prometheus/model/histogram/generic.go
Linas Medziunas 49613823f8 Reuse slices in [Float]Histogram.ReduceResolution
Signed-off-by: Linas Medziunas <linas.medziunas@gmail.com>
2023-11-28 15:45:31 +02:00

706 lines
28 KiB
Go

// Copyright 2022 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.
package histogram
import (
"errors"
"fmt"
"math"
"strings"
)
var (
ErrHistogramCountNotBigEnough = errors.New("histogram's observation count should be at least the number of observations found in the buckets")
ErrHistogramCountMismatch = errors.New("histogram's observation count should equal the number of observations found in the buckets (in absence of NaN)")
ErrHistogramNegativeBucketCount = errors.New("histogram has a bucket whose observation count is negative")
ErrHistogramSpanNegativeOffset = errors.New("histogram has a span whose offset is negative")
ErrHistogramSpansBucketsMismatch = errors.New("histogram spans specify different number of buckets than provided")
)
// BucketCount is a type constraint for the count in a bucket, which can be
// float64 (for type FloatHistogram) or uint64 (for type Histogram).
type BucketCount interface {
float64 | uint64
}
// InternalBucketCount is used internally by Histogram and FloatHistogram. The
// difference to the BucketCount above is that Histogram internally uses deltas
// between buckets rather than absolute counts (while FloatHistogram uses
// absolute counts directly). Go type parameters don't allow type
// specialization. Therefore, where special treatment of deltas between buckets
// vs. absolute counts is important, this information has to be provided as a
// separate boolean parameter "deltaBuckets".
type InternalBucketCount interface {
float64 | int64
}
// Bucket represents a bucket with lower and upper limit and the absolute count
// of samples in the bucket. It also specifies if each limit is inclusive or
// not. (Mathematically, inclusive limits create a closed interval, and
// non-inclusive limits an open interval.)
//
// To represent cumulative buckets, Lower is set to -Inf, and the Count is then
// cumulative (including the counts of all buckets for smaller values).
type Bucket[BC BucketCount] struct {
Lower, Upper float64
LowerInclusive, UpperInclusive bool
Count BC
// Index within schema. To easily compare buckets that share the same
// schema and sign (positive or negative). Irrelevant for the zero bucket.
Index int32
}
// strippedBucket is Bucket without bound values (which are expensive to calculate
// and not used in certain use cases).
type strippedBucket[BC BucketCount] struct {
count BC
index int32
}
// String returns a string representation of a Bucket, using the usual
// mathematical notation of '['/']' for inclusive bounds and '('/')' for
// non-inclusive bounds.
func (b Bucket[BC]) String() string {
var sb strings.Builder
if b.LowerInclusive {
sb.WriteRune('[')
} else {
sb.WriteRune('(')
}
fmt.Fprintf(&sb, "%g,%g", b.Lower, b.Upper)
if b.UpperInclusive {
sb.WriteRune(']')
} else {
sb.WriteRune(')')
}
fmt.Fprintf(&sb, ":%v", b.Count)
return sb.String()
}
// BucketIterator iterates over the buckets of a Histogram, returning decoded
// buckets.
type BucketIterator[BC BucketCount] interface {
// Next advances the iterator by one.
Next() bool
// At returns the current bucket.
At() Bucket[BC]
}
// baseBucketIterator provides a struct that is shared by most BucketIterator
// implementations, together with an implementation of the At method. This
// iterator can be embedded in full implementations of BucketIterator to save on
// code replication.
type baseBucketIterator[BC BucketCount, IBC InternalBucketCount] struct {
schema int32
spans []Span
buckets []IBC
positive bool // Whether this is for positive buckets.
spansIdx int // Current span within spans slice.
idxInSpan uint32 // Index in the current span. 0 <= idxInSpan < span.Length.
bucketsIdx int // Current bucket within buckets slice.
currCount IBC // Count in the current bucket.
currIdx int32 // The actual bucket index.
