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bsi64.go
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bsi64.go
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package roaring64
import (
"fmt"
"io"
"math/bits"
"runtime"
"sync"
"sync/atomic"
)
const (
// Min64BitSigned - Minimum 64 bit value
Min64BitSigned = -9223372036854775808
// Max64BitSigned - Maximum 64 bit value
Max64BitSigned = 9223372036854775807
)
// BSI is at its simplest is an array of bitmaps that represent an encoded
// binary value. The advantage of a BSI is that comparisons can be made
// across ranges of values whereas a bitmap can only represent the existence
// of a single value for a given column ID. Another usage scenario involves
// storage of high cardinality values.
//
// It depends upon the bitmap libraries. It is not thread safe, so
// upstream concurrency guards must be provided.
type BSI struct {
bA []Bitmap
eBM Bitmap // Existence BitMap
MaxValue int64
MinValue int64
runOptimized bool
}
// NewBSI constructs a new BSI. Min/Max values are optional. If set to 0
// then the underlying BSI will be automatically sized.
func NewBSI(maxValue int64, minValue int64) *BSI {
bitsz := bits.Len64(uint64(minValue))
if bits.Len64(uint64(maxValue)) > bitsz {
bitsz = bits.Len64(uint64(maxValue))
}
ba := make([]Bitmap, bitsz)
return &BSI{bA: ba, MaxValue: maxValue, MinValue: minValue}
}
// NewDefaultBSI constructs an auto-sized BSI
func NewDefaultBSI() *BSI {
return NewBSI(int64(0), int64(0))
}
// RunOptimize attempts to further compress the runs of consecutive values found in the bitmap
func (b *BSI) RunOptimize() {
b.eBM.RunOptimize()
for i := 0; i < len(b.bA); i++ {
b.bA[i].RunOptimize()
}
b.runOptimized = true
}
// HasRunCompression returns true if the bitmap benefits from run compression
func (b *BSI) HasRunCompression() bool {
return b.runOptimized
}
// GetExistenceBitmap returns a pointer to the underlying existence bitmap of the BSI
func (b *BSI) GetExistenceBitmap() *Bitmap {
return &b.eBM
}
// ValueExists tests whether the value exists.
func (b *BSI) ValueExists(columnID uint64) bool {
return b.eBM.Contains(uint64(columnID))
}
// GetCardinality returns a count of unique column IDs for which a value has been set.
func (b *BSI) GetCardinality() uint64 {
return b.eBM.GetCardinality()
}
// BitCount returns the number of bits needed to represent values.
func (b *BSI) BitCount() int {
return len(b.bA)
}
// SetValue sets a value for a given columnID.
func (b *BSI) SetValue(columnID uint64, value int64) {
// If max/min values are set to zero then automatically determine bit array size
if b.MaxValue == 0 && b.MinValue == 0 {
minBits := bits.Len64(uint64(value))
for len(b.bA) < minBits {
b.bA = append(b.bA, Bitmap{})
}
}
for i := 0; i < b.BitCount(); i++ {
if uint64(value)&(1<<uint64(i)) > 0 {
b.bA[i].Add(columnID)
} else {
b.bA[i].Remove(columnID)
}
}
b.eBM.Add(columnID)
}
// GetValue gets the value at the column ID. Second param will be false for non-existent values.
func (b *BSI) GetValue(columnID uint64) (value int64, exists bool) {
exists = b.eBM.Contains(columnID)
if !exists {
return
}
for i := 0; i < b.BitCount(); i++ {
if b.bA[i].Contains(columnID) {
value |= 1 << i
}
}
return
}
type action func(t *task, batch []uint64, resultsChan chan *Bitmap, wg *sync.WaitGroup)
func parallelExecutor(parallelism int, t *task, e action, foundSet *Bitmap) *Bitmap {
var n int = parallelism
if n == 0 {
n = runtime.NumCPU()
}
resultsChan := make(chan *Bitmap, n)
card := foundSet.GetCardinality()
x := card / uint64(n)
remainder := card - (x * uint64(n))
var batch []uint64
var wg sync.WaitGroup
iter := foundSet.ManyIterator()
for i := 0; i < n; i++ {
if i == n-1 {
batch = make([]uint64, x+remainder)
} else {
batch = make([]uint64, x)
}
iter.NextMany(batch)
wg.Add(1)
go e(t, batch, resultsChan, &wg)
}
wg.Wait()
close(resultsChan)
ba := make([]*Bitmap, 0)
for bm := range resultsChan {
ba = append(ba, bm)
}
return ParOr(0, ba...)
