/// <summary>
/// Copies color values from block to the destination image buffer.
/// </summary>
/// <param name="block"></param>
/// <param name="buffer"></param>
/// <param name="stride"></param>
internal static unsafe void CopyColorsTo(ref Block8x8F block, MutableSpan <byte> buffer, int stride)
{
fixed(Block8x8F *p = &block)
{
float *b = (float *)p;
for (int y = 0; y < 8; y++)
{
int y8 = y * 8;
int yStride = y * stride;
for (int x = 0; x < 8; x++)
{
float c = b[y8 + x];
if (c < -128)
{
c = 0;
}
else if (c > 127)
{
c = 255;
}
else
{
c += 128;
}
buffer[yStride + x] = (byte)c;
}
}
}
}
internal static void fDCT1Dllm_32f(MutableSpan <float> x, MutableSpan <float> y)
{
float t0, t1, t2, t3, t4, t5, t6, t7;
float c0, c1, c2, c3;
float[] r = new float[8];
//for(i = 0;i < 8;i++){ r[i] = (float)(cos((double)i / 16.0 * M_PI) * M_SQRT2); }
r[0] = 1.414214f;
r[1] = 1.387040f;
r[2] = 1.306563f;
r[3] = 1.175876f;
r[4] = 1.000000f;
r[5] = 0.785695f;
r[6] = 0.541196f;
r[7] = 0.275899f;
const float invsqrt2 = 0.707107f; //(float)(1.0f / M_SQRT2);
//const float invsqrt2h = 0.353554f; //invsqrt2*0.5f;
c1 = x[0];
c2 = x[7];
t0 = c1 + c2;
t7 = c1 - c2;
c1 = x[1];
c2 = x[6];
t1 = c1 + c2;
t6 = c1 - c2;
c1 = x[2];
c2 = x[5];
t2 = c1 + c2;
t5 = c1 - c2;
c1 = x[3];
c2 = x[4];
t3 = c1 + c2;
t4 = c1 - c2;
c0 = t0 + t3;
c3 = t0 - t3;
c1 = t1 + t2;
c2 = t1 - t2;
y[0] = c0 + c1;
y[4] = c0 - c1;
y[2] = c2 * r[6] + c3 * r[2];
y[6] = c3 * r[6] - c2 * r[2];
c3 = t4 * r[3] + t7 * r[5];
c0 = t7 * r[3] - t4 * r[5];
c2 = t5 * r[1] + t6 * r[7];
c1 = t6 * r[1] - t5 * r[7];
y[5] = c3 - c1;
y[3] = c0 - c2;
c0 = (c0 + c2) * invsqrt2;
c3 = (c3 + c1) * invsqrt2;
y[1] = c0 + c3;
y[7] = c0 - c3;
}
public static void fDCT8x8_llm_sse(MutableSpan <float> s, MutableSpan <float> d, MutableSpan <float> temp)
{
Transpose8x8(s, temp);
fDCT2D8x4_32f(temp, d);
fDCT2D8x4_32f(temp.Slice(4), d.Slice(4));
Transpose8x8(d, temp);
fDCT2D8x4_32f(temp, d);
fDCT2D8x4_32f(temp.Slice(4), d.Slice(4));
Vector4 c = new Vector4(0.1250f);
_mm_store_ps(d, 0, (_mm_load_ps(d, 0) * c)); d.AddOffset(4); //0
_mm_store_ps(d, 0, (_mm_load_ps(d, 0) * c)); d.AddOffset(4); //1
_mm_store_ps(d, 0, (_mm_load_ps(d, 0) * c)); d.AddOffset(4); //2
_mm_store_ps(d, 0, (_mm_load_ps(d, 0) * c)); d.AddOffset(4); //3
_mm_store_ps(d, 0, (_mm_load_ps(d, 0) * c)); d.AddOffset(4); //4
_mm_store_ps(d, 0, (_mm_load_ps(d, 0) * c)); d.AddOffset(4); //5
_mm_store_ps(d, 0, (_mm_load_ps(d, 0) * c)); d.AddOffset(4); //6
_mm_store_ps(d, 0, (_mm_load_ps(d, 0) * c)); d.AddOffset(4); //7
_mm_store_ps(d, 0, (_mm_load_ps(d, 0) * c)); d.AddOffset(4); //8
_mm_store_ps(d, 0, (_mm_load_ps(d, 0) * c)); d.AddOffset(4); //9
_mm_store_ps(d, 0, (_mm_load_ps(d, 0) * c)); d.AddOffset(4); //10
_mm_store_ps(d, 0, (_mm_load_ps(d, 0) * c)); d.AddOffset(4); //11
_mm_store_ps(d, 0, (_mm_load_ps(d, 0) * c)); d.AddOffset(4); //12
_mm_store_ps(d, 0, (_mm_load_ps(d, 0) * c)); d.AddOffset(4); //13
_mm_store_ps(d, 0, (_mm_load_ps(d, 0) * c)); d.AddOffset(4); //14
