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 //////////////////////////////////////////////////////////////////////////////
 //
 // (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.
 //
 //////////////////////////////////////////////////////////////////////////////
 
 #ifndef BOOST_MOVE_ADAPTIVE_SORT_HPP
 #define BOOST_MOVE_ADAPTIVE_SORT_HPP
 
 #include <boost/move/detail/config_begin.hpp>
 
 #include <boost/move/algo/detail/adaptive_sort_merge.hpp>
 #include <cassert>
 
 #if defined(BOOST_CLANG) || (defined(BOOST_GCC) && (BOOST_GCC >= 40600))
 #pragma GCC diagnostic push
 #pragma GCC diagnostic ignored "-Wsign-conversion"
 #endif
 
 namespace boost {
 namespace movelib {
 
 ///@cond
 namespace detail_adaptive {
 
 template<class RandIt>
 void move_data_backward( RandIt cur_pos
               , typename iter_size<RandIt>::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 iter_size<RandIt>::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);
    }
 }
 
 // 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, class XBuf>
 typename iter_size<RandIt>::type  
    adaptive_sort_build_blocks
       ( RandIt const first
       , typename iter_size<RandIt>::type const len
       , typename iter_size<RandIt>::type const l_base
       , typename iter_size<RandIt>::type const l_build_buf
       , XBuf & xbuf
       , Compare comp)
 {
    typedef typename iter_size<RandIt>::type       size_type;
    assert(l_build_buf <= len);
    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 = size_type(len - l_build_buf);
 
    //////////////////////////////////
    // Start of merge to left step
    //////////////////////////////////
    size_type l_merged = 0u;
 
    assert(l_build_buf);
    //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_multiple
          ( first_block - l_merged, elements_in_blocks, l_merged, l_build_buf, size_type(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_multiple
       (first_block-l_merged, elements_in_blocks, l_merged, l_build_buf, size_type(l_build_buf - l_merged), comp, swap_op());
 
    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_once(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_once(first, elements_in_blocks, l_build_buf, comp, swap_op());
    }
    xbuf.clear();
    //2*l_build_buf or total already merged
    return min_value<size_type>(elements_in_blocks, size_type(2u*l_build_buf));
 }
 
 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 iter_size<RandIt>::type const len
    , typename iter_size<RandIt>::type const l_prev_merged
    , typename iter_size<RandIt>::type const l_block
    , bool const use_buf
    , bool const xbuf_used
    , XBuf & xbuf
    , Compare comp
    , bool merge_left)
 {
    boost::movelib::ignore(xbuf);
    typedef typename iter_size<RandIt>::type         size_type;
 
    size_type const l_reg_combined   = size_type(2u*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;
 
    boost::movelib::ignore(l_total_combined);
    assert(l_total_combined <= len);
 
    size_type const max_i = size_type(n_reg_combined + (l_irreg_combined != 0));
 
    if(merge_left || !use_buf) {
       for( size_type combined_i = 0; combined_i != max_i; ) {
          //Now merge blocks
          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, size_type, move_op> rbuf( (use_buf && xbuf_used) ? (combined_first-l_block) : combined_first, combined_first);
          size_type n_block_a, n_block_b, l_irreg1, l_irreg2;
          combine_params( keys, key_comp, l_cur_combined
                         , l_prev_merged, l_block, rbuf
                         , n_block_a, n_block_b, l_irreg1, l_irreg2);   //Outputs
          BOOST_MOVE_ADAPTIVE_SORT_PRINT_L2("   A combpar:            ", len + l_block);
          BOOST_MOVE_ADAPTIVE_SORT_INVARIANT(boost::movelib::is_sorted(combined_first, combined_first + n_block_a*l_block+l_irreg1, comp));
             BOOST_MOVE_ADAPTIVE_SORT_INVARIANT(boost::movelib::is_sorted(combined_first + n_block_a*l_block+l_irreg1, combined_first + n_block_a*l_block+l_irreg1+n_block_b*l_block+l_irreg2, comp));
          if(!use_buf){
             merge_blocks_bufferless
                (keys, key_comp, combined_first, l_block, 0u, n_block_a, n_block_b, l_irreg2, comp);
          }
          else{
             merge_blocks_left
                (keys, key_comp, combined_first, l_block, 0u, n_block_a, n_block_b, l_irreg2, comp, xbuf_used);
          }
          BOOST_MOVE_ADAPTIVE_SORT_PRINT_L2("   After merge_blocks_L: ", len + l_block);
          ++combined_i;
          if(combined_i != max_i)
             combined_first += l_reg_combined;
       }
    }
    else{
       combined_first += size_type(l_reg_combined*(max_i-1u));
       for( size_type combined_i = max_i; combined_i; ) {
          --combined_i;
          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, size_type, move_op> rbuf(combined_last, xbuf_used ? (combined_last+l_block) : combined_last);
          size_type n_block_a, n_block_b, l_irreg1, l_irreg2;
          combine_params( keys, key_comp, l_cur_combined
                         , l_prev_merged, l_block, rbuf
                         , n_block_a, n_block_b, l_irreg1, l_irreg2);  //Outputs
          BOOST_MOVE_ADAPTIVE_SORT_PRINT_L2("   A combpar:            ", len + l_block);
          BOOST_MOVE_ADAPTIVE_SORT_INVARIANT(boost::movelib::is_sorted(combined_first, combined_first + n_block_a*l_block+l_irreg1, comp));
          BOOST_MOVE_ADAPTIVE_SORT_INVARIANT(boost::movelib::is_sorted(combined_first + n_block_a*l_block+l_irreg1, combined_first + n_block_a*l_block+l_irreg1+n_block_b*l_block+l_irreg2, comp));
          merge_blocks_right
             (keys, key_comp, combined_first, l_block, n_block_a, n_block_b, l_irreg2, comp, xbuf_used);
          BOOST_MOVE_ADAPTIVE_SORT_PRINT_L2("   After merge_blocks_R: ", len + l_block);
          if(combined_i)
             combined_first -= l_reg_combined;
       }
    }
 }
 
