image/jpeg: add DCT tests, do a small optimization (common sub-expression

elimination) in idct.go.

benchmark                   old ns/op    new ns/op    delta
BenchmarkIDCT                    5649         5610   -0.69%
BenchmarkDecodeRGBOpaque      2948607      2941051   -0.26%

The "type block" declaration moved so that idct.go is compilable
as a stand-alone file: "go tool 6g -S idct.go" works.

R=r
CC=golang-dev
https://golang.org/cl/6619056

src/pkg/image/jpeg/dct_test.go

+// Copyright 2012 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package jpeg
+
+import (
+	"bytes"
+	"fmt"
+	"math"
+	"math/rand"
+	"testing"
+)
+
+func BenchmarkFDCT(b *testing.B) {
+	b.StopTimer()
+	blocks := make([]block, 0, b.N*len(testBlocks))
+	for i := 0; i < b.N; i++ {
+		blocks = append(blocks, testBlocks[:]...)
+	}
+	b.StartTimer()
+	for i := range blocks {
+		fdct(&blocks[i])
+	}
+}
+
+func BenchmarkIDCT(b *testing.B) {
+	b.StopTimer()
+	dummy := make([]byte, 64)
+	blocks := make([]block, 0, b.N*len(testBlocks))
+	for i := 0; i < b.N; i++ {
+		blocks = append(blocks, testBlocks[:]...)
+	}
+	b.StartTimer()
+	for i := range blocks {
+		idct(dummy, 8, &blocks[i])
+	}
+}
+
+func TestDCT(t *testing.T) {
+	blocks := make([]block, len(testBlocks))
+	copy(blocks, testBlocks[:])
+
+	// Append some randomly generated blocks of varying sparseness.
+	r := rand.New(rand.NewSource(123))
+	for i := 0; i < 100; i++ {
+		b := block{}
+		n := r.Int() % 64
+		for j := 0; j < n; j++ {
+			b[r.Int()%len(b)] = r.Int() % 256
+		}
+		blocks = append(blocks, b)
+	}
+
+	// Check that the FDCT and IDCT functions are inverses, after a scale and
+	// level shift. Scaling reduces the rounding errors in the conversion from
+	// floats to ints.
+	for i, b := range blocks {
+		got, want := b, b
+		for j := range got {
+			got[j] = (got[j] - 128) * 8
+		}
+		slowFDCT(&got)
+		slowIDCT(&got)
+		for j := range got {
+			got[j] = got[j]/8 + 128
+		}
+		if differ(&got, &want) {
+			t.Errorf("i=%d: IDCT(FDCT)\nsrc\n%s\ngot\n%s\nwant\n%s\n", i, &b, &got, &want)
+		}
+	}
+
+	// Check that the optimized and slow FDCT implementations agree.
+	// The fdct function already does a scale and level shift.
+	for i, b := range blocks {
+		got, want := b, b
+		fdct(&got)
+		for j := range want {
+			want[j] = (want[j] - 128) * 8
+		}
+		slowFDCT(&want)
+		if differ(&got, &want) {
+			t.Errorf("i=%d: FDCT\nsrc\n%s\ngot\n%s\nwant\n%s\n", i, &b, &got, &want)
+		}
+	}
+
+	// Check that the optimized and slow IDCT implementations agree.
+	dummy := make([]byte, 64)
+	for i, b := range blocks {
+		got, want := b, b
+		idct(dummy, 8, &got)
+		slowIDCT(&want)
+		if differ(&got, &want) {
+			t.Errorf("i=%d: IDCT\nsrc\n%s\ngot\n%s\nwant\n%s\n", i, &b, &got, &want)
+		}
+	}
+}
+
+// differ returns whether any pair-wise elements in b0 and b1 differ by 2 or
+// more. That tolerance is because there isn't a single definitive decoding of
+// a given JPEG image, even before the YCbCr to RGB conversion; implementations
+// can have different IDCT rounding errors.
+func differ(b0, b1 *block) bool {
+	for i := range b0 {
+		delta := b0[i] - b1[i]
+		if delta < -2 || +2 < delta {
+			return true
+		}
+	}
+	return false
+}
+
+// alpha returns 1 if i is 0 and returns √2 otherwise.
