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// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package jpeg
import (
"fmt"
"math"
"math/big"
"math/rand"
"strings"
"testing"
)
func benchmarkDCT(b *testing.B, f func(*block)) {
var blk block // avoid potential allocation in loop
for b.Loop() {
for _, blk = range testBlocks {
f(&blk)
}
}
}
func BenchmarkFDCT(b *testing.B) {
benchmarkDCT(b, fdct)
}
func BenchmarkIDCT(b *testing.B) {
benchmarkDCT(b, idct)
}
const testSlowVsBig = true
func TestDCT(t *testing.T) {
blocks := make([]block, len(testBlocks))
copy(blocks, testBlocks[:])
// All zeros
blocks = append(blocks, block{})
// Every possible unit impulse.
for i := range blockSize {
var b block
b[i] = 255
blocks = append(blocks, b)
}
// All ones.
var ones block
for i := range ones {
ones[i] = 255
}
blocks = append(blocks, ones)
// Every possible inverted unit impulse.
for i := range blockSize {
ones[i] = 0
blocks = append(blocks, ones)
ones[i] = 255
}
// 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 slow FDCT and IDCT functions are inverses,
// after a scale and level shift.
// Scaling reduces the rounding errors in the conversion.
// The “fast” ones are not inverses because the fast IDCT
// is optimized for 8-bit inputs, not full 16-bit ones.
slowRoundTrip := func(b *block) {
slowFDCT(b)
slowIDCT(b)
for j := range b {
b[j] = b[j]/8 + 128
}
}
nop := func(*block) {}
testDCT(t, "IDCT(FDCT)", blocks, slowRoundTrip, nop, 1, 8)
if testSlowVsBig {
testDCT(t, "slowFDCT", blocks, slowFDCT, slowerFDCT, 0, 64)
testDCT(t, "slowIDCT", blocks, slowIDCT, slowerIDCT, 0, 64)
}
// Check that the optimized and slow FDCT implementations agree.
testDCT(t, "FDCT", blocks, fdct, slowFDCT, 1, 8)
testDCT(t, "IDCT", blocks, idct, slowIDCT, 1, 8)
}
func testDCT(t *testing.T, name string, blocks []block, fhave, fwant func(*block), tolerance int32, maxCloseCalls int) {
t.Run(name, func(t *testing.T) {
totalClose := 0
for i, b := range blocks {
have, want := b, b
fhave(&have)
fwant(&want)
d, n := differ(&have, &want, tolerance)
if d >= 0 || n > maxCloseCalls {
fail := ""
if d >= 0 {
fail = fmt.Sprintf("diff at %d,%d", d/8, d%8)
}
if n > maxCloseCalls {
if fail != "" {
fail += "; "
}
fail += fmt.Sprintf("%d close calls", n)
}
t.Errorf("i=%d: %s (%s)\nsrc\n%s\nhave\n%s\nwant\n%s\n",
i, name, fail, &b, &have, &want)
}
totalClose += n
}
if tolerance > 0 {
t.Logf("%d/%d total close calls", totalClose, len(blocks)*blockSize)
}
})
}
// differ returns the index of the first pair-wise elements in b0 and b1
// that differ by more than 'ok', along with the total number of elements
// that differ by at least ok ("close calls").
//
// 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.
//
// If there are no differences, differ returns -1, 0.
func differ(b0, b1 *block, ok int32) (index, closeCalls int) {
index = -1
for i := range b0 {
delta := b0[i] - b1[i]
if delta < -ok || ok < delta {
if index < 0 {
index = i
}
}
if delta <= -ok || ok <= delta {
closeCalls++
}
}
return
}
// alpha returns 1 if i is 0 and returns √2 otherwise.
func alpha(i int) float64 {
if i == 0 {
return 1
}
return math.Sqrt2
}
// bigAlpha returns 1 if i is 0 and returns √2 otherwise.