 //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, class XBuf>
 bool adaptive_sort_combine_all_blocks
    ( RandIt keys
    , typename iter_size<RandIt>::type &n_keys
    , RandIt const buffer
    , typename iter_size<RandIt>::type const l_buf_plus_data
    , typename iter_size<RandIt>::type l_merged
    , typename iter_size<RandIt>::type &l_intbuf
    , XBuf & xbuf
    , Compare comp)
 {
    typedef typename iter_size<RandIt>::type       size_type;
 
    RandIt const first = buffer + l_intbuf;
    size_type const l_data = size_type(l_buf_plus_data - l_intbuf);
    size_type const l_unique = size_type(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 = l_merged, l_prev_block = 0;
    bool prev_use_internal_buf = true;
 
    for( size_type n = 0; l_data > l_merged
       ; l_merged = size_type(2u*l_merged)
       , ++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, size_type(2*l_merged), use_internal_buf);
       assert(!l_intbuf || (l_block == l_intbuf));
       assert(n == 0 || (!use_internal_buf || prev_use_internal_buf) );
       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 = size_type(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 = size_type(l_total_combined - l_prev_total_combined);
                move_data_forward(buf_end, l_diff, buf_beg, common_xbuf);
             }
          }
          BOOST_MOVE_ADAPTIVE_SORT_PRINT_L2("   After move_data     : ", l_data + l_intbuf);
       }
 
       //Combine to form l_merged*2 segments
       if(n_keys){
          size_type upper_n_keys_this_iter = size_type(2u*l_merged/l_block);
          if(upper_n_keys_this_iter > 256){
             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{
             unsigned char uint_keys[256];
             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);
             }
       }
       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_L1(is_merge_left ? "   After comb blocks L:  " : "   After comb blocks R:  ", 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;
    }
    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 = size_type(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, class XBuf>
 void adaptive_sort_final_merge( bool buffer_right
                               , RandIt const first
                               , typename iter_size<RandIt>::type const l_intbuf
                               , typename iter_size<RandIt>::type const n_keys
                               , typename iter_size<RandIt>::type const len
                               , XBuf & xbuf
                               , Compare comp)
 {
    //assert(n_keys || xbuf.size() == l_intbuf);
    xbuf.clear();
 
    typedef typename iter_size<RandIt>::type         size_type;
 
    size_type const n_key_plus_buf = size_type(l_intbuf+n_keys);
    if(buffer_right){
       //Use stable sort as some buffer elements might not be unique (see non_unique_buf)
       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);
       unstable_sort(first, first+n_keys, comp, xbuf);
       stable_merge(first, first+n_keys, first+len, comp, xbuf);
    }
    else{
       //Use stable sort as some buffer elements might not be unique (see non_unique_buf)
       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{
          stable_merge(first, first+n_key_plus_buf, first+len, comp, xbuf);
       }
    }
    BOOST_MOVE_ADAPTIVE_SORT_PRINT_L1("   After final_merge   : ", len);
 }
 
 template<class RandIt, class Compare, class Unsigned, class XBuf>
 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
    , XBuf & xbuf
    )
 {
    typedef typename iter_size<RandIt>::type         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));
 
    //The internal buffer can be expanded if there is enough external memory
    while(xbuf.capacity() >= l_intbuf*2){
       l_intbuf = size_type(2u*l_intbuf);
    }
 
