VictoriaMetrics/app/vmselect/promql/aggr.go

package promql

import (
	"fmt"
	"math"
	"sort"
	"strconv"
	"strings"

	"github.com/VictoriaMetrics/VictoriaMetrics/lib/logger"
	"github.com/VictoriaMetrics/VictoriaMetrics/lib/storage"
	"github.com/VictoriaMetrics/metrics"
	"github.com/VictoriaMetrics/metricsql"
	xxhash "github.com/cespare/xxhash/v2"
)

var aggrFuncs = map[string]aggrFunc{
	// See https://prometheus.io/docs/prometheus/latest/querying/operators/#aggregation-operators
	"sum":          newAggrFunc(aggrFuncSum),
	"min":          newAggrFunc(aggrFuncMin),
	"max":          newAggrFunc(aggrFuncMax),
	"avg":          newAggrFunc(aggrFuncAvg),
	"stddev":       newAggrFunc(aggrFuncStddev),
	"stdvar":       newAggrFunc(aggrFuncStdvar),
	"count":        newAggrFunc(aggrFuncCount),
	"count_values": aggrFuncCountValues,
	"bottomk":      newAggrFuncTopK(true),
	"topk":         newAggrFuncTopK(false),
	"quantile":     aggrFuncQuantile,
	"group":        newAggrFunc(aggrFuncGroup),

	// PromQL extension funcs
	"median":         aggrFuncMedian,
	"limitk":         aggrFuncLimitK,
	"distinct":       newAggrFunc(aggrFuncDistinct),
	"sum2":           newAggrFunc(aggrFuncSum2),
	"geomean":        newAggrFunc(aggrFuncGeomean),
	"histogram":      newAggrFunc(aggrFuncHistogram),
	"topk_min":       newAggrFuncRangeTopK(minValue, false),
	"topk_max":       newAggrFuncRangeTopK(maxValue, false),
	"topk_avg":       newAggrFuncRangeTopK(avgValue, false),
	"topk_median":    newAggrFuncRangeTopK(medianValue, false),
	"topk_last":      newAggrFuncRangeTopK(lastValue, false),
	"bottomk_min":    newAggrFuncRangeTopK(minValue, true),
	"bottomk_max":    newAggrFuncRangeTopK(maxValue, true),
	"bottomk_avg":    newAggrFuncRangeTopK(avgValue, true),
	"bottomk_median": newAggrFuncRangeTopK(medianValue, true),
	"bottomk_last":   newAggrFuncRangeTopK(lastValue, true),
	"any":            aggrFuncAny,
	"mad":            newAggrFunc(aggrFuncMAD),
	"outliers_mad":   aggrFuncOutliersMAD,
	"outliersk":      aggrFuncOutliersK,
	"mode":           newAggrFunc(aggrFuncMode),
	"zscore":         aggrFuncZScore,
	"quantiles":      aggrFuncQuantiles,
}

type aggrFunc func(afa *aggrFuncArg) ([]*timeseries, error)

type aggrFuncArg struct {
	args [][]*timeseries
	ae   *metricsql.AggrFuncExpr
	ec   *EvalConfig
}

func getAggrFunc(s string) aggrFunc {
	s = strings.ToLower(s)
	return aggrFuncs[s]
}

func newAggrFunc(afe func(tss []*timeseries) []*timeseries) aggrFunc {
	return func(afa *aggrFuncArg) ([]*timeseries, error) {
		tss, err := getAggrTimeseries(afa.args)
		if err != nil {
			return nil, err
		}
		return aggrFuncExt(func(tss []*timeseries, modififer *metricsql.ModifierExpr) []*timeseries {
			return afe(tss)
		}, tss, &afa.ae.Modifier, afa.ae.Limit, false)
	}
}

func getAggrTimeseries(args [][]*timeseries) ([]*timeseries, error) {
	if len(args) == 0 {
		return nil, fmt.Errorf("expecting at least one arg")
	}
	tss := args[0]
	for _, arg := range args[1:] {
		tss = append(tss, arg...)
	}
	return tss, nil
}

func removeGroupTags(metricName *storage.MetricName, modifier *metricsql.ModifierExpr) {
	groupOp := strings.ToLower(modifier.Op)
	switch groupOp {
	case "", "by":
		metricName.RemoveTagsOn(modifier.Args)
	case "without":
		metricName.RemoveTagsIgnoring(modifier.Args)
		// Reset metric group as Prometheus does on `aggr(...) without (...)` call.
		metricName.ResetMetricGroup()
	default:
		logger.Panicf("BUG: unknown group modifier: %q", groupOp)
	}
}

func aggrFuncExt(afe func(tss []*timeseries, modifier *metricsql.ModifierExpr) []*timeseries, argOrig []*timeseries,
	modifier *metricsql.ModifierExpr, maxSeries int, keepOriginal bool) ([]*timeseries, error) {
	arg := copyTimeseriesMetricNames(argOrig, keepOriginal)

