featurebase/fragment.go

// Copyright 2017 Pilosa Corp.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//     http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.

package pilosa

import (
	"archive/tar"
	"bufio"
	"bytes"
	"container/heap"
	"context"
	"encoding/binary"
	"fmt"
	"hash"
	"io"
	"io/ioutil"
	"math"
	"os"
	"sort"
	"strings"
	"sync"
	"syscall"
	"time"
	"unsafe"

	"github.com/cespare/xxhash"
	"github.com/gogo/protobuf/proto"
	"github.com/pilosa/pilosa/internal"
	"github.com/pilosa/pilosa/logger"
	"github.com/pilosa/pilosa/pql"
	"github.com/pilosa/pilosa/roaring"
	"github.com/pilosa/pilosa/stats"
	"github.com/pilosa/pilosa/tracing"
	"github.com/pkg/errors"
)

const (
	// ShardWidth is the number of column IDs in a shard. It must be a power of 2 greater than or equal to 16.
	shardWidthExponent = 20
	ShardWidth         = 1 << shardWidthExponent

	// shardVsContainerExponent is the power of 2 of ShardWith minus the power
	// of two of roaring container width (which is 16).
	// 2^shardVsContainerExponent is the number of containers in a shard row.
	//
	// It is represented in this rather awkward way because calculating the row
	// which a given container is in means dividing by the number of rows per
	// container which is performantly expressed as a right shift by this
	// exponent.
	shardVsContainerExponent = shardWidthExponent - 16

	// width of roaring containers is 2^16
	containerWidth = 1 << 16

	// snapshotExt is the file extension used for an in-process snapshot.
	snapshotExt = ".snapshotting"

	// copyExt is the file extension used for the temp file used while copying.
	copyExt = ".copying"

	// cacheExt is the file extension for persisted cache ids.
	cacheExt = ".cache"

	// HashBlockSize is the number of rows in a merkle hash block.
	HashBlockSize = 100

	// defaultFragmentMaxOpN is the default value for Fragment.MaxOpN.
	defaultFragmentMaxOpN = 2000

	// Row ids used for boolean fields.
	falseRowID = uint64(0)
	trueRowID  = uint64(1)
)

// fragment represents the intersection of a field and shard in an index.
type fragment struct {
	mu sync.RWMutex

	// Composite identifiers
	index string
	field string
	view  string
	shard uint64

	// File-backed storage
	path        string
	file        *os.File
	storage     *roaring.Bitmap
	storageData []byte
	opN         int // number of ops since snapshot

	// Cache for row counts.
	CacheType string // passed in by field
	cache     cache
	CacheSize uint32

	// Stats reporting.
	maxRowID uint64

	// Cache containing full rows (not just counts).
	rowCache bitmapCache

	// Cached checksums for each block.
	checksums map[int][]byte

	// Number of operations performed before performing a snapshot.
	// This limits the size of fragments on the heap and flushes them to disk
	// so that they can be mmapped and heap utilization can be kept low.
	MaxOpN int

	// Logger used for out-of-band log entries.
	Logger logger.Logger

	// Row attribute storage.
	// This is set by the parent field unless overridden for testing.
	RowAttrStore AttrStore

	// mutexVector is used for mutex field types. It's checked for an
	// existing value (to clear) prior to setting a new value.
	mutexVector vector

	stats stats.StatsClient
}

// newFragment returns a new instance of Fragment.
func newFragment(path, index, field, view string, shard uint64) *fragment {
	return &fragment{
		path:      path,
		index:     index,
		field:     field,
		view:      view,
		shard:     shard,
		CacheType: DefaultCacheType,
		CacheSize: DefaultCacheSize,

		Logger: logger.NopLogger,
		MaxOpN: defaultFragmentMaxOpN,

		stats: stats.NopStatsClient,
	}
}

// cachePath returns the path to the fragment's cache data.
func (f *fragment) cachePath() string { return f.path + cacheExt }

// Open opens the underlying storage.
func (f *fragment) Open() error {
	f.mu.Lock()
	defer f.mu.Unlock()

	if err := func() error {
		// Initialize storage in a function so we can close if anything goes wrong.
		if err := f.openStorage(); err != nil {
			return errors.Wrap(err, "opening storage")
		}

		// Fill cache with rows persisted to disk.
		if err := f.openCache(); err != nil {
			return errors.Wrap(err, "opening cache")
		}

		// Clear checksums.
		f.checksums = make(map[int][]byte)

		// Read last bit to determine max row.
		pos := f.storage.Max()
		f.maxRowID = pos / ShardWidth
		f.stats.Gauge("rows", float64(f.maxRowID), 1.0)
		return nil
	}(); err != nil {
		f.close()
		return err
	}

	return nil
}

// openStorage opens the storage bitmap.
func (f *fragment) openStorage() error {
	// Create a roaring bitmap to serve as storage for the shard.
	if f.storage == nil {
		f.storage = roaring.NewFileBitmap()
	}
	// Open the data file to be mmap'd and used as an ops log.
	file, err := os.OpenFile(f.path, os.O_RDWR|os.O_CREATE|os.O_APPEND, 0666)
	if err != nil {
		return fmt.Errorf("open file: %s", err)
	}
	f.file = file

	// Lock the underlying file.
	if err := syscall.Flock(int(f.file.Fd()), syscall.LOCK_EX|syscall.LOCK_NB); err != nil {
		return fmt.Errorf("flock: %s", err)
	}

	// If the file is empty then initialize it with an empty bitmap.
	fi, err := f.file.Stat()
	if err != nil {
		return errors.Wrap(err, "statting file before")
	} else if fi.Size() == 0 {
		bi := bufio.NewWriter(f.file)
		if _, err := f.storage.WriteTo(bi); err != nil {
			return fmt.Errorf("init storage file: %s", err)
		}
		bi.Flush()
		fi, err = f.file.Stat()
		if err != nil {
			return errors.Wrap(err, "statting file after")
		}
	}

	// Mmap the underlying file so it can be zero copied.
	storageData, err := syscall.Mmap(int(f.file.Fd()), 0, int(fi.Size()), syscall.PROT_READ, syscall.MAP_SHARED)
	if err != nil {
		return fmt.Errorf("mmap: %s", err)
	}
	f.storageData = storageData

	// Advise the kernel that the mmap is accessed randomly.
	if err := madvise(f.storageData, syscall.MADV_RANDOM); err != nil {
		return fmt.Errorf("madvise: %s", err)
	}

	// Attach the mmap file to the bitmap.
	data := f.storageData
	if err := f.storage.UnmarshalBinary(data); err != nil {
		return fmt.Errorf("unmarshal storage: file=%s, err=%s", f.file.Name(), err)
	}

	// Attach the file to the bitmap to act as a write-ahead log.
	f.storage.OpWriter = f.file
	f.rowCache = &simpleCache{make(map[uint64]*Row)}

	return nil

}

// openCache initializes the cache from row ids persisted to disk.
func (f *fragment) openCache() error {
	// Determine cache type from field name.
	switch f.CacheType {
	case CacheTypeRanked:
		f.cache = NewRankCache(f.CacheSize)
	case CacheTypeLRU:
		f.cache = newLRUCache(f.CacheSize)
	case CacheTypeNone:
		f.cache = globalNopCache
		return nil
	default:
		return ErrInvalidCacheType
	}

	// Read cache data from disk.
	path := f.cachePath()
	buf, err := ioutil.ReadFile(path)
	if os.IsNotExist(err) {
		return nil
	} else if err != nil {
		return fmt.Errorf("open cache: %s", err)
	}

	// Unmarshal cache data.
	var pb internal.Cache
	if err := proto.Unmarshal(buf, &pb); err != nil {
		f.Logger.Printf("error unmarshaling cache data, skipping: path=%s, err=%s", path, err)
		return nil
	}

	// Read in all rows by ID.
	// This will cause them to be added to the cache.
	for _, id := range pb.IDs {
		n := f.storage.CountRange(id*ShardWidth, (id+1)*ShardWidth)
		f.cache.BulkAdd(id, n)
	}
	f.cache.Invalidate()

	return nil
}

// Close flushes the underlying storage, closes the file and unlocks it.
func (f *fragment) Close() error {
	f.mu.Lock()
	defer f.mu.Unlock()
	return f.close()
}

func (f *fragment) close() error {
	// Flush cache if closing gracefully.
	if err := f.flushCache(); err != nil {
		f.Logger.Printf("fragment: error flushing cache on close: err=%s, path=%s", err, f.path)
		return errors.Wrap(err, "flushing cache")
	}

	// Close underlying storage.
	if err := f.closeStorage(); err != nil {
		f.Logger.Printf("fragment: error closing storage: err=%s, path=%s", err, f.path)
		return errors.Wrap(err, "closing storage")
	}

	// Remove checksums.
	f.checksums = nil

	return nil
}

func (f *fragment) closeStorage() error {
	// Clear the storage bitmap so it doesn't access the closed mmap.

