// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2020 Everton Constantino (everton.constantino@ibm.com)
// Copyright (C) 2021 Chip Kerchner (chip.kerchner@ibm.com)
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_MATRIX_PRODUCT_ALTIVEC_H
#define EIGEN_MATRIX_PRODUCT_ALTIVEC_H

#ifndef EIGEN_ALTIVEC_USE_CUSTOM_PACK
#define EIGEN_ALTIVEC_USE_CUSTOM_PACK    1
#endif

#include "MatrixProductCommon.h"

#if !defined(EIGEN_ALTIVEC_DISABLE_MMA)
#define EIGEN_ALTIVEC_DISABLE_MMA 0
#endif

// Check for MMA builtin support. 
#if !EIGEN_ALTIVEC_DISABLE_MMA && defined(__has_builtin)
#if __has_builtin(__builtin_mma_assemble_acc)
  #define EIGEN_ALTIVEC_MMA_SUPPORT
#endif
#endif

// Check if and how we should actually use MMA if supported.
#if defined(EIGEN_ALTIVEC_MMA_SUPPORT)

#if !defined(EIGEN_ALTIVEC_ENABLE_MMA_DYNAMIC_DISPATCH)
#define EIGEN_ALTIVEC_ENABLE_MMA_DYNAMIC_DISPATCH 0
#endif

// Check if we want to enable dynamic dispatch. Not supported by LLVM.
#if EIGEN_ALTIVEC_ENABLE_MMA_DYNAMIC_DISPATCH && !EIGEN_COMP_LLVM
#define EIGEN_ALTIVEC_MMA_DYNAMIC_DISPATCH 1
// Otherwise, use MMA by default if available.
#elif defined(__MMA__)
#define EIGEN_ALTIVEC_MMA_ONLY 1
#endif

#endif // EIGEN_ALTIVEC_MMA_SUPPORT

#if defined(EIGEN_ALTIVEC_MMA_ONLY) || defined(EIGEN_ALTIVEC_MMA_DYNAMIC_DISPATCH)
  #include "MatrixProductMMA.h"
#endif

/**************************************************************************************************
 * TODO                                                                                           *
 * - Check StorageOrder on dhs_pack (the innermost second loop seems unvectorized when it could). *
 * - Check the possibility of transposing as GETREAL and GETIMAG when needed.                     *
 **************************************************************************************************/
#include "../../InternalHeaderCheck.h"

namespace Eigen {

namespace internal {

/**************************
 * Constants and typedefs *
 **************************/
template<typename Scalar>
struct quad_traits
{
  typedef typename packet_traits<Scalar>::type    vectortype;
  typedef PacketBlock<vectortype,4>                     type;
  typedef vectortype                                 rhstype;
  enum
  {
    vectorsize = packet_traits<Scalar>::size,
    size = 4,
    rows = 4
  };
};

template<>
struct quad_traits<double>
{
  typedef Packet2d                        vectortype;
  typedef PacketBlock<vectortype,4>             type;
  typedef PacketBlock<Packet2d,2>            rhstype;
  enum
  {
    vectorsize = packet_traits<double>::size,
    size = 2,
    rows = 4
  };
};

template<>
struct quad_traits<bfloat16>
{
  typedef Packet8bf                       vectortype;
  typedef PacketBlock<vectortype,4>             type;
  typedef vectortype                         rhstype;
  enum
  {
    vectorsize = packet_traits<bfloat16>::size,
    size = 8,
    rows = 4
  };
};

// MatrixProduct decomposes real/imaginary vectors into a real vector and an imaginary vector, this turned out
// to be faster than Eigen's usual approach of having real/imaginary pairs on a single vector. This constants then
// are responsible to extract from convert between Eigen's and MatrixProduct approach.

const static Packet16uc p16uc_GETREAL32 = {  0,  1,  2,  3,
                                             8,  9, 10, 11,
                                            16, 17, 18, 19,
                                            24, 25, 26, 27};

const static Packet16uc p16uc_GETIMAG32 = {  4,  5,  6,  7,
                                            12, 13, 14, 15,
                                            20, 21, 22, 23,
                                            28, 29, 30, 31};

/*********************************************
 * Single precision real and complex packing *
 * *******************************************/

/**
 * Symm packing is related to packing of symmetric adjoint blocks, as expected the packing leaves
 * the diagonal real, whatever is below it is copied from the respective upper diagonal element and 
 * conjugated. There's no PanelMode available for symm packing.
 *
 * Packing in general is supposed to leave the lhs block and the rhs block easy to be read by gemm using 
 * its respective rank-update instructions. The float32/64 versions are different because at this moment
 * the size of the accumulator is fixed at 512-bits so you can't have a 4x4 accumulator of 64-bit elements.
 * 
 * As mentioned earlier MatrixProduct breaks complex numbers into a real vector and a complex vector so packing has
 * to take that into account, at the moment, we run pack the real part and then the imaginary part, this is the main
 * reason why packing for complex is broken down into several different parts, also the reason why we endup having a
 * float32/64 and complex float32/64 version.
 **/
template<typename Scalar, int StorageOrder>
EIGEN_ALWAYS_INLINE std::complex<Scalar> getAdjointVal(Index i, Index j, const_blas_data_mapper<std::complex<Scalar>, Index, StorageOrder>& dt)
{
  std::complex<Scalar> v;
  if(i < j)
  {
    v.real( dt(j,i).real());
    v.imag(-dt(j,i).imag());
  } else if(i > j)
  {
    v.real( dt(i,j).real());
    v.imag( dt(i,j).imag());
  } else {
    v.real( dt(i,j).real());
    v.imag((Scalar)0.0);
  }
  return v;
}

template<typename Scalar, int StorageOrder, int N>
EIGEN_STRONG_INLINE void symm_pack_complex_rhs_helper(std::complex<Scalar>* blockB, const std::complex<Scalar>* _rhs, Index rhsStride, Index rows, Index cols, Index k2)
{
  const Index depth = k2 + rows;
  const_blas_data_mapper<std::complex<Scalar>, Index, StorageOrder> rhs(_rhs, rhsStride);
  const Index vectorSize = N*quad_traits<Scalar>::vectorsize;
  const Index vectorDelta = vectorSize * rows;
  Scalar* blockBf = reinterpret_cast<Scalar *>(blockB);

  Index rir = 0, rii, j = 0;
  for(; j + vectorSize <= cols; j+=vectorSize)
  {
    rii = rir + vectorDelta;

    for(Index i = k2; i < depth; i++)
    {
      for(Index k = 0; k < vectorSize; k++)
      {
        std::complex<Scalar> v = getAdjointVal<Scalar, StorageOrder>(i, j + k, rhs);

        blockBf[rir + k] = v.real();
        blockBf[rii + k] = v.imag();
      }
      rir += vectorSize;
      rii += vectorSize;
    }

    rir += vectorDelta;
  }

  for(; j < cols; j++)
  {
    rii = rir + rows;

    for(Index i = k2; i < depth; i++)
    {
      std::complex<Scalar> v = getAdjointVal<Scalar, StorageOrder>(i, j, rhs);

      blockBf[rir] = v.real();
      blockBf[rii] = v.imag();

      rir += 1;
      rii += 1;
    }

    rir += rows;
  }
}

template<typename Scalar, int StorageOrder>
EIGEN_STRONG_INLINE void symm_pack_complex_lhs_helper(std::complex<Scalar>* blockA, const std::complex<Scalar>* _lhs, Index lhsStride, Index cols, Index rows)
{
  const Index depth = cols;
  const_blas_data_mapper<std::complex<Scalar>, Index, StorageOrder> lhs(_lhs, lhsStride);
  const Index vectorSize = quad_traits<Scalar>::vectorsize;
  const Index vectorDelta = vectorSize * depth;
  Scalar* blockAf = reinterpret_cast<Scalar *>(blockA);

  Index rir = 0, rii, j = 0;
  for(; j + vectorSize <= rows; j+=vectorSize)
  {
    rii = rir + vectorDelta;

    for(Index i = 0; i < depth; i++)
    {
      for(Index k = 0; k < vectorSize; k++)
      {
        std::complex<Scalar> v = getAdjointVal<Scalar, StorageOrder>(j+k, i, lhs);

        blockAf[rir + k] = v.real();
        blockAf[rii + k] = v.imag();
      }
      rir += vectorSize;
      rii += vectorSize;
    }

    rir += vectorDelta;
  }

  if (j < rows)
  {
    rii = rir + ((rows - j) * depth);

    for(Index i = 0; i < depth; i++)
    {
      Index k = j;
      for(; k < rows; k++)
      {
        std::complex<Scalar> v = getAdjointVal<Scalar, StorageOrder>(k, i, lhs);

        blockAf[rir] = v.real();
        blockAf[rii] = v.imag();

        rir += 1;
        rii += 1;
      }
    }
  }
}

template<typename Scalar, int StorageOrder, int N>
EIGEN_STRONG_INLINE void symm_pack_rhs_helper(Scalar* blockB, const Scalar* _rhs, Index rhsStride, Index rows, Index cols, Index k2)
{
  const Index depth = k2 + rows;
  const_blas_data_mapper<Scalar, Index, StorageOrder> rhs(_rhs, rhsStride);
  const Index vectorSize = quad_traits<Scalar>::vectorsize;

  Index ri = 0, j = 0;
  for(; j + N*vectorSize <= cols; j+=N*vectorSize)
  {
    Index i = k2;
    for(; i < depth; i++)
    {
      for(Index k = 0; k < N*vectorSize; k++)
      {
        if(i <= j+k)
          blockB[ri + k] = rhs(j+k, i);
        else
          blockB[ri + k] = rhs(i, j+k);
      }
      ri += N*vectorSize;
    }
  }

  for(; j < cols; j++)
  {
    for(Index i = k2; i < depth; i++)
    {
      if(j <= i)
        blockB[ri] = rhs(i, j);
      else
        blockB[ri] = rhs(j, i);
      ri += 1;
    }
  }
}

template<typename Scalar, int StorageOrder>
EIGEN_STRONG_INLINE void symm_pack_lhs_helper(Scalar* blockA, const Scalar* _lhs, Index lhsStride, Index cols, Index rows)
{
  const Index depth = cols;
  const_blas_data_mapper<Scalar, Index, StorageOrder> lhs(_lhs, lhsStride);
  const Index vectorSize = quad_traits<Scalar>::vectorsize;

  Index ri = 0, j = 0;
  for(; j + vectorSize <= rows; j+=vectorSize)
  {
    Index i = 0;

    for(; i < depth; i++)
    {
      for(Index k = 0; k < vectorSize; k++)
      {
        if(i <= j+k)
          blockA[ri + k] = lhs(j+k, i);
        else
          blockA[ri + k] = lhs(i, j+k);
      }
      ri += vectorSize;
    }
  }

  if (j < rows)
  {
    for(Index i = 0; i < depth; i++)
    {
      Index k = j;
      for(; k < rows; k++)
      {
        if(i <= k)
          blockA[ri] = lhs(k, i);
        else
          blockA[ri] = lhs(i, k);
        ri += 1;
      }
    }
  }
}

template<typename Index, int nr, int StorageOrder>
struct symm_pack_rhs<std::complex<float>, Index, nr, StorageOrder>
{
  void operator()(std::complex<float>* blockB, const std::complex<float>* _rhs, Index rhsStride, Index rows, Index cols, Index k2)
  {
    symm_pack_complex_rhs_helper<float, StorageOrder, 1>(blockB, _rhs, rhsStride, rows, cols, k2);
  }
};

template<typename Index, int Pack1, int Pack2_dummy, int StorageOrder>
struct symm_pack_lhs<std::complex<float>, Index, Pack1, Pack2_dummy, StorageOrder>
{
  void operator()(std::complex<float>* blockA, const std::complex<float>* _lhs, Index lhsStride, Index cols, Index rows)
  {
    symm_pack_complex_lhs_helper<float, StorageOrder>(blockA, _lhs, lhsStride, cols, rows);
  }
};

// *********** symm_pack std::complex<float64> ***********

template<typename Index, int nr, int StorageOrder>
struct symm_pack_rhs<std::complex<double>, Index, nr, StorageOrder>
{
  void operator()(std::complex<double>* blockB, const std::complex<double>* _rhs, Index rhsStride, Index rows, Index cols, Index k2)
  {
    symm_pack_complex_rhs_helper<double, StorageOrder, 2>(blockB, _rhs, rhsStride, rows, cols, k2);
  }
};

template<typename Index, int Pack1, int Pack2_dummy, int StorageOrder>
struct symm_pack_lhs<std::complex<double>, Index, Pack1, Pack2_dummy, StorageOrder>
{
  void operator()(std::complex<double>* blockA, const std::complex<double>* _lhs, Index lhsStride, Index cols, Index rows)
  {
    symm_pack_complex_lhs_helper<double, StorageOrder>(blockA, _lhs, lhsStride, cols, rows);
  }
};

// *********** symm_pack float32 ***********
template<typename Index, int nr, int StorageOrder>
struct symm_pack_rhs<float, Index, nr, StorageOrder>
{
  void operator()(float* blockB, const float* _rhs, Index rhsStride, Index rows, Index cols, Index k2)
  {
    symm_pack_rhs_helper<float, StorageOrder, 1>(blockB, _rhs, rhsStride, rows, cols, k2);
  }
};

template<typename Index, int Pack1, int Pack2_dummy, int StorageOrder>
struct symm_pack_lhs<float, Index, Pack1, Pack2_dummy, StorageOrder>
{
  void operator()(float* blockA, const float* _lhs, Index lhsStride, Index cols, Index rows)
  {
    symm_pack_lhs_helper<float, StorageOrder>(blockA, _lhs, lhsStride, cols, rows);
  }
};

// *********** symm_pack float64 ***********
template<typename Index, int nr, int StorageOrder>
struct symm_pack_rhs<double, Index, nr, StorageOrder>
{
  void operator()(double* blockB, const double* _rhs, Index rhsStride, Index rows, Index cols, Index k2)
  {
    symm_pack_rhs_helper<double, StorageOrder, 2>(blockB, _rhs, rhsStride, rows, cols, k2);
  }
};

template<typename Index, int Pack1, int Pack2_dummy, int StorageOrder>
struct symm_pack_lhs<double, Index, Pack1, Pack2_dummy, StorageOrder>
{
  void operator()(double* blockA, const double* _lhs, Index lhsStride, Index cols, Index rows)
  {
    symm_pack_lhs_helper<double, StorageOrder>(blockA, _lhs, lhsStride, cols, rows);
  }
};

/**
 * PanelMode
 * Packing might be called several times before being multiplied by gebp_kernel, this happens because 
 * on special occasions it fills part of block with other parts of the matrix. Two variables control
 * how PanelMode should behave: offset and stride. The idea is that those variables represent whatever
 * is going to be the real offset and stride in the future and this is what you should obey. The process
 * is to behave as you would with normal packing but leave the start of each part with the correct offset
 * and the end as well respecting the real stride the block will have. Gebp is aware of both blocks stride
 * and offset and behaves accordingly.
 **/

template<typename Scalar, typename Packet, int N>
EIGEN_ALWAYS_INLINE void storeBlock(Scalar* to, PacketBlock<Packet,N>& block)
{
  const Index size = 16 / sizeof(Scalar);
  pstore<Scalar>(to + (0 * size), block.packet[0]);
  pstore<Scalar>(to + (1 * size), block.packet[1]);
  if (N > 2) {
    pstore<Scalar>(to + (2 * size), block.packet[2]);
  }
  if (N > 3) {
    pstore<Scalar>(to + (3 * size), block.packet[3]);
  }
}

