// Copyright 2021 The Prometheus 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. // The code in this file was largely written by Damian Gryski as part of // https://github.com/dgryski/go-tsz and published under the license below. // It was modified to accommodate reading from byte slices without modifying // the underlying bytes, which would panic when reading from mmap'd // read-only byte slices. // Copyright (c) 2015,2016 Damian Gryski // All rights reserved. // Redistribution and use in source and binary forms, with or without // modification, are permitted provided that the following conditions are met: // * Redistributions of source code must retain the above copyright notice, // this list of conditions and the following disclaimer. // // * Redistributions in binary form must reproduce the above copyright notice, // this list of conditions and the following disclaimer in the documentation // and/or other materials provided with the distribution. // // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND // ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED // WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE // DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE // FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL // DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR // SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER // CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, // OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. package chunkenc import ( "encoding/binary" "math" "math/bits" "github.com/prometheus/prometheus/pkg/histogram" "github.com/prometheus/prometheus/pkg/value" ) const () // HistoChunk holds sparse histogram encoded sample data. // Appends a histogram sample // * schema defines the resolution (number of buckets per power of 2) // Currently, valid numbers are -4 <= n <= 8. // They are all for base-2 bucket schemas, where 1 is a bucket boundary in each case, and // then each power of two is divided into 2^n logarithmic buckets. // Or in other words, each bucket boundary is the previous boundary times 2^(2^-n). // In the future, more bucket schemas may be added using numbers < -4 or > 8. // The bucket with upper boundary of 1 is always bucket 0. // Then negative numbers for smaller boundaries and positive for uppers. // // fields are stored like so: // field ts count zeroCount sum []posbuckets negbuckets // observation 1 raw raw raw raw []raw []raw // observation 2 delta delta delta xor []delta []delta // observation >2 dod dod dod xor []dod []dod // TODO zerothreshold type HistoChunk struct { b bstream } // NewHistoChunk returns a new chunk with Histo encoding of the given size. func NewHistoChunk() *HistoChunk { b := make([]byte, 2, 128) return &HistoChunk{b: bstream{stream: b, count: 0}} } // Encoding returns the encoding type. func (c *HistoChunk) Encoding() Encoding { return EncSHS } // Bytes returns the underlying byte slice of the chunk. func (c *HistoChunk) Bytes() []byte { return c.b.bytes() } // NumSamples returns the number of samples in the chunk. func (c *HistoChunk) NumSamples() int { return int(binary.BigEndian.Uint16(c.Bytes())) } // Meta returns the histogram metadata. // callers may only call this on chunks that have at least one sample func (c *HistoChunk) Meta() (int32, float64, []histogram.Span, []histogram.Span, error) { if c.NumSamples() == 0 { panic("HistoChunk.Meta() called on an empty chunk") } b := newBReader(c.Bytes()[2:]) return readHistoChunkMeta(&b) } // Compact implements the Chunk interface. func (c *HistoChunk) Compact() { if l := len(c.b.stream); cap(c.b.stream) > l+chunkCompactCapacityThreshold { buf := make([]byte, l) copy(buf, c.b.stream) c.b.stream = buf } } // Appender