gc/parallel/cardTableExtension.cpp

/*
 * Copyright (c) 2001, 2016, Oracle and/or its affiliates. All rights reserved.
 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
 *
 * This code is free software; you can redistribute it and/or modify it
 * under the terms of the GNU General Public License version 2 only, as
 * published by the Free Software Foundation.
 *
 * This code is distributed in the hope that it will be useful, but WITHOUT
 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
 * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
 * version 2 for more details (a copy is included in the LICENSE file that
 * accompanied this code).
 *
 * You should have received a copy of the GNU General Public License version
 * 2 along with this work; if not, write to the Free Software Foundation,
 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
 *
 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
 * or visit www.oracle.com if you need additional information or have any
 * questions.
 *
 */

#include "precompiled.hpp"
#include "gc/parallel/cardTableExtension.hpp"
#include "gc/parallel/gcTaskManager.hpp"
#include "gc/parallel/objectStartArray.inline.hpp"
#include "gc/parallel/parallelScavengeHeap.hpp"
#include "gc/parallel/psPromotionManager.inline.hpp"
#include "gc/parallel/psScavenge.hpp"
#include "gc/parallel/psTasks.hpp"
#include "gc/parallel/psYoungGen.hpp"
#include "oops/oop.inline.hpp"
#include "runtime/prefetch.inline.hpp"

// Checks an individual oop for missing precise marks. Mark
// may be either dirty or newgen.
class CheckForUnmarkedOops : public OopClosure {
 private:
  PSYoungGen*         _young_gen;
  CardTableExtension* _card_table;
  HeapWord*           _unmarked_addr;

 protected:
  template <class T> void do_oop_work(T* p) {
    oop obj = oopDesc::load_decode_heap_oop(p);
    if (_young_gen->is_in_reserved(obj) &&
        !_card_table->addr_is_marked_imprecise(p)) {
      // Don't overwrite the first missing card mark
      if (_unmarked_addr == NULL) {
        _unmarked_addr = (HeapWord*)p;
      }
    }
  }

 public:
  CheckForUnmarkedOops(PSYoungGen* young_gen, CardTableExtension* card_table) :
    _young_gen(young_gen), _card_table(card_table), _unmarked_addr(NULL) { }

  virtual void do_oop(oop* p)       { CheckForUnmarkedOops::do_oop_work(p); }
  virtual void do_oop(narrowOop* p) { CheckForUnmarkedOops::do_oop_work(p); }

  bool has_unmarked_oop() {
    return _unmarked_addr != NULL;
  }
};

// Checks all objects for the existence of some type of mark,
// precise or imprecise, dirty or newgen.
class CheckForUnmarkedObjects : public ObjectClosure {
 private:
  PSYoungGen*         _young_gen;
  CardTableExtension* _card_table;

 public:
  CheckForUnmarkedObjects() {
    ParallelScavengeHeap* heap = ParallelScavengeHeap::heap();
    _young_gen = heap->young_gen();
    _card_table = barrier_set_cast<CardTableExtension>(heap->barrier_set());
    // No point in asserting barrier set type here. Need to make CardTableExtension
    // a unique barrier set type.
  }

  // Card marks are not precise. The current system can leave us with
  // a mismatch of precise marks and beginning of object marks. This means
  // we test for missing precise marks first. If any are found, we don't
  // fail unless the object head is also unmarked.
  virtual void do_object(oop obj) {
    CheckForUnmarkedOops object_check(_young_gen, _card_table);
    obj->oop_iterate_no_header(&object_check);
    if (object_check.has_unmarked_oop()) {
      guarantee(_card_table->addr_is_marked_imprecise(obj), "Found unmarked young_gen object");
    }
  }
};

// Checks for precise marking of oops as newgen.
class CheckForPreciseMarks : public OopClosure {
 private:
  PSYoungGen*         _young_gen;
  CardTableExtension* _card_table;

 protected:
  template <class T> void do_oop_work(T* p) {
    oop obj = oopDesc::load_decode_heap_oop_not_null(p);
    if (_young_gen->is_in_reserved(obj)) {
      assert(_card_table->addr_is_marked_precise(p), "Found unmarked precise oop");
      _card_table->set_card_newgen(p);
    }
  }

 public:
  CheckForPreciseMarks( PSYoungGen* young_gen, CardTableExtension* card_table ) :
    _young_gen(young_gen), _card_table(card_table) { }

  virtual void do_oop(oop* p)       { CheckForPreciseMarks::do_oop_work(p); }
  virtual void do_oop(narrowOop* p) { CheckForPreciseMarks::do_oop_work(p); }
};

// We get passed the space_top value to prevent us from traversing into
// the old_gen promotion labs, which cannot be safely parsed.