}
type bsiAction func(input *BSI, filterSet *Bitmap, batch []uint64, resultsChan chan *BSI, wg *sync.WaitGroup)
func parallelExecutorBSIResults(parallelism int, input *BSI, e bsiAction, foundSet, filterSet *Bitmap, sumResults bool) *BSI {
var n int = parallelism
if n == 0 {
n = runtime.NumCPU()
}
resultsChan := make(chan *BSI, n)
card := foundSet.GetCardinality()
x := card / uint64(n)
remainder := card - (x * uint64(n))
var batch []uint64
var wg sync.WaitGroup
iter := foundSet.ManyIterator()
for i := 0; i < n; i++ {
if i == n-1 {
batch = make([]uint64, x+remainder)
} else {
batch = make([]uint64, x)
}
iter.NextMany(batch)
wg.Add(1)
go e(input, filterSet, batch, resultsChan, &wg)
}
wg.Wait()
close(resultsChan)
ba := make([]*BSI, 0)
for bm := range resultsChan {
ba = append(ba, bm)
}
results := NewDefaultBSI()
if sumResults {
for _, v := range ba {
results.Add(v)
}
} else {
results.ParOr(0, ba...)
}
return results
}
// Operation identifier
type Operation int
const (
// LT less than
LT Operation = 1 + iota
// LE less than or equal
LE
// EQ equal
EQ
// GE greater than or equal
GE
// GT greater than
GT
// RANGE range
RANGE
// MIN find minimum
MIN
// MAX find maximum
MAX
)
type task struct {
bsi *BSI
op Operation
valueOrStart int64
end int64
values map[int64]struct{}
bits *Bitmap
}
// CompareValue compares value.
// For all operations with the exception of RANGE, the value to be compared is specified by valueOrStart.
// For the RANGE parameter the comparison criteria is >= valueOrStart and <= end.
// The parallelism parameter indicates the number of CPU threads to be applied for processing. A value
// of zero indicates that all available CPU resources will be potentially utilized.
func (b *BSI) CompareValue(parallelism int, op Operation, valueOrStart, end int64,
foundSet *Bitmap) *Bitmap {
comp := &task{bsi: b, op: op, valueOrStart: valueOrStart, end: end}
if foundSet == nil {
return parallelExecutor(parallelism, comp, compareValue, &b.eBM)
}
return parallelExecutor(parallelism, comp, compareValue, foundSet)
}
func compareValue(e *task, batch []uint64, resultsChan chan *Bitmap, wg *sync.WaitGroup) {
defer wg.Done()
results := NewBitmap()
if e.bsi.runOptimized {
results.RunOptimize()
}
x := e.bsi.BitCount()
startIsNegative := x == 64 && uint64(e.valueOrStart)&(1<<uint64(x-1)) > 0
endIsNegative := x == 64 && uint64(e.end)&(1<<uint64(x-1)) > 0
for i := 0; i < len(batch); i++ {
cID := batch[i]
eq1, eq2 := true, true
lt1, lt2, gt1 := false, false, false
j := e.bsi.BitCount() - 1
isNegative := false
if x == 64 {
isNegative = e.bsi.bA[j].Contains(cID)
j--
}
compStartValue := e.valueOrStart
compEndValue := e.end
if isNegative != startIsNegative {
compStartValue = ^e.valueOrStart + 1
}
if isNegative != endIsNegative {
compEndValue = ^e.end + 1
}
for ; j >= 0; j-- {
sliceContainsBit := e.bsi.bA[j].Contains(cID)
if uint64(compStartValue)&(1<<uint64(j)) > 0 {
// BIT in value is SET
if !sliceContainsBit {
if eq1 {
if (e.op == GT || e.op == GE || e.op == RANGE) && startIsNegative && !isNegative {
gt1 = true
}
if e.op == LT || e.op == LE {
if !startIsNegative || (startIsNegative == isNegative) {
lt1 = true
}
}
eq1 = false
break
}
}
} else {
// BIT in value is CLEAR
if sliceContainsBit {
if eq1 {
if (e.op == LT || e.op == LE) && isNegative && !startIsNegative {
