text: // This file is part of Eigen, a lightweight C++ template library
  // for linear algebra.
  //
  // Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
  //
  // 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_GENERAL_BLOCK_PANEL_H
  #define EIGEN_GENERAL_BLOCK_PANEL_H
  
  namespace Eigen { 
    
  namespace internal {
  
  template<typename _LhsScalar, typename _RhsScalar, bool _ConjLhs=false, bool _ConjRhs=false>
  class gebp_traits;
  
  
  /** \internal \returns b if a<=0, and returns a otherwise. */
  inline std::ptrdiff_t manage_caching_sizes_helper(std::ptrdiff_t a, std::ptrdiff_t b)
  {
    return a<=0 ? b : a;
  }
  
  /** \internal */
  inline void manage_caching_sizes(Action action, std::ptrdiff_t* l1=0, std::ptrdiff_t* l2=0)
  {
    static std::ptrdiff_t m_l1CacheSize = 0;
    static std::ptrdiff_t m_l2CacheSize = 0;
    if(m_l2CacheSize==0)
    {
      m_l1CacheSize = manage_caching_sizes_helper(queryL1CacheSize(),8 * 1024);
      m_l2CacheSize = manage_caching_sizes_helper(queryTopLevelCacheSize(),1*1024*1024);
    }
    
    if(action==SetAction)
    {
      // set the cpu cache size and cache all block sizes from a global cache size in byte
      eigen_internal_assert(l1!=0 && l2!=0);
      m_l1CacheSize = *l1;
      m_l2CacheSize = *l2;
    }
    else if(action==GetAction)
    {
      eigen_internal_assert(l1!=0 && l2!=0);
      *l1 = m_l1CacheSize;
      *l2 = m_l2CacheSize;
    }
    else
    {
      eigen_internal_assert(false);
    }
  }
  
  /** \brief Computes the blocking parameters for a m x k times k x n matrix product
    *
    * \param[in,out] k Input: the third dimension of the product. Output: the blocking size along the same dimension.
    * \param[in,out] m Input: the number of rows of the left hand side. Output: the blocking size along the same dimension.
    * \param[in,out] n Input: the number of columns of the right hand side. Output: the blocking size along the same dimension.
    *
    * Given a m x k times k x n matrix product of scalar types \c LhsScalar and \c RhsScalar,
    * this function computes the blocking size parameters along the respective dimensions
    * for matrix products and related algorithms. The blocking sizes depends on various
    * parameters:
    * - the L1 and L2 cache sizes,
    * - the register level blocking sizes defined by gebp_traits,
    * - the number of scalars that fit into a packet (when vectorization is enabled).
    *
    * \sa setCpuCacheSizes */
  template<typename LhsScalar, typename RhsScalar, int KcFactor, typename SizeType>
  void computeProductBlockingSizes(SizeType& k, SizeType& m, SizeType& n)
  {
    EIGEN_UNUSED_VARIABLE(n);
    // Explanations:
    // Let's recall the product algorithms form kc x nc horizontal panels B' on the rhs and
    // mc x kc blocks A' on the lhs. A' has to fit into L2 cache. Moreover, B' is processed
    // per kc x nr vertical small panels where nr is the blocking size along the n dimension
    // at the register level. For vectorization purpose, these small vertical panels are unpacked,
    // e.g., each coefficient is replicated to fit a packet. This small vertical panel has to
    // stay in L1 cache.
    std::ptrdiff_t l1, l2;
  
    typedef gebp_traits<LhsScalar,RhsScalar> Traits;
    enum {
      kdiv = KcFactor * 2 * Traits::nr
           * Traits::RhsProgress * sizeof(RhsScalar),
      mr = gebp_traits<LhsScalar,RhsScalar>::mr,
      mr_mask = (0xffffffff/mr)*mr
    };
  
    manage_caching_sizes(GetAction, &l1, &l2);
    k = std::min<SizeType>(k, l1/kdiv);
    SizeType _m = k>0 ? l2/(4 * sizeof(LhsScalar) * k) : 0;
    if(_m<m) m = _m & mr_mask;
  }
  
  template<typename LhsScalar, typename RhsScalar, typename SizeType>
  inline void computeProductBlockingSizes(SizeType& k, SizeType& m, SizeType& n)
  {
    computeProductBlockingSizes<LhsScalar,RhsScalar,1>(k, m, n);
  }
  
  #ifdef EIGEN_HAS_FUSE_CJMADD
    #define MADD(CJ,A,B,C,T)  C = CJ.pmadd(A,B,C);
  #else
  
    // FIXME (a bit overkill maybe ?)
  
    template<typename CJ, typename A, typename B, typename C, typename T> struct gebp_madd_selector {
      EIGEN_ALWAYS_INLINE static void run(const CJ& cj, A& a, B& b, C& c, T& /*t*/)
      {
        c = cj.pmadd(a,b,c);
      }
    };
  
    template<typename CJ, typename T> struct gebp_madd_selector<CJ,T,T,T,T> {
      EIGEN_ALWAYS_INLINE static void run(const CJ& cj, T& a, T& b, T& c, T& t)
      {
        t = b; t = cj.pmul(a,t); c = padd(c,t);
      }
    };
  
    template<typename CJ, typename A, typename B, typename C, typename T>
    EIGEN_STRONG_INLINE void gebp_madd(const CJ& cj, A& a, B& b, C& c, T& t)
    {
      gebp_madd_selector<CJ,A,B,C,T>::run(cj,a,b,c,t);
    }
  
    #define MADD(CJ,A,B,C,T)  gebp_madd(CJ,A,B,C,T);
  //   #define MADD(CJ,A,B,C,T)  T = B; T = CJ.pmul(A,T); C = padd(C,T);
  #endif
  
  /* Vectorization logic
   *  real*real: unpack rhs to constant packets, ...
   * 
   *  cd*cd : unpack rhs to (b_r,b_r), (b_i,b_i), mul to get (a_r b_r,a_i b_r) (a_r b_i,a_i b_i),
   *          storing each res packet into two packets (2x2),
   *          at the end combine them: swap the second and addsub them 
   *  cf*cf : same but with 2x4 blocks
   *  cplx*real : unpack rhs to constant packets, ...
   *  real*cplx : load lhs as (a0,a0,a1,a1), and mul as usual
   */
  template<typename _LhsScalar, typename _RhsScalar, bool _ConjLhs, bool _ConjRhs>
  class gebp_traits
  {
  public:
    typedef _LhsScalar LhsScalar;
    typedef _RhsScalar RhsScalar;
    typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar;
  
    enum {
      ConjLhs = _ConjLhs,
      ConjRhs = _ConjRhs,
      Vectorizable = packet_traits<LhsScalar>::Vectorizable && packet_traits<RhsScalar>::Vectorizable,
      LhsPacketSize = Vectorizable ? packet_traits<LhsScalar>::size : 1,
      RhsPacketSize = Vectorizable ? packet_traits<RhsScalar>::size : 1,
      ResPacketSize = Vectorizable ? packet_traits<ResScalar>::size : 1,
      
      NumberOfRegisters = EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS,
  
      // register block size along the N direction (must be either 2 or 4)
      nr = NumberOfRegisters/4,
  
      // register block size along the M direction (currently, this one cannot be modified)
      mr = 2 * LhsPacketSize,
      
