level_checker.go

// Copyright 2019 The LevelDB-Go and Pebble Authors. All rights reserved. Use
// of this source code is governed by a BSD-style license that can be found in
// the LICENSE file.

package pebble

import (
	"context"
	"fmt"
	"io"
	"sort"
	"sync/atomic"

	"github.com/cockroachdb/errors"
	"github.com/cockroachdb/pebble/internal/base"
	"github.com/cockroachdb/pebble/internal/keyspan"
	"github.com/cockroachdb/pebble/internal/manifest"
)

// This file implements DB.CheckLevels() which checks that every entry in the
// DB is consistent with respect to the level invariant: any point (or the
// infinite number of points in a range tombstone) has a seqnum such that a
// point with the same UserKey at a lower level has a lower seqnum. This is an
// expensive check since it involves iterating over all the entries in the DB,
// hence only intended for tests or tools.
//
// If we ignore range tombstones, the consistency checking of points can be
// done with a simplified version of mergingIter. simpleMergingIter is that
// simplified version of mergingIter that only needs to step through points
// (analogous to only doing Next()). It can also easily accommodate
// consistency checking of points relative to range tombstones.
// simpleMergingIter does not do any seek optimizations present in mergingIter
// (it minimally needs to seek the range delete iterators to position them at
// or past the current point) since it does not want to miss points for
// purposes of consistency checking.
//
// Mutual consistency of range tombstones is non-trivial to check. One needs
// to detect inversions of the form [a, c)#8 at higher level and [b, c)#10 at
// a lower level. The start key of the former is not contained in the latter
// and we can't use the exclusive end key, c, for a containment check since it
// is the sentinel key. We observe that if these tombstones were fragmented
// wrt each other we would have [a, b)#8 and [b, c)#8 at the higher level and
// [b, c)#10 at the lower level and then it is is trivial to compare the two
// [b, c) tombstones. Note that this fragmentation needs to take into account
// that tombstones in a file may be untruncated and need to act within the
// bounds of the file. This checking is performed by checkRangeTombstones()
// and its helper functions.

// The per-level structure used by simpleMergingIter.
type simpleMergingIterLevel struct {
	iter         internalIterator
	rangeDelIter keyspan.FragmentIterator
	levelIterBoundaryContext

	iterKey   *InternalKey
	iterValue base.LazyValue
	tombstone *keyspan.Span
}

type simpleMergingIter struct {
	levels   []simpleMergingIterLevel
	snapshot uint64
	heap     simpleMergingIterHeap
	// The last point's key and level. For validation.
	lastKey     InternalKey
	lastLevel   int
	lastIterMsg string
	// A non-nil valueMerger means MERGE record processing is ongoing.
	valueMerger base.ValueMerger
	// The first error will cause step() to return false.
	err       error
	numPoints int64
	merge     Merge
	formatKey base.FormatKey
}

func (m *simpleMergingIter) init(
	merge Merge,
	cmp Compare,
	snapshot uint64,
	formatKey base.FormatKey,
	levels ...simpleMergingIterLevel,
) {
	m.levels = levels
	m.formatKey = formatKey
	m.merge = merge
	m.snapshot = snapshot
	m.lastLevel = -1
	m.heap.cmp = cmp
	m.heap.items = make([]simpleMergingIterItem, 0, len(levels))
	for i := range m.levels {
		l := &m.levels[i]
		l.iterKey, l.iterValue = l.iter.First()
		if l.iterKey != nil {
			item := simpleMergingIterItem{
				index: i,
				value: l.iterValue,
			}
			item.key.Trailer = l.iterKey.Trailer
			item.key.UserKey = append(item.key.UserKey[:0], l.iterKey.UserKey...)
			m.heap.items = append(m.heap.items, item)
		}
	}
	m.heap.init()

	if m.heap.len() == 0 {
		return
	}
	m.positionRangeDels()
}

// Positions all the rangedel iterators at or past the current top of the
// heap, using SeekGE().
func (m *simpleMergingIter) positionRangeDels() {
	item := &m.heap.items[0]
	for i := range m.levels {
		l := &m.levels[i]
		if l.rangeDelIter == nil {
			continue
		}
		l.tombstone = l.rangeDelIter.SeekGE(item.key.UserKey)
	}
}