// General template for lhs & rhs complex packing.
template<typename Scalar, typename DataMapper, typename Packet, typename PacketC, int StorageOrder, bool Conjugate, bool PanelMode, bool UseLhs>
struct dhs_cpack {
  EIGEN_STRONG_INLINE void operator()(std::complex<Scalar>* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride, Index offset)
  {
    const Index vectorSize = quad_traits<Scalar>::vectorsize;
    const Index vectorDelta = vectorSize * ((PanelMode) ? stride : depth);
    Index rir = ((PanelMode) ? (vectorSize*offset) : 0), rii;
    Scalar* blockAt = reinterpret_cast<Scalar *>(blockA);
    Index j = 0;

    for(; j + vectorSize <= rows; j+=vectorSize)
    {
      const DataMapper lhs2 = UseLhs ? lhs.getSubMapper(j, 0) : lhs.getSubMapper(0, j);
      Index i = 0;

      rii = rir + vectorDelta;

      for(; i + vectorSize <= depth; i+=vectorSize)
      {
        PacketBlock<Packet,4> blockr, blocki;
        PacketBlock<PacketC,8> cblock;

        if (UseLhs) {
          bload<DataMapper, PacketC, 2, StorageOrder, true, 4>(cblock, lhs2, 0, i);
        } else {
          bload<DataMapper, PacketC, 2, StorageOrder, true, 4>(cblock, lhs2, i, 0);
        }

        blockr.packet[0] = vec_perm(cblock.packet[0].v, cblock.packet[4].v, p16uc_GETREAL32);
        blockr.packet[1] = vec_perm(cblock.packet[1].v, cblock.packet[5].v, p16uc_GETREAL32);
        blockr.packet[2] = vec_perm(cblock.packet[2].v, cblock.packet[6].v, p16uc_GETREAL32);
        blockr.packet[3] = vec_perm(cblock.packet[3].v, cblock.packet[7].v, p16uc_GETREAL32);

        blocki.packet[0] = vec_perm(cblock.packet[0].v, cblock.packet[4].v, p16uc_GETIMAG32);
        blocki.packet[1] = vec_perm(cblock.packet[1].v, cblock.packet[5].v, p16uc_GETIMAG32);
        blocki.packet[2] = vec_perm(cblock.packet[2].v, cblock.packet[6].v, p16uc_GETIMAG32);
        blocki.packet[3] = vec_perm(cblock.packet[3].v, cblock.packet[7].v, p16uc_GETIMAG32);

        if(Conjugate)
        {
          blocki.packet[0] = -blocki.packet[0];
          blocki.packet[1] = -blocki.packet[1];
          blocki.packet[2] = -blocki.packet[2];
          blocki.packet[3] = -blocki.packet[3];
        }

        if(((StorageOrder == RowMajor) && UseLhs) || (((StorageOrder == ColMajor) && !UseLhs)))
        {
          ptranspose(blockr);
          ptranspose(blocki);
        }

        storeBlock<Scalar, Packet, 4>(blockAt + rir, blockr);
        storeBlock<Scalar, Packet, 4>(blockAt + rii, blocki);

        rir += 4*vectorSize;
        rii += 4*vectorSize;
      }
      for(; i < depth; i++)
      {
        PacketBlock<Packet,1> blockr, blocki;
        PacketBlock<PacketC,2> cblock;

        if(((StorageOrder == ColMajor) && UseLhs) || (((StorageOrder == RowMajor) && !UseLhs)))
        {
          if (UseLhs) {
            cblock.packet[0] = lhs2.template loadPacket<PacketC>(0, i);
            cblock.packet[1] = lhs2.template loadPacket<PacketC>(2, i);
          } else {
            cblock.packet[0] = lhs2.template loadPacket<PacketC>(i, 0);
            cblock.packet[1] = lhs2.template loadPacket<PacketC>(i, 2);
          }
        } else {
          if (UseLhs) {
            cblock.packet[0] = pload2(lhs2(0, i), lhs2(1, i));
            cblock.packet[1] = pload2(lhs2(2, i), lhs2(3, i));
          } else {
            cblock.packet[0] = pload2(lhs2(i, 0), lhs2(i, 1));
            cblock.packet[1] = pload2(lhs2(i, 2), lhs2(i, 3));
          }
        }

        blockr.packet[0] = vec_perm(cblock.packet[0].v, cblock.packet[1].v, p16uc_GETREAL32);
        blocki.packet[0] = vec_perm(cblock.packet[0].v, cblock.packet[1].v, p16uc_GETIMAG32);

        if(Conjugate)
        {
          blocki.packet[0] = -blocki.packet[0];
        }

        pstore<Scalar>(blockAt + rir, blockr.packet[0]);
        pstore<Scalar>(blockAt + rii, blocki.packet[0]);

        rir += vectorSize;
        rii += vectorSize;
      }

      rir += ((PanelMode) ? (vectorSize*(2*stride - depth)) : vectorDelta);
    }

    if (!UseLhs)
    {
      if(PanelMode) rir -= (offset*(vectorSize - 1));

      for(; j < rows; j++)
      {
        const DataMapper lhs2 = lhs.getSubMapper(0, j);
        rii = rir + ((PanelMode) ? stride : depth);

        for(Index i = 0; i < depth; i++)
        {
          blockAt[rir] = lhs2(i, 0).real();

          if(Conjugate)
            blockAt[rii] = -lhs2(i, 0).imag();
          else
            blockAt[rii] =  lhs2(i, 0).imag();

          rir += 1;
          rii += 1;
        }

        rir += ((PanelMode) ? (2*stride - depth) : depth);
      }
    } else {
      if (j < rows)
      {
        if(PanelMode) rir += (offset*(rows - j - vectorSize));
        rii = rir + (((PanelMode) ? stride : depth) * (rows - j));

        for(Index i = 0; i < depth; i++)
        {
          Index k = j;
          for(; k < rows; k++)
          {
            blockAt[rir] = lhs(k, i).real();

            if(Conjugate)
              blockAt[rii] = -lhs(k, i).imag();
            else
              blockAt[rii] =  lhs(k, i).imag();

            rir += 1;
            rii += 1;
          }
        }
      }
    }
  }
};

// General template for lhs & rhs packing.
template<typename Scalar, typename DataMapper, typename Packet, int StorageOrder, bool PanelMode, bool UseLhs>
struct dhs_pack{
  EIGEN_STRONG_INLINE void operator()(Scalar* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride, Index offset)
  {
    const Index vectorSize = quad_traits<Scalar>::vectorsize;
    Index ri = 0, j = 0;

    for(; j + vectorSize <= rows; j+=vectorSize)
    {
      const DataMapper lhs2 = UseLhs ? lhs.getSubMapper(j, 0) : lhs.getSubMapper(0, j);
      Index i = 0;

      if(PanelMode) ri += vectorSize*offset;

      for(; i + vectorSize <= depth; i+=vectorSize)
      {
        PacketBlock<Packet,4> block;

        if (UseLhs) {
          bload<DataMapper, Packet, 4, StorageOrder, false, 4>(block, lhs2, 0, i);
        } else {
          bload<DataMapper, Packet, 4, StorageOrder, false, 4>(block, lhs2, i, 0);
        }
        if(((StorageOrder == RowMajor) && UseLhs) || ((StorageOrder == ColMajor) && !UseLhs))
        {
          ptranspose(block);
        }

        storeBlock<Scalar, Packet, 4>(blockA + ri, block);

        ri += 4*vectorSize;
      }
      for(; i < depth; i++)
      {
        if(((StorageOrder == RowMajor) && UseLhs) || ((StorageOrder == ColMajor) && !UseLhs))
        {
          if (UseLhs) {
            blockA[ri+0] = lhs2(0, i);
            blockA[ri+1] = lhs2(1, i);
            blockA[ri+2] = lhs2(2, i);
            blockA[ri+3] = lhs2(3, i);
          } else {
            blockA[ri+0] = lhs2(i, 0);
            blockA[ri+1] = lhs2(i, 1);
            blockA[ri+2] = lhs2(i, 2);
            blockA[ri+3] = lhs2(i, 3);
          }
        } else {
          Packet lhsV;
          if (UseLhs) {
            lhsV = lhs2.template loadPacket<Packet>(0, i);
          } else {
            lhsV = lhs2.template loadPacket<Packet>(i, 0);
          }
          pstore<Scalar>(blockA + ri, lhsV);
        }

        ri += vectorSize;
      }

      if(PanelMode) ri += vectorSize*(stride - offset - depth);
    }

    if (!UseLhs)
    {
      if(PanelMode) ri += offset;

      for(; j < rows; j++)
      {
        const DataMapper lhs2 = lhs.getSubMapper(0, j);
        for(Index i = 0; i < depth; i++)
        {
          blockA[ri] = lhs2(i, 0);
          ri += 1;
        }

        if(PanelMode) ri += stride - depth;
      }
    } else {
      if (j < rows)
      {
        if(PanelMode) ri += offset*(rows - j);

        for(Index i = 0; i < depth; i++)
        {
          Index k = j;
          for(; k < rows; k++)
          {
            blockA[ri] = lhs(k, i);
            ri += 1;
          }
        }
      }
    }
  }
};

// General template for lhs packing, float64 specialization.
template<typename DataMapper, int StorageOrder, bool PanelMode>
struct dhs_pack<double, DataMapper, Packet2d, StorageOrder, PanelMode, true>
{
  EIGEN_STRONG_INLINE void operator()(double* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride, Index offset)
  {
    const Index vectorSize = quad_traits<double>::vectorsize;
    Index ri = 0, j = 0;

    for(; j + vectorSize <= rows; j+=vectorSize)
    {
      const DataMapper lhs2 = lhs.getSubMapper(j, 0);
      Index i = 0;

      if(PanelMode) ri += vectorSize*offset;

      for(; i + vectorSize <= depth; i+=vectorSize)
      {
        PacketBlock<Packet2d,2> block;
        if(StorageOrder == RowMajor)
        {
          block.packet[0] = lhs2.template loadPacket<Packet2d>(0, i);
          block.packet[1] = lhs2.template loadPacket<Packet2d>(1, i);

          ptranspose(block);
        } else {
          block.packet[0] = lhs2.template loadPacket<Packet2d>(0, i + 0);
          block.packet[1] = lhs2.template loadPacket<Packet2d>(0, i + 1);
        }

        storeBlock<double, Packet2d, 2>(blockA + ri, block);

        ri += 2*vectorSize;
      }
      for(; i < depth; i++)
      {
        if(StorageOrder == RowMajor)
        {
          blockA[ri+0] = lhs2(0, i);
          blockA[ri+1] = lhs2(1, i);
        } else {
          Packet2d lhsV = lhs2.template loadPacket<Packet2d>(0, i);
          pstore<double>(blockA + ri, lhsV);
        }

        ri += vectorSize;
      }

      if(PanelMode) ri += vectorSize*(stride - offset - depth);
    }

    if (j < rows)
    {
      if(PanelMode) ri += offset*(rows - j);

      for(Index i = 0; i < depth; i++)
      {
        Index k = j;
        for(; k < rows; k++)
        {
          blockA[ri] = lhs(k, i);
          ri += 1;
        }
      }
    }
  }
};

// General template for rhs packing, float64 specialization.
template<typename DataMapper, int StorageOrder, bool PanelMode>
struct dhs_pack<double, DataMapper, Packet2d, StorageOrder, PanelMode, false>
{
  EIGEN_STRONG_INLINE void operator()(double* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride, Index offset)
  {
    const Index vectorSize = quad_traits<double>::vectorsize;
    Index ri = 0, j = 0;

    for(; j + 2*vectorSize <= cols; j+=2*vectorSize)
    {
      const DataMapper rhs2 = rhs.getSubMapper(0, j);
      Index i = 0;

      if(PanelMode) ri += offset*(2*vectorSize);

      for(; i + vectorSize <= depth; i+=vectorSize)
      {
        PacketBlock<Packet2d,4> block;
        if(StorageOrder == ColMajor)
        {
          PacketBlock<Packet2d,2> block1, block2;
          block1.packet[0] = rhs2.template loadPacket<Packet2d>(i, 0);
          block1.packet[1] = rhs2.template loadPacket<Packet2d>(i, 1);
          block2.packet[0] = rhs2.template loadPacket<Packet2d>(i, 2);
          block2.packet[1] = rhs2.template loadPacket<Packet2d>(i, 3);

          ptranspose(block1);
          ptranspose(block2);

          pstore<double>(blockB + ri    , block1.packet[0]);
          pstore<double>(blockB + ri + 2, block2.packet[0]);
          pstore<double>(blockB + ri + 4, block1.packet[1]);
          pstore<double>(blockB + ri + 6, block2.packet[1]);
        } else {
          block.packet[0] = rhs2.template loadPacket<Packet2d>(i + 0, 0); //[a1 a2]
          block.packet[1] = rhs2.template loadPacket<Packet2d>(i + 0, 2); //[a3 a4]
          block.packet[2] = rhs2.template loadPacket<Packet2d>(i + 1, 0); //[b1 b2]
          block.packet[3] = rhs2.template loadPacket<Packet2d>(i + 1, 2); //[b3 b4]

          storeBlock<double, Packet2d, 4>(blockB + ri, block);
        }

        ri += 4*vectorSize;
      }
      for(; i < depth; i++)
      {
        if(StorageOrder == ColMajor)
        {
          blockB[ri+0] = rhs2(i, 0);
          blockB[ri+1] = rhs2(i, 1);

          ri += vectorSize;

          blockB[ri+0] = rhs2(i, 2);
          blockB[ri+1] = rhs2(i, 3);
        } else {
          Packet2d rhsV = rhs2.template loadPacket<Packet2d>(i, 0);
          pstore<double>(blockB + ri, rhsV);

          ri += vectorSize;

          rhsV = rhs2.template loadPacket<Packet2d>(i, 2);
          pstore<double>(blockB + ri, rhsV);
        }
        ri += vectorSize;
      }

      if(PanelMode) ri += (2*vectorSize)*(stride - offset - depth);
    }

    if(PanelMode) ri += offset;

    for(; j < cols; j++)
    {
      const DataMapper rhs2 = rhs.getSubMapper(0, j);
      for(Index i = 0; i < depth; i++)
      {
        blockB[ri] = rhs2(i, 0);
        ri += 1;
      }

      if(PanelMode) ri += stride - depth;
    }
  }
};

