...
Run Format

Source file src/image/jpeg/dct_test.go

Documentation: image/jpeg

  // 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,
  	},
  }
  

View as plain text