implements the Chunk interface. func (c *HistoChunk) Appender() (Appender, error) { it := c.iterator(nil) // To get an appender we must know the state it would have if we had // appended all existing data from scratch. // We iterate through the end and populate via the iterator's state. for it.Next() { } if err := it.Err(); err != nil { return nil, err } a := &HistoAppender{ b: &c.b, schema: it.schema, zeroThreshold: it.zeroThreshold, posSpans: it.posSpans, negSpans: it.negSpans, t: it.t, cnt: it.cnt, zcnt: it.zcnt, tDelta: it.tDelta, cntDelta: it.cntDelta, zcntDelta: it.zcntDelta, posbuckets: it.posbuckets, negbuckets: it.negbuckets, posbucketsDelta: it.posbucketsDelta, negbucketsDelta: it.negbucketsDelta, sum: it.sum, leading: it.leading, trailing: it.trailing, buf64: make([]byte, binary.MaxVarintLen64), } if binary.BigEndian.Uint16(a.b.bytes()) == 0 { a.leading = 0xff } return a, nil } func countSpans(spans []histogram.Span) int { var cnt int for _, s := range spans { cnt += int(s.Length) } return cnt } func newHistoIterator(b []byte) *histoIterator { it := &histoIterator{ br: newBReader(b), numTotal: binary.BigEndian.Uint16(b), t: math.MinInt64, } // The first 2 bytes contain chunk headers. // We skip that for actual samples. _, _ = it.br.readBits(16) return it } func (c *HistoChunk) iterator(it Iterator) *histoIterator { // TODO fix this. this is taken from xor.go // dieter not sure what the purpose of this is // Should iterators guarantee to act on a copy of the data so it doesn't lock append? // When using striped locks to guard access to chunks, probably yes. // Could only copy data if the chunk is not completed yet. //if histoIter, ok := it.(*histoIterator); ok { // histoIter.Reset(c.b.bytes()) // return histoIter //} return newHistoIterator(c.b.bytes()) } // Iterator implements the Chunk interface. func (c *HistoChunk) Iterator(it Iterator) Iterator { return c.iterator(it) } // HistoAppender is an Appender implementation for sparse histograms. type HistoAppender struct { b *bstream // Metadata: schema int32 zeroThreshold float64 posSpans, negSpans []histogram.Span // For the fields that are tracked as dod's. Note that we expect to // handle negative deltas (e.g. resets) by creating new chunks, we still // want to support it in general hence signed integer types. t int64 cnt, zcnt uint64 tDelta, cntDelta, zcntDelta int64 posbuckets, negbuckets []int64 posbucketsDelta, negbucketsDelta []int64 // The sum is Gorilla xor encoded. sum float64 leading uint8 trailing uint8 buf64 []byte // For working on varint64's. } func putVarint(b *bstream, buf []byte, x int64) { for _, byt := range buf[:binary.PutVarint(buf, x)] { b.writeByte(byt) } } func putUvarint(b *bstream, buf []byte, x uint64) { for _, byt := range buf[:binary.PutUvarint(buf, x)] { b.writeByte(byt) } } // Append implements Appender. This implementation does nothing for now. // TODO(beorn7): Implement in a meaningful way, i.e. we need to support // appending of stale markers, but this should never be used for "real" // samples. func (a *HistoAppender) Append(int64, float64) {} // Appendable returns whether the chunk can be appended to, and if so // whether any recoding needs to happen using the provided interjections // (in case of any new buckets, positive or negative range, respectively) // The chunk is not appendable if: // * the schema has changed // * the zerobucket threshold has changed // * any buckets disappeared // * there was a counter reset in the count of observations or in any bucket, including the zero bucket // * the last sample in the chunk was stale while the current sample is not stale // If the given sample is stale, it will always return true. func (a *HistoAppender) Appendable(h