+func alpha(i int) float64 {
+	if i == 0 {
+		return 1
+	}
+	return math.Sqrt2
+}
+
+// slowFDCT performs the 8*8 2-dimensional forward discrete cosine transform:
+//
+//	dst[u,v] = (1/8) * Σ_x Σ_y alpha(u) * alpha(v) * src[x,y] *
+//		cos((π/2) * (2*x + 1) * u / 8) *
+//		cos((π/2) * (2*y + 1) * v / 8)
+//
+// x and y are in pixel space, and u and v are in transform space.
+//
+// b acts as both dst and src.
+func slowFDCT(b *block) {
+	var dst [blockSize]float64
+	for v := 0; v < 8; v++ {
+		for u := 0; u < 8; u++ {
+			sum := 0.0
+			for y := 0; y < 8; y++ {
+				for x := 0; x < 8; x++ {
+					sum += alpha(u) * alpha(v) * float64(b[8*y+x]) *
+						math.Cos(math.Pi*float64((2*x+1)*u)/16) *
+						math.Cos(math.Pi*float64((2*y+1)*v)/16)
+				}
+			}
+			dst[8*v+u] = sum / 8
+		}
+	}
+	// Convert from float64 to int.
+	for i := range dst {
+		b[i] = int(dst[i] + 0.5)
+	}
+}
+
+// slowIDCT performs the 8*8 2-dimensional inverse discrete cosine transform:
+//
+//	dst[x,y] = (1/8) * Σ_u Σ_v alpha(u) * alpha(v) * src[u,v] *
+//		cos((π/2) * (2*x + 1) * u / 8) *
+//		cos((π/2) * (2*y + 1) * v / 8)
+//
+// x and y are in pixel space, and u and v are in transform space.
+//
+// b acts as both dst and src.
+func slowIDCT(b *block) {
+	var dst [blockSize]float64
+	for y := 0; y < 8; y++ {
+		for x := 0; x < 8; x++ {
+			sum := 0.0
+			for v := 0; v < 8; v++ {
+				for u := 0; u < 8; u++ {
+					sum += alpha(u) * alpha(v) * float64(b[8*v+u]) *
+						math.Cos(math.Pi*float64((2*x+1)*u)/16) *
+						math.Cos(math.Pi*float64((2*y+1)*v)/16)
+				}
+			}
+			dst[8*y+x] = sum / 8
+		}
+	}
+	// Convert from float64 to int.
+	for i := range dst {
+		b[i] = int(dst[i] + 0.5)
+	}
+}
+
+func (b *block) String() string {
+	s := bytes.NewBuffer(nil)
+	fmt.Fprintf(s, "{\n")
+	for y := 0; y < 8; y++ {
+		fmt.Fprintf(s, "\t")
+		for x := 0; x < 8; x++ {
+			fmt.Fprintf(s, "0x%04x, ", uint16(b[8*y+x]))
+		}
+		fmt.Fprintln(s)
+	}
+	fmt.Fprintf(s, "}")
+	return s.String()
+}
+
+// testBlocks are the first 10 pre-IDCT blocks from ../testdata/video-001.jpeg.
+var testBlocks = [10]block{
+	{
+		0x7f, 0xf6, 0x01, 0x07, 0xff, 0x00, 0x00, 0x00,
+		0xf5, 0x01, 0xfa, 0x01, 0xfe, 0x00, 0x01, 0x00,
+		0x05, 0x05, 0x01, 0x00, 0x00, 0x00, 0x00, 0x00,
+		0x01, 0xff, 0xf8, 0x00, 0x01, 0xff, 0x00, 0x00,
+		0x00, 0x01, 0x00, 0x01, 0x00, 0xff, 0xff, 0x00,
+		0xff, 0x0c, 0x00, 0x00, 0x00, 0x00, 0xff, 0x01,
+		0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00, 0x00,
+		0x01, 0x00, 0x00, 0x01, 0xff, 0x01, 0x00, 0xfe,
+	},
+	{
+		0x29, 0x07, 0x00, 0xfc, 0x01, 0x01, 0x00, 0x00,
+		0x07, 0x00, 0x03, 0x00, 0x01, 0x00, 0xff, 0xff,
+		0xff, 0xfd, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00,
+		0x00, 0x00, 0x04, 0x00, 0xff, 0x01, 0x00, 0x00,
+		0x01, 0x00, 0x01, 0xff, 0x00, 0x00, 0x00, 0x00,
+		0x01, 0xfa, 0x01, 0x00, 0x01, 0x00, 0x01, 0xff,
+		0x00, 0x00, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00,
+		0x00, 0x00, 0x00, 0xff, 0x00, 0xff, 0x00, 0x02,
+	},
+	{
+		0xc5, 0xfa, 0x01, 0x00, 0x00, 0x01, 0x00, 0xff,
+		0x02, 0xff, 0x01, 0x00, 0x01, 0x00, 0xff, 0x00,
+		0xff, 0xff, 0x00, 0xff, 0x01, 0x00, 0x00, 0x00,
+		0xff, 0x00, 0x01, 0x00, 0x00, 0x00, 0xff, 0x00,
+		0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xff,