_mm_store_ps(d, 0, (_mm_load_ps(d, 0) * c)); d.AddOffset(4); //15
}
internal static void fDCT2D_llm(
MutableSpan <float> s,
MutableSpan <float> d,
MutableSpan <float> temp,
bool downscaleBy8 = false,
bool offsetSourceByNeg128 = false)
{
MutableSpan <float> sWorker = offsetSourceByNeg128 ? s.AddScalarToAllValues(-128f) : s;
for (int j = 0; j < 8; j++)
{
fDCT1Dllm_32f(sWorker.Slice(j * 8), temp.Slice(j * 8));
}
Transpose8x8(temp, d);
for (int j = 0; j < 8; j++)
{
fDCT1Dllm_32f(d.Slice(j * 8), temp.Slice(j * 8));
}
Transpose8x8(temp, d);
if (downscaleBy8)
{
for (int j = 0; j < 64; j++)
{
d[j] *= 0.125f;
}
}
}
public void TransformIDCT(int seed)
{
MutableSpan <float> sourceArray = Create8x8RandomFloatData(-200, 200, seed);
float[] expectedDestArray = new float[64];
float[] tempArray = new float[64];
ReferenceImplementations.iDCT2D_llm(sourceArray, expectedDestArray, tempArray);
// ReferenceImplementations.iDCT8x8_llm_sse(sourceArray, expectedDestArray, tempArray);
Block8x8F source = new Block8x8F();
source.LoadFrom(sourceArray);
Block8x8F dest = new Block8x8F();
Block8x8F tempBuffer = new Block8x8F();
DCT.TransformIDCT(ref source, ref dest, ref tempBuffer);
float[] actualDestArray = new float[64];
dest.CopyTo(actualDestArray);
this.Print8x8Data(expectedDestArray);
this.Output.WriteLine("**************");
this.Print8x8Data(actualDestArray);
Assert.Equal(expectedDestArray, actualDestArray, new ApproximateFloatComparer(1f));
Assert.Equal(expectedDestArray, actualDestArray, new ApproximateFloatComparer(1f));
}
private static void _mm_store_ps(MutableSpan <float> dest, int offset, Vector4 src)
{
dest = dest.Slice(offset);
dest[0] = src.X;
dest[1] = src.Y;
dest[2] = src.Z;
dest[3] = src.W;
}
/// <summary>
/// Transpose 8x8 block stored linearly in a span
/// </summary>
internal static void Transpose8x8(MutableSpan <float> src, MutableSpan <float> dest)
{
for (int i = 0; i < 8; i++)
{
int i8 = i * 8;
for (int j = 0; j < 8; j++)
{
dest[j * 8 + i] = src[i8 + j];
}
}
}
/// <summary>
/// Transpose 8x8 block stored linearly in a span (inplace)
/// </summary>
/// <param name="data"></param>
internal static void Transpose8x8(MutableSpan <float> data)
{
for (int i = 1; i < 8; i++)
{
int i8 = i * 8;
for (int j = 0; j < i; j++)
{
float tmp = data[i8 + j];
data[i8 + j] = data[j * 8 + i];
data[j * 8 + i] = tmp;
}
}
}
/// <summary>
/// https://github.com/norishigefukushima/dct_simd/blob/master/dct/dct8x8_simd.cpp#L200
/// </summary>
/// <param name="y"></param>
/// <param name="x"></param>
private static void iDCT1Dllm_32f(MutableSpan <float> y, MutableSpan <float> x)
{
float a0, a1, a2, a3, b0, b1, b2, b3;
float z0, z1, z2, z3, z4;
//float r0 = 1.414214f;
float r1 = 1.387040f;
float r2 = 1.306563f;
float r3 = 1.175876f;
//float r4 = 1.000000f;
float r5 = 0.785695f;
float r6 = 0.541196f;
float r7 = 0.275899f;
z0 = y[1] + y[7];
z1 = y[3] + y[5];
z2 = y[3] + y[7];
z3 = y[1] + y[5];
z4 = (z0 + z1) * r3;
z0 = z0 * (-r3 + r7);
