diff --git a/image.go b/image.go
index 574b9261a..5a8105763 100644
--- a/image.go
+++ b/image.go
@@ -251,12 +251,18 @@ func (i *Image) DrawImage(img *Image, options *DrawImageOptions) error {
 
 	a, b, c, d, tx, ty := geom.elements()
 
-	level := uint(0)
+	level := 0
 	if filter == graphics.FilterLinear {
-		det := math.Abs(float64(geom.det()))
-		for det < 0.25 {
-			level++
-			det *= 4
+		det := geom.det()
+		if det == 0 {
+			return
+		}
+		if math.IsNan(det) {
+			return
+		}
+		level = graphicsutil.MipmapLevel(det)
+		if level < 0 {
+			panic("not reached")
 		}
 	}
 	if level > 6 {
@@ -264,7 +270,7 @@ func (i *Image) DrawImage(img *Image, options *DrawImageOptions) error {
 	}
 
 	if level > 0 {
-		s := 1 << level
+		s := 1 << uint(level)
 		a *= float32(s)
 		b *= float32(s)
 		c *= float32(s)
@@ -276,8 +282,8 @@ func (i *Image) DrawImage(img *Image, options *DrawImageOptions) error {
 	}
 
 	w, h = img.shareableImages[len(img.shareableImages)-1].Size()
-	for uint(len(img.shareableImages)) < level+1 {
-		lastl := uint(len(img.shareableImages)) - 1
+	for len(img.shareableImages) < level+1 {
+		lastl := len(img.shareableImages) - 1
 		src := img.shareableImages[lastl]
 		w2 := int(math.Ceil(float64(w) / 2.0))
 		h2 := int(math.Ceil(float64(h) / 2.0))
@@ -298,7 +304,7 @@ func (i *Image) DrawImage(img *Image, options *DrawImageOptions) error {
 		h = h2
 	}
 
-	if level < uint(len(img.shareableImages)) {
+	if level < len(img.shareableImages) {
 		src := img.shareableImages[level]
 		vs := src.QuadVertices(sx0, sy0, sx1, sy1, a, b, c, d, tx, ty, options.ColorM.impl)
 		is := graphicsutil.QuadIndices()
diff --git a/internal/graphicsutil/mipmap.go b/internal/graphicsutil/mipmap.go
new file mode 100644
index 000000000..035c649cd
--- /dev/null
+++ b/internal/graphicsutil/mipmap.go
@@ -0,0 +1,41 @@
+// Copyright 2018 The Ebiten 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 graphicsutil
+
+import (
+	"math"
+)
+
+// MipmapLevel returns an appropriate mipmap level for the given determinant of a geometry matrix.
+//
+// MipmapLevel returns -1 if det is 0.
+//
+// MipmapLevel panics if det is NaN.
+func MipmapLevel(det float32) int {
+	if math.IsNaN(float64(det)) {
+		panic("graphicsutil: det must be finite")
+	}
+	if det == 0 {
+		return -1
+	}
+
+	d := math.Abs(float64(det))
+	level := 0
+	for d < 0.25 {
+		level++
+		d *= 4
+	}
+	return level
+}
diff --git a/internal/graphicsutil/mipmap_test.go b/internal/graphicsutil/mipmap_test.go
new file mode 100644
index 000000000..6dbb3507c
--- /dev/null
+++ b/internal/graphicsutil/mipmap_test.go
@@ -0,0 +1,64 @@
+// Copyright 2018 The Ebiten 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 graphicsutil_test
+
+import (
+	"math"
+	"testing"
+
+	. "github.com/hajimehoshi/ebiten/internal/graphicsutil"
+)
+
+func TestMipmapLevel(t *testing.T) {
+	inf := float32(math.Inf(1))
+	cases := []struct {
+		In  float32
+		Out int
+	}{
+		{0, -1},
+		{1, 0},
+		{-1, 0},
+		{2, 0},
+		{-2, 0},
+		{100, 0},
+		{-100, 0},
+		{1.0 / 2.0, 0},
+		{-1.0 / 2.0, 0},
+		{1.0 / 4.0, 0},
+		{-1.0 / 4.0, 0},
+		{math.Nextafter32(1.0/4.0, 0), 1},
+		{math.Nextafter32(-1.0/4.0, 0), 1},
+		{1.0 / 8.0, 1},
+		{-1.0 / 8.0, 1},
+		{1.0 / 16.0, 1},
+		{-1.0 / 16.0, 1},
+		{math.Nextafter32(1.0/16.0, 0), 2},
+		{math.Nextafter32(-1.0/16.0, 0), 2},
+		{math.Nextafter32(1.0/256.0, 0), 4},
+		{math.Nextafter32(-1.0/256.0, 0), 4},
+		{math.SmallestNonzeroFloat32, 74},
+		{-math.SmallestNonzeroFloat32, 74},
+		{inf, 0},
+		{-inf, 0},
+	}
+
+	for _, c := range cases {
+		got := MipmapLevel(c.In)
+		want := c.Out
+		if got != want {
+			t.Errorf("MipmapLevel(%v): got %v, want %v", c.In, got, want)
+		}
+	}
+}