}
func (b *baseBucketIterator[BC, IBC]) At() Bucket[BC] {
return b.at(b.schema)
}
// at is an internal version of the exported At to enable using a different schema.
func (b *baseBucketIterator[BC, IBC]) at(schema int32) Bucket[BC] {
bucket := Bucket[BC]{
Count: BC(b.currCount),
Index: b.currIdx,
}
if b.positive {
bucket.Upper = getBound(b.currIdx, schema)
bucket.Lower = getBound(b.currIdx-1, schema)
} else {
bucket.Lower = -getBound(b.currIdx, schema)
bucket.Upper = -getBound(b.currIdx-1, schema)
}
bucket.LowerInclusive = bucket.Lower < 0
bucket.UpperInclusive = bucket.Upper > 0
return bucket
}
// strippedAt returns current strippedBucket (which lacks bucket bounds but is cheaper to compute).
func (b *baseBucketIterator[BC, IBC]) strippedAt() strippedBucket[BC] {
return strippedBucket[BC]{
count: BC(b.currCount),
index: b.currIdx,
}
}
// compactBuckets is a generic function used by both Histogram.Compact and
// FloatHistogram.Compact. Set deltaBuckets to true if the provided buckets are
// deltas. Set it to false if the buckets contain absolute counts.
func compactBuckets[IBC InternalBucketCount](buckets []IBC, spans []Span, maxEmptyBuckets int, deltaBuckets bool) ([]IBC, []Span) {
// Fast path: If there are no empty buckets AND no offset in any span is
// <= maxEmptyBuckets AND no span has length 0, there is nothing to do and we can return
// immediately. We check that first because it's cheap and presumably
// common.
nothingToDo := true
var currentBucketAbsolute IBC
for _, bucket := range buckets {
if deltaBuckets {
currentBucketAbsolute += bucket
} else {
currentBucketAbsolute = bucket
}
if currentBucketAbsolute == 0 {
nothingToDo = false
break
}
}
if nothingToDo {
for _, span := range spans {
if int(span.Offset) <= maxEmptyBuckets || span.Length == 0 {
nothingToDo = false
break
}
}
if nothingToDo {
return buckets, spans
}
}
var iBucket, iSpan int
var posInSpan uint32
currentBucketAbsolute = 0
// Helper function.
emptyBucketsHere := func() int {
i := 0
abs := currentBucketAbsolute
for uint32(i)+posInSpan < spans[iSpan].Length && abs == 0 {
i++
if i+iBucket >= len(buckets) {
break
}
abs = buckets[i+iBucket]
}
return i
}
// Merge spans with zero-offset to avoid special cases later.
if len(spans) > 1 {
for i, span := range spans[1:] {
if span.Offset == 0 {
spans[iSpan].Length += span.Length
continue
}
iSpan++
if i+1 != iSpan {
spans[iSpan] = span
}
}
spans = spans[:iSpan+1]
iSpan = 0
}
// Merge spans with zero-length to avoid special cases later.
for i, span := range spans {
if span.Length == 0 {
if i+1 < len(spans) {
spans[i+1].Offset += span.Offset
}
continue
}
if i != iSpan {
spans[iSpan] = span
}
iSpan++
}
spans = spans[:iSpan]
iSpan = 0
// Cut out empty buckets from start and end of spans, no matter
// what. Also cut out empty buckets from the middle of a span but only
// if there are more than maxEmptyBuckets consecutive empty buckets.
for iBucket < len(buckets) {
if deltaBuckets {
currentBucketAbsolute += buckets[iBucket]
} else {
currentBucketAbsolute = buckets[iBucket]
}
if nEmpty := emptyBucketsHere(); nEmpty > 0 {
if posInSpan > 0 &&
nEmpty < int(spans[iSpan].Length-posInSpan) &&
nEmpty <= maxEmptyBuckets {
// The empty buckets are in the middle of a
// span, and there are few enough to not bother.