      WorkSpaceFactor = nr * RhsPacketSize,
  
      LhsProgress = LhsPacketSize,
      RhsProgress = RhsPacketSize
    };
  
    typedef typename packet_traits<LhsScalar>::type  _LhsPacket;
    typedef typename packet_traits<RhsScalar>::type  _RhsPacket;
    typedef typename packet_traits<ResScalar>::type  _ResPacket;
  
    typedef typename conditional<Vectorizable,_LhsPacket,LhsScalar>::type LhsPacket;
    typedef typename conditional<Vectorizable,_RhsPacket,RhsScalar>::type RhsPacket;
    typedef typename conditional<Vectorizable,_ResPacket,ResScalar>::type ResPacket;
  
    typedef ResPacket AccPacket;
    
    EIGEN_STRONG_INLINE void initAcc(AccPacket& p)
    {
      p = pset1<ResPacket>(ResScalar(0));
    }
  
    EIGEN_STRONG_INLINE void unpackRhs(DenseIndex n, const RhsScalar* rhs, RhsScalar* b)
    {
      for(DenseIndex k=0; k<n; k++)
        pstore1<RhsPacket>(&b[k*RhsPacketSize], rhs[k]);
    }
  
    EIGEN_STRONG_INLINE void loadRhs(const RhsScalar* b, RhsPacket& dest) const
    {
      dest = pload<RhsPacket>(b);
    }
  
    EIGEN_STRONG_INLINE void loadLhs(const LhsScalar* a, LhsPacket& dest) const
    {
      dest = pload<LhsPacket>(a);
    }
  
    EIGEN_STRONG_INLINE void madd(const LhsPacket& a, const RhsPacket& b, AccPacket& c, AccPacket& tmp) const
    {
      tmp = b; tmp = pmul(a,tmp); c = padd(c,tmp);
    }
  
    EIGEN_STRONG_INLINE void acc(const AccPacket& c, const ResPacket& alpha, ResPacket& r) const
    {
      r = pmadd(c,alpha,r);
    }
  
  protected:
  //   conj_helper<LhsScalar,RhsScalar,ConjLhs,ConjRhs> cj;
  //   conj_helper<LhsPacket,RhsPacket,ConjLhs,ConjRhs> pcj;
  };
  
  template<typename RealScalar, bool _ConjLhs>
  class gebp_traits<std::complex<RealScalar>, RealScalar, _ConjLhs, false>
  {
  public:
    typedef std::complex<RealScalar> LhsScalar;
    typedef RealScalar RhsScalar;
    typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar;
  
    enum {
      ConjLhs = _ConjLhs,
      ConjRhs = false,
      Vectorizable = packet_traits<LhsScalar>::Vectorizable && packet_traits<RhsScalar>::Vectorizable,
      LhsPacketSize = Vectorizable ? packet_traits<LhsScalar>::size : 1,
      RhsPacketSize = Vectorizable ? packet_traits<RhsScalar>::size : 1,
      ResPacketSize = Vectorizable ? packet_traits<ResScalar>::size : 1,
      
      NumberOfRegisters = EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS,
      nr = NumberOfRegisters/4,
      mr = 2 * LhsPacketSize,
      WorkSpaceFactor = nr*RhsPacketSize,
  
      LhsProgress = LhsPacketSize,
      RhsProgress = RhsPacketSize
    };
  
    typedef typename packet_traits<LhsScalar>::type  _LhsPacket;
    typedef typename packet_traits<RhsScalar>::type  _RhsPacket;
    typedef typename packet_traits<ResScalar>::type  _ResPacket;
  
    typedef typename conditional<Vectorizable,_LhsPacket,LhsScalar>::type LhsPacket;
    typedef typename conditional<Vectorizable,_RhsPacket,RhsScalar>::type RhsPacket;
    typedef typename conditional<Vectorizable,_ResPacket,ResScalar>::type ResPacket;
  
    typedef ResPacket AccPacket;
  
    EIGEN_STRONG_INLINE void initAcc(AccPacket& p)
    {
      p = pset1<ResPacket>(ResScalar(0));
    }
  
    EIGEN_STRONG_INLINE void unpackRhs(DenseIndex n, const RhsScalar* rhs, RhsScalar* b)
    {
      for(DenseIndex k=0; k<n; k++)
        pstore1<RhsPacket>(&b[k*RhsPacketSize], rhs[k]);
    }
  
    EIGEN_STRONG_INLINE void loadRhs(const RhsScalar* b, RhsPacket& dest) const
    {
      dest = pload<RhsPacket>(b);
    }
  
    EIGEN_STRONG_INLINE void loadLhs(const LhsScalar* a, LhsPacket& dest) const
    {
      dest = pload<LhsPacket>(a);
    }
  
    EIGEN_STRONG_INLINE void madd(const LhsPacket& a, const RhsPacket& b, AccPacket& c, RhsPacket& tmp) const
    {
      madd_impl(a, b, c, tmp, typename conditional<Vectorizable,true_type,false_type>::type());
    }
  
    EIGEN_STRONG_INLINE void madd_impl(const LhsPacket& a, const RhsPacket& b, AccPacket& c, RhsPacket& tmp, const true_type&) const
    {
      tmp = b; tmp = pmul(a.v,tmp); c.v = padd(c.v,tmp);
    }
  
    EIGEN_STRONG_INLINE void madd_impl(const LhsScalar& a, const RhsScalar& b, ResScalar& c, RhsScalar& /*tmp*/, const false_type&) const
    {
      c += a * b;
    }
  
    EIGEN_STRONG_INLINE void acc(const AccPacket& c, const ResPacket& alpha, ResPacket& r) const
    {
      r = cj.pmadd(c,alpha,r);
    }
  
  protected:
    conj_helper<ResPacket,ResPacket,ConjLhs,false> cj;
  };
  
  template<typename RealScalar, bool _ConjLhs, bool _ConjRhs>
  class gebp_traits<std::complex<RealScalar>, std::complex<RealScalar>, _ConjLhs, _ConjRhs >
  {
  public:
    typedef std::complex<RealScalar>  Scalar;
    typedef std::complex<RealScalar>  LhsScalar;
    typedef std::complex<RealScalar>  RhsScalar;
    typedef std::complex<RealScalar>  ResScalar;
    
    enum {
      ConjLhs = _ConjLhs,
      ConjRhs = _ConjRhs,
      Vectorizable = packet_traits<RealScalar>::Vectorizable
                  && packet_traits<Scalar>::Vectorizable,
      RealPacketSize  = Vectorizable ? packet_traits<RealScalar>::size : 1,
      ResPacketSize   = Vectorizable ? packet_traits<ResScalar>::size : 1,
      
      nr = 2,
      mr = 2 * ResPacketSize,
      WorkSpaceFactor = Vectorizable ? 2*nr*RealPacketSize : nr,
  
      LhsProgress = ResPacketSize,
      RhsProgress = Vectorizable ? 2*ResPacketSize : 1
    };
    
    typedef typename packet_traits<RealScalar>::type RealPacket;
    typedef typename packet_traits<Scalar>::type     ScalarPacket;
    struct DoublePacket
    {
      RealPacket first;
      RealPacket second;
    };
  
    typedef typename conditional<Vectorizable,RealPacket,  Scalar>::type LhsPacket;
    typedef typename conditional<Vectorizable,DoublePacket,Scalar>::type RhsPacket;
    typedef typename conditional<Vectorizable,ScalarPacket,Scalar>::type ResPacket;
    typedef typename conditional<Vectorizable,DoublePacket,Scalar>::type AccPacket;
    