lt1 = true
}
if e.op == GT || e.op == GE || e.op == RANGE {
if startIsNegative || (startIsNegative == isNegative) {
gt1 = true
}
}
eq1 = false
if e.op != RANGE {
break
}
}
}
}
if e.op == RANGE && uint64(compEndValue)&(1<<uint64(j)) > 0 {
// BIT in value is SET
if !sliceContainsBit {
if eq2 {
if !endIsNegative || (endIsNegative == isNegative) {
lt2 = true
}
eq2 = false
if startIsNegative && !endIsNegative {
break
}
}
}
} else if e.op == RANGE {
// BIT in value is CLEAR
if sliceContainsBit {
if eq2 {
if isNegative && !endIsNegative {
lt2 = true
}
eq2 = false
break
}
}
}
}
switch e.op {
case LT:
if lt1 {
results.Add(cID)
}
case LE:
if lt1 || (eq1 && (!startIsNegative || (startIsNegative && isNegative))) {
results.Add(cID)
}
case EQ:
if eq1 {
results.Add(cID)
}
case GE:
if gt1 || (eq1 && (startIsNegative || (!startIsNegative && !isNegative))) {
results.Add(cID)
}
case GT:
if gt1 {
results.Add(cID)
}
case RANGE:
if (eq1 || gt1) && (eq2 || lt2) {
results.Add(cID)
}
default:
panic(fmt.Sprintf("Operation [%v] not supported here", e.op))
}
}
resultsChan <- results
}
// MinMax - Find minimum or maximum value.
func (b *BSI) MinMax(parallelism int, op Operation, foundSet *Bitmap) int64 {
var n int = parallelism
if n == 0 {
n = runtime.NumCPU()
}
resultsChan := make(chan int64, n)
card := foundSet.GetCardinality()
x := card / uint64(n)
remainder := card - (x * uint64(n))
var batch []uint64
var wg sync.WaitGroup
iter := foundSet.ManyIterator()
for i := 0; i < n; i++ {
if i == n-1 {
batch = make([]uint64, x+remainder)
} else {
batch = make([]uint64, x)
}
iter.NextMany(batch)
wg.Add(1)
go b.minOrMax(op, batch, resultsChan, &wg)
}
wg.Wait()
close(resultsChan)
var minMax int64
if op == MAX {
minMax = Min64BitSigned
} else {
minMax = Max64BitSigned
}
for val := range resultsChan {
if (op == MAX && val > minMax) || (op == MIN && val <= minMax) {
minMax = val
}
}
return minMax
}
func (b *BSI) minOrMax(op Operation, batch []uint64, resultsChan chan int64, wg *sync.WaitGroup) {
defer wg.Done()
x := b.BitCount()
var value int64 = Max64BitSigned
if op == MAX {
value = Min64BitSigned
}
for i := 0; i < len(batch); i++ {
cID := batch[i]
eq := true
lt, gt := false, false
j := b.BitCount() - 1
var cVal int64
valueIsNegative := uint64(value)&(1<<uint64(x-1)) > 0 && bits.Len64(uint64(value)) == 64
isNegative := false
if x == 64 {
isNegative = b.bA[j].Contains(cID)
if isNegative {
cVal |= 1 << uint64(j)
}
j--
}
compValue := value
if isNegative != valueIsNegative {
compValue = ^value + 1
}
for ; j >= 0; j-- {
sliceContainsBit := b.bA[j].Contains(cID)
if sliceContainsBit {
cVal |= 1 << uint64(j)
}
if uint64(compValue)&(1<<uint64(j)) > 0 {
// BIT in value is SET
if !sliceContainsBit {
if eq {
eq = false
if op == MAX && valueIsNegative && !isNegative {
gt = true
break
}
if op == MIN && (!valueIsNegative || (valueIsNegative == isNegative)) {
lt = true
}
}
}
} else {
// BIT in value is CLEAR
if sliceContainsBit {
if eq {
eq = false
if op == MIN && isNegative && !valueIsNegative {
lt = true
}
if op == MAX && (valueIsNegative || (valueIsNegative == isNegative)) {
gt = true
}
}
}
}
}
if lt || gt {
value = cVal
}
}
resultsChan <- value
}
// Sum all values contained within the foundSet. As a convenience, the cardinality of the foundSet
// is also returned (for calculating the average).