// Returns true if not yet done.
func (m *simpleMergingIter) step() bool {
	if m.heap.len() == 0 || m.err != nil {
		return false
	}
	item := &m.heap.items[0]
	l := &m.levels[item.index]
	// Sentinels are not relevant for this point checking.
	if !item.key.IsExclusiveSentinel() && item.key.Visible(m.snapshot, base.InternalKeySeqNumMax) {
		m.numPoints++
		keyChanged := m.heap.cmp(item.key.UserKey, m.lastKey.UserKey) != 0
		if !keyChanged {
			// At the same user key. We will see them in decreasing seqnum
			// order so the lastLevel must not be lower.
			if m.lastLevel > item.index {
				m.err = errors.Errorf("found InternalKey %s in %s and InternalKey %s in %s",
					item.key.Pretty(m.formatKey), l.iter, m.lastKey.Pretty(m.formatKey),
					m.lastIterMsg)
				return false
			}
			m.lastLevel = item.index
		} else {
			// The user key has changed.
			m.lastKey.Trailer = item.key.Trailer
			m.lastKey.UserKey = append(m.lastKey.UserKey[:0], item.key.UserKey...)
			m.lastLevel = item.index
		}
		// Ongoing series of MERGE records ends with a MERGE record.
		if keyChanged && m.valueMerger != nil {
			var closer io.Closer
			_, closer, m.err = m.valueMerger.Finish(true /* includesBase */)
			if m.err == nil && closer != nil {
				m.err = closer.Close()
			}
			m.valueMerger = nil
		}
		itemValue, _, err := item.value.Value(nil)
		if err != nil {
			m.err = err
			return false
		}
		if m.valueMerger != nil {
			// Ongoing series of MERGE records.
			switch item.key.Kind() {
			case InternalKeyKindSingleDelete, InternalKeyKindDelete:
				var closer io.Closer
				_, closer, m.err = m.valueMerger.Finish(true /* includesBase */)
				if m.err == nil && closer != nil {
					m.err = closer.Close()
				}
				m.valueMerger = nil
			case InternalKeyKindSet, InternalKeyKindSetWithDelete:
				m.err = m.valueMerger.MergeOlder(itemValue)
				if m.err == nil {
					var closer io.Closer
					_, closer, m.err = m.valueMerger.Finish(true /* includesBase */)
					if m.err == nil && closer != nil {
						m.err = closer.Close()
					}
				}
				m.valueMerger = nil
			case InternalKeyKindMerge:
				m.err = m.valueMerger.MergeOlder(itemValue)
			default:
				m.err = errors.Errorf("pebble: invalid internal key kind %s in %s",
					item.key.Pretty(m.formatKey),
					l.iter)
				return false
			}
		} else if item.key.Kind() == InternalKeyKindMerge && m.err == nil {
			// New series of MERGE records.
			m.valueMerger, m.err = m.merge(item.key.UserKey, itemValue)
		}
		if m.err != nil {
			m.err = errors.Wrapf(m.err, "merge processing error on key %s in %s",
				item.key.Pretty(m.formatKey), l.iter)
			return false
		}
		// Is this point covered by a tombstone at a lower level? Note that all these
		// iterators must be positioned at a key > item.key. So the Largest key bound
		// of the sstable containing the tombstone >= item.key. So the upper limit of
		// the tombstone cannot be file-bounds-constrained to < item.key. But it is
		// possible that item.key < smallest key bound of the sstable, in which case
		// this tombstone should be ignored.
		for level := item.index + 1; level < len(m.levels); level++ {
			lvl := &m.levels[level]
			if lvl.rangeDelIter == nil || lvl.tombstone.Empty() {
				continue
			}
			if (lvl.smallestUserKey == nil || m.heap.cmp(lvl.smallestUserKey, item.key.UserKey) <= 0) &&
				lvl.tombstone.Contains(m.heap.cmp, item.key.UserKey) {
				if lvl.tombstone.CoversAt(m.snapshot, item.key.SeqNum()) {
					m.err = errors.Errorf("tombstone %s in %s deletes key %s in %s",
						lvl.tombstone.Pretty(m.formatKey), lvl.iter, item.key.Pretty(m.formatKey),
						l.iter)
					return false
				}
			}
		}
	}

