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fast_int_set.go
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fast_int_set.go
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// Copyright 2022 PingCAP, Inc.
//
// 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 funcdep
import (
"bytes"
"fmt"
"math/bits"
"golang.org/x/tools/container/intsets"
)
const smallCutOff = 64
// FastIntSet is wrapper of sparse with an optimization that number [0 ~ 64) can be cached for quick access.
// From the benchmark in fd_graph_test.go, we choose to use sparse to accelerate int set. And when the set
// size is quite small we can just skip the block allocation in the sparse chain list.
type FastIntSet struct {
// an uint64 used like quick-small bitmap of 0~63.
small uint64
// when some is bigger than 64, then all that previous inserted will be dumped into sparse.
large *intsets.Sparse
}
// NewFastIntSet is used to make the instance of FastIntSet with initial values.
func NewFastIntSet(values ...int) FastIntSet {
var res FastIntSet
for _, v := range values {
res.Insert(v)
}
return res
}
// Len return the size of the int set.
func (s FastIntSet) Len() int {
if s.large == nil {
return bits.OnesCount64(s.small)
}
return s.large.Len()
}
// Only1Zero is a usage function for convenience judgement.
func (s FastIntSet) Only1Zero() bool {
return s.Len() == 1 && s.Has(0)
}
// Insert is used to insert a value into int-set.
func (s *FastIntSet) Insert(i int) {
isSmall := i >= 0 && i < smallCutOff
if isSmall {
s.small |= 1 << uint64(i)
}
if !isSmall && s.large == nil {
// first encounter a larger/smaller number, dump all that in `small` into `large`.
s.large = s.toLarge()
}
if s.large != nil {
s.large.Insert(i)
}
}
func (s FastIntSet) toLarge() *intsets.Sparse {
if s.large != nil {
return s.large
}
large := new(intsets.Sparse)
for i, ok := s.Next(0); ok; i, ok = s.Next(i + 1) {
large.Insert(i)
}
return large
}
// Next returns the next existing number in the Set.
// If there's no larger one than the given start val, return (MaxInt, false).
func (s FastIntSet) Next(startVal int) (int, bool) {
if startVal < smallCutOff {
if startVal < 0 {
startVal = 0
}
// x=0, gap=64, which means there is no `1` after right shift.
if gap := bits.TrailingZeros64(s.small >> uint64(startVal)); gap < 64 {
return gap + startVal, true
}
}
if s.large != nil {
res := s.large.LowerBound(startVal)
return res, res != intsets.MaxInt
}
return intsets.MaxInt, false
}
// Remove is used to remove a value from the set. Nothing done if the value is not in the set.
func (s *FastIntSet) Remove(i int) {
if i >= 0 && i < smallCutOff {
s.small &^= 1 << uint64(i)
}
if s.large != nil {
s.large.Remove(i)
}
}
// Clear is used to clear a fastIntSet and reuse it as an empty one.
func (s *FastIntSet) Clear() {
s.small = 0
if s.large != nil {
s.large.Clear()
}
}
// Has is used ot judge whether a value is in the set.
func (s FastIntSet) Has(i int) bool {
if i >= 0 && i < smallCutOff {
return (s.small & (1 << uint64(i))) != 0
}
if s.large != nil {
return s.large.Has(i)
}
return false
}
// IsEmpty is used to judge whether the int-set is empty.
func (s FastIntSet) IsEmpty() bool {
return s.small == 0 && (s.large == nil || s.large.IsEmpty())
}
// SortedArray is used to return the in array of the set.
func (s FastIntSet) SortedArray() []int {
if s.IsEmpty() {
return nil
}
if s.large != nil {
return s.large.AppendTo([]int(nil))
}
res := make([]int, 0, s.Len())
s.ForEach(func(i int) {
res = append(res, i)
})
return res
}
// ForEach call a function for each value in the int-set. (Ascend)
func (s FastIntSet) ForEach(f func(i int)) {
if s.large != nil {
for x := s.large.Min(); x != intsets.MaxInt; x = s.large.LowerBound(x + 1) {
f(x)
}
return
}
for v := s.small; v != 0; {
// from the left to right.
i := bits.TrailingZeros64(v)
f(i)
v &^= 1 << uint(i)
}
}
// Copy returns a copy of s.
func (s FastIntSet) Copy() FastIntSet {
c := FastIntSet{}
c.small = s.small
if s.large != nil {
c.large = new(intsets.Sparse)
c.large.Copy(s.large)
}
return c
}
// CopyFrom clear the receiver to be a copy of the param.
func (s *FastIntSet) CopyFrom(target FastIntSet) {
s.small = target.small
if target.large != nil {
if s.large == nil {
s.large = new(intsets.Sparse)
}
s.large.Copy(target.large)
} else {
if s.large != nil {
s.large.Clear()
}
}
}
// Equals returns whether two int-set are identical.
func (s FastIntSet) Equals(rhs FastIntSet) bool {
if s.large == nil && rhs.large == nil {
return s.small == rhs.small
}
if s.large != nil && rhs.large != nil {
return s.large.Equals(rhs.large)
}
// how come to this? eg: a set operates like:
// {insert:1, insert:65, remove:65}, resulting a large int-set with only small numbers.
