIt first1, RandIt const last1, RandIt first2, RandIt last2 , Buf &buf, typename Buf::iterator &buf_first1_in_out, typename Buf::iterator &buf_last1_in_out , Compare comp, Op op ) { typedef typename Buf::iterator buf_iterator; BOOST_ASSERT(first1 != last1); BOOST_ASSERT(first2 != last2); buf_iterator buf_first1 = buf_first1_in_out; buf_iterator buf_last1 = buf_last1_in_out; if(buf_first1 == buf_last1){ //Skip any element that does not need to be moved first1 = skip_until_merge(first1, last1, *last1, comp); if(first1 == last1){ return first1; } buf_first1 = buf.data(); buf_last1 = op_buffered_partial_merge_to_left_placed(first1, last1, first2, last2, buf_first1, comp, op); BOOST_ASSERT(buf_last1 == (buf.data() + (last1-first1))); first1 = last1; } else{ BOOST_ASSERT((last1-first1) == (buf_last1 - buf_first1)); } //Now merge from buffer first1 = op_partial_merge(buf_first1, buf_last1, first2, last2, first1, comp, op); buf_first1_in_out = buf_first1; buf_last1_in_out = buf_last1; return first1; } template<class RandIt, class Buf, class Compare, class Op> RandIt op_partial_merge_with_buf ( RandIt first1, RandIt const last1, RandIt first2, RandIt last2 , Buf &buf , typename Buf::iterator &buf_first1_in_out , typename Buf::iterator &buf_last1_in_out , Compare comp , Op op , bool is_stable) { return is_stable ? op_partial_merge_with_buf_impl (first1, last1, first2, last2, buf, buf_first1_in_out, buf_last1_in_out, comp, op) : op_partial_merge_with_buf_impl (first1, last1, first2, last2, buf, buf_first1_in_out, buf_last1_in_out, antistable<Compare>(comp), op) ; } // key_first - sequence of keys, in same order as blocks. key_comp(key, midkey) means stream A // first - first element to merge. // first[-l_block, 0) - buffer // l_block - length of regular blocks. Blocks are stable sorted by 1st elements and key-coded // l_irreg1 is the irregular block to be merged before n_bef_irreg2 blocks (can be 0) // n_bef_irreg2/n_aft_irreg2 are regular blocks // l_irreg2 is a irregular block, that is to be merged after n_bef_irreg2 blocks and before n_aft_irreg2 blocks // If l_irreg2==0 then n_aft_irreg2==0 (no irregular blocks). template<class RandItKeys, class KeyCompare, class RandIt, class Compare, class Op, class Buf> void op_merge_blocks_with_buf ( RandItKeys key_first , const typename iterator_traits<RandItKeys>::value_type &midkey , KeyCompare key_comp , RandIt const first , typename iterator_traits<RandIt>::size_type const l_block , typename iterator_traits<RandIt>::size_type const l_irreg1 , typename iterator_traits<RandIt>::size_type const n_bef_irreg2 , typename iterator_traits<RandIt>::size_type const n_aft_irreg2 , typename iterator_traits<RandIt>::size_type const l_irreg2 , Compare comp , Op op , Buf & xbuf) { typedef typename Buf::iterator buf_iterator; buf_iterator buffer = xbuf.data(); buf_iterator buffer_end = buffer; RandIt first1 = first; RandIt last1 = first1 + l_irreg1; RandItKeys const key_end (key_first+n_bef_irreg2); bool is_range1_A = true; //first l_irreg1 elements are always from range A for( ; key_first != key_end; ++key_first, last1 += l_block){ //If the trailing block is empty, we'll make it equal to the previous if empty bool const is_range2_A = key_comp(*key_first, midkey); if(is_range1_A == is_range2_A){ //If buffered, put those elements in place RandIt res = op(forward_t(), buffer, buffer_end, first1); BOOST_ASSERT(buffer == buffer_end || res == last1); (void)res; buffer_end = buffer; first1 = last1; } else { first1 = op_partial_merge_with_buf(first1, last1, last1, last1 + l_block, xbuf, buffer, buffer_end, comp, op, is_range1_A); BOOST_ASSERT(buffer == buffer_end || (buffer_end-buffer) == (last1+l_block-first1)); is_range1_A ^= buffer == buffer_end; } } //Now the trailing irregular block, first put buffered elements in place RandIt res = op(forward_t(), buffer, buffer_end, first1); BOOST_ASSERT(buffer == buffer_end || res == last1); (void)res; BOOST_ASSERT(l_irreg2 || n_aft_irreg2); if(l_irreg2){ bool const is_range2_A = false; //last l_irreg2 elements always from range B if(is_range1_A == is_range2_A){ first1 = last1; last1 = last1+l_block*n_aft_irreg2; } else { last1 += l_block*n_aft_irreg2; } xbuf.clear(); op_buffered_merge(first1, last1, last1+l_irreg2, comp, op, xbuf); } } template<class RandItKeys, class KeyCompare, class RandIt, class Compare, class Buf> void merge_blocks_with_buf ( RandItKeys key_first , const typename iterator_traits<RandItKeys>::value_type &midkey , KeyCompare key_comp , RandIt const first , typename iterator_traits<RandIt>::size_type const l_block , typename iterator_traits<RandIt>::size_type const l_irreg1 , typename iterator_traits<RandIt>::size_type const n_bef_irreg2 , typename iterator_traits<RandIt>::size_type const n_aft_irreg2 , typename iterator_traits<RandIt>::size_type const l_irreg2 , Compare comp , Buf & xbuf , bool const xbuf_used) { if(xbuf_used){ op_merge_blocks_with_buf (key_first, midkey, key_comp, first, l_block, l_irreg1, n_bef_irreg2, n_aft_irreg2, l_irreg2, comp, move_op(), xbuf); } else{ op_merge_blocks_with_buf (key_first, midkey, key_comp, first, l_block, l_irreg1, n_bef_irreg2, n_aft_irreg2, l_irreg2, comp, swap_op(), xbuf); } } /////////////////////////////////////////////////////////////////////////////// // // PARTIAL MERGE LEFT // /////////////////////////////////////////////////////////////////////////////// template<class RandIt, class Compare, class Op> RandIt op_partial_merge_left_middle_buffer_impl (RandIt first1, RandIt const last1, RandIt const first2 , const typename iterator_traits<RandIt>::value_type &next_key, Compare comp , Op op) { first1 = skip_until_merge(first1, last1, next_key, comp); //Even if we copy backward, no overlapping occurs so use forward copy //that can be faster specially with trivial types RandIt const new_first1 = first2 - (last1 - first1); BOOST_ASSERT(last1 <= new_first1); op(forward_t(), first1, last1, new_first1); return new_first1; } template<class RandIt, class Compare, class Op> RandIt op_partial_merge_left_middle_buffer ( RandIt first1, RandIt const last1, RandIt const first2 , const typename iterator_traits<RandIt>::value_type &next_key, Compare comp, Op op, bool is_stable) { return is_stable ? op_partial_merge_left_middle_buffer_impl(first1, last1, first2, next_key, comp, op) : op_partial_merge_left_middle_buffer_impl(first1, last1, first2, next_key, antistable<Compare>(comp), op); } // Partially merges two ordered ranges. Partially means that elements are merged // until one of two ranges is exhausted (M elements from ranges 1 y 2). // [buf_first, ...) -> buffer that can be overwritten // [first1, last1) merge [last1,last2) -> [buf_first, buf_first+M) // Note: distance(buf_first, first1) >= distance(last1, last2), so no overlapping occurs. template<class RandIt, class Compare, class Op> RandIt op_partial_merge_left_smart_impl ( RandIt first1, RandIt last1, RandIt first2, RandIt const last2, Compare comp, Op op) { RandIt dest; if(last1 != first2){ BOOST_ASSERT(0 != (last1-first1)); BOOST_ASSERT((first2-last1)==(last2-first2)); //Skip any element that does not need to be moved first1 = skip_until_merge(first1, last1, *first2, comp); if(first1 == last1) return first2; RandIt buf_first1 = first2 - (last1-first1); dest = last1; last1 = op_buffered_partial_merge_to_left_placed(first1, last1, first2, last2, buf_first1, comp, op); first1 = buf_first1; BOOST_ASSERT((first1-dest) == (last2-first2)); } else{ dest = first1-(last2-first2); } op_partial_merge(first1, last1, first2, last2, dest, comp, op); return first1 == last1 ? first2 : first1; } template<class RandIt, class Compare, class Op> RandIt op_partial_merge_left_smart (RandIt first1, RandIt const last1, RandIt first2, RandIt const last2, Compare comp, Op op, bool is_stable) { return is_stable ? op_partial_merge_left_smart_impl(first1, last1, first2, last2, comp, op) : op_partial_merge_left_smart_impl(first1, last1, first2, last2, antistable<Compare>(comp), op); } // first - first element to merge. // first[-l_block, 0) - buffer // l_block - length of regular blocks. Blocks are stable sorted by 1st elements and key-coded // key_first - sequence of keys, in same order as blocks. key<midkey means stream A // n_bef_irreg2/n_aft_irreg2 are regular blocks // l_irreg2 is a irregular block, that is to be merged after n_bef_irreg2 blocks and before n_aft_irreg2 blocks // If l_irreg2==0 then n_aft_irreg2==0 (no irregular blocks). template<class RandItKeys, class KeyCompare, class RandIt, class Compare, class Op> void op_merge_blocks_left ( RandItKeys key_first , const typename iterator_traits<RandItKeys>::value_type &midkey , KeyCompare key_comp , RandIt const first , typename