	// Perform grouping.
	m := make(map[string][]*timeseries)
	bb := bbPool.Get()
	for i, ts := range arg {
		removeGroupTags(&ts.MetricName, modifier)
		bb.B = marshalMetricNameSorted(bb.B[:0], &ts.MetricName)
		if keepOriginal {
			ts = argOrig[i]
		}
		tss := m[string(bb.B)]
		if tss == nil && maxSeries > 0 && len(m) >= maxSeries {
			// We already reached time series limit after grouping. Skip other time series.
			continue
		}
		tss = append(tss, ts)
		m[string(bb.B)] = tss
	}
	bbPool.Put(bb)

	srcTssCount := 0
	dstTssCount := 0
	rvs := make([]*timeseries, 0, len(m))
	for _, tss := range m {
		rv := afe(tss, modifier)
		rvs = append(rvs, rv...)
		srcTssCount += len(tss)
		dstTssCount += len(rv)
		if dstTssCount > 2000 && dstTssCount > 16*srcTssCount {
			// This looks like count_values explosion.
			return nil, fmt.Errorf(`too many timeseries after aggragation; got %d; want less than %d`, dstTssCount, 16*srcTssCount)
		}
	}
	return rvs, nil
}

func aggrFuncAny(afa *aggrFuncArg) ([]*timeseries, error) {
	tss, err := getAggrTimeseries(afa.args)
	if err != nil {
		return nil, err
	}
	afe := func(tss []*timeseries, modifier *metricsql.ModifierExpr) []*timeseries {
		return tss[:1]
	}
	limit := afa.ae.Limit
	if limit > 1 {
		// Only a single time series per group must be returned
		limit = 1
	}
	return aggrFuncExt(afe, tss, &afa.ae.Modifier, limit, true)
}

func aggrFuncGroup(tss []*timeseries) []*timeseries {
	// See https://github.com/prometheus/prometheus/commit/72425d4e3d14d209cc3f3f6e10e3240411303399
	dst := tss[0]
	for i := range dst.Values {
		v := nan
		for _, ts := range tss {
			if math.IsNaN(ts.Values[i]) {
				continue
			}
			v = 1
		}
		dst.Values[i] = v
	}
	return tss[:1]
}

func aggrFuncSum(tss []*timeseries) []*timeseries {
	if len(tss) == 1 {
		// Fast path - nothing to sum.
		return tss
	}
	dst := tss[0]
	for i := range dst.Values {
		sum := float64(0)
		count := 0
		for _, ts := range tss {
			v := ts.Values[i]
			if math.IsNaN(v) {
				continue
			}
			sum += v
			count++
		}
		if count == 0 {
			sum = nan
		}
		dst.Values[i] = sum
	}
	return tss[:1]
}

func aggrFuncSum2(tss []*timeseries) []*timeseries {
	dst := tss[0]
	for i := range dst.Values {
		sum2 := float64(0)
		count := 0
		for _, ts := range tss {
			v := ts.Values[i]
			if math.IsNaN(v) {
				continue
			}
			sum2 += v * v
			count++
		}
		if count == 0 {
			sum2 = nan
		}
		dst.Values[i] = sum2
	}
	return tss[:1]
}

func aggrFuncGeomean(tss []*timeseries) []*timeseries {
	if len(tss) == 1 {
		// Fast path - nothing to geomean.
		return tss
	}
	dst := tss[0]
	for i := range dst.Values {
		p := 1.0
		count := 0
		for _, ts := range tss {
			v := ts.Values[i]
			if math.IsNaN(v) {
				continue
			}
			p *= v
			count++
		}
		if count == 0 {
			p = nan
		}
		dst.Values[i] = math.Pow(p, 1/float64(count))
	}
	return tss[:1]
}