func (b *BSI) Sum(foundSet *Bitmap) (sum int64, count uint64) {
count = foundSet.GetCardinality()
var wg sync.WaitGroup
for i := 0; i < b.BitCount(); i++ {
wg.Add(1)
go func(j int) {
defer wg.Done()
atomic.AddInt64(&sum, int64(foundSet.AndCardinality(&b.bA[j])<<uint(j)))
}(i)
}
wg.Wait()
return
}
// Transpose calls b.IntersectAndTranspose(0, b.eBM)
func (b *BSI) Transpose() *Bitmap {
return b.IntersectAndTranspose(0, &b.eBM)
}
// IntersectAndTranspose is a matrix transpose function. Return a bitmap such that the values are represented as column IDs
// in the returned bitmap. This is accomplished by iterating over the foundSet and only including
// the column IDs in the source (foundSet) as compared with this BSI. This can be useful for
// vectoring one set of integers to another.
//
// TODO: This implementation is functional but not performant, needs to be re-written perhaps using SIMD SSE2 instructions.
func (b *BSI) IntersectAndTranspose(parallelism int, foundSet *Bitmap) *Bitmap {
trans := &task{bsi: b}
return parallelExecutor(parallelism, trans, transpose, foundSet)
}
func transpose(e *task, batch []uint64, resultsChan chan *Bitmap, wg *sync.WaitGroup) {
defer wg.Done()
results := NewBitmap()
if e.bsi.runOptimized {
results.RunOptimize()
}
for _, cID := range batch {
if value, ok := e.bsi.GetValue(uint64(cID)); ok {
results.Add(uint64(value))
}
}
resultsChan <- results
}
// ParOr is intended primarily to be a concatenation function to be used during bulk load operations.
// Care should be taken to make sure that columnIDs do not overlap (unless overlapping values are
// identical).
func (b *BSI) ParOr(parallelism int, bsis ...*BSI) {
// Consolidate sets
bits := len(b.bA)
for i := 0; i < len(bsis); i++ {
if len(bsis[i].bA) > bits {
bits = bsis[i].BitCount()
}
}
// Make sure we have enough bit slices
for bits > b.BitCount() {
bm := Bitmap{}
bm.RunOptimize()
b.bA = append(b.bA, bm)
}
a := make([][]*Bitmap, bits)
for i := range a {
a[i] = make([]*Bitmap, 0)
for _, x := range bsis {
if len(x.bA) > i {
a[i] = append(a[i], &x.bA[i])
} else {
if b.runOptimized {
a[i][0].RunOptimize()
}
}
}
}
// Consolidate existence bit maps
ebms := make([]*Bitmap, len(bsis))
for i := range ebms {
ebms[i] = &bsis[i].eBM
}
// First merge all the bit slices from all bsi maps that exist in target
var wg sync.WaitGroup
for i := 0; i < bits; i++ {
wg.Add(1)
go func(j int) {
defer wg.Done()
x := []*Bitmap{&b.bA[j]}
x = append(x, a[j]...)
b.bA[j] = *ParOr(parallelism, x...)
}(i)
}
wg.Wait()
// merge all the EBM maps
x := []*Bitmap{&b.eBM}
x = append(x, ebms...)
b.eBM = *ParOr(parallelism, x...)