// General template for lhs complex packing, float64 specialization.
template<typename DataMapper, typename Packet, typename PacketC, int StorageOrder, bool Conjugate, bool PanelMode>
struct dhs_cpack<double, DataMapper, Packet, PacketC, StorageOrder, Conjugate, PanelMode, true>
{
  EIGEN_STRONG_INLINE void operator()(std::complex<double>* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride, Index offset)
  {
    const Index vectorSize = quad_traits<double>::vectorsize;
    const Index vectorDelta = vectorSize * ((PanelMode) ? stride : depth);
    Index rir = ((PanelMode) ? (vectorSize*offset) : 0), rii;
    double* blockAt = reinterpret_cast<double *>(blockA);
    Index j = 0;

    for(; j + vectorSize <= rows; j+=vectorSize)
    {
      const DataMapper lhs2 = lhs.getSubMapper(j, 0);
      Index i = 0;

      rii = rir + vectorDelta;

      for(; i + vectorSize <= depth; i+=vectorSize)
      {
        PacketBlock<Packet,2> blockr, blocki;
        PacketBlock<PacketC,4> cblock;

        if(StorageOrder == ColMajor)
        {
          cblock.packet[0] = lhs2.template loadPacket<PacketC>(0, i + 0); //[a1 a1i]
          cblock.packet[1] = lhs2.template loadPacket<PacketC>(0, i + 1); //[b1 b1i]

          cblock.packet[2] = lhs2.template loadPacket<PacketC>(1, i + 0); //[a2 a2i]
          cblock.packet[3] = lhs2.template loadPacket<PacketC>(1, i + 1); //[b2 b2i]

          blockr.packet[0] = vec_mergeh(cblock.packet[0].v, cblock.packet[2].v); //[a1 a2]
          blockr.packet[1] = vec_mergeh(cblock.packet[1].v, cblock.packet[3].v); //[b1 b2]

          blocki.packet[0] = vec_mergel(cblock.packet[0].v, cblock.packet[2].v);
          blocki.packet[1] = vec_mergel(cblock.packet[1].v, cblock.packet[3].v);
        } else {
          cblock.packet[0] = lhs2.template loadPacket<PacketC>(0, i); //[a1 a1i]
          cblock.packet[1] = lhs2.template loadPacket<PacketC>(1, i); //[a2 a2i]

          cblock.packet[2] = lhs2.template loadPacket<PacketC>(0, i + 1); //[b1 b1i]
          cblock.packet[3] = lhs2.template loadPacket<PacketC>(1, i + 1); //[b2 b2i

          blockr.packet[0] = vec_mergeh(cblock.packet[0].v, cblock.packet[1].v); //[a1 a2]
          blockr.packet[1] = vec_mergeh(cblock.packet[2].v, cblock.packet[3].v); //[b1 b2]

          blocki.packet[0] = vec_mergel(cblock.packet[0].v, cblock.packet[1].v);
          blocki.packet[1] = vec_mergel(cblock.packet[2].v, cblock.packet[3].v);
        }

        if(Conjugate)
        {
          blocki.packet[0] = -blocki.packet[0];
          blocki.packet[1] = -blocki.packet[1];
        }

        storeBlock<double, Packet, 2>(blockAt + rir, blockr);
        storeBlock<double, Packet, 2>(blockAt + rii, blocki);

        rir += 2*vectorSize;
        rii += 2*vectorSize;
      }
      for(; i < depth; i++)
      {
        PacketBlock<Packet,1> blockr, blocki;
        PacketBlock<PacketC,2> cblock;

        cblock.packet[0] = lhs2.template loadPacket<PacketC>(0, i);
        cblock.packet[1] = lhs2.template loadPacket<PacketC>(1, i);

        blockr.packet[0] = vec_mergeh(cblock.packet[0].v, cblock.packet[1].v);
        blocki.packet[0] = vec_mergel(cblock.packet[0].v, cblock.packet[1].v);

        if(Conjugate)
        {
          blocki.packet[0] = -blocki.packet[0];
        }

        pstore<double>(blockAt + rir, blockr.packet[0]);
        pstore<double>(blockAt + rii, blocki.packet[0]);

        rir += vectorSize;
        rii += vectorSize;
      }

      rir += ((PanelMode) ? (vectorSize*(2*stride - depth)) : vectorDelta);
    }

    if (j < rows)
    {
      if(PanelMode) rir += (offset*(rows - j - vectorSize));
      rii = rir + (((PanelMode) ? stride : depth) * (rows - j));

      for(Index i = 0; i < depth; i++)
      {
        Index k = j;
        for(; k < rows; k++)
        {
          blockAt[rir] = lhs(k, i).real();

          if(Conjugate)
            blockAt[rii] = -lhs(k, i).imag();
          else
            blockAt[rii] =  lhs(k, i).imag();

          rir += 1;
          rii += 1;
        }
      }
    }
  }
};

// General template for rhs complex packing, float64 specialization.
template<typename DataMapper, typename Packet, typename PacketC, int StorageOrder, bool Conjugate, bool PanelMode>
struct dhs_cpack<double, DataMapper, Packet, PacketC, StorageOrder, Conjugate, PanelMode, false>
{
  EIGEN_STRONG_INLINE void operator()(std::complex<double>* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride, Index offset)
  {
    const Index vectorSize = quad_traits<double>::vectorsize;
    const Index vectorDelta = 2*vectorSize * ((PanelMode) ? stride : depth);
    Index rir = ((PanelMode) ? (2*vectorSize*offset) : 0), rii;
    double* blockBt = reinterpret_cast<double *>(blockB);
    Index j = 0;

    for(; j + 2*vectorSize <= cols; j+=2*vectorSize)
    {
      const DataMapper rhs2 = rhs.getSubMapper(0, j);
      Index i = 0;

      rii = rir + vectorDelta;

      for(; i < depth; i++)
      {
        PacketBlock<PacketC,4> cblock;
        PacketBlock<Packet,2> blockr, blocki;

        bload<DataMapper, PacketC, 2, ColMajor, false, 4>(cblock, rhs2, i, 0);

        blockr.packet[0] = vec_mergeh(cblock.packet[0].v, cblock.packet[1].v);
        blockr.packet[1] = vec_mergeh(cblock.packet[2].v, cblock.packet[3].v);

        blocki.packet[0] = vec_mergel(cblock.packet[0].v, cblock.packet[1].v);
        blocki.packet[1] = vec_mergel(cblock.packet[2].v, cblock.packet[3].v);

        if(Conjugate)
        {
          blocki.packet[0] = -blocki.packet[0];
          blocki.packet[1] = -blocki.packet[1];
        }

        storeBlock<double, Packet, 2>(blockBt + rir, blockr);
        storeBlock<double, Packet, 2>(blockBt + rii, blocki);

        rir += 2*vectorSize;
        rii += 2*vectorSize;
      }

      rir += ((PanelMode) ? (2*vectorSize*(2*stride - depth)) : vectorDelta);
    }

    if(PanelMode) rir -= (offset*(2*vectorSize - 1));

    for(; j < cols; j++)
    {
      const DataMapper rhs2 = rhs.getSubMapper(0, j);
      rii = rir + ((PanelMode) ? stride : depth);

      for(Index i = 0; i < depth; i++)
      {
        blockBt[rir] = rhs2(i, 0).real();

        if(Conjugate)
          blockBt[rii] = -rhs2(i, 0).imag();
        else
          blockBt[rii] =  rhs2(i, 0).imag();

        rir += 1;
        rii += 1;
      }

      rir += ((PanelMode) ? (2*stride - depth) : depth);
    }
  }
};

/**************
 * GEMM utils *
 **************/

// 512-bits rank1-update of acc. It can either positive or negative accumulate (useful for complex gemm).
template<typename Packet, bool NegativeAccumulate, int N>
EIGEN_ALWAYS_INLINE void pger_common(PacketBlock<Packet,N>* acc, const Packet& lhsV, const Packet* rhsV)
{
  if(NegativeAccumulate)
  {
    for (int M = 0; M < N; M++) {
      acc->packet[M] = vec_nmsub(lhsV, rhsV[M], acc->packet[M]);
    }
  } else {
    for (int M = 0; M < N; M++) {
      acc->packet[M] = vec_madd(lhsV, rhsV[M], acc->packet[M]);
    }
  }
}

template<int N, typename Scalar, typename Packet, bool NegativeAccumulate>
EIGEN_ALWAYS_INLINE void pger(PacketBlock<Packet,N>* acc, const Scalar* lhs, const Packet* rhsV)
{
  Packet lhsV = pload<Packet>(lhs);

  pger_common<Packet, NegativeAccumulate, N>(acc, lhsV, rhsV);
}

// 512-bits rank1-update of complex acc. It takes decoupled accumulators as entries. It also takes cares of mixed types real * complex and complex * real.
template<int N, typename Packet, bool ConjugateLhs, bool ConjugateRhs, bool LhsIsReal, bool RhsIsReal>
EIGEN_ALWAYS_INLINE void pgerc_common(PacketBlock<Packet,N>* accReal, PacketBlock<Packet,N>* accImag, const Packet &lhsV, Packet &lhsVi, const Packet* rhsV, const Packet* rhsVi)
{
  pger_common<Packet, false, N>(accReal, lhsV, rhsV);
  if(LhsIsReal)
  {
    pger_common<Packet, ConjugateRhs, N>(accImag, lhsV, rhsVi);
    EIGEN_UNUSED_VARIABLE(lhsVi);
  } else {
    if (!RhsIsReal) {
      pger_common<Packet, ConjugateLhs == ConjugateRhs, N>(accReal, lhsVi, rhsVi);
      pger_common<Packet, ConjugateRhs, N>(accImag, lhsV, rhsVi);
    } else {
      EIGEN_UNUSED_VARIABLE(rhsVi);
    }
    pger_common<Packet, ConjugateLhs, N>(accImag, lhsVi, rhsV);
  }
}

template<int N, typename Scalar, typename Packet, bool ConjugateLhs, bool ConjugateRhs, bool LhsIsReal, bool RhsIsReal>
EIGEN_ALWAYS_INLINE void pgerc(PacketBlock<Packet,N>* accReal, PacketBlock<Packet,N>* accImag, const Scalar* lhs_ptr, const Scalar* lhs_ptr_imag, const Packet* rhsV, const Packet* rhsVi)
{
  Packet lhsV = ploadLhs<Packet>(lhs_ptr);
  Packet lhsVi;
  if(!LhsIsReal) lhsVi = ploadLhs<Packet>(lhs_ptr_imag);
  else EIGEN_UNUSED_VARIABLE(lhs_ptr_imag);

  pgerc_common<N, Packet, ConjugateLhs, ConjugateRhs, LhsIsReal, RhsIsReal>(accReal, accImag, lhsV, lhsVi, rhsV, rhsVi);
}

template<typename Packet>
EIGEN_ALWAYS_INLINE Packet ploadLhs(const __UNPACK_TYPE__(Packet)* lhs)
{
  return ploadu<Packet>(lhs);
}

// Zero the accumulator on PacketBlock.
template<typename Packet, int N>
EIGEN_ALWAYS_INLINE void bsetzero(PacketBlock<Packet,N>& acc)
{
  for (int M = 0; M < N; M++) {
    acc.packet[M] = pset1<Packet>((__UNPACK_TYPE__(Packet))0);
  }
}

template<typename Packet, int N>
EIGEN_ALWAYS_INLINE void bscalec_common(PacketBlock<Packet,N>& acc, PacketBlock<Packet,N>& accZ, const Packet& pAlpha)
{
  for (int M = 0; M < N; M++) {
    acc.packet[M] = vec_mul(accZ.packet[M], pAlpha);
  }
}

template<typename Packet, int N>
EIGEN_ALWAYS_INLINE void band(PacketBlock<Packet,N>& acc, const Packet& pMask)
{
  for (int M = 0; M < N; M++) {
    acc.packet[M] = pand<Packet>(acc.packet[M], pMask);
  }
}

// Complex version of PacketBlock scaling.
template<typename Packet, int N, bool mask>
EIGEN_ALWAYS_INLINE void bscalec(PacketBlock<Packet,N>& aReal, PacketBlock<Packet,N>& aImag, const Packet& bReal, const Packet& bImag, PacketBlock<Packet,N>& cReal, PacketBlock<Packet,N>& cImag, const Packet& pMask)
{
  if (mask && (sizeof(__UNPACK_TYPE__(Packet)) == sizeof(float))) {
    band<Packet, N>(aReal, pMask);
    band<Packet, N>(aImag, pMask);
  } else {
    EIGEN_UNUSED_VARIABLE(pMask);
  }

  bscalec_common<Packet, N>(cReal, aReal, bReal);

  bscalec_common<Packet, N>(cImag, aImag, bReal);

  pger_common<Packet, true, N>(&cReal, bImag, aImag.packet);

  pger_common<Packet, false, N>(&cImag, bImag, aReal.packet);
}

// Load a PacketBlock, the N parameters make tunning gemm easier so we can add more accumulators as needed.
//
// full = operate (load) on the entire PacketBlock or only half
template<typename DataMapper, typename Packet, const Index accCols, int StorageOrder, bool Complex, int N, bool full>
EIGEN_ALWAYS_INLINE void bload(PacketBlock<Packet,N*(Complex?2:1)>& acc, const DataMapper& res, Index row, Index col)
{
  if (StorageOrder == RowMajor) {
    for (int M = 0; M < N; M++) {
      acc.packet[M] = res.template loadPacket<Packet>(row + M, col);
    }
    if (Complex) {
      for (int M = 0; M < N; M++) {
        acc.packet[M+N] = res.template loadPacket<Packet>(row + M, col + accCols);
      }
    }
  } else {
    for (int M = 0; M < N; M++) {
      acc.packet[M] = res.template loadPacket<Packet>(row, col + M);
    }
    if (Complex && full) {
      for (int M = 0; M < N; M++) {
        acc.packet[M+N] = res.template loadPacket<Packet>(row + accCols, col + M);
      }
    }
  }
}

template<typename DataMapper, typename Packet, int N>
EIGEN_ALWAYS_INLINE void bstore(PacketBlock<Packet,N>& acc, const DataMapper& res, Index row)
{
  for (int M = 0; M < N; M++) {
    res.template storePacket<Packet>(row, M, acc.packet[M]);
  }
}

#ifdef USE_PARTIAL_PACKETS
template<typename DataMapper, typename Packet, const Index accCols, bool Complex, Index N, bool full>
EIGEN_ALWAYS_INLINE void bload_partial(PacketBlock<Packet,N*(Complex?2:1)>& acc, const DataMapper& res, Index row, Index elements)
{
  for (Index M = 0; M < N; M++) {
    acc.packet[M] = res.template loadPacketPartial<Packet>(row, M, elements);
  }
  if (Complex && full) {
    for (Index M = 0; M < N; M++) {
      acc.packet[M+N] = res.template loadPacketPartial<Packet>(row + accCols, M, elements);
    }
  }
}

template<typename DataMapper, typename Packet, Index N>
EIGEN_ALWAYS_INLINE void bstore_partial(PacketBlock<Packet,N>& acc, const DataMapper& res, Index row, Index elements)
{
  for (Index M = 0; M < N; M++) {
    res.template storePacketPartial<Packet>(row, M, acc.packet[M], elements);
  }
}
#endif

#ifdef _ARCH_PWR10
#define USE_P10_AND_PVIPR2_0 (EIGEN_COMP_LLVM || (__GNUC__ >= 11))
#else
#define USE_P10_AND_PVIPR2_0 0
#endif

#if !USE_P10_AND_PVIPR2_0
const static Packet4i mask4[4] = { {  0,  0,  0,  0 }, { -1,  0,  0,  0 }, { -1, -1,  0,  0 }, { -1, -1, -1,  0 } };
#endif

template<typename Packet>
EIGEN_ALWAYS_INLINE Packet bmask(const Index remaining_rows)
{
#if USE_P10_AND_PVIPR2_0
#ifdef _BIG_ENDIAN
  return Packet(vec_reve(vec_genwm((1 << remaining_rows) - 1)));
#else
  return Packet(vec_genwm((1 << remaining_rows) - 1));
#endif
#else
  return Packet(mask4[remaining_rows]);
#endif
}

template<>
EIGEN_ALWAYS_INLINE Packet2d bmask<Packet2d>(const Index remaining_rows)
{
#if USE_P10_AND_PVIPR2_0
  Packet2d mask2 = Packet2d(vec_gendm(remaining_rows));
#ifdef _BIG_ENDIAN
  return preverse(mask2);
#else
  return mask2;
#endif
#else
  Packet2l ret = { -remaining_rows, 0 };
  return Packet2d(ret);
#endif
}

template<typename Packet, int N>
EIGEN_ALWAYS_INLINE void bscale(PacketBlock<Packet,N>& acc, PacketBlock<Packet,N>& accZ, const Packet& pAlpha)
{
  for (int M = 0; M < N; M++) {
    acc.packet[M] = pmadd<Packet>(pAlpha, accZ.packet[M], acc.packet[M]);
  }
}

// Scale the PacketBlock vectors by alpha.
template<typename Packet, int N, bool mask>
EIGEN_ALWAYS_INLINE void bscale(PacketBlock<Packet,N>& acc, PacketBlock<Packet,N>& accZ, const Packet& pAlpha, const Packet& pMask)
{
  if (mask) {
    band<Packet, N>(accZ, pMask);
  } else {
    EIGEN_UNUSED_VARIABLE(pMask);
  }

  bscale<Packet, N>(acc, accZ, pAlpha);
}

template<typename Packet, int N, bool real>
EIGEN_ALWAYS_INLINE void pbroadcastN(const __UNPACK_TYPE__(Packet) *ap0,
        const __UNPACK_TYPE__(Packet) *ap1, const __UNPACK_TYPE__(Packet) *ap2,
        Packet& a0, Packet& a1, Packet& a2, Packet& a3)
{
  a0 = pset1<Packet>(ap0[0]);
  if (N == 4) {
    a1 = pset1<Packet>(ap0[1]);
    a2 = pset1<Packet>(ap0[2]);
    a3 = pset1<Packet>(ap0[3]);
    EIGEN_UNUSED_VARIABLE(ap1);
    EIGEN_UNUSED_VARIABLE(ap2);
  } else {
    if (N > 1) {
      a1 = pset1<Packet>(ap1[0]);
    } else {
      EIGEN_UNUSED_VARIABLE(a1);
      EIGEN_UNUSED_VARIABLE(ap1);
    }
    if (N > 2) {
      a2 = pset1<Packet>(ap2[0]);
    } else {
      EIGEN_UNUSED_VARIABLE(a2);
      EIGEN_UNUSED_VARIABLE(ap2);
    }
  }
}

template<> EIGEN_ALWAYS_INLINE void
pbroadcastN<Packet4f,4,true>(const float *ap0, const float *, const float *,
                             Packet4f& a0, Packet4f& a1, Packet4f& a2, Packet4f& a3)
{
  pbroadcast4<Packet4f>(ap0, a0, a1, a2, a3);
}

template<> EIGEN_ALWAYS_INLINE void
pbroadcastN<Packet4f,4,false>(const float *ap0, const float *ap1, const float *ap2,
                              Packet4f& a0, Packet4f& a1, Packet4f& a2, Packet4f& a3)
{
  pbroadcastN<Packet4f,4,true>(ap0, ap1, ap2, a0, a1, a2, a3);
}

template<>
EIGEN_ALWAYS_INLINE void pbroadcastN<Packet2d,4,false>(const double* ap0, const double *,
    const double *, Packet2d& a0, Packet2d& a1, Packet2d& a2, Packet2d& a3)
{
  a1 = pload<Packet2d>(ap0);
  a3 = pload<Packet2d>(ap0 + 2);
  a0 = vec_splat(a1, 0);
  a1 = vec_splat(a1, 1);
  a2 = vec_splat(a3, 0);
  a3 = vec_splat(a3, 1);
}

