sort.h

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/***************************************************************************
 * include/stxxl/bits/algo/sort.h
 *
 * Part of the STXXL. See http://stxxl.sourceforge.net
 *
 * Copyright (C) 2002-2003 Roman Dementiev <[email protected]>
 * Copyright (C) 2006 Johannes Singler <[email protected]>
 * Copyright (C) 2008-2011 Andreas Beckmann <[email protected]>
 * Copyright (C) 2013 Timo Bingmann <[email protected]>
 *
 * 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)
 **************************************************************************/

#ifndef STXXL_ALGO_SORT_HEADER
#define STXXL_ALGO_SORT_HEADER

#include <functional>

#include <stxxl/bits/mng/block_manager.h>
#include <stxxl/bits/common/rand.h>
#include <stxxl/bits/mng/adaptor.h>
#include <stxxl/bits/common/simple_vector.h>
#include <stxxl/bits/common/settings.h>
#include <stxxl/bits/common/error_handling.h>
#include <stxxl/bits/mng/block_alloc_interleaved.h>
#include <stxxl/bits/io/request_operations.h>
#include <stxxl/bits/algo/sort_base.h>
#include <stxxl/bits/algo/sort_helper.h>
#include <stxxl/bits/algo/intksort.h>
#include <stxxl/bits/algo/adaptor.h>
#include <stxxl/bits/algo/async_schedule.h>
#include <stxxl/bits/mng/block_prefetcher.h>
#include <stxxl/bits/mng/buf_writer.h>
#include <stxxl/bits/algo/run_cursor.h>
#include <stxxl/bits/algo/losertree.h>
#include <stxxl/bits/algo/inmemsort.h>
#include <stxxl/bits/parallel.h>
#include <stxxl/bits/common/is_sorted.h>

STXXL_BEGIN_NAMESPACE

//! \addtogroup stlalgo
//! \{

/*! \internal
 */
namespace sort_local {

template <typename BlockType, typename BidType>
struct read_next_after_write_completed
{
 typedef BlockType block_type;
 block_type* block;
 BidType bid;
 request_ptr* req;
 void operator () (request* /*completed_req*/)
 {
 * req = block->read(bid);
 }
};

template <
 typename BlockType,
 typename RunType,
 typename InputBidIterator,
 typename ValueCmp>
void
create_runs(
 InputBidIterator it,
 RunType** runs,
 int_type nruns,
 int_type _m,
 ValueCmp cmp)
{
 typedef BlockType block_type;
 typedef RunType run_type;

 typedef typename block_type::bid_type bid_type;
 STXXL_VERBOSE1("stxxl::create_runs nruns=" << nruns << " m=" << _m);

 int_type m2 = _m / 2;
 block_manager* bm = block_manager::get_instance();
 block_type* Blocks1 = new block_type[m2];
 block_type* Blocks2 = new block_type[m2];
 bid_type* bids1 = new bid_type[m2];
 bid_type* bids2 = new bid_type[m2];
 request_ptr* read_reqs1 = new request_ptr[m2];
 request_ptr* read_reqs2 = new request_ptr[m2];
 request_ptr* write_reqs = new request_ptr[m2];
 read_next_after_write_completed<block_type, bid_type>* next_run_reads =
 new read_next_after_write_completed<block_type, bid_type>[m2];

 disk_queues::get_instance()->set_priority_op(request_queue::WRITE);

 int_type i;
 int_type run_size = 0;

 assert(nruns >= 2);

 run_size = runs[0]->size();
 assert(run_size == m2);

 for (i = 0; i < run_size; ++i)
 {
 STXXL_VERBOSE1("stxxl::create_runs posting read " << Blocks1[i].elem);
 bids1[i] = *(it++);
 read_reqs1[i] = Blocks1[i].read(bids1[i]);
 }

 run_size = runs[1]->size();

 for (i = 0; i < run_size; ++i)
 {
 STXXL_VERBOSE1("stxxl::create_runs posting read " << Blocks2[i].elem);
 bids2[i] = *(it++);
 read_reqs2[i] = Blocks2[i].read(bids2[i]);
 }

 for (int_type k = 0; k < nruns - 1; ++k)
 {
 run_type* run = runs[k];
 run_size = run->size();
 assert(run_size == m2);
 int_type next_run_size = runs[k + 1]->size();
 STXXL_ASSERT((next_run_size == m2) || (next_run_size <= m2 && k == nruns - 2));