// Just fast-forward.
iBucket += nEmpty
if deltaBuckets {
currentBucketAbsolute = 0
}
posInSpan += uint32(nEmpty)
continue
}
// In all other cases, we cut out the empty buckets.
if deltaBuckets && iBucket+nEmpty < len(buckets) {
currentBucketAbsolute = -buckets[iBucket]
buckets[iBucket+nEmpty] += buckets[iBucket]
}
buckets = append(buckets[:iBucket], buckets[iBucket+nEmpty:]...)
if posInSpan == 0 {
// Start of span.
if nEmpty == int(spans[iSpan].Length) {
// The whole span is empty.
offset := spans[iSpan].Offset
spans = append(spans[:iSpan], spans[iSpan+1:]...)
if len(spans) > iSpan {
spans[iSpan].Offset += offset + int32(nEmpty)
}
continue
}
spans[iSpan].Length -= uint32(nEmpty)
spans[iSpan].Offset += int32(nEmpty)
continue
}
// It's in the middle or in the end of the span.
// Split the current span.
newSpan := Span{
Offset: int32(nEmpty),
Length: spans[iSpan].Length - posInSpan - uint32(nEmpty),
}
spans[iSpan].Length = posInSpan
// In any case, we have to split to the next span.
iSpan++
posInSpan = 0
if newSpan.Length == 0 {
// The span is empty, so we were already at the end of a span.
// We don't have to insert the new span, just adjust the next
// span's offset, if there is one.
if iSpan < len(spans) {
spans[iSpan].Offset += int32(nEmpty)
}
continue
}
// Insert the new span.
spans = append(spans, Span{})
if iSpan+1 < len(spans) {
copy(spans[iSpan+1:], spans[iSpan:])
}
spans[iSpan] = newSpan
continue
}
iBucket++
posInSpan++
if posInSpan >= spans[iSpan].Length {
posInSpan = 0
iSpan++
}
}
if maxEmptyBuckets == 0 || len(buckets) == 0 {
return buckets, spans
}
// Finally, check if any offsets between spans are small enough to merge
// the spans.
iBucket = int(spans[0].Length)
if deltaBuckets {
currentBucketAbsolute = 0
for _, bucket := range buckets[:iBucket] {
currentBucketAbsolute += bucket
}
}
iSpan = 1
for iSpan < len(spans) {
if int(spans[iSpan].Offset) > maxEmptyBuckets {
l := int(spans[iSpan].Length)
if deltaBuckets {
for _, bucket := range buckets[iBucket : iBucket+l] {
currentBucketAbsolute += bucket
}
}
iBucket += l
iSpan++
continue
}
// Merge span with previous one and insert empty buckets.
offset := int(spans[iSpan].Offset)
spans[iSpan-1].Length += uint32(offset) + spans[iSpan].Length
spans = append(spans[:iSpan], spans[iSpan+1:]...)
newBuckets := make([]IBC, len(buckets)+offset)
copy(newBuckets, buckets[:iBucket])
copy(newBuckets[iBucket+offset:], buckets[iBucket:])
if deltaBuckets {
newBuckets[iBucket] = -currentBucketAbsolute
newBuckets[iBucket+offset] += currentBucketAbsolute
}
iBucket += offset
buckets = newBuckets
currentBucketAbsolute = buckets[iBucket]
// Note that with many merges, it would be more efficient to
// first record all the chunks of empty buckets to insert and
// then do it in one go through all the buckets.