iterator_traits<RandIt>::size_type const l_block , typename iterator_traits<RandIt>::size_type const l_irreg1 , typename iterator_traits<RandIt>::size_type const n_bef_irreg2 , typename iterator_traits<RandIt>::size_type const n_aft_irreg2 , typename iterator_traits<RandIt>::size_type const l_irreg2 , Compare comp, Op op) { RandIt buffer = first - l_block; RandIt first1 = first; RandIt last1 = first1 + l_irreg1; RandIt first2 = last1; RandItKeys const key_end (key_first+n_bef_irreg2); bool is_range1_A = true; for( ; key_first != key_end; first2 += l_block, ++key_first){ //If the trailing block is empty, we'll make it equal to the previous if empty bool const is_range2_A = key_comp(*key_first, midkey); if(is_range1_A == is_range2_A){ if(last1 != buffer){ //equiv. to if(!is_buffer_middle) buffer = op(forward_t(), first1, last1, buffer); } first1 = first2; last1 = first2 + l_block; } else { RandIt const last2 = first2 + l_block; first1 = op_partial_merge_left_smart(first1, last1, first2, last2, comp, op, is_range1_A); if(first1 < first2){ //is_buffer_middle for the next iteration last1 = first2; buffer = last1; } else{ //!is_buffer_middle for the next iteration is_range1_A = is_range2_A; buffer = first1 - l_block; last1 = last2; } } } //Now the trailing irregular block bool const is_range2_A = false; //Trailing l_irreg2 is always from Range B bool const is_buffer_middle = last1 == buffer; if(!l_irreg2 || is_range1_A == is_range2_A){ //trailing is always B type //If range1 is buffered, write it to its final position if(!is_buffer_middle){ buffer = op(forward_t(), first1, last1, buffer); } first1 = first2; } else { if(is_buffer_middle){ first1 = op_partial_merge_left_middle_buffer(first1, last1, first2, first2[l_block*n_aft_irreg2], comp, op, is_range1_A); buffer = first1 - l_block; } } last1 = first2 + l_block*n_aft_irreg2; op_merge_left(buffer, first1, last1, last1+l_irreg2, comp, op); } /////////////////////////////////////////////////////////////////////////////// // // PARTIAL MERGE BUFFERLESS // /////////////////////////////////////////////////////////////////////////////// // [first1, last1) merge [last1,last2) -> [first1,last2) template<class RandIt, class Compare> RandIt partial_merge_bufferless_impl (RandIt first1, RandIt last1, RandIt const last2, bool *const pis_range1_A, Compare comp) { if(last1 == last2){ return first1; } bool const is_range1_A = *pis_range1_A; if(first1 != last1 && comp(*last1, last1[-1])){ do{ RandIt const old_last1 = last1; last1 = lower_bound(last1, last2, *first1, comp); first1 = rotate_gcd(first1, old_last1, last1);//old_last1 == last1 supported if(last1 == last2){ return first1; } do{ ++first1; } while(last1 != first1 && !comp(*last1, *first1) ); } while(first1 != last1); } *pis_range1_A = !is_range1_A; return last1; } // [first1, last1) merge [last1,last2) -> [first1,last2) template<class RandIt, class Compare> RandIt partial_merge_bufferless (RandIt first1, RandIt last1, RandIt const last2, bool *const pis_range1_A, Compare comp) { return *pis_range1_A ? partial_merge_bufferless_impl(first1, last1, last2, pis_range1_A, comp) : partial_merge_bufferless_impl(first1, last1, last2, pis_range1_A, antistable<Compare>(comp)); } // l_block - length of regular blocks. First nblocks are stable sorted by 1st elements and key-coded // keys - sequence of keys, in same order as blocks. key<midkey means stream A // n_aft_irreg2 are regular blocks from stream A. l_irreg2 is length of last (irregular) block from stream B, that should go before n_aft_irreg2 blocks. // l_irreg2=0 requires n_aft_irreg2=0 (no irregular blocks). l_irreg2>0, n_aft_irreg2=0 is possible. template<class RandItKeys, class KeyCompare, class RandIt, class Compare> void merge_blocks_bufferless ( RandItKeys key_first , const typename iterator_traits<RandItKeys>::value_type &midkey , KeyCompare key_comp , RandIt first , typename iterator_traits<RandIt>::size_type const l_block , typename iterator_traits<RandIt>::size_type const l_irreg1 , typename iterator_traits<RandIt>::size_type const n_bef_irreg2 , typename iterator_traits<RandIt>::size_type const n_aft_irreg2 , typename iterator_traits<RandIt>::size_type const l_irreg2 , Compare comp) { if(n_bef_irreg2 == 0){ RandIt const last_reg(first+l_irreg1+n_aft_irreg2*l_block); merge_bufferless(first, last_reg, last_reg+l_irreg2, comp); } else{ RandIt first1 = first; RandIt last1 = l_irreg1 ? first + l_irreg1: first + l_block; RandItKeys const key_end (key_first+n_bef_irreg2); bool is_range1_A = l_irreg1 ? true : key_comp(*key_first++, midkey); for( ; key_first != key_end; ++key_first){ bool is_range2_A = key_comp(*key_first, midkey); if(is_range1_A == is_range2_A){ first1 = last1; } else{ first1 = partial_merge_bufferless(first1, last1, last1 + l_block, &is_range1_A, comp); } last1 += l_block; } if(l_irreg2){ if(!is_range1_A){ first1 = last1; } last1 += l_block*n_aft_irreg2; merge_bufferless(first1, last1, last1+l_irreg2, comp); } } } /////////////////////////////////////////////////////////////////////////////// // // BUFFERED MERGE // /////////////////////////////////////////////////////////////////////////////// template<class RandIt, class Compare, class Op, class Buf> void op_buffered_merge ( RandIt first, RandIt const middle, RandIt last , Compare comp, Op op , Buf &xbuf) { if(first != middle && middle != last && comp(*middle, middle[-1])){ typedef typename iterator_traits<RandIt>::size_type size_type; size_type const len1 = size_type(middle-first); size_type const len2 = size_type(last-middle); if(len1 <= len2){ first = upper_bound(first, middle, *middle, comp); xbuf.move_assign(first, size_type(middle-first)); op_merge_with_right_placed (xbuf.data(), xbuf.end(), first, middle, last, comp, op); } else{ last = lower_bound(middle, last, middle[-1], comp); xbuf.move_assign(middle, size_type(last-middle)); op_merge_with_left_placed (first, middle, last, xbuf.data(), xbuf.end(), comp, op); } } } template<class RandIt, class Compare> void buffered_merge ( RandIt first, RandIt const middle, RandIt last , Compare comp , adaptive_xbuf<typename iterator_traits<RandIt>::value_type> &xbuf) { op_buffered_merge(first, middle, last, comp, move_op(), xbuf); } // Complexity: 2*distance(first, last)+max_collected^2/2 // // Tries to collect at most n_keys unique elements from [first, last), // in the begining of the range, and ordered according to comp // // Returns the number of collected keys template<class RandIt, class Compare> typename iterator_traits<RandIt>::size_type collect_unique ( RandIt const first, RandIt const last , typename iterator_traits<RandIt>::size_type const max_collected, Compare comp , adaptive_xbuf<typename iterator_traits<RandIt>::value_type> & xbuf) { typedef typename iterator_traits<RandIt>::size_type size_type; typedef typename iterator_traits<RandIt>::value_type value_type; size_type h = 0; if(max_collected){ ++h; // first key is always here RandIt h0 = first; RandIt u = first; ++u; RandIt search_end = u; if(xbuf.capacity() >= max_collected){ value_type *const ph0 = xbuf.add(first); while(u != last && h < max_collected){ value_type * const r = lower_bound(ph0, xbuf.end(), *u, comp); //If key not found add it to [h, h+h0) if(r == xbuf.end() || comp(*u, *r) ){ RandIt const new_h0 = boost::move(search_end, u, h0); search_end = u; ++search_end; ++h; xbuf.insert(r, u); h0 = new_h0; } ++u; } boost::move_backward(first, h0, h0+h); boost::move(xbuf.data(), xbuf.end(), first); } else{ while(u != last && h < max_collected){ RandIt const r = lower_bound(h0, search_end, *u, comp); //If key not found add it to [h, h+h0) if(r == search_end || comp(*u, *r) ){ RandIt const new_h0 = rotate_gcd(h0, search_end, u); search_end = u; ++search_end; ++h; rotate_gcd(r+(new_h0-h0), u, search_end); h0 = new_h0; } ++u; } rotate_gcd(first, h0, h0+h); } } return h; } template<class Unsigned> Unsigned floor_sqrt(Unsigned const n) { Unsigned x = n; Unsigned y = x/2 + (x&1); while (y < x){ x = y; y = (x + n / x)/2; } return x; } template<class Unsigned> Unsigned ceil_sqrt(Unsigned const n) { Unsigned r = floor_sqrt(n); return r + Unsigned((n%r) != 0); } template<class Unsigned> Unsigned floor_merge_multiple(Unsigned const n, Unsigned &base, Unsigned &pow) { Unsigned s = n; Unsigned p = 0; while(s > AdaptiveSortInsertionSortThreshold){ s /= 2; ++p; } base = s; pow = p; return s << p; } template<class Unsigned> Unsigned ceil_merge_multiple(Unsigned const n, Unsigned &base, Unsigned &pow) { Unsigned fm = floor_merge_multiple(n, base, pow); if(fm != n){ if(base < AdaptiveSortInsertionSortThreshold){ ++base; } else{ base = AdaptiveSortInsertionSortThreshold/2 + 1; ++pow; } } return base << pow; } template<class Unsigned> Unsigned