func aggrFuncHistogram(tss []*timeseries) []*timeseries {
	var h metrics.Histogram
	m := make(map[string]*timeseries)
	for i := range tss[0].Values {
		h.Reset()
		for _, ts := range tss {
			v := ts.Values[i]
			h.Update(v)
		}
		h.VisitNonZeroBuckets(func(vmrange string, count uint64) {
			ts := m[vmrange]
			if ts == nil {
				ts = &timeseries{}
				ts.CopyFromShallowTimestamps(tss[0])
				ts.MetricName.RemoveTag("vmrange")
				ts.MetricName.AddTag("vmrange", vmrange)
				values := ts.Values
				for k := range values {
					values[k] = 0
				}
				m[vmrange] = ts
			}
			ts.Values[i] = float64(count)
		})
	}
	rvs := make([]*timeseries, 0, len(m))
	for _, ts := range m {
		rvs = append(rvs, ts)
	}
	return vmrangeBucketsToLE(rvs)
}

func aggrFuncMin(tss []*timeseries) []*timeseries {
	if len(tss) == 1 {
		// Fast path - nothing to min.
		return tss
	}
	dst := tss[0]
	for i := range dst.Values {
		min := dst.Values[i]
		for _, ts := range tss {
			if math.IsNaN(min) || ts.Values[i] < min {
				min = ts.Values[i]
			}
		}
		dst.Values[i] = min
	}
	return tss[:1]
}

func aggrFuncMax(tss []*timeseries) []*timeseries {
	if len(tss) == 1 {
		// Fast path - nothing to max.
		return tss
	}
	dst := tss[0]
	for i := range dst.Values {
		max := dst.Values[i]
		for _, ts := range tss {
			if math.IsNaN(max) || ts.Values[i] > max {
				max = ts.Values[i]
			}
		}
		dst.Values[i] = max
	}
	return tss[:1]
}

func aggrFuncAvg(tss []*timeseries) []*timeseries {
	if len(tss) == 1 {
		// Fast path - nothing to avg.
		return tss
	}
	dst := tss[0]
	for i := range dst.Values {
		// Do not use `Rapid calculation methods` at https://en.wikipedia.org/wiki/Standard_deviation,
		// since it is slower and has no obvious benefits in increased precision.
		var sum float64
		count := 0
		for _, ts := range tss {
			v := ts.Values[i]
			if math.IsNaN(v) {
				continue
			}
			count++
			sum += v
		}
		avg := nan
		if count > 0 {
			avg = sum / float64(count)
		}
		dst.Values[i] = avg
	}
	return tss[:1]
}

func aggrFuncStddev(tss []*timeseries) []*timeseries {
	if len(tss) == 1 {
		// Fast path - stddev over a single time series is zero
		values := tss[0].Values
		for i, v := range values {
			if !math.IsNaN(v) {
				values[i] = 0
			}
		}
		return tss
	}
	rvs := aggrFuncStdvar(tss)
	dst := rvs[0]
	for i, v := range dst.Values {
		dst.Values[i] = math.Sqrt(v)
	}
	return rvs
}

func aggrFuncStdvar(tss []*timeseries) []*timeseries {
	if len(tss) == 1 {
		// Fast path - stdvar over a single time series is zero
		values := tss[0].Values
		for i, v := range values {
			if !math.IsNaN(v) {
				values[i] = 0
			}
		}
		return tss
	}
	dst := tss[0]
	for i := range dst.Values {
		// See `Rapid calculation methods` at https://en.wikipedia.org/wiki/Standard_deviation
		var avg, count, q float64
		for _, ts := range tss {
			v := ts.Values[i]
			if math.IsNaN(v) {
				continue
			}
			count++
			avgNew := avg + (v-avg)/count
			q += (v - avg) * (v - avgNew)
			avg = avgNew
		}
		if count == 0 {
			q = nan
		}
		dst.Values[i] = q / count
	}
	return tss[:1]
}

func aggrFuncCount(tss []*timeseries) []*timeseries {
	dst := tss[0]
	for i := range dst.Values {
		count := 0
		for _, ts := range tss {
			if math.IsNaN(ts.Values[i]) {
				continue
			}
			count++
		}
		v := float64(count)
		if count == 0 {
			v = nan
		}
		dst.Values[i] = v
	}
	return tss[:1]
}

func aggrFuncDistinct(tss []*timeseries) []*timeseries {
	dst := tss[0]
	m := make(map[float64]struct{}, len(tss))
	for i := range dst.Values {
		for _, ts := range tss {
			v := ts.Values[i]
			if math.IsNaN(v) {
				continue
			}
			m[v] = struct{}{}
		}
		n := float64(len(m))
		if n == 0 {
			n = nan
		}
		dst.Values[i] = n
		for k := range m {
			delete(m, k)
		}
	}
	return tss[:1]
}