z1 = z1 * (-r3 - r1);
z2 = z2 * (-r3 - r5) + z4;
z3 = z3 * (-r3 + r5) + z4;
b3 = y[7] * (-r1 + r3 + r5 - r7) + z0 + z2;
b2 = y[5] * (r1 + r3 - r5 + r7) + z1 + z3;
b1 = y[3] * (r1 + r3 + r5 - r7) + z1 + z2;
b0 = y[1] * (r1 + r3 - r5 - r7) + z0 + z3;
z4 = (y[2] + y[6]) * r6;
z0 = y[0] + y[4];
z1 = y[0] - y[4];
z2 = z4 - y[6] * (r2 + r6);
z3 = z4 + y[2] * (r2 - r6);
a0 = z0 + z3;
a3 = z0 - z3;
a1 = z1 + z2;
a2 = z1 - z2;
x[0] = a0 + b0;
x[7] = a0 - b0;
x[1] = a1 + b1;
x[6] = a1 - b1;
x[2] = a2 + b2;
x[5] = a2 - b2;
x[3] = a3 + b3;
x[4] = a3 - b3;
}
internal void PrintLinearData <T>(MutableSpan <T> data, int count = -1)
{
if (count < 0)
{
count = data.TotalCount;
}
StringBuilder bld = new StringBuilder();
for (int i = 0; i < count; i++)
{
bld.Append($"{data[i],3} ");
}
this.Output.WriteLine(bld.ToString());
}
public void FloatingPointDCT_ReferenceImplementation_ForwardThenInverse(int seed, int startAt)
{
var data = Create8x8RandomIntData(-200, 200, seed);
MutableSpan <float> src = new MutableSpan <int>(data).ConvertToFloat32MutableSpan();
MutableSpan <float> dest = new MutableSpan <float>(64);
MutableSpan <float> temp = new MutableSpan <float>(64);
ReferenceImplementations.fDCT2D_llm(src, dest, temp, true);
ReferenceImplementations.iDCT2D_llm(dest, src, temp);
for (int i = startAt; i < 64; i++)
{
float expected = data[i];
float actual = (float)src[i];
Assert.Equal(expected, actual, new ApproximateFloatComparer(2f));
}
}
public void Idct_FloatingPointReferenceImplementation_IsEquivalentToIntegerImplementation(int seed)
{
MutableSpan <int> intData = Create8x8RandomIntData(-200, 200, seed);
MutableSpan <float> floatSrc = intData.ConvertToFloat32MutableSpan();
ReferenceImplementations.IntegerReferenceDCT.TransformIDCTInplace(intData);
MutableSpan <float> dest = new MutableSpan <float>(64);
MutableSpan <float> temp = new MutableSpan <float>(64);
ReferenceImplementations.iDCT2D_llm(floatSrc, dest, temp);
for (int i = 0; i < 64; i++)
{
float expected = intData[i];
float actual = dest[i];
Assert.Equal(expected, actual, new ApproximateFloatComparer(1f));
}
}
public void FDCT8x4_RightPart(int seed)
{
var src = Create8x8RandomFloatData(-200, 200, seed);
var srcBlock = new Block8x8F();
srcBlock.LoadFrom(src);
var destBlock = new Block8x8F();
var expectedDest = new MutableSpan <float>(64);
ReferenceImplementations.fDCT2D8x4_32f(src.Slice(4), expectedDest.Slice(4));
DCT.FDCT8x4_RightPart(ref srcBlock, ref destBlock);
var actualDest = new MutableSpan <float>(64);
destBlock.CopyTo(actualDest);
Assert.Equal(actualDest.Data, expectedDest.Data, new ApproximateFloatComparer(1f));
}
public void TransformFDCT(int seed)
{
var src = Create8x8RandomFloatData(-200, 200, seed);
var srcBlock = new Block8x8F();
srcBlock.LoadFrom(src);
var destBlock = new Block8x8F();
var expectedDest = new MutableSpan <float>(64);
var temp1 = new MutableSpan <float>(64);
var temp2 = new Block8x8F();
ReferenceImplementations.fDCT2D_llm(src, expectedDest, temp1, downscaleBy8: true);