// Grab two decouples real/imaginary PacketBlocks and return two coupled (real/imaginary pairs) PacketBlocks.
template<typename Packet, typename Packetc, int N, bool full>
EIGEN_ALWAYS_INLINE void bcouple_common(PacketBlock<Packet,N>& taccReal, PacketBlock<Packet,N>& taccImag, PacketBlock<Packetc, N>& acc1, PacketBlock<Packetc, N>& acc2)
{
  for (int M = 0; M < N; M++) {
    acc1.packet[M].v = vec_mergeh(taccReal.packet[M], taccImag.packet[M]);
  }

  if (full) {
    for (int M = 0; M < N; M++) {
      acc2.packet[M].v = vec_mergel(taccReal.packet[M], taccImag.packet[M]);
    }
  }
}

template<typename Packet, typename Packetc, int N, bool full>
EIGEN_ALWAYS_INLINE void bcouple(PacketBlock<Packet,N>& taccReal, PacketBlock<Packet,N>& taccImag, PacketBlock<Packetc,N*2>& tRes, PacketBlock<Packetc, N>& acc1, PacketBlock<Packetc, N>& acc2)
{
  bcouple_common<Packet, Packetc, N, full>(taccReal, taccImag, acc1, acc2);

  for (int M = 0; M < N; M++) {
    acc1.packet[M] = padd<Packetc>(tRes.packet[M], acc1.packet[M]);
  }

  if (full) {
    for (int M = 0; M < N; M++) {
      acc2.packet[M] = padd<Packetc>(tRes.packet[M+N], acc2.packet[M]);
    }
  }
}

// PEEL loop factor.
#define PEEL 7
#define PEEL_ROW 7

#define MICRO_UNROLL(func) \
  func(0) func(1) func(2) func(3) func(4) func(5) func(6) func(7)

#define MICRO_NORMAL_ROWS \
  accRows == quad_traits<Scalar>::rows || accRows == 1

#define MICRO_NEW_ROWS ((MICRO_NORMAL_ROWS) ? accRows : 1)

#define MICRO_RHS(ptr, N) rhs_##ptr##N

#define MICRO_ZERO_PEEL(peel) \
  if ((PEEL_ROW > peel) && (peel != 0)) { \
    bsetzero<Packet, accRows>(accZero##peel); \
  } else { \
    EIGEN_UNUSED_VARIABLE(accZero##peel); \
  }

#define MICRO_ADD(ptr, N) \
  if (MICRO_NORMAL_ROWS) { \
    MICRO_RHS(ptr,0) += (accRows * N); \
  } else { \
    MICRO_RHS(ptr,0) += N; \
    MICRO_RHS(ptr,1) += N; \
    if (accRows == 3) { \
       MICRO_RHS(ptr,2) += N; \
    } \
  }

#define MICRO_ADD_ROWS(N) MICRO_ADD(ptr, N)

#define MICRO_BROADCAST1(peel, ptr, rhsV, real) \
  if (MICRO_NORMAL_ROWS) { \
    pbroadcastN<Packet,accRows,real>(MICRO_RHS(ptr,0) + (accRows * peel), MICRO_RHS(ptr,0), MICRO_RHS(ptr,0), rhsV##peel[0], rhsV##peel[1], rhsV##peel[2], rhsV##peel[3]); \
  } else { \
    pbroadcastN<Packet,accRows,real>(MICRO_RHS(ptr,0) + peel, MICRO_RHS(ptr,1) + peel, MICRO_RHS(ptr,2) + peel, rhsV##peel[0], rhsV##peel[1], rhsV##peel[2], rhsV##peel[3]); \
  }

#define MICRO_BROADCAST(peel) MICRO_BROADCAST1(peel, ptr, rhsV, true)

#define MICRO_BROADCAST_EXTRA1(ptr, rhsV, real) \
  pbroadcastN<Packet,accRows,real>(MICRO_RHS(ptr,0), MICRO_RHS(ptr,1), MICRO_RHS(ptr,2), rhsV[0], rhsV[1], rhsV[2], rhsV[3]);

#define MICRO_BROADCAST_EXTRA \
  Packet rhsV[4]; \
  MICRO_BROADCAST_EXTRA1(ptr, rhsV, true) \
  MICRO_ADD_ROWS(1)

#define MICRO_SRC2(ptr, N, M) \
  if (MICRO_NORMAL_ROWS) { \
    EIGEN_UNUSED_VARIABLE(strideB); \
    EIGEN_UNUSED_VARIABLE(MICRO_RHS(ptr,1)); \
    EIGEN_UNUSED_VARIABLE(MICRO_RHS(ptr,2)); \
  } else { \
    MICRO_RHS(ptr,1) = rhs_base + N + M; \
    if (accRows == 3) { \
      MICRO_RHS(ptr,2) = rhs_base + N*2 + M; \
    } else { \
      EIGEN_UNUSED_VARIABLE(MICRO_RHS(ptr,2)); \
    } \
  }

#define MICRO_SRC2_PTR MICRO_SRC2(ptr, strideB, 0)

#define MICRO_ZERO_PEEL_ROW MICRO_UNROLL(MICRO_ZERO_PEEL)

#define MICRO_WORK_PEEL(peel) \
  if (PEEL_ROW > peel) { \
    MICRO_BROADCAST(peel) \
    pger<accRows, Scalar, Packet, false>(&accZero##peel, lhs_ptr + (remaining_rows * peel), rhsV##peel); \
  } else { \
    EIGEN_UNUSED_VARIABLE(rhsV##peel); \
  }

#define MICRO_WORK_PEEL_ROW \
  Packet rhsV0[4], rhsV1[4], rhsV2[4], rhsV3[4], rhsV4[4], rhsV5[4], rhsV6[4], rhsV7[4]; \
  MICRO_UNROLL(MICRO_WORK_PEEL) \
  lhs_ptr += (remaining_rows * PEEL_ROW); \
  MICRO_ADD_ROWS(PEEL_ROW)

#define MICRO_ADD_PEEL(peel, sum) \
  if (PEEL_ROW > peel) { \
    for (Index i = 0; i < accRows; i++) { \
      accZero##sum.packet[i] += accZero##peel.packet[i]; \
    } \
  }

#define MICRO_ADD_PEEL_ROW \
  MICRO_ADD_PEEL(4, 0) MICRO_ADD_PEEL(5, 1) MICRO_ADD_PEEL(6, 2) MICRO_ADD_PEEL(7, 3) \
  MICRO_ADD_PEEL(2, 0) MICRO_ADD_PEEL(3, 1) MICRO_ADD_PEEL(1, 0)

#define MICRO_PREFETCHN1(ptr, N) \
  EIGEN_POWER_PREFETCH(MICRO_RHS(ptr,0)); \
  if (N == 2 || N == 3) { \
    EIGEN_POWER_PREFETCH(MICRO_RHS(ptr,1)); \
    if (N == 3) { \
      EIGEN_POWER_PREFETCH(MICRO_RHS(ptr,2)); \
    } \
  }

#define MICRO_PREFETCHN(N) MICRO_PREFETCHN1(ptr, N)

#define MICRO_COMPLEX_PREFETCHN(N) \
  MICRO_PREFETCHN1(ptr_real, N); \
  if(!RhsIsReal) { \
    MICRO_PREFETCHN1(ptr_imag, N); \
  }

template<typename Scalar, typename Packet, const Index accRows, const Index remaining_rows>
EIGEN_ALWAYS_INLINE void MICRO_EXTRA_ROW(
  const Scalar* &lhs_ptr,
  const Scalar* &rhs_ptr0,
  const Scalar* &rhs_ptr1,
  const Scalar* &rhs_ptr2,
  PacketBlock<Packet,accRows> &accZero)
{
  MICRO_BROADCAST_EXTRA
  pger<accRows, Scalar, Packet, false>(&accZero, lhs_ptr, rhsV);
  lhs_ptr += remaining_rows;
}

template<typename Scalar, typename Packet, typename DataMapper, const Index accRows, const Index accCols, const Index remaining_rows>
EIGEN_ALWAYS_INLINE void gemm_unrolled_row_iteration(
  const DataMapper& res,
  const Scalar* lhs_base,
  const Scalar* rhs_base,
  Index depth,
  Index strideA,
  Index offsetA,
  Index strideB,
  Index row,
  Index rows,
  const Packet& pAlpha,
  const Packet& pMask)
{
  const Scalar* rhs_ptr0 = rhs_base, * rhs_ptr1 = NULL, * rhs_ptr2 = NULL;
  const Scalar* lhs_ptr = lhs_base + row*strideA + remaining_rows*offsetA;
  PacketBlock<Packet,accRows> accZero0, accZero1, accZero2, accZero3, accZero4, accZero5, accZero6, accZero7, acc;

  MICRO_SRC2_PTR
  bsetzero<Packet, accRows>(accZero0);

  Index remaining_depth = depth & -quad_traits<Scalar>::rows;
  Index k = 0;
  if (remaining_depth >= PEEL_ROW) {
    MICRO_ZERO_PEEL_ROW
    do
    {
      MICRO_PREFETCHN(accRows)
      EIGEN_POWER_PREFETCH(lhs_ptr);
      MICRO_WORK_PEEL_ROW
    } while ((k += PEEL_ROW) + PEEL_ROW <= remaining_depth);
    MICRO_ADD_PEEL_ROW
  }
  for(; k < depth; k++)
  {
    MICRO_EXTRA_ROW<Scalar, Packet, accRows, remaining_rows>(lhs_ptr, rhs_ptr0, rhs_ptr1, rhs_ptr2, accZero0);
  }

#ifdef USE_PARTIAL_PACKETS
  EIGEN_UNUSED_VARIABLE(rows);
  EIGEN_UNUSED_VARIABLE(pMask);
  bload_partial<DataMapper, Packet, 0, false, accRows>(acc, res, row, remaining_rows);
  bscale<Packet,accRows>(acc, accZero0, pAlpha);
  bstore_partial<DataMapper, Packet, accRows>(acc, res, row, remaining_rows);
#else
  bload<DataMapper, Packet, 0, ColMajor, false, accRows>(acc, res, row, 0);
  if ((accRows == 1) || (rows >= accCols))
  {
    bscale<Packet,accRows,true>(acc, accZero0, pAlpha, pMask);
    bstore<DataMapper, Packet, accRows>(acc, res, row);
  } else {
    bscale<Packet,accRows,false>(acc, accZero0, pAlpha, pMask);
    for(Index j = 0; j < accRows; j++) {
      for(Index i = 0; i < remaining_rows; i++) {
        res(row + i, j) = acc.packet[j][i];
      }
    }
  }
#endif
}

#define MICRO_EXTRA(MICRO_EXTRA_UNROLL, value, is_col) \
  switch(value) { \
    default: \
      MICRO_EXTRA_UNROLL(1) \
      break; \
    case 2: \
      if (is_col || (sizeof(Scalar) == sizeof(float))) { \
        MICRO_EXTRA_UNROLL(2) \
      } \
      break; \
    case 3: \
      if (is_col || (sizeof(Scalar) == sizeof(float))) { \
        MICRO_EXTRA_UNROLL(3) \
      } \
      break; \
  }

#define MICRO_EXTRA_ROWS(N) \
  gemm_unrolled_row_iteration<Scalar, Packet, DataMapper, accRows, accCols, N>(res, lhs_base, rhs_base, depth, strideA, offsetA, strideB, row, rows, pAlpha, pMask);

template<typename Scalar, typename Packet, typename DataMapper, const Index accRows, const Index accCols>
EIGEN_ALWAYS_INLINE void gemm_extra_row(
  const DataMapper& res,
  const Scalar* lhs_base,
  const Scalar* rhs_base,
  Index depth,
  Index strideA,
  Index offsetA,
  Index strideB,
  Index row,
  Index rows,
  Index remaining_rows,
  const Packet& pAlpha,
  const Packet& pMask)
{
  MICRO_EXTRA(MICRO_EXTRA_ROWS, remaining_rows, false)
}

#define MICRO_UNROLL_WORK(func, func2, peel) \
  MICRO_UNROLL(func2); \
  func(0,peel) func(1,peel) func(2,peel) func(3,peel) \
  func(4,peel) func(5,peel) func(6,peel) func(7,peel)

#define MICRO_WORK_ONE(iter, peel) \
  if (unroll_factor > iter) { \
    pger_common<Packet, false, accRows>(&accZero##iter, lhsV##iter, rhsV##peel); \
  }

#define MICRO_TYPE_PEEL4(func, func2, peel) \
  if (PEEL > peel) { \
    Packet lhsV0, lhsV1, lhsV2, lhsV3, lhsV4, lhsV5, lhsV6, lhsV7; \
    MICRO_BROADCAST(peel) \
    MICRO_UNROLL_WORK(func, func2, peel) \
  } else { \
    EIGEN_UNUSED_VARIABLE(rhsV##peel); \
  }

#define MICRO_UNROLL_TYPE_PEEL(M, func, func1, func2) \
  Packet rhsV0[M], rhsV1[M], rhsV2[M], rhsV3[M], rhsV4[M], rhsV5[M], rhsV6[M], rhsV7[M]; \
  func(func1,func2,0) func(func1,func2,1) \
  func(func1,func2,2) func(func1,func2,3) \
  func(func1,func2,4) func(func1,func2,5) \
  func(func1,func2,6) func(func1,func2,7)

#define MICRO_UNROLL_TYPE_ONE(M, func, func1, func2) \
  Packet rhsV0[M]; \
  func(func1,func2,0)

#define MICRO_UNROLL_TYPE(MICRO_TYPE, size) \
  MICRO_TYPE(4, MICRO_TYPE_PEEL4, MICRO_WORK_ONE, MICRO_LOAD_ONE) \
  MICRO_ADD_ROWS(size)

#define MICRO_ONE_PEEL4 MICRO_UNROLL_TYPE(MICRO_UNROLL_TYPE_PEEL, PEEL)

#define MICRO_ONE4 MICRO_UNROLL_TYPE(MICRO_UNROLL_TYPE_ONE, 1)

#define MICRO_DST_PTR_ONE(iter) \
  if (unroll_factor > iter) { \
    bsetzero<Packet, accRows>(accZero##iter); \
  } else { \
    EIGEN_UNUSED_VARIABLE(accZero##iter); \
  }

#define MICRO_DST_PTR MICRO_UNROLL(MICRO_DST_PTR_ONE)

#define MICRO_SRC_PTR MICRO_UNROLL(MICRO_SRC_PTR_ONE)

#define MICRO_PREFETCH MICRO_UNROLL(MICRO_PREFETCH_ONE)