ceil_sqrt_multiple(Unsigned const n, Unsigned *pbase = 0) { Unsigned const r = ceil_sqrt(n); Unsigned pow = 0; Unsigned base = 0; Unsigned const res = ceil_merge_multiple(r, base, pow); if(pbase) *pbase = base; return res; } template<class Unsigned> Unsigned ceil_sqrt_pow2(Unsigned const n) { Unsigned r=1; Unsigned exp = 0; Unsigned pow = 1u; while(pow != 0 && pow < n){ r*=2; ++exp; pow = r << exp; } return r; } struct less { template<class T> bool operator()(const T &l, const T &r) { return l < r; } }; /////////////////////////////////////////////////////////////////////////////// // // MERGE BLOCKS // /////////////////////////////////////////////////////////////////////////////// //#define ADAPTIVE_SORT_MERGE_SLOW_STABLE_SORT_IS_NLOGN #if defined ADAPTIVE_SORT_MERGE_SLOW_STABLE_SORT_IS_NLOGN template<class RandIt, class Compare> void slow_stable_sort ( RandIt const first, RandIt const last, Compare comp) { boost::movelib::inplace_stable_sort(first, last, comp); } #else //ADAPTIVE_SORT_MERGE_SLOW_STABLE_SORT_IS_NLOGN template<class RandIt, class Compare> void slow_stable_sort ( RandIt const first, RandIt const last, Compare comp) { typedef typename iterator_traits<RandIt>::size_type size_type; size_type L = size_type(last - first); { //Use insertion sort to merge first elements size_type m = 0; while((L - m) > size_type(AdaptiveSortInsertionSortThreshold)){ insertion_sort(first+m, first+m+size_type(AdaptiveSortInsertionSortThreshold), comp); m += AdaptiveSortInsertionSortThreshold; } insertion_sort(first+m, last, comp); } size_type h = AdaptiveSortInsertionSortThreshold; for(bool do_merge = L > h; do_merge; h*=2){ do_merge = (L - h) > h; size_type p0 = 0; if(do_merge){ size_type const h_2 = 2*h; while((L-p0) > h_2){ merge_bufferless(first+p0, first+p0+h, first+p0+h_2, comp); p0 += h_2; } } if((L-p0) > h){ merge_bufferless(first+p0, first+p0+h, last, comp); } } } #endif //ADAPTIVE_SORT_MERGE_SLOW_STABLE_SORT_IS_NLOGN //Returns new l_block and updates use_buf template<class Unsigned> Unsigned lblock_for_combine (Unsigned const l_block, Unsigned const n_keys, Unsigned const l_data, bool &use_buf) { BOOST_ASSERT(l_data > 1); //We need to guarantee lblock >= l_merged/(n_keys/2) keys for the combination. //We have at least 4 keys guaranteed (which are the minimum to merge 2 ranges) //If l_block != 0, then n_keys is already enough to merge all blocks in all //phases as we've found all needed keys for that buffer and length before. //If l_block == 0 then see if half keys can be used as buffer and the rest //as keys guaranteeing that n_keys >= (2*l_merged)/lblock = if(!l_block){ //If l_block == 0 then n_keys is power of two //(guaranteed by build_params(...)) BOOST_ASSERT(n_keys >= 4); //BOOST_ASSERT(0 == (n_keys &(n_keys-1))); //See if half keys are at least 4 and if half keys fulfill Unsigned const new_buf = n_keys/2; Unsigned const new_keys = n_keys-new_buf; use_buf = new_keys >= 4 && new_keys >= l_data/new_buf; if(use_buf){ return new_buf; } else{ return l_data/n_keys; } } else{ use_buf = true; return l_block; } } //Although "cycle" sort is known to have the minimum number of writes to target //selection sort is more appropriate here as we want to minimize swaps. template<class RandItKeys, class KeyCompare, class RandIt, class Compare, class XBuf> void selection_sort_blocks ( RandItKeys keys , typename iterator_traits<RandIt>::size_type &midkey_idx //inout , KeyCompare key_comp , RandIt const first_block , typename iterator_traits<RandIt>::size_type const l_block , typename iterator_traits<RandIt>::size_type const n_blocks , Compare comp , bool use_first_element , XBuf & xbuf ) { typedef typename iterator_traits<RandIt>::size_type size_type ; size_type const back_midkey_idx = midkey_idx; typedef typename iterator_traits<RandIt>::size_type size_type; typedef typename iterator_traits<RandIt>::value_type value_type; //Nothing to sort if 0 or 1 blocks or all belong to the first ordered half if(n_blocks < 2 || back_midkey_idx >= n_blocks){ return; } //One-past the position of the first untouched element of the second half size_type high_watermark = back_midkey_idx+1; BOOST_ASSERT(high_watermark <= n_blocks); const bool b_cache_on = xbuf.capacity() >= l_block; //const bool b_cache_on = false; const size_type cached_none = size_type(-1); size_type cached_block = cached_none; //Sort by first element if left merging, last element otherwise size_type const reg_off = use_first_element ? 0u: l_block-1; for(size_type block=0; block < n_blocks-1; ++block){ size_type min_block = block; //Since we are searching for the minimum value in two sorted halves: //Optimization 1: If block belongs to first half, don't waste time comparing elements of the first half. //Optimization 2: It is enough to compare until the first untouched element of the second half. //Optimization 3: If cache memory is available, instead of swapping blocks (3 writes per element), // play with the cache to aproximate it to 2 writes per element. high_watermark = size_type(max_value(block+2, high_watermark)); BOOST_ASSERT(high_watermark <= n_blocks); for(size_type next_block = size_type(max_value(block+1, back_midkey_idx)); next_block < high_watermark; ++next_block){ const value_type &min_v = (b_cache_on && (cached_block == min_block) ? xbuf.data()[reg_off] : first_block[min_block*l_block+reg_off]); const value_type &v = (b_cache_on && (cached_block == next_block) ? xbuf.data()[reg_off] : first_block[next_block*l_block+reg_off]); if( comp(v, min_v) || (!comp(min_v, v) && key_comp(keys[next_block], keys[min_block])) ){ min_block = next_block; } } if(min_block != block){ BOOST_ASSERT(block >= back_midkey_idx || min_block >= back_midkey_idx); BOOST_ASSERT(min_block < high_watermark); //Increase high watermark if not the maximum and min_block is just before the high watermark high_watermark += size_type((min_block + 1) != n_blocks && (min_block + 1) == high_watermark); BOOST_ASSERT(high_watermark <= n_blocks); if(!b_cache_on){ boost::adl_move_swap_ranges(first_block+block*l_block, first_block+(block+1)*l_block, first_block+min_block*l_block); } else if(cached_block == cached_none){ //Cache the biggest block and put the minimum into its final position xbuf.move_assign(first_block+block*l_block, l_block); boost::move(first_block+min_block*l_block, first_block+(min_block+1)*l_block, first_block+block*l_block); cached_block = min_block; } else if(cached_block == block){ //Since block is cached and is not the minimum, just put the minimum directly into its final position and update the cache index boost::move(first_block+min_block*l_block, first_block+(min_block+1)*l_block, first_block+block*l_block); cached_block = min_block; } else if(cached_block == min_block){ //Since the minimum is cached, move the block to the back position and flush the cache to its final position boost::move(first_block+block*l_block, first_block+(block+1)*l_block, first_block+min_block*l_block); boost::move(xbuf.data(), xbuf.end(), first_block+block*l_block); cached_block = cached_none; } else{ //Cached block is not any of two blocks to be exchanged, a smarter operation must be performed BOOST_ASSERT(cached_block != min_block); BOOST_ASSERT(cached_block != block); BOOST_ASSERT(cached_block > block); BOOST_ASSERT(cached_block < high_watermark); //Instead of moving block to the slot of the minimum (which is typical selection sort), before copying //data from the minimum slot to its final position: // -> move it to free slot pointed by cached index, and // -> move cached index into slot of the minimum. //Since both cached_block and min_block belong to the still unordered range of blocks, the change //does not break selection sort and saves one copy. boost::move(first_block+block*l_block, first_block+(block+1)*l_block, first_block+cached_block*l_block); boost::move(first_block+min_block*l_block, first_block+(min_block+1)*l_block, first_block+block*l_block); //Note that this trick requires an additionl fix for keys and midkey index boost::adl_move_swap(keys[cached_block], keys[min_block]); if(midkey_idx == cached_block) midkey_idx = min_block; else if(midkey_idx == min_block) midkey_idx = cached_block; boost::adl_move_swap(cached_block, min_block); } //Once min_block and block are exchanged, fix the movement imitation key buffer and midkey index. boost::adl_move_swap(keys[block], keys[min_block]); if(midkey_idx == block) midkey_idx = min_block; else if(midkey_idx == min_block) midkey_idx = block; } else if(b_cache_on && cached_block == block){ //The selected block was the minimum, but since it was cached, move it to its final position boost::move(xbuf.data(), xbuf.end(), first_block+block*l_block); cached_block = cached_none; } } //main for