// Do not call this method if the space is empty.
// It is a waste to start tasks and get here only to
// do no work.  If this method needs to be called
// when the space is empty, fix the calculation of
// end_card to allow sp_top == sp->bottom().

void CardTableExtension::scavenge_contents_parallel(ObjectStartArray* start_array,
                                                    MutableSpace* sp,
                                                    HeapWord* space_top,
                                                    PSPromotionManager* pm,
                                                    uint stripe_number,
                                                    uint stripe_total) {
  int ssize = 128; // Naked constant!  Work unit = 64k.
  int dirty_card_count = 0;

  // It is a waste to get here if empty.
  assert(sp->bottom() < sp->top(), "Should not be called if empty");
  oop* sp_top = (oop*)space_top;
  jbyte* start_card = byte_for(sp->bottom());
  jbyte* end_card   = byte_for(sp_top - 1) + 1;
  oop* last_scanned = NULL; // Prevent scanning objects more than once
  // The width of the stripe ssize*stripe_total must be
  // consistent with the number of stripes so that the complete slice
  // is covered.
  size_t slice_width = ssize * stripe_total;
  for (jbyte* slice = start_card; slice < end_card; slice += slice_width) {
    jbyte* worker_start_card = slice + stripe_number * ssize;
    if (worker_start_card >= end_card)
      return; // We're done.

    jbyte* worker_end_card = worker_start_card + ssize;
    if (worker_end_card > end_card)
      worker_end_card = end_card;

    // We do not want to scan objects more than once. In order to accomplish
    // this, we assert that any object with an object head inside our 'slice'
    // belongs to us. We may need to extend the range of scanned cards if the
    // last object continues into the next 'slice'.
    //
    // Note! ending cards are exclusive!
    HeapWord* slice_start = addr_for(worker_start_card);
    HeapWord* slice_end = MIN2((HeapWord*) sp_top, addr_for(worker_end_card));

#ifdef ASSERT
    if (GCWorkerDelayMillis > 0) {
      // Delay 1 worker so that it proceeds after all the work
      // has been completed.
      if (stripe_number < 2) {
        os::sleep(Thread::current(), GCWorkerDelayMillis, false);
      }
    }
#endif

    // If there are not objects starting within the chunk, skip it.
    if (!start_array->object_starts_in_range(slice_start, slice_end)) {
      continue;
    }
    // Update our beginning addr
    HeapWord* first_object = start_array->object_start(slice_start);
    debug_only(oop* first_object_within_slice = (oop*) first_object;)
    if (first_object < slice_start) {
      last_scanned = (oop*)(first_object + oop(first_object)->size());
      debug_only(first_object_within_slice = last_scanned;)
      worker_start_card = byte_for(last_scanned);
    }

    // Update the ending addr
    if (slice_end < (HeapWord*)sp_top) {
      // The subtraction is important! An object may start precisely at slice_end.
      HeapWord* last_object = start_array->object_start(slice_end - 1);
      slice_end = last_object + oop(last_object)->size();
      // worker_end_card is exclusive, so bump it one past the end of last_object's
      // covered span.
      worker_end_card = byte_for(slice_end) + 1;

      if (worker_end_card > end_card)
        worker_end_card = end_card;
    }

    assert(slice_end <= (HeapWord*)sp_top, "Last object in slice crosses space boundary");
    assert(is_valid_card_address(worker_start_card), "Invalid worker start card");
    assert(is_valid_card_address(worker_end_card), "Invalid worker end card");
    // Note that worker_start_card >= worker_end_card is legal, and happens when
    // an object spans an entire slice.
    assert(worker_start_card <= end_card, "worker start card beyond end card");
    assert(worker_end_card <= end_card, "worker end card beyond end card");

    jbyte* current_card = worker_start_card;
    while (current_card < worker_end_card) {
      // Find an unclean card.
      while (current_card < worker_end_card && card_is_clean(*current_card)) {
        current_card++;
      }
      jbyte* first_unclean_card = current_card;