 STXXL_VERBOSE1("stxxl::create_runs start waiting read_reqs1");
 wait_all(read_reqs1, run_size);
 STXXL_VERBOSE1("stxxl::create_runs finish waiting read_reqs1");
 for (i = 0; i < run_size; ++i)
 bm->delete_block(bids1[i]);

 check_sort_settings();
 potentially_parallel::
 sort(make_element_iterator(Blocks1, 0),
 make_element_iterator(Blocks1, run_size * block_type::size),
 cmp);

 STXXL_VERBOSE1("stxxl::create_runs start waiting write_reqs");
 if (k > 0)
 wait_all(write_reqs, m2);
 STXXL_VERBOSE1("stxxl::create_runs finish waiting write_reqs");

 int_type runplus2size = (k < nruns - 2) ? runs[k + 2]->size() : 0;
 for (i = 0; i < m2; ++i)
 {
 STXXL_VERBOSE1("stxxl::create_runs posting write " << Blocks1[i].elem);
 (*run)[i].value = Blocks1[i][0];
 if (i >= runplus2size) {
 write_reqs[i] = Blocks1[i].write((*run)[i].bid);
 }
 else
 {
 next_run_reads[i].block = Blocks1 + i;
 next_run_reads[i].req = read_reqs1 + i;
 bids1[i] = next_run_reads[i].bid = *(it++);
 write_reqs[i] = Blocks1[i].write((*run)[i].bid, next_run_reads[i]);
 }
 }
 std::swap(Blocks1, Blocks2);
 std::swap(bids1, bids2);
 std::swap(read_reqs1, read_reqs2);
 }

 run_type* run = runs[nruns - 1];
 run_size = run->size();
 STXXL_VERBOSE1("stxxl::create_runs start waiting read_reqs1");
 wait_all(read_reqs1, run_size);
 STXXL_VERBOSE1("stxxl::create_runs finish waiting read_reqs1");
 for (i = 0; i < run_size; ++i)
 bm->delete_block(bids1[i]);

 check_sort_settings();
 potentially_parallel::
 sort(make_element_iterator(Blocks1, 0),
 make_element_iterator(Blocks1, run_size * block_type::size),
 cmp);

 STXXL_VERBOSE1("stxxl::create_runs start waiting write_reqs");
 wait_all(write_reqs, m2);
 STXXL_VERBOSE1("stxxl::create_runs finish waiting write_reqs");

 for (i = 0; i < run_size; ++i)
 {
 STXXL_VERBOSE1("stxxl::create_runs posting write " << Blocks1[i].elem);
 (*run)[i].value = Blocks1[i][0];
 write_reqs[i] = Blocks1[i].write((*run)[i].bid);
 }

 STXXL_VERBOSE1("stxxl::create_runs start waiting write_reqs");
 wait_all(write_reqs, run_size);
 STXXL_VERBOSE1("stxxl::create_runs finish waiting write_reqs");

 delete[] Blocks1;
 delete[] Blocks2;
 delete[] bids1;
 delete[] bids2;
 delete[] read_reqs1;
 delete[] read_reqs2;
 delete[] write_reqs;
 delete[] next_run_reads;
}

template <typename BlockType, typename RunType, typename ValueCmp>
bool check_sorted_runs(RunType** runs,
 unsigned_type nruns,
 unsigned_type m,
 ValueCmp cmp)
{
 typedef BlockType block_type;
 typedef typename block_type::value_type value_type;