loop if(b_cache_on && cached_block != cached_none){ //The sort has ended with cached data, move it to its final position boost::move(xbuf.data(), xbuf.end(), first_block+cached_block*l_block); } } template<class RandIt, class Compare, class XBuf> void stable_sort( RandIt first, RandIt last, Compare comp, XBuf & xbuf) { typedef typename iterator_traits<RandIt>::size_type size_type; size_type const len = size_type(last - first); size_type const half_len = len/2 + (len&1); if(std::size_t(xbuf.capacity() - xbuf.size()) >= half_len) { merge_sort(first, last, comp, xbuf.data()+xbuf.size()); } else{ slow_stable_sort(first, last, comp); } } template<class RandIt, class Comp, class XBuf> void initialize_keys( RandIt first, RandIt last , Comp comp , XBuf & xbuf) { stable_sort(first, last, comp, xbuf); } template<class RandIt, class U> void initialize_keys( RandIt first, RandIt last , less , U &) { typedef typename iterator_traits<RandIt>::value_type value_type; std::size_t count = std::size_t(last - first); for(std::size_t i = 0; i != count; ++i){ *first = value_type(i); ++first; } } template<class RandItKeys, class KeyCompare, class RandIt, class Compare, class XBuf> void combine_params ( RandItKeys const keys , KeyCompare key_comp , RandIt const first , typename iterator_traits<RandIt>::size_type l_combined , typename iterator_traits<RandIt>::size_type const l_prev_merged , typename iterator_traits<RandIt>::size_type const l_block , XBuf & xbuf , Compare comp //Output , typename iterator_traits<RandIt>::size_type &midkey_idx , typename iterator_traits<RandIt>::size_type &l_irreg1 , typename iterator_traits<RandIt>::size_type &n_bef_irreg2 , typename iterator_traits<RandIt>::size_type &n_aft_irreg2 , typename iterator_traits<RandIt>::size_type &l_irreg2 //Options , bool is_merge_left_or_bufferless , bool do_initialize_keys = true) { typedef typename iterator_traits<RandIt>::size_type size_type; typedef typename iterator_traits<RandIt>::value_type value_type; //Initial parameters for selection sort blocks l_irreg1 = l_prev_merged%l_block; l_irreg2 = (l_combined-l_irreg1)%l_block; BOOST_ASSERT(((l_combined-l_irreg1-l_irreg2)%l_block) == 0); size_type const n_reg_block = (l_combined-l_irreg1-l_irreg2)/l_block; midkey_idx = l_prev_merged/l_block; BOOST_ASSERT(n_reg_block>=midkey_idx); //Key initialization if (do_initialize_keys) { initialize_keys(keys, keys+n_reg_block+(midkey_idx==n_reg_block), key_comp, xbuf); } BOOST_MOVE_ADAPTIVE_SORT_PRINT(" A initkey: ", l_combined + l_block); //Selection sort blocks selection_sort_blocks(keys, midkey_idx, key_comp, first+l_irreg1, l_block, n_reg_block, comp, is_merge_left_or_bufferless, xbuf); BOOST_MOVE_ADAPTIVE_SORT_PRINT(" A selsort: ", l_combined + l_block); //Special case for the last elements n_aft_irreg2 = 0; if(l_irreg2 != 0){ size_type const reg_off = is_merge_left_or_bufferless ? 0u: l_block-1; size_type const irreg_off = is_merge_left_or_bufferless ? 0u: l_irreg2-1; RandIt prev_block_first = first + l_combined - l_irreg2; const value_type &incomplete_block_first = prev_block_first[irreg_off]; while(n_aft_irreg2 != n_reg_block && comp(incomplete_block_first, (prev_block_first-= l_block)[reg_off]) ){ ++n_aft_irreg2; } } n_bef_irreg2 = n_reg_block-n_aft_irreg2; } // first - first element to merge. // first[-l_block, 0) - buffer (if use_buf == true) // l_block - length of regular blocks. First nblocks are stable sorted by 1st elements and key-coded // keys - sequence of keys, in same order as blocks. key<midkey means stream A // n_bef_irreg2/n_aft_irreg2 are regular blocks // l_irreg2 is a irregular block, that is to be combined after n_bef_irreg2 blocks and before n_aft_irreg2 blocks // If l_irreg2==0 then n_aft_irreg2==0 (no irregular blocks). template<class RandItKeys, class KeyCompare, class RandIt, class Compare> void merge_blocks_left ( RandItKeys const key_first , const typename iterator_traits<RandItKeys>::value_type &midkey , KeyCompare key_comp , RandIt const first , typename iterator_traits<RandIt>::size_type const l_block , typename iterator_traits<RandIt>::size_type const l_irreg1 , typename iterator_traits<RandIt>::size_type const n_bef_irreg2 , typename iterator_traits<RandIt>::size_type const n_aft_irreg2 , typename iterator_traits<RandIt>::size_type const l_irreg2 , Compare comp , bool const xbuf_used) { if(xbuf_used){ op_merge_blocks_left (key_first, midkey, key_comp, first, l_block, l_irreg1, n_bef_irreg2, n_aft_irreg2, l_irreg2, comp, move_op()); } else{ op_merge_blocks_left (key_first, midkey, key_comp, first, l_block, l_irreg1, n_bef_irreg2, n_aft_irreg2, l_irreg2, comp, swap_op()); } } // first - first element to merge. // [first+l_block*(n_bef_irreg2+n_aft_irreg2)+l_irreg2, first+l_block*(n_bef_irreg2+n_aft_irreg2+1)+l_irreg2) - buffer // l_block - length of regular blocks. First nblocks are stable sorted by 1st elements and key-coded // keys - sequence of keys, in same order as blocks. key<midkey means stream A // n_bef_irreg2/n_aft_irreg2 are regular blocks // l_irreg2 is a irregular block, that is to be combined after n_bef_irreg2 blocks and before n_aft_irreg2 blocks // If l_irreg2==0 then n_aft_irreg2==0 (no irregular blocks). template<class RandItKeys, class KeyCompare, class RandIt, class Compare> void merge_blocks_right ( RandItKeys const key_first , const typename iterator_traits<RandItKeys>::value_type &midkey , KeyCompare key_comp , RandIt const first , typename iterator_traits<RandIt>::size_type const l_block , typename iterator_traits<RandIt>::size_type const n_bef_irreg2 , typename iterator_traits<RandIt>::size_type const n_aft_irreg2 , typename iterator_traits<RandIt>::size_type const l_irreg2 , Compare comp , bool const xbuf_used) { merge_blocks_left ( make_reverse_iterator(key_first+n_aft_irreg2 + n_bef_irreg2) , midkey , negate<KeyCompare>(key_comp) , make_reverse_iterator(first+(n_bef_irreg2+n_aft_irreg2)*l_block+l_irreg2) , l_block , l_irreg2 , n_aft_irreg2 + n_bef_irreg2 , 0 , 0 , inverse<Compare>(comp), xbuf_used); } template<class RandIt> void move_data_backward( RandIt cur_pos , typename iterator_traits<RandIt>::size_type const l_data , RandIt new_pos , bool const xbuf_used) { //Move buffer to the total combination right if(xbuf_used){ boost::move_backward(cur_pos, cur_pos+l_data, new_pos+l_data); } else{ boost::adl_move_swap_ranges_backward(cur_pos, cur_pos+l_data, new_pos+l_data); //Rotate does less moves but it seems slower due to cache issues //rotate_gcd(first-l_block, first+len-l_block, first+len); } } template<class RandIt> void move_data_forward( RandIt cur_pos , typename iterator_traits<RandIt>::size_type const l_data , RandIt new_pos , bool const xbuf_used) { //Move buffer to the total combination right if(xbuf_used){ boost::move(cur_pos, cur_pos+l_data, new_pos); } else{ boost::adl_move_swap_ranges(cur_pos, cur_pos+l_data, new_pos); //Rotate does less moves but it seems slower due to cache issues //rotate_gcd(first-l_block, first+len-l_block, first+len); } } template <class Unsigned> Unsigned calculate_total_combined(Unsigned const len, Unsigned const l_prev_merged, Unsigned *pl_irreg_combined = 0) { typedef Unsigned size_type; size_type const l_combined = 2*l_prev_merged; size_type l_irreg_combined = len%l_combined; size_type l_total_combined = len; if(l_irreg_combined <= l_prev_merged){ l_total_combined -= l_irreg_combined; l_irreg_combined = 0; } if(pl_irreg_combined) *pl_irreg_combined = l_irreg_combined; return l_total_combined; } // keys are on the left of first: // If use_buf: [first - l_block - n_keys, first - l_block). // Otherwise: [first - n_keys, first). // Buffer (if use_buf) is also on the left of first [first - l_block, first). // Blocks of length l_prev_merged combined. We'll combine them in pairs // l_prev_merged and n_keys are powers of 2. (2*l_prev_merged/l_block) keys are guaranteed // Returns the number of combined elements (some trailing elements might be left uncombined) template<class RandItKeys, class KeyCompare, class RandIt, class Compare, class XBuf> void adaptive_sort_combine_blocks ( RandItKeys const keys , KeyCompare key_comp , RandIt const first , typename iterator_traits<RandIt>::size_type const len , typename iterator_traits<RandIt>::size_type const l_prev_merged , typename iterator_traits<RandIt>::size_type const l_block , bool const use_buf , bool const xbuf_used , XBuf & xbuf , Compare comp , bool merge_left) { (void)xbuf; typedef typename iterator_traits<RandIt>::size_type size_type; size_type const l_reg_combined = 2*l_prev_merged; size_type l_irreg_combined = 0; size_type const l_total_combined = calculate_total_combined(len, l_prev_merged, &l_irreg_combined); size_type const n_reg_combined = len/l_reg_combined; RandIt