      // Find the end of a run of contiguous unclean cards
      while (current_card < worker_end_card && !card_is_clean(*current_card)) {
        while (current_card < worker_end_card && !card_is_clean(*current_card)) {
          current_card++;
        }

        if (current_card < worker_end_card) {
          // Some objects may be large enough to span several cards. If such
          // an object has more than one dirty card, separated by a clean card,
          // we will attempt to scan it twice. The test against "last_scanned"
          // prevents the redundant object scan, but it does not prevent newly
          // marked cards from being cleaned.
          HeapWord* last_object_in_dirty_region = start_array->object_start(addr_for(current_card)-1);
          size_t size_of_last_object = oop(last_object_in_dirty_region)->size();
          HeapWord* end_of_last_object = last_object_in_dirty_region + size_of_last_object;
          jbyte* ending_card_of_last_object = byte_for(end_of_last_object);
          assert(ending_card_of_last_object <= worker_end_card, "ending_card_of_last_object is greater than worker_end_card");
          if (ending_card_of_last_object > current_card) {
            // This means the object spans the next complete card.
            // We need to bump the current_card to ending_card_of_last_object
            current_card = ending_card_of_last_object;
          }
        }
      }
      jbyte* following_clean_card = current_card;

      if (first_unclean_card < worker_end_card) {
        oop* p = (oop*) start_array->object_start(addr_for(first_unclean_card));
        assert((HeapWord*)p <= addr_for(first_unclean_card), "checking");
        // "p" should always be >= "last_scanned" because newly GC dirtied
        // cards are no longer scanned again (see comment at end
        // of loop on the increment of "current_card").  Test that
        // hypothesis before removing this code.
        // If this code is removed, deal with the first time through
        // the loop when the last_scanned is the object starting in
        // the previous slice.
        assert((p >= last_scanned) ||
               (last_scanned == first_object_within_slice),
               "Should no longer be possible");
        if (p < last_scanned) {
          // Avoid scanning more than once; this can happen because
          // newgen cards set by GC may a different set than the
          // originally dirty set
          p = last_scanned;
        }
        oop* to = (oop*)addr_for(following_clean_card);

        // Test slice_end first!
        if ((HeapWord*)to > slice_end) {
          to = (oop*)slice_end;
        } else if (to > sp_top) {
          to = sp_top;
        }

        // we know which cards to scan, now clear them
        if (first_unclean_card <= worker_start_card+1)
          first_unclean_card = worker_start_card+1;
        if (following_clean_card >= worker_end_card-1)
          following_clean_card = worker_end_card-1;

        while (first_unclean_card < following_clean_card) {
          *first_unclean_card++ = clean_card;
        }

        const int interval = PrefetchScanIntervalInBytes;
        // scan all objects in the range
        if (interval != 0) {
          while (p < to) {
            Prefetch::write(p, interval);
            oop m = oop(p);
            assert(m->is_oop_or_null(), "Expected an oop or NULL for header field at " PTR_FORMAT, p2i(m));
            pm->push_contents(m);
            p += m->size();
          }
          pm->drain_stacks_cond_depth();
        } else {
          while (p < to) {
            oop m = oop(p);
            assert(m->is_oop_or_null(), "Expected an oop or NULL for header field at " PTR_FORMAT, p2i(m));
            pm->push_contents(m);
            p += m->size();
          }
          pm->drain_stacks_cond_depth();
        }
        last_scanned = p;
      }
      // "current_card" is still the "following_clean_card" or
      // the current_card is >= the worker_end_card so the
      // loop will not execute again.
      assert((current_card == following_clean_card) ||
             (current_card >= worker_end_card),
        "current_card should only be incremented if it still equals "
        "following_clean_card");
      // Increment current_card so that it is not processed again.
      // It may now be dirty because a old-to-young pointer was
      // found on it an updated.  If it is now dirty, it cannot be
      // be safely cleaned in the next iteration.
      current_card++;
    }
  }
}

// This should be called before a scavenge.
void CardTableExtension::verify_all_young_refs_imprecise() {
  CheckForUnmarkedObjects check;

