* Draft of a eigenvalues solver

(does not support complex and does not re-use the QR decomposition)

* Rewrite the cache friendly product to have only one instance per scalar type !
  This significantly speeds up compilation time and reduces executable size.
  The current drawback is that some trivial expressions might be
  evaluated like conjugate or negate.

* Renamed "cache optimal" to "cache friendly"

* Added the ability to directly access matrix data of some expressions via:
  - the stride()/_stride() methods
  - DirectAccessBit flag (replace ReferencableBit)

Eigen/src/Core/Block.h

@@ -71,7 +71,7 @@ struct ei_traits<Block<MatrixType, BlockRows, BlockCols> >
                       || (ColsAtCompileTime != Dynamic && MatrixType::ColsAtCompileTime == Dynamic))
                       ? ~LargeBit
                       : ~(unsigned int)0,
-    Flags = MatrixType::Flags & (DefaultLostFlagMask | VectorizableBit | ReferencableBit) & FlagsMaskLargeBit,
+    Flags = MatrixType::Flags & (DefaultLostFlagMask | VectorizableBit | DirectAccessBit) & FlagsMaskLargeBit,
     CoeffReadCost = MatrixType::CoeffReadCost
   };
 };
@@ -132,6 +132,8 @@ template<typename MatrixType, int BlockRows, int BlockCols> class Block
     int _rows() const { return m_blockRows.value(); }
     int _cols() const { return m_blockCols.value(); }
 
+    int _stride(void) const { return m_matrix.stride(); }
+
     Scalar& _coeffRef(int row, int col)
     {
       return m_matrix.const_cast_derived()

