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// Copyright 2015 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 promql
import (
"math"
"sort"
"github.com/prometheus/prometheus/pkg/labels"
)
// Helpers to calculate quantiles.
// excludedLabels are the labels to exclude from signature calculation for
// quantiles.
var excludedLabels = []string{
labels.MetricName,
labels.BucketLabel,
}
type bucket struct {
upperBound float64
count float64
}
// buckets implements sort.Interface.
type buckets []bucket
func (b buckets) Len() int { return len(b) }
func (b buckets) Swap(i, j int) { b[i], b[j] = b[j], b[i] }
func (b buckets) Less(i, j int) bool { return b[i].upperBound < b[j].upperBound }
type metricWithBuckets struct {
metric labels.Labels
buckets buckets
}
// bucketQuantile calculates the quantile 'q' based on the given buckets. The
// buckets will be sorted by upperBound by this function (i.e. no sorting
// needed before calling this function). The quantile value is interpolated
// assuming a linear distribution within a bucket. However, if the quantile
// falls into the highest bucket, the upper bound of the 2nd highest bucket is
// returned. A natural lower bound of 0 is assumed if the upper bound of the
// lowest bucket is greater 0. In that case, interpolation in the lowest bucket
// happens linearly between 0 and the upper bound of the lowest bucket.
// However, if the lowest bucket has an upper bound less or equal 0, this upper
// bound is returned if the quantile falls into the lowest bucket.
//
// There are a number of special cases (once we have a way to report errors
// happening during evaluations of AST functions, we should report those
// explicitly):
//
// If 'buckets' has fewer than 2 elements, NaN is returned.
//
// If the highest bucket is not +Inf, NaN is returned.
//
// If q<0, -Inf is returned.
//
// If q>1, +Inf is returned.
func bucketQuantile(q float64, buckets buckets) float64 {
if q < 0 {
return math.Inf(-1)
}
if q > 1 {
return math.Inf(+1)
}
sort.Sort(buckets)
if !math.IsInf(buckets[len(buckets)-1].upperBound, +1) {
return math.NaN()
}
buckets = coalesceBuckets(buckets)
ensureMonotonic(buckets)
if len(buckets) < 2 {
return math.NaN()
}
rank := q * buckets[len(buckets)-1].count
b := sort.Search(len(buckets)-1, func(i int) bool { return buckets[i].count >= rank })
if b == len(buckets)-1 {
return buckets[len(buckets)-2].upperBound
}
if b == 0 && buckets[0].upperBound <= 0 {
return buckets[0].upperBound
}
var (
bucketStart float64
bucketEnd = buckets[b].upperBound
count = buckets[b].count
)
if b > 0 {
bucketStart = buckets[b-1].upperBound
count -= buckets[b-1].count
rank -= buckets[b-1].count
}
return bucketStart + (bucketEnd-bucketStart)*(rank/count)
}
// coalesceBuckets merges buckets with the same upper bound.
//
// The input buckets must be sorted.
func coalesceBuckets(buckets buckets) buckets {
last := buckets[0]
i := 0
for _, b := range buckets[1:] {
if b.upperBound == last.upperBound {
last.count += b.count
} else {
buckets[i] = last
last = b
i++
}
}
buckets[i] = last
return buckets[:i+1]
}
// The assumption that bucket counts increase monotonically with increasing
// upperBound may be violated during:
//
// * Recording rule evaluation of histogram_quantile, especially when rate()
// has been applied to the underlying bucket timeseries.
// * Evaluation of histogram_quantile computed over federated bucket
// timeseries, especially when rate() has been applied.
//
// This is because scraped data is not made available to rule evaluation or
// federation atomically, so some buckets are computed with data from the
// most recent scrapes, but the other buckets are missing data from the most
// recent scrape.
//
// Monotonicity is usually guaranteed because if a bucket with upper bound
// u1 has count c1, then any bucket with a higher upper bound u > u1 must
// have counted all c1 observations and perhaps more, so that c >= c1.
//
// Randomly interspersed partial sampling breaks that guarantee, and rate()
// exacerbates it. Specifically, suppose bucket le=1000 has a count of 10 from
// 4 samples but the bucket with le=2000 has a count of 7 from 3 samples. The
// monotonicity is broken. It is exacerbated by rate() because under normal
// operation, cumulative counting of buckets will cause the bucket counts to
// diverge such that small differences from missing samples are not a problem.
// rate() removes this divergence.)
//
// bucketQuantile depends on that monotonicity to do a binary search for the
// bucket with the φ-quantile count, so breaking the monotonicity
// guarantee causes bucketQuantile() to return undefined (nonsense) results.
//
// As a somewhat hacky solution until ingestion is atomic per scrape, we
// calculate the "envelope" of the histogram buckets, essentially removing
// any decreases in the count between successive buckets.
func ensureMonotonic(buckets buckets) {
max := buckets[0].count
for i := range buckets[1:] {
switch {
case buckets[i].count > max:
max = buckets[i].count
case buckets[i].count < max:
buckets[i].count = max
}
}
}
// quantile calculates the given quantile of a vector of samples.
//
// The Vector will be sorted.
// If 'values' has zero elements, NaN is returned.
// If q<0, -Inf is returned.
// If q>1, +Inf is returned.
func quantile(q float64, values vectorByValueHeap) float64 {
if len(values) == 0 {
return math.NaN()
}
if q < 0 {
return math.Inf(-1)
}
if q > 1 {
return math.Inf(+1)
}
sort.Sort(values)
n := float64(len(values))
// When the quantile lies between two samples,
// we use a weighted average of the two samples.
rank := q * (n - 1)
lowerIndex := math.Max(0, math.Floor(rank))
upperIndex := math.Min(n-1, lowerIndex+1)
weight := rank - math.Floor(rank)
return values[int(lowerIndex)].V*(1-weight) + values[int(upperIndex)].V*weight
}
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