histogram.SparseHistogram) ([]Interjection, []Interjection, bool) { if value.IsStaleNaN(h.Sum) { // This is a stale sample whose buckets and spans don't matter. return nil, nil, true } if value.IsStaleNaN(a.sum) { // If the last sample was stale, then we can only accept stale samples in this chunk. return nil, nil, false } if h.Schema != a.schema || h.ZeroThreshold != a.zeroThreshold { return nil, nil, false } posInterjections, ok := compareSpans(a.posSpans, h.PositiveSpans) if !ok { return nil, nil, false } negInterjections, ok := compareSpans(a.negSpans, h.NegativeSpans) if !ok { return nil, nil, false } if h.Count < a.cnt || h.ZeroCount < a.zcnt { // There has been a counter reset. return nil, nil, false } if counterResetInAnyBucket(a.posbuckets, h.PositiveBuckets, a.posSpans, h.PositiveSpans) { return nil, nil, false } if counterResetInAnyBucket(a.negbuckets, h.NegativeBuckets, a.negSpans, h.NegativeSpans) { return nil, nil, false } return posInterjections, negInterjections, ok } // counterResetInAnyBucket returns true if there was a counter reset for any bucket. // This should be called only when buckets are same or new buckets were added, // and does not handle the case of buckets missing. func counterResetInAnyBucket(oldBuckets, newBuckets []int64, oldSpans, newSpans []histogram.Span) bool { if len(oldSpans) == 0 || len(oldBuckets) == 0 { return false } oldSpanSliceIdx, newSpanSliceIdx := 0, 0 // Index for the span slices. oldInsideSpanIdx, newInsideSpanIdx := uint32(0), uint32(0) // Index inside a span. oldIdx, newIdx := oldSpans[0].Offset, newSpans[0].Offset oldBucketSliceIdx, newBucketSliceIdx := 0, 0 // Index inside bucket slice. oldVal, newVal := oldBuckets[0], newBuckets[0] // Since we assume that new spans won't have missing buckets, there will never be a case // where the old index will not find a matching new index. for { if oldIdx == newIdx { if newVal < oldVal { return true } } if oldIdx <= newIdx { // Moving ahead old bucket and span by 1 index. if oldInsideSpanIdx == oldSpans[oldSpanSliceIdx].Length-1 { // Current span is over. oldSpanSliceIdx++ oldInsideSpanIdx = 0 if oldSpanSliceIdx >= len(oldSpans) { // All old spans are over. break } oldIdx += 1 + oldSpans[oldSpanSliceIdx].Offset } else { oldInsideSpanIdx++ oldIdx++ } oldBucketSliceIdx++ oldVal += oldBuckets[oldBucketSliceIdx] } if oldIdx > newIdx { // Moving ahead new bucket and span by 1 index. if newInsideSpanIdx == newSpans[newSpanSliceIdx].Length-1 { // Current span is over. newSpanSliceIdx++ newInsideSpanIdx = 0 if newSpanSliceIdx >= len(newSpans) { // All new spans are over. // This should not happen, old spans above should catch this first. panic("new spans over before old spans in counterReset") } newIdx += 1 + newSpans[newSpanSliceIdx].Offset } else { newInsideSpanIdx++ newIdx++ } newBucketSliceIdx++ newVal += newBuckets[newBucketSliceIdx] } } return false } // AppendHistogram appends a SparseHistogram to the chunk. We assume the // histogram is properly structured. E.g. that the number of pos/neg buckets // used corresponds to the number conveyed by the pos/neg span structures. // callers must call Appendable() first and act accordingly! func (a *HistoAppender) AppendHistogram(t int64, h histogram.SparseHistogram) { var tDelta, cntDelta, zcntDelta int64 num := binary.BigEndian.Uint16(a.b.bytes()) if value.IsStaleNaN(h.Sum) { // Emptying out other fields to write no buckets, and an empty meta in case of // first histogram in the chunk. h = histogram.SparseHistogram{Sum: h.Sum} } switch num { case 0: // the first append gets the privilege to dictate the metadata // but it's also responsible for encoding it into the chunk! writeHistoChunkMeta(a.b, h.Schema, h.ZeroThreshold, h.PositiveSpans, h.NegativeSpans) a.schema = h.Schema a.zeroThreshold = h.ZeroThreshold a.posSpans, a.negSpans = h.PositiveSpans, h.NegativeSpans numPosBuckets, numNegBuckets := countSpans(h.PositiveSpans), countSpans(h.NegativeSpans) a.posbuckets = make([]int64, numPosBuckets) a.negbuckets = make([]int64, numNegBuckets) a.posbucketsDelta = make([]int64, numPosBuckets) a.negbucketsDelta = make([]int64, numNegBuckets) // now store actual data putVarint(a.b, a.buf64, t) putUvarint(a.b, a.buf64, h.Count) putUvarint(a.b, a.buf64, h.ZeroCount) a.b.writeBits(math.Float64bits(h.Sum), 64) for _, buck := range h.PositiveBuckets { putVarint(a.b, a.buf64, buck) } for _, buck := range h.NegativeBuckets { putVarint(a.b, a.buf64, buck) } case 1: tDelta = t - a.t cntDelta = int64(h.Count) - int64(a.cnt) zcntDelta = int64(h.ZeroCount) - int64(a.zcnt) if value.IsStaleNaN(h.Sum) { cntDelta, zcntDelta = 0, 0 } putVarint(a.b, a.buf64, tDelta) putVarint(a.b, a.buf64, cntDelta) putVarint(a.b, a.buf64, zcntDelta) a.writeSumDelta(h.Sum) for i, buck := range h.PositiveBuckets { delta := buck - a.posbuckets[i] putVarint(a.b, a.buf64, delta) a.posbucketsDelta[i] = delta } for i, buck := range h.NegativeBuckets { delta := buck - a.negbuckets[i] putVarint(a.b, a.buf64, delta) a.negbucketsDelta[i] = delta } default: tDelta = t - a.t cntDelta = int64(h.Count) - int64(a.cnt) zcntDelta = int64(h.ZeroCount) - int64(a.zcnt) tDod := tDelta - a.tDelta cntDod := cntDelta - a.cntDelta zcntDod := zcntDelta - a.zcntDelta if value.IsStaleNaN(h.Sum) { cntDod, zcntDod = 0, 0 } putInt64VBBucket(a.b, tDod) putInt64VBBucket(a.b, cntDod) putInt64VBBucket(a.b, zcntDod) a.writeSumDelta(h.Sum) for i, buck := range h.PositiveBuckets { delta := buck - a.posbuckets[i] dod := delta - a.posbucketsDelta[i] putInt64VBBucket(a.b, dod) a.posbucketsDelta[i] = delta } for i, buck := range h.NegativeBuckets { delta := buck - a.negbuckets[i] dod := delta - a.negbucketsDelta[i] putInt64VBBucket(a.b, dod) a.negbucketsDelta[i] = delta } } binary.BigEndian.PutUint16(a.b.bytes(), num+1) a.t = t a.cnt = h.Count a.zcnt = h.ZeroCount a.tDelta = tDelta a.cntDelta = cntDelta a.zcntDelta = zcntDelta a.posbuckets, a.negbuckets = h.PositiveBuckets, h.NegativeBuckets // note that the bucket deltas were already updated above a.sum = h.Sum } // Recode converts the current chunk to accommodate an expansion of the set of // (positive and/or negative) buckets used, according to the provided // interjections, resulting in the honoring of the provided new posSpans and // negSpans. func (a *HistoAppender) Recode(posInterjections, negInterjections []Interjection, posSpans, negSpans []histogram.Span) (Chunk, Appender) { // TODO(beorn7): This currently just decodes everything and then encodes // it again with the new span layout. This can probably be done in-place // by editing the chunk. But let's first see how expensive it is in the // big picture. it := newHistoIterator(a.b.bytes()) hc := NewHistoChunk() app, err := hc.Appender() if err != nil { panic(err) } numPosBuckets, numNegBuckets := countSpans(posSpans), countSpans(negSpans) for it.Next() { tOld, hOld := it.AtHistogram() // We have to newly allocate slices for the modified buckets // here because they are kept by the appender until the next // append. // TODO(beorn7): We might be able to optimize this. posBuckets := make([]int64, numPosBuckets) negBuckets := make([]int64, numNegBuckets) // Save the modified histogram to the new chunk. hOld.PositiveSpans, hOld.NegativeSpans = posSpans, negSpans if len(posInterjections) > 0 { hOld.PositiveBuckets = interject(hOld.PositiveBuckets, posBuckets, posInterjections) } if len(negInterjections) > 0 { hOld.NegativeBuckets = interject(hOld.NegativeBuckets, negBuckets, negInterjections) } app.AppendHistogram(tOld, hOld) } return