 STXXL_MSG("check_sorted_runs Runs: " << nruns);
 unsigned_type irun = 0;
 for (irun = 0; irun < nruns; ++irun)
 {
 const unsigned_type nblocks_per_run = runs[irun]->size();
 unsigned_type blocks_left = nblocks_per_run;
 block_type* blocks = new block_type[m];
 request_ptr* reqs = new request_ptr[m];
 value_type last = cmp.min_value();

 for (unsigned_type off = 0; off < nblocks_per_run; off += m)
 {
 const unsigned_type nblocks = STXXL_MIN(blocks_left, m);
 const unsigned_type nelements = nblocks * block_type::size;
 blocks_left -= nblocks;

 for (unsigned_type j = 0; j < nblocks; ++j)
 {
 reqs[j] = blocks[j].read((*runs[irun])[j + off].bid);
 }
 wait_all(reqs, reqs + nblocks);

 if (off && cmp(blocks[0][0], last))
 {
 STXXL_MSG("check_sorted_runs wrong first value in the run " << irun);
 STXXL_MSG(" first value: " << blocks[0][0]);
 STXXL_MSG(" last value: " << last);
 for (unsigned_type k = 0; k < block_type::size; ++k)
 STXXL_MSG("Element " << k << " in the block is :" << blocks[0][k]);

 delete[] reqs;
 delete[] blocks;
 return false;
 }

 for (unsigned_type j = 0; j < nblocks; ++j)
 {
 if (!(blocks[j][0] == (*runs[irun])[j + off].value))
 {
 STXXL_MSG("check_sorted_runs wrong trigger in the run " << irun << " block " << (j + off));
 STXXL_MSG(" trigger value: " << (*runs[irun])[j + off].value);
 STXXL_MSG("Data in the block:");
 for (unsigned_type k = 0; k < block_type::size; ++k)
 STXXL_MSG("Element " << k << " in the block is :" << blocks[j][k]);

 STXXL_MSG("BIDS:");
 for (unsigned_type k = 0; k < nblocks; ++k)
 {
 if (k == j)
 STXXL_MSG("Bad one comes next.");
 STXXL_MSG("BID " << (k + off) << " is: " << ((*runs[irun])[k + off].bid));
 }

 delete[] reqs;
 delete[] blocks;
 return false;
 }
 }
 if (!stxxl::is_sorted(make_element_iterator(blocks, 0),
 make_element_iterator(blocks, nelements),
 cmp))
 {
 STXXL_MSG("check_sorted_runs wrong order in the run " << irun);
 STXXL_MSG("Data in blocks:");
 for (unsigned_type j = 0; j < nblocks; ++j)
 {
 for (unsigned_type k = 0; k < block_type::size; ++k)
 STXXL_MSG(" Element " << k << " in block " << (j + off) << " is :" << blocks[j][k]);
 }
 STXXL_MSG("BIDS:");
 for (unsigned_type k = 0; k < nblocks; ++k)
 {
 STXXL_MSG("BID " << (k + off) << " is: " << ((*runs[irun])[k + off].bid));
 }

 delete[] reqs;
 delete[] blocks;
 return false;
 }

 last = blocks[nblocks - 1][block_type::size - 1];
 }

 assert(blocks_left == 0);
 delete[] reqs;
 delete[] blocks;
 }

 return true;
}

template <typename BlockType, typename RunType, typename ValueCmp>
void merge_runs(RunType** in_runs, int_type nruns,
 RunType* out_run, unsigned_type _m, ValueCmp cmp)
{
 typedef BlockType block_type;
 typedef RunType run_type;
 typedef ValueCmp value_cmp;
 typedef typename run_type::value_type trigger_entry_type;
 typedef block_prefetcher<block_type, typename run_type::iterator> prefetcher_type;
 typedef run_cursor2<block_type, prefetcher_type> run_cursor_type;
 typedef sort_helper::run_cursor2_cmp<block_type, prefetcher_type, value_cmp> run_cursor2_cmp_type;

 run_type consume_seq(out_run->size());

 int_type* prefetch_seq = new int_type[out_run->size()];

 typename run_type::iterator copy_start = consume_seq.begin();
 for (int_type i = 0; i < nruns; i++)
 {
 // \todo: try to avoid copy
 copy_start = std::copy(
 in_runs[i]->begin(),
 in_runs[i]->end(),
 copy_start);
 }

 std::stable_sort(consume_seq.begin(), consume_seq.end(),
 sort_helper::trigger_entry_cmp<trigger_entry_type, value_cmp>(cmp) _STXXL_SORT_TRIGGER_FORCE_SEQUENTIAL);

 int_type disks_number = config::get_instance()->disks_number();