	//f.storage = roaring.NewBitmap()

	// Unmap the file.
	if f.storageData != nil {
		if err := syscall.Munmap(f.storageData); err != nil {
			return fmt.Errorf("munmap: %s", err)
		}
		f.storageData = nil
	}

	// Flush file, unlock & close.
	if f.file != nil {
		if err := f.file.Sync(); err != nil {
			return fmt.Errorf("sync: %s", err)
		}
		if err := syscall.Flock(int(f.file.Fd()), syscall.LOCK_UN); err != nil {
			return fmt.Errorf("unlock: %s", err)
		}
		if err := f.file.Close(); err != nil {
			return fmt.Errorf("close file: %s", err)
		}
	}

	return nil
}

// row returns a row by ID.
func (f *fragment) row(rowID uint64) *Row {
	f.mu.Lock()
	defer f.mu.Unlock()
	return f.unprotectedRow(rowID)
}

func (f *fragment) unprotectedRow(rowID uint64) *Row {
	r, ok := f.rowCache.Fetch(rowID)
	if ok && r != nil {
		return r
	}

	// Only use a subset of the containers.
	// NOTE: The start & end ranges must be divisible by container width.
	data := f.storage.OffsetRange(f.shard*ShardWidth, rowID*ShardWidth, (rowID+1)*ShardWidth)

	// Reference bitmap subrange in storage.
	// We Clone() data because otherwise row will contain pointers to containers in storage.
	// This causes unexpected results when we cache the row and try to use it later.
	row := &Row{
		segments: []rowSegment{{
			data:     *data.Clone(),
			shard:    f.shard,
			writable: false,
		}},
	}
	row.invalidateCount()

	f.rowCache.Add(rowID, row)

	return row
}

// setBit sets a bit for a given column & row within the fragment.
// This updates both the on-disk storage and the in-cache bitmap.
func (f *fragment) setBit(rowID, columnID uint64) (changed bool, err error) {
	f.mu.Lock()
	defer f.mu.Unlock()

	// handle mutux field type
	if f.mutexVector != nil {
		if err := f.handleMutex(rowID, columnID); err != nil {
			return changed, errors.Wrap(err, "handling mutex")
		}
	}

	return f.unprotectedSetBit(rowID, columnID)
}

// handleMutex will clear an existing row and store the new row
// in the vector.
func (f *fragment) handleMutex(rowID, columnID uint64) error {
	if existingRowID, found, err := f.mutexVector.Get(columnID); err != nil {
		return errors.Wrap(err, "getting mutex vector data")
	} else if found && existingRowID != rowID {
		if _, err := f.unprotectedClearBit(existingRowID, columnID); err != nil {
			return errors.Wrap(err, "clearing mutex value")
		}
	}
	return nil
}

func (f *fragment) unprotectedSetBit(rowID, columnID uint64) (changed bool, err error) {
	changed = false
	// Determine the position of the bit in the storage.
	pos, err := f.pos(rowID, columnID)
	if err != nil {
		return false, errors.Wrap(err, "getting bit pos")
	}

	// Write to storage.
	if changed, err = f.storage.Add(pos); err != nil {
		return false, errors.Wrap(err, "writing")
	}

	// Don't update the cache if nothing changed.
	if !changed {
		return changed, nil
	}

	// Invalidate block checksum.
	delete(f.checksums, int(rowID/HashBlockSize))

	// Increment number of operations until snapshot is required.
	if err := f.incrementOpN(); err != nil {
		return false, errors.Wrap(err, "incrementing")
	}

	// Get the row from row cache or fragment.storage.
	row := f.unprotectedRow(rowID)
	row.SetBit(columnID)

	// Update the cache.
	f.cache.Add(rowID, row.Count())

	f.stats.Count("setBit", 1, 0.001)

	// Update row count if they have increased.
	if rowID > f.maxRowID {
		f.maxRowID = rowID
		f.stats.Gauge("rows", float64(f.maxRowID), 1.0)
	}

	return changed, nil
}

// clearBit clears a bit for a given column & row within the fragment.
// This updates both the on-disk storage and the in-cache bitmap.
func (f *fragment) clearBit(rowID, columnID uint64) (bool, error) {
	f.mu.Lock()
	defer f.mu.Unlock()
	return f.unprotectedClearBit(rowID, columnID)
}

func (f *fragment) unprotectedClearBit(rowID, columnID uint64) (changed bool, err error) {
	changed = false
	// Determine the position of the bit in the storage.
	pos, err := f.pos(rowID, columnID)
	if err != nil {
		return false, errors.Wrap(err, "getting bit pos")
	}

	// Write to storage.
	if changed, err = f.storage.Remove(pos); err != nil {
		return false, errors.Wrap(err, "writing")
	}

	// Don't update the cache if nothing changed.
	if !changed {
		return changed, nil
	}

	// Invalidate block checksum.
	delete(f.checksums, int(rowID/HashBlockSize))

	// Increment number of operations until snapshot is required.
	if err := f.incrementOpN(); err != nil {
		return false, errors.Wrap(err, "incrementing")
	}

	// Get the row from cache or fragment.storage.
	row := f.unprotectedRow(rowID)
	row.clearBit(columnID)

	// Update the cache.
	f.cache.Add(rowID, row.Count())

	f.stats.Count("clearBit", 1, 1.0)

	return changed, nil
}

// setRow replaces an existing row (specified by rowID) with the given
// Row. This updates both the on-disk storage and the in-cache bitmap.
func (f *fragment) setRow(row *Row, rowID uint64) (bool, error) {
	f.mu.Lock()
	defer f.mu.Unlock()
	return f.unprotectedSetRow(row, rowID)
}

func (f *fragment) unprotectedSetRow(row *Row, rowID uint64) (changed bool, err error) {
	// TODO: In order to return `changed`, we need to first compare
	// the existing row with the given row. Determine if the overhead
	// of this is worth having `changed`.
	// For now we will assume changed is always true.
	changed = true

	// First container of the row in storage.
	headContainerKey := rowID << shardVsContainerExponent

	// Remove every existing container in the row.
	for i := uint64(0); i < (1 << shardVsContainerExponent); i++ {
		f.storage.Containers.Remove(headContainerKey + i)
	}

	// From the given row, get the rowSegment for this shard.
	seg := row.segment(f.shard)
	if seg == nil {
		return changed, nil
	}

	// Put each container from rowSegment to fragment storage.
	citer, _ := seg.data.Containers.Iterator(f.shard << shardVsContainerExponent)
	for citer.Next() {
		k, c := citer.Value()
		f.storage.Containers.Put(headContainerKey+(k%(1<<shardVsContainerExponent)), c)
	}

	// Update the row in cache.
	n := f.storage.CountRange(rowID*ShardWidth, (rowID+1)*ShardWidth)
	f.cache.BulkAdd(rowID, n)

	// Snapshot storage.
	if err := f.snapshot(); err != nil {
		return false, errors.Wrap(err, "snapshotting")
	}

	f.stats.Count("setRow", 1, 1.0)

	return changed, nil
}

// ClearRow clears a row for a given rowID within the fragment.
// This updates both the on-disk storage and the in-cache bitmap.
func (f *fragment) clearRow(rowID uint64) (bool, error) {
	f.mu.Lock()
	defer f.mu.Unlock()
	return f.unprotectedClearRow(rowID)
}

func (f *fragment) unprotectedClearRow(rowID uint64) (changed bool, err error) {
	changed = false

	// First container of the row in storage.
	headContainerKey := rowID << shardVsContainerExponent

	// Remove every container in the row.
	for i := uint64(0); i < (1 << shardVsContainerExponent); i++ {
		k := headContainerKey + i
		// Technically we could bypass the Get() call and only
		// call Remove(), but the Get() gives us the ability
		// to return true if any existing data was removed.
		if cont := f.storage.Containers.Get(k); cont != nil {
			f.storage.Containers.Remove(k)
			changed = true
		}
	}

	// Clear the row in cache.
	f.cache.Add(rowID, 0)

	// Snapshot storage.
	if err := f.snapshot(); err != nil {
		return false, errors.Wrap(err, "snapshotting")
	}

	f.stats.Count("clearRow", 1, 1.0)

	return changed, nil
}

func (f *fragment) bit(rowID, columnID uint64) (bool, error) {
	pos, err := f.pos(rowID, columnID)
	if err != nil {
		return false, err
	}
	return f.storage.Contains(pos), nil
}

// value uses a column of bits to read a multi-bit value.
func (f *fragment) value(columnID uint64, bitDepth uint) (value uint64, exists bool, err error) {
	f.mu.Lock()
	defer f.mu.Unlock()

	// If existence bit is unset then ignore remaining bits.
	if v, err := f.bit(uint64(bitDepth), columnID); err != nil {
		return 0, false, errors.Wrap(err, "getting existence bit")
	} else if !v {
		return 0, false, nil
	}

	// Compute other bits into a value.
	for i := uint(0); i < bitDepth; i++ {
		if v, err := f.bit(uint64(i), columnID); err != nil {
			return 0, false, errors.Wrapf(err, "getting value bit %d", i)
		} else if v {
			value |= (1 << i)
		}
	}

	return value, true, nil
}

// clearValue uses a column of bits to clear a multi-bit value.
func (f *fragment) clearValue(columnID uint64, bitDepth uint, value uint64) (changed bool, err error) {
	return f.setValueBase(columnID, bitDepth, value, true)
}