// so we need calculate the exact numbers.
var excess bool
s1 := s.small
s2 := rhs.small
if s.large != nil {
s1, excess = s.largeToSmall()
} else {
s2, excess = rhs.largeToSmall()
}
return !excess && s1 == s2
}
func (s FastIntSet) largeToSmall() (small uint64, otherValues bool) {
if s.large == nil {
panic("set contains no large")
}
return s.small, s.large.Min() < 0 || s.large.Max() >= smallCutOff
}
// *************************************************************************
// * Logic Operators *
// *************************************************************************
// Difference is used to return the s without elements in rhs.
func (s FastIntSet) Difference(rhs FastIntSet) FastIntSet {
r := s.Copy()
r.DifferenceWith(rhs)
return r
}
// DifferenceWith removes any elements in rhs from source.
func (s *FastIntSet) DifferenceWith(rhs FastIntSet) {
s.small &^= rhs.small
if s.large == nil {
return
}
s.large.DifferenceWith(rhs.toLarge())
}
// Union is used to return a union of s and rhs as new set.
func (s FastIntSet) Union(rhs FastIntSet) FastIntSet {
cps := s.Copy()
cps.UnionWith(rhs)
return cps
}
// UnionWith is used to copy all the elements of rhs to source.
func (s *FastIntSet) UnionWith(rhs FastIntSet) {
s.small |= rhs.small
if s.large == nil && rhs.large == nil {
return
}
if s.large == nil {
s.large = s.toLarge()
}
if rhs.large == nil {
for i, ok := rhs.Next(0); ok; i, ok = rhs.Next(i + 1) {
s.large.Insert(i)
}
} else {
s.large.UnionWith(rhs.large)
}
}
// Intersection is used to return the intersection of s and rhs.
func (s FastIntSet) Intersection(rhs FastIntSet) FastIntSet {
r := s.Copy()
r.IntersectionWith(rhs)
return r
}
// IntersectionWith removes any elements not in rhs from source.
func (s *FastIntSet) IntersectionWith(rhs FastIntSet) {
s.small &= rhs.small
if rhs.large == nil {
s.large = nil
}
if s.large == nil {
return
}
s.large.IntersectionWith(rhs.toLarge())
}
// Intersects is used to judge whether two set has something in common.
func (s FastIntSet) Intersects(rhs FastIntSet) bool {
if (s.small & rhs.small) != 0 {
return true
}
if s.large == nil || rhs.large == nil {
return false
}
return s.large.Intersects(rhs.toLarge())
}
// SubsetOf is used to judge whether rhs contains source set.
func (s FastIntSet) SubsetOf(rhs FastIntSet) bool {
if s.large == nil {
return (s.small & rhs.small) == s.small
}
if s.large != nil && rhs.large != nil {
return s.large.SubsetOf(rhs.large)
}
// s is large and rhs is small.
if _, excess := s.largeToSmall(); excess {
// couldn't map s to small.
return false
}
// how come to this? eg: a set operates like: {insert:1, insert:65, remove:65}, resulting a large
// int-set with only small numbers.
return (s.small & rhs.small) == s.small
}
// Shift generates a new set which contains elements i+delta for elements i in
// the original set.
func (s *FastIntSet) Shift(delta int) FastIntSet {
if s.large == nil {
// Fast path.
if delta > 0 {
if bits.LeadingZeros64(s.small)-(64-smallCutOff) >= delta {
return FastIntSet{small: s.small << uint32(delta)}
}
} else {
if bits.TrailingZeros64(s.small) >= -delta {
return FastIntSet{small: s.small >> uint32(-delta)}
}
}
}
// Do the slow thing.
var result FastIntSet
s.ForEach(func(i int) {
result.Insert(i + delta)
})
return result
}
// AddRange adds the interval [from, to] to the Set.
func (s *FastIntSet) AddRange(from, to int) {
if to < from {
panic("invalid range when adding range to FastIntSet")
}
withinSmallBounds := from >= 0 && to < smallCutOff
if withinSmallBounds && s.large == nil {
nValues := to - from + 1
s.small |= (1<<uint64(nValues) - 1) << uint64(from)
} else {
for i := from; i <= to; i++ {
s.Insert(i)
}
}
}
func (s FastIntSet) String() string {
var buf bytes.Buffer
buf.WriteByte('(')
appendRange := func(start, end int) {
if buf.Len() > 1 {
buf.WriteByte(',')
}
if start == end {
fmt.Fprintf(&buf, "%d", start)
} else if start+1 == end {
fmt.Fprintf(&buf, "%d,%d", start, end)
} else {
fmt.Fprintf(&buf, "%d-%d", start, end)
}
}
rangeStart, rangeEnd := -1, -1
s.ForEach(func(i int) {
if i < 0 {
appendRange(i, i)
return
}
if rangeStart != -1 && rangeEnd == i-1 {
rangeEnd = i
} else {
if rangeStart != -1 {
appendRange(rangeStart, rangeEnd)
}
rangeStart, rangeEnd = i, i
}
})
if rangeStart != -1 {
appendRange(rangeStart, rangeEnd)
}
buf.WriteByte(')')
return buf.String()
}