#ifdef PLAY_WITH_OPT_PREF
 const int_type n_write_buffers = 4 * disks_number;
#else
 const int_type n_prefetch_buffers = STXXL_MAX(2 * disks_number, (3 * (int_type(_m) - nruns) / 4));
 const int_type n_write_buffers = STXXL_MAX(2 * disks_number, int_type(_m) - nruns - n_prefetch_buffers);
 #if STXXL_SORT_OPTIMAL_PREFETCHING
 // heuristic
 const int_type n_opt_prefetch_buffers = 2 * disks_number + (3 * (n_prefetch_buffers - 2 * disks_number)) / 10;
 #endif
#endif

#if STXXL_SORT_OPTIMAL_PREFETCHING
 compute_prefetch_schedule(
 consume_seq,
 prefetch_seq,
 n_opt_prefetch_buffers,
 config::get_instance()->get_max_device_id());
#else
 for (unsigned_type i = 0; i < out_run->size(); i++)
 prefetch_seq[i] = i;

#endif

 prefetcher_type prefetcher(consume_seq.begin(),
 consume_seq.end(),
 prefetch_seq,
 nruns + n_prefetch_buffers);

 buffered_writer<block_type> writer(n_write_buffers, n_write_buffers / 2);

 int_type out_run_size = out_run->size();

 block_type* out_buffer = writer.get_free_block();

//If parallelism is activated, one can still fall back to the
//native merge routine by setting stxxl::SETTINGS::native_merge= true, //otherwise, it is used anyway.

 if (do_parallel_merge())
 {
#if STXXL_PARALLEL_MULTIWAY_MERGE

// begin of STL-style merging

 typedef stxxl::int64 diff_type;
 typedef std::pair<typename block_type::iterator, typename block_type::iterator> sequence;
 std::vector<sequence> seqs(nruns);
 std::vector<block_type*> buffers(nruns);

 for (int_type i = 0; i < nruns; i++) // initialize sequences
 {
 buffers[i] = prefetcher.pull_block(); // get first block of each run
 seqs[i] = std::make_pair(buffers[i]->begin(), buffers[i]->end());
 // this memory location stays the same, only the data is exchanged
 }

 #if STXXL_CHECK_ORDER_IN_SORTS
 value_type last_elem = cmp.min_value();
 #endif
 diff_type num_currently_mergeable = 0;

 for (int_type j = 0; j < out_run_size; ++j) // for the whole output run, out_run_size is in blocks
 {
 diff_type rest = block_type::size; // elements still to merge for this output block

 STXXL_VERBOSE1("output block " << j);
 do {
 if (num_currently_mergeable < rest)
 {
 if (prefetcher.empty())
 {
 // anything remaining is already in memory
 num_currently_mergeable = (out_run_size - j) * block_type::size
 - (block_type::size - rest);
 }
 else
 {
 num_currently_mergeable = sort_helper::count_elements_less_equal(
 seqs, consume_seq[prefetcher.pos()].value, cmp);
 }
 }

 diff_type output_size = STXXL_MIN(num_currently_mergeable, rest); // at most rest elements

 STXXL_VERBOSE1("before merge " << output_size);

 stxxl::parallel::multiway_merge(seqs.begin(), seqs.end(), out_buffer->end() - rest, cmp, output_size);
 // sequence iterators are progressed appropriately

 rest -= output_size;
 num_currently_mergeable -= output_size;

 STXXL_VERBOSE1("after merge");

 sort_helper::refill_or_remove_empty_sequences(seqs, buffers, prefetcher);
 } while (rest > 0 && seqs.size() > 0);

 #if STXXL_CHECK_ORDER_IN_SORTS
 if (!stxxl::is_sorted(out_buffer->begin(), out_buffer->end(), cmp))
 {
 for (value_type* i = out_buffer->begin() + 1; i != out_buffer->end(); i++)
 if (cmp(*i, *(i - 1)))
 {
 STXXL_VERBOSE1("Error at position " << (i - out_buffer->begin()));
 }
 assert(false);
 }

 if (j > 0) // do not check in first iteration
 assert(cmp((*out_buffer)[0], last_elem) == false);

 last_elem = (*out_buffer)[block_type::size - 1];
 #endif

 (*out_run)[j].value = (*out_buffer)[0]; // save smallest value

 out_buffer = writer.write(out_buffer, (*out_run)[j].bid);
 }

// end of STL-style merging

#else
 STXXL_THROW_UNREACHABLE();
#endif
 }
 else
 {
// begin of native merging procedure

 loser_tree<run_cursor_type, run_cursor2_cmp_type>
 losers(&prefetcher, nruns, run_cursor2_cmp_type(cmp));