  ParallelScavengeHeap* heap = ParallelScavengeHeap::heap();
  PSOldGen* old_gen = heap->old_gen();

  old_gen->object_iterate(&check);
}

// This should be called immediately after a scavenge, before mutators resume.
void CardTableExtension::verify_all_young_refs_precise() {
  ParallelScavengeHeap* heap = ParallelScavengeHeap::heap();
  PSOldGen* old_gen = heap->old_gen();

  CheckForPreciseMarks check(
    heap->young_gen(),
    barrier_set_cast<CardTableExtension>(heap->barrier_set()));

  old_gen->oop_iterate_no_header(&check);

  verify_all_young_refs_precise_helper(old_gen->object_space()->used_region());
}

void CardTableExtension::verify_all_young_refs_precise_helper(MemRegion mr) {
  CardTableExtension* card_table =
    barrier_set_cast<CardTableExtension>(ParallelScavengeHeap::heap()->barrier_set());

  jbyte* bot = card_table->byte_for(mr.start());
  jbyte* top = card_table->byte_for(mr.end());
  while(bot <= top) {
    assert(*bot == clean_card || *bot == verify_card, "Found unwanted or unknown card mark");
    if (*bot == verify_card)
      *bot = youngergen_card;
    bot++;
  }
}

bool CardTableExtension::addr_is_marked_imprecise(void *addr) {
  jbyte* p = byte_for(addr);
  jbyte val = *p;

  if (card_is_dirty(val))
    return true;

  if (card_is_newgen(val))
    return true;

  if (card_is_clean(val))
    return false;

  assert(false, "Found unhandled card mark type");

  return false;
}

// Also includes verify_card
bool CardTableExtension::addr_is_marked_precise(void *addr) {
  jbyte* p = byte_for(addr);
  jbyte val = *p;

  if (card_is_newgen(val))
    return true;

  if (card_is_verify(val))
    return true;

  if (card_is_clean(val))
    return false;

  if (card_is_dirty(val))
    return false;

  assert(false, "Found unhandled card mark type");

  return false;
}

// Assumes that only the base or the end changes.  This allows indentification
// of the region that is being resized.  The
// CardTableModRefBS::resize_covered_region() is used for the normal case
// where the covered regions are growing or shrinking at the high end.
// The method resize_covered_region_by_end() is analogous to
// CardTableModRefBS::resize_covered_region() but
// for regions that grow or shrink at the low end.
void CardTableExtension::resize_covered_region(MemRegion new_region) {

  for (int i = 0; i < _cur_covered_regions; i++) {
    if (_covered[i].start() == new_region.start()) {
      // Found a covered region with the same start as the
      // new region.  The region is growing or shrinking
      // from the start of the region.
      resize_covered_region_by_start(new_region);
      return;
    }
    if (_covered[i].start() > new_region.start()) {
      break;
    }
  }

  int changed_region = -1;
  for (int j = 0; j < _cur_covered_regions; j++) {
    if (_covered[j].end() == new_region.end()) {
      changed_region = j;
      // This is a case where the covered region is growing or shrinking
      // at the start of the region.
      assert(changed_region != -1, "Don't expect to add a covered region");
      assert(_covered[changed_region].byte_size() != new_region.byte_size(),
        "The sizes should be different here");
      resize_covered_region_by_end(changed_region, new_region);
      return;
    }
  }
  // This should only be a new covered region (where no existing
  // covered region matches at the start or the end).
  assert(_cur_covered_regions < _max_covered_regions,
    "An existing region should have been found");
  resize_covered_region_by_start(new_region);
}

void CardTableExtension::resize_covered_region_by_start(MemRegion new_region) {
  CardTableModRefBS::resize_covered_region(new_region);
  debug_only(verify_guard();)
}

void CardTableExtension::resize_covered_region_by_end(int changed_region,
                                                      MemRegion new_region) {
  assert(SafepointSynchronize::is_at_safepoint(),
    "Only expect an expansion at the low end at a GC");
  debug_only(verify_guard();)
#ifdef ASSERT
  for (int k = 0; k < _cur_covered_regions; k++) {
    if (_covered[k].end() == new_region.end()) {
      assert(changed_region == k, "Changed region is incorrect");
      break;
    }
  }
#endif