Eigen/src/Core/CacheFriendlyProduct.h

@@ -0,0 +1,353 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_CACHE_FRIENDLY_PRODUCT_H
+#define EIGEN_CACHE_FRIENDLY_PRODUCT_H
+
+template<typename Scalar>
+static void ei_cache_friendly_product(
+  int _rows, int _cols, int depth,
+  bool _lhsRowMajor, const Scalar* _lhs, int _lhsStride,
+  bool _rhsRowMajor, const Scalar* _rhs, int _rhsStride,
+  bool resRowMajor, Scalar* res, int resStride)
+{
+  const Scalar* __restrict__ lhs;
+  const Scalar* __restrict__ rhs;
+  int lhsStride, rhsStride, rows, cols;
+  bool lhsRowMajor;
+
+  if (resRowMajor)
+  {
+    lhs = _rhs;
+    rhs = _lhs;
+    lhsStride = _rhsStride;
+    rhsStride = _lhsStride;
+    cols = _rows;
+    rows = _cols;
+    lhsRowMajor = _rhsRowMajor;
+    ei_assert(_lhsRowMajor);
+  }
+  else
+  {
+    lhs = _lhs;
+    rhs = _rhs;
+    lhsStride = _lhsStride;
+    rhsStride = _rhsStride;
+    rows = _rows;
+    cols = _cols;
+    lhsRowMajor = _lhsRowMajor;
+    ei_assert(!_rhsRowMajor);
+  }
+
+  typedef typename ei_packet_traits<Scalar>::type PacketType;
+
+  enum {
+    PacketSize = sizeof(PacketType)/sizeof(Scalar),
+    #if (defined __i386__)
+    // i386 architecture provides only 8 xmm registers,
+    // so let's reduce the max number of rows processed at once.
+    MaxBlockRows = 4,
+    MaxBlockRows_ClampingMask = 0xFFFFFC,
+    #else
+    MaxBlockRows = 8,
+    MaxBlockRows_ClampingMask = 0xFFFFF8,
+    #endif
+    // maximal size of the blocks fitted in L2 cache
+    MaxL2BlockSize = EIGEN_TUNE_FOR_L2_CACHE_SIZE / sizeof(Scalar)
+  };
+
+
+  //const bool rhsIsAligned = (PacketSize==1) || (((rhsStride%PacketSize) == 0) && (size_t(rhs)%16==0));
+  const bool resIsAligned = (PacketSize==1) || (((resStride%PacketSize) == 0) && (size_t(res)%16==0));
+
+  const int remainingSize = depth % PacketSize;
+  const int size = depth - remainingSize; // third dimension of the product clamped to packet boundaries
+  const int l2BlockRows = MaxL2BlockSize > rows ? rows : MaxL2BlockSize;
+  const int l2BlockCols = MaxL2BlockSize > cols ? cols : MaxL2BlockSize;
+  const int l2BlockSize = MaxL2BlockSize > size ? size : MaxL2BlockSize;
+  Scalar* __restrict__ block   = (Scalar*)alloca(sizeof(Scalar)*l2BlockRows*size);
+  Scalar* __restrict__ rhsCopy = (Scalar*)alloca(sizeof(Scalar)*l2BlockSize);
+
+  // loops on each L2 cache friendly blocks of the result
+  for(int l2i=0; l2i<rows; l2i+=l2BlockRows)
+  {
+    const int l2blockRowEnd = std::min(l2i+l2BlockRows, rows);
+    const int l2blockRowEndBW = l2blockRowEnd & MaxBlockRows_ClampingMask;    // end of the rows aligned to bw
+    const int l2blockRemainingRows = l2blockRowEnd - l2blockRowEndBW;         // number of remaining rows
+    //const int l2blockRowEndBWPlusOne = l2blockRowEndBW + (l2blockRemainingRows?0:MaxBlockRows);
+
+    // build a cache friendly blocky matrix
+    int count = 0;
+
+    // copy l2blocksize rows of m_lhs to blocks of ps x bw
+    asm("#eigen begin buildblocks");
+    for(int l2k=0; l2k<size; l2k+=l2BlockSize)
+    {
+      const int l2blockSizeEnd = std::min(l2k+l2BlockSize, size);
+
+      for (int i = l2i; i<l2blockRowEndBW/*PlusOne*/; i+=MaxBlockRows)
+      {
+        // TODO merge the if l2blockRemainingRows
+//         const int blockRows = std::min(i+MaxBlockRows, rows) - i;
+
+        for (int k=l2k; k<l2blockSizeEnd; k+=PacketSize)
+        {
+          // TODO write these loops using meta unrolling
+          // negligible for large matrices but useful for small ones
+          if (lhsRowMajor)
+          {
+            for (int w=0; w<MaxBlockRows; ++w)
+              for (int s=0; s<PacketSize; ++s)
+                block[count++] = lhs[(i+w)*lhsStride + (k+s)];
+          }
+          else
+          {
+            for (int w=0; w<MaxBlockRows; ++w)
+              for (int s=0; s<PacketSize; ++s)
+                block[count++] = lhs[(i+w) + (k+s)*lhsStride];
+          }
+        }
+      }
+      if (l2blockRemainingRows>0)
+      {
+        for (int k=l2k; k<l2blockSizeEnd; k+=PacketSize)
+        {
+          if (lhsRowMajor)
+          {
+            for (int w=0; w<l2blockRemainingRows; ++w)
+              for (int s=0; s<PacketSize; ++s)
+                block[count++] = lhs[(l2blockRowEndBW+w)*lhsStride + (k+s)];
+          }
+          else
+          {
+            for (int w=0; w<l2blockRemainingRows; ++w)
+              for (int s=0; s<PacketSize; ++s)
+                block[count++] = lhs[(l2blockRowEndBW+w) + (k+s)*lhsStride];
+          }
+        }
+      }
+    }
+    asm("#eigen end buildblocks");
+
+    for(int l2j=0; l2j<cols; l2j+=l2BlockCols)
+    {
+      int l2blockColEnd = std::min(l2j+l2BlockCols, cols);
+
+      for(int l2k=0; l2k<size; l2k+=l2BlockSize)
+      {
+        // acumulate bw rows of lhs time a single column of rhs to a bw x 1 block of res
+        int l2blockSizeEnd = std::min(l2k+l2BlockSize, size);
+
+        // for each bw x 1 result's block
+        for(int l1i=l2i; l1i<l2blockRowEndBW; l1i+=MaxBlockRows)
+        {
+          for(int l1j=l2j; l1j<l2blockColEnd; l1j+=1)
+          {
+            int offsetblock = l2k * (l2blockRowEnd-l2i) + (l1i-l2i)*(l2blockSizeEnd-l2k) - l2k*MaxBlockRows;
+            const Scalar* __restrict__ localB = &block[offsetblock];
+
+            const Scalar* __restrict__ rhsColumn = &(rhs[l1j*rhsStride]);
+
+            // copy unaligned rhs data
+            // YES it seems to be faster to copy some part of rhs multiple times
+            // to aligned memory rather than using unligned load.
+            // Moreover this avoids a "if" in the most nested loop :)
+            if (PacketSize>1 && size_t(rhsColumn)%16)
+            {
+              int count = 0;
+              for (int k = l2k; k<l2blockSizeEnd; ++k)
+              {
+                rhsCopy[count++] = rhsColumn[k];
+              }
+              rhsColumn = &(rhsCopy[-l2k]);
+            }
+
+            PacketType dst[MaxBlockRows];
+            dst[0] = ei_pset1(Scalar(0.));
+            dst[1] = dst[0];
+            dst[2] = dst[0];
+            dst[3] = dst[0];
+            if (MaxBlockRows==8)
+            {
+              dst[4] = dst[0];
+              dst[5] = dst[0];
+              dst[6] = dst[0];
+              dst[7] = dst[0];
+            }
+
+            PacketType tmp;
+
+            asm("#eigen begincore");
+            for(int k=l2k; k<l2blockSizeEnd; k+=PacketSize)