	// The iterator for the current level may be closed in the following call to
	// Next(). We save its debug string for potential use after it is closed -
	// either in this current step() invocation or on the next invocation.
	m.lastIterMsg = l.iter.String()

	// Step to the next point.
	if l.iterKey, l.iterValue = l.iter.Next(); l.iterKey != nil {
		// Check point keys in an sstable are ordered. Although not required, we check
		// for memtables as well. A subtle check here is that successive sstables of
		// L1 and higher levels are ordered. This happens when levelIter moves to the
		// next sstable in the level, in which case item.key is previous sstable's
		// last point key.
		if base.InternalCompare(m.heap.cmp, item.key, *l.iterKey) >= 0 {
			m.err = errors.Errorf("out of order keys %s >= %s in %s",
				item.key.Pretty(m.formatKey), l.iterKey.Pretty(m.formatKey), l.iter)
			return false
		}
		item.key.Trailer = l.iterKey.Trailer
		item.key.UserKey = append(item.key.UserKey[:0], l.iterKey.UserKey...)
		item.value = l.iterValue
		if m.heap.len() > 1 {
			m.heap.fix(0)
		}
	} else {
		m.err = l.iter.Close()
		l.iter = nil
		m.heap.pop()
	}
	if m.err != nil {
		return false
	}
	if m.heap.len() == 0 {
		// Last record was a MERGE record.
		if m.valueMerger != nil {
			var closer io.Closer
			_, closer, m.err = m.valueMerger.Finish(true /* includesBase */)
			if m.err == nil && closer != nil {
				m.err = closer.Close()
			}
			if m.err != nil {
				m.err = errors.Wrapf(m.err, "merge processing error on key %s in %s",
					item.key.Pretty(m.formatKey), m.lastIterMsg)
			}
			m.valueMerger = nil
		}
		return false
	}
	m.positionRangeDels()
	return true
}

// Checking that range tombstones are mutually consistent is performed by checkRangeTombstones().
// See the overview comment at the top of the file.
//
// We do this check as follows:
// - For each level that can have untruncated tombstones, compute the atomic compaction
//   bounds (getAtomicUnitBounds()) and use them to truncate tombstones.
// - Now that we have a set of truncated tombstones for each level, put them into one
//   pool of tombstones along with their level information (addTombstonesFromIter()).
// - Collect the start and end user keys from all these tombstones (collectAllUserKey()) and use
//   them to fragment all the tombstones (fragmentUsingUserKey()).
// - Sort tombstones by start key and decreasing seqnum (tombstonesByStartKeyAndSeqnum) -- all
//   tombstones that have the same start key will have the same end key because they have been
//   fragmented.
// - Iterate and check (iterateAndCheckTombstones()).
// Note that this simple approach requires holding all the tombstones across all levels in-memory.
// A more sophisticated incremental approach could be devised, if necessary.