+		0x00, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+		0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+		0xff, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+	},
+	{
+		0x86, 0x05, 0x00, 0x02, 0x00, 0x00, 0x01, 0x00,
+		0xf2, 0x06, 0x00, 0x00, 0x01, 0x02, 0x00, 0x00,
+		0xf6, 0xfa, 0xf9, 0x00, 0xff, 0x01, 0x00, 0x00,
+		0xf9, 0x00, 0x00, 0xff, 0x00, 0x00, 0x00, 0x00,
+		0x00, 0xff, 0x00, 0xff, 0xff, 0xff, 0x00, 0x00,
+		0xff, 0x00, 0x00, 0x01, 0x00, 0xff, 0x01, 0x00,
+		0x00, 0x00, 0x00, 0xff, 0x00, 0x00, 0x00, 0x01,
+		0x00, 0x01, 0xff, 0x01, 0x00, 0xff, 0x00, 0x00,
+	},
+	{
+		0x24, 0xfe, 0x00, 0xff, 0x00, 0xff, 0xff, 0x00,
+		0x08, 0xfd, 0x00, 0x01, 0x01, 0x00, 0x01, 0x00,
+		0x06, 0x03, 0x03, 0xff, 0x00, 0x00, 0x00, 0x00,
+		0x04, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, 0xff,
+		0x00, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x01,
+		0x01, 0x00, 0x01, 0xff, 0x00, 0x01, 0x00, 0x00,
+		0x01, 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+		0x01, 0x00, 0x01, 0x00, 0x00, 0x00, 0xff, 0x01,
+	},
+	{
+		0xcd, 0xff, 0x00, 0x00, 0x00, 0x00, 0x01, 0x01,
+		0x03, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, 0xff,
+		0x01, 0x01, 0x01, 0x01, 0x01, 0x00, 0x00, 0x00,
+		0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+		0x01, 0x00, 0x00, 0x00, 0x00, 0x01, 0x01, 0x00,
+		0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00, 0x00,
+		0x00, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+		0x00, 0x00, 0x00, 0x00, 0x00, 0x01, 0x00, 0xff,
+	},
+	{
+		0x81, 0xfe, 0x05, 0xff, 0x01, 0xff, 0x01, 0x00,
+		0xef, 0xf9, 0x00, 0xf9, 0x00, 0xff, 0x00, 0xff,
+		0x05, 0xf9, 0x00, 0xf8, 0x01, 0xff, 0x01, 0xff,
+		0x00, 0xff, 0x07, 0x00, 0x01, 0x00, 0x00, 0x00,
+		0x01, 0x00, 0x01, 0x01, 0x00, 0x00, 0x00, 0x00,
+		0x01, 0x00, 0x00, 0x00, 0xff, 0xff, 0x00, 0x01,
+		0xff, 0x01, 0x01, 0x00, 0xff, 0x00, 0x00, 0x00,
+		0x01, 0x01, 0x00, 0xff, 0x00, 0x00, 0x00, 0xff,
+	},
+	{
+		0x28, 0x00, 0xfe, 0x00, 0x00, 0x00, 0x00, 0x00,
+		0x0b, 0x02, 0x01, 0x03, 0x00, 0xff, 0x00, 0x01,
+		0xfe, 0x02, 0x01, 0x03, 0xff, 0x00, 0x00, 0x00,
+		0x01, 0x00, 0xfd, 0x00, 0x01, 0x00, 0xff, 0x00,
+		0x01, 0xff, 0x00, 0xff, 0x01, 0x00, 0x00, 0x00,
+		0x00, 0x00, 0x00, 0xff, 0x01, 0x01, 0x00, 0xff,
+		0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+		0xff, 0xff, 0x00, 0x00, 0x00, 0xff, 0x00, 0x01,
+	},
+	{
+		0xdf, 0xf9, 0xfe, 0x00, 0x03, 0x01, 0xff, 0xff,
+		0x04, 0x01, 0x00, 0x01, 0x00, 0x00, 0x00, 0x00,
+		0xff, 0x01, 0x01, 0x01, 0x00, 0x00, 0x00, 0x01,
+		0x00, 0x00, 0xfe, 0x01, 0x00, 0x00, 0x00, 0x00,
+		0x00, 0x00, 0xff, 0x01, 0x00, 0x00, 0x00, 0x01,
+		0xff, 0x00, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00,
+		0x00, 0xff, 0x00, 0xff, 0x01, 0x00, 0x00, 0x01,
+		0xff, 0xff, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00,
+	},
+	{
+		0x88, 0xfd, 0x00, 0x00, 0xff, 0x00, 0x01, 0xff,
+		0xe1, 0x06, 0x06, 0x01, 0xff, 0x00, 0x01, 0x00,
+		0x08, 0x00, 0xfa, 0x00, 0xff, 0xff, 0xff, 0xff,
+		0x08, 0x01, 0x00, 0xff, 0x01, 0xff, 0x00, 0x00,
+		0xf5, 0xff, 0x00, 0x01, 0xff, 0x01, 0x01, 0x00,
+		0xff, 0xff, 0x01, 0xff, 0x01, 0x00, 0x01, 0x00,
+		0x00, 0x01, 0x01, 0xff, 0x00, 0xff, 0x00, 0x01,
+		0x02, 0x00, 0x00, 0xff, 0xff, 0x00, 0xff, 0x00,
+	},
+}

