Merge pull request #9588 from darshanime/kahan

Use kahan summation for better numerical stability

promql/functions.go

@@ -367,7 +367,7 @@ func aggrOverTime(vals []parser.Value, enh *EvalNodeHelper, aggrFn func([]Point)
 // === avg_over_time(Matrix parser.ValueTypeMatrix) Vector ===
 func funcAvgOverTime(vals []parser.Value, args parser.Expressions, enh *EvalNodeHelper) Vector {
 	return aggrOverTime(vals, enh, func(values []Point) float64 {
-		var mean, count float64
+		var mean, count, c float64
 		for _, v := range values {
 			count++
 			if math.IsInf(mean, 0) {
@@ -387,9 +387,13 @@ func funcAvgOverTime(vals []parser.Value, args parser.Expressions, enh *EvalNode
 					continue
 				}
 			}
-			mean += v.V/count - mean/count
+			mean, c = kahanSumInc(v.V/count-mean/count, mean, c)
 		}
-		return mean
+
+		if math.IsInf(mean, 0) {
+			return mean
+		}
+		return mean + c
 	})
 }
 
@@ -439,11 +443,14 @@ func funcMinOverTime(vals []parser.Value, args parser.Expressions, enh *EvalNode
 // === sum_over_time(Matrix parser.ValueTypeMatrix) Vector ===
 func funcSumOverTime(vals []parser.Value, args parser.Expressions, enh *EvalNodeHelper) Vector {
 	return aggrOverTime(vals, enh, func(values []Point) float64 {
-		var sum float64
+		var sum, c float64
 		for _, v := range values {
-			sum += v.V
+			sum, c = kahanSumInc(v.V, sum, c)
 		}
-		return sum
+		if math.IsInf(sum, 0) {
+			return sum
+		}
+		return sum + c
 	})
 }
 
@@ -464,28 +471,32 @@ func funcQuantileOverTime(vals []parser.Value, args parser.Expressions, enh *Eva
 // === stddev_over_time(Matrix parser.ValueTypeMatrix) Vector ===
 func funcStddevOverTime(vals []parser.Value, args parser.Expressions, enh *EvalNodeHelper) Vector {
 	return aggrOverTime(vals, enh, func(values []Point) float64 {
-		var aux, count, mean float64
+		var count float64
+		var mean, cMean float64
+		var aux, cAux float64
 		for _, v := range values {
 			count++
-			delta := v.V - mean
+			delta := v.V - (mean + cMean)
-			mean += delta / count
+			mean, cMean = kahanSumInc(delta/count, mean, cMean)
-			aux += delta * (v.V - mean)
+			aux, cAux = kahanSumInc(delta*(v.V-(mean+cMean)), aux, cAux)
 		}
-		return math.Sqrt(aux / count)
+		return math.Sqrt((aux + cAux) / count)
 	})
 }
 
 // === stdvar_over_time(Matrix parser.ValueTypeMatrix) Vector ===
 func funcStdvarOverTime(vals []parser.Value, args parser.Expressions, enh *EvalNodeHelper) Vector {
 	return aggrOverTime(vals, enh, func(values []Point) float64 {
-		var aux, count, mean float64
+		var count float64
+		var mean, cMean float64
+		var aux, cAux float64
 		for _, v := range values {
 			count++
-			delta := v.V - mean
+			delta := v.V - (mean + cMean)
-			mean += delta / count
+			mean, cMean = kahanSumInc(delta/count, mean, cMean)
-			aux += delta * (v.V - mean)
+			aux, cAux = kahanSumInc(delta*(v.V-(mean+cMean)), aux, cAux)
 		}
-		return aux / count
+		return (aux + cAux) / count
 	})
 }
 
@@ -675,23 +686,51 @@ func funcTimestamp(vals []parser.Value, args parser.Expressions, enh *EvalNodeHe
 	return enh.Out
 }
 
+func kahanSum(samples []float64) float64 {
+	var sum, c float64
+
+	for _, v := range samples {
+		sum, c = kahanSumInc(v, sum, c)
+	}
+	return sum + c
+}
+
+func kahanSumInc(inc, sum, c float64) (newSum, newC float64) {
+	t := sum + inc
+	// Using Neumaier improvement, swap if next term larger than sum.
+	if math.Abs(sum) >= math.Abs(inc) {
+		c += (sum - t) + inc
+	} else {
+		c += (inc - t) + sum
+	}
+	return t, c
+}
+
 // linearRegression performs a least-square linear regression analysis on the
 // provided SamplePairs. It returns the slope, and the intercept value at the
 // provided time.
 func linearRegression(samples []Point, interceptTime int64) (slope, intercept float64) {
 	var (
-		n            float64
+		n          float64
-		sumX, sumY   float64
+		sumX, cX   float64
-		sumXY, sumX2 float64
+		sumY, cY   float64
+		sumXY, cXY float64
+		sumX2, cX2 float64
 	)
 	for _, sample := range samples {
-		x := float64(sample.T-interceptTime) / 1e3
 		n += 1.0
-		sumY += sample.V
+		x := float64(sample.T-interceptTime) / 1e3
-		sumX += x
+		sumX, cX = kahanSumInc(x, sumX, cX)
-		sumXY += x * sample.V
+		sumY, cY = kahanSumInc(sample.V, sumY, cY)
-		sumX2 += x * x
+		sumXY, cXY = kahanSumInc(x*sample.V, sumXY, cXY)
+		sumX2, cX2 = kahanSumInc(x*x, sumX2, cX2)
 	}
+
+	sumX = sumX + cX
+	sumY = sumY + cY
+	sumXY = sumXY + cXY
+	sumX2 = sumX2 + cX2
+
 	covXY := sumXY - sumX*sumY/n
 	varX := sumX2 - sumX*sumX/n
 

promql/functions_test.go

@@ -15,6 +15,7 @@ package promql
 
 import (
 	"context"
+	"math"
 	"testing"
 	"time"
 
@@ -71,3 +72,9 @@ func TestFunctionList(t *testing.T) {
 		require.True(t, ok, "function %s exists in parser package, but not in promql package", i)
 	}
 }
+
+func TestKahanSum(t *testing.T) {
+	vals := []float64{1.0, math.Pow(10, 100), 1.0, -1 * math.Pow(10, 100)}
+	expected := 2.0
+	require.Equal(t, expected, kahanSum(vals))
+}