func aggrFuncMode(tss []*timeseries) []*timeseries {
	dst := tss[0]
	a := make([]float64, 0, len(tss))
	for i := range dst.Values {
		a := a[:0]
		for _, ts := range tss {
			v := ts.Values[i]
			if !math.IsNaN(v) {
				a = append(a, v)
			}
		}
		dst.Values[i] = modeNoNaNs(nan, a)
	}
	return tss[:1]
}

func aggrFuncZScore(afa *aggrFuncArg) ([]*timeseries, error) {
	tss, err := getAggrTimeseries(afa.args)
	if err != nil {
		return nil, err
	}
	afe := func(tss []*timeseries, modifier *metricsql.ModifierExpr) []*timeseries {
		for i := range tss[0].Values {
			// Calculate avg and stddev for tss points at position i.
			// See `Rapid calculation methods` at https://en.wikipedia.org/wiki/Standard_deviation
			var avg, count, q float64
			for _, ts := range tss {
				v := ts.Values[i]
				if math.IsNaN(v) {
					continue
				}
				count++
				avgNew := avg + (v-avg)/count
				q += (v - avg) * (v - avgNew)
				avg = avgNew
			}
			if count == 0 {
				// Cannot calculate z-score for NaN points.
				continue
			}

			// Calculate z-score for tss points at position i.
			// See https://en.wikipedia.org/wiki/Standard_score
			stddev := math.Sqrt(q / count)
			for _, ts := range tss {
				v := ts.Values[i]
				if math.IsNaN(v) {
					continue
				}
				ts.Values[i] = (v - avg) / stddev
			}
		}
		// Remove MetricGroup from all the tss.
		for _, ts := range tss {
			ts.MetricName.ResetMetricGroup()
		}
		return tss
	}
	return aggrFuncExt(afe, tss, &afa.ae.Modifier, afa.ae.Limit, true)
}

// modeNoNaNs returns mode for a.
//
// It is expected that a doesn't contain NaNs.
//
// The function modifies contents for a, so the caller must prepare it accordingly.
//
// See https://en.wikipedia.org/wiki/Mode_(statistics)
func modeNoNaNs(prevValue float64, a []float64) float64 {
	if len(a) == 0 {
		return prevValue
	}
	sort.Float64s(a)
	j := -1
	dMax := 0
	mode := prevValue
	for i, v := range a {
		if prevValue == v {
			continue
		}
		if d := i - j; d > dMax || math.IsNaN(mode) {
			dMax = d
			mode = prevValue
		}
		j = i
		prevValue = v
	}
	if d := len(a) - j; d > dMax || math.IsNaN(mode) {
		mode = prevValue
	}
	return mode
}

func aggrFuncCountValues(afa *aggrFuncArg) ([]*timeseries, error) {
	args := afa.args
	if err := expectTransformArgsNum(args, 2); err != nil {
		return nil, err
	}
	dstLabel, err := getString(args[0], 0)
	if err != nil {
		return nil, err
	}

	// Remove dstLabel from grouping like Prometheus does.
	modifier := &afa.ae.Modifier
	switch strings.ToLower(modifier.Op) {
	case "without":
		modifier.Args = append(modifier.Args, dstLabel)
	case "by":
		dstArgs := modifier.Args[:0]
		for _, arg := range modifier.Args {
			if arg == dstLabel {
				continue
			}
			dstArgs = append(dstArgs, arg)
		}
		modifier.Args = dstArgs
	default:
		// Do nothing
	}

	afe := func(tss []*timeseries, modififer *metricsql.ModifierExpr) []*timeseries {
		m := make(map[float64]bool)
		for _, ts := range tss {
			for _, v := range ts.Values {
				if math.IsNaN(v) {
					continue
				}
				m[v] = true
			}
		}
		values := make([]float64, 0, len(m))
		for v := range m {
			values = append(values, v)
		}
		sort.Float64s(values)