DCT.TransformFDCT(ref srcBlock, ref destBlock, ref temp2, false);
var actualDest = new MutableSpan <float>(64);
destBlock.CopyTo(actualDest);
Assert.Equal(actualDest.Data, expectedDest.Data, new ApproximateFloatComparer(1f));
}
/// <summary>
/// Original: https://github.com/norishigefukushima/dct_simd/blob/master/dct/dct8x8_simd.cpp#L239
/// Applyies IDCT transformation on "s" copying transformed values to "d", using temporal block "temp"
/// </summary>
/// <param name="s"></param>
/// <param name="d"></param>
/// <param name="temp"></param>
internal static void iDCT2D_llm(MutableSpan <float> s, MutableSpan <float> d, MutableSpan <float> temp)
{
int j;
for (j = 0; j < 8; j++)
{
iDCT1Dllm_32f(s.Slice(j * 8), temp.Slice(j * 8));
}
Transpose8x8(temp, d);
for (j = 0; j < 8; j++)
{
iDCT1Dllm_32f(d.Slice(j * 8), temp.Slice(j * 8));
}
Transpose8x8(temp, d);
for (j = 0; j < 64; j++)
{
d[j] *= 0.125f;
}
}
public void IntegerDCT_ForwardThenInverse(int seed, int startAt)
{
MutableSpan <int> original = Create8x8RandomIntData(-200, 200, seed);
var block = original.AddScalarToAllValues(128);
ReferenceImplementations.IntegerReferenceDCT.TransformFDCTInplace(block);
for (int i = 0; i < 64; i++)
{
block[i] /= 8;
}
ReferenceImplementations.IntegerReferenceDCT.TransformIDCTInplace(block);
for (int i = startAt; i < 64; i++)
{
float expected = original[i];
float actual = (float)block[i];
Assert.Equal(expected, actual, new ApproximateFloatComparer(3f));
}
}
public void iDCT2D8x4_RightPart()
{
MutableSpan <float> sourceArray = Create8x8FloatData();
MutableSpan <float> expectedDestArray = new float[64];
ReferenceImplementations.iDCT2D8x4_32f(sourceArray.Slice(4), expectedDestArray.Slice(4));
Block8x8F source = new Block8x8F();
source.LoadFrom(sourceArray);
Block8x8F dest = new Block8x8F();
DCT.IDCT8x4_RightPart(ref source, ref dest);
float[] actualDestArray = new float[64];
dest.CopyTo(actualDestArray);
this.Print8x8Data(expectedDestArray);
this.Output.WriteLine("**************");
this.Print8x8Data(actualDestArray);
Assert.Equal(expectedDestArray.Data, actualDestArray);
}
private const int r2 = 181; // 256/sqrt(2)
/// <summary>
/// Performs a 2-D Inverse Discrete Cosine Transformation.
/// <para>
/// The input coefficients should already have been multiplied by the
/// appropriate quantization table. We use fixed-point computation, with the
/// number of bits for the fractional component varying over the intermediate
/// stages.
/// </para>
/// For more on the actual algorithm, see Z. Wang, "Fast algorithms for the
/// discrete W transform and for the discrete Fourier transform", IEEE Trans. on
/// ASSP, Vol. ASSP- 32, pp. 803-816, Aug. 1984.
/// </summary>
/// <param name="src">The source block of coefficients</param>
public static void TransformIDCTInplace(MutableSpan <int> src)
{
// Horizontal 1-D IDCT.
for (int y = 0; y < 8; y++)
{
int y8 = y * 8;
// If all the AC components are zero, then the IDCT is trivial.