// setValue uses a column of bits to set a multi-bit value.
func (f *fragment) setValue(columnID uint64, bitDepth uint, value uint64) (changed bool, err error) {
	return f.setValueBase(columnID, bitDepth, value, false)
}

func (f *fragment) setValueBase(columnID uint64, bitDepth uint, value uint64, clear bool) (changed bool, err error) {
	f.mu.Lock()
	defer f.mu.Unlock()

	for i := uint(0); i < bitDepth; i++ {
		if value&(1<<i) != 0 {
			if c, err := f.unprotectedSetBit(uint64(i), columnID); err != nil {
				return changed, err
			} else if c {
				changed = true
			}
		} else {
			if c, err := f.unprotectedClearBit(uint64(i), columnID); err != nil {
				return changed, err
			} else if c {
				changed = true
			}
		}
	}

	// Mark value as set (or cleared).
	if clear {
		if c, err := f.unprotectedClearBit(uint64(bitDepth), columnID); err != nil {
			return changed, errors.Wrap(err, "clearing not-null")
		} else if c {
			changed = true
		}
	} else {
		if c, err := f.unprotectedSetBit(uint64(bitDepth), columnID); err != nil {
			return changed, errors.Wrap(err, "marking not-null")
		} else if c {
			changed = true
		}
	}

	return changed, nil
}

// importSetValue is a more efficient SetValue just for imports.
func (f *fragment) importSetValue(columnID uint64, bitDepth uint, value uint64, clear bool) (changed bool, err error) { // nolint: unparam
	for i := uint(0); i < bitDepth; i++ {
		if value&(1<<i) != 0 {
			bit, err := f.pos(uint64(i), columnID)
			if err != nil {
				return changed, errors.Wrap(err, "getting set pos")
			}
			if c, err := f.storage.Add(bit); err != nil {
				return changed, errors.Wrap(err, "adding")
			} else if c {
				changed = true
			}
		} else {
			bit, err := f.pos(uint64(i), columnID)
			if err != nil {
				return changed, errors.Wrap(err, "getting clear pos")
			}
			if c, err := f.storage.Remove(bit); err != nil {
				return changed, errors.Wrap(err, "removing")
			} else if c {
				changed = true
			}
		}
	}

	// Mark value as set.
	p, err := f.pos(uint64(bitDepth), columnID)
	if err != nil {
		return changed, errors.Wrap(err, "getting not-null pos")
	}
	if clear {
		if c, err := f.storage.Remove(p); err != nil {
			return changed, errors.Wrap(err, "removing not-null from storage")
		} else if c {
			changed = true
		}
	} else {
		if c, err := f.storage.Add(p); err != nil {
			return changed, errors.Wrap(err, "adding not-null to storage")
		} else if c {
			changed = true
		}
	}

	return changed, nil
}

// sum returns the sum of a given bsiGroup as well as the number of columns involved.
// A bitmap can be passed in to optionally filter the computed columns.
func (f *fragment) sum(filter *Row, bitDepth uint) (sum, count uint64, err error) {
	// Compute count based on the existence row.
	consider := f.row(uint64(bitDepth))
	if filter != nil {
		consider = consider.Intersect(filter)
	}
	count = consider.Count()

	// Compute the sum based on the bit count of each row multiplied by the
	// place value of each row. For example, 10 bits in the 1's place plus
	// 4 bits in the 2's place plus 3 bits in the 4's place equals a total
	// sum of 30:
	//
	//   10*(2^0) + 4*(2^1) + 3*(2^2) = 30
	//
	var cnt uint64
	for i := uint(0); i < bitDepth; i++ {
		row := f.row(uint64(i))
		cnt = row.intersectionCount(consider)
		sum += (1 << i) * cnt
	}

	return sum, count, nil
}

// min returns the min of a given bsiGroup as well as the number of columns involved.
// A bitmap can be passed in to optionally filter the computed columns.
func (f *fragment) min(filter *Row, bitDepth uint) (min, count uint64, err error) {

	consider := f.row(uint64(bitDepth))
	if filter != nil {
		consider = consider.Intersect(filter)
	}

	// If there are no columns to consider, return early.
	if consider.Count() == 0 {
		return 0, 0, nil
	}

	for i := bitDepth; i > uint(0); i-- {
		ii := i - 1 // allow for uint range: (bitDepth-1) to 0
		row := f.row(uint64(ii))

		x := consider.Difference(row)
		count = x.Count()
		if count > 0 {
			consider = x
		} else {
			min += (1 << ii)
			if ii == 0 {
				count = consider.Count()
			}
		}
	}

	return min, count, nil
}

// max returns the max of a given bsiGroup as well as the number of columns involved.
// A bitmap can be passed in to optionally filter the computed columns.
func (f *fragment) max(filter *Row, bitDepth uint) (max, count uint64, err error) {

	consider := f.row(uint64(bitDepth))
	if filter != nil {
		consider = consider.Intersect(filter)
	}

	// If there are no columns to consider, return early.
	if consider.Count() == 0 {
		return 0, 0, nil
	}

	for i := bitDepth; i > uint(0); i-- {
		ii := i - 1 // allow for uint range: (bitDepth-1) to 0
		row := f.row(uint64(ii))

		x := row.Intersect(consider)
		count = x.Count()
		if count > 0 {
			max += (1 << ii)
			consider = x
		} else if ii == 0 {
			count = consider.Count()
		}
	}

	return max, count, nil
}

// rangeOp returns bitmaps with a bsiGroup value encoding matching the predicate.
func (f *fragment) rangeOp(op pql.Token, bitDepth uint, predicate uint64) (*Row, error) {
	switch op {
	case pql.EQ:
		return f.rangeEQ(bitDepth, predicate)
	case pql.NEQ:
		return f.rangeNEQ(bitDepth, predicate)
	case pql.LT, pql.LTE:
		return f.rangeLT(bitDepth, predicate, op == pql.LTE)
	case pql.GT, pql.GTE:
		return f.rangeGT(bitDepth, predicate, op == pql.GTE)
	default:
		return nil, ErrInvalidRangeOperation
	}
}

func (f *fragment) rangeEQ(bitDepth uint, predicate uint64) (*Row, error) {
	// Start with set of columns with values set.
	b := f.row(uint64(bitDepth))

	// Filter any bits that don't match the current bit value.
	for i := int(bitDepth - 1); i >= 0; i-- {
		row := f.row(uint64(i))
		bit := (predicate >> uint(i)) & 1

		if bit == 1 {
			b = b.Intersect(row)
		} else {
			b = b.Difference(row)
		}
	}

	return b, nil
}

func (f *fragment) rangeNEQ(bitDepth uint, predicate uint64) (*Row, error) {
	// Start with set of columns with values set.
	b := f.row(uint64(bitDepth))

	// Get the equal bitmap.
	eq, err := f.rangeEQ(bitDepth, predicate)
	if err != nil {
		return nil, err
	}

	// Not-null minus the equal bitmap.
	b = b.Difference(eq)

	return b, nil
}

func (f *fragment) rangeLT(bitDepth uint, predicate uint64, allowEquality bool) (*Row, error) {
	keep := NewRow()

	// Start with set of columns with values set.
	b := f.row(uint64(bitDepth))

	// Filter any bits that don't match the current bit value.
	leadingZeros := true
	for i := int(bitDepth - 1); i >= 0; i-- {
		row := f.row(uint64(i))
		bit := (predicate >> uint(i)) & 1

		// Remove any columns with higher bits set.
		if leadingZeros {
			if bit == 0 {
				b = b.Difference(row)
				continue
			} else {
				leadingZeros = false
			}
		}

		// Handle last bit differently.
		// If bit is zero then return only already kept columns.
		// If bit is one then remove any one columns.
		if i == 0 && !allowEquality {
			if bit == 0 {
				return keep, nil
			}
			return b.Difference(row.Difference(keep)), nil
		}

		// If bit is zero then remove all set columns not in excluded bitmap.
		if bit == 0 {
			b = b.Difference(row.Difference(keep))
			continue
		}

		// If bit is set then add columns for set bits to exclude.
		// Don't bother to compute this on the final iteration.
		if i > 0 {
			keep = keep.Union(b.Difference(row))
		}
	}

	return b, nil
}

func (f *fragment) rangeGT(bitDepth uint, predicate uint64, allowEquality bool) (*Row, error) {
	b := f.row(uint64(bitDepth))
	keep := NewRow()

	// Filter any bits that don't match the current bit value.
	for i := int(bitDepth - 1); i >= 0; i-- {
		row := f.row(uint64(i))
		bit := (predicate >> uint(i)) & 1

		// Handle last bit differently.
		// If bit is one then return only already kept columns.
		// If bit is zero then remove any unset columns.
		if i == 0 && !allowEquality {
			if bit == 1 {
				return keep, nil
			}
			return b.Difference(b.Difference(row).Difference(keep)), nil
		}

		// If bit is set then remove all unset columns not already kept.
		if bit == 1 {
			b = b.Difference(b.Difference(row).Difference(keep))
			continue
		}