#if STXXL_CHECK_ORDER_IN_SORTS
 value_type last_elem = cmp.min_value();
#endif

 for (int_type i = 0; i < out_run_size; ++i)
 {
 losers.multi_merge(out_buffer->elem, out_buffer->elem + block_type::size);
 (*out_run)[i].value = *(out_buffer->elem);

#if STXXL_CHECK_ORDER_IN_SORTS
 assert(stxxl::is_sorted(
 out_buffer->begin(),
 out_buffer->end(),
 cmp));

 if (i)
 assert(cmp(*(out_buffer->elem), last_elem) == false);

 last_elem = (*out_buffer).elem[block_type::size - 1];
#endif

 out_buffer = writer.write(out_buffer, (*out_run)[i].bid);
 }

// end of native merging procedure
 }

 delete[] prefetch_seq;

 block_manager* bm = block_manager::get_instance();
 for (int_type i = 0; i < nruns; ++i)
 {
 unsigned_type sz = in_runs[i]->size();
 for (unsigned_type j = 0; j < sz; ++j)
 bm->delete_block((*in_runs[i])[j].bid);

 delete in_runs[i];
 }
}

template <typename BlockType,
 typename AllocStrategy,
 typename InputBidIterator,
 typename ValueCmp>
simple_vector<sort_helper::trigger_entry<BlockType> >*
sort_blocks(InputBidIterator input_bids,
 unsigned_type _n,
 unsigned_type _m,
 ValueCmp cmp)
{
 typedef BlockType block_type;
 typedef AllocStrategy alloc_strategy;
 typedef InputBidIterator input_bid_iterator;
 typedef ValueCmp value_cmp;
 typedef typename block_type::bid_type bid_type;
 typedef sort_helper::trigger_entry<block_type> trigger_entry_type;
 typedef simple_vector<trigger_entry_type> run_type;
 typedef typename interleaved_alloc_traits<alloc_strategy>::strategy interleaved_alloc_strategy;

 unsigned_type m2 = _m / 2;
 unsigned_type full_runs = _n / m2;
 unsigned_type partial_runs = ((_n % m2) ? 1 : 0);
 unsigned_type nruns = full_runs + partial_runs;
 unsigned_type i;

 block_manager* mng = block_manager::get_instance();

 //STXXL_VERBOSE ("n=" << _n << " nruns=" << nruns << "=" << full_runs << "+" << partial_runs);

 double begin = timestamp(), after_runs_creation, end;

 run_type** runs = new run_type*[nruns];

 for (i = 0; i < full_runs; i++)
 runs[i] = new run_type(m2);

 if (partial_runs)
 runs[i] = new run_type(_n - full_runs * m2);

 for (i = 0; i < nruns; ++i)
 mng->new_blocks(alloc_strategy(), make_bid_iterator(runs[i]->begin()), make_bid_iterator(runs[i]->end()));

 sort_local::create_runs<block_type,
 run_type,
 input_bid_iterator,
 value_cmp>(input_bids, runs, nruns, _m, cmp);

 after_runs_creation = timestamp();

 double io_wait_after_rf = stats::get_instance()->get_io_wait_time();

 disk_queues::get_instance()->set_priority_op(request_queue::WRITE);

 const int_type merge_factor = optimal_merge_factor(nruns, _m);
 run_type** new_runs;

 while (nruns > 1)
 {
 int_type new_nruns = div_ceil(nruns, merge_factor);
 STXXL_VERBOSE("Starting new merge phase: nruns: " << nruns <<
 " opt_merge_factor: " << merge_factor << " m:" << _m << " new_nruns: " << new_nruns);

 new_runs = new run_type*[new_nruns];

 int_type runs_left = nruns;
 int_type cur_out_run = 0;
 int_type blocks_in_new_run = 0;

 while (runs_left > 0)
 {
 int_type runs2merge = STXXL_MIN(runs_left, merge_factor);
 blocks_in_new_run = 0;
 for (unsigned_type i = nruns - runs_left; i < (nruns - runs_left + runs2merge); i++)
 blocks_in_new_run += runs[i]->size();