hc, app } func (a *HistoAppender) writeSumDelta(v float64) { vDelta := math.Float64bits(v) ^ math.Float64bits(a.sum) if vDelta == 0 { a.b.writeBit(zero) return } a.b.writeBit(one) leading := uint8(bits.LeadingZeros64(vDelta)) trailing := uint8(bits.TrailingZeros64(vDelta)) // Clamp number of leading zeros to avoid overflow when encoding. if leading >= 32 { leading = 31 } if a.leading != 0xff && leading >= a.leading && trailing >= a.trailing { a.b.writeBit(zero) a.b.writeBits(vDelta>>a.trailing, 64-int(a.leading)-int(a.trailing)) } else { a.leading, a.trailing = leading, trailing a.b.writeBit(one) a.b.writeBits(uint64(leading), 5) // Note that if leading == trailing == 0, then sigbits == 64. But that value doesn't actually fit into the 6 bits we have. // Luckily, we never need to encode 0 significant bits, since that would put us in the other case (vdelta == 0). // So instead we write out a 0 and adjust it back to 64 on unpacking. sigbits := 64 - leading - trailing a.b.writeBits(uint64(sigbits), 6) a.b.writeBits(vDelta>>trailing, int(sigbits)) } } type histoIterator struct { br bstreamReader numTotal uint16 numRead uint16 // Metadata: schema int32 zeroThreshold float64 posSpans, negSpans []histogram.Span // For the fields that are tracked as dod's. t int64 cnt, zcnt uint64 tDelta, cntDelta, zcntDelta int64 posbuckets, negbuckets []int64 posbucketsDelta, negbucketsDelta []int64 // The sum is Gorilla xor encoded. sum float64 leading uint8 trailing uint8 err error } func (it *histoIterator) Seek(t int64) bool { if it.err != nil { return false } for t > it.t || it.numRead == 0 { if !it.Next() { return false } } return true } func (it *histoIterator) At() (int64, float64) { panic("cannot call histoIterator.At().") } func (it *histoIterator) ChunkEncoding() Encoding { return EncSHS } func (it *histoIterator) AtHistogram() (int64, histogram.SparseHistogram) { if value.IsStaleNaN(it.sum) { return it.t, histogram.SparseHistogram{Sum: it.sum} } return it.t, histogram.SparseHistogram{ Count: it.cnt, ZeroCount: it.zcnt, Sum: it.sum, ZeroThreshold: it.zeroThreshold, Schema: it.schema, PositiveSpans: it.posSpans, NegativeSpans: it.negSpans, PositiveBuckets: it.posbuckets, NegativeBuckets: it.negbuckets, } } func (it *histoIterator) Err() error { return it.err } func (it *histoIterator) Reset(b []byte) { // The first 2 bytes contain chunk headers. // We skip that for actual samples. it.br = newBReader(b[2:]) it.numTotal = binary.BigEndian.Uint16(b) it.numRead = 0 it.t, it.cnt, it.zcnt = 0, 0, 0 it.tDelta, it.cntDelta, it.zcntDelta = 0, 0, 0 for i := range it.posbuckets { it.posbuckets[i] = 0 it.posbucketsDelta[i] = 0 } for i := range it.negbuckets { it.negbuckets[i] = 0 it.negbucketsDelta[i] = 0 } it.sum = 0 it.leading = 0 it.trailing = 0 it.err = nil } func (it *histoIterator) Next() bool { if it.err != nil || it.numRead == it.numTotal { return false } if it.numRead == 0 { // first read is responsible for reading chunk metadata and initializing fields that depend on it schema, zeroThreshold, posSpans, negSpans, err := readHistoChunkMeta(&it.br) if err != nil { it.err = err return false } it.schema = schema it.zeroThreshold = zeroThreshold it.posSpans, it.negSpans = posSpans, negSpans numPosBuckets, numNegBuckets := countSpans(posSpans), countSpans(negSpans) if numPosBuckets > 0 { it.posbuckets = make([]int64, numPosBuckets) it.posbucketsDelta = make([]int64, numPosBuckets) } if numNegBuckets > 0 { it.negbuckets = make([]int64, numNegBuckets) it.negbucketsDelta = make([]int64, numNegBuckets) } // now read actual data t, err := binary.ReadVarint(&it.br) if err != nil { it.err = err return false } it.t = t cnt, err := binary.ReadUvarint(&it.br) if err != nil { it.err = err