+            {
+              tmp = ei_pload(&rhsColumn[k]);
+
+              dst[0] = ei_pmadd(tmp, ei_pload(&(localB[k*MaxBlockRows             ])), dst[0]);
+              dst[1] = ei_pmadd(tmp, ei_pload(&(localB[k*MaxBlockRows+  PacketSize])), dst[1]);
+              dst[2] = ei_pmadd(tmp, ei_pload(&(localB[k*MaxBlockRows+2*PacketSize])), dst[2]);
+              dst[3] = ei_pmadd(tmp, ei_pload(&(localB[k*MaxBlockRows+3*PacketSize])), dst[3]);
+              if (MaxBlockRows==8)
+              {
+                dst[4] = ei_pmadd(tmp, ei_pload(&(localB[k*MaxBlockRows+4*PacketSize])), dst[4]);
+                dst[5] = ei_pmadd(tmp, ei_pload(&(localB[k*MaxBlockRows+5*PacketSize])), dst[5]);
+                dst[6] = ei_pmadd(tmp, ei_pload(&(localB[k*MaxBlockRows+6*PacketSize])), dst[6]);
+                dst[7] = ei_pmadd(tmp, ei_pload(&(localB[k*MaxBlockRows+7*PacketSize])), dst[7]);
+              }
+            }
+
+            Scalar* __restrict__ localRes = &(res[l1i + l1j*resStride]);
+
+            if (PacketSize>1 && resIsAligned)
+            {
+              ei_pstore(&(localRes[0]), ei_padd(ei_pload(&(localRes[0])), ei_preduxp(dst)));
+              if (PacketSize==2)
+                ei_pstore(&(localRes[2]), ei_padd(ei_pload(&(localRes[2])), ei_preduxp(&(dst[2]))));
+              if (MaxBlockRows==8)
+              {
+                ei_pstore(&(localRes[4]), ei_padd(ei_pload(&(localRes[4])), ei_preduxp(&(dst[4]))));
+                if (PacketSize==2)
+                  ei_pstore(&(localRes[6]), ei_padd(ei_pload(&(localRes[6])), ei_preduxp(&(dst[6]))));
+              }
+            }
+            else
+            {
+              localRes[0] += ei_predux(dst[0]);
+              localRes[1] += ei_predux(dst[1]);
+              localRes[2] += ei_predux(dst[2]);
+              localRes[3] += ei_predux(dst[3]);
+              if (MaxBlockRows==8)
+              {
+                localRes[4] += ei_predux(dst[4]);
+                localRes[5] += ei_predux(dst[5]);
+                localRes[6] += ei_predux(dst[6]);
+                localRes[7] += ei_predux(dst[7]);
+              }
+            }
+            asm("#eigen endcore");
+          }
+        }
+        if (l2blockRemainingRows>0)
+        {
+          int offsetblock = l2k * (l2blockRowEnd-l2i) + (l2blockRowEndBW-l2i)*(l2blockSizeEnd-l2k) - l2k*l2blockRemainingRows;
+          const Scalar* localB = &block[offsetblock];
+
+          asm("#eigen begin dynkernel");
+          for(int l1j=l2j; l1j<l2blockColEnd; l1j+=1)
+          {
+            const Scalar* __restrict__ rhsColumn = &(rhs[l1j*rhsStride]);
+
+            // copy unaligned rhs data
+            if (PacketSize>1 && size_t(rhsColumn)%16)
+            {
+              int count = 0;
+              for (int k = l2k; k<l2blockSizeEnd; ++k)
+              {
+                rhsCopy[count++] = rhsColumn[k];
+              }
+              rhsColumn = &(rhsCopy[-l2k]);
+            }
+
+            PacketType dst[MaxBlockRows];
+            dst[0] = ei_pset1(Scalar(0.));
+            dst[1] = dst[0];
+            dst[2] = dst[0];
+            dst[3] = dst[0];
+            if (MaxBlockRows>4)
+            {
+              dst[4] = dst[0];
+              dst[5] = dst[0];
+              dst[6] = dst[0];
+              dst[7] = dst[0];
+            }
+
+            // let's declare a few other temporary registers
+            PacketType tmp;
+
+            for(int k=l2k; k<l2blockSizeEnd; k+=PacketSize)
+            {
+              tmp = ei_pload(&rhsColumn[k]);
+
+                                           dst[0] = ei_pmadd(tmp, ei_pload(&(localB[k*l2blockRemainingRows             ])), dst[0]);
+              if (l2blockRemainingRows>=2) dst[1] = ei_pmadd(tmp, ei_pload(&(localB[k*l2blockRemainingRows+  PacketSize])), dst[1]);
+              if (l2blockRemainingRows>=3) dst[2] = ei_pmadd(tmp, ei_pload(&(localB[k*l2blockRemainingRows+2*PacketSize])), dst[2]);
+              if (l2blockRemainingRows>=4) dst[3] = ei_pmadd(tmp, ei_pload(&(localB[k*l2blockRemainingRows+3*PacketSize])), dst[3]);
+              if (MaxBlockRows>4)
+              {
+                if (l2blockRemainingRows>=5) dst[4] = ei_pmadd(tmp, ei_pload(&(localB[k*l2blockRemainingRows+4*PacketSize])), dst[4]);
+                if (l2blockRemainingRows>=6) dst[5] = ei_pmadd(tmp, ei_pload(&(localB[k*l2blockRemainingRows+5*PacketSize])), dst[5]);
+                if (l2blockRemainingRows>=7) dst[6] = ei_pmadd(tmp, ei_pload(&(localB[k*l2blockRemainingRows+6*PacketSize])), dst[6]);
+                if (l2blockRemainingRows>=8) dst[7] = ei_pmadd(tmp, ei_pload(&(localB[k*l2blockRemainingRows+7*PacketSize])), dst[7]);
+              }
+            }
+
+            Scalar* __restrict__ localRes = &(res[l2blockRowEndBW + l1j*resStride]);
+
+            // process the remaining rows once at a time
+                                         localRes[0] += ei_predux(dst[0]);
+            if (l2blockRemainingRows>=2) localRes[1] += ei_predux(dst[1]);
+            if (l2blockRemainingRows>=3) localRes[2] += ei_predux(dst[2]);
+            if (l2blockRemainingRows>=4) localRes[3] += ei_predux(dst[3]);
+            if (MaxBlockRows>4)
+            {
+              if (l2blockRemainingRows>=5) localRes[4] += ei_predux(dst[4]);
+              if (l2blockRemainingRows>=6) localRes[5] += ei_predux(dst[5]);
+              if (l2blockRemainingRows>=7) localRes[6] += ei_predux(dst[6]);
+              if (l2blockRemainingRows>=8) localRes[7] += ei_predux(dst[7]);
+            }
+
+            asm("#eigen end dynkernel");
+          }
+        }
+      }
+    }
+  }
+  if (PacketSize>1 && remainingSize)
+  {
+    if (lhsRowMajor)
+    {
+      for (int j=0; j<cols; ++j)
+        for (int i=0; i<rows; ++i)
+        {
+          Scalar tmp = lhs[i*lhsStride+size] * rhs[j*rhsStride+size];
+          for (int k=1; k<remainingSize; ++k)
+            tmp += lhs[i*lhsStride+size+k] * rhs[j*rhsStride+size+k];
+          res[i+j*resStride] += tmp;
+        }
+    }
+    else
+    {
+      for (int j=0; j<cols; ++j)
+        for (int i=0; i<rows; ++i)
+        {
+          Scalar tmp = lhs[i+size*lhsStride] * rhs[j*rhsStride+size];
+          for (int k=1; k<remainingSize; ++k)
+            tmp += lhs[i+(size+k)*lhsStride] * rhs[j*rhsStride+size+k];
+          res[i+j*resStride] += tmp;
+        }
+    }
+  }
+}
+
+
+#endif // EIGEN_CACHE_FRIENDLY_PRODUCT_H

