public static unsafe ComplexFloat[] Kernel32(ComplexFloat[] i, ref ComplexFloat[][] omegas)
{
ComplexFloat[] result = new ComplexFloat[32];
ComplexFloat[] tmp = new ComplexFloat[48];
ComplexFloat ami = i[0] - i[8];
ComplexFloat api = i[0] + i[8];
ComplexFloat fmn = i[5] - i[13];
ComplexFloat fpn = i[5] + i[13];
ComplexFloat xami = i[16] - i[24];
ComplexFloat xapi = i[16] + i[24];
ComplexFloat xfmn = i[21] - i[29];
ComplexFloat xfpn = i[21] + i[29];
tmp[0] = api + i[2] + i[4] + i[6] + i[10] + i[12] + i[14];
tmp[1] = ami + (i[2] - i[10] + (i[6] - i[14]).TimesMinusI()) * omegas[3][1] + (i[4] - i[12]).TimesMinusI();
tmp[2] = api - i[4] - i[12] + (i[2] - i[6] + i[10] - i[14]).TimesMinusI();
tmp[3] = ami - (i[4] - i[12]).TimesMinusI() - (i[10] - i[2] + (i[6] - i[14]).TimesMinusI()) * omegas[3][3];
tmp[4] = api - i[2] + i[4] - i[6] - i[10] + i[12] - i[14];
tmp[5] = ami - (i[2] - i[10] + (i[6] - i[14]).TimesMinusI()) * omegas[3][1] + (i[4] - i[12]).TimesMinusI();
tmp[6] = api - i[4] - i[12] - (i[2] - i[6] + i[10] - i[14]).TimesMinusI();
tmp[7] = ami - (i[4] - i[12]).TimesMinusI() + (i[10] - i[2] + (i[6] - i[14]).TimesMinusI()).TimesMinusI();
tmp[8] = i[1] + i[3] + fpn + i[7] + i[9] + i[11] + i[15];
tmp[9] = omegas[4][1] * (i[1] - i[9] + (i[3] - i[11] + (i[7] - i[15]).TimesMinusI()) * omegas[3][1] + (fmn).TimesMinusI());
tmp[10] = omegas[4][2] * ((i[3] - i[7] + i[11] - i[15]).TimesMinusI() + i[1] - fpn + i[9]);
tmp[11] = omegas[4][3] * (omegas[3][3] * (i[11] - i[3] + (i[7] - i[15]).TimesMinusI()) - i[1] + i[9] + (fmn).TimesMinusI());
tmp[12] = (i[1] - i[3] + fpn - i[7] + i[9] - i[11] - i[15]).TimesMinusI();
tmp[13] = (i[1] - i[9] - (i[3] - i[11] + (i[7] - i[15]).TimesMinusI()) * omegas[3][1] + (fmn).TimesMinusI()) * omegas[4][5];
tmp[14] = omegas[4][6] * ((i[3] - i[7] + i[11] - i[15]).TimesMinusI() - i[1] + fpn - i[9]);
tmp[15] = omegas[4][7] * ((i[11] - i[3] + (i[7] - i[15]).TimesMinusI()).TimesMinusI() + i[1] - i[9] - (fmn).TimesMinusI());
tmp[16] = xapi + i[18] + i[20] + i[22] + i[28] + i[26] + i[30];
tmp[17] = xami + (i[18] - i[26] + (i[22] - i[30]).TimesMinusI()) * omegas[3][1] + (i[20] - i[28]).TimesMinusI();
tmp[18] = xapi - i[20] - i[28] + (i[18] - i[22] + i[26] - i[30]).TimesMinusI();
tmp[19] = xami - (i[20] - i[28]).TimesMinusI() - (i[26] - i[18] + (i[22] - i[30]).TimesMinusI()) * omegas[3][3];
tmp[20] = xapi - i[28] + i[20] - i[22] - i[26] + i[28] - i[30];
tmp[21] = xami - (i[28] - i[26] + (i[22] - i[30]).TimesMinusI()) * omegas[3][1] + (i[20] - i[22]).TimesMinusI();
tmp[22] = xapi - i[20] - i[28] - (i[18] - i[22] + i[26] - i[30]).TimesMinusI();
tmp[23] = xami - (i[20] - i[28]).TimesMinusI() + (i[26] - i[18] + (i[22] - i[30]).TimesMinusI()).TimesMinusI();
tmp[24] = i[17] + i[19] + xfpn + i[23] + i[25] + i[27] + i[31];
tmp[25] = omegas[4][1] * (i[17] - i[25] + (i[19] - i[27] + (i[23] - i[31]).TimesMinusI()) * omegas[3][1] + (xfmn).TimesMinusI());
tmp[26] = omegas[4][2] * ((i[19] - i[23] + i[27] - i[31]).TimesMinusI() + i[17] - xfpn + i[25]);