return false } it.cnt = cnt zcnt, err := binary.ReadUvarint(&it.br) if err != nil { it.err = err return false } it.zcnt = zcnt sum, err := it.br.readBits(64) if err != nil { it.err = err return false } it.sum = math.Float64frombits(sum) for i := range it.posbuckets { v, err := binary.ReadVarint(&it.br) if err != nil { it.err = err return false } it.posbuckets[i] = v } for i := range it.negbuckets { v, err := binary.ReadVarint(&it.br) if err != nil { it.err = err return false } it.negbuckets[i] = v } it.numRead++ return true } if it.numRead == 1 { tDelta, err := binary.ReadVarint(&it.br) if err != nil { it.err = err return false } it.tDelta = tDelta it.t += int64(it.tDelta) cntDelta, err := binary.ReadVarint(&it.br) if err != nil { it.err = err return false } it.cntDelta = cntDelta it.cnt = uint64(int64(it.cnt) + it.cntDelta) zcntDelta, err := binary.ReadVarint(&it.br) if err != nil { it.err = err return false } it.zcntDelta = zcntDelta it.zcnt = uint64(int64(it.zcnt) + it.zcntDelta) ok := it.readSum() if !ok { return false } if value.IsStaleNaN(it.sum) { it.numRead++ return true } for i := range it.posbuckets { delta, err := binary.ReadVarint(&it.br) if err != nil { it.err = err return false } it.posbucketsDelta[i] = delta it.posbuckets[i] = it.posbuckets[i] + delta } for i := range it.negbuckets { delta, err := binary.ReadVarint(&it.br) if err != nil { it.err = err return false } it.negbucketsDelta[i] = delta it.negbuckets[i] = it.negbuckets[i] + delta } it.numRead++ return true } tDod, err := readInt64VBBucket(&it.br) if err != nil { it.err = err return false } it.tDelta = it.tDelta + tDod it.t += it.tDelta cntDod, err := readInt64VBBucket(&it.br) if err != nil { it.err = err return false } it.cntDelta = it.cntDelta + cntDod it.cnt = uint64(int64(it.cnt) + it.cntDelta) zcntDod, err := readInt64VBBucket(&it.br) if err != nil { it.err = err return false } it.zcntDelta = it.zcntDelta + zcntDod it.zcnt = uint64(int64(it.zcnt) + it.zcntDelta) ok := it.readSum() if !ok { return false } if value.IsStaleNaN(it.sum) { it.numRead++ return true } for i := range it.posbuckets { dod, err := readInt64VBBucket(&it.br) if err != nil { it.err = err return false } it.posbucketsDelta[i] = it.posbucketsDelta[i] + dod it.posbuckets[i] = it.posbuckets[i] + it.posbucketsDelta[i] } for i := range it.negbuckets { dod, err := readInt64VBBucket(&it.br) if err != nil { it.err = err return false } it.negbucketsDelta[i] = it.negbucketsDelta[i] + dod it.negbuckets[i] = it.negbuckets[i] + it.negbucketsDelta[i] } it.numRead++ return true } func (it *histoIterator) readSum() bool { bit, err := it.br.readBitFast() if err != nil { bit, err = it.br.readBit() } if err != nil { it.err = err return false } if bit == zero { // it.sum = it.sum } else { bit, err := it.br.readBitFast() if err != nil { bit, err = it.br.readBit() } if err != nil { it.err = err return false } if bit == zero { // reuse leading/trailing zero bits // it.leading, it.trailing = it.leading, it.trailing } else { bits, err := it.br.readBitsFast(5) if err != nil { bits, err = it.br.readBits(5) } if err != nil { it.err = err return false } it.leading = uint8(bits) bits, err = it.br.readBitsFast(6) if err != nil { bits, err = it.br.readBits(6) } if err != nil { it.err = err return false } mbits := uint8(bits) // 0 significant bits here means we overflowed and we actually need 64; see comment in encoder if mbits == 0 { mbits = 64 } it.trailing = 64 - it.leading - mbits } mbits := 64 - it.leading - it.trailing bits, err := it.br.readBitsFast(mbits) if err != nil { bits, err = it.br.readBits(mbits) } if err != nil { it.err = err return false } vbits := math.Float64bits(it.sum) vbits ^= bits << it.trailing it.sum = math.Float64frombits(vbits) } return true }