Eigen/src/Core/Map.h

@@ -47,7 +47,7 @@ struct ei_traits<Map<MatrixType> >
     ColsAtCompileTime = MatrixType::ColsAtCompileTime,
     MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
     MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
-    Flags = MatrixType::Flags & (DefaultLostFlagMask | ReferencableBit),
+    Flags = MatrixType::Flags & (DefaultLostFlagMask | DirectAccessBit),
     CoeffReadCost = NumTraits<Scalar>::ReadCost
   };
 };

Eigen/src/Core/MathFunctions.h

@@ -46,7 +46,7 @@ inline int ei_log(int)  { ei_assert(false); return 0; }
 inline int ei_sin(int)  { ei_assert(false); return 0; }
 inline int ei_cos(int)  { ei_assert(false); return 0; }
 
-#if EIGEN_GNUC_AT_LEAST(4,3)
+#if EIGEN_GNUC_AT_LEAST(4,2)
 inline int ei_pow(int x, int y) { return int(std::pow(double(x), y)); }
 #else
 inline int ei_pow(int x, int y) { return std::pow(x, y); }

Eigen/src/Core/Matrix.h

@@ -100,6 +100,14 @@ class Matrix : public MatrixBase<Matrix<_Scalar, _Rows, _Cols, _Flags, _MaxRows,
     int _rows() const { return m_storage.rows(); }
     int _cols() const { return m_storage.cols(); }
 
+    int _stride(void) const
+    {
+      if(Flags & RowMajorBit)
+        return m_storage.cols();
+      else
+        return m_storage.rows();
+    }
+
     const Scalar& _coeff(int row, int col) const
     {
       if(Flags & RowMajorBit)

Eigen/src/Core/MatrixBase.h

@@ -185,7 +185,7 @@ template<typename Derived> class MatrixBase
 
     /** Overloaded for optimal product evaluation */
     template<typename Derived1, typename Derived2>
-    Derived& lazyAssign(const Product<Derived1,Derived2,CacheOptimalProduct>& product);
+    Derived& lazyAssign(const Product<Derived1,Derived2,CacheFriendlyProduct>& product);
 
     CommaInitializer operator<< (const Scalar& s);
 
@@ -419,6 +419,13 @@ template<typename Derived> class MatrixBase
 
     const Lazy<Derived> lazy() const;
     const Temporary<Derived> temporary() const;
+
+    /** \returns number of elements to skip to pass from one row (resp. column) to another
+      * for a row-major (resp. column-major) matrix.
+      * Combined with coeffRef() and the compile times flags, it allows a direct access to the data
+      * of the underlying matrix.
+      */
+    int stride(void) const { return derived()._stride(); }
     //@}
 
     /// \name Coefficient-wise operations

Eigen/src/Core/Product.h

@@ -60,6 +60,12 @@ struct ei_product_unroller<Index, 0, Lhs, Rhs>
   static void run(int, int, const Lhs&, const Rhs&, typename Lhs::Scalar&) {}
 };
 
+template<typename Lhs, typename Rhs>
+struct ei_product_unroller<0, Dynamic, Lhs, Rhs>
+{
+  static void run(int, int, const Lhs&, const Rhs&, typename Lhs::Scalar&) {}
+};
+
 template<bool RowMajor, int Index, int Size, typename Lhs, typename Rhs, typename PacketScalar>
 struct ei_packet_product_unroller;
 
@@ -113,6 +119,12 @@ struct ei_packet_product_unroller<false, Index, Dynamic, Lhs, Rhs, PacketScalar>
   static void run(int, int, const Lhs&, const Rhs&, PacketScalar&) {}
 };
 
+template<typename Lhs, typename Rhs, typename PacketScalar>
+struct ei_packet_product_unroller<false, 0, Dynamic, Lhs, Rhs, PacketScalar>
+{
+  static void run(int, int, const Lhs&, const Rhs&, PacketScalar&) {}
+};
+
 template<typename Product, bool RowMajor = true> struct ProductPacketCoeffImpl {
   inline static typename Product::PacketScalar execute(const Product& product, int row, int col)
   { return product._packetCoeffRowMajor(row,col); }
@@ -142,7 +154,7 @@ template<typename Lhs, typename Rhs> struct ei_product_eval_mode
   enum{ value =  Lhs::MaxRowsAtCompileTime >= EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
               && Rhs::MaxColsAtCompileTime >= EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
               && (!( (Lhs::Flags&RowMajorBit) && ((Rhs::Flags&RowMajorBit) ^ RowMajorBit)))
-              ? CacheOptimalProduct : NormalProduct };
+              ? CacheFriendlyProduct : NormalProduct };
 };
 