  // Commit new or uncommit old pages, if necessary.
  if (resize_commit_uncommit(changed_region, new_region)) {
    // Set the new start of the committed region
    resize_update_committed_table(changed_region, new_region);
  }

  // Update card table entries
  resize_update_card_table_entries(changed_region, new_region);

  // Update the covered region
  resize_update_covered_table(changed_region, new_region);

  int ind = changed_region;
  log_trace(gc, barrier)("CardTableModRefBS::resize_covered_region: ");
  log_trace(gc, barrier)("    _covered[%d].start(): " INTPTR_FORMAT "  _covered[%d].last(): " INTPTR_FORMAT,
                ind, p2i(_covered[ind].start()), ind, p2i(_covered[ind].last()));
  log_trace(gc, barrier)("    _committed[%d].start(): " INTPTR_FORMAT "  _committed[%d].last(): " INTPTR_FORMAT,
                ind, p2i(_committed[ind].start()), ind, p2i(_committed[ind].last()));
  log_trace(gc, barrier)("    byte_for(start): " INTPTR_FORMAT "  byte_for(last): " INTPTR_FORMAT,
                p2i(byte_for(_covered[ind].start())),  p2i(byte_for(_covered[ind].last())));
  log_trace(gc, barrier)("    addr_for(start): " INTPTR_FORMAT "  addr_for(last): " INTPTR_FORMAT,
                p2i(addr_for((jbyte*) _committed[ind].start())), p2i(addr_for((jbyte*) _committed[ind].last())));

  debug_only(verify_guard();)
}

bool CardTableExtension::resize_commit_uncommit(int changed_region,
                                                MemRegion new_region) {
  bool result = false;
  // Commit new or uncommit old pages, if necessary.
  MemRegion cur_committed = _committed[changed_region];
  assert(_covered[changed_region].end() == new_region.end(),
    "The ends of the regions are expected to match");
  // Extend the start of this _committed region to
  // to cover the start of any previous _committed region.
  // This forms overlapping regions, but never interior regions.
  HeapWord* min_prev_start = lowest_prev_committed_start(changed_region);
  if (min_prev_start < cur_committed.start()) {
    // Only really need to set start of "cur_committed" to
    // the new start (min_prev_start) but assertion checking code
    // below use cur_committed.end() so make it correct.
    MemRegion new_committed =
        MemRegion(min_prev_start, cur_committed.end());
    cur_committed = new_committed;
  }
#ifdef ASSERT
  ParallelScavengeHeap* heap = ParallelScavengeHeap::heap();
  assert(cur_committed.start() ==
    (HeapWord*) align_size_up((uintptr_t) cur_committed.start(),
                              os::vm_page_size()),
    "Starts should have proper alignment");
#endif

  jbyte* new_start = byte_for(new_region.start());
  // Round down because this is for the start address
  HeapWord* new_start_aligned =
    (HeapWord*)align_size_down((uintptr_t)new_start, os::vm_page_size());
  // The guard page is always committed and should not be committed over.
  // This method is used in cases where the generation is growing toward
  // lower addresses but the guard region is still at the end of the
  // card table.  That still makes sense when looking for writes
  // off the end of the card table.
  if (new_start_aligned < cur_committed.start()) {
    // Expand the committed region
    //
    // Case A
    //                                          |+ guard +|
    //                          |+ cur committed +++++++++|
    //                  |+ new committed +++++++++++++++++|
    //
    // Case B
    //                                          |+ guard +|
    //                        |+ cur committed +|
    //                  |+ new committed +++++++|
    //
    // These are not expected because the calculation of the
    // cur committed region and the new committed region
    // share the same end for the covered region.
    // Case C
    //                                          |+ guard +|
    //                        |+ cur committed +|
    //                  |+ new committed +++++++++++++++++|
    // Case D
    //                                          |+ guard +|
    //                        |+ cur committed +++++++++++|
    //                  |+ new committed +++++++|