#ifdef USE_PARTIAL_PACKETS
#define MICRO_STORE_ONE(iter) \
  if (unroll_factor > iter) { \
    if (MICRO_NORMAL_PARTIAL(iter)) { \
      bload<DataMapper, Packet, 0, ColMajor, false, accRows>(acc, res, row + iter*accCols, 0); \
      bscale<Packet,accRows>(acc, accZero##iter, pAlpha); \
      bstore<DataMapper, Packet, accRows>(acc, res, row + iter*accCols); \
    } else { \
      bload_partial<DataMapper, Packet, 0, false, accRows>(acc, res, row + iter*accCols, accCols2); \
      bscale<Packet,accRows>(acc, accZero##iter, pAlpha); \
      bstore_partial<DataMapper, Packet, accRows>(acc, res, row + iter*accCols, accCols2); \
    } \
  }
#else
#define MICRO_STORE_ONE(iter) \
  if (unroll_factor > iter) { \
    bload<DataMapper, Packet, 0, ColMajor, false, accRows>(acc, res, row + iter*accCols, 0); \
    bscale<Packet,accRows,!(MICRO_NORMAL(iter))>(acc, accZero##iter, pAlpha, pMask); \
    bstore<DataMapper, Packet, accRows>(acc, res, row + iter*accCols); \
  }
#endif

#define MICRO_STORE MICRO_UNROLL(MICRO_STORE_ONE)

#ifdef USE_PARTIAL_PACKETS
template<int unroll_factor, typename Scalar, typename Packet, typename DataMapper, const Index accRows, const Index accCols, bool full>
#else
template<int unroll_factor, typename Scalar, typename Packet, typename DataMapper, const Index accRows, const Index accCols, const Index accCols2>
#endif
EIGEN_ALWAYS_INLINE void gemm_unrolled_iteration(
  const DataMapper& res,
  const Scalar* lhs_base,
  const Scalar* rhs_base,
  Index depth,
  Index strideA,
  Index offsetA,
  Index strideB,
  Index& row,
  const Packet& pAlpha,
#ifdef USE_PARTIAL_PACKETS
  Index accCols2
#else
  const Packet& pMask
#endif
  )
{
  const Scalar* rhs_ptr0 = rhs_base, * rhs_ptr1 = NULL, * rhs_ptr2 = NULL;
  const Scalar* lhs_ptr0 = NULL, * lhs_ptr1 = NULL, * lhs_ptr2 = NULL, * lhs_ptr3 = NULL, * lhs_ptr4 = NULL, * lhs_ptr5 = NULL, * lhs_ptr6 = NULL, * lhs_ptr7 = NULL;
  PacketBlock<Packet,accRows> accZero0, accZero1, accZero2, accZero3, accZero4, accZero5, accZero6, accZero7;
  PacketBlock<Packet,accRows> acc;

  MICRO_SRC2_PTR
  MICRO_SRC_PTR
  MICRO_DST_PTR

  Index k = 0;
  for(; k + PEEL <= depth; k+= PEEL)
  {
    MICRO_PREFETCHN(accRows)
    MICRO_PREFETCH
    MICRO_ONE_PEEL4
  }
  for(; k < depth; k++)
  {
    MICRO_ONE4
  }
  MICRO_STORE

  MICRO_UPDATE
}

#ifdef USE_PARTIAL_PACKETS
#define MICRO_UNROLL_ITER2(N, M) \
  gemm_unrolled_iteration<N + ((M) ? 1 : 0), Scalar, Packet, DataMapper, accRows, accCols, !M>(res3, lhs_base, rhs_base, depth, strideA, offsetA, strideB, row, pAlpha, M ? remaining_rows : accCols); \
  if (M) return;
#else
#define MICRO_UNROLL_ITER2(N, M) \
  gemm_unrolled_iteration<N + ((M) ? 1 : 0), Scalar, Packet, DataMapper, accRows, accCols, M ? M : accCols>(res3, lhs_base, rhs_base, depth, strideA, offsetA, strideB, row, pAlpha, pMask); \
  if (M) return;
#endif

template<typename Scalar, typename Packet, typename DataMapper, const Index accRows, const Index accCols>
EIGEN_ALWAYS_INLINE void gemm_cols(
  const DataMapper& res,
  const Scalar* blockA,
  const Scalar* blockB,
  Index depth,
  Index strideA,
  Index offsetA,
  Index strideB,
  Index offsetB,
  Index col,
  Index rows,
  Index remaining_rows,
  const Packet& pAlpha,
  const Packet& pMask)
{
  const DataMapper res3 = res.getSubMapper(0, col);

  const Scalar* rhs_base = blockB + col*strideB + MICRO_NEW_ROWS*offsetB;
  const Scalar* lhs_base = blockA + accCols*offsetA;
  Index row = 0;

#define MAX_UNROLL 7
  while(row + MAX_UNROLL*accCols <= rows) {
    MICRO_UNROLL_ITER2(MAX_UNROLL, 0);
  }
  switch( (rows-row)/accCols ) {
#if MAX_UNROLL > 7
    case 7:
      MICRO_UNROLL_ITER(MICRO_UNROLL_ITER2, 7)
      break;
#endif
#if MAX_UNROLL > 6
    case 6:
      MICRO_UNROLL_ITER(MICRO_UNROLL_ITER2, 6)
      break;
#endif
#if MAX_UNROLL > 5
    case 5:
      MICRO_UNROLL_ITER(MICRO_UNROLL_ITER2, 5)
      break;
#endif
#if MAX_UNROLL > 4
    case 4:
      MICRO_UNROLL_ITER(MICRO_UNROLL_ITER2, 4)
      break;
#endif
#if MAX_UNROLL > 3
    case 3:
      MICRO_UNROLL_ITER(MICRO_UNROLL_ITER2, 3)
      break;
#endif
#if MAX_UNROLL > 2
    case 2:
      MICRO_UNROLL_ITER(MICRO_UNROLL_ITER2, 2)
      break;
#endif
#if MAX_UNROLL > 1
    case 1:
      MICRO_UNROLL_ITER(MICRO_UNROLL_ITER2, 1)
      break;
#endif
    default:
      break;
  }
#undef MAX_UNROLL

  if(remaining_rows > 0)
  {
    gemm_extra_row<Scalar, Packet, DataMapper, accRows, accCols>(res3, blockA, rhs_base, depth, strideA, offsetA, strideB, row, rows, remaining_rows, pAlpha, pMask);
  }
}

#define MICRO_EXTRA_COLS(N) \
  gemm_cols<Scalar, Packet, DataMapper, N, accCols>(res, blockA, blockB, depth, strideA, offsetA, strideB, offsetB, col, rows, remaining_rows, pAlpha, pMask);

template<typename Scalar, typename Packet, typename DataMapper, const Index accCols>
EIGEN_STRONG_INLINE void gemm_extra_cols(
  const DataMapper& res,
  const Scalar* blockA,
  const Scalar* blockB,
  Index depth,
  Index strideA,
  Index offsetA,
  Index strideB,
  Index offsetB,
  Index col,
  Index rows,
  Index cols,
  Index remaining_rows,
  const Packet& pAlpha,
  const Packet& pMask)
{
  MICRO_EXTRA(MICRO_EXTRA_COLS, cols-col, true)
}

/****************
 * GEMM kernels *
 * **************/
template<typename Scalar, typename Packet, typename RhsPacket, typename DataMapper, const Index accRows, const Index accCols>
EIGEN_STRONG_INLINE void gemm(const DataMapper& res, const Scalar* blockA, const Scalar* blockB, Index rows, Index depth, Index cols, Scalar alpha, Index strideA, Index strideB, Index offsetA, Index offsetB)
{
      const Index remaining_rows = rows % accCols;

      if( strideA == -1 ) strideA = depth;
      if( strideB == -1 ) strideB = depth;

      const Packet pAlpha = pset1<Packet>(alpha);
      const Packet pMask  = bmask<Packet>(remaining_rows);

      Index col = 0;
      for(; col + accRows <= cols; col += accRows)
      {
        gemm_cols<Scalar, Packet, DataMapper, accRows, accCols>(res, blockA, blockB, depth, strideA, offsetA, strideB, offsetB, col, rows, remaining_rows, pAlpha, pMask);
      }

      if (col != cols)
      {
        gemm_extra_cols<Scalar, Packet, DataMapper, accCols>(res, blockA, blockB, depth, strideA, offsetA, strideB, offsetB, col, rows, cols, remaining_rows, pAlpha, pMask);
      }
}

#define accColsC (accCols / 2)
#define advanceRows ((LhsIsReal) ? 1 : 2)
#define advanceCols ((RhsIsReal) ? 1 : 2)

// PEEL_COMPLEX loop factor.
#define PEEL_COMPLEX 3
#define PEEL_COMPLEX_ROW 3

#define MICRO_COMPLEX_UNROLL(func) \
  func(0) func(1) func(2) func(3)

#define MICRO_COMPLEX_ZERO_PEEL(peel) \
  if ((PEEL_COMPLEX_ROW > peel) && (peel != 0)) { \
    bsetzero<Packet, accRows>(accReal##peel); \
    bsetzero<Packet, accRows>(accImag##peel); \
  } else { \
    EIGEN_UNUSED_VARIABLE(accReal##peel); \
    EIGEN_UNUSED_VARIABLE(accImag##peel); \
  }

#define MICRO_COMPLEX_ADD_ROWS(N, used) \
  MICRO_ADD(ptr_real, N) \
  if (!RhsIsReal) { \
    MICRO_ADD(ptr_imag, N) \
  } else if (used) { \
    EIGEN_UNUSED_VARIABLE(MICRO_RHS(ptr_imag,0)); \
    EIGEN_UNUSED_VARIABLE(MICRO_RHS(ptr_imag,1)); \
    EIGEN_UNUSED_VARIABLE(MICRO_RHS(ptr_imag,2)); \
  }

#define MICRO_COMPLEX_BROADCAST(peel) \
  MICRO_BROADCAST1(peel, ptr_real, rhsV, false) \
  if (!RhsIsReal) { \
    MICRO_BROADCAST1(peel, ptr_imag, rhsVi, false) \
  } else { \
    EIGEN_UNUSED_VARIABLE(rhsVi##peel); \
  }

#define MICRO_COMPLEX_BROADCAST_EXTRA \
  Packet rhsV[4], rhsVi[4]; \
  MICRO_BROADCAST_EXTRA1(ptr_real, rhsV, false) \
  if(!RhsIsReal) { \
    MICRO_BROADCAST_EXTRA1(ptr_imag, rhsVi, false) \
  } else { \
    EIGEN_UNUSED_VARIABLE(rhsVi); \
  } \
  MICRO_COMPLEX_ADD_ROWS(1, true)

#define MICRO_COMPLEX_SRC2_PTR \
  MICRO_SRC2(ptr_real, strideB*advanceCols, 0) \
  if (!RhsIsReal) { \
    MICRO_RHS(ptr_imag,0) = rhs_base + MICRO_NEW_ROWS*strideB; \
    MICRO_SRC2(ptr_imag, strideB*advanceCols, strideB) \
  } else { \
    EIGEN_UNUSED_VARIABLE(MICRO_RHS(ptr_imag,0)); \
    EIGEN_UNUSED_VARIABLE(MICRO_RHS(ptr_imag,1)); \
    EIGEN_UNUSED_VARIABLE(MICRO_RHS(ptr_imag,2)); \
  }

#define MICRO_COMPLEX_ZERO_PEEL_ROW MICRO_COMPLEX_UNROLL(MICRO_COMPLEX_ZERO_PEEL)

#define MICRO_COMPLEX_WORK_PEEL(peel) \
  if (PEEL_COMPLEX_ROW > peel) { \
    MICRO_COMPLEX_BROADCAST(peel) \
    pgerc<accRows, Scalar, Packet, ConjugateLhs, ConjugateRhs, LhsIsReal, RhsIsReal>(&accReal##peel, &accImag##peel, lhs_ptr_real + (remaining_rows * peel), lhs_ptr_imag + (remaining_rows * peel), rhsV##peel, rhsVi##peel); \
  } else { \
    EIGEN_UNUSED_VARIABLE(rhsV##peel); \
    EIGEN_UNUSED_VARIABLE(rhsVi##peel); \
  }

#define MICRO_COMPLEX_ADD_COLS(size) \
  lhs_ptr_real += (remaining_rows * size); \
  if(!LhsIsReal) lhs_ptr_imag += (remaining_rows * size); \
  else EIGEN_UNUSED_VARIABLE(lhs_ptr_imag);

#define MICRO_COMPLEX_WORK_PEEL_ROW \
  Packet rhsV0[4], rhsV1[4], rhsV2[4], rhsV3[4]; \
  Packet rhsVi0[4], rhsVi1[4], rhsVi2[4], rhsVi3[4]; \
  MICRO_COMPLEX_UNROLL(MICRO_COMPLEX_WORK_PEEL) \
  MICRO_COMPLEX_ADD_COLS(PEEL_COMPLEX_ROW) \
  MICRO_COMPLEX_ADD_ROWS(PEEL_COMPLEX_ROW, false)

#define MICRO_COMPLEX_ADD_PEEL(peel, sum) \
  if (PEEL_COMPLEX_ROW > peel) { \
    for (Index i = 0; i < accRows; i++) { \
      accReal##sum.packet[i] += accReal##peel.packet[i]; \
      accImag##sum.packet[i] += accImag##peel.packet[i]; \
    } \
  }

#define MICRO_COMPLEX_ADD_PEEL_ROW \
  MICRO_COMPLEX_ADD_PEEL(2, 0) MICRO_COMPLEX_ADD_PEEL(3, 1) \
  MICRO_COMPLEX_ADD_PEEL(1, 0)

template<typename Scalar, typename Packet, const Index accRows, bool ConjugateLhs, bool ConjugateRhs, bool LhsIsReal, bool RhsIsReal, const Index remaining_rows>
EIGEN_ALWAYS_INLINE void MICRO_COMPLEX_EXTRA_ROW(
  const Scalar* &lhs_ptr_real, const Scalar* &lhs_ptr_imag,
  const Scalar* &rhs_ptr_real0, const Scalar* &rhs_ptr_real1, const Scalar* &rhs_ptr_real2,
  const Scalar* &rhs_ptr_imag0, const Scalar* &rhs_ptr_imag1, const Scalar* &rhs_ptr_imag2,
  PacketBlock<Packet,accRows> &accReal, PacketBlock<Packet,accRows> &accImag)
{
  MICRO_COMPLEX_BROADCAST_EXTRA
  pgerc<accRows, Scalar, Packet, ConjugateLhs, ConjugateRhs, LhsIsReal, RhsIsReal>(&accReal, &accImag, lhs_ptr_real, lhs_ptr_imag, rhsV, rhsVi);
  MICRO_COMPLEX_ADD_COLS(1)
}

template<typename Scalar, typename Packet, typename Packetc, typename DataMapper, const Index accRows, const Index accCols, bool ConjugateLhs, bool ConjugateRhs, bool LhsIsReal, bool RhsIsReal, const Index remaining_rows>
EIGEN_ALWAYS_INLINE void gemm_unrolled_complex_row_iteration(
  const DataMapper& res,
  const Scalar* lhs_base,
  const Scalar* rhs_base,
  Index depth,
  Index strideA,
  Index offsetA,
  Index strideB,
  Index row,
  Index rows,
  const Packet& pAlphaReal,
  const Packet& pAlphaImag,
  const Packet& pMask)
{
  const Scalar* rhs_ptr_real0 = rhs_base, * rhs_ptr_real1 = NULL, * rhs_ptr_real2 = NULL;
  const Scalar* rhs_ptr_imag0 = NULL, * rhs_ptr_imag1 = NULL, * rhs_ptr_imag2 = NULL;
  const Scalar* lhs_ptr_real = lhs_base + advanceRows*row*strideA + remaining_rows*offsetA;
  const Scalar* lhs_ptr_imag = NULL;
  if(!LhsIsReal) lhs_ptr_imag = lhs_ptr_real + remaining_rows*strideA;
  else EIGEN_UNUSED_VARIABLE(lhs_ptr_imag);
  PacketBlock<Packet,accRows> accReal0, accImag0, accReal1, accImag1, accReal2, accImag2, accReal3, accImag3;
  PacketBlock<Packet,accRows> taccReal, taccImag;
  PacketBlock<Packetc,accRows> acc0, acc1;
  PacketBlock<Packetc,accRows*2> tRes;