 template<typename Lhs, typename Rhs, int EvalMode>
@@ -166,7 +178,7 @@ struct ei_traits<Product<Lhs, Rhs, EvalMode> >
     _LhsVectorizable = (!(LhsFlags & RowMajorBit)) && (LhsFlags & VectorizableBit) && (RowsAtCompileTime % ei_packet_traits<Scalar>::size == 0),
     _Vectorizable = (_LhsVectorizable || _RhsVectorizable) ? 1 : 0,
     _RowMajor = (RhsFlags & RowMajorBit)
-              && (EvalMode==(int)CacheOptimalProduct ? (int)LhsFlags & RowMajorBit : (!_LhsVectorizable)),
+              && (EvalMode==(int)CacheFriendlyProduct ? (int)LhsFlags & RowMajorBit : (!_LhsVectorizable)),
     _LostBits = DefaultLostFlagMask & ~(
                 (_RowMajor ? 0 : RowMajorBit)
               | ((RowsAtCompileTime == Dynamic || ColsAtCompileTime == Dynamic) ? 0 : LargeBit)),
@@ -312,7 +324,7 @@ MatrixBase<Derived>::operator*=(const MatrixBase<OtherDerived> &other)
 
 template<typename Derived>
 template<typename Lhs, typename Rhs>
-Derived& MatrixBase<Derived>::lazyAssign(const Product<Lhs,Rhs,CacheOptimalProduct>& product)
+Derived& MatrixBase<Derived>::lazyAssign(const Product<Lhs,Rhs,CacheFriendlyProduct>& product)
 {
   product.template _cacheOptimalEval<Derived, Aligned>(derived(),
     #ifdef EIGEN_VECTORIZE

Eigen/src/Core/ProductWIP.h

@@ -26,9 +26,7 @@
 #ifndef EIGEN_PRODUCT_H
 #define EIGEN_PRODUCT_H
 
-#ifndef EIGEN_VECTORIZE
-#error you must enable vectorization to try this experimental product implementation
-#endif
+#include "CacheFriendlyProduct.h"
 
 template<int Index, int Size, typename Lhs, typename Rhs>
 struct ei_product_unroller
@@ -145,7 +143,7 @@ template<typename Lhs, typename Rhs> struct ei_product_eval_mode
 {
   enum{ value =  Lhs::MaxRowsAtCompileTime >= EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
               && Rhs::MaxColsAtCompileTime >= EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
-              ? CacheOptimalProduct : NormalProduct };
+              ? CacheFriendlyProduct : NormalProduct };
 };
 
 template<typename T> class ei_product_eval_to_column_major
@@ -173,7 +171,22 @@ template<typename T, int n=1> struct ei_product_nested_rhs
     typename ei_meta_if<
          (ei_traits<T>::Flags & EvalBeforeNestingBit)
       || (ei_traits<T>::Flags & RowMajorBit)
-      || (!(ei_traits<T>::Flags & ReferencableBit))
+      || (!(ei_traits<T>::Flags & DirectAccessBit))
+      || (n+1) * NumTraits<typename ei_traits<T>::Scalar>::ReadCost < (n-1) * T::CoeffReadCost,
+      typename ei_product_eval_to_column_major<T>::type,
+      const T&
+    >::ret
+  >::ret type;
+};
+
+template<typename T, int n=1> struct ei_product_nested_lhs
+{
+  typedef typename ei_meta_if<
+    ei_is_temporary<T>::ret && !(ei_traits<T>::Flags & RowMajorBit),
+    T,
+    typename ei_meta_if<
+         (ei_traits<T>::Flags & EvalBeforeNestingBit)
+      || (!(ei_traits<T>::Flags & DirectAccessBit))
       || (n+1) * NumTraits<typename ei_traits<T>::Scalar>::ReadCost < (n-1) * T::CoeffReadCost,
       typename ei_product_eval_to_column_major<T>::type,
       const T&
@@ -187,9 +200,12 @@ struct ei_traits<Product<Lhs, Rhs, EvalMode> >
   typedef typename Lhs::Scalar Scalar;
   // the cache friendly product evals lhs once only
   // FIXME what to do if we chose to dynamically call the normal product from the cache friendly one for small matrices ?
-  typedef typename ei_nested<Lhs, EvalMode==CacheOptimalProduct ? 0 : Rhs::ColsAtCompileTime>::type LhsNested;
+  typedef typename ei_meta_if<EvalMode==CacheFriendlyProduct,
+      typename ei_product_nested_lhs<Rhs,0>::type,
+      typename ei_nested<Lhs,Rhs::ColsAtCompileTime>::type>::ret LhsNested;
+
   // NOTE that rhs must be ColumnMajor, so we might need a special nested type calculation
-  typedef typename ei_meta_if<EvalMode==CacheOptimalProduct,
+  typedef typename ei_meta_if<EvalMode==CacheFriendlyProduct,
       typename ei_product_nested_rhs<Rhs,Lhs::RowsAtCompileTime>::type,
       typename ei_nested<Rhs,Lhs::RowsAtCompileTime>::type>::ret RhsNested;
   typedef typename ei_unref<LhsNested>::type _LhsNested;
@@ -209,7 +225,7 @@ struct ei_traits<Product<Lhs, Rhs, EvalMode> >
     _LhsVectorizable = (!(LhsFlags & RowMajorBit)) && (LhsFlags & VectorizableBit) && (RowsAtCompileTime % ei_packet_traits<Scalar>::size == 0),
     _Vectorizable = (_LhsVectorizable || _RhsVectorizable) ? 0 : 0,
     _RowMajor = (RhsFlags & RowMajorBit)
-              && (EvalMode==(int)CacheOptimalProduct ? (int)LhsFlags & RowMajorBit : (!_LhsVectorizable)),
+              && (EvalMode==(int)CacheFriendlyProduct ? (int)LhsFlags & RowMajorBit : (!_LhsVectorizable)),
     _LostBits = DefaultLostFlagMask & ~(
                 (_RowMajor ? 0 : RowMajorBit)
               | ((RowsAtCompileTime == Dynamic || ColsAtCompileTime == Dynamic) ? 0 : LargeBit)),
@@ -241,19 +257,7 @@ template<typename Lhs, typename Rhs, int EvalMode> class Product : ei_no_assignm
     typedef typename ei_traits<Product>::_RhsNested _RhsNested;
 