combined_first = first; (void)l_total_combined; BOOST_ASSERT(l_total_combined <= len); size_type n_bef_irreg2, n_aft_irreg2, midkey_idx, l_irreg1, l_irreg2; size_type const max_i = n_reg_combined + (l_irreg_combined != 0); if(merge_left || !use_buf) { for( size_type combined_i = 0; combined_i != max_i; ++combined_i, combined_first += l_reg_combined) { bool const is_last = combined_i==n_reg_combined; size_type const l_cur_combined = is_last ? l_irreg_combined : l_reg_combined; range_xbuf<RandIt, move_op> rbuf( (use_buf && xbuf_used) ? (combined_first-l_block) : combined_first, combined_first); combine_params( keys, key_comp, combined_first, l_cur_combined , l_prev_merged, l_block, rbuf, comp , midkey_idx, l_irreg1, n_bef_irreg2, n_aft_irreg2, l_irreg2, true); //Outputs //Now merge blocks if(!use_buf){ merge_blocks_bufferless (keys, keys[midkey_idx], key_comp, combined_first, l_block, 0u, n_bef_irreg2, n_aft_irreg2, l_irreg2, comp); } else{ merge_blocks_left (keys, keys[midkey_idx], key_comp, combined_first, l_block, 0u, n_bef_irreg2, n_aft_irreg2, l_irreg2, comp, xbuf_used); } //BOOST_MOVE_ADAPTIVE_SORT_PRINT(" After merge_blocks_l: ", len + l_block); } } else{ combined_first += l_reg_combined*(max_i-1); for( size_type combined_i = max_i; combined_i--; combined_first -= l_reg_combined) { bool const is_last = combined_i==n_reg_combined; size_type const l_cur_combined = is_last ? l_irreg_combined : l_reg_combined; RandIt const combined_last(combined_first+l_cur_combined); range_xbuf<RandIt, move_op> rbuf(combined_last, xbuf_used ? (combined_last+l_block) : combined_last); combine_params( keys, key_comp, combined_first, l_cur_combined , l_prev_merged, l_block, rbuf, comp , midkey_idx, l_irreg1, n_bef_irreg2, n_aft_irreg2, l_irreg2, false); //Outputs //BOOST_MOVE_ADAPTIVE_SORT_PRINT(" After combine_params: ", len + l_block); merge_blocks_right (keys, keys[midkey_idx], key_comp, combined_first, l_block, n_bef_irreg2, n_aft_irreg2, l_irreg2, comp, xbuf_used); //BOOST_MOVE_ADAPTIVE_SORT_PRINT(" After merge_blocks_r: ", len + l_block); } } } template<class RandIt, class Compare> typename iterator_traits<RandIt>::size_type buffered_merge_blocks ( RandIt const first, RandIt const last , typename iterator_traits<RandIt>::size_type const input_combined_size , Compare comp , adaptive_xbuf<typename iterator_traits<RandIt>::value_type> &xbuf) { typedef typename iterator_traits<RandIt>::size_type size_type; size_type combined_size = input_combined_size; for( size_type const elements_in_blocks = size_type(last - first) ; elements_in_blocks > combined_size && size_type(xbuf.capacity()) >= combined_size ; combined_size *=2){ RandIt merge_point = first; while(size_type(last - merge_point) > 2*combined_size) { RandIt const second_half = merge_point+combined_size; RandIt const next_merge_point = second_half+combined_size; buffered_merge(merge_point, second_half, next_merge_point, comp, xbuf); merge_point = next_merge_point; } if(size_type(last-merge_point) > combined_size){ buffered_merge(merge_point, merge_point+combined_size, last, comp, xbuf); } } return combined_size; } template<class RandIt, class Compare, class Op> typename iterator_traits<RandIt>::size_type op_insertion_sort_step_left ( RandIt const first , typename iterator_traits<RandIt>::size_type const length , typename iterator_traits<RandIt>::size_type const step , Compare comp, Op op) { typedef typename iterator_traits<RandIt>::size_type size_type; size_type const s = min_value<size_type>(step, AdaptiveSortInsertionSortThreshold); size_type m = 0; while((length - m) > s){ insertion_sort_op(first+m, first+m+s, first+m-s, comp, op); m += s; } insertion_sort_op(first+m, first+length, first+m-s, comp, op); return s; } template<class RandIt, class Compare> typename iterator_traits<RandIt>::size_type insertion_sort_step ( RandIt const first , typename iterator_traits<RandIt>::size_type const length , typename iterator_traits<RandIt>::size_type const step , Compare comp) { typedef typename iterator_traits<RandIt>::size_type size_type; size_type const s = min_value<size_type>(step, AdaptiveSortInsertionSortThreshold); size_type m = 0; while((length - m) > s){ insertion_sort(first+m, first+m+s, comp); m += s; } insertion_sort(first+m, first+length, comp); return s; } template<class RandIt, class Compare, class Op> typename iterator_traits<RandIt>::size_type op_merge_left_step ( RandIt first_block , typename iterator_traits<RandIt>::size_type const elements_in_blocks , typename iterator_traits<RandIt>::size_type l_merged , typename iterator_traits<RandIt>::size_type const l_build_buf , typename iterator_traits<RandIt>::size_type l_left_space , Compare comp , Op op) { typedef typename iterator_traits<RandIt>::size_type size_type; for(; l_merged < l_build_buf && l_left_space >= l_merged; l_merged*=2){ size_type p0=0; RandIt pos = first_block; while((elements_in_blocks - p0) > 2*l_merged) { op_merge_left(pos-l_merged, pos, pos+l_merged, pos+2*l_merged, comp, op); p0 += 2*l_merged; pos = first_block+p0; } if((elements_in_blocks-p0) > l_merged) { op_merge_left(pos-l_merged, pos, pos+l_merged, first_block+elements_in_blocks, comp, op); } else { op(forward_t(), pos, first_block+elements_in_blocks, pos-l_merged); } first_block -= l_merged; l_left_space -= l_merged; } return l_merged; } template<class RandIt, class Compare, class Op> void op_merge_right_step ( RandIt first_block , typename iterator_traits<RandIt>::size_type const elements_in_blocks , typename iterator_traits<RandIt>::size_type const l_build_buf , Compare comp , Op op) { typedef typename iterator_traits<RandIt>::size_type size_type; size_type restk = elements_in_blocks%(2*l_build_buf); size_type p = elements_in_blocks - restk; BOOST_ASSERT(0 == (p%(2*l_build_buf))); if(restk <= l_build_buf){ op(backward_t(),first_block+p, first_block+p+restk, first_block+p+restk+l_build_buf); } else{ op_merge_right(first_block+p, first_block+p+l_build_buf, first_block+p+restk, first_block+p+restk+l_build_buf, comp, op); } while(p>0){ p -= 2*l_build_buf; op_merge_right(first_block+p, first_block+p+l_build_buf, first_block+p+2*l_build_buf, first_block+p+3*l_build_buf, comp, op); } } // build blocks of length 2*l_build_buf. l_build_buf is power of two // input: [0, l_build_buf) elements are buffer, rest unsorted elements // output: [0, l_build_buf) elements are buffer, blocks 2*l_build_buf and last subblock sorted // // First elements are merged from right to left until elements start // at first. All old elements [first, first + l_build_buf) are placed at the end // [first+len-l_build_buf, first+len). To achieve this: // - If we have external memory to merge, we save elements from the buffer // so that a non-swapping merge is used. Buffer elements are restored // at the end of the buffer from the external memory. // // - When the external memory is not available or it is insufficient // for a merge operation, left swap merging is used. // // Once elements are merged left to right in blocks of l_build_buf, then a single left // to right merge step is performed to achieve merged blocks of size 2K. // If external memory is available, usual merge is used, swap merging otherwise. // // As a last step, if auxiliary memory is available in-place merge is performed. // until all is merged or auxiliary memory is not large enough. template<class RandIt, class Compare> typename iterator_traits<RandIt>::size_type adaptive_sort_build_blocks ( RandIt const first , typename iterator_traits<RandIt>::size_type const len , typename iterator_traits<RandIt>::size_type const l_base , typename iterator_traits<RandIt>::size_type const l_build_buf , adaptive_xbuf<typename iterator_traits<RandIt>::value_type> & xbuf , Compare comp) { typedef typename iterator_traits<RandIt>::size_type size_type; BOOST_ASSERT(l_build_buf <= len); BOOST_ASSERT(0 == ((l_build_buf / l_base)&(l_build_buf/l_base-1))); //Place the start pointer after the buffer RandIt first_block = first + l_build_buf; size_type const elements_in_blocks = len - l_build_buf; ////////////////////////////////// // Start of merge to left step ////////////////////////////////// size_type l_merged = 0u; // if(xbuf.capacity()>=2*l_build_buf){ if(!l_build_buf){ l_merged = insertion_sort_step(first_block, elements_in_blocks, l_base, comp); //2*l_build_buf already merged, now try to merge further //using classic in-place mergesort if enough auxiliary memory is available return buffered_merge_blocks (first_block, first_block + elements_in_blocks, l_merged, comp, xbuf); } else{ //If there is no enough buffer for the insertion sort step, just avoid the external buffer size_type kbuf = min_value<size_type>(l_build_buf, size_type(xbuf.capacity())); kbuf = kbuf < l_base ? 