src/pkg/image/jpeg/idct.go

@@ -37,6 +37,10 @@ package jpeg
  *
  */
 
+const blockSize = 64 // A DCT block is 8x8.
+
+type block [blockSize]int
+
 const (
 	w1 = 2841 // 2048*sqrt(2)*cos(1*pi/16)
 	w2 = 2676 // 2048*sqrt(2)*cos(2*pi/16)
@@ -70,30 +74,31 @@ const (
 func idct(dst []byte, stride int, src *block) {
 	// Horizontal 1-D IDCT.
 	for y := 0; y < 8; y++ {
+		y8 := y * 8
 		// If all the AC components are zero, then the IDCT is trivial.
-		if src[y*8+1] == 0 && src[y*8+2] == 0 && src[y*8+3] == 0 &&
-			src[y*8+4] == 0 && src[y*8+5] == 0 && src[y*8+6] == 0 && src[y*8+7] == 0 {
-			dc := src[y*8+0] << 3
-			src[y*8+0] = dc
-			src[y*8+1] = dc
-			src[y*8+2] = dc
-			src[y*8+3] = dc
-			src[y*8+4] = dc
-			src[y*8+5] = dc
-			src[y*8+6] = dc
-			src[y*8+7] = dc
+		if src[y8+1] == 0 && src[y8+2] == 0 && src[y8+3] == 0 &&
+			src[y8+4] == 0 && src[y8+5] == 0 && src[y8+6] == 0 && src[y8+7] == 0 {
+			dc := src[y8+0] << 3
+			src[y8+0] = dc
+			src[y8+1] = dc
+			src[y8+2] = dc
+			src[y8+3] = dc
+			src[y8+4] = dc
+			src[y8+5] = dc
+			src[y8+6] = dc
+			src[y8+7] = dc
 			continue
 		}
 