// A tombstone and the corresponding level it was found in.
type tombstoneWithLevel struct {
	keyspan.Span
	level int
	// The level in LSM. A -1 means it's a memtable.
	lsmLevel int
	fileNum  FileNum
}

// For sorting tombstoneWithLevels in increasing order of start UserKey and
// for the same start UserKey in decreasing order of seqnum.
type tombstonesByStartKeyAndSeqnum struct {
	cmp Compare
	buf []tombstoneWithLevel
}

func (v *tombstonesByStartKeyAndSeqnum) Len() int { return len(v.buf) }
func (v *tombstonesByStartKeyAndSeqnum) Less(i, j int) bool {
	less := v.cmp(v.buf[i].Start, v.buf[j].Start)
	if less == 0 {
		return v.buf[i].LargestSeqNum() > v.buf[j].LargestSeqNum()
	}
	return less < 0
}
func (v *tombstonesByStartKeyAndSeqnum) Swap(i, j int) {
	v.buf[i], v.buf[j] = v.buf[j], v.buf[i]
}

func iterateAndCheckTombstones(
	cmp Compare, formatKey base.FormatKey, tombstones []tombstoneWithLevel,
) error {
	sortBuf := tombstonesByStartKeyAndSeqnum{
		cmp: cmp,
		buf: tombstones,
	}
	sort.Sort(&sortBuf)

	// For a sequence of tombstones that share the same start UserKey, we will
	// encounter them in non-increasing seqnum order and so should encounter them
	// in non-decreasing level order.
	lastTombstone := tombstoneWithLevel{}
	for _, t := range tombstones {
		if cmp(lastTombstone.Start, t.Start) == 0 && lastTombstone.level > t.level {
			return errors.Errorf("encountered tombstone %s in %s"+
				" that has a lower seqnum than the same tombstone in %s",
				t.Span.Pretty(formatKey), levelOrMemtable(t.lsmLevel, t.fileNum),
				levelOrMemtable(lastTombstone.lsmLevel, lastTombstone.fileNum))
		}
		lastTombstone = t
	}
	return nil
}

type checkConfig struct {
	logger    Logger
	cmp       Compare
	readState *readState
	newIters  tableNewIters
	seqNum    uint64
	stats     *CheckLevelsStats
	merge     Merge
	formatKey base.FormatKey
}

func checkRangeTombstones(c *checkConfig) error {
	var level int
	var tombstones []tombstoneWithLevel
	var err error

	memtables := c.readState.memtables
	for i := len(memtables) - 1; i >= 0; i-- {
		iter := memtables[i].newRangeDelIter(nil)
		if iter == nil {
			continue
		}
		if tombstones, err = addTombstonesFromIter(iter, level, -1, 0, tombstones,
			c.seqNum, c.cmp, c.formatKey, nil); err != nil {
			return err
		}
		level++
	}

	current := c.readState.current
	addTombstonesFromLevel := func(files manifest.LevelIterator, lsmLevel int) error {
		for f := files.First(); f != nil; f = files.Next() {
			lf := files.Take()
			atomicUnit, _ := expandToAtomicUnit(c.cmp, lf.Slice(), true /* disableIsCompacting */)
			lower, upper := manifest.KeyRange(c.cmp, atomicUnit.Iter())
			iterToClose, iter, err := c.newIters(
				context.Background(), lf.FileMetadata, nil, internalIterOpts{})
			if err != nil {
				return err
			}
			iterToClose.Close()
			if iter == nil {
				continue
			}
			truncate := func(t keyspan.Span) keyspan.Span {
				// Same checks as in keyspan.Truncate.
				if c.cmp(t.Start, lower.UserKey) < 0 {
					t.Start = lower.UserKey
				}
				if c.cmp(t.End, upper.UserKey) > 0 {
					t.End = upper.UserKey
				}
				if c.cmp(t.Start, t.End) >= 0 {
					// Remove the keys.
					t.Keys = t.Keys[:0]
				}
				return t
			}
			if tombstones, err = addTombstonesFromIter(iter, level, lsmLevel, f.FileNum,
				tombstones, c.seqNum, c.cmp, c.formatKey, truncate); err != nil {
				return err
			}
		}
		return nil
	}
	// Now the levels with untruncated tombsones.
	for i := len(current.L0SublevelFiles) - 1; i >= 0; i-- {
		if current.L0SublevelFiles[i].Empty() {
			continue
		}
		err := addTombstonesFromLevel(current.L0SublevelFiles[i].Iter(), 0)
		if err != nil {
			return err
		}
		level++
	}
	for i := 1; i < len(current.Levels); i++ {
		if err := addTombstonesFromLevel(current.Levels[i].Iter(), i); err != nil {
			return err
		}
		level++
	}
	if c.stats != nil {
		c.stats.NumTombstones = len(tombstones)
	}
	// We now have truncated tombstones.
	// Fragment them all.
	userKeys := collectAllUserKeys(c.cmp, tombstones)
	tombstones = fragmentUsingUserKeys(c.cmp, tombstones, userKeys)
	return iterateAndCheckTombstones(c.cmp, c.formatKey, tombstones)
}