    EIGEN_STRONG_INLINE void initAcc(Scalar& p) { p = Scalar(0); }
  
    EIGEN_STRONG_INLINE void initAcc(DoublePacket& p)
    {
      p.first   = pset1<RealPacket>(RealScalar(0));
      p.second  = pset1<RealPacket>(RealScalar(0));
    }
  
    /* Unpack the rhs coeff such that each complex coefficient is spread into
     * two packects containing respectively the real and imaginary coefficient
     * duplicated as many time as needed: (x+iy) => [x, ..., x] [y, ..., y]
     */
    EIGEN_STRONG_INLINE void unpackRhs(DenseIndex n, const Scalar* rhs, Scalar* b)
    {
      for(DenseIndex k=0; k<n; k++)
      {
        if(Vectorizable)
        {
          pstore1<RealPacket>((RealScalar*)&b[k*ResPacketSize*2+0],             real(rhs[k]));
          pstore1<RealPacket>((RealScalar*)&b[k*ResPacketSize*2+ResPacketSize], imag(rhs[k]));
        }
        else
          b[k] = rhs[k];
      }
    }
  
    EIGEN_STRONG_INLINE void loadRhs(const RhsScalar* b, ResPacket& dest) const { dest = *b; }
  
    EIGEN_STRONG_INLINE void loadRhs(const RhsScalar* b, DoublePacket& dest) const
    {
      dest.first  = pload<RealPacket>((const RealScalar*)b);
      dest.second = pload<RealPacket>((const RealScalar*)(b+ResPacketSize));
    }
  
    // nothing special here
    EIGEN_STRONG_INLINE void loadLhs(const LhsScalar* a, LhsPacket& dest) const
    {
      dest = pload<LhsPacket>((const typename unpacket_traits<LhsPacket>::type*)(a));
    }
  
    EIGEN_STRONG_INLINE void madd(const LhsPacket& a, const RhsPacket& b, DoublePacket& c, RhsPacket& /*tmp*/) const
    {
      c.first   = padd(pmul(a,b.first), c.first);
      c.second  = padd(pmul(a,b.second),c.second);
    }
  
    EIGEN_STRONG_INLINE void madd(const LhsPacket& a, const RhsPacket& b, ResPacket& c, RhsPacket& /*tmp*/) const
    {
      c = cj.pmadd(a,b,c);
    }
    
    EIGEN_STRONG_INLINE void acc(const Scalar& c, const Scalar& alpha, Scalar& r) const { r += alpha * c; }
    
    EIGEN_STRONG_INLINE void acc(const DoublePacket& c, const ResPacket& alpha, ResPacket& r) const
    {
      // assemble c
      ResPacket tmp;
      if((!ConjLhs)&&(!ConjRhs))
      {
        tmp = pcplxflip(pconj(ResPacket(c.second)));
        tmp = padd(ResPacket(c.first),tmp);
      }
      else if((!ConjLhs)&&(ConjRhs))
      {
        tmp = pconj(pcplxflip(ResPacket(c.second)));
        tmp = padd(ResPacket(c.first),tmp);
      }
      else if((ConjLhs)&&(!ConjRhs))
      {
        tmp = pcplxflip(ResPacket(c.second));
        tmp = padd(pconj(ResPacket(c.first)),tmp);
      }
      else if((ConjLhs)&&(ConjRhs))
      {
        tmp = pcplxflip(ResPacket(c.second));
        tmp = psub(pconj(ResPacket(c.first)),tmp);
      }
      
      r = pmadd(tmp,alpha,r);
    }
  
  protected:
    conj_helper<LhsScalar,RhsScalar,ConjLhs,ConjRhs> cj;
  };
  
  template<typename RealScalar, bool _ConjRhs>
  class gebp_traits<RealScalar, std::complex<RealScalar>, false, _ConjRhs >
  {
  public:
    typedef std::complex<RealScalar>  Scalar;
    typedef RealScalar  LhsScalar;
    typedef Scalar      RhsScalar;
    typedef Scalar      ResScalar;
  
    enum {
      ConjLhs = false,
      ConjRhs = _ConjRhs,
      Vectorizable = packet_traits<RealScalar>::Vectorizable
                  && packet_traits<Scalar>::Vectorizable,
      LhsPacketSize = Vectorizable ? packet_traits<LhsScalar>::size : 1,
      RhsPacketSize = Vectorizable ? packet_traits<RhsScalar>::size : 1,
      ResPacketSize = Vectorizable ? packet_traits<ResScalar>::size : 1,
      
      NumberOfRegisters = EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS,
      nr = 4,
      mr = 2*ResPacketSize,
      WorkSpaceFactor = nr*RhsPacketSize,
  
      LhsProgress = ResPacketSize,
      RhsProgress = ResPacketSize
    };
  
    typedef typename packet_traits<LhsScalar>::type  _LhsPacket;
    typedef typename packet_traits<RhsScalar>::type  _RhsPacket;
    typedef typename packet_traits<ResScalar>::type  _ResPacket;
  
    typedef typename conditional<Vectorizable,_LhsPacket,LhsScalar>::type LhsPacket;
    typedef typename conditional<Vectorizable,_RhsPacket,RhsScalar>::type RhsPacket;
    typedef typename conditional<Vectorizable,_ResPacket,ResScalar>::type ResPacket;
  
    typedef ResPacket AccPacket;
  
    EIGEN_STRONG_INLINE void initAcc(AccPacket& p)
    {
      p = pset1<ResPacket>(ResScalar(0));
    }
  
    EIGEN_STRONG_INLINE void unpackRhs(DenseIndex n, const RhsScalar* rhs, RhsScalar* b)
    {
      for(DenseIndex k=0; k<n; k++)
        pstore1<RhsPacket>(&b[k*RhsPacketSize], rhs[k]);
    }
  
    EIGEN_STRONG_INLINE void loadRhs(const RhsScalar* b, RhsPacket& dest) const
    {
      dest = pload<RhsPacket>(b);
    }
  
    EIGEN_STRONG_INLINE void loadLhs(const LhsScalar* a, LhsPacket& dest) const
    {
      dest = ploaddup<LhsPacket>(a);
    }
  
    EIGEN_STRONG_INLINE void madd(const LhsPacket& a, const RhsPacket& b, AccPacket& c, RhsPacket& tmp) const
    {
      madd_impl(a, b, c, tmp, typename conditional<Vectorizable,true_type,false_type>::type());
    }
  
    EIGEN_STRONG_INLINE void madd_impl(const LhsPacket& a, const RhsPacket& b, AccPacket& c, RhsPacket& tmp, const true_type&) const
    {
      tmp = b; tmp.v = pmul(a,tmp.v); c = padd(c,tmp);
    }
  
    EIGEN_STRONG_INLINE void madd_impl(const LhsScalar& a, const RhsScalar& b, ResScalar& c, RhsScalar& /*tmp*/, const false_type&) const
    {
      c += a * b;
    }
  
    EIGEN_STRONG_INLINE void acc(const AccPacket& c, const ResPacket& alpha, ResPacket& r) const
    {
      r = cj.pmadd(alpha,c,r);
    }
  
  protected:
    conj_helper<ResPacket,ResPacket,false,ConjRhs> cj;
  };
  
