diff --git a/promql/functions.go b/promql/functions.go
index 9b3be2287..dec3abc25 100644
--- a/promql/functions.go
+++ b/promql/functions.go
@@ -950,10 +950,14 @@ func funcTimestamp(vals []parser.Value, args parser.Expressions, enh *EvalNodeHe
 
 func kahanSumInc(inc, sum, c float64) (newSum, newC float64) {
 	t := sum + inc
+	switch {
+	case math.IsInf(t, 0):
+		c = 0
+
 	// Using Neumaier improvement, swap if next term larger than sum.
-	if math.Abs(sum) >= math.Abs(inc) {
+	case math.Abs(sum) >= math.Abs(inc):
 		c += (sum - t) + inc
-	} else {
+	default:
 		c += (inc - t) + sum
 	}
 	return t, c
diff --git a/promql/functions_internal_test.go b/promql/functions_internal_test.go
new file mode 100644
index 000000000..85c6cd797
--- /dev/null
+++ b/promql/functions_internal_test.go
@@ -0,0 +1,81 @@
+// 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 (
+	"fmt"
+	"math"
+	"testing"
+
+	"github.com/stretchr/testify/require"
+)
+
+func TestKahanSumInc(t *testing.T) {
+	testCases := map[string]struct {
+		first    float64
+		second   float64
+		expected float64
+	}{
+		"+Inf + anything = +Inf": {
+			first:    math.Inf(1),
+			second:   2.0,
+			expected: math.Inf(1),
+		},
+		"-Inf + anything = -Inf": {
+			first:    math.Inf(-1),
+			second:   2.0,
+			expected: math.Inf(-1),
+		},
+		"+Inf + -Inf = NaN": {
+			first:    math.Inf(1),
+			second:   math.Inf(-1),
+			expected: math.NaN(),
+		},
+		"NaN + anything = NaN": {
+			first:    math.NaN(),
+			second:   2,
+			expected: math.NaN(),
+		},
+		"NaN + Inf = NaN": {
+			first:    math.NaN(),
+			second:   math.Inf(1),
+			expected: math.NaN(),
+		},
+		"NaN + -Inf = NaN": {
+			first:    math.NaN(),
+			second:   math.Inf(-1),
+			expected: math.NaN(),
+		},
+	}
+
+	runTest := func(t *testing.T, a, b, expected float64) {
+		t.Run(fmt.Sprintf("%v + %v = %v", a, b, expected), func(t *testing.T) {
+			sum, c := kahanSumInc(b, a, 0)
+			result := sum + c
+
+			if math.IsNaN(expected) {
+				require.Truef(t, math.IsNaN(result), "expected result to be NaN, but got %v (from %v + %v)", result, sum, c)
+			} else {
+				require.Equalf(t, expected, result, "expected result to be %v, but got %v (from %v + %v)", expected, result, sum, c)
+			}
+		})
+	}
+
+	for name, testCase := range testCases {
+		t.Run(name, func(t *testing.T) {
+			runTest(t, testCase.first, testCase.second, testCase.expected)
+			runTest(t, testCase.second, testCase.first, testCase.expected)
+		})
+	}
+}
diff --git a/promql/promqltest/testdata/aggregators.test b/promql/promqltest/testdata/aggregators.test
index be689c65f..2a0ce01ee 100644
--- a/promql/promqltest/testdata/aggregators.test
+++ b/promql/promqltest/testdata/aggregators.test
@@ -511,10 +511,39 @@ load 10s
 	data{test="ten",point="b"} 8
 	data{test="ten",point="c"} 1e+100
 	data{test="ten",point="d"} -1e100
+	data{test="pos_inf",group="1",point="a"} Inf
+	data{test="pos_inf",group="1",point="b"} 2
+	data{test="pos_inf",group="2",point="a"} 2
+	data{test="pos_inf",group="2",point="b"} Inf
+	data{test="neg_inf",group="1",point="a"} -Inf
+	data{test="neg_inf",group="1",point="b"} 2
+	data{test="neg_inf",group="2",point="a"} 2
+	data{test="neg_inf",group="2",point="b"} -Inf
+	data{test="inf_inf",point="a"} Inf
+	data{test="inf_inf",point="b"} -Inf
+	data{test="nan",group="1",point="a"} NaN
+	data{test="nan",group="1",point="b"} 2
+	data{test="nan",group="2",point="a"} 2
+	data{test="nan",group="2",point="b"} NaN
 
 eval instant at 1m sum(data{test="ten"})
 	{} 10
 
+eval instant at 1m sum by (group) (data{test="pos_inf"})
+	{group="1"} Inf
+	{group="2"} Inf
+
+eval instant at 1m sum by (group) (data{test="neg_inf"})
+	{group="1"} -Inf
+	{group="2"} -Inf
+
+eval instant at 1m sum(data{test="inf_inf"})
+	{} NaN
+
+eval instant at 1m sum by (group) (data{test="nan"})
+	{group="1"} NaN
+	{group="2"} NaN
+
 clear
 
 # Test that aggregations are deterministic.
diff --git a/promql/promqltest/testdata/native_histograms.test b/promql/promqltest/testdata/native_histograms.test
index f79517023..01c2a2157 100644
--- a/promql/promqltest/testdata/native_histograms.test
+++ b/promql/promqltest/testdata/native_histograms.test
@@ -355,10 +355,10 @@ load 10m
    histogram_stddev_stdvar_7 {{schema:3 count:7 sum:Inf z_bucket:1 buckets:[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ] n_buckets:[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ]}}x1
 
 eval instant at 10m histogram_stddev(histogram_stddev_stdvar_7)
-    {} NaN
+    {} Inf
 
 eval instant at 10m histogram_stdvar(histogram_stddev_stdvar_7)
-    {} NaN
+    {} Inf
 
 # Apply quantile function to histogram with all positive buckets with zero bucket.
 load 10m