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)
{
int 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.
int x0 = (src[y8 + 0] << 11) + 128;
int x1 = src[y8 + 4] << 11;
int x2 = src[y8 + 6];
int x3 = src[y8 + 2];
int x4 = src[y8 + 1];
int x5 = src[y8 + 7];
int x6 = src[y8 + 5];
int x7 = src[y8 + 3];
// Stage 1.
int x8 = w7 * (x4 + x5);
x4 = x8 + (w1mw7 * x4);
x5 = x8 - (w1pw7 * x5);
x8 = w3 * (x6 + x7);
x6 = x8 - (w3mw5 * x6);
x7 = x8 - (w3pw5 * x7);
// Stage 2.
x8 = x0 + x1;
x0 -= x1;
x1 = w6 * (x3 + x2);
x2 = x1 - (w2pw6 * x2);
x3 = x1 + (w2mw6 * x3);
x1 = x4 + x6;
x4 -= x6;
x6 = x5 + x7;
x5 -= x7;
// Stage 3.
x7 = x8 + x3;
x8 -= x3;
x3 = x0 + x2;
x0 -= x2;
x2 = ((r2 * (x4 + x5)) + 128) >> 8;
x4 = ((r2 * (x4 - x5)) + 128) >> 8;
// Stage 4.
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.
for (int x = 0; x < 8; x++)
{
// Similar to the horizontal 1-D IDCT case, if all the AC components are zero, then the IDCT is trivial.
// However, after performing the horizontal 1-D IDCT, there are typically non-zero AC components, so
// we do not bother to check for the all-zero case.
// Prescale.
int y0 = (src[x] << 8) + 8192;
int y1 = src[32 + x] << 8;
int y2 = src[48 + x];
int y3 = src[16 + x];
int y4 = src[8 + x];
int y5 = src[56 + x];
int y6 = src[40 + x];
int y7 = src[24 + x];
// Stage 1.
int y8 = (w7 * (y4 + y5)) + 4;
y4 = (y8 + (w1mw7 * y4)) >> 3;
y5 = (y8 - (w1pw7 * y5)) >> 3;
y8 = (w3 * (y6 + y7)) + 4;
y6 = (y8 - (w3mw5 * y6)) >> 3;
y7 = (y8 - (w3pw5 * y7)) >> 3;
// Stage 2.
y8 = y0 + y1;
y0 -= y1;
y1 = (w6 * (y3 + y2)) + 4;
y2 = (y1 - (w2pw6 * y2)) >> 3;
y3 = (y1 + (w2mw6 * y3)) >> 3;
y1 = y4 + y6;
y4 -= y6;
y6 = y5 + y7;
y5 -= y7;
// Stage 3.
y7 = y8 + y3;
y8 -= y3;
y3 = y0 + y2;
y0 -= y2;
y2 = ((r2 * (y4 + y5)) + 128) >> 8;
y4 = ((r2 * (y4 - y5)) + 128) >> 8;
// Stage 4.
src[x] = (y7 + y1) >> 14;
src[8 + x] = (y3 + y2) >> 14;
src[16 + x] = (y0 + y4) >> 14;
src[24 + x] = (y8 + y6) >> 14;
src[32 + x] = (y8 - y6) >> 14;
src[40 + x] = (y0 - y4) >> 14;
src[48 + x] = (y3 - y2) >> 14;
src[56 + x] = (y7 - y1) >> 14;
}
}
/// <summary>
/// Original:
/// <see>
/// <cref>https://github.com/norishigefukushima/dct_simd/blob/master/dct/dct8x8_simd.cpp#L15</cref>
/// </see>
/// </summary>
/// <param name="s">Source</param>
/// <param name="d">Destination</param>
public static void fDCT2D8x4_32f(MutableSpan <float> s, MutableSpan <float> d)
{
Vector4 c0 = _mm_load_ps(s, 0);
Vector4 c1 = _mm_load_ps(s, 56);
Vector4 t0 = (c0 + c1);
Vector4 t7 = (c0 - c1);
c1 = _mm_load_ps(s, 48);
c0 = _mm_load_ps(s, 8);
Vector4 t1 = (c0 + c1);
Vector4 t6 = (c0 - c1);
c1 = _mm_load_ps(s, 40);
c0 = _mm_load_ps(s, 16);
