blob: 845e758878934fe67848796ca34e4efb0d43a999 [file] [log] [blame]
 // 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 benchmarkDCT(b *testing.B, f func(*block)) { 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 { f(&blocks[i]) } } func BenchmarkFDCT(b *testing.B) { benchmarkDCT(b, fdct) } func BenchmarkIDCT(b *testing.B) { benchmarkDCT(b, idct) } 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.Int31() % 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. for i, b := range blocks { got, want := b, b idct(&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 reports 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 } var cosines [32]float64 // cosines[k] = cos(π/2 * k/8) func init() { for k := range cosines { cosines[k] = math.Cos(math.Pi * float64(k) / 16) } } // 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]) * cosines[((2*x+1)*u)%32] * cosines[((2*y+1)*v)%32] } } dst[8*v+u] = sum / 8 } } // Convert from float64 to int32. for i := range dst { b[i] = int32(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]) * cosines[((2*x+1)*u)%32] * cosines[((2*y+1)*v)%32] } } dst[8*y+x] = sum / 8 } } // Convert from float64 to int32. for i := range dst { b[i] = int32(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, }, }