     enum {
-      PacketSize = ei_packet_traits<Scalar>::size,
-      #if (defined __i386__)
-      // i386 architectures provides only 8 xmmm register,
-      // so let's reduce the max number of rows processed at once.
-      // NOTE that so far the maximal supported value is 8.
-      MaxBlockRows = 4,
-      MaxBlockRows_ClampingMask = 0xFFFFFC,
-      #else
-      MaxBlockRows = 8,
-      MaxBlockRows_ClampingMask = 0xFFFFF8,
-      #endif
-      // maximal size of the blocks fitted in L2 cache
-      MaxL2BlockSize = EIGEN_TUNE_FOR_L2_CACHE_SIZE / sizeof(Scalar)
+      PacketSize = ei_packet_traits<Scalar>::size
     };
 
     Product(const Lhs& lhs, const Rhs& rhs)
@@ -327,14 +331,8 @@ template<typename Lhs, typename Rhs, int EvalMode> class Product : ei_no_assignm
     }
 
     /** \internal */
-    template<typename DestDerived, int RhsAlignment, int ResAlignment>
-    void _cacheFriendlyEvalImpl(DestDerived& res) const __attribute__ ((noinline));
-
-    /** \internal */
-    template<typename DestDerived, int RhsAlignment, int ResAlignment, int BlockRows>
-    void _cacheFriendlyEvalKernel(DestDerived& res,
-      int l2i, int l2j, int l2k, int l1i,
-      int l2blockRowEnd, int l2blockColEnd, int l2blockSizeEnd, const Scalar* block) const EIGEN_DONT_INLINE;
+    template<typename DestDerived, int RhsAlignment>
+    void _cacheFriendlyEvalImpl(DestDerived& res) const EIGEN_DONT_INLINE;
 
   protected:
     const LhsNested m_lhs;
@@ -370,7 +368,7 @@ MatrixBase<Derived>::operator*=(const MatrixBase<OtherDerived> &other)
 