		// If bit is unset then add columns with set bit to keep.
		// Don't bother to compute this on the final iteration.
		if i > 0 {
			keep = keep.Union(b.Intersect(row))
		}
	}

	return b, nil
}

// notNull returns the not-null row (stored at bitDepth).
func (f *fragment) notNull(bitDepth uint) (*Row, error) {
	return f.row(uint64(bitDepth)), nil
}

// rangeBetween returns bitmaps with a bsiGroup value encoding matching any value between predicateMin and predicateMax.
func (f *fragment) rangeBetween(bitDepth uint, predicateMin, predicateMax uint64) (*Row, error) {
	b := f.row(uint64(bitDepth))
	keep1 := NewRow() // GTE
	keep2 := NewRow() // LTE

	// Filter any bits that don't match the current bit value.
	for i := int(bitDepth - 1); i >= 0; i-- {
		row := f.row(uint64(i))
		bit1 := (predicateMin >> uint(i)) & 1
		bit2 := (predicateMax >> uint(i)) & 1

		// GTE predicateMin
		// If bit is set then remove all unset columns not already kept.
		if bit1 == 1 {
			b = b.Difference(b.Difference(row).Difference(keep1))
		} else {
			// If bit is unset then add columns with set bit to keep.
			// Don't bother to compute this on the final iteration.
			if i > 0 {
				keep1 = keep1.Union(b.Intersect(row))
			}
		}

		// LTE predicateMin
		// If bit is zero then remove all set bits not in excluded bitmap.
		if bit2 == 0 {
			b = b.Difference(row.Difference(keep2))
		} else {
			// If bit is set then add columns for set bits to exclude.
			// Don't bother to compute this on the final iteration.
			if i > 0 {
				keep2 = keep2.Union(b.Difference(row))
			}
		}
	}

	return b, nil
}

// pos translates the row ID and column ID into a position in the storage bitmap.
func (f *fragment) pos(rowID, columnID uint64) (uint64, error) {
	// Return an error if the column ID is out of the range of the fragment's shard.
	minColumnID := f.shard * ShardWidth
	if columnID < minColumnID || columnID >= minColumnID+ShardWidth {
		return 0, errors.New("column out of bounds")
	}
	return pos(rowID, columnID), nil
}

// forEachBit executes fn for every bit set in the fragment.
// Errors returned from fn are passed through.
func (f *fragment) forEachBit(fn func(rowID, columnID uint64) error) error {
	f.mu.Lock()
	defer f.mu.Unlock()

	var err error
	f.storage.ForEach(func(i uint64) {
		// Skip if an error has already occurred.
		if err != nil {
			return
		}

		// Invoke caller's function.
		err = fn(i/ShardWidth, (f.shard*ShardWidth)+(i%ShardWidth))
	})
	return err
}

// top returns the top rows from the fragment.
// If opt.Src is specified then only rows which intersect src are returned.
// If opt.FilterValues exist then the row attribute specified by field is matched.
func (f *fragment) top(opt topOptions) ([]Pair, error) {
	// Retrieve pairs. If no row ids specified then return from cache.
	pairs := f.topBitmapPairs(opt.RowIDs)

	// If row ids are provided, we don't want to truncate the result set
	if len(opt.RowIDs) > 0 {
		opt.N = 0
	}

	// Create a fast lookup of filter values.
	var filters map[interface{}]struct{}
	if opt.FilterName != "" && len(opt.FilterValues) > 0 {
		filters = make(map[interface{}]struct{})
		for _, v := range opt.FilterValues {
			filters[v] = struct{}{}
		}
	}

	// Use `tanimotoThreshold > 0` to indicate whether or not we are considering Tanimoto.
	var tanimotoThreshold uint64
	var minTanimoto, maxTanimoto float64
	var srcCount uint64
	if opt.TanimotoThreshold > 0 && opt.Src != nil {
		tanimotoThreshold = opt.TanimotoThreshold
		srcCount = opt.Src.Count()
		minTanimoto = float64(srcCount*tanimotoThreshold) / 100
		maxTanimoto = float64(srcCount*100) / float64(tanimotoThreshold)
	}

	// Iterate over rankings and add to results until we have enough.
	results := &pairHeap{}
	for _, pair := range pairs {
		rowID, cnt := pair.ID, pair.Count

		// Ignore empty rows.
		if cnt <= 0 {
			continue
		}

		// Check against either Tanimoto threshold or minimum threshold.
		if tanimotoThreshold > 0 {
			// Ignore counts outside of the Tanimoto min/max values.
			if float64(cnt) <= minTanimoto || float64(cnt) >= maxTanimoto {
				continue
			}
		} else {
			// Ignore counts less than MinThreshold.
			if cnt < opt.MinThreshold {
				continue
			}
		}

		// Apply filter, if set.
		if filters != nil {
			attr, err := f.RowAttrStore.Attrs(rowID)
			if err != nil {
				return nil, errors.Wrap(err, "getting attrs")
			} else if attr == nil {
				continue
			} else if attrValue := attr[opt.FilterName]; attrValue == nil {
				continue
			} else if _, ok := filters[attrValue]; !ok {
				continue
			}
		}

		// The initial n pairs should simply be added to the results.
		if opt.N == 0 || results.Len() < opt.N {
			// Calculate count and append.
			count := cnt
			if opt.Src != nil {
				count = opt.Src.intersectionCount(f.row(rowID))
			}
			if count == 0 {
				continue
			}

			// Check against either Tanimoto threshold or minimum threshold.
			if tanimotoThreshold > 0 {
				tanimoto := math.Ceil(float64(count*100) / float64(cnt+srcCount-count))
				if tanimoto <= float64(tanimotoThreshold) {
					continue
				}
			} else {
				if count < opt.MinThreshold {
					continue
				}
			}

			heap.Push(results, Pair{ID: rowID, Count: count})

			// If we reach the requested number of pairs and we are not computing
			// intersections then simply exit. If we are intersecting then sort
			// and then only keep pairs that are higher than the lowest count.
			if opt.N > 0 && results.Len() == opt.N {
				if opt.Src == nil {
					break
				}
			}

			continue
		}

		// Retrieve the lowest count we have.
		// If it's too low then don't try finding anymore pairs.
		threshold := results.Pairs[0].Count

		// If the row doesn't have enough columns set before the intersection
		// then we can assume that any remaining rows also have a count too low.
		if threshold < opt.MinThreshold || cnt < threshold {
			break
		}

		// Calculate the intersecting column count and skip if it's below our
		// last row in our current result set.
		count := opt.Src.intersectionCount(f.row(rowID))
		if count < threshold {
			continue
		}

		heap.Push(results, Pair{ID: rowID, Count: count})
	}

	//Pop first opt.N elements out of heap
	r := make(Pairs, results.Len())
	x := results.Len()
	i := 1
	for results.Len() > 0 {
		r[x-i] = heap.Pop(results).(Pair)
		i++
	}
	return r, nil
}

func (f *fragment) topBitmapPairs(rowIDs []uint64) []bitmapPair {
	// Don't retrieve from storage if CacheTypeNone.
	if f.CacheType == CacheTypeNone {
		return f.cache.Top()
	}
	// If no specific rows are requested, retrieve top rows.
	if len(rowIDs) == 0 {
		f.mu.Lock()
		defer f.mu.Unlock()
		f.cache.Invalidate()
		return f.cache.Top()
	}

	// Otherwise retrieve specific rows.
	pairs := make([]bitmapPair, 0, len(rowIDs))
	for _, rowID := range rowIDs {
		// Look up cache first, if available.
		if n := f.cache.Get(rowID); n > 0 {
			pairs = append(pairs, bitmapPair{
				ID:    rowID,
				Count: n,
			})
			continue
		}

		row := f.row(rowID)
		if row.Count() > 0 {
			// Otherwise load from storage.
			pairs = append(pairs, bitmapPair{
				ID:    rowID,
				Count: row.Count(),
			})
		}
	}
	sort.Sort(bitmapPairs(pairs))
	return pairs
}

// topOptions represents options passed into the Top() function.
type topOptions struct {
	// Number of rows to return.
	N int

	// Bitmap to intersect with.
	Src *Row

	// Specific rows to filter against.
	RowIDs       []uint64
	MinThreshold uint64

	// Filter field name & values.
	FilterName        string
	FilterValues      []interface{}
	TanimotoThreshold uint64
}

// Checksum returns a checksum for the entire fragment.
// If two fragments have the same checksum then they have the same data.
func (f *fragment) Checksum() []byte {
	h := xxhash.New()
	for _, block := range f.Blocks() {
		h.Write(block.Checksum)
	}
	return h.Sum(nil)
}

// InvalidateChecksums clears all cached block checksums.
func (f *fragment) InvalidateChecksums() {
	f.mu.Lock()
	f.checksums = make(map[int][]byte)
	f.mu.Unlock()
}

// Blocks returns info for all blocks containing data.
func (f *fragment) Blocks() []FragmentBlock {
	f.mu.Lock()
	defer f.mu.Unlock()

	var a []FragmentBlock

	// Initialize the iterator.
	itr := f.storage.Iterator()
	itr.Seek(0)

