prometheus/promql/quantile.go

// 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)
	}
	if len(buckets) < 2 {
		return math.NaN()
	}
	sort.Sort(buckets)
	if !math.IsInf(buckets[len(buckets)-1].upperBound, +1) {
		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)*float64(rank/count)
}

// qauntile 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 float64(values[int(lowerIndex)].V)*(1-weight) + float64(values[int(upperIndex)].V)*weight
}