    HeapWord* new_end_for_commit =
      MIN2(cur_committed.end(), _guard_region.start());
    if(new_start_aligned < new_end_for_commit) {
      MemRegion new_committed =
        MemRegion(new_start_aligned, new_end_for_commit);
      os::commit_memory_or_exit((char*)new_committed.start(),
                                new_committed.byte_size(), !ExecMem,
                                "card table expansion");
    }
    result = true;
  } else if (new_start_aligned > cur_committed.start()) {
    // Shrink the committed region
#if 0 // uncommitting space is currently unsafe because of the interactions
      // of growing and shrinking regions.  One region A can uncommit space
      // that it owns but which is being used by another region B (maybe).
      // Region B has not committed the space because it was already
      // committed by region A.
    MemRegion uncommit_region = committed_unique_to_self(changed_region,
      MemRegion(cur_committed.start(), new_start_aligned));
    if (!uncommit_region.is_empty()) {
      if (!os::uncommit_memory((char*)uncommit_region.start(),
                               uncommit_region.byte_size())) {
        // If the uncommit fails, ignore it.  Let the
        // committed table resizing go even though the committed
        // table will over state the committed space.
      }
    }
#else
    assert(!result, "Should be false with current workaround");
#endif
  }
  assert(_committed[changed_region].end() == cur_committed.end(),
    "end should not change");
  return result;
}

void CardTableExtension::resize_update_committed_table(int changed_region,
                                                       MemRegion new_region) {

  jbyte* new_start = byte_for(new_region.start());
  // Set the new start of the committed region
  HeapWord* new_start_aligned =
    (HeapWord*)align_size_down((uintptr_t)new_start,
                             os::vm_page_size());
  MemRegion new_committed = MemRegion(new_start_aligned,
    _committed[changed_region].end());
  _committed[changed_region] = new_committed;
  _committed[changed_region].set_start(new_start_aligned);
}

void CardTableExtension::resize_update_card_table_entries(int changed_region,
                                                          MemRegion new_region) {
  debug_only(verify_guard();)
  MemRegion original_covered = _covered[changed_region];
  // Initialize the card entries.  Only consider the
  // region covered by the card table (_whole_heap)
  jbyte* entry;
  if (new_region.start() < _whole_heap.start()) {
    entry = byte_for(_whole_heap.start());
  } else {
    entry = byte_for(new_region.start());
  }
  jbyte* end = byte_for(original_covered.start());
  // If _whole_heap starts at the original covered regions start,
  // this loop will not execute.
  while (entry < end) { *entry++ = clean_card; }
}

void CardTableExtension::resize_update_covered_table(int changed_region,
                                                     MemRegion new_region) {
  // Update the covered region
  _covered[changed_region].set_start(new_region.start());
  _covered[changed_region].set_word_size(new_region.word_size());

  // reorder regions.  There should only be at most 1 out
  // of order.
  for (int i = _cur_covered_regions-1 ; i > 0; i--) {
    if (_covered[i].start() < _covered[i-1].start()) {
        MemRegion covered_mr = _covered[i-1];
        _covered[i-1] = _covered[i];
        _covered[i] = covered_mr;
        MemRegion committed_mr = _committed[i-1];
      _committed[i-1] = _committed[i];
      _committed[i] = committed_mr;
      break;
    }
  }
#ifdef ASSERT
  for (int m = 0; m < _cur_covered_regions-1; m++) {
    assert(_covered[m].start() <= _covered[m+1].start(),
      "Covered regions out of order");
    assert(_committed[m].start() <= _committed[m+1].start(),
      "Committed regions out of order");
  }
#endif
}

// Returns the start of any committed region that is lower than
// the target committed region (index ind) and that intersects the
// target region.  If none, return start of target region.
//
//      -------------
//      |           |
//      -------------
//              ------------
//              | target   |
//              ------------
//                               -------------
//                               |           |
//                               -------------
//      ^ returns this
//
//      -------------
//      |           |
//      -------------
//                      ------------
//                      | target   |
//                      ------------
//                               -------------
//                               |           |
//                               -------------
//                      ^ returns this

HeapWord* CardTableExtension::lowest_prev_committed_start(int ind) const {
  assert(_cur_covered_regions >= 0, "Expecting at least on region");
  HeapWord* min_start = _committed[ind].start();
  for (int j = 0; j < ind; j++) {
    HeapWord* this_start = _committed[j].start();
    if ((this_start < min_start) &&
        !(_committed[j].intersection(_committed[ind])).is_empty()) {
       min_start = this_start;
    }
  }
  return min_start;
}