}
// UnmarshalBinary de-serialize a BSI. The value at bitData[0] is the EBM. Other indices are in least to most
// significance order starting at bitData[1] (bit position 0).
func (b *BSI) UnmarshalBinary(bitData [][]byte) error {
for i := 1; i < len(bitData); i++ {
if bitData == nil || len(bitData[i]) == 0 {
continue
}
if b.BitCount() < i {
newBm := Bitmap{}
if b.runOptimized {
newBm.RunOptimize()
}
b.bA = append(b.bA, newBm)
}
if err := b.bA[i-1].UnmarshalBinary(bitData[i]); err != nil {
return err
}
if b.runOptimized {
b.bA[i-1].RunOptimize()
}
}
// First element of bitData is the EBM
if bitData[0] == nil {
b.eBM = Bitmap{}
if b.runOptimized {
b.eBM.RunOptimize()
}
return nil
}
if err := b.eBM.UnmarshalBinary(bitData[0]); err != nil {
return err
}
if b.runOptimized {
b.eBM.RunOptimize()
}
return nil
}
// ReadFrom reads a serialized version of this BSI from stream.
func (b *BSI) ReadFrom(stream io.Reader) (p int64, err error) {
bm, n, err := readBSIContainerFromStream(stream)
p += n
if err != nil {
err = fmt.Errorf("reading existence bitmap: %w", err)
return
}
b.eBM = bm
b.bA = b.bA[:0]
for {
// This forces a new memory location to be allocated and if we're lucky it only escapes if
// there's no error.
var bm Bitmap
bm, n, err = readBSIContainerFromStream(stream)
p += n
if err == io.EOF {
err = nil
return
}
if err != nil {
err = fmt.Errorf("reading bit slice index %v: %w", len(b.bA), err)
return
}
b.bA = append(b.bA, bm)
}
}
func readBSIContainerFromStream(r io.Reader) (bm Bitmap, p int64, err error) {
p, err = bm.ReadFrom(r)
return
}
// MarshalBinary serializes a BSI
func (b *BSI) MarshalBinary() ([][]byte, error) {
var err error
data := make([][]byte, b.BitCount()+1)
// Add extra element for EBM (BitCount() + 1)
for i := 1; i < b.BitCount()+1; i++ {
data[i], err = b.bA[i-1].MarshalBinary()
if err != nil {
return nil, err
}
}
// Marshal EBM
data[0], err = b.eBM.MarshalBinary()
if err != nil {
return nil, err
}
return data, nil
}
// WriteTo writes a serialized version of this BSI to stream.
func (b *BSI) WriteTo(w io.Writer) (n int64, err error) {
n1, err := b.eBM.WriteTo(w)
n += n1
if err != nil {
return
}
for _, bm := range b.bA {
n1, err = bm.WriteTo(w)
n += n1
if err != nil {
return
}
}
return
}
// BatchEqual returns a bitmap containing the column IDs where the values are contained within the list of values provided.
func (b *BSI) BatchEqual(parallelism int, values []int64) *Bitmap {
valMap := make(map[int64]struct{}, len(values))
for i := 0; i < len(values); i++ {
valMap[values[i]] = struct{}{}
}
comp := &task{bsi: b, values: valMap}
return parallelExecutor(parallelism, comp, batchEqual, &b.eBM)
}
func batchEqual(e *task, batch []uint64, resultsChan chan *Bitmap,
wg *sync.WaitGroup) {
defer wg.Done()
results := NewBitmap()
if e.bsi.runOptimized {
results.RunOptimize()
}
for i := 0; i < len(batch); i++ {
cID := batch[i]
if value, ok := e.bsi.GetValue(uint64(cID)); ok {
if _, yes := e.values[int64(value)]; yes {
results.Add(cID)
}
}
}
resultsChan <- results
}
// ClearBits cleared the bits that exist in the target if they are also in the found set.