  /* optimized GEneral packed Block * packed Panel product kernel
   *
   * Mixing type logic: C += A * B
   *  |  A  |  B  | comments
   *  |real |cplx | no vectorization yet, would require to pack A with duplication
   *  |cplx |real | easy vectorization
   */
  template<typename LhsScalar, typename RhsScalar, typename Index, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
  struct gebp_kernel
  {
    typedef gebp_traits<LhsScalar,RhsScalar,ConjugateLhs,ConjugateRhs> Traits;
    typedef typename Traits::ResScalar ResScalar;
    typedef typename Traits::LhsPacket LhsPacket;
    typedef typename Traits::RhsPacket RhsPacket;
    typedef typename Traits::ResPacket ResPacket;
    typedef typename Traits::AccPacket AccPacket;
  
    enum {
      Vectorizable  = Traits::Vectorizable,
      LhsProgress   = Traits::LhsProgress,
      RhsProgress   = Traits::RhsProgress,
      ResPacketSize = Traits::ResPacketSize
    };
  
    EIGEN_DONT_INLINE
    void operator()(ResScalar* res, Index resStride, const LhsScalar* blockA, const RhsScalar* blockB, Index rows, Index depth, Index cols, ResScalar alpha,
                    Index strideA=-1, Index strideB=-1, Index offsetA=0, Index offsetB=0, RhsScalar* unpackedB=0);
  };
  
  template<typename LhsScalar, typename RhsScalar, typename Index, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
  EIGEN_DONT_INLINE
  void gebp_kernel<LhsScalar,RhsScalar,Index,mr,nr,ConjugateLhs,ConjugateRhs>
    ::operator()(ResScalar* res, Index resStride, const LhsScalar* blockA, const RhsScalar* blockB, Index rows, Index depth, Index cols, ResScalar alpha,
                 Index strideA, Index strideB, Index offsetA, Index offsetB, RhsScalar* unpackedB)
    {
      Traits traits;
      
      if(strideA==-1) strideA = depth;
      if(strideB==-1) strideB = depth;
      conj_helper<LhsScalar,RhsScalar,ConjugateLhs,ConjugateRhs> cj;
  //     conj_helper<LhsPacket,RhsPacket,ConjugateLhs,ConjugateRhs> pcj;
      Index packet_cols = (cols/nr) * nr;
      const Index peeled_mc = (rows/mr)*mr;
      // FIXME:
      const Index peeled_mc2 = peeled_mc + (rows-peeled_mc >= LhsProgress ? LhsProgress : 0);
      const Index peeled_kc = (depth/4)*4;
  
      if(unpackedB==0)
        unpackedB = const_cast<RhsScalar*>(blockB - strideB * nr * RhsProgress);
  
      // loops on each micro vertical panel of rhs (depth x nr)
      for(Index j2=0; j2<packet_cols; j2+=nr)
      {
        traits.unpackRhs(depth*nr,&blockB[j2*strideB+offsetB*nr],unpackedB); 
  
        // loops on each largest micro horizontal panel of lhs (mr x depth)
        // => we select a mr x nr micro block of res which is entirely
        //    stored into mr/packet_size x nr registers.
        for(Index i=0; i<peeled_mc; i+=mr)
        {
          const LhsScalar* blA = &blockA[i*strideA+offsetA*mr];
          prefetch(&blA[0]);
  
          // gets res block as register
          AccPacket C0, C1, C2, C3, C4, C5, C6, C7;
                    traits.initAcc(C0);
                    traits.initAcc(C1);
          if(nr==4) traits.initAcc(C2);
          if(nr==4) traits.initAcc(C3);
                    traits.initAcc(C4);
                    traits.initAcc(C5);
          if(nr==4) traits.initAcc(C6);
          if(nr==4) traits.initAcc(C7);
  
          ResScalar* r0 = &res[(j2+0)*resStride + i];
          ResScalar* r1 = r0 + resStride;
          ResScalar* r2 = r1 + resStride;
          ResScalar* r3 = r2 + resStride;
  
          prefetch(r0+16);
          prefetch(r1+16);
          prefetch(r2+16);
          prefetch(r3+16);
  
          // performs "inner" product
          // TODO let's check wether the folowing peeled loop could not be
          //      optimized via optimal prefetching from one loop to the other
          const RhsScalar* blB = unpackedB;
          for(Index k=0; k<peeled_kc; k+=4)
          {
            if(nr==2)
            {
              LhsPacket A0, A1;
              RhsPacket B_0;
              RhsPacket T0;
              
  EIGEN_ASM_COMMENT("mybegin2");
              traits.loadLhs(&blA[0*LhsProgress], A0);
              traits.loadLhs(&blA[1*LhsProgress], A1);
              traits.loadRhs(&blB[0*RhsProgress], B_0);
              traits.madd(A0,B_0,C0,T0);
              traits.madd(A1,B_0,C4,B_0);
              traits.loadRhs(&blB[1*RhsProgress], B_0);
              traits.madd(A0,B_0,C1,T0);
              traits.madd(A1,B_0,C5,B_0);
  
              traits.loadLhs(&blA[2*LhsProgress], A0);
              traits.loadLhs(&blA[3*LhsProgress], A1);
              traits.loadRhs(&blB[2*RhsProgress], B_0);
              traits.madd(A0,B_0,C0,T0);
              traits.madd(A1,B_0,C4,B_0);
              traits.loadRhs(&blB[3*RhsProgress], B_0);
              traits.madd(A0,B_0,C1,T0);
              traits.madd(A1,B_0,C5,B_0);
  
              traits.loadLhs(&blA[4*LhsProgress], A0);
              traits.loadLhs(&blA[5*LhsProgress], A1);
              traits.loadRhs(&blB[4*RhsProgress], B_0);
              traits.madd(A0,B_0,C0,T0);
              traits.madd(A1,B_0,C4,B_0);
              traits.loadRhs(&blB[5*RhsProgress], B_0);
              traits.madd(A0,B_0,C1,T0);
              traits.madd(A1,B_0,C5,B_0);
  
              traits.loadLhs(&blA[6*LhsProgress], A0);
              traits.loadLhs(&blA[7*LhsProgress], A1);
              traits.loadRhs(&blB[6*RhsProgress], B_0);
              traits.madd(A0,B_0,C0,T0);
              traits.madd(A1,B_0,C4,B_0);
              traits.loadRhs(&blB[7*RhsProgress], B_0);
              traits.madd(A0,B_0,C1,T0);
              traits.madd(A1,B_0,C5,B_0);
  EIGEN_ASM_COMMENT("myend");
            }
            else
            {
  EIGEN_ASM_COMMENT("mybegin4");
              LhsPacket A0, A1;
              RhsPacket B_0, B1, B2, B3;
              RhsPacket T0;
              
              traits.loadLhs(&blA[0*LhsProgress], A0);
              traits.loadLhs(&blA[1*LhsProgress], A1);
              traits.loadRhs(&blB[0*RhsProgress], B_0);
              traits.loadRhs(&blB[1*RhsProgress], B1);
  