    //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 = size_type(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;
    assert(n_min_ideal_keys <= l_intbuf);
 
    if(xbuf.template supports_aligned_trailing<size_type>
          (l_intbuf, size_type((size_type(len-l_intbuf)-1u)/l_intbuf+1u))){
       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() >= l_intbuf;
       size_type const to_collect = non_unique_buf ? n_min_ideal_keys : size_type(l_intbuf*2u);
       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){
          l_build_buf = l_intbuf;
          n_keys = n_min_ideal_keys;
       }
       else if(collected == 2*l_intbuf){
          //l_intbuf*2 elements found. Use all of them in the build phase 
          l_build_buf = size_type(l_intbuf*2);
          n_keys = l_intbuf;
       }
       else if(collected >= (n_min_ideal_keys+l_intbuf)){ 
          l_build_buf = l_intbuf;
          n_keys = size_type(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.
       else{
          assert(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-1u)){
             n_keys &= size_type(n_keys-1u);  // 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;
       }
       assert((n_keys+l_intbuf) >= l_build_buf);
    }
 
    return true;
 }
 
 // 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 whether they are going
 //           to be merged to left or right) and keys are reordered accordingly as an imitation-buffer.
 //         * Elements of each block pair are 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 and "combine_blocks" will use bigger blocks when merging.
 template<class RandIt, class Compare, class XBuf>
 void adaptive_sort_impl
    ( RandIt first
    , typename iter_size<RandIt>::type const len
    , Compare comp
    , XBuf & xbuf
    )
 {
    typedef typename iter_size<RandIt>::type         size_type;
 
    //Small sorts go directly to insertion sort
    if(len <= size_type(AdaptiveSortInsertionSortThreshold)){
       insertion_sort(first, first + len, comp);
    }
    else if((len-len/2) <= xbuf.capacity()){
       merge_sort(first, first+len, comp, xbuf.data());
    }
    else{
       //Make sure it is at least four
       BOOST_MOVE_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 a slow stable sort
       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);
       }
       else{
          assert(l_build_buf);
          //Otherwise, continue the adaptive_sort
          BOOST_MOVE_ADAPTIVE_SORT_PRINT_L1("\n   After collect_unique: ", len);
          size_type const n_key_plus_buf = size_type(l_intbuf+n_keys);
          //l_build_buf is always power of two if l_intbuf is zero
          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
             , size_type(len-n_key_plus_buf+l_build_buf)
             , l_base, l_build_buf, xbuf, comp);
          BOOST_MOVE_ADAPTIVE_SORT_PRINT_L1("   After build_blocks:   ", len);
 
          //Non-trivial merge
          bool const buffer_right = adaptive_sort_combine_all_blocks
             (first, n_keys, first+n_keys, size_type(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);
       }
    }
 }
 
 }  //namespace detail_adaptive {
 
 ///@endcond
 
 //! <b>Effects</b>: Sorts the elements in the range [first, last) in ascending order according
 //!   to comparison functor "comp". The sort is stable (order of equal elements
 //!   is guaranteed to be preserved). Performance is improved if additional raw storage is
 //!   provided.
 //!
 //! <b>Requires</b>:
 //!   - RandIt must meet the requirements of ValueSwappable and RandomAccessIterator.
 //!   - The type of dereferenced RandIt must meet the requirements of MoveAssignable and MoveConstructible.
 //!
 //! <b>Parameters</b>:
 //!   - first, last: the range of elements to sort
 //!   - comp: comparison function object which returns true if the first argument is is ordered before the second.
 //!   - uninitialized, uninitialized_len: raw storage starting on "uninitialized", able to hold "uninitialized_len"
 //!      elements of type iterator_traits<RandIt>::value_type. Maximum performance is achieved when uninitialized_len
 //!      is ceil(std::distance(first, last)/2).
 //!
 //! <b>Throws</b>: If comp throws or the move constructor, move assignment or swap of the type
 //!   of dereferenced RandIt throws.
 //!
 //! <b>Complexity</b>: Always K x O(Nxlog(N)) comparisons and move assignments/constructors/swaps.
 //!   Comparisons are close to minimum even with no additional memory. Constant factor for data movement is minimized
 //!   when uninitialized_len is ceil(std::distance(first, last)/2). Pretty good enough performance is achieved when
 //!   ceil(sqrt(std::distance(first, last)))*2.
 //!
 //! <b>Caution</b>: Experimental implementation, not production-ready.
 template<class RandIt, class RandRawIt, class Compare>
 void adaptive_sort( RandIt first, RandIt last, Compare comp
                , RandRawIt uninitialized
                , typename iter_size<RandIt>::type uninitialized_len)
 {
    typedef typename iter_size<RandIt>::type  size_type;
    typedef typename iterator_traits<RandIt>::value_type value_type;
 
    ::boost::movelib::adaptive_xbuf<value_type, RandRawIt, size_type> xbuf(uninitialized, uninitialized_len);
    ::boost::movelib::detail_adaptive::adaptive_sort_impl(first, size_type(last - first), comp, xbuf);
 }
 
 template<class RandIt, class Compare>
 void adaptive_sort( RandIt first, RandIt last, Compare comp)
 {
    typedef typename iterator_traits<RandIt>::value_type value_type;
    adaptive_sort(first, last, comp, (value_type*)0, 0u);
 }
 
 }  //namespace movelib {
 }  //namespace boost {
 
 #include <boost/move/detail/config_end.hpp>
 
 #if defined(BOOST_CLANG) || (defined(BOOST_GCC) && (BOOST_GCC >= 40600))
 #pragma GCC diagnostic pop
 #endif
 
 #endif   //#define BOOST_MOVE_ADAPTIVE_SORT_HPP

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