  MICRO_COMPLEX_SRC2_PTR

  bsetzero<Packet, accRows>(accReal0);
  bsetzero<Packet, accRows>(accImag0);

  Index remaining_depth = depth & -quad_traits<Scalar>::rows;
  Index k = 0;
  if (remaining_depth >= PEEL_COMPLEX_ROW) {
    MICRO_COMPLEX_ZERO_PEEL_ROW
    do
    {
      MICRO_COMPLEX_PREFETCHN(accRows)
      EIGEN_POWER_PREFETCH(lhs_ptr_real);
      if(!LhsIsReal) {
        EIGEN_POWER_PREFETCH(lhs_ptr_imag);
      }
      MICRO_COMPLEX_WORK_PEEL_ROW
    } while ((k += PEEL_COMPLEX_ROW) + PEEL_COMPLEX_ROW <= remaining_depth);
    MICRO_COMPLEX_ADD_PEEL_ROW
  }
  for(; k < depth; k++)
  {
    MICRO_COMPLEX_EXTRA_ROW<Scalar, Packet, accRows, ConjugateLhs, ConjugateRhs, LhsIsReal, RhsIsReal, remaining_rows>(lhs_ptr_real, lhs_ptr_imag, rhs_ptr_real0, rhs_ptr_real1, rhs_ptr_real2, rhs_ptr_imag0, rhs_ptr_imag1, rhs_ptr_imag2, accReal0, accImag0);
  }

  constexpr bool full = (remaining_rows > accColsC);
  bload<DataMapper, Packetc, accColsC, ColMajor, true, accRows, full>(tRes, res, row, 0);
  if ((accRows == 1) || (rows >= accCols))
  {
    bscalec<Packet,accRows,true>(accReal0, accImag0, pAlphaReal, pAlphaImag, taccReal, taccImag, pMask);
    bcouple<Packet, Packetc, accRows, full>(taccReal, taccImag, tRes, acc0, acc1);
    bstore<DataMapper, Packetc, accRows>(acc0, res, row + 0);
    if (full) {
      bstore<DataMapper, Packetc, accRows>(acc1, res, row + accColsC);
    }
  } else {
    bscalec<Packet,accRows,false>(accReal0, accImag0, pAlphaReal, pAlphaImag, taccReal, taccImag, pMask);
    bcouple<Packet, Packetc, accRows, full>(taccReal, taccImag, tRes, acc0, acc1);

    if ((sizeof(Scalar) == sizeof(float)) && (remaining_rows == 1))
    {
      for(Index j = 0; j < accRows; j++) {
        res(row + 0, j) = pfirst<Packetc>(acc0.packet[j]);
      }
    } else {
      bstore<DataMapper, Packetc, accRows>(acc0, res, row + 0);
      if (full) {
        for(Index j = 0; j < accRows; j++) {
          res(row + accColsC, j) = pfirst<Packetc>(acc1.packet[j]);
        }
      }
    }
  }
}

#define MICRO_COMPLEX_EXTRA_ROWS(N) \
  gemm_unrolled_complex_row_iteration<Scalar, Packet, Packetc, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, LhsIsReal, RhsIsReal, N>(res, lhs_base, rhs_base, depth, strideA, offsetA, strideB, row, rows, pAlphaReal, pAlphaImag, pMask);

template<typename Scalar, typename Packet, typename Packetc, typename DataMapper, const Index accRows, const Index accCols, bool ConjugateLhs, bool ConjugateRhs, bool LhsIsReal, bool RhsIsReal>
EIGEN_ALWAYS_INLINE void gemm_complex_extra_row(
  const DataMapper& res,
  const Scalar* lhs_base,
  const Scalar* rhs_base,
  Index depth,
  Index strideA,
  Index offsetA,
  Index strideB,
  Index row,
  Index rows,
  Index remaining_rows,
  const Packet& pAlphaReal,
  const Packet& pAlphaImag,
  const Packet& pMask)
{
  MICRO_EXTRA(MICRO_COMPLEX_EXTRA_ROWS, remaining_rows, false)
}

#define MICRO_COMPLEX_UNROLL_WORK(func, func2, peel) \
  MICRO_COMPLEX_UNROLL(func2); \
  func(0,peel) func(1,peel) func(2,peel) func(3,peel)

#define MICRO_COMPLEX_WORK_ONE4(iter, peel) \
  if (unroll_factor > iter) { \
    pgerc_common<accRows, Packet, ConjugateLhs, ConjugateRhs, LhsIsReal, RhsIsReal>(&accReal##iter, &accImag##iter, lhsV##iter, lhsVi##iter, rhsV##peel, rhsVi##peel); \
  }

#define MICRO_COMPLEX_TYPE_PEEL4(func, func2, peel) \
  if (PEEL_COMPLEX > peel) { \
    Packet lhsV0, lhsV1, lhsV2, lhsV3; \
    Packet lhsVi0, lhsVi1, lhsVi2, lhsVi3; \
    MICRO_COMPLEX_BROADCAST(peel) \
    MICRO_COMPLEX_UNROLL_WORK(func, func2, peel) \
  } else { \
    EIGEN_UNUSED_VARIABLE(rhsV##peel); \
    EIGEN_UNUSED_VARIABLE(rhsVi##peel); \
  }

#define MICRO_COMPLEX_UNROLL_TYPE_PEEL(M, func, func1, func2) \
  Packet rhsV0[M], rhsV1[M], rhsV2[M], rhsV3[M]; \
  Packet rhsVi0[M], rhsVi1[M], rhsVi2[M], rhsVi3[M]; \
  func(func1,func2,0) func(func1,func2,1) \
  func(func1,func2,2) func(func1,func2,3)

#define MICRO_COMPLEX_UNROLL_TYPE_ONE(M, func, func1, func2) \
  Packet rhsV0[M], rhsVi0[M];\
  func(func1,func2,0)

#define MICRO_COMPLEX_UNROLL_TYPE(MICRO_COMPLEX_TYPE, size) \
  MICRO_COMPLEX_TYPE(4, MICRO_COMPLEX_TYPE_PEEL4, MICRO_COMPLEX_WORK_ONE4, MICRO_COMPLEX_LOAD_ONE) \
  MICRO_COMPLEX_ADD_ROWS(size, false)

#define MICRO_COMPLEX_ONE_PEEL4 MICRO_COMPLEX_UNROLL_TYPE(MICRO_COMPLEX_UNROLL_TYPE_PEEL, PEEL_COMPLEX)

#define MICRO_COMPLEX_ONE4 MICRO_COMPLEX_UNROLL_TYPE(MICRO_COMPLEX_UNROLL_TYPE_ONE, 1)

#define MICRO_COMPLEX_DST_PTR_ONE(iter) \
  if (unroll_factor > iter) { \
    bsetzero<Packet, accRows>(accReal##iter); \
    bsetzero<Packet, accRows>(accImag##iter); \
  } else { \
    EIGEN_UNUSED_VARIABLE(accReal##iter); \
    EIGEN_UNUSED_VARIABLE(accImag##iter); \
  }

#define MICRO_COMPLEX_DST_PTR MICRO_COMPLEX_UNROLL(MICRO_COMPLEX_DST_PTR_ONE)

#define MICRO_COMPLEX_SRC_PTR MICRO_COMPLEX_UNROLL(MICRO_COMPLEX_SRC_PTR_ONE)

#define MICRO_COMPLEX_PREFETCH MICRO_COMPLEX_UNROLL(MICRO_COMPLEX_PREFETCH_ONE)

#define MICRO_COMPLEX_STORE_ONE(iter) \
  if (unroll_factor > iter) { \
    constexpr bool full = ((MICRO_NORMAL(iter)) || (accCols2 > accColsC)); \
    bload<DataMapper, Packetc, accColsC, ColMajor, true, accRows, full>(tRes, res, row + iter*accCols, 0); \
    bscalec<Packet,accRows,!(MICRO_NORMAL(iter))>(accReal##iter, accImag##iter, pAlphaReal, pAlphaImag, taccReal, taccImag, pMask); \
    bcouple<Packet, Packetc, accRows, full>(taccReal, taccImag, tRes, acc0, acc1); \
    bstore<DataMapper, Packetc, accRows>(acc0, res, row + iter*accCols + 0); \
    if (full) { \
      bstore<DataMapper, Packetc, accRows>(acc1, res, row + iter*accCols + accColsC); \
    } \
  }

#define MICRO_COMPLEX_STORE MICRO_COMPLEX_UNROLL(MICRO_COMPLEX_STORE_ONE)

template<int unroll_factor, typename Scalar, typename Packet, typename Packetc, typename DataMapper, const Index accRows, const Index accCols, const Index accCols2, bool ConjugateLhs, bool ConjugateRhs, bool LhsIsReal, bool RhsIsReal>
EIGEN_ALWAYS_INLINE void gemm_complex_unrolled_iteration(
  const DataMapper& res,
  const Scalar* lhs_base,
  const Scalar* rhs_base,
  Index depth,
  Index strideA,
  Index offsetA,
  Index strideB,
  Index& row,
  const Packet& pAlphaReal,
  const Packet& pAlphaImag,
  const Packet& pMask)
{
  const Scalar* rhs_ptr_real0 = rhs_base, * rhs_ptr_real1 = NULL, * rhs_ptr_real2 = NULL;
  const Scalar* rhs_ptr_imag0 = NULL, * rhs_ptr_imag1 = NULL, * rhs_ptr_imag2 = NULL;
  const Index imag_delta = accCols*strideA;
  const Index imag_delta2 = accCols2*strideA;
  const Scalar* lhs_ptr_real0 = NULL, * lhs_ptr_real1 = NULL;
  const Scalar* lhs_ptr_real2 = NULL, * lhs_ptr_real3 = NULL;
  PacketBlock<Packet,accRows> accReal0, accImag0, accReal1, accImag1;
  PacketBlock<Packet,accRows> accReal2, accImag2, accReal3, accImag3;
  PacketBlock<Packet,accRows> taccReal, taccImag;
  PacketBlock<Packetc,accRows> acc0, acc1;
  PacketBlock<Packetc,accRows*2> tRes;

  MICRO_COMPLEX_SRC2_PTR
  MICRO_COMPLEX_SRC_PTR
  MICRO_COMPLEX_DST_PTR

  Index k = 0;
  for(; k + PEEL_COMPLEX <= depth; k+= PEEL_COMPLEX)
  {
    MICRO_COMPLEX_PREFETCHN(accRows)
    MICRO_COMPLEX_PREFETCH
    MICRO_COMPLEX_ONE_PEEL4
  }
  for(; k < depth; k++)
  {
    MICRO_COMPLEX_ONE4
  }
  MICRO_COMPLEX_STORE

  MICRO_COMPLEX_UPDATE
}

#define MICRO_COMPLEX_UNROLL_ITER2(N, M) \
  gemm_complex_unrolled_iteration<N + (M ? 1 : 0), Scalar, Packet, Packetc, DataMapper, accRows, accCols, M ? M : accCols, ConjugateLhs, ConjugateRhs, LhsIsReal, RhsIsReal>(res3, lhs_base, rhs_base, depth, strideA, offsetA, strideB, row, pAlphaReal, pAlphaImag, pMask); \
  if (M) return;

template<typename Scalar, typename Packet, typename Packetc, typename DataMapper, const Index accRows, const Index accCols, bool ConjugateLhs, bool ConjugateRhs, bool LhsIsReal, bool RhsIsReal>
EIGEN_ALWAYS_INLINE void gemm_complex_cols(
  const DataMapper& res,
  const Scalar* blockA,
  const Scalar* blockB,
  Index depth,
  Index strideA,
  Index offsetA,
  Index strideB,
  Index offsetB,
  Index col,
  Index rows,
  Index remaining_rows,
  const Packet& pAlphaReal,
  const Packet& pAlphaImag,
  const Packet& pMask)
{
  const DataMapper res3 = res.getSubMapper(0, col);

  const Scalar* rhs_base = blockB + advanceCols*col*strideB + MICRO_NEW_ROWS*offsetB;
  const Scalar* lhs_base = blockA + accCols*offsetA;
  Index row = 0;

#define MAX_COMPLEX_UNROLL 4
  while(row + MAX_COMPLEX_UNROLL*accCols <= rows) {
    MICRO_COMPLEX_UNROLL_ITER2(MAX_COMPLEX_UNROLL, 0);
  }
  switch( (rows-row)/accCols ) {
#if MAX_COMPLEX_UNROLL > 4
    case 4:
      MICRO_COMPLEX_UNROLL_ITER(MICRO_COMPLEX_UNROLL_ITER2, 4)
      break;
#endif
#if MAX_COMPLEX_UNROLL > 3
    case 3:
      MICRO_COMPLEX_UNROLL_ITER(MICRO_COMPLEX_UNROLL_ITER2, 3)
      break;
#endif
#if MAX_COMPLEX_UNROLL > 2
    case 2:
      MICRO_COMPLEX_UNROLL_ITER(MICRO_COMPLEX_UNROLL_ITER2, 2)
      break;
#endif
#if MAX_COMPLEX_UNROLL > 1
    case 1:
      MICRO_COMPLEX_UNROLL_ITER(MICRO_COMPLEX_UNROLL_ITER2, 1)
      break;
#endif
    default:
      break;
  }
#undef MAX_COMPLEX_UNROLL

  if(remaining_rows > 0)
  {
    gemm_complex_extra_row<Scalar, Packet, Packetc, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, LhsIsReal, RhsIsReal>(res3, blockA, rhs_base, depth, strideA, offsetA, strideB, row, rows, remaining_rows, pAlphaReal, pAlphaImag, pMask);
  }
}

#define MICRO_COMPLEX_EXTRA_COLS(N) \
  gemm_complex_cols<Scalar, Packet, Packetc, DataMapper, N, accCols, ConjugateLhs, ConjugateRhs, LhsIsReal, RhsIsReal>(res, blockA, blockB, depth, strideA, offsetA, strideB, offsetB, col, rows, remaining_rows, pAlphaReal, pAlphaImag, pMask);

template<typename Scalar, typename Packet, typename Packetc, typename DataMapper, const Index accCols, bool ConjugateLhs, bool ConjugateRhs, bool LhsIsReal, bool RhsIsReal>
EIGEN_STRONG_INLINE void gemm_complex_extra_cols(
  const DataMapper& res,
  const Scalar* blockA,
  const Scalar* blockB,
  Index depth,
  Index strideA,
  Index offsetA,
  Index strideB,
  Index offsetB,
  Index col,
  Index rows,
  Index cols,
  Index remaining_rows,
  const Packet& pAlphaReal,
  const Packet& pAlphaImag,
  const Packet& pMask)
{
  MICRO_EXTRA(MICRO_COMPLEX_EXTRA_COLS, cols-col, true)
}

template<typename LhsScalar, typename RhsScalar, typename Scalarc, typename Scalar, typename Packet, typename Packetc, typename RhsPacket, typename DataMapper, const Index accRows, const Index accCols, bool ConjugateLhs, bool ConjugateRhs, bool LhsIsReal, bool RhsIsReal>
EIGEN_STRONG_INLINE void gemm_complex(const DataMapper& res, const LhsScalar* blockAc, const RhsScalar* blockBc, Index rows, Index depth, Index cols, Scalarc alpha, Index strideA, Index strideB, Index offsetA, Index offsetB)
{
      const Index remaining_rows = rows % accCols;

      if( strideA == -1 ) strideA = depth;
      if( strideB == -1 ) strideB = depth;

      const Packet pAlphaReal = pset1<Packet>(alpha.real());
      const Packet pAlphaImag = pset1<Packet>(alpha.imag());
      const Packet pMask = bmask<Packet>(remaining_rows);

      const Scalar* blockA = (Scalar *) blockAc;
      const Scalar* blockB = (Scalar *) blockBc;