 // allocate run
 new_runs[cur_out_run++] = new run_type(blocks_in_new_run);
 runs_left -= runs2merge;
 }
 // allocate blocks for the new runs
 if (cur_out_run == 1 && blocks_in_new_run == int_type(_n) && !input_bids->is_managed())
 {
 // if we sort a file we can reuse the input bids for the output
 input_bid_iterator cur = input_bids;
 for (int_type i = 0; cur != (input_bids + _n); ++cur)
 {
 (*new_runs[0])[i++].bid = *cur;
 }

 bid_type& firstBID = (*new_runs[0])[0].bid;
 if (firstBID.is_managed())
 {
 // the first block does not belong to the file
 // need to reallocate it
 mng->new_block(FR(), firstBID);
 }
 bid_type& lastBID = (*new_runs[0])[_n - 1].bid;
 if (lastBID.is_managed())
 {
 // the first block does not belong to the file
 // need to reallocate it
 mng->new_block(FR(), lastBID);
 }
 }
 else
 {
 mng->new_blocks(interleaved_alloc_strategy(new_nruns, alloc_strategy()),
 runs2bid_array_adaptor2<block_type::raw_size, run_type>(new_runs, 0, new_nruns, blocks_in_new_run),
 runs2bid_array_adaptor2<block_type::raw_size, run_type>(new_runs, _n, new_nruns, blocks_in_new_run));
 }
 // merge all
 runs_left = nruns;
 cur_out_run = 0;
 while (runs_left > 0)
 {
 int_type runs2merge = STXXL_MIN(runs_left, merge_factor);
#if STXXL_CHECK_ORDER_IN_SORTS
 assert((check_sorted_runs<block_type, run_type, value_cmp>(runs + nruns - runs_left, runs2merge, m2, cmp)));
#endif
 STXXL_VERBOSE("Merging " << runs2merge << " runs");
 merge_runs<block_type, run_type>(runs + nruns - runs_left,
 runs2merge, *(new_runs + (cur_out_run++)), _m, cmp
 );
 runs_left -= runs2merge;
 }

 nruns = new_nruns;
 delete[] runs;
 runs = new_runs;
 }

 run_type* result = *runs;
 delete[] runs;

 end = timestamp();

 STXXL_VERBOSE("Elapsed time : " << end - begin << " s. Run creation time: " <<
 after_runs_creation - begin << " s");
 STXXL_VERBOSE("Time in I/O wait(rf): " << io_wait_after_rf << " s");
 STXXL_VERBOSE(*stats::get_instance());

 return result;
}

} // namespace sort_local

/*!
 * Sort records comparison-based, see \ref design_algo_sort.
 *
 * stxxl::sort sorts the elements in [first, last) into ascending order,
 * meaning that if \c i and \c j are any two valid iterators in [first, last)
 * such that \c i precedes \c j, then \c *j is not less than \c *i. Note: as
 * std::sort, stxxl::sort is not guaranteed to be stable. That is, suppose that
 * \c *i and \c *j are equivalent: neither one is less than the other. It is
 * not guaranteed that the relative order of these two elements will be
 * preserved by stxxl::sort.
 *
 * The order is defined by the \c cmp parameter. The sorter's internal memory
 * consumption is bounded by \a M bytes.
 *
 * \param first object of model of \c ext_random_access_iterator concept
 * \param last object of model of \c ext_random_access_iterator concept
 * \param cmp comparison object of \ref StrictWeakOrdering
 * \param M amount of memory for internal use (in bytes)
 */
template <typename ExtIterator, typename StrictWeakOrdering>
void sort(ExtIterator first, ExtIterator last, StrictWeakOrdering cmp, unsigned_type M)
{
 sort_helper::verify_sentinel_strict_weak_ordering(cmp);