 		// Prescale.
-		x0 := (src[y*8+0] << 11) + 128
-		x1 := src[y*8+4] << 11
-		x2 := src[y*8+6]
-		x3 := src[y*8+2]
-		x4 := src[y*8+1]
-		x5 := src[y*8+7]
-		x6 := src[y*8+5]
-		x7 := src[y*8+3]
+		x0 := (src[y8+0] << 11) + 128
+		x1 := src[y8+4] << 11
+		x2 := src[y8+6]
+		x3 := src[y8+2]
+		x4 := src[y8+1]
+		x5 := src[y8+7]
+		x6 := src[y8+5]
+		x7 := src[y8+3]
 
 		// Stage 1.
 		x8 := w7 * (x4 + x5)
@@ -123,14 +128,14 @@ func idct(dst []byte, stride int, src *block) {
 		x4 = (r2*(x4-x5) + 128) >> 8
 
 		// Stage 4.
-		src[8*y+0] = (x7 + x1) >> 8
-		src[8*y+1] = (x3 + x2) >> 8
-		src[8*y+2] = (x0 + x4) >> 8
-		src[8*y+3] = (x8 + x6) >> 8
-		src[8*y+4] = (x8 - x6) >> 8
-		src[8*y+5] = (x0 - x4) >> 8
-		src[8*y+6] = (x3 - x2) >> 8
-		src[8*y+7] = (x7 - x1) >> 8
+		src[y8+0] = (x7 + x1) >> 8
+		src[y8+1] = (x3 + x2) >> 8
+		src[y8+2] = (x0 + x4) >> 8
+		src[y8+3] = (x8 + x6) >> 8
+		src[y8+4] = (x8 - x6) >> 8
+		src[y8+5] = (x0 - x4) >> 8
+		src[y8+6] = (x3 - x2) >> 8
+		src[y8+7] = (x7 - x1) >> 8
 	}
 
 	// Vertical 1-D IDCT.
@@ -189,8 +194,10 @@ func idct(dst []byte, stride int, src *block) {
 
 	// Level shift by +128, clip to [0, 255], and write to dst.
 	for y := 0; y < 8; y++ {
+		y8 := y * 8
+		yStride := y * stride
 		for x := 0; x < 8; x++ {
-			c := src[y*8+x]
+			c := src[y8+x]
 			if c < -128 {
 				c = 0
 			} else if c > 127 {
@@ -198,7 +205,7 @@ func idct(dst []byte, stride int, src *block) {
 			} else {
 				c += 128
 			}
-			dst[y*stride+x] = uint8(c)
+			dst[yStride+x] = uint8(c)
 		}
 	}
 }

src/pkg/image/jpeg/reader.go

@@ -35,11 +35,7 @@ type component struct {
 	tq uint8 // Quantization table destination selector.
 }
 
-type block [blockSize]int
-
 const (
-	blockSize = 64 // A DCT block is 8x8.
-
 	dcTable = 0
 	acTable = 1
 	maxTc   = 1

src/pkg/image/jpeg/writer_test.go

@@ -171,6 +171,23 @@ func TestWriter(t *testing.T) {
 	}
 }
 
+func BenchmarkDecodeRGBOpaque(b *testing.B) {
+	b.StopTimer()
+	data, err := ioutil.ReadFile("../testdata/video-001.jpeg")
+	if err != nil {
+		b.Fatal(err)
+	}
+	cfg, err := DecodeConfig(bytes.NewReader(data))
+	if err != nil {
+		b.Fatal(err)
+	}
+	b.SetBytes(int64(cfg.Width * cfg.Height * 4))
+	b.StartTimer()
+	for i := 0; i < b.N; i++ {
+		Decode(bytes.NewReader(data))
+	}
+}
+
 func BenchmarkEncodeRGBOpaque(b *testing.B) {
 	b.StopTimer()
 	img := image.NewRGBA(image.Rect(0, 0, 640, 480))