      Index col = 0;
      for(; col + accRows <= cols; col += accRows)
      {
        gemm_complex_cols<Scalar, Packet, Packetc, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, LhsIsReal, RhsIsReal>(res, blockA, blockB, depth, strideA, offsetA, strideB, offsetB, col, rows, remaining_rows, pAlphaReal, pAlphaImag, pMask);
      }

      if (col != cols)
      {
        gemm_complex_extra_cols<Scalar, Packet, Packetc, DataMapper, accCols, ConjugateLhs, ConjugateRhs, LhsIsReal, RhsIsReal>(res, blockA, blockB, depth, strideA, offsetA, strideB, offsetB, col, rows, cols, remaining_rows, pAlphaReal, pAlphaImag, pMask);
      }
}

#undef accColsC
#undef advanceCols
#undef advanceRows

#include "MatrixVectorProduct.h"

/************************************
 * ppc64le template specializations *
 * **********************************/
template<typename Index, typename DataMapper, int Pack1, int Pack2, typename Packet, bool Conjugate, bool PanelMode>
struct gemm_pack_lhs<double, Index, DataMapper, Pack1, Pack2, Packet, ColMajor, Conjugate, PanelMode>
{
  void operator()(double* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride=0, Index offset=0);
};

template<typename Index, typename DataMapper, int Pack1, int Pack2, typename Packet, bool Conjugate, bool PanelMode>
void gemm_pack_lhs<double, Index, DataMapper, Pack1, Pack2, Packet, ColMajor, Conjugate, PanelMode>
  ::operator()(double* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride, Index offset)
{
    dhs_pack<double, DataMapper, Packet2d, ColMajor, PanelMode, true> pack;
    pack(blockA, lhs, depth, rows, stride, offset);
}

template<typename Index, typename DataMapper, int Pack1, int Pack2, typename Packet, bool Conjugate, bool PanelMode>
struct gemm_pack_lhs<double, Index, DataMapper, Pack1, Pack2, Packet, RowMajor, Conjugate, PanelMode>
{
  void operator()(double* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride=0, Index offset=0);
};

template<typename Index, typename DataMapper, int Pack1, int Pack2, typename Packet, bool Conjugate, bool PanelMode>
void gemm_pack_lhs<double, Index, DataMapper, Pack1, Pack2, Packet, RowMajor, Conjugate, PanelMode>
  ::operator()(double* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride, Index offset)
{
    dhs_pack<double, DataMapper, Packet2d, RowMajor, PanelMode, true> pack;
    pack(blockA, lhs, depth, rows, stride, offset);
}

#if EIGEN_ALTIVEC_USE_CUSTOM_PACK
template<typename Index, typename DataMapper, int nr, bool Conjugate, bool PanelMode>
struct gemm_pack_rhs<double, Index, DataMapper, nr, ColMajor, Conjugate, PanelMode>
{
  void operator()(double* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride=0, Index offset=0);
};

template<typename Index, typename DataMapper, int nr, bool Conjugate, bool PanelMode>
void gemm_pack_rhs<double, Index, DataMapper, nr, ColMajor, Conjugate, PanelMode>
  ::operator()(double* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride, Index offset)
{
  dhs_pack<double, DataMapper, Packet2d, ColMajor, PanelMode, false> pack;
  pack(blockB, rhs, depth, cols, stride, offset);
}

template<typename Index, typename DataMapper, int nr, bool Conjugate, bool PanelMode>
struct gemm_pack_rhs<double, Index, DataMapper, nr, RowMajor, Conjugate, PanelMode>
{
  void operator()(double* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride=0, Index offset=0);
};

template<typename Index, typename DataMapper, int nr, bool Conjugate, bool PanelMode>
void gemm_pack_rhs<double, Index, DataMapper, nr, RowMajor, Conjugate, PanelMode>
  ::operator()(double* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride, Index offset)
{
  dhs_pack<double, DataMapper, Packet2d, RowMajor, PanelMode, false> pack;
  pack(blockB, rhs, depth, cols, stride, offset);
}
#endif

template<typename Index, typename DataMapper, int Pack1, int Pack2, typename Packet, bool Conjugate, bool PanelMode>
struct gemm_pack_lhs<float, Index, DataMapper, Pack1, Pack2, Packet, RowMajor, Conjugate, PanelMode>
{
  void operator()(float* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride=0, Index offset=0);
};

template<typename Index, typename DataMapper, int Pack1, int Pack2, typename Packet, bool Conjugate, bool PanelMode>
void gemm_pack_lhs<float, Index, DataMapper, Pack1, Pack2, Packet, RowMajor, Conjugate, PanelMode>
  ::operator()(float* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride, Index offset)
{
  dhs_pack<float, DataMapper, Packet4f, RowMajor, PanelMode, true> pack;
  pack(blockA, lhs, depth, rows, stride, offset);
}

template<typename Index, typename DataMapper, int Pack1, int Pack2, typename Packet, bool Conjugate, bool PanelMode>
struct gemm_pack_lhs<float, Index, DataMapper, Pack1, Pack2, Packet, ColMajor, Conjugate, PanelMode>
{
  void operator()(float* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride=0, Index offset=0);
};

template<typename Index, typename DataMapper, int Pack1, int Pack2, typename Packet, bool Conjugate, bool PanelMode>
void gemm_pack_lhs<float, Index, DataMapper, Pack1, Pack2, Packet, ColMajor, Conjugate, PanelMode>
  ::operator()(float* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride, Index offset)
{
  dhs_pack<float, DataMapper, Packet4f, ColMajor, PanelMode, true> pack;
  pack(blockA, lhs, depth, rows, stride, offset);
}

template<typename Index, typename DataMapper, int Pack1, int Pack2, typename Packet, bool Conjugate, bool PanelMode>
struct gemm_pack_lhs<std::complex<float>, Index, DataMapper, Pack1, Pack2, Packet, RowMajor, Conjugate, PanelMode>
{
  void operator()(std::complex<float>* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride=0, Index offset=0);
};

template<typename Index, typename DataMapper, int Pack1, int Pack2, typename Packet, bool Conjugate, bool PanelMode>
void gemm_pack_lhs<std::complex<float>, Index, DataMapper, Pack1, Pack2, Packet, RowMajor, Conjugate, PanelMode>
  ::operator()(std::complex<float>* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride, Index offset)
{
  dhs_cpack<float, DataMapper, Packet4f, Packet2cf, RowMajor, Conjugate, PanelMode, true> pack;
  pack(blockA, lhs, depth, rows, stride, offset);
}

template<typename Index, typename DataMapper, int Pack1, int Pack2, typename Packet, bool Conjugate, bool PanelMode>
struct gemm_pack_lhs<std::complex<float>, Index, DataMapper, Pack1, Pack2, Packet, ColMajor, Conjugate, PanelMode>
{
  void operator()(std::complex<float>* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride=0, Index offset=0);
};

template<typename Index, typename DataMapper, int Pack1, int Pack2, typename Packet, bool Conjugate, bool PanelMode>
void gemm_pack_lhs<std::complex<float>, Index, DataMapper, Pack1, Pack2, Packet, ColMajor, Conjugate, PanelMode>
  ::operator()(std::complex<float>* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride, Index offset)
{
  dhs_cpack<float, DataMapper, Packet4f, Packet2cf, ColMajor, Conjugate, PanelMode, true> pack;
  pack(blockA, lhs, depth, rows, stride, offset);
}

#if EIGEN_ALTIVEC_USE_CUSTOM_PACK
template<typename Index, typename DataMapper, int nr, bool Conjugate, bool PanelMode>
struct gemm_pack_rhs<float, Index, DataMapper, nr, ColMajor, Conjugate, PanelMode>
{
  void operator()(float* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride=0, Index offset=0);
};

template<typename Index, typename DataMapper, int nr, bool Conjugate, bool PanelMode>
void gemm_pack_rhs<float, Index, DataMapper, nr, ColMajor, Conjugate, PanelMode>
  ::operator()(float* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride, Index offset)
{
  dhs_pack<float, DataMapper, Packet4f, ColMajor, PanelMode, false> pack;
  pack(blockB, rhs, depth, cols, stride, offset);
}

template<typename Index, typename DataMapper, int nr, bool Conjugate, bool PanelMode>
struct gemm_pack_rhs<float, Index, DataMapper, nr, RowMajor, Conjugate, PanelMode>
{
  void operator()(float* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride=0, Index offset=0);
};

template<typename Index, typename DataMapper, int nr, bool Conjugate, bool PanelMode>
void gemm_pack_rhs<float, Index, DataMapper, nr, RowMajor, Conjugate, PanelMode>
  ::operator()(float* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride, Index offset)
{
  dhs_pack<float, DataMapper, Packet4f, RowMajor, PanelMode, false> pack;
  pack(blockB, rhs, depth, cols, stride, offset);
}
#endif

template<typename Index, typename DataMapper, int nr, bool Conjugate, bool PanelMode>
struct gemm_pack_rhs<std::complex<float>, Index, DataMapper, nr, ColMajor, Conjugate, PanelMode>
{
  void operator()(std::complex<float>* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride=0, Index offset=0);
};

template<typename Index, typename DataMapper, int nr, bool Conjugate, bool PanelMode>
void gemm_pack_rhs<std::complex<float>, Index, DataMapper, nr, ColMajor, Conjugate, PanelMode>
  ::operator()(std::complex<float>* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride, Index offset)
{
  dhs_cpack<float, DataMapper, Packet4f, Packet2cf, ColMajor, Conjugate, PanelMode, false> pack;
  pack(blockB, rhs, depth, cols, stride, offset);
}

template<typename Index, typename DataMapper, int nr, bool Conjugate, bool PanelMode>
struct gemm_pack_rhs<std::complex<float>, Index, DataMapper, nr, RowMajor, Conjugate, PanelMode>
{
  void operator()(std::complex<float>* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride=0, Index offset=0);
};

template<typename Index, typename DataMapper, int nr, bool Conjugate, bool PanelMode>
void gemm_pack_rhs<std::complex<float>, Index, DataMapper, nr, RowMajor, Conjugate, PanelMode>
  ::operator()(std::complex<float>* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride, Index offset)
{
  dhs_cpack<float, DataMapper, Packet4f, Packet2cf, RowMajor, Conjugate, PanelMode, false> pack;
  pack(blockB, rhs, depth, cols, stride, offset);
}

template<typename Index, typename DataMapper, int Pack1, int Pack2, typename Packet, bool Conjugate, bool PanelMode>
struct gemm_pack_lhs<std::complex<double>, Index, DataMapper, Pack1, Pack2, Packet, RowMajor, Conjugate, PanelMode>
{
  void operator()(std::complex<double>* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride=0, Index offset=0);
};

template<typename Index, typename DataMapper, int Pack1, int Pack2, typename Packet, bool Conjugate, bool PanelMode>
void gemm_pack_lhs<std::complex<double>, Index, DataMapper, Pack1, Pack2, Packet, RowMajor, Conjugate, PanelMode>
  ::operator()(std::complex<double>* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride, Index offset)
{
  dhs_cpack<double, DataMapper, Packet2d, Packet1cd, RowMajor, Conjugate, PanelMode, true> pack;
  pack(blockA, lhs, depth, rows, stride, offset);
}

template<typename Index, typename DataMapper, int Pack1, int Pack2, typename Packet, bool Conjugate, bool PanelMode>
struct gemm_pack_lhs<std::complex<double>, Index, DataMapper, Pack1, Pack2, Packet, ColMajor, Conjugate, PanelMode>
{
  void operator()(std::complex<double>* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride=0, Index offset=0);
};

template<typename Index, typename DataMapper, int Pack1, int Pack2, typename Packet, bool Conjugate, bool PanelMode>
void gemm_pack_lhs<std::complex<double>, Index, DataMapper, Pack1, Pack2, Packet, ColMajor, Conjugate, PanelMode>
  ::operator()(std::complex<double>* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride, Index offset)
{
  dhs_cpack<double, DataMapper, Packet2d, Packet1cd, ColMajor, Conjugate, PanelMode, true> pack;
  pack(blockA, lhs, depth, rows, stride, offset);
}

template<typename Index, typename DataMapper, int nr, bool Conjugate, bool PanelMode>
struct gemm_pack_rhs<std::complex<double>, Index, DataMapper, nr, ColMajor, Conjugate, PanelMode>
{
  void operator()(std::complex<double>* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride=0, Index offset=0);
};

template<typename Index, typename DataMapper, int nr, bool Conjugate, bool PanelMode>
void gemm_pack_rhs<std::complex<double>, Index, DataMapper, nr, ColMajor, Conjugate, PanelMode>
  ::operator()(std::complex<double>* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride, Index offset)
{
  dhs_cpack<double, DataMapper, Packet2d, Packet1cd, ColMajor, Conjugate, PanelMode, false> pack;
  pack(blockB, rhs, depth, cols, stride, offset);
}

template<typename Index, typename DataMapper, int nr, bool Conjugate, bool PanelMode>
struct gemm_pack_rhs<std::complex<double>, Index, DataMapper, nr, RowMajor, Conjugate, PanelMode>
{
  void operator()(std::complex<double>* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride=0, Index offset=0);
};

template<typename Index, typename DataMapper, int nr, bool Conjugate, bool PanelMode>
void gemm_pack_rhs<std::complex<double>, Index, DataMapper, nr, RowMajor, Conjugate, PanelMode>
  ::operator()(std::complex<double>* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride, Index offset)
{
  dhs_cpack<double, DataMapper, Packet2d, Packet1cd, RowMajor, Conjugate, PanelMode, false> pack;
  pack(blockB, rhs, depth, cols, stride, offset);
}

// ********* gebp specializations *********
template<typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
struct gebp_kernel<float, float, Index, DataMapper, mr, nr, ConjugateLhs, ConjugateRhs>
{
  typedef typename quad_traits<float>::vectortype   Packet;
  typedef typename quad_traits<float>::rhstype      RhsPacket;

  void operator()(const DataMapper& res, const float* blockA, const float* blockB,
                  Index rows, Index depth, Index cols, float alpha,
                  Index strideA=-1, Index strideB=-1, Index offsetA=0, Index offsetB=0);
};

template<typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
void gebp_kernel<float, float, Index, DataMapper, mr, nr, ConjugateLhs, ConjugateRhs>
  ::operator()(const DataMapper& res, const float* blockA, const float* blockB,
               Index rows, Index depth, Index cols, float alpha,
               Index strideA, Index strideB, Index offsetA, Index offsetB)
  {
    const Index accRows = quad_traits<float>::rows;
    const Index accCols = quad_traits<float>::size;
    void (*gemm_function)(const DataMapper&, const float*, const float*, Index, Index, Index, float, Index, Index, Index, Index);

    #if defined(EIGEN_ALTIVEC_MMA_ONLY)
      //generate with MMA only
      gemm_function = &Eigen::internal::gemmMMA<float, Packet, RhsPacket, DataMapper, accRows, accCols>;
    #elif defined(EIGEN_ALTIVEC_MMA_DYNAMIC_DISPATCH)
      if (__builtin_cpu_supports ("arch_3_1") && __builtin_cpu_supports ("mma")){
        gemm_function = &Eigen::internal::gemmMMA<float, Packet, RhsPacket, DataMapper, accRows, accCols>;
      }
      else{
        gemm_function = &Eigen::internal::gemm<float, Packet, RhsPacket, DataMapper, accRows, accCols>;
      }
    #else
      gemm_function = &Eigen::internal::gemm<float, Packet, RhsPacket, DataMapper, accRows, accCols>;
    #endif
    gemm_function(res, blockA, blockB, rows, depth, cols, alpha, strideA, strideB, offsetA, offsetB);
  }

template<typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
struct gebp_kernel<std::complex<float>, std::complex<float>, Index, DataMapper, mr, nr, ConjugateLhs, ConjugateRhs>
{
  typedef Packet4f   Packet;
  typedef Packet2cf  Packetc;
  typedef Packet4f   RhsPacket;

  void operator()(const DataMapper& res, const std::complex<float>* blockA, const std::complex<float>* blockB,
                  Index rows, Index depth, Index cols, std::complex<float> alpha,
                  Index strideA=-1, Index strideB=-1, Index offsetA=0, Index offsetB=0);
};

template<typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
void gebp_kernel<std::complex<float>, std::complex<float>, Index, DataMapper, mr, nr, ConjugateLhs, ConjugateRhs>
  ::operator()(const DataMapper& res, const std::complex<float>* blockA, const std::complex<float>* blockB,
               Index rows, Index depth, Index cols, std::complex<float> alpha,
               Index strideA, Index strideB, Index offsetA, Index offsetB)
  {
    const Index accRows = quad_traits<float>::rows;
    const Index accCols = quad_traits<float>::size;
    void (*gemm_function)(const DataMapper&, const std::complex<float>*, const std::complex<float>*,
          Index, Index, Index, std::complex<float>, Index, Index, Index, Index);