}
return buckets, spans
}
func checkHistogramSpans(spans []Span, numBuckets int) error {
var spanBuckets int
for n, span := range spans {
if n > 0 && span.Offset < 0 {
return fmt.Errorf("span number %d with offset %d: %w", n+1, span.Offset, ErrHistogramSpanNegativeOffset)
}
spanBuckets += int(span.Length)
}
if spanBuckets != numBuckets {
return fmt.Errorf("spans need %d buckets, have %d buckets: %w", spanBuckets, numBuckets, ErrHistogramSpansBucketsMismatch)
}
return nil
}
func checkHistogramBuckets[BC BucketCount, IBC InternalBucketCount](buckets []IBC, count *BC, deltas bool) error {
if len(buckets) == 0 {
return nil
}
var last IBC
for i := 0; i < len(buckets); i++ {
var c IBC
if deltas {
c = last + buckets[i]
} else {
c = buckets[i]
}
if c < 0 {
return fmt.Errorf("bucket number %d has observation count of %v: %w", i+1, c, ErrHistogramNegativeBucketCount)
}
last = c
*count += BC(c)
}
return nil
}
func getBound(idx, schema int32) float64 {
// Here a bit of context about the behavior for the last bucket counting
// regular numbers (called simply "last bucket" below) and the bucket
// counting observations of ±Inf (called "inf bucket" below, with an idx
// one higher than that of the "last bucket"):
//
// If we apply the usual formula to the last bucket, its upper bound
// would be calculated as +Inf. The reason is that the max possible
// regular float64 number (math.MaxFloat64) doesn't coincide with one of
// the calculated bucket boundaries. So the calculated boundary has to
// be larger than math.MaxFloat64, and the only float64 larger than
// math.MaxFloat64 is +Inf. However, we want to count actual
// observations of ±Inf in the inf bucket. Therefore, we have to treat
// the upper bound of the last bucket specially and set it to
// math.MaxFloat64. (The upper bound of the inf bucket, with its idx
// being one higher than that of the last bucket, naturally comes out as
// +Inf by the usual formula. So that's fine.)
//
// math.MaxFloat64 has a frac of 0.9999999999999999 and an exp of
// 1024. If there were a float64 number following math.MaxFloat64, it
// would have a frac of 1.0 and an exp of 1024, or equivalently a frac
// of 0.5 and an exp of 1025. However, since frac must be smaller than
// 1, and exp must be smaller than 1025, either representation overflows
// a float64. (Which, in turn, is the reason that math.MaxFloat64 is the
// largest possible float64. Q.E.D.) However, the formula for
// calculating the upper bound from the idx and schema of the last
// bucket results in precisely that. It is either frac=1.0 & exp=1024
// (for schema < 0) or frac=0.5 & exp=1025 (for schema >=0). (This is,
// by the way, a power of two where the exponent itself is a power of
// two, 2¹⁰ in fact, which coinicides with a bucket boundary in all
// schemas.) So these are the special cases we have to catch below.
if schema < 0 {
exp := int(idx) << -schema
if exp == 1024 {
// This is the last bucket before the overflow bucket
// (for ±Inf observations). Return math.MaxFloat64 as
// explained above.
return math.MaxFloat64
}
return math.Ldexp(1, exp)
}
fracIdx := idx & ((1 << schema) - 1)
frac := exponentialBounds[schema][fracIdx]
exp := (int(idx) >> schema) + 1
if frac == 0.5 && exp == 1025 {
// This is the last bucket before the overflow bucket (for ±Inf
// observations). Return math.MaxFloat64 as explained above.
return math.MaxFloat64
}
return math.Ldexp(frac, exp)
}
// exponentialBounds is a precalculated table of bucket bounds in the interval
// [0.5,1) in schema 0 to 8.