func bigAlpha(i int) *big.Float {
if i == 0 {
return bigFloat1
}
return bigFloatSqrt2
}
var cosines = [32]float64{
+1.0000000000000000000000000000000000000000000000000000000000000000, // cos(π/16 * 0)
+0.9807852804032304491261822361342390369739337308933360950029160885, // cos(π/16 * 1)
+0.9238795325112867561281831893967882868224166258636424861150977312, // cos(π/16 * 2)
+0.8314696123025452370787883776179057567385608119872499634461245902, // cos(π/16 * 3)
+0.7071067811865475244008443621048490392848359376884740365883398689, // cos(π/16 * 4)
+0.5555702330196022247428308139485328743749371907548040459241535282, // cos(π/16 * 5)
+0.3826834323650897717284599840303988667613445624856270414338006356, // cos(π/16 * 6)
+0.1950903220161282678482848684770222409276916177519548077545020894, // cos(π/16 * 7)
-0.0000000000000000000000000000000000000000000000000000000000000000, // cos(π/16 * 8)
-0.1950903220161282678482848684770222409276916177519548077545020894, // cos(π/16 * 9)
-0.3826834323650897717284599840303988667613445624856270414338006356, // cos(π/16 * 10)
-0.5555702330196022247428308139485328743749371907548040459241535282, // cos(π/16 * 11)
-0.7071067811865475244008443621048490392848359376884740365883398689, // cos(π/16 * 12)
-0.8314696123025452370787883776179057567385608119872499634461245902, // cos(π/16 * 13)
-0.9238795325112867561281831893967882868224166258636424861150977312, // cos(π/16 * 14)
-0.9807852804032304491261822361342390369739337308933360950029160885, // cos(π/16 * 15)
-1.0000000000000000000000000000000000000000000000000000000000000000, // cos(π/16 * 16)
-0.9807852804032304491261822361342390369739337308933360950029160885, // cos(π/16 * 17)
-0.9238795325112867561281831893967882868224166258636424861150977312, // cos(π/16 * 18)
-0.8314696123025452370787883776179057567385608119872499634461245902, // cos(π/16 * 19)
-0.7071067811865475244008443621048490392848359376884740365883398689, // cos(π/16 * 20)
-0.5555702330196022247428308139485328743749371907548040459241535282, // cos(π/16 * 21)
-0.3826834323650897717284599840303988667613445624856270414338006356, // cos(π/16 * 22)
-0.1950903220161282678482848684770222409276916177519548077545020894, // cos(π/16 * 23)
+0.0000000000000000000000000000000000000000000000000000000000000000, // cos(π/16 * 24)
+0.1950903220161282678482848684770222409276916177519548077545020894, // cos(π/16 * 25)
+0.3826834323650897717284599840303988667613445624856270414338006356, // cos(π/16 * 26)
+0.5555702330196022247428308139485328743749371907548040459241535282, // cos(π/16 * 27)
+0.7071067811865475244008443621048490392848359376884740365883398689, // cos(π/16 * 28)
+0.8314696123025452370787883776179057567385608119872499634461245902, // cos(π/16 * 29)
+0.9238795325112867561281831893967882868224166258636424861150977312, // cos(π/16 * 30)
+0.9807852804032304491261822361342390369739337308933360950029160885, // cos(π/16 * 31)
}
func bigFloat(s string) *big.Float {
f, ok := new(big.Float).SetString(s)
if !ok {
panic("bad float")
}
return f
}
var (
bigFloat1 = big.NewFloat(1)
bigFloatSqrt2 = bigFloat("1.41421356237309504880168872420969807856967187537694807317667974")
)
var bigCosines = [32]*big.Float{
bigFloat("+1.0000000000000000000000000000000000000000000000000000000000000000"), // cos(π/16 * 0)
bigFloat("+0.9807852804032304491261822361342390369739337308933360950029160885"), // cos(π/16 * 1)
bigFloat("+0.9238795325112867561281831893967882868224166258636424861150977312"), // cos(π/16 * 2)
bigFloat("+0.8314696123025452370787883776179057567385608119872499634461245902"), // cos(π/16 * 3)
bigFloat("+0.7071067811865475244008443621048490392848359376884740365883398689"), // cos(π/16 * 4)
bigFloat("+0.5555702330196022247428308139485328743749371907548040459241535282"), // cos(π/16 * 5)
bigFloat("+0.3826834323650897717284599840303988667613445624856270414338006356"), // cos(π/16 * 6)
bigFloat("+0.1950903220161282678482848684770222409276916177519548077545020894"), // cos(π/16 * 7)
bigFloat("-0.0000000000000000000000000000000000000000000000000000000000000000"), // cos(π/16 * 8)
bigFloat("-0.1950903220161282678482848684770222409276916177519548077545020894"), // cos(π/16 * 9)