func levelOrMemtable(lsmLevel int, fileNum FileNum) string {
	if lsmLevel == -1 {
		return "memtable"
	}
	return fmt.Sprintf("L%d: fileNum=%s", lsmLevel, fileNum)
}

func addTombstonesFromIter(
	iter keyspan.FragmentIterator,
	level int,
	lsmLevel int,
	fileNum FileNum,
	tombstones []tombstoneWithLevel,
	seqNum uint64,
	cmp Compare,
	formatKey base.FormatKey,
	truncate func(tombstone keyspan.Span) keyspan.Span,
) (_ []tombstoneWithLevel, err error) {
	defer func() {
		err = firstError(err, iter.Close())
	}()

	var prevTombstone keyspan.Span
	for tomb := iter.First(); tomb != nil; tomb = iter.Next() {
		t := tomb.Visible(seqNum)
		if t.Empty() {
			continue
		}
		t = t.DeepClone()
		// This is mainly a test for rangeDelV2 formatted blocks which are expected to
		// be ordered and fragmented on disk. But we anyways check for memtables,
		// rangeDelV1 as well.
		if cmp(prevTombstone.End, t.Start) > 0 {
			return nil, errors.Errorf("unordered or unfragmented range delete tombstones %s, %s in %s",
				prevTombstone.Pretty(formatKey), t.Pretty(formatKey), levelOrMemtable(lsmLevel, fileNum))
		}
		prevTombstone = t

		// Truncation of a tombstone must happen after checking its ordering,
		// fragmentation wrt previous tombstone. Since it is possible that after
		// truncation the tombstone is ordered, fragmented when it originally wasn't.
		if truncate != nil {
			t = truncate(t)
		}
		if !t.Empty() {
			tombstones = append(tombstones, tombstoneWithLevel{
				Span:     t,
				level:    level,
				lsmLevel: lsmLevel,
				fileNum:  fileNum,
			})
		}
	}
	return tombstones, nil
}

type userKeysSort struct {
	cmp Compare
	buf [][]byte
}

func (v *userKeysSort) Len() int { return len(v.buf) }
func (v *userKeysSort) Less(i, j int) bool {
	return v.cmp(v.buf[i], v.buf[j]) < 0
}
func (v *userKeysSort) Swap(i, j int) {
	v.buf[i], v.buf[j] = v.buf[j], v.buf[i]
}
func collectAllUserKeys(cmp Compare, tombstones []tombstoneWithLevel) [][]byte {
	keys := make([][]byte, 0, len(tombstones)*2)
	for _, t := range tombstones {
		keys = append(keys, t.Start)
		keys = append(keys, t.End)
	}
	sorter := userKeysSort{
		cmp: cmp,
		buf: keys,
	}
	sort.Sort(&sorter)
	var last, curr int
	for last, curr = -1, 0; curr < len(keys); curr++ {
		if last < 0 || cmp(keys[last], keys[curr]) != 0 {
			last++
			keys[last] = keys[curr]
		}
	}
	keys = keys[:last+1]
	return keys
}

