// Copyright 2021 The gVisor Authors. // // 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 bitmap provides the implementation of bitmap. package bitmap import ( "fmt" "math" "math/bits" ) // MaxBitEntryLimit defines the upper limit on how many bit entries are supported by this Bitmap // implementation. const MaxBitEntryLimit uint32 = math.MaxInt32 // Bitmap implements an efficient bitmap. // // +stateify savable type Bitmap struct { // numOnes is the number of ones in the bitmap. numOnes uint32 // bitBlock holds the bits. The type of bitBlock is uint64 which means // each number in bitBlock contains 64 entries. bitBlock []uint64 } // New create a new empty Bitmap. func New(size uint32) Bitmap { b := Bitmap{} bSize := (size + 63) / 64 b.bitBlock = make([]uint64, bSize) return b } // IsEmpty verifies whether the Bitmap is empty. func (b *Bitmap) IsEmpty() bool { return b.numOnes == 0 } // Minimum return the smallest value in the Bitmap. func (b *Bitmap) Minimum() uint32 { for i := 0; i < len(b.bitBlock); i++ { if w := b.bitBlock[i]; w != 0 { r := bits.TrailingZeros64(w) return uint32(r + i*64) } } return MaxBitEntryLimit } // FirstZero returns the first unset bit from the range [start, ). func (b *Bitmap) FirstZero(start uint32) (bit uint32, err error) { i, nbit := int(start/64), start%64 n := len(b.bitBlock) if i >= n { return MaxBitEntryLimit, fmt.Errorf("given start of range exceeds bitmap size") } w := b.bitBlock[i] | ((1 << nbit) - 1) for { if w != ^uint64(0) { r := bits.TrailingZeros64(^w) return uint32(r + i*64), nil } i++ if i == n { break } w = b.bitBlock[i] } return MaxBitEntryLimit, fmt.Errorf("bitmap has no unset bits") } // FirstOne returns the first set bit from the range [start, ) func (b *Bitmap) FirstOne(start uint32) (bit uint32, err error) { i, nbit := int(start/64), start%64 n := len(b.bitBlock) if i >= n { return MaxBitEntryLimit, fmt.Errorf("given start of range exceeds bitmap size") } w := b.bitBlock[i] & (math.MaxUint64 << nbit) for { if w != uint64(0) { r := bits.TrailingZeros64(w) return uint32(r + i*64), nil } i++ if i == n { break } w = b.bitBlock[i] } return MaxBitEntryLimit, fmt.Errorf("bitmap has no set bits") } // Maximum return the largest value in the Bitmap. func (b *Bitmap) Maximum() uint32 { for i := len(b.bitBlock) - 1; i >= 0; i-- { if w := b.bitBlock[i]; w != 0 { r := bits.LeadingZeros64(w) return uint32(i*64 + 63 - r) } } return uint32(0) } // Add add i to the Bitmap. func (b *Bitmap) Add(i uint32) { blockNum, mask := i/64, uint64(1)<<(i%64) // if blockNum is out of range, extend b.bitBlock if x, y := int(blockNum), len(b.bitBlock); x >= y { b.bitBlock = append(b.bitBlock, make([]uint64, x-y+1)...) } oldBlock := b.bitBlock[blockNum] newBlock := oldBlock | mask if oldBlock != newBlock { b.bitBlock[blockNum] = newBlock b.numOnes++ } } // Remove i from the Bitmap. func (b *Bitmap) Remove(i uint32) { blockNum, mask := i/64, uint64(1)<<(i%64) oldBlock := b.bitBlock[blockNum] newBlock := oldBlock &^ mask if oldBlock != newBlock { b.bitBlock[blockNum] = newBlock b.numOnes-- } } // Clone the Bitmap. func (b *Bitmap) Clone() Bitmap { bitmap := Bitmap{b.numOnes, make([]uint64, len(b.bitBlock))} copy(bitmap.bitBlock, b.bitBlock[:]) return bitmap } // countOnesForBlocks count all 1 bits within b.bitBlock of begin and that of end. // The begin block and end block are inclusive. func (b *Bitmap) countOnesForBlocks(begin, end uint32) uint64 { ones := uint64(0) beginBlock := begin / 64 endBlock := end / 64 for i := beginBlock; i <= endBlock; i++ { ones += uint64(bits.OnesCount64(b.bitBlock[i])) } return ones } // countOnesForAllBlocks count all 1 bits in b.bitBlock. func (b *Bitmap) countOnesForAllBlocks() uint64 { ones := uint64(0) for i := 0; i < len(b.bitBlock); i++ { ones += uint64(bits.OnesCount64(b.bitBlock[i])) } return ones } // flipRange flip the bits within range (begin and end). begin is inclusive and end is exclusive. func (b *Bitmap) flipRange(begin, end uint32) { end-- beginBlock := begin / 64 endBlock := end / 64 if beginBlock == endBlock { b.bitBlock[endBlock] ^= ((^uint64(0) << uint(begin%64)) & ((uint64(1) << (uint(end)%64 + 1)) - 1)) } else { b.bitBlock[beginBlock] ^= ^(^uint64(0) << uint(begin%64)) for i := beginBlock; i < endBlock; i++ { b.bitBlock[i] = ^b.bitBlock[i] } b.bitBlock[endBlock] ^= ((uint64(1) << (uint(end)%64 + 1)) - 1) } } // clearRange clear the bits within range (begin and end). begin is inclusive and end is exclusive. func (b *Bitmap) clearRange(begin, end uint32) { end-- beginBlock := begin / 64 endBlock := end / 64 if beginBlock == endBlock { b.bitBlock[beginBlock] &= (((uint64(1) << uint(begin%64)) - 1) | ^((uint64(1) << (uint(end)%64 + 1)) - 1)) } else { b.bitBlock[beginBlock] &= ((uint64(1) << uint(begin%64)) - 1) for i := beginBlock + 1; i < endBlock; i++ { b.bitBlock[i] &= ^b.bitBlock[i] } b.bitBlock[endBlock] &= ^((uint64(1) << (uint(end)%64 + 1)) - 1) } } // ClearRange clear bits within range (begin and end) for the Bitmap. begin is inclusive and end is exclusive. func (b *Bitmap) ClearRange(begin, end uint32) { blockRange := end/64 - begin/64 // When the number of cleared blocks is larger than half of the length of b.bitBlock, // counting 1s for the entire bitmap has better performance. if blockRange > uint32(len(b.bitBlock)/2) { b.clearRange(begin, end) b.numOnes = uint32(b.countOnesForAllBlocks()) } else { oldRangeOnes := b.countOnesForBlocks(begin, end) b.clearRange(begin, end) newRangeOnes := b.countOnesForBlocks(begin, end) b.numOnes += uint32(newRangeOnes - oldRangeOnes) } } // FlipRange flip bits within range (begin and end) for the Bitmap. begin is inclusive and end is exclusive. func (b *Bitmap) FlipRange(begin, end uint32) { blockRange := end/64 - begin/64 // When the number of flipped blocks is larger than half of the length of b.bitBlock, // counting 1s for the entire bitmap has better performance. if blockRange > uint32(len(b.bitBlock)/2) { b.flipRange(begin, end) b.numOnes = uint32(b.countOnesForAllBlocks()) } else { oldRangeOnes := b.countOnesForBlocks(begin, end) b.flipRange(begin, end) newRangeOnes := b.countOnesForBlocks(begin, end) b.numOnes += uint32(newRangeOnes - oldRangeOnes) } } // ToSlice transform the Bitmap into slice. For example, a bitmap of [0, 1, 0, 1] // will return the slice [1, 3]. func (b *Bitmap) ToSlice() []uint32 { bitmapSlice := make([]uint32, 0, b.numOnes) // base is the start number of a bitBlock base := 0 for i := 0; i < len(b.bitBlock); i++ { bitBlock := b.bitBlock[i] // Iterate through all the numbers held by this bit block. for bitBlock != 0 { // Extract the lowest set 1 bit. j := bitBlock & -bitBlock // Interpret the bit as the in32 number it represents and add it to result. bitmapSlice = append(bitmapSlice, uint32((base + int(bits.OnesCount64(j-1))))) bitBlock ^= j } base += 64 } return bitmapSlice } // GetNumOnes return the the number of ones in the Bitmap. func (b *Bitmap) GetNumOnes() uint32 { return b.numOnes }