bigFloat("-0.3826834323650897717284599840303988667613445624856270414338006356"), // cos(π/16 * 10)
bigFloat("-0.5555702330196022247428308139485328743749371907548040459241535282"), // cos(π/16 * 11)
bigFloat("-0.7071067811865475244008443621048490392848359376884740365883398689"), // cos(π/16 * 12)
bigFloat("-0.8314696123025452370787883776179057567385608119872499634461245902"), // cos(π/16 * 13)
bigFloat("-0.9238795325112867561281831893967882868224166258636424861150977312"), // cos(π/16 * 14)
bigFloat("-0.9807852804032304491261822361342390369739337308933360950029160885"), // cos(π/16 * 15)
bigFloat("-1.0000000000000000000000000000000000000000000000000000000000000000"), // cos(π/16 * 16)
bigFloat("-0.9807852804032304491261822361342390369739337308933360950029160885"), // cos(π/16 * 17)
bigFloat("-0.9238795325112867561281831893967882868224166258636424861150977312"), // cos(π/16 * 18)
bigFloat("-0.8314696123025452370787883776179057567385608119872499634461245902"), // cos(π/16 * 19)
bigFloat("-0.7071067811865475244008443621048490392848359376884740365883398689"), // cos(π/16 * 20)
bigFloat("-0.5555702330196022247428308139485328743749371907548040459241535282"), // cos(π/16 * 21)
bigFloat("-0.3826834323650897717284599840303988667613445624856270414338006356"), // cos(π/16 * 22)
bigFloat("-0.1950903220161282678482848684770222409276916177519548077545020894"), // cos(π/16 * 23)
bigFloat("+0.0000000000000000000000000000000000000000000000000000000000000000"), // cos(π/16 * 24)
bigFloat("+0.1950903220161282678482848684770222409276916177519548077545020894"), // cos(π/16 * 25)
bigFloat("+0.3826834323650897717284599840303988667613445624856270414338006356"), // cos(π/16 * 26)
bigFloat("+0.5555702330196022247428308139485328743749371907548040459241535282"), // cos(π/16 * 27)
bigFloat("+0.7071067811865475244008443621048490392848359376884740365883398689"), // cos(π/16 * 28)
bigFloat("+0.8314696123025452370787883776179057567385608119872499634461245902"), // cos(π/16 * 29)
bigFloat("+0.9238795325112867561281831893967882868224166258636424861150977312"), // cos(π/16 * 30)
bigFloat("+0.9807852804032304491261822361342390369739337308933360950029160885"), // cos(π/16 * 31)
}
// 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 block
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]-128) *
cosines[((2*x+1)*u)%32] *
cosines[((2*y+1)*v)%32]
}
}
dst[8*v+u] = int32(math.Round(sum))
}
}
*b = dst
}
// slowerFDCT is slowFDCT but using big.Floats to validate slowFDCT.
func slowerFDCT(b *block) {
var dst block
for v := 0; v < 8; v++ {
for u := 0; u < 8; u++ {
sum := big.NewFloat(0)
for y := 0; y < 8; y++ {
for x := 0; x < 8; x++ {
f := big.NewFloat(float64(b[8*y+x] - 128))
f = new(big.Float).Mul(f, bigAlpha(u))
f = new(big.Float).Mul(f, bigAlpha(v))
f = new(big.Float).Mul(f, bigCosines[((2*x+1)*u)%32])
f = new(big.Float).Mul(f, bigCosines[((2*y+1)*v)%32])
sum = new(big.Float).Add(sum, f)
}
}
// Int64 truncates toward zero, so add ±0.5
// as needed to round
if sum.Sign() > 0 {
sum = new(big.Float).Add(sum, big.NewFloat(+0.5))
} else {
sum = new(big.Float).Add(sum, big.NewFloat(-0.5))
}
i, _ := sum.Int64()
dst[8*v+u] = int32(i)
}
}
*b = dst
}
// 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 block
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] = int32(math.Round(sum / 8))
}
}
*b = dst
}
// slowerIDCT is slowIDCT but using big.Floats to validate slowIDCT.
func slowerIDCT(b *block) {
var dst block
for y := 0; y < 8; y++ {
for x := 0; x < 8; x++ {
sum := big.NewFloat(0)
for v := 0; v < 8; v++ {
for u := 0; u < 8; u++ {
f := big.NewFloat(float64(b[8*v+u]))
f = new(big.Float).Mul(f, bigAlpha(u))
f = new(big.Float).Mul(f, bigAlpha(v))
f = new(big.Float).Mul(f, bigCosines[((2*x+1)*u)%32])
f = new(big.Float).Mul(f, bigCosines[((2*y+1)*v)%32])
f = new(big.Float).Quo(f, big.NewFloat(8))
sum = new(big.Float).Add(sum, f)
}
}
// Int64 truncates toward zero, so add ±0.5
// as needed to round
if sum.Sign() > 0 {
sum = new(big.Float).Add(sum, big.NewFloat(+0.5))
} else {
sum = new(big.Float).Add(sum, big.NewFloat(-0.5))
}
i, _ := sum.Int64()
dst[8*y+x] = int32(i)
}
}
*b = dst
}
func (b *block) String() string {
s := &strings.Builder{}
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,
},
}
|