              traits.madd(A0,B_0,C0,T0);
              traits.loadRhs(&blB[2*RhsProgress], B2);
              traits.madd(A1,B_0,C4,B_0);
              traits.loadRhs(&blB[3*RhsProgress], B3);
              traits.loadRhs(&blB[4*RhsProgress], B_0);
              traits.madd(A0,B1,C1,T0);
              traits.madd(A1,B1,C5,B1);
              traits.loadRhs(&blB[5*RhsProgress], B1);
              traits.madd(A0,B2,C2,T0);
              traits.madd(A1,B2,C6,B2);
              traits.loadRhs(&blB[6*RhsProgress], B2);
              traits.madd(A0,B3,C3,T0);
              traits.loadLhs(&blA[2*LhsProgress], A0);
              traits.madd(A1,B3,C7,B3);
              traits.loadLhs(&blA[3*LhsProgress], A1);
              traits.loadRhs(&blB[7*RhsProgress], B3);
              traits.madd(A0,B_0,C0,T0);
              traits.madd(A1,B_0,C4,B_0);
              traits.loadRhs(&blB[8*RhsProgress], B_0);
              traits.madd(A0,B1,C1,T0);
              traits.madd(A1,B1,C5,B1);
              traits.loadRhs(&blB[9*RhsProgress], B1);
              traits.madd(A0,B2,C2,T0);
              traits.madd(A1,B2,C6,B2);
              traits.loadRhs(&blB[10*RhsProgress], B2);
              traits.madd(A0,B3,C3,T0);
              traits.loadLhs(&blA[4*LhsProgress], A0);
              traits.madd(A1,B3,C7,B3);
              traits.loadLhs(&blA[5*LhsProgress], A1);
              traits.loadRhs(&blB[11*RhsProgress], B3);
  
              traits.madd(A0,B_0,C0,T0);
              traits.madd(A1,B_0,C4,B_0);
              traits.loadRhs(&blB[12*RhsProgress], B_0);
              traits.madd(A0,B1,C1,T0);
              traits.madd(A1,B1,C5,B1);
              traits.loadRhs(&blB[13*RhsProgress], B1);
              traits.madd(A0,B2,C2,T0);
              traits.madd(A1,B2,C6,B2);
              traits.loadRhs(&blB[14*RhsProgress], B2);
              traits.madd(A0,B3,C3,T0);
              traits.loadLhs(&blA[6*LhsProgress], A0);
              traits.madd(A1,B3,C7,B3);
              traits.loadLhs(&blA[7*LhsProgress], A1);
              traits.loadRhs(&blB[15*RhsProgress], B3);
              traits.madd(A0,B_0,C0,T0);
              traits.madd(A1,B_0,C4,B_0);
              traits.madd(A0,B1,C1,T0);
              traits.madd(A1,B1,C5,B1);
              traits.madd(A0,B2,C2,T0);
              traits.madd(A1,B2,C6,B2);
              traits.madd(A0,B3,C3,T0);
              traits.madd(A1,B3,C7,B3);
            }
  
            blB += 4*nr*RhsProgress;
            blA += 4*mr;
          }
          // process remaining peeled loop
          for(Index k=peeled_kc; k<depth; k++)
          {
            if(nr==2)
            {
              LhsPacket A0, A1;
              RhsPacket B_0;
              RhsPacket T0;
  
              traits.loadLhs(&blA[0*LhsProgress], A0);
              traits.loadLhs(&blA[1*LhsProgress], A1);
              traits.loadRhs(&blB[0*RhsProgress], B_0);
              traits.madd(A0,B_0,C0,T0);
              traits.madd(A1,B_0,C4,B_0);
              traits.loadRhs(&blB[1*RhsProgress], B_0);
              traits.madd(A0,B_0,C1,T0);
              traits.madd(A1,B_0,C5,B_0);
            }
            else
            {
              LhsPacket A0, A1;
              RhsPacket B_0, B1, B2, B3;
              RhsPacket T0;
  
              traits.loadLhs(&blA[0*LhsProgress], A0);
              traits.loadLhs(&blA[1*LhsProgress], A1);
              traits.loadRhs(&blB[0*RhsProgress], B_0);
              traits.loadRhs(&blB[1*RhsProgress], B1);
  
              traits.madd(A0,B_0,C0,T0);
              traits.loadRhs(&blB[2*RhsProgress], B2);
              traits.madd(A1,B_0,C4,B_0);
              traits.loadRhs(&blB[3*RhsProgress], B3);
              traits.madd(A0,B1,C1,T0);
              traits.madd(A1,B1,C5,B1);
              traits.madd(A0,B2,C2,T0);
              traits.madd(A1,B2,C6,B2);
              traits.madd(A0,B3,C3,T0);
              traits.madd(A1,B3,C7,B3);
            }
  
            blB += nr*RhsProgress;
            blA += mr;
          }
  
          if(nr==4)
          {
            ResPacket R0, R1, R2, R3, R4, R5, R6;
            ResPacket alphav = pset1<ResPacket>(alpha);
  
            R0 = ploadu<ResPacket>(r0);
            R1 = ploadu<ResPacket>(r1);
            R2 = ploadu<ResPacket>(r2);
            R3 = ploadu<ResPacket>(r3);
            R4 = ploadu<ResPacket>(r0 + ResPacketSize);
            R5 = ploadu<ResPacket>(r1 + ResPacketSize);
            R6 = ploadu<ResPacket>(r2 + ResPacketSize);
            traits.acc(C0, alphav, R0);
            pstoreu(r0, R0);
            R0 = ploadu<ResPacket>(r3 + ResPacketSize);
  
            traits.acc(C1, alphav, R1);
            traits.acc(C2, alphav, R2);
            traits.acc(C3, alphav, R3);
            traits.acc(C4, alphav, R4);
            traits.acc(C5, alphav, R5);
            traits.acc(C6, alphav, R6);
            traits.acc(C7, alphav, R0);
            
            pstoreu(r1, R1);
            pstoreu(r2, R2);
            pstoreu(r3, R3);
            pstoreu(r0 + ResPacketSize, R4);
            pstoreu(r1 + ResPacketSize, R5);
            pstoreu(r2 + ResPacketSize, R6);
            pstoreu(r3 + ResPacketSize, R0);
          }
          else
          {
            ResPacket R0, R1, R4;
            ResPacket alphav = pset1<ResPacket>(alpha);
  
            R0 = ploadu<ResPacket>(r0);
            R1 = ploadu<ResPacket>(r1);
            R4 = ploadu<ResPacket>(r0 + ResPacketSize);
            traits.acc(C0, alphav, R0);
            pstoreu(r0, R0);
            R0 = ploadu<ResPacket>(r1 + ResPacketSize);
            traits.acc(C1, alphav, R1);
            traits.acc(C4, alphav, R4);
            traits.acc(C5, alphav, R0);
            pstoreu(r1, R1);
            pstoreu(r0 + ResPacketSize, R4);
            pstoreu(r1 + ResPacketSize, R0);
          }
          
        }
        
        if(rows-peeled_mc>=LhsProgress)
        {
          Index i = peeled_mc;
          const LhsScalar* blA = &blockA[i*strideA+offsetA*LhsProgress];
          prefetch(&blA[0]);
  
          // gets res block as register
          AccPacket C0, C1, C2, C3;
                    traits.initAcc(C0);
                    traits.initAcc(C1);
          if(nr==4) traits.initAcc(C2);
          if(nr==4) traits.initAcc(C3);
  