 typedef typename ExtIterator::vector_type::value_type value_type;
 typedef typename ExtIterator::block_type block_type;
 typedef typename ExtIterator::bid_type bid_type;
 typedef typename ExtIterator::vector_type::alloc_strategy_type alloc_strategy_type;
 typedef typename ExtIterator::bids_container_iterator bids_container_iterator;

 typedef simple_vector<sort_helper::trigger_entry<block_type> > run_type;

 unsigned_type n = 0;

 block_manager* mng = block_manager::get_instance();

 first.flush();

 if ((last - first) * sizeof(value_type) * sort_memory_usage_factor() < M)
 {
 stl_in_memory_sort(first, last, cmp);
 }
 else
 {
 if (!(2 * block_type::raw_size * (unsigned_type)sort_memory_usage_factor() <= M)) {
 throw bad_parameter("stxxl::sort(): INSUFFICIENT MEMORY provided, please increase parameter 'M'");
 }

 if (first.block_offset())
 {
 if (last.block_offset()) // first and last element are
 // not the first elements of their block
 {
 block_type* first_block = new block_type;
 block_type* last_block = new block_type;
 typename ExtIterator::bid_type first_bid, last_bid;
 request_ptr req;

 req = first_block->read(*first.bid());
 mng->new_block(FR(), first_bid); // try to overlap
 mng->new_block(FR(), last_bid);
 req->wait();

 req = last_block->read(*last.bid());

 unsigned_type i = 0;
 for ( ; i < first.block_offset(); ++i)
 {
 first_block->elem[i] = cmp.min_value();
 }

 req->wait();

 req = first_block->write(first_bid);
 for (i = last.block_offset(); i < block_type::size; ++i)
 {
 last_block->elem[i] = cmp.max_value();
 }

 req->wait();

 req = last_block->write(last_bid);

 n = last.bid() - first.bid() + 1;

 std::swap(first_bid, *first.bid());
 std::swap(last_bid, *last.bid());

 req->wait();

 delete first_block;
 delete last_block;

 run_type* out =
 sort_local::sort_blocks<
 block_type, alloc_strategy_type, bids_container_iterator
 >(first.bid(), n,
 M / sort_memory_usage_factor() / block_type::raw_size, cmp);

 first_block = new block_type;
 last_block = new block_type;
 block_type* sorted_first_block = new block_type;
 block_type* sorted_last_block = new block_type;
 request_ptr* reqs = new request_ptr[2];

 reqs[0] = first_block->read(first_bid);
 reqs[1] = sorted_first_block->read((*(out->begin())).bid);

 reqs[0]->wait();
 reqs[1]->wait();

 reqs[0] = last_block->read(last_bid);
 reqs[1] = sorted_last_block->read(((*out)[out->size() - 1]).bid);

 for (i = first.block_offset(); i < block_type::size; i++)
 {
 first_block->elem[i] = sorted_first_block->elem[i];
 }

 reqs[0]->wait();
 reqs[1]->wait();

 req = first_block->write(first_bid);

 for (i = 0; i < last.block_offset(); ++i)
 {
 last_block->elem[i] = sorted_last_block->elem[i];
 }

 req->wait();

 req = last_block->write(last_bid);

 mng->delete_block(out->begin()->bid);
 mng->delete_block((*out)[out->size() - 1].bid);

 *first.bid() = first_bid;
 *last.bid() = last_bid;

 typename run_type::iterator it = out->begin();
 ++it;
 bids_container_iterator cur_bid = first.bid();
 ++cur_bid;

 for ( ; cur_bid != last.bid(); ++cur_bid, ++it)
 {
 *cur_bid = (*it).bid;
 }

 delete first_block;
 delete sorted_first_block;
 delete sorted_last_block;
 delete[] reqs;
 delete out;

 req->wait();

 delete last_block;
 }
 else
 {
 // first element is
 // not the first element of its block
 block_type* first_block = new block_type;
 bid_type first_bid;
 request_ptr req;

 req = first_block->read(*first.bid());
 mng->new_block(FR(), first_bid); // try to overlap
 req->wait();

 unsigned_type i = 0;
 for ( ; i < first.block_offset(); ++i)
 {
 first_block->elem[i] = cmp.min_value();
 }