 template<typename Derived>
 template<typename Lhs, typename Rhs>
-Derived& MatrixBase<Derived>::lazyAssign(const Product<Lhs,Rhs,CacheOptimalProduct>& product)
+Derived& MatrixBase<Derived>::lazyAssign(const Product<Lhs,Rhs,CacheFriendlyProduct>& product)
 {
   product._cacheFriendlyEval(derived());
   return derived();
@@ -380,326 +378,16 @@ template<typename Lhs, typename Rhs, int EvalMode>
 template<typename DestDerived>
 void Product<Lhs,Rhs,EvalMode>::_cacheFriendlyEval(DestDerived& res) const
 {
-  const bool rhsIsAligned = (m_lhs.cols()%PacketSize == 0);
-  const bool resIsAligned = ((_rows()%PacketSize) == 0);
-
-  if (rhsIsAligned && resIsAligned)
-    _cacheFriendlyEvalImpl<DestDerived, Aligned, Aligned>(res);
-  else if (rhsIsAligned && (!resIsAligned))
-    _cacheFriendlyEvalImpl<DestDerived, Aligned, UnAligned>(res);
-  else if ((!rhsIsAligned) && resIsAligned)
-    _cacheFriendlyEvalImpl<DestDerived, UnAligned, Aligned>(res);
-  else
-    _cacheFriendlyEvalImpl<DestDerived, UnAligned, UnAligned>(res);
-
-}
-
-template<typename Lhs, typename Rhs, int EvalMode>
-template<typename DestDerived, int RhsAlignment, int ResAlignment, int BlockRows>
-void Product<Lhs,Rhs,EvalMode>::_cacheFriendlyEvalKernel(DestDerived& res,
-  int l2i, int l2j, int l2k, int l1i,
-  int l2blockRowEnd, int l2blockColEnd, int l2blockSizeEnd, const Scalar* block) const
-{
-  asm("#eigen begin kernel");
-
-  ei_internal_assert(BlockRows<=8);
-
-  // NOTE: sounds like we cannot rely on meta-unrolling to access dst[I] without enforcing GCC
-  // to create the dst's elements in memory, hence killing the performance.
-
-  for(int l1j=l2j; l1j<l2blockColEnd; l1j+=1)
-  {
-    int offsetblock = l2k * (l2blockRowEnd-l2i) + (l1i-l2i)*(l2blockSizeEnd-l2k) - l2k*BlockRows;
-    const Scalar* localB = &block[offsetblock];
-
-//     int l1jsize = l1j * m_lhs.cols(); //TODO find a better way to optimize address computation ?
-    Scalar* rhsColumn = &(m_rhs.const_cast_derived().coeffRef(0, l1j));
-
-    // don't worry, dst is a set of registers
-    PacketScalar dst[BlockRows];
-    dst[0] = ei_pset1(Scalar(0.));
-    switch(BlockRows)
-    {
-    case 8: dst[7] = dst[0];
-    case 7: dst[6] = dst[0];
-    case 6: dst[5] = dst[0];
-    case 5: dst[4] = dst[0];
-    case 4: dst[3] = dst[0];
-    case 3: dst[2] = dst[0];
-    case 2: dst[1] = dst[0];
-    default: break;
-    }
-
-    // let's declare a few other temporary registers
-    PacketScalar tmp, tmp1;
-
-    // unaligned loads are expensive, therefore let's preload the next element in advance
-    if (RhsAlignment==UnAligned)
-      //tmp1 = ei_ploadu(&m_rhs.data()[l1jsize+l2k]);
-      tmp1 = ei_ploadu(&rhsColumn[l2k]);
-
-    for(int k=l2k; k<l2blockSizeEnd; k+=PacketSize)
-    {
-      // FIXME if we don't cache l1j*m_lhs.cols() then the performance are poor,
-      // let's directly access to the data
-      //PacketScalar tmp = m_rhs.template packetCoeff<Aligned>(k, l1j);
-      if (RhsAlignment==Aligned)
-      {
-        //tmp = ei_pload(&m_rhs.data()[l1jsize + k]);
-        tmp = ei_pload(&rhsColumn[k]);
-      }
-      else
-      {
-        tmp = tmp1;
-        if (k+PacketSize<l2blockSizeEnd)
-          //tmp1 = ei_ploadu(&m_rhs.data()[l1jsize + k+PacketSize]);
-          tmp1 = ei_ploadu(&rhsColumn[k+PacketSize]);
-      }
-
-                        dst[0] = ei_pmadd(tmp, ei_pload(&(localB[k*BlockRows             ])), dst[0]);
-      if (BlockRows>=2) dst[1] = ei_pmadd(tmp, ei_pload(&(localB[k*BlockRows+  PacketSize])), dst[1]);
-      if (BlockRows>=3) dst[2] = ei_pmadd(tmp, ei_pload(&(localB[k*BlockRows+2*PacketSize])), dst[2]);
-      if (BlockRows>=4) dst[3] = ei_pmadd(tmp, ei_pload(&(localB[k*BlockRows+3*PacketSize])), dst[3]);
-      if (BlockRows>=5) dst[4] = ei_pmadd(tmp, ei_pload(&(localB[k*BlockRows+4*PacketSize])), dst[4]);
-      if (BlockRows>=6) dst[5] = ei_pmadd(tmp, ei_pload(&(localB[k*BlockRows+5*PacketSize])), dst[5]);
-      if (BlockRows>=7) dst[6] = ei_pmadd(tmp, ei_pload(&(localB[k*BlockRows+6*PacketSize])), dst[6]);
-      if (BlockRows>=8) dst[7] = ei_pmadd(tmp, ei_pload(&(localB[k*BlockRows+7*PacketSize])), dst[7]);
-    }
-
-    enum {
-      // Number of rows we can reduce per packet
-      PacketRows = (ResAlignment==Aligned && PacketSize>1) ? (BlockRows / PacketSize) : 0,
-      // First row index from which we have to to do redux once at a time
-      RemainingStart = PacketSize * PacketRows
-    };
-
-    // we have up to 4 packets (for doubles: 8 rows / 2)
-    if (PacketRows>=1)
-      res.template writePacketCoeff<Aligned>(l1i, l1j,
-        ei_padd(res.template packetCoeff<Aligned>(l1i, l1j), ei_preduxp(&(dst[0]))));
-    if (PacketRows>=2)
-      res.template writePacketCoeff<Aligned>(l1i+PacketSize, l1j,
-        ei_padd(res.template packetCoeff<Aligned>(l1i+PacketSize, l1j), ei_preduxp(&(dst[PacketSize]))));
-    if (PacketRows>=3)
-      res.template writePacketCoeff<Aligned>(l1i+2*PacketSize, l1j,
-        ei_padd(res.template packetCoeff<Aligned>(l1i+2*PacketSize, l1j), ei_preduxp(&(dst[2*PacketSize]))));
-    if (PacketRows>=4)
-      res.template writePacketCoeff<Aligned>(l1i+3*PacketSize, l1j,
-        ei_padd(res.template packetCoeff<Aligned>(l1i+3*PacketSize, l1j), ei_preduxp(&(dst[3*PacketSize]))));
-
-    // process the remaining rows one at a time
-    if (RemainingStart<=0 && BlockRows>=1) res.coeffRef(l1i+0, l1j) += ei_predux(dst[0]);
-    if (RemainingStart<=1 && BlockRows>=2) res.coeffRef(l1i+1, l1j) += ei_predux(dst[1]);
-    if (RemainingStart<=2 && BlockRows>=3) res.coeffRef(l1i+2, l1j) += ei_predux(dst[2]);
-    if (RemainingStart<=3 && BlockRows>=4) res.coeffRef(l1i+3, l1j) += ei_predux(dst[3]);
-    if (RemainingStart<=4 && BlockRows>=5) res.coeffRef(l1i+4, l1j) += ei_predux(dst[4]);
-    if (RemainingStart<=5 && BlockRows>=6) res.coeffRef(l1i+5, l1j) += ei_predux(dst[5]);
-    if (RemainingStart<=6 && BlockRows>=7) res.coeffRef(l1i+6, l1j) += ei_predux(dst[6]);
-    if (RemainingStart<=7 && BlockRows>=8) res.coeffRef(l1i+7, l1j) += ei_predux(dst[7]);
-
-    asm("#eigen end kernel");
-  }
-}
-
-template<typename Lhs, typename Rhs, int EvalMode>
-template<typename DestDerived, int RhsAlignment, int ResAlignment>
-void Product<Lhs,Rhs,EvalMode>::_cacheFriendlyEvalImpl(DestDerived& res) const
-{
-  // FIXME find a way to optimize: (an_xpr) + (a * b)
-  // then we don't need to clear res and avoid and additional mat-mat sum
   #ifndef EIGEN_WIP_PRODUCT_DIRTY
-//   std::cout << "wip product\n";
   res.setZero();
   #endif
 