tmp[27] = omegas[4][3] * (omegas[3][3] * (i[27] - i[19] + (i[23] - i[31]).TimesMinusI()) - i[17] + i[25] + (xfmn).TimesMinusI());
tmp[28] = (i[17] - i[19] + xfpn - i[23] + i[25] - i[27] - i[31]).TimesMinusI();
tmp[29] = (i[17] - i[25] - (i[19] - i[27] + (i[23] - i[31]).TimesMinusI()) * omegas[3][1] + (xfmn).TimesMinusI()) * omegas[4][5];
tmp[30] = omegas[4][6] * ((i[19] - i[23] + i[27] - i[31]).TimesMinusI() - i[17] + xfpn - i[25]);
tmp[31] = omegas[4][7] * ((i[27] - i[19] + (i[23] - i[31]).TimesMinusI()).TimesMinusI() + i[17] - i[25] - (xfmn).TimesMinusI());
//32 complex floats = 64 floats
//Divided into 4 parts A, B, C, D = each containing 8 complex floats, so 16 floats
//AVX takes 8 floats at once, so will calculate in halves of those parts
//Tmp will ocntain 6 octets
fixed(ComplexFloat *entry = result, om5 = omegas[5], t = tmp)
{
Vector256 <float> a;
Vector256 <float> b;
Vector256 <float> bSwap;
Vector256 <float> aIm;
Vector256 <float> aRe;
Vector256 <float> aIM_bSwap;
float *partA = (float *)entry;
float *partB = partA + 16;
float *partC = partA + 32;
float *partD = partA + 48;
float *omPart1 = (float *)om5;
float *omPart2 = omPart1 + 16;
float *tmpPart1 = (float *)t;
float *tmpPart2 = tmpPart1 + 16;
float *tmpPart3 = tmpPart1 + 32;
float *tmpPart4 = tmpPart1 + 48;
float *tmpPart5 = tmpPart1 + 64;
float *tmpPart6 = tmpPart1 + 80;
//Summing up result
Avx2.Store(partA, Avx2.Add(Avx2.LoadVector256(tmpPart1), Avx2.LoadVector256(tmpPart2)));
Avx2.Store(partA + 8, Avx2.Add(Avx2.LoadVector256(tmpPart1 + 8), Avx2.LoadVector256(tmpPart2 + 8)));
Avx2.Store(partB, Avx2.Subtract(Avx2.LoadVector256(tmpPart1), Avx2.LoadVector256(tmpPart2)));
Avx2.Store(partB + 8, Avx2.Subtract(Avx2.LoadVector256(tmpPart1 + 8), Avx2.LoadVector256(tmpPart2 + 8)));
Avx2.Store(partC, Avx2.Add(Avx2.LoadVector256(tmpPart3), Avx2.LoadVector256(tmpPart4)));
Avx2.Store(partC + 8, Avx2.Add(Avx2.LoadVector256(tmpPart3 + 8), Avx2.LoadVector256(tmpPart4 + 8)));
Avx2.Store(partD, Avx2.Subtract(Avx2.LoadVector256(tmpPart3), Avx2.LoadVector256(tmpPart4)));
Avx2.Store(partD + 8, Avx2.Subtract(Avx2.LoadVector256(tmpPart3 + 8), Avx2.LoadVector256(tmpPart4 + 8)));
//-------------------------------------------------------------------------------------------------------------
//First part of each 8 complex part
//Tmp[0] = A + B
Avx2.Store(tmpPart1, Avx2.Add(Avx2.LoadVector256(partA), Avx2.LoadVector256(partB)));
//Tmp[1] = A - B
Avx2.Store(tmpPart2, Avx2.Subtract(Avx2.LoadVector256(partA), Avx2.LoadVector256(partB)));
//Tmp[2] = C + D
Avx2.Store(tmpPart3, Avx2.Add(Avx2.LoadVector256(partC), Avx2.LoadVector256(partD)));
//Tmp[3] = C - D
Avx2.Store(tmpPart4, Avx2.Subtract(Avx2.LoadVector256(partC), Avx2.LoadVector256(partD)));
//Complex multiplication based on: https://www.researchgate.net/figure/Vectorized-complex-multiplication-using-AVX-2_fig2_337532904
//Tmp[4] = omega * (C+D)
a = Avx2.LoadVector256(tmpPart3);
b = Avx2.LoadVector256(omPart1);
bSwap = Avx2.Shuffle(b, b, imm8bShuffle);
aIm = Avx2.Shuffle(a, a, imm8aImShuffle);
aRe = Avx2.Shuffle(a, a, imm8aReShuffle);