Vector4 t2 = (c0 + c1);
Vector4 t5 = (c0 - c1);
c0 = _mm_load_ps(s, 24);
c1 = _mm_load_ps(s, 32);
Vector4 t3 = (c0 + c1);
Vector4 t4 = (c0 - c1);
/*
* c1 = x[0]; c2 = x[7]; t0 = c1 + c2; t7 = c1 - c2;
* c1 = x[1]; c2 = x[6]; t1 = c1 + c2; t6 = c1 - c2;
* c1 = x[2]; c2 = x[5]; t2 = c1 + c2; t5 = c1 - c2;
* c1 = x[3]; c2 = x[4]; t3 = c1 + c2; t4 = c1 - c2;
*/
c0 = (t0 + t3);
Vector4 c3 = (t0 - t3);
c1 = (t1 + t2);
Vector4 c2 = (t1 - t2);
/*
* c0 = t0 + t3; c3 = t0 - t3;
* c1 = t1 + t2; c2 = t1 - t2;
*/
_mm_store_ps(d, 0, (c0 + c1));
_mm_store_ps(d, 32, (c0 - c1));
/*y[0] = c0 + c1;
* y[4] = c0 - c1;*/
Vector4 w0 = new Vector4(0.541196f);
Vector4 w1 = new Vector4(1.306563f);
_mm_store_ps(d, 16, ((w0 * c2) + (w1 * c3)));
_mm_store_ps(d, 48, ((w0 * c3) - (w1 * c2)));
/*
* y[2] = c2 * r[6] + c3 * r[2];
* y[6] = c3 * r[6] - c2 * r[2];
*/
w0 = new Vector4(1.175876f);
w1 = new Vector4(0.785695f);
c3 = ((w0 * t4) + (w1 * t7));
c0 = ((w0 * t7) - (w1 * t4));
/*
* c3 = t4 * r[3] + t7 * r[5];
* c0 = t7 * r[3] - t4 * r[5];
*/
w0 = new Vector4(1.387040f);
w1 = new Vector4(0.275899f);
c2 = ((w0 * t5) + (w1 * t6));
c1 = ((w0 * t6) - (w1 * t5));
/*
* c2 = t5 * r[1] + t6 * r[7];
* c1 = t6 * r[1] - t5 * r[7];
*/
_mm_store_ps(d, 24, (c0 - c2));
_mm_store_ps(d, 40, (c3 - c1));
//y[5] = c3 - c1; y[3] = c0 - c2;
Vector4 invsqrt2 = new Vector4(0.707107f);
c0 = ((c0 + c2) * invsqrt2);
c3 = ((c3 + c1) * invsqrt2);
//c0 = (c0 + c2) * invsqrt2;
//c3 = (c3 + c1) * invsqrt2;
_mm_store_ps(d, 8, (c0 + c3));
_mm_store_ps(d, 56, (c0 - c3));
//y[1] = c0 + c3; y[7] = c0 - c3;
/*for(i = 0;i < 8;i++)
* {
* y[i] *= invsqrt2h;
* }*/
}
private static Vector4 _mm_load_ps(MutableSpan <float> src, int offset)
{
src = src.Slice(offset);
return(new Vector4(src[0], src[1], src[2], src[3]));
}
internal void Print8x8Data <T>(MutableSpan <T> data) => this.Print8x8Data(data.Data);
/// <summary>
/// Performs a forward DCT on an 8x8 block of coefficients, including a level shift.
/// Leave results scaled up by an overall factor of 8.
/// </summary>
/// <param name="block">The block of coefficients.</param>
public static void TransformFDCTInplace(MutableSpan <int> block)
{
// Pass 1: process rows.
for (int y = 0; y < 8; y++)
{
int y8 = y * 8;
int x0 = block[y8];
int x1 = block[y8 + 1];
int x2 = block[y8 + 2];
int x3 = block[y8 + 3];
int x4 = block[y8 + 4];
int x5 = block[y8 + 5];
int x6 = block[y8 + 6];
int x7 = block[y8 + 7];
int tmp0 = x0 + x7;
int tmp1 = x1 + x6;
int tmp2 = x2 + x5;
int tmp3 = x3 + x4;
int tmp10 = tmp0 + tmp3;
int tmp12 = tmp0 - tmp3;
int tmp11 = tmp1 + tmp2;
int tmp13 = tmp1 - tmp2;
tmp0 = x0 - x7;
tmp1 = x1 - x6;
tmp2 = x2 - x5;
tmp3 = x3 - x4;