0 : kbuf; if(kbuf){ //Backup internal buffer values in external buffer so they can be overwritten xbuf.move_assign(first+l_build_buf-kbuf, kbuf); l_merged = op_insertion_sort_step_left(first_block, elements_in_blocks, l_base, comp, move_op()); //Now combine them using the buffer. Elements from buffer can be //overwritten since they've been saved to xbuf l_merged = op_merge_left_step ( first_block - l_merged, elements_in_blocks, l_merged, l_build_buf, kbuf - l_merged, comp, move_op()); //Restore internal buffer from external buffer unless kbuf was l_build_buf, //in that case restoration will happen later if(kbuf != l_build_buf){ boost::move(xbuf.data()+kbuf-l_merged, xbuf.data() + kbuf, first_block-l_merged+elements_in_blocks); } } else{ l_merged = insertion_sort_step(first_block, elements_in_blocks, l_base, comp); rotate_gcd(first_block - l_merged, first_block, first_block+elements_in_blocks); } //Now combine elements using the buffer. Elements from buffer can't be //overwritten since xbuf was not big enough, so merge swapping elements. l_merged = op_merge_left_step (first_block - l_merged, elements_in_blocks, l_merged, l_build_buf, l_build_buf - l_merged, comp, swap_op()); BOOST_ASSERT(l_merged == l_build_buf); ////////////////////////////////// // Start of merge to right step ////////////////////////////////// //If kbuf is l_build_buf then we can merge right without swapping //Saved data is still in xbuf if(kbuf && kbuf == l_build_buf){ op_merge_right_step(first, elements_in_blocks, l_build_buf, comp, move_op()); //Restore internal buffer from external buffer if kbuf was l_build_buf. //as this operation was previously delayed. boost::move(xbuf.data(), xbuf.data() + kbuf, first); } else{ op_merge_right_step(first, elements_in_blocks, l_build_buf, comp, swap_op()); } xbuf.clear(); //2*l_build_buf already merged, now try to merge further //using classic in-place mergesort if enough auxiliary memory is available return buffered_merge_blocks (first_block, first_block + elements_in_blocks, l_build_buf*2, comp, xbuf); } } //Returns true if buffer is placed in //[buffer+len-l_intbuf, buffer+len). Otherwise, buffer is //[buffer,buffer+l_intbuf) template<class RandIt, class Compare> bool adaptive_sort_combine_all_blocks ( RandIt keys , typename iterator_traits<RandIt>::size_type &n_keys , RandIt const buffer , typename iterator_traits<RandIt>::size_type const l_buf_plus_data , typename iterator_traits<RandIt>::size_type l_merged , typename iterator_traits<RandIt>::size_type &l_intbuf , adaptive_xbuf<typename iterator_traits<RandIt>::value_type> & xbuf , Compare comp) { typedef typename iterator_traits<RandIt>::size_type size_type; RandIt const first = buffer + l_intbuf; size_type const l_data = l_buf_plus_data - l_intbuf; size_type const l_unique = l_intbuf+n_keys; //Backup data to external buffer once if possible bool const common_xbuf = l_data > l_merged && l_intbuf && l_intbuf <= xbuf.capacity(); if(common_xbuf){ xbuf.move_assign(buffer, l_intbuf); } bool prev_merge_left = true; size_type l_prev_total_combined = 0u, l_prev_block = 0; bool prev_use_internal_buf = true; for( size_type n = 0; l_data > l_merged ; l_merged*=2 , ++n){ //If l_intbuf is non-zero, use that internal buffer. // Implies l_block == l_intbuf && use_internal_buf == true //If l_intbuf is zero, see if half keys can be reused as a reduced emergency buffer, // Implies l_block == n_keys/2 && use_internal_buf == true //Otherwise, just give up and and use all keys to merge using rotations (use_internal_buf = false) bool use_internal_buf = false; size_type const l_block = lblock_for_combine(l_intbuf, n_keys, 2*l_merged, use_internal_buf); BOOST_ASSERT(!l_intbuf || (l_block == l_intbuf)); BOOST_ASSERT(n == 0 || (!use_internal_buf || prev_use_internal_buf) ); BOOST_ASSERT(n == 0 || (!use_internal_buf || l_prev_block == l_block) ); bool const is_merge_left = (n&1) == 0; size_type const l_total_combined = calculate_total_combined(l_data, l_merged); if(n && prev_use_internal_buf && prev_merge_left){ if(is_merge_left || !use_internal_buf){ move_data_backward(first-l_prev_block, l_prev_total_combined, first, common_xbuf); } else{ //Put the buffer just after l_total_combined RandIt const buf_end = first+l_prev_total_combined; RandIt const buf_beg = buf_end-l_block; if(l_prev_total_combined > l_total_combined){ size_type const l_diff = l_prev_total_combined - l_total_combined; move_data_backward(buf_beg-l_diff, l_diff, buf_end-l_diff, common_xbuf); } else if(l_prev_total_combined < l_total_combined){ size_type const l_diff = l_total_combined - l_prev_total_combined; move_data_forward(buf_end, l_diff, buf_beg, common_xbuf); } } } BOOST_MOVE_ADAPTIVE_SORT_PRINT(" After move_data : ", l_data + l_intbuf); //Combine to form l_merged*2 segments if(n_keys){ adaptive_sort_combine_blocks ( keys, comp, !use_internal_buf || is_merge_left ? first : first-l_block , l_data, l_merged, l_block, use_internal_buf, common_xbuf, xbuf, comp, is_merge_left); } else{ size_type *const uint_keys = xbuf.template aligned_trailing<size_type>(); adaptive_sort_combine_blocks ( uint_keys, less(), !use_internal_buf || is_merge_left ? first : first-l_block , l_data, l_merged, l_block, use_internal_buf, common_xbuf, xbuf, comp, is_merge_left); } BOOST_MOVE_ADAPTIVE_SORT_PRINT(" After combine_blocks: ", l_data + l_intbuf); prev_merge_left = is_merge_left; l_prev_total_combined = l_total_combined; l_prev_block = l_block; prev_use_internal_buf = use_internal_buf; } BOOST_ASSERT(l_prev_total_combined == l_data); bool const buffer_right = prev_use_internal_buf && prev_merge_left; l_intbuf = prev_use_internal_buf ? l_prev_block : 0u; n_keys = l_unique - l_intbuf; //Restore data from to external common buffer if used if(common_xbuf){ if(buffer_right){ boost::move(xbuf.data(), xbuf.data() + l_intbuf, buffer+l_data); } else{ boost::move(xbuf.data(), xbuf.data() + l_intbuf, buffer); } } return buffer_right; } template<class RandIt, class Compare> void stable_merge ( RandIt first, RandIt const middle, RandIt last , Compare comp , adaptive_xbuf<typename iterator_traits<RandIt>::value_type> &xbuf) { BOOST_ASSERT(xbuf.empty()); typedef typename iterator_traits<RandIt>::size_type size_type; size_type const len1 = size_type(middle-first); size_type const len2 = size_type(last-middle); size_type const l_min = min_value(len1, len2); if(xbuf.capacity() >= l_min){ buffered_merge(first, middle, last, comp, xbuf); xbuf.clear(); } else{ merge_bufferless(first, middle, last, comp); } } template<class RandIt, class Compare> void adaptive_sort_final_merge( bool buffer_right , RandIt const first , typename iterator_traits<RandIt>::size_type const l_intbuf , typename iterator_traits<RandIt>::size_type const n_keys , typename iterator_traits<RandIt>::size_type const len , adaptive_xbuf<typename iterator_traits<RandIt>::value_type> & xbuf , Compare comp) { //BOOST_ASSERT(n_keys || xbuf.size() == l_intbuf); xbuf.clear(); typedef typename iterator_traits<RandIt>::size_type size_type; size_type const n_key_plus_buf = l_intbuf+n_keys; if(buffer_right){ stable_sort(first+len-l_intbuf, first+len, comp, xbuf); stable_merge(first+n_keys, first+len-l_intbuf, first+len, antistable<Compare>(comp), xbuf); stable_sort(first, first+n_keys, comp, xbuf); stable_merge(first, first+n_keys, first+len, comp, xbuf); } else{ stable_sort(first, first+n_key_plus_buf, comp, xbuf); if(xbuf.capacity() >= n_key_plus_buf){ buffered_merge(first, first+n_key_plus_buf, first+len, comp, xbuf); } else if(xbuf.capacity() >= min_value<size_type>(l_intbuf, n_keys)){ stable_merge(first+n_keys, first+n_key_plus_buf, first+len, comp, xbuf); stable_merge(first, first+n_keys, first+len, comp, xbuf); } else{ merge_bufferless(first, first+n_key_plus_buf, first+len, comp); } } BOOST_MOVE_ADAPTIVE_SORT_PRINT(" After final_merge : ", len); } template<class RandIt, class Compare, class Unsigned, class T> bool adaptive_sort_build_params (RandIt first, Unsigned const len, Compare comp , Unsigned &n_keys, Unsigned &l_intbuf, Unsigned &l_base, Unsigned &l_build_buf , adaptive_xbuf<T> & xbuf ) { typedef Unsigned size_type; //Calculate ideal parameters and try to collect needed unique keys l_base = 0u; //Try to find a value near sqrt(len) that is 2^N*l_base where //l_base <= AdaptiveSortInsertionSortThreshold. This property is important //as build_blocks merges to the left iteratively duplicating the //merged size and all the buffer must be used just before the final //merge to right step. This guarantees "build_blocks" produces //segments of size l_build_buf*2, maximizing the classic merge phase. l_intbuf = size_type(ceil_sqrt_multiple(len, &l_base)); //This is the minimum number