          // performs "inner" product
          const RhsScalar* blB = unpackedB;
          for(Index k=0; k<peeled_kc; k+=4)
          {
            if(nr==2)
            {
              LhsPacket A0;
              RhsPacket B_0, B1;
  
              traits.loadLhs(&blA[0*LhsProgress], A0);
              traits.loadRhs(&blB[0*RhsProgress], B_0);
              traits.loadRhs(&blB[1*RhsProgress], B1);
              traits.madd(A0,B_0,C0,B_0);
              traits.loadRhs(&blB[2*RhsProgress], B_0);
              traits.madd(A0,B1,C1,B1);
              traits.loadLhs(&blA[1*LhsProgress], A0);
              traits.loadRhs(&blB[3*RhsProgress], B1);
              traits.madd(A0,B_0,C0,B_0);
              traits.loadRhs(&blB[4*RhsProgress], B_0);
              traits.madd(A0,B1,C1,B1);
              traits.loadLhs(&blA[2*LhsProgress], A0);
              traits.loadRhs(&blB[5*RhsProgress], B1);
              traits.madd(A0,B_0,C0,B_0);
              traits.loadRhs(&blB[6*RhsProgress], B_0);
              traits.madd(A0,B1,C1,B1);
              traits.loadLhs(&blA[3*LhsProgress], A0);
              traits.loadRhs(&blB[7*RhsProgress], B1);
              traits.madd(A0,B_0,C0,B_0);
              traits.madd(A0,B1,C1,B1);
            }
            else
            {
              LhsPacket A0;
              RhsPacket B_0, B1, B2, B3;
  
              traits.loadLhs(&blA[0*LhsProgress], A0);
              traits.loadRhs(&blB[0*RhsProgress], B_0);
              traits.loadRhs(&blB[1*RhsProgress], B1);
  
              traits.madd(A0,B_0,C0,B_0);
              traits.loadRhs(&blB[2*RhsProgress], B2);
              traits.loadRhs(&blB[3*RhsProgress], B3);
              traits.loadRhs(&blB[4*RhsProgress], B_0);
              traits.madd(A0,B1,C1,B1);
              traits.loadRhs(&blB[5*RhsProgress], B1);
              traits.madd(A0,B2,C2,B2);
              traits.loadRhs(&blB[6*RhsProgress], B2);
              traits.madd(A0,B3,C3,B3);
              traits.loadLhs(&blA[1*LhsProgress], A0);
              traits.loadRhs(&blB[7*RhsProgress], B3);
              traits.madd(A0,B_0,C0,B_0);
              traits.loadRhs(&blB[8*RhsProgress], B_0);
              traits.madd(A0,B1,C1,B1);
              traits.loadRhs(&blB[9*RhsProgress], B1);
              traits.madd(A0,B2,C2,B2);
              traits.loadRhs(&blB[10*RhsProgress], B2);
              traits.madd(A0,B3,C3,B3);
              traits.loadLhs(&blA[2*LhsProgress], A0);
              traits.loadRhs(&blB[11*RhsProgress], B3);
  
              traits.madd(A0,B_0,C0,B_0);
              traits.loadRhs(&blB[12*RhsProgress], B_0);
              traits.madd(A0,B1,C1,B1);
              traits.loadRhs(&blB[13*RhsProgress], B1);
              traits.madd(A0,B2,C2,B2);
              traits.loadRhs(&blB[14*RhsProgress], B2);
              traits.madd(A0,B3,C3,B3);
  
              traits.loadLhs(&blA[3*LhsProgress], A0);
              traits.loadRhs(&blB[15*RhsProgress], B3);
              traits.madd(A0,B_0,C0,B_0);
              traits.madd(A0,B1,C1,B1);
              traits.madd(A0,B2,C2,B2);
              traits.madd(A0,B3,C3,B3);
            }
  
            blB += nr*4*RhsProgress;
            blA += 4*LhsProgress;
          }
          // process remaining peeled loop
          for(Index k=peeled_kc; k<depth; k++)
          {
            if(nr==2)
            {
              LhsPacket A0;
              RhsPacket B_0, B1;
  
              traits.loadLhs(&blA[0*LhsProgress], A0);
              traits.loadRhs(&blB[0*RhsProgress], B_0);
              traits.loadRhs(&blB[1*RhsProgress], B1);
              traits.madd(A0,B_0,C0,B_0);
              traits.madd(A0,B1,C1,B1);
            }
            else
            {
              LhsPacket A0;
              RhsPacket B_0, B1, B2, B3;
  
              traits.loadLhs(&blA[0*LhsProgress], A0);
              traits.loadRhs(&blB[0*RhsProgress], B_0);
              traits.loadRhs(&blB[1*RhsProgress], B1);
              traits.loadRhs(&blB[2*RhsProgress], B2);
              traits.loadRhs(&blB[3*RhsProgress], B3);
  
              traits.madd(A0,B_0,C0,B_0);
              traits.madd(A0,B1,C1,B1);
              traits.madd(A0,B2,C2,B2);
              traits.madd(A0,B3,C3,B3);
            }
  
            blB += nr*RhsProgress;
            blA += LhsProgress;
          }
  
          ResPacket R0, R1, R2, R3;
          ResPacket alphav = pset1<ResPacket>(alpha);
  
          ResScalar* r0 = &res[(j2+0)*resStride + i];
          ResScalar* r1 = r0 + resStride;
          ResScalar* r2 = r1 + resStride;
          ResScalar* r3 = r2 + resStride;
  
                    R0 = ploadu<ResPacket>(r0);
                    R1 = ploadu<ResPacket>(r1);
          if(nr==4) R2 = ploadu<ResPacket>(r2);
          if(nr==4) R3 = ploadu<ResPacket>(r3);
  
                    traits.acc(C0, alphav, R0);
                    traits.acc(C1, alphav, R1);
          if(nr==4) traits.acc(C2, alphav, R2);
          if(nr==4) traits.acc(C3, alphav, R3);
  
                    pstoreu(r0, R0);
                    pstoreu(r1, R1);
          if(nr==4) pstoreu(r2, R2);
          if(nr==4) pstoreu(r3, R3);
        }
        for(Index i=peeled_mc2; i<rows; i++)
        {
          const LhsScalar* blA = &blockA[i*strideA+offsetA];
          prefetch(&blA[0]);
  
          // gets a 1 x nr res block as registers
          ResScalar C0(0), C1(0), C2(0), C3(0);
          // TODO directly use blockB ???
          const RhsScalar* blB = &blockB[j2*strideB+offsetB*nr];
          for(Index k=0; k<depth; k++)
          {
            if(nr==2)
            {
              LhsScalar A0;
              RhsScalar B_0, B1;
  
              A0 = blA[k];
              B_0 = blB[0];
              B1 = blB[1];
              MADD(cj,A0,B_0,C0,B_0);
              MADD(cj,A0,B1,C1,B1);
            }
            else
            {
              LhsScalar A0;
              RhsScalar B_0, B1, B2, B3;
  
              A0 = blA[k];
              B_0 = blB[0];
              B1 = blB[1];
              B2 = blB[2];
              B3 = blB[3];
  