	// Initialize block hasher.
	h := newBlockHasher()

	// Iterate over each value in the fragment.
	v, eof := itr.Next()
	if eof {
		return nil
	}
	blockID := int(v / (HashBlockSize * ShardWidth))
	for {
		// Check for multiple block checksums in a row.
		if n := f.readContiguousChecksums(&a, blockID); n > 0 {
			itr.Seek(uint64(blockID+n) * HashBlockSize * ShardWidth)
			v, eof = itr.Next()
			if eof {
				break
			}
			blockID = int(v / (HashBlockSize * ShardWidth))
			continue
		}

		// Reset hasher.
		h.blockID = blockID
		h.Reset()

		// Read all values for the block.
		for ; ; v, eof = itr.Next() {
			// Once we hit the next block, save the value for the next iteration.
			blockID = int(v / (HashBlockSize * ShardWidth))
			if blockID != h.blockID || eof {
				break
			}

			h.WriteValue(v)
		}

		// Cache checksum.
		chksum := h.Sum()
		f.checksums[h.blockID] = chksum

		// Append block.
		a = append(a, FragmentBlock{
			ID:       h.blockID,
			Checksum: chksum,
		})

		// Exit if we're at the end.
		if eof {
			break
		}
	}

	return a
}

// readContiguousChecksums appends multiple checksums in a row and returns the count added.
func (f *fragment) readContiguousChecksums(a *[]FragmentBlock, blockID int) (n int) {
	for i := 0; ; i++ {
		chksum := f.checksums[blockID+i]
		if chksum == nil {
			return i
		}

		*a = append(*a, FragmentBlock{
			ID:       blockID + i,
			Checksum: chksum,
		})
	}
}

// blockData returns bits in a block as row & column ID pairs.
func (f *fragment) blockData(id int) (rowIDs, columnIDs []uint64) {
	f.mu.Lock()
	defer f.mu.Unlock()
	f.storage.ForEachRange(uint64(id)*HashBlockSize*ShardWidth, (uint64(id)+1)*HashBlockSize*ShardWidth, func(i uint64) {
		rowIDs = append(rowIDs, i/ShardWidth)
		columnIDs = append(columnIDs, i%ShardWidth)
	})
	return rowIDs, columnIDs
}

// mergeBlock compares the block's bits and computes a diff with another set of block bits.
// The state of a bit is determined by consensus from all blocks being considered.
//
// For example, if 3 blocks are compared and two have a set bit and one has a
// cleared bit then the bit is considered cleared. The function returns the
// diff per incoming block so that all can be in sync.
func (f *fragment) mergeBlock(id int, data []pairSet) (sets, clears []pairSet, err error) {
	// Ensure that all pair sets are of equal length.
	for i := range data {
		if len(data[i].rowIDs) != len(data[i].columnIDs) {
			return nil, nil, fmt.Errorf("pair set mismatch(idx=%d): %d != %d", i, len(data[i].rowIDs), len(data[i].columnIDs))
		}
	}

	f.mu.Lock()
	defer f.mu.Unlock()

	// Track sets and clears for all blocks (including local).
	sets = make([]pairSet, len(data)+1)
	clears = make([]pairSet, len(data)+1)

	// Limit upper row/column pair.
	maxRowID := uint64(id+1) * HashBlockSize
	maxColumnID := uint64(ShardWidth)

	// Create buffered iterator for local block.
	itrs := make([]*bufIterator, 1, len(data)+1)
	itrs[0] = newBufIterator(
		newLimitIterator(
			newRoaringIterator(f.storage.Iterator()), maxRowID, maxColumnID,
		),
	)

	// Append buffered iterators for each incoming block.
	for i := range data {
		var itr iterator = newSliceIterator(data[i].rowIDs, data[i].columnIDs)
		itr = newLimitIterator(itr, maxRowID, maxColumnID)
		itrs = append(itrs, newBufIterator(itr))
	}

	// Seek to initial pair.
	for _, itr := range itrs {
		itr.Seek(uint64(id)*HashBlockSize, 0)
	}

	// Determine the number of blocks needed to meet consensus.
	// If there is an even split then a set is used.
	majorityN := (len(itrs) + 1) / 2

	// Iterate over all values in all iterators to determine differences.
	values := make([]bool, len(itrs))
	for {
		var min struct {
			rowID    uint64
			columnID uint64
		}

		// Find the lowest pair.
		var hasData bool
		for _, itr := range itrs {
			bid, pid, eof := itr.Peek()
			if eof { // no more data
				continue
			} else if !hasData { // first pair
				min.rowID, min.columnID, hasData = bid, pid, true
			} else if bid < min.rowID || (bid == min.rowID && pid < min.columnID) { // lower pair
				min.rowID, min.columnID = bid, pid
			}
		}

		// If all iterators are EOF then exit.
		if !hasData {
			break
		}

		// Determine consensus of point.
		var setN int
		for i, itr := range itrs {
			bid, pid, eof := itr.Next()

			values[i] = !eof && bid == min.rowID && pid == min.columnID
			if values[i] {
				setN++ // set
			} else {
				itr.Unread() // clear
			}
		}

		// Determine consensus value.
		newValue := setN >= majorityN

		// Add a diff for any node with a different value.
		for i := range itrs {
			// Value matches, ignore.
			if values[i] == newValue {
				continue
			}

			// Append to either the set or clear diff.
			if newValue {
				sets[i].rowIDs = append(sets[i].rowIDs, min.rowID)
				sets[i].columnIDs = append(sets[i].columnIDs, min.columnID)
			} else {
				clears[i].rowIDs = append(sets[i].rowIDs, min.rowID)
				clears[i].columnIDs = append(sets[i].columnIDs, min.columnID)
			}
		}
	}

	// Set local bits.
	for i := range sets[0].columnIDs {
		if _, err := f.unprotectedSetBit(sets[0].rowIDs[i], (f.shard*ShardWidth)+sets[0].columnIDs[i]); err != nil {
			return nil, nil, errors.Wrap(err, "setting")
		}
	}

	// Clear local bits.
	for i := range clears[0].columnIDs {
		if _, err := f.unprotectedClearBit(clears[0].rowIDs[i], (f.shard*ShardWidth)+clears[0].columnIDs[i]); err != nil {
			return nil, nil, errors.Wrap(err, "clearing")
		}
	}

	return sets[1:], clears[1:], nil
}

// bulkImport bulk imports a set of bits and then snapshots the storage.
// The cache is updated to reflect the new data.
func (f *fragment) bulkImport(rowIDs, columnIDs []uint64, options *ImportOptions) error {
	// Verify that there are an equal number of row ids and column ids.
	if len(rowIDs) != len(columnIDs) {
		return fmt.Errorf("mismatch of row/column len: %d != %d", len(rowIDs), len(columnIDs))
	}

	if f.mutexVector != nil && !options.Clear {
		return f.bulkImportMutex(rowIDs, columnIDs)
	}
	return f.bulkImportStandard(rowIDs, columnIDs, options)
}

// bulkImportStandard performs a bulk import on a standard fragment.
func (f *fragment) bulkImportStandard(rowIDs, columnIDs []uint64, options *ImportOptions) error {
	// Create a temporary bitmap which will be populated by rowIDs and columnIDs
	// and then merged into the existing fragment's bitmap.
	localBitmap := roaring.NewBitmap()

	// Disconnect op writer so we don't append updates.
	localBitmap.OpWriter = nil

	// rowSet maintains the set of rowIDs present in this import.
	// It allows the cache to be updated once per row, instead of once
	// per bit.
	rowSet := make(map[uint64]struct{})
	lastRowID := uint64(0)

	// Process every bit by writing to a local bitmap,
	// to be merged with fragment storage next.
	for i := range rowIDs {
		rowID, columnID := rowIDs[i], columnIDs[i]

		// Determine the position of the bit in the storage.
		pos, err := f.pos(rowID, columnID)
		if err != nil {
			return err
		}

		// Write to local storage.
		_, err = localBitmap.Add(pos)
		if err != nil {
			return err
		}

		// Reduce the StatsD rate for high volume stats
		f.stats.Count("ImportBit", 1, 0.0001)

		// Add row to rowSet.
		if i == 0 || rowID != lastRowID {
			lastRowID = rowID
			rowSet[rowID] = struct{}{}
		}
	}

	f.mu.Lock()
	defer f.mu.Unlock()

	// Merge localBitmap into fragment's existing data.
	var results *roaring.Bitmap
	if options.Clear {
		if f.storage.Count() > 0 {
			results = f.storage.Difference(localBitmap)
		} else {
			results = roaring.NewBitmap()
		}
	} else {
		if f.storage.Count() > 0 {
			results = f.storage.Union(localBitmap)
		} else {
			results = localBitmap
		}
	}

	// Update cache counts for all affected rows.
	for rowID := range rowSet {
		// Invalidate block checksum.
		delete(f.checksums, int(rowID/HashBlockSize))

		n := results.CountRange(rowID*ShardWidth, (rowID+1)*ShardWidth)
		f.cache.BulkAdd(rowID, n)
	}

	f.cache.Recalculate()
	return unprotectedWriteToFragment(f, results)
}

// bulkImportMutex performs a bulk import on a fragment while ensuring
// mutex restrictions. Because the mutex requirements must be checked
// against storage, this method must acquire a write lock on the fragment
// during the entire process, and it handles every bit independently.
func (f *fragment) bulkImportMutex(rowIDs, columnIDs []uint64) error {
	f.mu.Lock()
	defer f.mu.Unlock()