var exponentialBounds = [][]float64{
// Schema "0":
{0.5},
// Schema 1:
{0.5, 0.7071067811865475},
// Schema 2:
{0.5, 0.5946035575013605, 0.7071067811865475, 0.8408964152537144},
// Schema 3:
{
0.5, 0.5452538663326288, 0.5946035575013605, 0.6484197773255048,
0.7071067811865475, 0.7711054127039704, 0.8408964152537144, 0.9170040432046711,
},
// Schema 4:
{
0.5, 0.5221368912137069, 0.5452538663326288, 0.5693943173783458,
0.5946035575013605, 0.620928906036742, 0.6484197773255048, 0.6771277734684463,
0.7071067811865475, 0.7384130729697496, 0.7711054127039704, 0.805245165974627,
0.8408964152537144, 0.8781260801866495, 0.9170040432046711, 0.9576032806985735,
},
// Schema 5:
{
0.5, 0.5109485743270583, 0.5221368912137069, 0.5335702003384117,
0.5452538663326288, 0.5571933712979462, 0.5693943173783458, 0.5818624293887887,
0.5946035575013605, 0.6076236799902344, 0.620928906036742, 0.6345254785958666,
0.6484197773255048, 0.6626183215798706, 0.6771277734684463, 0.6919549409819159,
0.7071067811865475, 0.7225904034885232, 0.7384130729697496, 0.7545822137967112,
0.7711054127039704, 0.7879904225539431, 0.805245165974627, 0.8228777390769823,
0.8408964152537144, 0.8593096490612387, 0.8781260801866495, 0.8973545375015533,
0.9170040432046711, 0.9370838170551498, 0.9576032806985735, 0.9785720620876999,
},
// Schema 6:
{
0.5, 0.5054446430258502, 0.5109485743270583, 0.5165124395106142,
0.5221368912137069, 0.5278225891802786, 0.5335702003384117, 0.5393803988785598,
0.5452538663326288, 0.5511912916539204, 0.5571933712979462, 0.5632608093041209,
0.5693943173783458, 0.5755946149764913, 0.5818624293887887, 0.5881984958251406,
0.5946035575013605, 0.6010783657263515, 0.6076236799902344, 0.6142402680534349,
0.620928906036742, 0.6276903785123455, 0.6345254785958666, 0.6414350080393891,
0.6484197773255048, 0.6554806057623822, 0.6626183215798706, 0.6698337620266515,
0.6771277734684463, 0.6845012114872953, 0.6919549409819159, 0.6994898362691555,
0.7071067811865475, 0.7148066691959849, 0.7225904034885232, 0.7304588970903234,
0.7384130729697496, 0.7464538641456323, 0.7545822137967112, 0.762799075372269,
0.7711054127039704, 0.7795022001189185, 0.7879904225539431, 0.7965710756711334,
0.805245165974627, 0.8140137109286738, 0.8228777390769823, 0.8318382901633681,
0.8408964152537144, 0.8500531768592616, 0.8593096490612387, 0.8686669176368529,
0.8781260801866495, 0.8876882462632604, 0.8973545375015533, 0.9071260877501991,
0.9170040432046711, 0.9269895625416926, 0.9370838170551498, 0.9472879907934827,
0.9576032806985735, 0.9680308967461471, 0.9785720620876999, 0.9892280131939752,
},
// Schema 7:
{
0.5, 0.5027149505564014, 0.5054446430258502, 0.5081891574554764,
0.5109485743270583, 0.5137229745593818, 0.5165124395106142, 0.5193170509806894,
0.5221368912137069, 0.5249720429003435, 0.5278225891802786, 0.5306886136446309,
0.5335702003384117, 0.5364674337629877, 0.5393803988785598, 0.5423091811066545,
0.5452538663326288, 0.5482145409081883, 0.5511912916539204, 0.5541842058618393,
0.5571933712979462, 0.5602188762048033, 0.5632608093041209, 0.5663192597993595,
0.5693943173783458, 0.572486072215902, 0.5755946149764913, 0.5787200368168754,
0.5818624293887887, 0.585021884841625, 0.5881984958251406, 0.5913923554921704,
0.5946035575013605, 0.5978321960199137, 0.6010783657263515, 0.6043421618132907,
0.6076236799902344, 0.6109230164863786, 0.6142402680534349, 0.6175755319684665,
0.620928906036742, 0.6243004885946023, 0.6276903785123455, 0.6310986751971253,