func ClearBits(foundSet, target *Bitmap) {
iter := foundSet.Iterator()
for iter.HasNext() {
cID := iter.Next()
target.Remove(cID)
}
}
// ClearValues removes the values found in foundSet
func (b *BSI) ClearValues(foundSet *Bitmap) {
var wg sync.WaitGroup
wg.Add(1)
go func() {
defer wg.Done()
ClearBits(foundSet, &b.eBM)
}()
for i := 0; i < b.BitCount(); i++ {
wg.Add(1)
go func(j int) {
defer wg.Done()
ClearBits(foundSet, &b.bA[j])
}(i)
}
wg.Wait()
}
// NewBSIRetainSet - Construct a new BSI from a clone of existing BSI, retain only values contained in foundSet
func (b *BSI) NewBSIRetainSet(foundSet *Bitmap) *BSI {
newBSI := NewBSI(b.MaxValue, b.MinValue)
newBSI.bA = make([]Bitmap, b.BitCount())
var wg sync.WaitGroup
wg.Add(1)
go func() {
defer wg.Done()
newBSI.eBM = *b.eBM.Clone()
newBSI.eBM.And(foundSet)
}()
for i := 0; i < b.BitCount(); i++ {
wg.Add(1)
go func(j int) {
defer wg.Done()
newBSI.bA[j] = *b.bA[j].Clone()
newBSI.bA[j].And(foundSet)
}(i)
}
wg.Wait()
return newBSI
}
// Clone performs a deep copy of BSI contents.
func (b *BSI) Clone() *BSI {
return b.NewBSIRetainSet(&b.eBM)
}
// Add - In-place sum the contents of another BSI with this BSI, column wise.
func (b *BSI) Add(other *BSI) {
b.eBM.Or(&other.eBM)
for i := 0; i < len(other.bA); i++ {
b.addDigit(&other.bA[i], i)
}
}
func (b *BSI) addDigit(foundSet *Bitmap, i int) {
if i >= len(b.bA) {
b.bA = append(b.bA, Bitmap{})
}
carry := And(&b.bA[i], foundSet)
b.bA[i].Xor(foundSet)
if !carry.IsEmpty() {
if i+1 >= len(b.bA) {
b.bA = append(b.bA, Bitmap{})
}
b.addDigit(carry, i+1)
}
}
// TransposeWithCounts is a matrix transpose function that returns a BSI that has a columnID system defined by the values
// contained within the input BSI. Given that for BSIs, different columnIDs can have the same value. TransposeWithCounts
// is useful for situations where there is a one-to-many relationship between the vectored integer sets. The resulting BSI
// contains the number of times a particular value appeared in the input BSI.
func (b *BSI) TransposeWithCounts(parallelism int, foundSet, filterSet *Bitmap) *BSI {
return parallelExecutorBSIResults(parallelism, b, transposeWithCounts, foundSet, filterSet, true)
}
func transposeWithCounts(input *BSI, filterSet *Bitmap, batch []uint64, resultsChan chan *BSI, wg *sync.WaitGroup) {
defer wg.Done()
results := NewDefaultBSI()
if input.runOptimized {
results.RunOptimize()
}
for _, cID := range batch {
if value, ok := input.GetValue(uint64(cID)); ok {
if !filterSet.Contains(uint64(value)) {
continue
}
if val, ok2 := results.GetValue(uint64(value)); !ok2 {
results.SetValue(uint64(value), 1)
} else {
val++
results.SetValue(uint64(value), val)
}
}
}
resultsChan <- results
}
// Increment - In-place increment of values in a BSI. Found set select columns for incrementing.
func (b *BSI) Increment(foundSet *Bitmap) {
b.addDigit(foundSet, 0)
b.eBM.Or(foundSet)
}
// IncrementAll - In-place increment of all values in a BSI.
func (b *BSI) IncrementAll() {
b.Increment(b.GetExistenceBitmap())
}
// Equals - Check for semantic equality of two BSIs.
func (b *BSI) Equals(other *BSI) bool {
if !b.eBM.Equals(&other.eBM) {
return false
}
for i := 0; i < len(b.bA) || i < len(other.bA); i++ {
if i >= len(b.bA) {
if !other.bA[i].IsEmpty() {
return false
}
} else if i >= len(other.bA) {
if !b.bA[i].IsEmpty() {
return false
}
} else {
if !b.bA[i].Equals(&other.bA[i]) {
return false
}
}
}
return true
}
// GetSizeInBytes - the size in bytes of the data structure
func (b *BSI) GetSizeInBytes() int {
size := b.eBM.GetSizeInBytes()
for _, bm := range b.bA {
size += bm.GetSizeInBytes()
}
return int(size)
}