aIM_bSwap = Avx.Multiply(aIm, bSwap);
Avx2.Store(tmpPart5, Fma.MultiplyAddSubtract(aRe, b, aIM_bSwap));
//Tmp[4] = omega * (C-D)
a = Avx2.LoadVector256(tmpPart4);
b = Avx2.LoadVector256(omPart2);
bSwap = Avx2.Shuffle(b, b, imm8bShuffle);
aIm = Avx2.Shuffle(a, a, imm8aImShuffle);
aRe = Avx2.Shuffle(a, a, imm8aReShuffle);
aIM_bSwap = Avx.Multiply(aIm, bSwap);
Avx2.Store(tmpPart6, Fma.MultiplyAddSubtract(aRe, b, aIM_bSwap));
//(A+B) + (C+D)
Avx2.Store(partA, Avx.Add(Avx.LoadVector256(tmpPart1), Avx.LoadVector256(tmpPart3)));
//(A-B) + (C-D)
Avx2.Store(partB, Avx.Add(Avx.LoadVector256(tmpPart2), Avx.LoadVector256(tmpPart4)));
//(A+B) + omega*(C+D)
Avx2.Store(partC, Avx.Add(Avx.LoadVector256(tmpPart1), Avx.LoadVector256(tmpPart5)));
//(A-B) + omega*(C-D)
Avx2.Store(partD, Avx.Add(Avx.LoadVector256(tmpPart2), Avx.LoadVector256(tmpPart6)));
//--------------------------------------------------------------------------------------------------------------
//Second part of each 8 complex part
//Tmp[0] = A + B
Avx2.Store(tmpPart1, Avx2.Add(Avx2.LoadVector256(partA + 8), Avx2.LoadVector256(partB + 8)));
//Tmp[1] = A - B
Avx2.Store(tmpPart2, Avx2.Subtract(Avx2.LoadVector256(partA + 8), Avx2.LoadVector256(partB + 8)));
//Tmp[2] = C + D
Avx2.Store(tmpPart3, Avx2.Add(Avx2.LoadVector256(partC + 8), Avx2.LoadVector256(partD + 8)));
//Tmp[2] = C - D
Avx2.Store(tmpPart4, Avx2.Subtract(Avx2.LoadVector256(partC + 8), Avx2.LoadVector256(partD + 8)));
//Complex multiplication based on: https://www.researchgate.net/figure/Vectorized-complex-multiplication-using-AVX-2_fig2_337532904
//Tmp[4] = omega * (C+D)
a = Avx2.LoadVector256(tmpPart3);
b = Avx2.LoadVector256(omPart1 + 8);
bSwap = Avx2.Shuffle(b, b, imm8bShuffle);
aIm = Avx2.Shuffle(a, a, imm8aImShuffle);
aRe = Avx2.Shuffle(a, a, imm8aReShuffle);
aIM_bSwap = Avx.Multiply(aIm, bSwap);
Avx2.Store(tmpPart5, Fma.MultiplyAddSubtract(aRe, b, aIM_bSwap));
//Tmp[4] = omega * (C-D)
a = Avx2.LoadVector256(tmpPart4);
b = Avx2.LoadVector256(omPart2 + 8);
bSwap = Avx2.Shuffle(b, b, imm8bShuffle);
aIm = Avx2.Shuffle(a, a, imm8aImShuffle);
aRe = Avx2.Shuffle(a, a, imm8aReShuffle);
aIM_bSwap = Avx.Multiply(aIm, bSwap);
Avx2.Store(tmpPart6, Fma.MultiplyAddSubtract(aRe, b, aIM_bSwap));
//(A+B) + (C+D)
Avx2.Store(partA + 8, Avx.Add(Avx.LoadVector256(tmpPart1), Avx.LoadVector256(tmpPart3)));
//(A-B) + (C-D)
Avx2.Store(partB + 8, Avx.Add(Avx.LoadVector256(tmpPart2), Avx.LoadVector256(tmpPart4)));
//(A+B) + omega*(C+D)
Avx2.Store(partC + 8, Avx.Add(Avx.LoadVector256(tmpPart1), Avx.LoadVector256(tmpPart5)));
//(A-B) + omega*(C-D)
Avx2.Store(partD + 8, Avx.Add(Avx.LoadVector256(tmpPart2), Avx.LoadVector256(tmpPart6)));
}
return(result);
//ComplexFloat[] result = new ComplexFloat[32];
//ArraySegment<ComplexFloat> partA = new ArraySegment<ComplexFloat>(i, 0, 16);
//ArraySegment<ComplexFloat> partB = new ArraySegment<ComplexFloat>(i, 16, 16);
//Kernel16(partA.ToArray(), ref omegas).CopyTo(result, 0);
//Kernel16(partA.ToArray(), ref omegas).CopyTo(result, 16);
//return result;
}