func fragmentUsingUserKeys(
	cmp Compare, tombstones []tombstoneWithLevel, userKeys [][]byte,
) []tombstoneWithLevel {
	var buf []tombstoneWithLevel
	for _, t := range tombstones {
		// Find the first position with tombstone start < user key
		i := sort.Search(len(userKeys), func(i int) bool {
			return cmp(t.Start, userKeys[i]) < 0
		})
		for ; i < len(userKeys); i++ {
			if cmp(userKeys[i], t.End) >= 0 {
				break
			}
			tPartial := t
			tPartial.End = userKeys[i]
			buf = append(buf, tPartial)
			t.Start = userKeys[i]
		}
		buf = append(buf, t)
	}
	return buf
}

// CheckLevelsStats provides basic stats on points and tombstones encountered.
type CheckLevelsStats struct {
	NumPoints     int64
	NumTombstones int
}

// CheckLevels checks:
//   - Every entry in the DB is consistent with the level invariant. See the
//     comment at the top of the file.
//   - Point keys in sstables are ordered.
//   - Range delete tombstones in sstables are ordered and fragmented.
//   - Successful processing of all MERGE records.
func (d *DB) CheckLevels(stats *CheckLevelsStats) error {
	// Grab and reference the current readState.
	readState := d.loadReadState()
	defer readState.unref()

	// Determine the seqnum to read at after grabbing the read state (current and
	// memtables) above.
	seqNum := atomic.LoadUint64(&d.mu.versions.atomic.visibleSeqNum)

	checkConfig := &checkConfig{
		logger:    d.opts.Logger,
		cmp:       d.cmp,
		readState: readState,
		newIters:  d.newIters,
		seqNum:    seqNum,
		stats:     stats,
		merge:     d.merge,
		formatKey: d.opts.Comparer.FormatKey,
	}
	return checkLevelsInternal(checkConfig)
}

func checkLevelsInternal(c *checkConfig) (err error) {
	// Phase 1: Use a simpleMergingIter to step through all the points and ensure
	// that points with the same user key at different levels are not inverted
	// wrt sequence numbers and the same holds for tombstones that cover points.
	// To do this, one needs to construct a simpleMergingIter which is similar to
	// how one constructs a mergingIter.

	// Add mem tables from newest to oldest.
	var mlevels []simpleMergingIterLevel
	defer func() {
		for i := range mlevels {
			l := &mlevels[i]
			if l.iter != nil {
				err = firstError(err, l.iter.Close())
				l.iter = nil
			}
			if l.rangeDelIter != nil {
				err = firstError(err, l.rangeDelIter.Close())
				l.rangeDelIter = nil
			}
		}
	}()

	memtables := c.readState.memtables
	for i := len(memtables) - 1; i >= 0; i-- {
		mem := memtables[i]
		mlevels = append(mlevels, simpleMergingIterLevel{
			iter:         mem.newIter(nil),
			rangeDelIter: mem.newRangeDelIter(nil),
		})
	}

	current := c.readState.current
	// Determine the final size for mlevels so that there are no more
	// reallocations. levelIter will hold a pointer to elements in mlevels.
	start := len(mlevels)
	for sublevel := len(current.L0SublevelFiles) - 1; sublevel >= 0; sublevel-- {
		if current.L0SublevelFiles[sublevel].Empty() {
			continue
		}
		mlevels = append(mlevels, simpleMergingIterLevel{})
	}
	for level := 1; level < len(current.Levels); level++ {
		if current.Levels[level].Empty() {
			continue
		}
		mlevels = append(mlevels, simpleMergingIterLevel{})
	}
	mlevelAlloc := mlevels[start:]
	// Add L0 files by sublevel.
	for sublevel := len(current.L0SublevelFiles) - 1; sublevel >= 0; sublevel-- {
		if current.L0SublevelFiles[sublevel].Empty() {
			continue
		}
		manifestIter := current.L0SublevelFiles[sublevel].Iter()
		iterOpts := IterOptions{logger: c.logger}
		li := &levelIter{}
		li.init(context.Background(), iterOpts, c.cmp, nil /* split */, c.newIters, manifestIter,
			manifest.L0Sublevel(sublevel), internalIterOpts{})
		li.initRangeDel(&mlevelAlloc[0].rangeDelIter)
		li.initBoundaryContext(&mlevelAlloc[0].levelIterBoundaryContext)
		mlevelAlloc[0].iter = li
		mlevelAlloc = mlevelAlloc[1:]
	}
	for level := 1; level < len(current.Levels); level++ {
		if current.Levels[level].Empty() {
			continue
		}