		var rvs []*timeseries
		for _, v := range values {
			var dst timeseries
			dst.CopyFromShallowTimestamps(tss[0])
			dst.MetricName.RemoveTag(dstLabel)
			dst.MetricName.AddTag(dstLabel, strconv.FormatFloat(v, 'f', -1, 64))
			for i := range dst.Values {
				count := 0
				for _, ts := range tss {
					if ts.Values[i] == v {
						count++
					}
				}
				n := float64(count)
				if n == 0 {
					n = nan
				}
				dst.Values[i] = n
			}
			rvs = append(rvs, &dst)
		}
		return rvs
	}
	return aggrFuncExt(afe, args[1], &afa.ae.Modifier, afa.ae.Limit, false)
}

func newAggrFuncTopK(isReverse bool) aggrFunc {
	return func(afa *aggrFuncArg) ([]*timeseries, error) {
		args := afa.args
		if err := expectTransformArgsNum(args, 2); err != nil {
			return nil, err
		}
		ks, err := getScalar(args[0], 0)
		if err != nil {
			return nil, err
		}
		afe := func(tss []*timeseries, modififer *metricsql.ModifierExpr) []*timeseries {
			for n := range tss[0].Values {
				sort.Slice(tss, func(i, j int) bool {
					a := tss[i].Values[n]
					b := tss[j].Values[n]
					if isReverse {
						a, b = b, a
					}
					return lessWithNaNs(a, b)
				})
				fillNaNsAtIdx(n, ks[n], tss)
			}
			tss = removeNaNs(tss)
			reverseSeries(tss)
			return tss
		}
		return aggrFuncExt(afe, args[1], &afa.ae.Modifier, afa.ae.Limit, true)
	}
}

func newAggrFuncRangeTopK(f func(values []float64) float64, isReverse bool) aggrFunc {
	return func(afa *aggrFuncArg) ([]*timeseries, error) {
		args := afa.args
		if len(args) < 2 {
			return nil, fmt.Errorf(`unexpected number of args; got %d; want at least %d`, len(args), 2)
		}
		if len(args) > 3 {
			return nil, fmt.Errorf(`unexpected number of args; got %d; want no more than %d`, len(args), 3)
		}
		ks, err := getScalar(args[0], 0)
		if err != nil {
			return nil, err
		}
		remainingSumTagName := ""
		if len(args) == 3 {
			remainingSumTagName, err = getString(args[2], 2)
			if err != nil {
				return nil, err
			}
		}
		afe := func(tss []*timeseries, modifier *metricsql.ModifierExpr) []*timeseries {
			return getRangeTopKTimeseries(tss, modifier, ks, remainingSumTagName, f, isReverse)
		}
		return aggrFuncExt(afe, args[1], &afa.ae.Modifier, afa.ae.Limit, true)
	}
}

func getRangeTopKTimeseries(tss []*timeseries, modifier *metricsql.ModifierExpr, ks []float64, remainingSumTagName string,
	f func(values []float64) float64, isReverse bool) []*timeseries {
	type tsWithValue struct {
		ts    *timeseries
		value float64
	}
	maxs := make([]tsWithValue, len(tss))
	for i, ts := range tss {
		value := f(ts.Values)
		maxs[i] = tsWithValue{
			ts:    ts,
			value: value,
		}
	}
	sort.Slice(maxs, func(i, j int) bool {
		a := maxs[i].value
		b := maxs[j].value
		if isReverse {
			a, b = b, a
		}
		return lessWithNaNs(a, b)
	})
	for i := range maxs {
		tss[i] = maxs[i].ts
	}
	remainingSumTS := getRemainingSumTimeseries(tss, modifier, ks, remainingSumTagName)
	for i, k := range ks {
		fillNaNsAtIdx(i, k, tss)
	}
	if remainingSumTS != nil {
		tss = append(tss, remainingSumTS)
	}
	tss = removeNaNs(tss)
	reverseSeries(tss)
	return tss
}

func reverseSeries(tss []*timeseries) {
	j := len(tss)
	for i := 0; i < len(tss)/2; i++ {
		j--
		tss[i], tss[j] = tss[j], tss[i]
	}
}