 req = first_block->write(first_bid);

 n = last.bid() - first.bid();

 std::swap(first_bid, *first.bid());

 req->wait();

 delete first_block;

 run_type* out =
 sort_local::sort_blocks<
 block_type, alloc_strategy_type, bids_container_iterator
 >(first.bid(), n,
 M / sort_memory_usage_factor() / block_type::raw_size, cmp);

 first_block = new block_type;

 block_type* sorted_first_block = new block_type;

 request_ptr* reqs = new request_ptr[2];

 reqs[0] = first_block->read(first_bid);
 reqs[1] = sorted_first_block->read((*(out->begin())).bid);

 reqs[0]->wait();
 reqs[1]->wait();

 for (i = first.block_offset(); i < block_type::size; ++i)
 {
 first_block->elem[i] = sorted_first_block->elem[i];
 }

 req = first_block->write(first_bid);

 mng->delete_block(out->begin()->bid);

 *first.bid() = first_bid;

 typename run_type::iterator it = out->begin();
 ++it;
 bids_container_iterator cur_bid = first.bid();
 ++cur_bid;

 for ( ; cur_bid != last.bid(); ++cur_bid, ++it)
 {
 *cur_bid = (*it).bid;
 }

 *cur_bid = (*it).bid;

 delete sorted_first_block;
 delete[] reqs;
 delete out;

 req->wait();

 delete first_block;
 }
 }
 else
 {
 if (last.block_offset()) // last is
 // not the first element of its block
 {
 block_type* last_block = new block_type;
 bid_type last_bid;
 request_ptr req;
 unsigned_type i;

 req = last_block->read(*last.bid());
 mng->new_block(FR(), last_bid);
 req->wait();

 for (i = last.block_offset(); i < block_type::size; ++i)
 {
 last_block->elem[i] = cmp.max_value();
 }

 req = last_block->write(last_bid);

 n = last.bid() - first.bid() + 1;

 std::swap(last_bid, *last.bid());

 req->wait();

 delete last_block;

 run_type* out =
 sort_local::sort_blocks<
 block_type, alloc_strategy_type, bids_container_iterator
 >(first.bid(), n,
 M / sort_memory_usage_factor() / block_type::raw_size, cmp);

 last_block = new block_type;
 block_type* sorted_last_block = new block_type;
 request_ptr* reqs = new request_ptr[2];

 reqs[0] = last_block->read(last_bid);
 reqs[1] = sorted_last_block->read(((*out)[out->size() - 1]).bid);

 reqs[0]->wait();
 reqs[1]->wait();

 for (i = 0; i < last.block_offset(); ++i)
 {
 last_block->elem[i] = sorted_last_block->elem[i];
 }

 req = last_block->write(last_bid);

 mng->delete_block((*out)[out->size() - 1].bid);

 *last.bid() = last_bid;

 typename run_type::iterator it = out->begin();
 bids_container_iterator cur_bid = first.bid();

 for ( ; cur_bid != last.bid(); ++cur_bid, ++it)
 {
 *cur_bid = (*it).bid;
 }

 delete sorted_last_block;
 delete[] reqs;
 delete out;

 req->wait();

 delete last_block;
 }
 else
 {
 // first and last element are first elements of their of blocks
 n = last.bid() - first.bid();

 run_type* out =
 sort_local::sort_blocks<
 block_type, alloc_strategy_type, bids_container_iterator
 >(first.bid(), n,
 M / sort_memory_usage_factor() / block_type::raw_size, cmp);

 typename run_type::iterator it = out->begin();
 bids_container_iterator cur_bid = first.bid();

 for ( ; cur_bid != last.bid(); ++cur_bid, ++it)
 {
 *cur_bid = (*it).bid;
 }

 delete out;
 }
 }
 }

#if STXXL_CHECK_ORDER_IN_SORTS
 typedef typename ExtIterator::const_iterator const_iterator;
 assert(stxxl::is_sorted(const_iterator(first), const_iterator(last), cmp));
#endif
}

//! \}

STXXL_END_NAMESPACE

#endif // !STXXL_ALGO_SORT_HEADER
// vim: et:ts=4:sw=4