	// Disconnect op writer so we don't append updates.
	f.storage.OpWriter = nil

	// If an error occurs then reopen the storage.
	if err := func() error {
		// rowSet maintains the set of rowIDs present in this import.
		// It allows the cache to be updated once per row, instead of once
		// per bit.
		rowSet := make(map[uint64]struct{})
		lastRowID := uint64(0)

		// Process every bit.
		for i := range rowIDs {
			rowID, columnID := rowIDs[i], columnIDs[i]

			// Handle mutex vector (i.e. clear an existing row).
			if existingRowID, found, err := f.mutexVector.Get(columnID); err != nil {
				return errors.Wrap(err, "getting mutex vector data")
			} else if found && existingRowID != rowID {
				// Determine the position of the bit in the storage.
				pos, err := f.pos(existingRowID, columnID)
				if err != nil {
					return err
				}

				// Clear storage.
				_, err = f.storage.Remove(pos)
				if err != nil {
					return err
				}

				rowSet[existingRowID] = struct{}{}
			}

			// Determine the position of the bit in the storage.
			pos, err := f.pos(rowID, columnID)
			if err != nil {
				return err
			}

			// Write to storage.
			_, err = f.storage.Add(pos)
			if err != nil {
				return err
			}

			// Reduce the StatsD rate for high volume stats
			f.stats.Count("ImportBit", 1, 0.0001)

			// Add row to rowSet.
			if i == 0 || rowID != lastRowID {
				lastRowID = rowID
				rowSet[rowID] = struct{}{}
			}

			// Invalidate block checksum.
			delete(f.checksums, int(rowID/HashBlockSize))
		}

		// Update cache counts for all rows.
		for rowID := range rowSet {
			// Import should ALWAYS have row() load a new bm from fragment.storage
			// because the row that's in rowCache hasn't been updated with
			// this import's data.
			f.cache.BulkAdd(rowID, f.unprotectedRow(rowID).Count())
		}

		f.cache.Invalidate()

		return nil
	}(); err != nil {
		_ = f.closeStorage()
		_ = f.openStorage()
		return err
	}

	// Write the storage to disk and reload.
	if err := f.snapshot(); err != nil {
		return err
	}

	return nil
}

// importValue bulk imports a set of range-encoded values.
func (f *fragment) importValue(columnIDs, values []uint64, bitDepth uint, clear bool) error {
	f.mu.Lock()
	defer f.mu.Unlock()
	// Verify that there are an equal number of column ids and values.
	if len(columnIDs) != len(values) {
		return fmt.Errorf("mismatch of column/value len: %d != %d", len(columnIDs), len(values))
	}

	f.storage.OpWriter = nil
	// Process every value.
	// If an error occurs then reopen the storage.
	if err := func() error {
		for i := range columnIDs {
			columnID, value := columnIDs[i], values[i]

			_, err := f.importSetValue(columnID, bitDepth, value, clear)
			if err != nil {
				return errors.Wrap(err, "setting")
			}
		}
		return nil
	}(); err != nil {
		_ = f.closeStorage()
		_ = f.openStorage()
		return err
	}
	if err := f.snapshot(); err != nil {
		return errors.Wrap(err, "snapshotting")
	}
	return nil
}

// importRoaring imports from the official roaring data format defined at
// https://github.com/RoaringBitmap/RoaringFormatSpec or from pilosa's version
// of the roaring format. The cache is updated to reflect the new data.
func (f *fragment) importRoaring(data []byte, clear bool) error {
	f.mu.Lock()
	defer f.mu.Unlock()
	bm := roaring.NewBitmap()
	err := bm.UnmarshalBinary(data)
	if err != nil {
		return err
	}

	// get a list of keys in order to update the cache
	iter, _ := bm.Containers.Iterator(0)
	rowSet := make([]uint64, 0)
	var lastRow uint64 = math.MaxUint64

	for iter.Next() {
		key, _ := iter.Value()

		// virtual row for the current container
		vRow := key >> shardVsContainerExponent

		// skip dups
		if vRow == lastRow {
			continue
		}
		rowSet = append(rowSet, vRow)
		lastRow = vRow
	}

	if clear {
		bm = f.storage.Difference(bm)
	} else {
		if f.storage.Count() > 0 {
			bm = f.storage.Union(bm)
		}
	}

	for _, rowID := range rowSet {
		n := bm.CountRange(rowID*ShardWidth, (rowID+1)*ShardWidth)
		f.cache.BulkAdd(rowID, n)
	}
	f.cache.Recalculate()

	err = unprotectedWriteToFragment(f, bm)
	return err
}

// incrementOpN increase the operation count by one.
// If the count exceeds the maximum allowed then a snapshot is performed.
func (f *fragment) incrementOpN() error {
	f.opN++
	if f.opN <= f.MaxOpN {
		return nil
	}

	if err := f.snapshot(); err != nil {
		return fmt.Errorf("snapshot: %s", err)
	}
	return nil
}

// Snapshot writes the storage bitmap to disk and reopens it.
func (f *fragment) Snapshot() error {
	f.mu.Lock()
	defer f.mu.Unlock()
	return f.snapshot()
}
func track(start time.Time, message string, stats stats.StatsClient, logger logger.Logger) {
	elapsed := time.Since(start)
	logger.Printf("%s took %s", message, elapsed)
	stats.Histogram("snapshot", elapsed.Seconds(), 1.0)
}

func (f *fragment) snapshot() error {
	return unprotectedWriteToFragment(f, f.storage)
}

// unprotectedWriteToFragment writes the fragment f with bm as the data. It is unprotected, and
// f.mu must be locked when calling it.
func unprotectedWriteToFragment(f *fragment, bm *roaring.Bitmap) error { // nolint: interfacer

	completeMessage := fmt.Sprintf("fragment: snapshot complete %s/%s/%s/%d", f.index, f.field, f.view, f.shard)
	start := time.Now()
	defer track(start, completeMessage, f.stats, f.Logger)

	// Create a temporary file to snapshot to.
	snapshotPath := f.path + snapshotExt
	file, err := os.Create(snapshotPath)
	if err != nil {
		return fmt.Errorf("create snapshot file: %s", err)
	}
	defer file.Close()

	// Write storage to snapshot.
	bw := bufio.NewWriter(file)
	if _, err := bm.WriteTo(bw); err != nil {
		return fmt.Errorf("snapshot write to: %s", err)
	}

	if err := bw.Flush(); err != nil {
		return fmt.Errorf("flush: %s", err)
	}

	// Close current storage.
	if err := f.closeStorage(); err != nil {
		return fmt.Errorf("close storage: %s", err)
	}

	// Move snapshot to data file location.
	if err := os.Rename(snapshotPath, f.path); err != nil {
		return fmt.Errorf("rename snapshot: %s", err)
	}

	// Reopen storage.
	if err := f.openStorage(); err != nil {
		return fmt.Errorf("open storage: %s", err)
	}

	// Reset operation count.
	f.opN = 0

	return nil
}

// RecalculateCache rebuilds the cache regardless of invalidate time delay.
func (f *fragment) RecalculateCache() {
	f.mu.Lock()
	f.cache.Recalculate()
	f.mu.Unlock()
}

// FlushCache writes the cache data to disk.
func (f *fragment) FlushCache() error {
	f.mu.Lock()
	defer f.mu.Unlock()
	return f.flushCache()
}

func (f *fragment) flushCache() error {
	if f.cache == nil {
		return nil
	}

	if f.CacheType == CacheTypeNone {
		return nil
	}

	// Retrieve a list of row ids from the cache.
	ids := f.cache.IDs()

	// Marshal cache data to bytes.
	buf, err := proto.Marshal(&internal.Cache{IDs: ids})
	if err != nil {
		return errors.Wrap(err, "marshalling")
	}

	// Write to disk.
	if err := ioutil.WriteFile(f.cachePath(), buf, 0666); err != nil {
		return errors.Wrap(err, "writing")
	}

	return nil
}

// WriteTo writes the fragment's data to w.
func (f *fragment) WriteTo(w io.Writer) (n int64, err error) {
	// Force cache flush.
	if err := f.FlushCache(); err != nil {
		return 0, errors.Wrap(err, "flushing cache")
	}

	// Write out data and cache to a tar archive.
	tw := tar.NewWriter(w)
	if err := f.writeStorageToArchive(tw); err != nil {
		return 0, fmt.Errorf("write storage: %s", err)
	}
	if err := f.writeCacheToArchive(tw); err != nil {
		return 0, fmt.Errorf("write cache: %s", err)
	}
	return 0, nil
}

func (f *fragment) writeStorageToArchive(tw *tar.Writer) error {
	// Open separate file descriptor to read from.
	file, err := os.Open(f.path)
	if err != nil {
		return errors.Wrap(err, "opening file")
	}
	defer file.Close()