              MADD(cj,A0,B_0,C0,B_0);
              MADD(cj,A0,B1,C1,B1);
              MADD(cj,A0,B2,C2,B2);
              MADD(cj,A0,B3,C3,B3);
            }
  
            blB += nr;
          }
                    res[(j2+0)*resStride + i] += alpha*C0;
                    res[(j2+1)*resStride + i] += alpha*C1;
          if(nr==4) res[(j2+2)*resStride + i] += alpha*C2;
          if(nr==4) res[(j2+3)*resStride + i] += alpha*C3;
        }
      }
      // process remaining rhs/res columns one at a time
      // => do the same but with nr==1
      for(Index j2=packet_cols; j2<cols; j2++)
      {
        // unpack B
        traits.unpackRhs(depth, &blockB[j2*strideB+offsetB], unpackedB);
  
        for(Index i=0; i<peeled_mc; i+=mr)
        {
          const LhsScalar* blA = &blockA[i*strideA+offsetA*mr];
          prefetch(&blA[0]);
  
          // TODO move the res loads to the stores
  
          // get res block as registers
          AccPacket C0, C4;
          traits.initAcc(C0);
          traits.initAcc(C4);
  
          const RhsScalar* blB = unpackedB;
          for(Index k=0; k<depth; k++)
          {
            LhsPacket A0, A1;
            RhsPacket B_0;
            RhsPacket T0;
  
            traits.loadLhs(&blA[0*LhsProgress], A0);
            traits.loadLhs(&blA[1*LhsProgress], A1);
            traits.loadRhs(&blB[0*RhsProgress], B_0);
            traits.madd(A0,B_0,C0,T0);
            traits.madd(A1,B_0,C4,B_0);
  
            blB += RhsProgress;
            blA += 2*LhsProgress;
          }
          ResPacket R0, R4;
          ResPacket alphav = pset1<ResPacket>(alpha);
  
          ResScalar* r0 = &res[(j2+0)*resStride + i];
  
          R0 = ploadu<ResPacket>(r0);
          R4 = ploadu<ResPacket>(r0+ResPacketSize);
  
          traits.acc(C0, alphav, R0);
          traits.acc(C4, alphav, R4);
  
          pstoreu(r0,               R0);
          pstoreu(r0+ResPacketSize, R4);
        }
        if(rows-peeled_mc>=LhsProgress)
        {
          Index i = peeled_mc;
          const LhsScalar* blA = &blockA[i*strideA+offsetA*LhsProgress];
          prefetch(&blA[0]);
  
          AccPacket C0;
          traits.initAcc(C0);
  
          const RhsScalar* blB = unpackedB;
          for(Index k=0; k<depth; k++)
          {
            LhsPacket A0;
            RhsPacket B_0;
            traits.loadLhs(blA, A0);
            traits.loadRhs(blB, B_0);
            traits.madd(A0, B_0, C0, B_0);
            blB += RhsProgress;
            blA += LhsProgress;
          }
  
          ResPacket alphav = pset1<ResPacket>(alpha);
          ResPacket R0 = ploadu<ResPacket>(&res[(j2+0)*resStride + i]);
          traits.acc(C0, alphav, R0);
          pstoreu(&res[(j2+0)*resStride + i], R0);
        }
        for(Index i=peeled_mc2; i<rows; i++)
        {
          const LhsScalar* blA = &blockA[i*strideA+offsetA];
          prefetch(&blA[0]);
  
          // gets a 1 x 1 res block as registers
          ResScalar C0(0);
          // FIXME directly use blockB ??
          const RhsScalar* blB = &blockB[j2*strideB+offsetB];
          for(Index k=0; k<depth; k++)
          {
            LhsScalar A0 = blA[k];
            RhsScalar B_0 = blB[k];
            MADD(cj, A0, B_0, C0, B_0);
          }
          res[(j2+0)*resStride + i] += alpha*C0;
        }
      }
    }
  
  
  #undef CJMADD
  
  // pack a block of the lhs
  // The traversal is as follow (mr==4):
  //   0  4  8 12 ...
  //   1  5  9 13 ...
  //   2  6 10 14 ...
  //   3  7 11 15 ...
  //
  //  16 20 24 28 ...
  //  17 21 25 29 ...
  //  18 22 26 30 ...
  //  19 23 27 31 ...
  //
  //  32 33 34 35 ...
  //  36 36 38 39 ...
  template<typename Scalar, typename Index, int Pack1, int Pack2, int StorageOrder, bool Conjugate, bool PanelMode>
  struct gemm_pack_lhs
  {
    EIGEN_DONT_INLINE void operator()(Scalar* blockA, const Scalar* EIGEN_RESTRICT _lhs, Index lhsStride, Index depth, Index rows, Index stride=0, Index offset=0);
  };
  
  template<typename Scalar, typename Index, int Pack1, int Pack2, int StorageOrder, bool Conjugate, bool PanelMode>
  EIGEN_DONT_INLINE void gemm_pack_lhs<Scalar, Index, Pack1, Pack2, StorageOrder, Conjugate, PanelMode>
    ::operator()(Scalar* blockA, const Scalar* EIGEN_RESTRICT _lhs, Index lhsStride, Index depth, Index rows, Index stride, Index offset)
  {
    typedef typename packet_traits<Scalar>::type Packet;
    enum { PacketSize = packet_traits<Scalar>::size };
  
    EIGEN_ASM_COMMENT("EIGEN PRODUCT PACK LHS");
    eigen_assert(((!PanelMode) && stride==0 && offset==0) || (PanelMode && stride>=depth && offset<=stride));
    eigen_assert( (StorageOrder==RowMajor) || ((Pack1%PacketSize)==0 && Pack1<=4*PacketSize) );
    conj_if<NumTraits<Scalar>::IsComplex && Conjugate> cj;
    const_blas_data_mapper<Scalar, Index, StorageOrder> lhs(_lhs,lhsStride);
    Index count = 0;
    Index peeled_mc = (rows/Pack1)*Pack1;
    for(Index i=0; i<peeled_mc; i+=Pack1)
    {
      if(PanelMode) count += Pack1 * offset;
  
      if(StorageOrder==ColMajor)
      {
        for(Index k=0; k<depth; k++)
        {
          Packet A, B, C, D;
          if(Pack1>=1*PacketSize) A = ploadu<Packet>(&lhs(i+0*PacketSize, k));
          if(Pack1>=2*PacketSize) B = ploadu<Packet>(&lhs(i+1*PacketSize, k));
          if(Pack1>=3*PacketSize) C = ploadu<Packet>(&lhs(i+2*PacketSize, k));
          if(Pack1>=4*PacketSize) D = ploadu<Packet>(&lhs(i+3*PacketSize, k));
          if(Pack1>=1*PacketSize) { pstore(blockA+count, cj.pconj(A)); count+=PacketSize; }
          if(Pack1>=2*PacketSize) { pstore(blockA+count, cj.pconj(B)); count+=PacketSize; }
          if(Pack1>=3*PacketSize) { pstore(blockA+count, cj.pconj(C)); count+=PacketSize; }
          if(Pack1>=4*PacketSize) { pstore(blockA+count, cj.pconj(D)); count+=PacketSize; }
        }
      }
      else
      {
        for(Index k=0; k<depth; k++)
        {
          // TODO add a vectorized transpose here
          Index w=0;
          for(; w<Pack1-3; w+=4)
          {
            Scalar a(cj(lhs(i+w+0, k))),
                    b(cj(lhs(i+w+1, k))),
                    c(cj(lhs(i+w+2, k))),
                    d(cj(lhs(i+w+3, k)));
            blockA[count++] = a;
            blockA[count++] = b;
            blockA[count++] = c;
            blockA[count++] = d;
          }
          if(Pack1%4)
            for(;w<Pack1;++w)
              blockA[count++] = cj(lhs(i+w, k));
        }
      }
      if(PanelMode) count += Pack1 * (stride-offset-depth);
    }
    if(rows-peeled_mc>=Pack2)
    {
      if(PanelMode) count += Pack2*offset;
      for(Index k=0; k<depth; k++)
        for(Index w=0; w<Pack2; w++)
          blockA[count++] = cj(lhs(peeled_mc+w, k));
      if(PanelMode) count += Pack2 * (stride-offset-depth);
      peeled_mc += Pack2;
    }
    for(Index i=peeled_mc; i<rows; i++)
    {
      if(PanelMode) count += offset;
      for(Index k=0; k<depth; k++)
        blockA[count++] = cj(lhs(i, k));
      if(PanelMode) count += (stride-offset-depth);
    }
  }
  