func getRemainingSumTimeseries(tss []*timeseries, modifier *metricsql.ModifierExpr, ks []float64, remainingSumTagName string) *timeseries {
	if len(remainingSumTagName) == 0 || len(tss) == 0 {
		return nil
	}
	var dst timeseries
	dst.CopyFromShallowTimestamps(tss[0])
	removeGroupTags(&dst.MetricName, modifier)
	tagValue := remainingSumTagName
	n := strings.IndexByte(remainingSumTagName, '=')
	if n >= 0 {
		tagValue = remainingSumTagName[n+1:]
		remainingSumTagName = remainingSumTagName[:n]
	}
	dst.MetricName.RemoveTag(remainingSumTagName)
	dst.MetricName.AddTag(remainingSumTagName, tagValue)
	for i, k := range ks {
		kn := getIntK(k, len(tss))
		var sum float64
		count := 0
		for _, ts := range tss[:len(tss)-kn] {
			v := ts.Values[i]
			if math.IsNaN(v) {
				continue
			}
			sum += v
			count++
		}
		if count == 0 {
			sum = nan
		}
		dst.Values[i] = sum
	}
	return &dst
}

func fillNaNsAtIdx(idx int, k float64, tss []*timeseries) {
	kn := getIntK(k, len(tss))
	for _, ts := range tss[:len(tss)-kn] {
		ts.Values[idx] = nan
	}
}

func getIntK(k float64, kMax int) int {
	if math.IsNaN(k) {
		return 0
	}
	kn := int(k)
	if kn < 0 {
		return 0
	}
	if kn > kMax {
		return kMax
	}
	return kn
}

func minValue(values []float64) float64 {
	min := nan
	for len(values) > 0 && math.IsNaN(min) {
		min = values[0]
		values = values[1:]
	}
	for _, v := range values {
		if !math.IsNaN(v) && v < min {
			min = v
		}
	}
	return min
}

func maxValue(values []float64) float64 {
	max := nan
	for len(values) > 0 && math.IsNaN(max) {
		max = values[0]
		values = values[1:]
	}
	for _, v := range values {
		if !math.IsNaN(v) && v > max {
			max = v
		}
	}
	return max
}

func avgValue(values []float64) float64 {
	sum := float64(0)
	count := 0
	for _, v := range values {
		if math.IsNaN(v) {
			continue
		}
		count++
		sum += v
	}
	if count == 0 {
		return nan
	}
	return sum / float64(count)
}

func medianValue(values []float64) float64 {
	return quantile(0.5, values)
}

func lastValue(values []float64) float64 {
	values = skipTrailingNaNs(values)
	if len(values) == 0 {
		return nan
	}
	return values[len(values)-1]
}

// quantiles calculates the given phis from originValues without modifying originValues, appends them to qs and returns the result.
func quantiles(qs, phis []float64, originValues []float64) []float64 {
	a := getFloat64s()
	a.A = prepareForQuantileFloat64(a.A[:0], originValues)
	qs = quantilesSorted(qs, phis, a.A)
	putFloat64s(a)
	return qs
}

// quantile calculates the given phi from originValues without modifying originValues
func quantile(phi float64, originValues []float64) float64 {
	a := getFloat64s()
	a.A = prepareForQuantileFloat64(a.A[:0], originValues)
	q := quantileSorted(phi, a.A)
	putFloat64s(a)
	return q
}

// prepareForQuantileFloat64 copies items from src to dst but removes NaNs and sorts the dst
func prepareForQuantileFloat64(dst, src []float64) []float64 {
	for _, v := range src {
		if math.IsNaN(v) {
			continue
		}
		dst = append(dst, v)
	}
	sort.Float64s(dst)
	return dst
}

// quantilesSorted calculates the given phis over a sorted list of values, appends them to qs and returns the result.
//
// It is expected that values won't contain NaN items.
// The implementation mimics Prometheus implementation for compatibility's sake.
func quantilesSorted(qs, phis []float64, values []float64) []float64 {
	for _, phi := range phis {
		q := quantileSorted(phi, values)
		qs = append(qs, q)
	}
	return qs
}

// quantileSorted calculates the given quantile over a sorted list of values.
//
// It is expected that values won't contain NaN items.
// The implementation mimics Prometheus implementation for compatibility's sake.
func quantileSorted(phi float64, values []float64) float64 {
	if len(values) == 0 || math.IsNaN(phi) {
		return nan
	}
	if phi < 0 {
		return math.Inf(-1)
	}
	if phi > 1 {
		return math.Inf(+1)
	}
	n := float64(len(values))
	rank := phi * (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)]*(1-weight) + values[int(upperIndex)]*weight
}

func aggrFuncMAD(tss []*timeseries) []*timeseries {
	// Calculate medians for each point across tss.
	medians := getPerPointMedians(tss)
	// Calculate MAD values multipled by tolerance for each point across tss.
	// See https://en.wikipedia.org/wiki/Median_absolute_deviation
	mads := getPerPointMADs(tss, medians)
	tss[0].Values = append(tss[0].Values[:0], mads...)
	return tss[:1]
}