	// Retrieve the current file size under lock so we don't read
	// while an operation is appending to the end.
	var sz int64
	if err := func() error {
		f.mu.Lock()
		defer f.mu.Unlock()

		fi, err := file.Stat()
		if err != nil {
			return errors.Wrap(err, "statting")
		}
		sz = fi.Size()

		return nil
	}(); err != nil {
		return err
	}

	// Write archive header.
	if err := tw.WriteHeader(&tar.Header{
		Name:    "data",
		Mode:    0600,
		Size:    sz,
		ModTime: time.Now(),
	}); err != nil {
		return errors.Wrap(err, "writing header")
	}

	// Copy the file up to the last known size.
	// This is done outside the lock because the storage format is append-only.
	if _, err := io.CopyN(tw, file, sz); err != nil {
		return errors.Wrap(err, "copying")
	}
	return nil
}

func (f *fragment) writeCacheToArchive(tw *tar.Writer) error {
	f.mu.Lock()
	defer f.mu.Unlock()

	// Read cache into buffer.
	buf, err := ioutil.ReadFile(f.cachePath())
	if os.IsNotExist(err) {
		return nil
	} else if err != nil {
		return errors.Wrap(err, "reading cache")
	}

	// Write archive header.
	if err := tw.WriteHeader(&tar.Header{
		Name:    "cache",
		Mode:    0600,
		Size:    int64(len(buf)),
		ModTime: time.Now(),
	}); err != nil {
		return errors.Wrap(err, "writing header")
	}

	// Write data to archive.
	if _, err := tw.Write(buf); err != nil {
		return errors.Wrap(err, "writing")
	}
	return nil
}

// ReadFrom reads a data file from r and loads it into the fragment.
func (f *fragment) ReadFrom(r io.Reader) (n int64, err error) {
	f.mu.Lock()
	defer f.mu.Unlock()

	tr := tar.NewReader(r)
	for {
		// Read next tar header.
		hdr, err := tr.Next()
		if err == io.EOF {
			break
		} else if err != nil {
			return 0, errors.Wrap(err, "opening")
		}

		// Process file based on file name.
		switch hdr.Name {
		case "data":
			if err := f.readStorageFromArchive(tr); err != nil {
				return 0, errors.Wrap(err, "reading storage")
			}
		case "cache":
			if err := f.readCacheFromArchive(tr); err != nil {
				return 0, errors.Wrap(err, "reading cache")
			}
		default:
			return 0, fmt.Errorf("invalid fragment archive file: %s", hdr.Name)
		}
	}

	return 0, nil
}

func (f *fragment) readStorageFromArchive(r io.Reader) error {
	// Create a temporary file to copy into.
	path := f.path + copyExt
	file, err := os.Create(path)
	if err != nil {
		return errors.Wrap(err, "creating directory")
	}
	defer file.Close()

	// Copy reader into temporary path.
	if _, err = io.Copy(file, r); err != nil {
		return errors.Wrap(err, "copying")
	}

	// Close current storage.
	if err := f.closeStorage(); err != nil {
		return errors.Wrap(err, "closing")
	}

	// Move snapshot to data file location.
	if err := os.Rename(path, f.path); err != nil {
		return errors.Wrap(err, "renaming")
	}

	// Reopen storage.
	if err := f.openStorage(); err != nil {
		return errors.Wrap(err, "opening")
	}

	return nil
}

func (f *fragment) readCacheFromArchive(r io.Reader) error {
	// Slurp data from reader and write to disk.
	buf, err := ioutil.ReadAll(r)
	if err != nil {
		return errors.Wrap(err, "reading")
	} else if err := ioutil.WriteFile(f.cachePath(), buf, 0666); err != nil {
		return errors.Wrap(err, "writing")
	}

	// Re-open cache.
	if err := f.openCache(); err != nil {
		return errors.Wrap(err, "opening")
	}

	return nil
}

// rowFilter is a function signature for controlling iteration over containers
// in a fragment. It will be invoked on each container found and returns two
// booleans. The first is whether the row this container is in should be
// included or skipped, and the second is whether to stop processing or
// continue.
type rowFilter func(rowID, key uint64, c *roaring.Container) (include, done bool)

// filterWithLimit returns a filter which will only allow a limited number of
// rows to be returned. It should be applied last so that it is only called (and
// therefore only updates its internal state) if the row is being included by
// every other filter.
func filterWithLimit(limit uint64) rowFilter {
	return func(rowID, key uint64, c *roaring.Container) (include, done bool) {
		if limit > 0 {
			limit--
			return true, false
		}
		return false, true
	}
}

func filterColumn(col uint64) rowFilter {
	return func(rowID, key uint64, c *roaring.Container) (include, done bool) {
		colID := col % ShardWidth
		colKey := ((rowID * ShardWidth) + colID) >> 16
		colVal := uint16(colID & 0xFFFF) // columnID within the container
		return colKey == key && c.Contains(colVal), false
	}
}

// TODO: this works, but it would be more performant if the fragment could seek
// to the next row in the rows list rather than asking the filter for each
// container serially. The container iterator would need to expose a seek
// method, and the rowFilter would need some way of communicating to
// fragment.rows what the next rowID to seek to is.
func filterWithRows(rows []uint64) rowFilter {
	loc := 0
	return func(rowID, key uint64, c *roaring.Container) (include, done bool) {
		if loc >= len(rows) {
			return false, true
		}
		i := sort.Search(len(rows[loc:]), func(i int) bool {
			return rows[loc+i] >= rowID
		})
		loc += i
		if loc >= len(rows) {
			return false, true
		}
		if rows[loc] == rowID {
			if loc == len(rows)-1 {
				done = true
			}
			return true, done
		}
		return false, false
	}
}

// rows returns all rows starting from 'start'. Filters will be applied in
// order. All filters must return true to include the row. Once a row is
// included, further containers in that row will be skipped. So, for a row to be
// included, there must be one container in that row where all filters return
// true. For a row to be skipped, at least one filter must return false for each
// container in that row (it need not be the same filter for each). Any filter
// returning done == true will cause processing to stop after all filters for
// this container have been processed. The rows accumulated up to this point
// (including this row if all filters passed) will be returned.
func (f *fragment) rows(start uint64, filters ...rowFilter) []uint64 {
	startKey := rowToKey(start)
	i, _ := f.storage.Containers.Iterator(startKey)
	rows := make([]uint64, 0)
	var lastRow uint64 = math.MaxUint64

	// Loop over the existing containers.
	for i.Next() {
		key, c := i.Value()

		// virtual row for the current container
		vRow := key >> shardVsContainerExponent

		// skip dups
		if vRow == lastRow {
			continue
		}

		// apply filters
		addRow, done := true, false
		for _, filter := range filters {
			var d bool
			addRow, d = filter(vRow, key, c)
			done = done || d
			if !addRow {
				break
			}
		}
		if addRow {
			lastRow = vRow
			rows = append(rows, vRow)
		}
		if done {
			return rows
		}
	}
	return rows
}

type rowIterator struct {
	f      *fragment
	rowIDs []uint64
	cur    int
	wrap   bool
}

func (f *fragment) rowIterator(wrap bool, filters ...rowFilter) *rowIterator {
	return &rowIterator{
		f:      f,
		rowIDs: f.rows(0, filters...), // TODO: this may be memory intensive in high cardinality cases
		wrap:   wrap,
	}
}

func (ri *rowIterator) Seek(rowID uint64) {
	idx := sort.Search(len(ri.rowIDs), func(i int) bool {
		return ri.rowIDs[i] >= rowID
	})
	ri.cur = idx
}

func (ri *rowIterator) Next() (r *Row, rowID uint64, wrapped bool) {
	if ri.cur >= len(ri.rowIDs) {
		if !ri.wrap || len(ri.rowIDs) == 0 {
			return nil, 0, true
		}
		ri.Seek(0)
		wrapped = true
	}
	rowID = ri.rowIDs[ri.cur]
	r = ri.f.row(rowID)
	ri.cur += 1
	return r, rowID, wrapped
}

// FragmentBlock represents info about a subsection of the rows in a block.
// This is used for comparing data in remote blocks for active anti-entropy.
type FragmentBlock struct {
	ID       int    `json:"id"`
	Checksum []byte `json:"checksum"`
}

type blockHasher struct {
	blockID int
	buf     [8]byte
	hash    hash.Hash
}

func newBlockHasher() blockHasher {
	return blockHasher{
		blockID: -1,
		hash:    xxhash.New(),
	}
}
func (h *blockHasher) Reset() {
	h.hash.Reset()
}

func (h *blockHasher) Sum() []byte {
	return h.hash.Sum(nil)[:]
}

func (h *blockHasher) WriteValue(v uint64) {
	binary.BigEndian.PutUint64(h.buf[:], v)
	h.hash.Write(h.buf[:])
}

// fragmentSyncer syncs a local fragment to one on a remote host.
type fragmentSyncer struct {
	Fragment *fragment

	Node    *Node
	Cluster *cluster

	Closing <-chan struct{}
}

// isClosing returns true if the closing channel is closed.
func (s *fragmentSyncer) isClosing() bool {
	select {
	case <-s.Closing:
		return true
	default:
		return false
	}
}