of keys to implement the ideal algorithm // //l_intbuf is used as buffer plus the key count size_type n_min_ideal_keys = l_intbuf-1u; while(n_min_ideal_keys >= (len-l_intbuf-n_min_ideal_keys)/l_intbuf){ --n_min_ideal_keys; } ++n_min_ideal_keys; BOOST_ASSERT(n_min_ideal_keys < l_intbuf); if(xbuf.template supports_aligned_trailing<size_type>(l_intbuf, n_min_ideal_keys)){ n_keys = 0u; l_build_buf = l_intbuf; } else{ //Try to achieve a l_build_buf of length l_intbuf*2, so that we can merge with that //l_intbuf*2 buffer in "build_blocks" and use half of them as buffer and the other half //as keys in combine_all_blocks. In that case n_keys >= n_min_ideal_keys but by a small margin. // //If available memory is 2*sqrt(l), then only sqrt(l) unique keys are needed, //(to be used for keys in combine_all_blocks) as the whole l_build_buf //will be backuped in the buffer during build_blocks. bool const non_unique_buf = xbuf.capacity() >= 2*l_intbuf; size_type const to_collect = non_unique_buf ? l_intbuf : l_intbuf*2; size_type collected = collect_unique(first, first+len, to_collect, comp, xbuf); //If available memory is 2*sqrt(l), then for "build_params" //the situation is the same as if 2*l_intbuf were collected. if(non_unique_buf && (collected >= n_min_ideal_keys)) collected += l_intbuf; //If collected keys are not enough, try to fix n_keys and l_intbuf. If no fix //is possible (due to very low unique keys), then go to a slow sort based on rotations. if(collected < (n_min_ideal_keys+l_intbuf)){ if(collected < 4){ //No combination possible with less that 4 keys return false; } n_keys = l_intbuf; while(n_keys&(n_keys-1)){ n_keys &= n_keys-1; // make it power or 2 } while(n_keys > collected){ n_keys/=2; } //AdaptiveSortInsertionSortThreshold is always power of two so the minimum is power of two l_base = min_value<Unsigned>(n_keys, AdaptiveSortInsertionSortThreshold); l_intbuf = 0; l_build_buf = n_keys; } else if((collected - l_intbuf) >= l_intbuf){ //l_intbuf*2 elements found. Use all of them in the build phase l_build_buf = l_intbuf*2; n_keys = l_intbuf; } else{ l_build_buf = l_intbuf; n_keys = n_min_ideal_keys; } BOOST_ASSERT((n_keys+l_intbuf) >= l_build_buf); } return true; } #define BOOST_MOVE_ADAPTIVE_MERGE_WITH_BUF template<class RandIt, class Compare> inline void adaptive_merge_combine_blocks( RandIt first , typename iterator_traits<RandIt>::size_type len1 , typename iterator_traits<RandIt>::size_type len2 , typename iterator_traits<RandIt>::size_type collected , typename iterator_traits<RandIt>::size_type n_keys , typename iterator_traits<RandIt>::size_type l_block , bool use_internal_buf , bool xbuf_used , Compare comp , adaptive_xbuf<typename iterator_traits<RandIt>::value_type> & xbuf ) { typedef typename iterator_traits<RandIt>::size_type size_type; size_type const len = len1+len2; size_type const l_combine = len-collected; size_type const l_combine1 = len1-collected; size_type n_bef_irreg2, n_aft_irreg2, l_irreg1, l_irreg2, midkey_idx; if(n_keys){ RandIt const first_data = first+collected; RandIt const keys = first; combine_params( keys, comp, first_data, l_combine , l_combine1, l_block, xbuf, comp , midkey_idx, l_irreg1, n_bef_irreg2, n_aft_irreg2, l_irreg2, true, false); //Outputs BOOST_MOVE_ADAPTIVE_SORT_PRINT(" A combine: ", len); if(xbuf_used){ BOOST_ASSERT(xbuf.size() >= l_block); merge_blocks_with_buf (keys, keys[midkey_idx], comp, first_data, l_block, l_irreg1, n_bef_irreg2, n_aft_irreg2, l_irreg2, comp, xbuf, xbuf_used); BOOST_MOVE_ADAPTIVE_SORT_PRINT(" A mrg xbf: ", len); } else if(use_internal_buf){ #ifdef BOOST_MOVE_ADAPTIVE_MERGE_WITH_BUF range_xbuf<RandIt, swap_op> rbuf(first_data-l_block, first_data); merge_blocks_with_buf (keys, keys[midkey_idx], comp, first_data, l_block, l_irreg1, n_bef_irreg2, n_aft_irreg2, l_irreg2, comp, rbuf, xbuf_used); BOOST_MOVE_ADAPTIVE_SORT_PRINT(" A mrg buf: ", len); #else merge_blocks_left (keys, keys[midkey_idx], comp, first_data, l_block, l_irreg1, n_bef_irreg2, n_aft_irreg2, l_irreg2, comp, xbuf_used); BOOST_MOVE_ADAPTIVE_SORT_PRINT(" A mrg lft: ", len); #endif } else{ merge_blocks_bufferless (keys, keys[midkey_idx], comp, first_data, l_block, l_irreg1, n_bef_irreg2, n_aft_irreg2, l_irreg2, comp); BOOST_MOVE_ADAPTIVE_SORT_PRINT(" A mrg xbf: ", len); } } else{ xbuf.shrink_to_fit(l_block); if(xbuf.size() < l_block){ xbuf.initialize_until(l_block, *first); } size_type *const uint_keys = xbuf.template aligned_trailing<size_type>(l_block); combine_params( uint_keys, less(), first, l_combine , l_combine1, l_block, xbuf, comp , midkey_idx, l_irreg1, n_bef_irreg2, n_aft_irreg2, l_irreg2, true, true); //Outputs BOOST_MOVE_ADAPTIVE_SORT_PRINT(" A combine: ", len); BOOST_ASSERT(xbuf.size() >= l_block); merge_blocks_with_buf (uint_keys, uint_keys[midkey_idx], less(), first, l_block, l_irreg1, n_bef_irreg2, n_aft_irreg2, l_irreg2, comp, xbuf, true); xbuf.clear(); BOOST_MOVE_ADAPTIVE_SORT_PRINT(" A mrg buf: ", len); } } template<class RandIt, class Compare> inline void adaptive_merge_final_merge( RandIt first , typename iterator_traits<RandIt>::size_type len1 , typename iterator_traits<RandIt>::size_type len2 , typename iterator_traits<RandIt>::size_type collected , typename iterator_traits<RandIt>::size_type l_intbuf , typename iterator_traits<RandIt>::size_type l_block , bool use_internal_buf , bool xbuf_used , Compare comp , adaptive_xbuf<typename iterator_traits<RandIt>::value_type> & xbuf ) { typedef typename iterator_traits<RandIt>::size_type size_type; (void)l_block; size_type n_keys = collected-l_intbuf; size_type len = len1+len2; if(use_internal_buf){ if(xbuf_used){ xbuf.clear(); //Nothing to do if(n_keys){ stable_sort(first, first+n_keys, comp, xbuf); stable_merge(first, first+n_keys, first+len, comp, xbuf); BOOST_MOVE_ADAPTIVE_SORT_PRINT(" A key mrg: ", len); } } else{ #ifdef BOOST_MOVE_ADAPTIVE_MERGE_WITH_BUF xbuf.clear(); stable_sort(first, first+collected, comp, xbuf); BOOST_MOVE_ADAPTIVE_SORT_PRINT(" A k/b srt: ", len); stable_merge(first, first+collected, first+len, comp, xbuf); BOOST_MOVE_ADAPTIVE_SORT_PRINT(" A k/b mrg: ", len); #else xbuf.clear(); stable_sort(first+len-l_block, first+len, comp, xbuf); BOOST_MOVE_ADAPTIVE_SORT_PRINT(" A buf srt: ", len); RandIt const pos1 = lower_bound(first+n_keys, first+len-l_block, first[len-1], comp); RandIt const pos2 = rotate_gcd(pos1, first+len-l_block, first+len); stable_merge(first+n_keys, pos1, pos2, antistable<Compare>(comp), xbuf); BOOST_MOVE_ADAPTIVE_SORT_PRINT(" A buf mrg: ", len); if(n_keys){ stable_sort(first, first+n_keys, comp, xbuf); BOOST_MOVE_ADAPTIVE_SORT_PRINT(" A key srt: ", len); stable_merge(first, first+n_keys, first+len, comp, xbuf); BOOST_MOVE_ADAPTIVE_SORT_PRINT(" A key mrg: ", len); } #endif } } else{ xbuf.clear(); stable_sort(first, first+collected, comp, xbuf); BOOST_MOVE_ADAPTIVE_SORT_PRINT(" A k/b srt: ", len); stable_merge(first, first+collected, first+len1+len2, comp, xbuf); BOOST_MOVE_ADAPTIVE_SORT_PRINT(" A k/b mrg: ", len); } } template<class SizeType, class Xbuf> inline SizeType adaptive_merge_n_keys_intbuf(SizeType l_block, SizeType len, Xbuf & xbuf, SizeType &l_intbuf_inout) { typedef SizeType size_type; size_type l_intbuf = xbuf.capacity() >= l_block ? 0u : l_block; //This is the minimum number of keys to implement the ideal algorithm //ceil(len/l_block) - 1 (as the first block is used as buffer) size_type n_keys = len/l_block+1; while(n_keys >= (len-l_intbuf-n_keys)/l_block){ --n_keys; } ++n_keys; //BOOST_ASSERT(n_keys < l_block); if(xbuf.template supports_aligned_trailing<size_type>(l_block, n_keys)){ n_keys = 0u; } l_intbuf_inout = l_intbuf; return n_keys; } /////////////////////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////////////////////////////// // Main explanation of the sort algorithm. // // csqrtlen = ceil(sqrt(len)); // // * First, 2*csqrtlen unique elements elements are extracted from elements to be // sorted and placed in the beginning of the range. // // * Step "build_blocks": In this nearly-classic merge step, 2*csqrtlen unique elements // will be used as auxiliary memory, so trailing len-2*csqrtlen elements are // are grouped in blocks of sorted 4*csqrtlen elements. At the end of the step // 2*csqrtlen unique elements are again the leading elements of the whole range. // // * Step "combine_blocks": pairs of previously formed blocks are merged with a different // ("smart") algorithm to form blocks of 8*csqrtlen elements. This step is slower than the // "build_blocks" step and repeated iteratively (forming blocks of 16*csqrtlen, 32*csqrtlen // elements, etc) of until all trailing (len-2*csqrtlen) elements are merged. // // In "combine_blocks" len/csqrtlen elements used are as "keys" (markers) to // know if elements belong to the first or second block to be merged and another // leading csqrtlen elements are used as buffer. Explanation of the "combine_blocks" step: // // Iteratively until all trailing (len-2*csqrtlen) elements are merged: // Iteratively for each pair of previously merged block: // * Blocks are divided groups of csqrtlen elements and // 2*merged_block/csqrtlen keys are sorted to be used as markers // * Groups are selection-sorted by first or last element (depending wheter they // merged to left or right) and keys are reordered accordingly as an imitation-buffer. // * Elements of each block pair is merged using the csqrtlen buffer taking into account // if they belong to the first half or second half (marked by the key). // // * In the final merge step leading elements (2*csqrtlen) are sorted and merged with // rotations with the rest of sorted elements in the "combine_blocks" step. // // Corner cases: // // * If no 2*csqrtlen elements can be extracted: // // * If csqrtlen+len/csqrtlen are extracted, then only csqrtlen elements are used // as buffer in the "build_blocks" step forming blocks of 2*csqrtlen elements. This // means that an additional "combine_blocks" step will be needed to merge all elements. // // * If no csqrtlen+len/csqrtlen elements can be extracted, but still more than a minimum, // then reduces the number of elements used as buffer and keys in the "build_blocks" // and "combine_blocks" steps. If "combine_blocks" has no enough keys due to this reduction // then uses a rotation based smart merge. // // * If the minimum number of keys can't be extracted, a rotation-based sorting is performed. // // * If auxiliary memory is more or equal than ceil(len/2), half-copying mergesort is used. // // * If auxiliary memory is more than csqrtlen+n_keys*sizeof(std::size_t), // then only csqrtlen elements need to be extracted and "combine_blocks" will use integral // keys to combine blocks. // // * If auxiliary memory is available, the "build_blocks" will be extended to build bigger blocks // using classic merge. template<class RandIt, class Compare> void adaptive_sort_impl ( RandIt first , typename iterator_traits<RandIt>::size_type const len , Compare comp , adaptive_xbuf<typename iterator_traits<RandIt>::value_type> & xbuf ) { typedef typename iterator_traits<RandIt>::size_type size_type; //Small sorts go directly to insertion sort if(len <= size_type(AdaptiveSortInsertionSortThreshold)){ insertion_sort(first, first + len, comp); return; } if((len-len/2) <= xbuf.capacity()){ merge_sort(first, first+len, comp, xbuf.data()); return; } //Make sure it is at least four BOOST_STATIC_ASSERT(AdaptiveSortInsertionSortThreshold >= 4); size_type l_base = 0; size_type l_intbuf = 0; size_type n_keys = 0; size_type l_build_buf = 0; //Calculate and extract needed unique elements. If a minimum is not achieved //fallback to rotation-based merge if(!adaptive_sort_build_params(first, len, comp, n_keys, l_intbuf, l_base, l_build_buf, xbuf)){ stable_sort(first, first+len, comp, xbuf); return; } //Otherwise, continue the adaptive_sort BOOST_MOVE_ADAPTIVE_SORT_PRINT("\n After collect_unique: ", len); size_type const n_key_plus_buf = l_intbuf+n_keys; //l_build_buf is always power of two if l_intbuf is zero BOOST_ASSERT(l_intbuf || (0 == (l_build_buf & (l_build_buf-1)))); //Classic merge sort until internal buffer and xbuf are exhausted size_type const l_merged = adaptive_sort_build_blocks (first+n_key_plus_buf-l_build_buf, len-n_key_plus_buf+l_build_buf, l_base, l_build_buf, xbuf, comp); BOOST_MOVE_ADAPTIVE_SORT_PRINT(" After build_blocks: ", len); //Non-trivial merge bool const buffer_right = adaptive_sort_combine_all_blocks (first, n_keys, first+n_keys, len-n_keys, l_merged, l_intbuf, xbuf, comp); //Sort keys and buffer and merge the whole sequence adaptive_sort_final_merge(buffer_right, first, l_intbuf, n_keys, len, xbuf, comp); } // Main explanation of the merge algorithm. // // csqrtlen = ceil(sqrt(len)); // // * First, csqrtlen [to be used as buffer] + (len/csqrtlen - 1) [to be used as keys] => to_collect // unique elements are extracted from elements to be sorted and placed in the beginning of the range. // // * Step "combine_blocks": the leading (len1-to_collect) elements plus trailing len2 elements // are merged with a non-trivial ("smart") algorithm to form an ordered range trailing "len-to_collect" elements. // // Explanation of the "combine_blocks" step: // // * Trailing [first+to_collect, first+len1) elements are divided in groups of cqrtlen elements. // Remaining elements that can't form a group are grouped in the front of those elements. // * Trailing [first+len1, first+len1+len2) elements are divided in groups of cqrtlen elements. // Remaining elements that can't form a group are grouped in the back of those elements. // * Groups are selection-sorted by first or last element (depending wheter they // merged to left or right) and keys are reordered accordingly as an imitation-buffer. // * Elements of each block pair is merged using the csqrtlen buffer taking into account // if they belong to the first half or second half (marked by the key). // // * In the final merge step leading "to_collect" elements are merged with rotations // with the rest of merged elements in the "combine_blocks" step. // // Corner cases: // // * If no "to_collect" elements can be extracted: // // * If more than a minimum number of elements is extracted // then reduces the number of elements used as buffer and keys in the // and "combine_blocks" steps. If "combine_blocks" has no enough keys due to this reduction // then uses a rotation based smart merge. // // * If the minimum number of keys can't be extracted, a rotation-based merge is performed. // // * If auxiliary memory is more or equal than min(len1, len2), a buffered merge is performed. // // * If the len1 or len2 are less than 2*csqrtlen then a rotation-based merge is performed. // // * If auxiliary memory is more than csqrtlen+n_keys*sizeof(std::size_t), // then no csqrtlen need to be extracted and "combine_blocks" will use integral // keys to combine blocks. template<class RandIt, class Compare> void adaptive_merge_impl ( RandIt first , typename iterator_traits<RandIt>::size_type const len1 , typename iterator_traits<RandIt>::size_type const len2 , Compare comp , adaptive_xbuf<typename iterator_traits<RandIt>::value_type> & xbuf ) { typedef typename iterator_traits<RandIt>::size_type size_type; if(xbuf.capacity() >= min_value<size_type>(len1, len2)){ buffered_merge(first, first+len1, first+(len1+len2), comp, xbuf); } else{ const size_type len = len1+len2; //Calculate ideal parameters and try to collect needed unique keys size_type l_block = size_type(ceil_sqrt(len)); //One range is not big enough to extract keys and the internal buffer so a //rotation-based based merge will do just fine if(len1 <= l_block*2 || len2 <= l_block*2){ merge_bufferless(first, first+len1, first+len1+len2, comp); return; } //Detail the number of keys and internal buffer. If xbuf has enough memory, no //internal buffer is needed so l_intbuf will remain 0. size_type l_intbuf = 0; size_type n_keys = adaptive_merge_n_keys_intbuf(l_block, len, xbuf, l_intbuf); size_type const to_collect = l_intbuf+n_keys; //Try to extract needed unique values from the first range size_type const collected = collect_unique(first, first+len1, to_collect, comp, xbuf); BOOST_MOVE_ADAPTIVE_SORT_PRINT("\n A collect: ", len); //Not the minimum number of keys is not available on the first range, so fallback to rotations if(collected != to_collect && collected < 4){ merge_bufferless(first, first+len1, first+len1+len2, comp); return; } //If not enough keys but more than minimum, adjust the internal buffer and key count bool use_internal_buf = collected == to_collect; if (!use_internal_buf){ l_intbuf = 0u; n_keys = collected; l_block = lblock_for_combine(l_intbuf, n_keys, len, use_internal_buf); //If use_internal_buf is false, then then internal buffer will be zero and rotation-based combination will be used l_intbuf = use_internal_buf ? l_block : 0u; } bool const xbuf_used = collected == to_collect && xbuf.capacity() >= l_block; //Merge trailing elements using smart merges adaptive_merge_combine_blocks(first, len1, len2, collected, n_keys, l_block, use_internal_buf, xbuf_used, comp, xbuf); //Merge buffer and keys with the rest of the values adaptive_merge_final_merge (first, len1, len2, collected, l_intbuf, l_block, use_internal_buf, xbuf_used, comp, xbuf); } } } //namespace detail_adaptive { } //namespace movelib { } //namespace boost { #include <boost/move/detail/config_end.hpp> #endif //#define BOOST_MOVE_ADAPTIVE_SORT_MERGE_HPP