0.6345254785958666, 0.637970889198196, 0.6414350080393891, 0.6449179367033329,
0.6484197773255048, 0.6519406325959679, 0.6554806057623822, 0.659039800633032,
0.6626183215798706, 0.6662162735415805, 0.6698337620266515, 0.6734708931164728,
0.6771277734684463, 0.6808045103191123, 0.6845012114872953, 0.688217985377265,
0.6919549409819159, 0.6957121878859629, 0.6994898362691555, 0.7032879969095076,
0.7071067811865475, 0.7109463010845827, 0.7148066691959849, 0.718687998724491,
0.7225904034885232, 0.7265139979245261, 0.7304588970903234, 0.7344252166684908,
0.7384130729697496, 0.7424225829363761, 0.7464538641456323, 0.7505070348132126,
0.7545822137967112, 0.7586795205991071, 0.762799075372269, 0.7669409989204777,
0.7711054127039704, 0.7752924388424999, 0.7795022001189185, 0.7837348199827764,
0.7879904225539431, 0.7922691326262467, 0.7965710756711334, 0.8008963778413465,
0.805245165974627, 0.8096175675974316, 0.8140137109286738, 0.8184337248834821,
0.8228777390769823, 0.8273458838280969, 0.8318382901633681, 0.8363550898207981,
0.8408964152537144, 0.8454623996346523, 0.8500531768592616, 0.8546688815502312,
0.8593096490612387, 0.8639756154809185, 0.8686669176368529, 0.8733836930995842,
0.8781260801866495, 0.8828942179666361, 0.8876882462632604, 0.8925083056594671,
0.8973545375015533, 0.9022270839033115, 0.9071260877501991, 0.9120516927035263,
0.9170040432046711, 0.9219832844793128, 0.9269895625416926, 0.9320230241988943,
0.9370838170551498, 0.9421720895161669, 0.9472879907934827, 0.9524316709088368,
0.9576032806985735, 0.9628029718180622, 0.9680308967461471, 0.9732872087896164,
0.9785720620876999, 0.9838856116165875, 0.9892280131939752, 0.9945994234836328,
},
// Schema 8:
{
0.5, 0.5013556375251013, 0.5027149505564014, 0.5040779490592088,
0.5054446430258502, 0.5068150424757447, 0.5081891574554764, 0.509566998038869,
0.5109485743270583, 0.5123338964485679, 0.5137229745593818, 0.5151158188430205,
0.5165124395106142, 0.5179128468009786, 0.5193170509806894, 0.520725062344158,
0.5221368912137069, 0.5235525479396449, 0.5249720429003435, 0.526395386502313,
0.5278225891802786, 0.5292536613972564, 0.5306886136446309, 0.5321274564422321,
0.5335702003384117, 0.5350168559101208, 0.5364674337629877, 0.5379219445313954,
0.5393803988785598, 0.5408428074966075, 0.5423091811066545, 0.5437795304588847,
0.5452538663326288, 0.5467321995364429, 0.5482145409081883, 0.549700901315111,
0.5511912916539204, 0.5526857228508706, 0.5541842058618393, 0.5556867516724088,
0.5571933712979462, 0.5587040757836845, 0.5602188762048033, 0.5617377836665098,
0.5632608093041209, 0.564787964283144, 0.5663192597993595, 0.5678547070789026,
0.5693943173783458, 0.5709381019847808, 0.572486072215902, 0.5740382394200894,
0.5755946149764913, 0.5771552102951081, 0.5787200368168754, 0.5802891060137493,
0.5818624293887887, 0.5834400184762408, 0.585021884841625, 0.5866080400818185,
0.5881984958251406, 0.5897932637314379, 0.5913923554921704, 0.5929957828304968,
0.5946035575013605, 0.5962156912915756, 0.5978321960199137, 0.5994530835371903,
0.6010783657263515, 0.6027080545025619, 0.6043421618132907, 0.6059806996384005,
0.6076236799902344, 0.6092711149137041, 0.6109230164863786, 0.6125793968185725,
0.6142402680534349, 0.6159056423670379, 0.6175755319684665, 0.6192499490999082,
0.620928906036742, 0.622612415087629, 0.6243004885946023, 0.6259931389331581,
0.6276903785123455, 0.6293922197748583, 0.6310986751971253, 0.6328097572894031,