block[y8] = (tmp10 + tmp11 - (8 * CenterJSample)) << Pass1Bits;
block[y8 + 4] = (tmp10 - tmp11) << Pass1Bits;
int z1 = (tmp12 + tmp13) * fix_0_541196100;
z1 += 1 << (Bits - Pass1Bits - 1);
block[y8 + 2] = (z1 + (tmp12 * fix_0_765366865)) >> (Bits - Pass1Bits);
block[y8 + 6] = (z1 - (tmp13 * fix_1_847759065)) >> (Bits - Pass1Bits);
tmp10 = tmp0 + tmp3;
tmp11 = tmp1 + tmp2;
tmp12 = tmp0 + tmp2;
tmp13 = tmp1 + tmp3;
z1 = (tmp12 + tmp13) * fix_1_175875602;
z1 += 1 << (Bits - Pass1Bits - 1);
tmp0 = tmp0 * fix_1_501321110;
tmp1 = tmp1 * fix_3_072711026;
tmp2 = tmp2 * fix_2_053119869;
tmp3 = tmp3 * fix_0_298631336;
tmp10 = tmp10 * -fix_0_899976223;
tmp11 = tmp11 * -fix_2_562915447;
tmp12 = tmp12 * -fix_0_390180644;
tmp13 = tmp13 * -fix_1_961570560;
tmp12 += z1;
tmp13 += z1;
block[y8 + 1] = (tmp0 + tmp10 + tmp12) >> (Bits - Pass1Bits);
block[y8 + 3] = (tmp1 + tmp11 + tmp13) >> (Bits - Pass1Bits);
block[y8 + 5] = (tmp2 + tmp11 + tmp12) >> (Bits - Pass1Bits);
block[y8 + 7] = (tmp3 + tmp10 + tmp13) >> (Bits - Pass1Bits);
}
// Pass 2: process columns.
// We remove pass1Bits scaling, but leave results scaled up by an overall factor of 8.
for (int x = 0; x < 8; x++)
{
int tmp0 = block[x] + block[56 + x];
int tmp1 = block[8 + x] + block[48 + x];
int tmp2 = block[16 + x] + block[40 + x];
int tmp3 = block[24 + x] + block[32 + x];
int tmp10 = tmp0 + tmp3 + (1 << (Pass1Bits - 1));
int tmp12 = tmp0 - tmp3;
int tmp11 = tmp1 + tmp2;
int tmp13 = tmp1 - tmp2;
tmp0 = block[x] - block[56 + x];
tmp1 = block[8 + x] - block[48 + x];
tmp2 = block[16 + x] - block[40 + x];
tmp3 = block[24 + x] - block[32 + x];
block[x] = (tmp10 + tmp11) >> Pass1Bits;
block[32 + x] = (tmp10 - tmp11) >> Pass1Bits;
int z1 = (tmp12 + tmp13) * fix_0_541196100;
z1 += 1 << (Bits + Pass1Bits - 1);
block[16 + x] = (z1 + (tmp12 * fix_0_765366865)) >> (Bits + Pass1Bits);
block[48 + x] = (z1 - (tmp13 * fix_1_847759065)) >> (Bits + Pass1Bits);
tmp10 = tmp0 + tmp3;
tmp11 = tmp1 + tmp2;
tmp12 = tmp0 + tmp2;
tmp13 = tmp1 + tmp3;
z1 = (tmp12 + tmp13) * fix_1_175875602;
z1 += 1 << (Bits + Pass1Bits - 1);
tmp0 = tmp0 * fix_1_501321110;
tmp1 = tmp1 * fix_3_072711026;
tmp2 = tmp2 * fix_2_053119869;
tmp3 = tmp3 * fix_0_298631336;
tmp10 = tmp10 * -fix_0_899976223;
tmp11 = tmp11 * -fix_2_562915447;
tmp12 = tmp12 * -fix_0_390180644;
tmp13 = tmp13 * -fix_1_961570560;
tmp12 += z1;
tmp13 += z1;
block[8 + x] = (tmp0 + tmp10 + tmp12) >> (Bits + Pass1Bits);
block[24 + x] = (tmp1 + tmp11 + tmp13) >> (Bits + Pass1Bits);
block[40 + x] = (tmp2 + tmp11 + tmp12) >> (Bits + Pass1Bits);
block[56 + x] = (tmp3 + tmp10 + tmp13) >> (Bits + Pass1Bits);
}
}
/// <summary>
/// Original:
/// https://github.com/norishigefukushima/dct_simd/blob/master/dct/dct8x8_simd.cpp#L261
/// Does a part of the IDCT job on the given parts of the blocks
/// </summary>
/// <param name="y"></param>
/// <param name="x"></param>
internal static void iDCT2D8x4_32f(MutableSpan <float> y, MutableSpan <float> x)
{
/*
* float a0,a1,a2,a3,b0,b1,b2,b3; float z0,z1,z2,z3,z4; float r[8]; int i;
* for(i = 0;i < 8;i++){ r[i] = (float)(cos((double)i / 16.0 * M_PI) * M_SQRT2); }
*/
/*
* 0: 1.414214
* 1: 1.387040
* 2: 1.306563
* 3:
* 4: 1.000000
* 5: 0.785695
* 6:
* 7: 0.275899
*/
Vector4 my1 = _mm_load_ps(y, 8);
Vector4 my7 = _mm_load_ps(y, 56);
Vector4 mz0 = my1 + my7;
Vector4 my3 = _mm_load_ps(y, 24);
Vector4 mz2 = my3 + my7;
Vector4 my5 = _mm_load_ps(y, 40);
Vector4 mz1 = my3 + my5;
Vector4 mz3 = my1 + my5;
Vector4 mz4 = ((mz0 + mz1) * _1_175876);
//z0 = y[1] + y[7]; z1 = y[3] + y[5]; z2 = y[3] + y[7]; z3 = y[1] + y[5];
//z4 = (z0 + z1) * r[3];
mz2 = mz2 * _1_961571 + mz4;
mz3 = mz3 * _0_390181 + mz4;
mz0 = mz0 * _0_899976;
mz1 = mz1 * _2_562915;
/*
* -0.899976
* -2.562915
* -1.961571
* -0.390181
* z0 = z0 * (-r[3] + r[7]);
* z1 = z1 * (-r[3] - r[1]);
* z2 = z2 * (-r[3] - r[5]) + z4;
* z3 = z3 * (-r[3] + r[5]) + z4;*/
Vector4 mb3 = my7 * _0_298631 + mz0 + mz2;
Vector4 mb2 = my5 * _2_053120 + mz1 + mz3;
Vector4 mb1 = my3 * _3_072711 + mz1 + mz2;
Vector4 mb0 = my1 * _1_501321 + mz0 + mz3;
/*
* 0.298631
* 2.053120
* 3.072711
* 1.501321
* b3 = y[7] * (-r[1] + r[3] + r[5] - r[7]) + z0 + z2;
* b2 = y[5] * ( r[1] + r[3] - r[5] + r[7]) + z1 + z3;
* b1 = y[3] * ( r[1] + r[3] + r[5] - r[7]) + z1 + z2;
* b0 = y[1] * ( r[1] + r[3] - r[5] - r[7]) + z0 + z3;
*/
Vector4 my2 = _mm_load_ps(y, 16);
Vector4 my6 = _mm_load_ps(y, 48);
mz4 = (my2 + my6) * _0_541196;
Vector4 my0 = _mm_load_ps(y, 0);
Vector4 my4 = _mm_load_ps(y, 32);
mz0 = my0 + my4;
mz1 = my0 - my4;
mz2 = mz4 + my6 * _1_847759;
mz3 = mz4 + my2 * _0_765367;
my0 = mz0 + mz3;
my3 = mz0 - mz3;
my1 = mz1 + mz2;
my2 = mz1 - mz2;
/*
* 1.847759
* 0.765367
* z4 = (y[2] + y[6]) * r[6];
* z0 = y[0] + y[4]; z1 = y[0] - y[4];
* z2 = z4 - y[6] * (r[2] + r[6]);
* z3 = z4 + y[2] * (r[2] - r[6]);
* a0 = z0 + z3; a3 = z0 - z3;
* a1 = z1 + z2; a2 = z1 - z2;
*/
_mm_store_ps(x, 0, my0 + mb0);
_mm_store_ps(x, 56, my0 - mb0);
_mm_store_ps(x, 8, my1 + mb1);
_mm_store_ps(x, 48, my1 - mb1);
_mm_store_ps(x, 16, my2 + mb2);
_mm_store_ps(x, 40, my2 - mb2);
_mm_store_ps(x, 24, my3 + mb3);
_mm_store_ps(x, 32, my3 - mb3);
/*
* x[0] = a0 + b0; x[7] = a0 - b0;
* x[1] = a1 + b1; x[6] = a1 - b1;
* x[2] = a2 + b2; x[5] = a2 - b2;
* x[3] = a3 + b3; x[4] = a3 - b3;
* for(i = 0;i < 8;i++){ x[i] *= 0.353554f; }
*/
}