func aggrFuncOutliersMAD(afa *aggrFuncArg) ([]*timeseries, error) {
	args := afa.args
	if err := expectTransformArgsNum(args, 2); err != nil {
		return nil, err
	}
	tolerances, err := getScalar(args[0], 0)
	if err != nil {
		return nil, err
	}
	afe := func(tss []*timeseries, modifier *metricsql.ModifierExpr) []*timeseries {
		// Calculate medians for each point across tss.
		medians := getPerPointMedians(tss)
		// Calculate MAD values multipled by tolerance for each point across tss.
		// See https://en.wikipedia.org/wiki/Median_absolute_deviation
		mads := getPerPointMADs(tss, medians)
		for n := range mads {
			mads[n] *= tolerances[n]
		}
		// Leave only time series with at least a single peak above the MAD multiplied by tolerance.
		tssDst := tss[:0]
		for _, ts := range tss {
			values := ts.Values
			for n, v := range values {
				ad := math.Abs(v - medians[n])
				mad := mads[n]
				if ad > mad {
					tssDst = append(tssDst, ts)
					break
				}
			}
		}
		return tssDst
	}
	return aggrFuncExt(afe, args[1], &afa.ae.Modifier, afa.ae.Limit, true)
}

func aggrFuncOutliersK(afa *aggrFuncArg) ([]*timeseries, error) {
	args := afa.args
	if err := expectTransformArgsNum(args, 2); err != nil {
		return nil, err
	}
	ks, err := getScalar(args[0], 0)
	if err != nil {
		return nil, err
	}
	afe := func(tss []*timeseries, modifier *metricsql.ModifierExpr) []*timeseries {
		// Calculate medians for each point across tss.
		medians := getPerPointMedians(tss)
		// Return topK time series with the highest variance from median.
		f := func(values []float64) float64 {
			sum2 := float64(0)
			for n, v := range values {
				d := v - medians[n]
				sum2 += d * d
			}
			return sum2
		}
		return getRangeTopKTimeseries(tss, &afa.ae.Modifier, ks, "", f, false)
	}
	return aggrFuncExt(afe, args[1], &afa.ae.Modifier, afa.ae.Limit, true)
}

func getPerPointMedians(tss []*timeseries) []float64 {
	if len(tss) == 0 {
		logger.Panicf("BUG: expecting non-empty tss")
	}
	medians := make([]float64, len(tss[0].Values))
	a := getFloat64s()
	values := a.A
	for n := range medians {
		values = values[:0]
		for j := range tss {
			v := tss[j].Values[n]
			if !math.IsNaN(v) {
				values = append(values, v)
			}
		}
		medians[n] = quantile(0.5, values)
	}
	a.A = values
	putFloat64s(a)
	return medians
}

func getPerPointMADs(tss []*timeseries, medians []float64) []float64 {
	mads := make([]float64, len(medians))
	a := getFloat64s()
	values := a.A
	for n, median := range medians {
		values = values[:0]
		for j := range tss {
			v := tss[j].Values[n]
			if !math.IsNaN(v) {
				ad := math.Abs(v - median)
				values = append(values, ad)
			}
		}
		mads[n] = quantile(0.5, values)
	}
	a.A = values
	putFloat64s(a)
	return mads
}

func aggrFuncLimitK(afa *aggrFuncArg) ([]*timeseries, error) {
	args := afa.args
	if err := expectTransformArgsNum(args, 2); err != nil {
		return nil, err
	}
	ks, err := getScalar(args[0], 0)
	if err != nil {
		return nil, err
	}
	maxK := 0
	for _, kf := range ks {
		k := int(kf)
		if k > maxK {
			maxK = k
		}
	}
	afe := func(tss []*timeseries, modifier *metricsql.ModifierExpr) []*timeseries {
		// Sort series by metricName in order to get consistent set of output series
		// across multiple calls to limitk() function.
		// Sort series by hash in order to guarantee uniform selection across series.
		type hashSeries struct {
			h  uint64
			ts *timeseries
		}
		hss := make([]hashSeries, len(tss))
		d := xxhash.New()
		for i, ts := range tss {
			h := getHash(d, &ts.MetricName)
			hss[i] = hashSeries{
				h:  h,
				ts: ts,
			}
		}
		sort.Slice(hss, func(i, j int) bool {
			return hss[i].h < hss[j].h
		})
		for i, hs := range hss {
			tss[i] = hs.ts
		}
		if len(tss) > maxK {
			tss = tss[:maxK]
		}
		for i, kf := range ks {
			k := int(kf)
			if k < 0 {
				k = 0
			}
			for j := k; j < len(tss); j++ {
				tss[j].Values[i] = nan
			}
		}
		return tss
	}
	return aggrFuncExt(afe, args[1], &afa.ae.Modifier, afa.ae.Limit, true)
}