  // copy a complete panel of the rhs
  // this version is optimized for column major matrices
  // The traversal order is as follow: (nr==4):
  //  0  1  2  3   12 13 14 15   24 27
  //  4  5  6  7   16 17 18 19   25 28
  //  8  9 10 11   20 21 22 23   26 29
  //  .  .  .  .    .  .  .  .    .  .
  template<typename Scalar, typename Index, int nr, bool Conjugate, bool PanelMode>
  struct gemm_pack_rhs<Scalar, Index, nr, ColMajor, Conjugate, PanelMode>
  {
    typedef typename packet_traits<Scalar>::type Packet;
    enum { PacketSize = packet_traits<Scalar>::size };
    EIGEN_DONT_INLINE void operator()(Scalar* blockB, const Scalar* rhs, Index rhsStride, Index depth, Index cols, Index stride=0, Index offset=0);
  };
  
  template<typename Scalar, typename Index, int nr, bool Conjugate, bool PanelMode>
  EIGEN_DONT_INLINE void gemm_pack_rhs<Scalar, Index, nr, ColMajor, Conjugate, PanelMode>
    ::operator()(Scalar* blockB, const Scalar* rhs, Index rhsStride, Index depth, Index cols, Index stride, Index offset)
  {
    EIGEN_ASM_COMMENT("EIGEN PRODUCT PACK RHS COLMAJOR");
    eigen_assert(((!PanelMode) && stride==0 && offset==0) || (PanelMode && stride>=depth && offset<=stride));
    conj_if<NumTraits<Scalar>::IsComplex && Conjugate> cj;
    Index packet_cols = (cols/nr) * nr;
    Index count = 0;
    for(Index j2=0; j2<packet_cols; j2+=nr)
    {
      // skip what we have before
      if(PanelMode) count += nr * offset;
      const Scalar* b0 = &rhs[(j2+0)*rhsStride];
      const Scalar* b1 = &rhs[(j2+1)*rhsStride];
      const Scalar* b2 = &rhs[(j2+2)*rhsStride];
      const Scalar* b3 = &rhs[(j2+3)*rhsStride];
      for(Index k=0; k<depth; k++)
      {
                  blockB[count+0] = cj(b0[k]);
                  blockB[count+1] = cj(b1[k]);
        if(nr==4) blockB[count+2] = cj(b2[k]);
        if(nr==4) blockB[count+3] = cj(b3[k]);
        count += nr;
      }
      // skip what we have after
      if(PanelMode) count += nr * (stride-offset-depth);
    }
  
    // copy the remaining columns one at a time (nr==1)
    for(Index j2=packet_cols; j2<cols; ++j2)
    {
      if(PanelMode) count += offset;
      const Scalar* b0 = &rhs[(j2+0)*rhsStride];
      for(Index k=0; k<depth; k++)
      {
        blockB[count] = cj(b0[k]);
        count += 1;
      }
      if(PanelMode) count += (stride-offset-depth);
    }
  }
  
  // this version is optimized for row major matrices
  template<typename Scalar, typename Index, int nr, bool Conjugate, bool PanelMode>
  struct gemm_pack_rhs<Scalar, Index, nr, RowMajor, Conjugate, PanelMode>
  {
    enum { PacketSize = packet_traits<Scalar>::size };
    EIGEN_DONT_INLINE void operator()(Scalar* blockB, const Scalar* rhs, Index rhsStride, Index depth, Index cols, Index stride=0, Index offset=0);
  };
  
  template<typename Scalar, typename Index, int nr, bool Conjugate, bool PanelMode>
  EIGEN_DONT_INLINE void gemm_pack_rhs<Scalar, Index, nr, RowMajor, Conjugate, PanelMode>
    ::operator()(Scalar* blockB, const Scalar* rhs, Index rhsStride, Index depth, Index cols, Index stride, Index offset)
  {
    EIGEN_ASM_COMMENT("EIGEN PRODUCT PACK RHS ROWMAJOR");
    eigen_assert(((!PanelMode) && stride==0 && offset==0) || (PanelMode && stride>=depth && offset<=stride));
    conj_if<NumTraits<Scalar>::IsComplex && Conjugate> cj;
    Index packet_cols = (cols/nr) * nr;
    Index count = 0;
    for(Index j2=0; j2<packet_cols; j2+=nr)
    {
      // skip what we have before
      if(PanelMode) count += nr * offset;
      for(Index k=0; k<depth; k++)
      {
        const Scalar* b0 = &rhs[k*rhsStride + j2];
                  blockB[count+0] = cj(b0[0]);
                  blockB[count+1] = cj(b0[1]);
        if(nr==4) blockB[count+2] = cj(b0[2]);
        if(nr==4) blockB[count+3] = cj(b0[3]);
        count += nr;
      }
      // skip what we have after
      if(PanelMode) count += nr * (stride-offset-depth);
    }
    // copy the remaining columns one at a time (nr==1)
    for(Index j2=packet_cols; j2<cols; ++j2)
    {
      if(PanelMode) count += offset;
      const Scalar* b0 = &rhs[j2];
      for(Index k=0; k<depth; k++)
      {
        blockB[count] = cj(b0[k*rhsStride]);
        count += 1;
      }
      if(PanelMode) count += stride-offset-depth;
    }
  }
  
  } // end namespace internal
  
  /** \returns the currently set level 1 cpu cache size (in bytes) used to estimate the ideal blocking size parameters.
    * \sa setCpuCacheSize */
  inline std::ptrdiff_t l1CacheSize()
  {
    std::ptrdiff_t l1, l2;
    internal::manage_caching_sizes(GetAction, &l1, &l2);
    return l1;
  }
  
  /** \returns the currently set level 2 cpu cache size (in bytes) used to estimate the ideal blocking size parameters.
    * \sa setCpuCacheSize */
  inline std::ptrdiff_t l2CacheSize()
  {
    std::ptrdiff_t l1, l2;
    internal::manage_caching_sizes(GetAction, &l1, &l2);
    return l2;
  }
  
  /** Set the cpu L1 and L2 cache sizes (in bytes).
    * These values are use to adjust the size of the blocks
    * for the algorithms working per blocks.
    *
    * \sa computeProductBlockingSizes */
  inline void setCpuCacheSizes(std::ptrdiff_t l1, std::ptrdiff_t l2)
  {
    internal::manage_caching_sizes(SetAction, &l1, &l2);
  }
  
  } // end namespace Eigen
  
  #endif // EIGEN_GENERAL_BLOCK_PANEL_H
  