// syncFragment compares checksums for the local and remote fragments and
// then merges any blocks which have differences.
func (s *fragmentSyncer) syncFragment() error {
	span, ctx := tracing.StartSpanFromContext(context.Background(), "FragmentSyncer.syncFragment")
	defer span.Finish()

	// Determine replica set.
	nodes := s.Cluster.shardNodes(s.Fragment.index, s.Fragment.shard)
	if len(nodes) == 1 {
		return nil
	}

	// Create a set of blocks.
	blockSets := make([][]FragmentBlock, 0, len(nodes))
	for _, node := range nodes {
		// Read local blocks.
		if node.ID == s.Node.ID {
			b := s.Fragment.Blocks()
			blockSets = append(blockSets, b)
			continue
		}

		// Retrieve remote blocks.
		blocks, err := s.Cluster.InternalClient.FragmentBlocks(ctx, &node.URI, s.Fragment.index, s.Fragment.field, s.Fragment.view, s.Fragment.shard)
		if err != nil && err != ErrFragmentNotFound {
			return errors.Wrap(err, "getting blocks")
		}
		blockSets = append(blockSets, blocks)

		// Verify sync is not prematurely closing.
		if s.isClosing() {
			return nil
		}
	}

	// Iterate over all blocks and find differences.
	checksums := make([][]byte, len(nodes))
	for {
		// Find min block id.
		blockID := -1
		for _, blocks := range blockSets {
			if len(blocks) == 0 {
				continue
			} else if blockID == -1 || blocks[0].ID < blockID {
				blockID = blocks[0].ID
			}
		}

		// Exit loop if no blocks are left.
		if blockID == -1 {
			break
		}

		// Read the checksum for the current block.
		for i, blocks := range blockSets {
			// Clear checksum if the next block for the node doesn't match current ID.
			if len(blocks) == 0 || blocks[0].ID != blockID {
				checksums[i] = nil
				continue
			}

			// Otherwise set checksum and move forward.
			checksums[i] = blocks[0].Checksum
			blockSets[i] = blockSets[i][1:]
		}

		// Ignore if all the blocks on each node match.
		if byteSlicesEqual(checksums) {
			continue
		}
		// Synchronize block.
		if err := s.syncBlock(blockID); err != nil {
			return fmt.Errorf("sync block: id=%d, err=%s", blockID, err)
		}
		s.Fragment.stats.Count("BlockRepair", 1, 1.0)
	}

	return nil
}

// syncBlock sends and receives all rows for a given block.
// Returns an error if any remote hosts are unreachable.
func (s *fragmentSyncer) syncBlock(id int) error {
	span, ctx := tracing.StartSpanFromContext(context.Background(), "FragmentSyncer.syncBlock")
	defer span.Finish()

	f := s.Fragment

	// Read pairs from each remote block.
	var uris []*URI
	var pairSets []pairSet
	for _, node := range s.Cluster.shardNodes(f.index, f.shard) {
		if s.Node.ID == node.ID {
			continue
		}

		// Verify sync is not prematurely closing.
		if s.isClosing() {
			return nil
		}

		uri := &node.URI
		uris = append(uris, uri)

		// Only sync the standard block.
		rowIDs, columnIDs, err := s.Cluster.InternalClient.BlockData(ctx, &node.URI, f.index, f.field, f.view, f.shard, id)
		if err != nil {
			return errors.Wrap(err, "getting block")
		}

		pairSets = append(pairSets, pairSet{
			columnIDs: columnIDs,
			rowIDs:    rowIDs,
		})
	}

	// Verify sync is not prematurely closing.
	if s.isClosing() {
		return nil
	}

	// Merge blocks together.
	sets, clears, err := f.mergeBlock(id, pairSets)
	if err != nil {
		return errors.Wrap(err, "merging")
	}

	// Write updates to remote blocks.
	for i := 0; i < len(uris); i++ {
		set, clear := sets[i], clears[i]

		// Handle Sets.
		if len(set.columnIDs) > 0 {
			setData, err := bitsToRoaringData(set)
			if err != nil {
				return errors.Wrap(err, "converting bits to roaring data (set)")
			}

			setReq := &ImportRoaringRequest{
				Clear: false,
				Views: map[string][]byte{cleanViewName(f.view): setData},
			}

			if err := s.Cluster.InternalClient.ImportRoaring(ctx, uris[i], f.index, f.field, f.shard, true, setReq); err != nil {
				return errors.Wrap(err, "sending roaring data (set)")
			}
		}

		// Handle Clears.
		if len(clear.columnIDs) > 0 {
			clearData, err := bitsToRoaringData(clear)
			if err != nil {
				return errors.Wrap(err, "converting bits to roaring data (clear)")
			}

			clearReq := &ImportRoaringRequest{
				Clear: true,
				Views: map[string][]byte{"": clearData},
			}

			if err := s.Cluster.InternalClient.ImportRoaring(ctx, uris[i], f.index, f.field, f.shard, true, clearReq); err != nil {
				return errors.Wrap(err, "sending roaring data (clear)")
			}
		}
	}

	return nil
}

// cleanViewName converts a viewname into the equivalent
// string required by the external api. Because views are
// not exposed externally, the conversion looks like this:
// "standard" -> ""
// "standard_YYYYMMDD" -> "YYYYMMDD"
// "other" -> "other" (there is currently not a use for this)
func cleanViewName(v string) string {
	viewPrefix := viewStandard + "_"
	if strings.HasPrefix(v, viewPrefix) {
		return v[len(viewPrefix):]
	} else if v == viewStandard {
		return ""
	}
	return v
}

// bitsToRoaringData converts a pairSet into a roaring.Bitmap
// which represents the data within a single shard.
func bitsToRoaringData(ps pairSet) ([]byte, error) {
	bmp := roaring.NewBitmap()
	for j := 0; j < len(ps.columnIDs); j++ {
		bmp.DirectAdd(ps.rowIDs[j]*ShardWidth + (ps.columnIDs[j] % ShardWidth))
	}

	var buf bytes.Buffer
	_, err := bmp.WriteTo(&buf)
	if err != nil {
		return nil, errors.Wrap(err, "writing to buffer")
	}

	return buf.Bytes(), nil
}

func madvise(b []byte, advice int) error { // nolint: unparam
	_, _, err := syscall.Syscall(syscall.SYS_MADVISE, uintptr(unsafe.Pointer(&b[0])), uintptr(len(b)), uintptr(advice))
	if err != 0 {
		return err
	}
	return nil
}

// pairSet is a list of equal length row and column id lists.
type pairSet struct {
	rowIDs    []uint64
	columnIDs []uint64
}

// byteSlicesEqual returns true if all slices are equal.
func byteSlicesEqual(a [][]byte) bool {
	if len(a) == 0 {
		return true
	}

	for _, v := range a[1:] {
		if !bytes.Equal(a[0], v) {
			return false
		}
	}
	return true
}

// pos returns the row position of a row/column pair.
func pos(rowID, columnID uint64) uint64 {
	return (rowID * ShardWidth) + (columnID % ShardWidth)
}

// vector stores the mapping of colID to rowID.
// It's used for a mutex field type.
type vector interface {
	Get(colID uint64) (uint64, bool, error)
}

// rowsVector implements the vector interface by looking
// at row data as needed.
type rowsVector struct {
	f *fragment
}

// newRowsVector returns a rowsVector for a given fragment.
func newRowsVector(f *fragment) *rowsVector {
	return &rowsVector{
		f: f,
	}
}

// Get returns the rowID associated to the given colID.
// Additionally, it returns true if a value was found,
// otherwise it returns false.
func (v *rowsVector) Get(colID uint64) (uint64, bool, error) {
	rows := v.f.rows(0, filterColumn(colID))
	if len(rows) > 1 {
		return 0, false, errors.New("found multiple row values for column")
	} else if len(rows) == 1 {
		return rows[0], true, nil
	}
	return 0, false, nil
}

// rowToKey converts a Pilosa row ID to the key of the container which starts
// that row in the bitmap which represents this entire fragment. A fragment is
// all the rows within a shard within a field concatenated together.
func rowToKey(rowID uint64) (key uint64) {
	return rowID * (ShardWidth / containerWidth)
}

// boolVector implements the vector interface by looking
// at data in rows 0 and 1.
type boolVector struct {
	f *fragment
}

// newBoolVector returns a boolVector for a given fragment.
func newBoolVector(f *fragment) *boolVector {
	return &boolVector{
		f: f,
	}
}

// Get returns the rowID associated to the given colID.
// Additionally, it returns true if a value was found,
// otherwise it returns false.
func (v *boolVector) Get(colID uint64) (uint64, bool, error) {
	rows := v.f.rows(0, filterColumn(colID))
	if len(rows) > 1 {
		return 0, false, errors.New("found multiple row values for column")
	} else if len(rows) == 1 {
		switch rows[0] {
		case falseRowID, trueRowID:
			return rows[0], true, nil
		default:
			return 0, false, errors.New("found non-boolean value")
		}
	}
	return 0, false, nil
}