func getHash(d *xxhash.Digest, mn *storage.MetricName) uint64 {
	d.Reset()
	_, _ = d.Write(mn.MetricGroup)
	for _, tag := range mn.Tags {
		_, _ = d.Write(tag.Key)
		_, _ = d.Write(tag.Value)
	}
	return d.Sum64()

}

func aggrFuncQuantiles(afa *aggrFuncArg) ([]*timeseries, error) {
	args := afa.args
	if len(args) < 3 {
		return nil, fmt.Errorf("unexpected number of args: %d; expecting at least 3 args", len(args))
	}
	dstLabel, err := getString(args[0], 0)
	if err != nil {
		return nil, fmt.Errorf("cannot obtain dstLabel: %w", err)
	}
	phiArgs := args[1 : len(args)-1]
	phis := make([]float64, len(phiArgs))
	for i, phiArg := range phiArgs {
		phisLocal, err := getScalar(phiArg, i+1)
		if err != nil {
			return nil, err
		}
		if len(phis) == 0 {
			logger.Panicf("BUG: expecting at least a single sample")
		}
		phis[i] = phisLocal[0]
	}
	argOrig := args[len(args)-1]
	afe := func(tss []*timeseries, modifier *metricsql.ModifierExpr) []*timeseries {
		tssDst := make([]*timeseries, len(phiArgs))
		for j := range tssDst {
			ts := &timeseries{}
			ts.CopyFromShallowTimestamps(tss[0])
			ts.MetricName.RemoveTag(dstLabel)
			ts.MetricName.AddTag(dstLabel, fmt.Sprintf("%g", phis[j]))
			tssDst[j] = ts
		}

		b := getFloat64s()
		qs := b.A
		a := getFloat64s()
		values := a.A
		for n := range tss[0].Values {
			values = values[:0]
			for j := range tss {
				values = append(values, tss[j].Values[n])
			}
			qs = quantiles(qs[:0], phis, values)
			for j := range tssDst {
				tssDst[j].Values[n] = qs[j]
			}
		}
		a.A = values
		putFloat64s(a)
		b.A = qs
		putFloat64s(b)
		return tssDst
	}
	return aggrFuncExt(afe, argOrig, &afa.ae.Modifier, afa.ae.Limit, false)
}

func aggrFuncQuantile(afa *aggrFuncArg) ([]*timeseries, error) {
	args := afa.args
	if err := expectTransformArgsNum(args, 2); err != nil {
		return nil, err
	}
	phis, err := getScalar(args[0], 0)
	if err != nil {
		return nil, err
	}
	afe := newAggrQuantileFunc(phis)
	return aggrFuncExt(afe, args[1], &afa.ae.Modifier, afa.ae.Limit, false)
}

func aggrFuncMedian(afa *aggrFuncArg) ([]*timeseries, error) {
	tss, err := getAggrTimeseries(afa.args)
	if err != nil {
		return nil, err
	}
	phis := evalNumber(afa.ec, 0.5)[0].Values
	afe := newAggrQuantileFunc(phis)
	return aggrFuncExt(afe, tss, &afa.ae.Modifier, afa.ae.Limit, false)
}

func newAggrQuantileFunc(phis []float64) func(tss []*timeseries, modifier *metricsql.ModifierExpr) []*timeseries {
	return func(tss []*timeseries, modifier *metricsql.ModifierExpr) []*timeseries {
		dst := tss[0]
		a := getFloat64s()
		values := a.A
		for n := range dst.Values {
			values = values[:0]
			for j := range tss {
				values = append(values, tss[j].Values[n])
			}
			dst.Values[n] = quantile(phis[n], values)
		}
		a.A = values
		putFloat64s(a)
		tss[0] = dst
		return tss[:1]
	}
}

func lessWithNaNs(a, b float64) bool {
	if math.IsNaN(a) {
		return !math.IsNaN(b)
	}
	return a < b
}