    #if defined(EIGEN_ALTIVEC_MMA_ONLY)
      //generate with MMA only
      gemm_function = &Eigen::internal::gemm_complexMMA<std::complex<float>, std::complex<float>, std::complex<float>, float, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, false>;
    #elif defined(EIGEN_ALTIVEC_MMA_DYNAMIC_DISPATCH)
      if (__builtin_cpu_supports ("arch_3_1") && __builtin_cpu_supports ("mma")){
        gemm_function = &Eigen::internal::gemm_complexMMA<std::complex<float>, std::complex<float>, std::complex<float>, float, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, false>;
      }
      else{
        gemm_function = &Eigen::internal::gemm_complex<std::complex<float>, std::complex<float>, std::complex<float>, float, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, false>;
      }
    #else
      gemm_function = &Eigen::internal::gemm_complex<std::complex<float>, std::complex<float>, std::complex<float>, float, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, false>;
    #endif
    gemm_function(res, blockA, blockB, rows, depth, cols, alpha, strideA, strideB, offsetA, offsetB);
  }

template<typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
struct gebp_kernel<float, std::complex<float>, Index, DataMapper, mr, nr, ConjugateLhs, ConjugateRhs>
{
  typedef Packet4f   Packet;
  typedef Packet2cf  Packetc;
  typedef Packet4f   RhsPacket;

  void operator()(const DataMapper& res, const float* blockA, const std::complex<float>* blockB,
                  Index rows, Index depth, Index cols, std::complex<float> alpha,
                  Index strideA=-1, Index strideB=-1, Index offsetA=0, Index offsetB=0);
};

template<typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
void gebp_kernel<float, std::complex<float>, Index, DataMapper, mr, nr, ConjugateLhs, ConjugateRhs>
  ::operator()(const DataMapper& res, const float* blockA, const std::complex<float>* blockB,
               Index rows, Index depth, Index cols, std::complex<float> alpha,
               Index strideA, Index strideB, Index offsetA, Index offsetB)
  {
    const Index accRows = quad_traits<float>::rows;
    const Index accCols = quad_traits<float>::size;
    void (*gemm_function)(const DataMapper&, const float*, const std::complex<float>*,
          Index, Index, Index, std::complex<float>, Index, Index, Index, Index);
    #if defined(EIGEN_ALTIVEC_MMA_ONLY)
      //generate with MMA only
      gemm_function = &Eigen::internal::gemm_complexMMA<float, std::complex<float>, std::complex<float>, float, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, true, false>;
    #elif defined(EIGEN_ALTIVEC_MMA_DYNAMIC_DISPATCH)
      if (__builtin_cpu_supports ("arch_3_1") && __builtin_cpu_supports ("mma")){
        gemm_function = &Eigen::internal::gemm_complexMMA<float, std::complex<float>, std::complex<float>, float, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, true, false>;
      }
      else{
        gemm_function = &Eigen::internal::gemm_complex<float, std::complex<float>, std::complex<float>, float, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, true, false>;
      }
    #else
      gemm_function = &Eigen::internal::gemm_complex<float, std::complex<float>, std::complex<float>, float, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, true, false>;
    #endif
    gemm_function(res, blockA, blockB, rows, depth, cols, alpha, strideA, strideB, offsetA, offsetB);
  }

template<typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
struct gebp_kernel<std::complex<float>, float, Index, DataMapper, mr, nr, ConjugateLhs, ConjugateRhs>
{
  typedef Packet4f   Packet;
  typedef Packet2cf  Packetc;
  typedef Packet4f   RhsPacket;

  void operator()(const DataMapper& res, const std::complex<float>* blockA, const float* blockB,
                  Index rows, Index depth, Index cols, std::complex<float> alpha,
                  Index strideA=-1, Index strideB=-1, Index offsetA=0, Index offsetB=0);
};

template<typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
void gebp_kernel<std::complex<float>, float, Index, DataMapper, mr, nr, ConjugateLhs, ConjugateRhs>
  ::operator()(const DataMapper& res, const std::complex<float>* blockA, const float* blockB,
               Index rows, Index depth, Index cols, std::complex<float> alpha,
               Index strideA, Index strideB, Index offsetA, Index offsetB)
  {
    const Index accRows = quad_traits<float>::rows;
    const Index accCols = quad_traits<float>::size;
    void (*gemm_function)(const DataMapper&, const std::complex<float>*, const float*,
          Index, Index, Index, std::complex<float>, Index, Index, Index, Index);
    #if defined(EIGEN_ALTIVEC_MMA_ONLY)
      //generate with MMA only
      gemm_function = &Eigen::internal::gemm_complexMMA<std::complex<float>, float, std::complex<float>, float, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, true>;
    #elif defined(EIGEN_ALTIVEC_MMA_DYNAMIC_DISPATCH)
      if (__builtin_cpu_supports ("arch_3_1") && __builtin_cpu_supports ("mma")){
        gemm_function = &Eigen::internal::gemm_complexMMA<std::complex<float>, float, std::complex<float>, float, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, true>;
      }
      else{
        gemm_function = &Eigen::internal::gemm_complex<std::complex<float>, float, std::complex<float>, float, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, true>;
      }
    #else
      gemm_function = &Eigen::internal::gemm_complex<std::complex<float>, float, std::complex<float>, float, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, true>;
    #endif
    gemm_function(res, blockA, blockB, rows, depth, cols, alpha, strideA, strideB, offsetA, offsetB);
  }

template<typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
struct gebp_kernel<double, double, Index, DataMapper, mr, nr, ConjugateLhs, ConjugateRhs>
{
  typedef typename quad_traits<double>::vectortype  Packet;
  typedef typename quad_traits<double>::rhstype     RhsPacket;

  void operator()(const DataMapper& res, const double* blockA, const double* blockB,
                  Index rows, Index depth, Index cols, double alpha,
                  Index strideA=-1, Index strideB=-1, Index offsetA=0, Index offsetB=0);
};

template<typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
void gebp_kernel<double, double, Index, DataMapper, mr, nr, ConjugateLhs, ConjugateRhs>
  ::operator()(const DataMapper& res, const double* blockA, const double* blockB,
               Index rows, Index depth, Index cols, double alpha,
               Index strideA, Index strideB, Index offsetA, Index offsetB)
  {
    const Index accRows = quad_traits<double>::rows;
    const Index accCols = quad_traits<double>::size;
    void (*gemm_function)(const DataMapper&, const double*, const double*, Index, Index, Index, double, Index, Index, Index, Index);

    #if defined(EIGEN_ALTIVEC_MMA_ONLY)
      //generate with MMA only
      gemm_function = &Eigen::internal::gemmMMA<double, Packet, RhsPacket, DataMapper, accRows, accCols>;
    #elif defined(EIGEN_ALTIVEC_MMA_DYNAMIC_DISPATCH)
      if (__builtin_cpu_supports ("arch_3_1") && __builtin_cpu_supports ("mma")){
        gemm_function = &Eigen::internal::gemmMMA<double, Packet, RhsPacket, DataMapper, accRows, accCols>;
      }
      else{
        gemm_function = &Eigen::internal::gemm<double, Packet, RhsPacket, DataMapper, accRows, accCols>;
      }
    #else
      gemm_function = &Eigen::internal::gemm<double, Packet, RhsPacket, DataMapper, accRows, accCols>;
    #endif
    gemm_function(res, blockA, blockB, rows, depth, cols, alpha, strideA, strideB, offsetA, offsetB);
  }

template<typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
struct gebp_kernel<std::complex<double>, std::complex<double>, Index, DataMapper, mr, nr, ConjugateLhs, ConjugateRhs>
{
  typedef quad_traits<double>::vectortype   Packet;
  typedef Packet1cd  Packetc;
  typedef quad_traits<double>::rhstype   RhsPacket;

  void operator()(const DataMapper& res, const std::complex<double>* blockA, const std::complex<double>* blockB,
                  Index rows, Index depth, Index cols, std::complex<double> alpha,
                  Index strideA=-1, Index strideB=-1, Index offsetA=0, Index offsetB=0);
};

template<typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
void gebp_kernel<std::complex<double>, std::complex<double>, Index, DataMapper, mr, nr, ConjugateLhs, ConjugateRhs>
  ::operator()(const DataMapper& res, const std::complex<double>* blockA, const std::complex<double>* blockB,
               Index rows, Index depth, Index cols, std::complex<double> alpha,
               Index strideA, Index strideB, Index offsetA, Index offsetB)
  {
    const Index accRows = quad_traits<double>::rows;
    const Index accCols = quad_traits<double>::size;
    void (*gemm_function)(const DataMapper&, const std::complex<double>*, const std::complex<double>*,
          Index, Index, Index, std::complex<double>, Index, Index, Index, Index);
    #if defined(EIGEN_ALTIVEC_MMA_ONLY)
      //generate with MMA only
      gemm_function = &Eigen::internal::gemm_complexMMA<std::complex<double>, std::complex<double>, std::complex<double>, double, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, false>;
    #elif defined(EIGEN_ALTIVEC_MMA_DYNAMIC_DISPATCH)
      if (__builtin_cpu_supports ("arch_3_1") && __builtin_cpu_supports ("mma")){
        gemm_function = &Eigen::internal::gemm_complexMMA<std::complex<double>, std::complex<double>, std::complex<double>, double, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, false>;
      }
      else{
        gemm_function = &Eigen::internal::gemm_complex<std::complex<double>, std::complex<double>, std::complex<double>, double, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, false>;
      }
    #else
      gemm_function = &Eigen::internal::gemm_complex<std::complex<double>, std::complex<double>, std::complex<double>, double, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, false>;
    #endif
    gemm_function(res, blockA, blockB, rows, depth, cols, alpha, strideA, strideB, offsetA, offsetB);
  }

template<typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
struct gebp_kernel<std::complex<double>, double, Index, DataMapper, mr, nr, ConjugateLhs, ConjugateRhs>
{
  typedef quad_traits<double>::vectortype   Packet;
  typedef Packet1cd  Packetc;
  typedef quad_traits<double>::rhstype   RhsPacket;

  void operator()(const DataMapper& res, const std::complex<double>* blockA, const double* blockB,
                  Index rows, Index depth, Index cols, std::complex<double> alpha,
                  Index strideA=-1, Index strideB=-1, Index offsetA=0, Index offsetB=0);
};

template<typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
void gebp_kernel<std::complex<double>, double, Index, DataMapper, mr, nr, ConjugateLhs, ConjugateRhs>
  ::operator()(const DataMapper& res, const std::complex<double>* blockA, const double* blockB,
               Index rows, Index depth, Index cols, std::complex<double> alpha,
               Index strideA, Index strideB, Index offsetA, Index offsetB)
  {
    const Index accRows = quad_traits<double>::rows;
    const Index accCols = quad_traits<double>::size;
    void (*gemm_function)(const DataMapper&, const std::complex<double>*, const double*,
          Index, Index, Index, std::complex<double>, Index, Index, Index, Index);
    #if defined(EIGEN_ALTIVEC_MMA_ONLY)
      //generate with MMA only
      gemm_function = &Eigen::internal::gemm_complexMMA<std::complex<double>, double, std::complex<double>, double, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, true>;
    #elif defined(EIGEN_ALTIVEC_MMA_DYNAMIC_DISPATCH)
      if (__builtin_cpu_supports ("arch_3_1") && __builtin_cpu_supports ("mma")){
        gemm_function = &Eigen::internal::gemm_complexMMA<std::complex<double>, double, std::complex<double>, double, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, true>;
      }
      else{
        gemm_function = &Eigen::internal::gemm_complex<std::complex<double>, double, std::complex<double>, double, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, true>;
      }
    #else
      gemm_function = &Eigen::internal::gemm_complex<std::complex<double>, double, std::complex<double>, double, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, true>;
    #endif
    gemm_function(res, blockA, blockB, rows, depth, cols, alpha, strideA, strideB, offsetA, offsetB);
  }

template<typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
struct gebp_kernel<double, std::complex<double>, Index, DataMapper, mr, nr, ConjugateLhs, ConjugateRhs>
{
  typedef quad_traits<double>::vectortype   Packet;
  typedef Packet1cd  Packetc;
  typedef quad_traits<double>::rhstype   RhsPacket;

  void operator()(const DataMapper& res, const double* blockA, const std::complex<double>* blockB,
                  Index rows, Index depth, Index cols, std::complex<double> alpha,
                  Index strideA=-1, Index strideB=-1, Index offsetA=0, Index offsetB=0);
};

template<typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
void gebp_kernel<double, std::complex<double>, Index, DataMapper, mr, nr, ConjugateLhs, ConjugateRhs>
  ::operator()(const DataMapper& res, const double* blockA, const std::complex<double>* blockB,
               Index rows, Index depth, Index cols, std::complex<double> alpha,
               Index strideA, Index strideB, Index offsetA, Index offsetB)
  {
    const Index accRows = quad_traits<double>::rows;
    const Index accCols = quad_traits<double>::size;
    void (*gemm_function)(const DataMapper&, const double*, const std::complex<double>*,
          Index, Index, Index, std::complex<double>, Index, Index, Index, Index);
    #if defined(EIGEN_ALTIVEC_MMA_ONLY)
      //generate with MMA only
      gemm_function = &Eigen::internal::gemm_complexMMA<double, std::complex<double>, std::complex<double>, double, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, true, false>;
    #elif defined(EIGEN_ALTIVEC_MMA_DYNAMIC_DISPATCH)
      if (__builtin_cpu_supports ("arch_3_1") && __builtin_cpu_supports ("mma")){
        gemm_function = &Eigen::internal::gemm_complexMMA<double, std::complex<double>, std::complex<double>, double, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, true, false>;
      }
      else{
        gemm_function = &Eigen::internal::gemm_complex<double, std::complex<double>, std::complex<double>, double, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, true, false>;
      }
    #else
      gemm_function = &Eigen::internal::gemm_complex<double, std::complex<double>, std::complex<double>, double, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, true, false>;
    #endif
    gemm_function(res, blockA, blockB, rows, depth, cols, alpha, strideA, strideB, offsetA, offsetB);
  }

#if defined(__MMA__)
template<typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
struct gebp_kernel<bfloat16, bfloat16, Index, DataMapper, mr, nr, ConjugateLhs, ConjugateRhs>
{
  typedef typename quad_traits<bfloat16>::vectortype   Packet;
  typedef typename quad_traits<bfloat16>::rhstype      RhsPacket;

  void operator()(const DataMapper& res, const bfloat16* blockA, const bfloat16* blockB,
                  Index rows, Index depth, Index cols, bfloat16 alpha,
                  Index strideA=-1, Index strideB=-1, Index offsetA=0, Index offsetB=0);
};

template<typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
void gebp_kernel<bfloat16, bfloat16, Index, DataMapper, mr, nr, ConjugateLhs, ConjugateRhs>
  ::operator()(const DataMapper& res, const bfloat16* blockA, const bfloat16* blockB,
               Index rows, Index depth, Index cols, bfloat16 alpha,
               Index strideA, Index strideB, Index offsetA, Index offsetB)
  {
    const Index accRows = quad_traits<bfloat16>::rows;
    const Index accCols = quad_traits<bfloat16>::size;

    Eigen::internal::gemmMMAbfloat16<Index, Packet, RhsPacket, DataMapper, accRows, accCols>(res, blockA, blockB, rows, depth, cols, alpha, strideA, strideB, offsetA, offsetB);
  }
#endif
} // end namespace internal

} // end namespace Eigen

#endif // EIGEN_MATRIX_PRODUCT_ALTIVEC_H