0.6345254785958666, 0.6362458516947014, 0.637970889198196, 0.6397006037528346,
0.6414350080393891, 0.6431741147730128, 0.6449179367033329, 0.6466664866145447,
0.6484197773255048, 0.6501778216898253, 0.6519406325959679, 0.6537082229673385,
0.6554806057623822, 0.6572577939746774, 0.659039800633032, 0.6608266388015788,
0.6626183215798706, 0.6644148621029772, 0.6662162735415805, 0.6680225691020727,
0.6698337620266515, 0.6716498655934177, 0.6734708931164728, 0.6752968579460171,
0.6771277734684463, 0.6789636531064505, 0.6808045103191123, 0.6826503586020058,
0.6845012114872953, 0.6863570825438342, 0.688217985377265, 0.690083933630119,
0.6919549409819159, 0.6938310211492645, 0.6957121878859629, 0.6975984549830999,
0.6994898362691555, 0.7013863456101023, 0.7032879969095076, 0.7051948041086352,
0.7071067811865475, 0.7090239421602076, 0.7109463010845827, 0.7128738720527471,
0.7148066691959849, 0.7167447066838943, 0.718687998724491, 0.7206365595643126,
0.7225904034885232, 0.7245495448210174, 0.7265139979245261, 0.7284837772007218,
0.7304588970903234, 0.7324393720732029, 0.7344252166684908, 0.7364164454346837,
0.7384130729697496, 0.7404151139112358, 0.7424225829363761, 0.7444354947621984,
0.7464538641456323, 0.7484777058836176, 0.7505070348132126, 0.7525418658117031,
0.7545822137967112, 0.7566280937263048, 0.7586795205991071, 0.7607365094544071,
0.762799075372269, 0.7648672334736434, 0.7669409989204777, 0.7690203869158282,
0.7711054127039704, 0.7731960915705107, 0.7752924388424999, 0.7773944698885442,
0.7795022001189185, 0.7816156449856788, 0.7837348199827764, 0.7858597406461707,
0.7879904225539431, 0.7901268813264122, 0.7922691326262467, 0.7944171921585818,
0.7965710756711334, 0.7987307989543135, 0.8008963778413465, 0.8030678282083853,
0.805245165974627, 0.8074284071024302, 0.8096175675974316, 0.8118126635086642,
0.8140137109286738, 0.8162207259936375, 0.8184337248834821, 0.820652723822003,
0.8228777390769823, 0.8251087869603088, 0.8273458838280969, 0.8295890460808079,
0.8318382901633681, 0.8340936325652911, 0.8363550898207981, 0.8386226785089391,
0.8408964152537144, 0.8431763167241966, 0.8454623996346523, 0.8477546807446661,
0.8500531768592616, 0.8523579048290255, 0.8546688815502312, 0.8569861239649629,
0.8593096490612387, 0.8616394738731368, 0.8639756154809185, 0.8663180910111553,
0.8686669176368529, 0.871022112577578, 0.8733836930995842, 0.8757516765159389,
0.8781260801866495, 0.8805069215187917, 0.8828942179666361, 0.8852879870317771,
0.8876882462632604, 0.890095013257712, 0.8925083056594671, 0.8949281411607002,
0.8973545375015533, 0.8997875124702672, 0.9022270839033115, 0.9046732696855155,
0.9071260877501991, 0.909585556079304, 0.9120516927035263, 0.9145245157024483,
0.9170040432046711, 0.9194902933879467, 0.9219832844793128, 0.9244830347552253,
0.9269895625416926, 0.92950288621441, 0.9320230241988943, 0.9345499949706191,
0.9370838170551498, 0.93962450902828, 0.9421720895161669, 0.9447265771954693,
0.9472879907934827, 0.9498563490882775, 0.9524316709088368, 0.9550139751351947,
0.9576032806985735, 0.9601996065815236, 0.9628029718180622, 0.9654133954938133,
0.9680308967461471, 0.9706554947643201, 0.9732872087896164, 0.9759260581154889,
0.9785720620876999, 0.9812252401044634, 0.9838856116165875, 0.9865531961276168,
0.9892280131939752, 0.9919100824251095, 0.9945994234836328, 0.9972960560854698,
},
}
// reduceResolution reduces the input spans, buckets in origin schema to the spans, buckets in target schema.