		iterOpts := IterOptions{logger: c.logger}
		li := &levelIter{}
		li.init(context.Background(), iterOpts, c.cmp, nil /* split */, c.newIters,
			current.Levels[level].Iter(), manifest.Level(level), internalIterOpts{})
		li.initRangeDel(&mlevelAlloc[0].rangeDelIter)
		li.initBoundaryContext(&mlevelAlloc[0].levelIterBoundaryContext)
		mlevelAlloc[0].iter = li
		mlevelAlloc = mlevelAlloc[1:]
	}

	mergingIter := &simpleMergingIter{}
	mergingIter.init(c.merge, c.cmp, c.seqNum, c.formatKey, mlevels...)
	for cont := mergingIter.step(); cont; cont = mergingIter.step() {
	}
	if err := mergingIter.err; err != nil {
		return err
	}
	if c.stats != nil {
		c.stats.NumPoints = mergingIter.numPoints
	}

	// Phase 2: Check that the tombstones are mutually consistent.
	return checkRangeTombstones(c)
}

type simpleMergingIterItem struct {
	index int
	key   InternalKey
	value base.LazyValue
}

type simpleMergingIterHeap struct {
	cmp     Compare
	reverse bool
	items   []simpleMergingIterItem
}

func (h *simpleMergingIterHeap) len() int {
	return len(h.items)
}

func (h *simpleMergingIterHeap) less(i, j int) bool {
	ikey, jkey := h.items[i].key, h.items[j].key
	if c := h.cmp(ikey.UserKey, jkey.UserKey); c != 0 {
		if h.reverse {
			return c > 0
		}
		return c < 0
	}
	if h.reverse {
		return ikey.Trailer < jkey.Trailer
	}
	return ikey.Trailer > jkey.Trailer
}

func (h *simpleMergingIterHeap) swap(i, j int) {
	h.items[i], h.items[j] = h.items[j], h.items[i]
}

// init, fix, up and down are copied from the go stdlib.
func (h *simpleMergingIterHeap) init() {
	// heapify
	n := h.len()
	for i := n/2 - 1; i >= 0; i-- {
		h.down(i, n)
	}
}

func (h *simpleMergingIterHeap) fix(i int) {
	if !h.down(i, h.len()) {
		h.up(i)
	}
}

func (h *simpleMergingIterHeap) pop() *simpleMergingIterItem {
	n := h.len() - 1
	h.swap(0, n)
	h.down(0, n)
	item := &h.items[n]
	h.items = h.items[:n]
	return item
}

func (h *simpleMergingIterHeap) up(j int) {
	for {
		i := (j - 1) / 2 // parent
		if i == j || !h.less(j, i) {
			break
		}
		h.swap(i, j)
		j = i
	}
}

func (h *simpleMergingIterHeap) down(i0, n int) bool {
	i := i0
	for {
		j1 := 2*i + 1
		if j1 >= n || j1 < 0 { // j1 < 0 after int overflow
			break
		}
		j := j1 // left child
		if j2 := j1 + 1; j2 < n && h.less(j2, j1) {
			j = j2 // = 2*i + 2  // right child
		}
		if !h.less(j, i) {
			break
		}
		h.swap(i, j)
		i = j
	}
	return i > i0
}