// The target schema must be smaller than the original schema.
// Set deltaBuckets to true if the provided buckets are
// deltas. Set it to false if the buckets contain absolute counts.
// Set inplace to true to reuse input slices and avoid allocations (otherwise
// new slices will be allocated for result).
func reduceResolution[IBC InternalBucketCount](
originSpans []Span,
originBuckets []IBC,
originSchema,
targetSchema int32,
deltaBuckets bool,
inplace bool,
) ([]Span, []IBC) {
var (
targetSpans []Span // The spans in the target schema.
targetBuckets []IBC // The bucket counts in the target schema.
bucketIdx int32 // The index of bucket in the origin schema.
bucketCountIdx int // The position of a bucket in origin bucket count slice `originBuckets`.
targetBucketIdx int32 // The index of bucket in the target schema.
lastBucketCount IBC // The last visited bucket's count in the origin schema.
lastTargetBucketIdx int32 // The index of the last added target bucket.
lastTargetBucketCount IBC
)
if inplace {
// Slice reuse is safe because when reducing the resolution,
// target slices don't grow faster than origin slices are being read.
targetSpans = originSpans[:0]
targetBuckets = originBuckets[:0]
}
for _, span := range originSpans {
// Determine the index of the first bucket in this span.
bucketIdx += span.Offset
for j := 0; j < int(span.Length); j++ {
// Determine the index of the bucket in the target schema from the index in the original schema.
targetBucketIdx = targetIdx(bucketIdx, originSchema, targetSchema)
switch {
case len(targetSpans) == 0:
// This is the first span in the targetSpans.
span := Span{
Offset: targetBucketIdx,
Length: 1,
}
targetSpans = append(targetSpans, span)
targetBuckets = append(targetBuckets, originBuckets[bucketCountIdx])
lastTargetBucketIdx = targetBucketIdx
lastBucketCount = originBuckets[bucketCountIdx]
lastTargetBucketCount = originBuckets[bucketCountIdx]
case lastTargetBucketIdx == targetBucketIdx:
// The current bucket has to be merged into the same target bucket as the previous bucket.
if deltaBuckets {
lastBucketCount += originBuckets[bucketCountIdx]
targetBuckets[len(targetBuckets)-1] += lastBucketCount
lastTargetBucketCount += lastBucketCount
} else {
targetBuckets[len(targetBuckets)-1] += originBuckets[bucketCountIdx]
}
case (lastTargetBucketIdx + 1) == targetBucketIdx:
// The current bucket has to go into a new target bucket,
// and that bucket is next to the previous target bucket,
// so we add it to the current target span.
targetSpans[len(targetSpans)-1].Length++
lastTargetBucketIdx++
if deltaBuckets {
lastBucketCount += originBuckets[bucketCountIdx]
targetBuckets = append(targetBuckets, lastBucketCount-lastTargetBucketCount)
lastTargetBucketCount = lastBucketCount
} else {
targetBuckets = append(targetBuckets, originBuckets[bucketCountIdx])
}
case (lastTargetBucketIdx + 1) < targetBucketIdx:
// The current bucket has to go into a new target bucket,
// and that bucket is separated by a gap from the previous target bucket,
// so we need to add a new target span.
span := Span{
Offset: targetBucketIdx - lastTargetBucketIdx - 1,
Length: 1,
}
targetSpans = append(targetSpans, span)
lastTargetBucketIdx = targetBucketIdx
if deltaBuckets {
lastBucketCount += originBuckets[bucketCountIdx]
targetBuckets = append(targetBuckets, lastBucketCount-lastTargetBucketCount)
lastTargetBucketCount = lastBucketCount
} else {
targetBuckets = append(targetBuckets, originBuckets[bucketCountIdx])
}
}
bucketIdx++
bucketCountIdx++
}
}
return targetSpans, targetBuckets
}