-  const int rows = _rows();
-  const int cols = _cols();
-  const int remainingSize = m_lhs.cols()%PacketSize;
-  const int size = m_lhs.cols() - remainingSize; // third dimension of the product clamped to packet boundaries
-  const int l2BlockRows = MaxL2BlockSize > _rows() ? _rows() : MaxL2BlockSize;
-  const int l2BlockCols = MaxL2BlockSize > _cols() ? _cols() : MaxL2BlockSize;
-  const int l2BlockSize = MaxL2BlockSize > size    ? size    : MaxL2BlockSize;
-  //Scalar* __restrict__ block = new Scalar[l2blocksize*size];;
-  Scalar* __restrict__ block = (Scalar*)alloca(sizeof(Scalar)*l2BlockRows*size);
-
-  // loops on each L2 cache friendly blocks of the result
-  for(int l2i=0; l2i<_rows(); l2i+=l2BlockRows)
-  {
-    const int l2blockRowEnd = std::min(l2i+l2BlockRows, rows);
-    const int l2blockRowEndBW = l2blockRowEnd & MaxBlockRows_ClampingMask;    // end of the rows aligned to bw
-    const int l2blockRemainingRows = l2blockRowEnd - l2blockRowEndBW;         // number of remaining rows
-
-    // build a cache friendly block
-    int count = 0;
-
-    // copy l2blocksize rows of m_lhs to blocks of ps x bw
-    for(int l2k=0; l2k<size; l2k+=l2BlockSize)
-    {
-      const int l2blockSizeEnd = std::min(l2k+l2BlockSize, size);
-
-      for (int i = l2i; i<l2blockRowEndBW; i+=MaxBlockRows)
-      {
-        for (int k=l2k; k<l2blockSizeEnd; k+=PacketSize)
-        {
-          // TODO write these two loops using meta unrolling
-          // negligible for large matrices but useful for small ones
-          for (int w=0; w<MaxBlockRows; ++w)
-            for (int s=0; s<PacketSize; ++s)
-              block[count++] = m_lhs.coeff(i+w,k+s);
-        }
-      }
-      if (l2blockRemainingRows>0)
-      {
-        for (int k=l2k; k<l2blockSizeEnd; k+=PacketSize)
-        {
-          for (int w=0; w<l2blockRemainingRows; ++w)
-            for (int s=0; s<PacketSize; ++s)
-              block[count++] = m_lhs.coeff(l2blockRowEndBW+w,k+s);
-        }
-      }
-    }
-
-    for(int l2j=0; l2j<cols; l2j+=l2BlockCols)
-    {
-      int l2blockColEnd = std::min(l2j+l2BlockCols, cols);
-
-      for(int l2k=0; l2k<size; l2k+=l2BlockSize)
-      {
-        // acumulate a bw rows of lhs time a single column of rhs to a bw x 1 block of res
-        int l2blockSizeEnd = std::min(l2k+l2BlockSize, size);
-
-        // for each bw x 1 result's block
-        for(int l1i=l2i; l1i<l2blockRowEndBW; l1i+=MaxBlockRows)
-        {
-            _cacheFriendlyEvalKernel<DestDerived, RhsAlignment, ResAlignment, MaxBlockRows>(
-              res, l2i, l2j, l2k, l1i, l2blockRowEnd, l2blockColEnd, l2blockSizeEnd, block);
-#if 0
-          for(int l1j=l2j; l1j<l2blockColEnd; l1j+=1)
-          {
-            int offsetblock = l2k * (l2blockRowEnd-l2i) + (l1i-l2i)*(l2blockSizeEnd-l2k) - l2k*MaxBlockRows;
-            const Scalar* localB = &block[offsetblock];
-
-            int l1jsize = l1j * m_lhs.cols(); //TODO find a better way to optimize address computation ?
-
-            PacketScalar dst[bw];
-            dst[0] = ei_pset1(Scalar(0.));
-            dst[1] = dst[0];
-            dst[2] = dst[0];
-            dst[3] = dst[0];
-            if (MaxBlockRows==8)
-            {
-              dst[4] = dst[0];
-              dst[5] = dst[0];
-              dst[6] = dst[0];
-              dst[7] = dst[0];
-            }
-            PacketScalar b0, b1, tmp;
-            // TODO in unaligned mode, preload the next element
-//             PacketScalar tmp1 = _mm_load_ps(&m_rhs.derived().data()[l1jsize+l2k]);
-            asm("#eigen begincore");
-            for(int k=l2k; k<l2blockSizeEnd; k+=PacketSize)
-            {
-//               PacketScalar tmp = m_rhs.template packetCoeff<Aligned>(k, l1j);
-              // TODO make this branching compile time (costly for doubles)
-              if (rhsIsAligned)
-                tmp = ei_pload(&m_rhs.derived().data()[l1jsize + k]);
-              else
-                tmp = ei_ploadu(&m_rhs.derived().data()[l1jsize + k]);
-
-              b0 = ei_pload(&(localB[k*bw]));
-              b1 = ei_pload(&(localB[k*bw+ps]));
-              dst[0] = ei_pmadd(tmp, b0, dst[0]);
-              b0 = ei_pload(&(localB[k*bw+2*ps]));
-              dst[1] = ei_pmadd(tmp, b1, dst[1]);
-              b1 = ei_pload(&(localB[k*bw+3*ps]));
-              dst[2] = ei_pmadd(tmp, b0, dst[2]);
-              if (MaxBlockRows==8)
-                b0 = ei_pload(&(localB[k*bw+4*ps]));
-              dst[3] = ei_pmadd(tmp, b1, dst[3]);
-              if (MaxBlockRows==8)
-              {
-                b1 = ei_pload(&(localB[k*bw+5*ps]));
-                dst[4] = ei_pmadd(tmp, b0, dst[4]);
-                b0 = ei_pload(&(localB[k*bw+6*ps]));
-                dst[5] = ei_pmadd(tmp, b1, dst[5]);
-                b1 = ei_pload(&(localB[k*bw+7*ps]));
-                dst[6] = ei_pmadd(tmp, b0, dst[6]);
-                dst[7] = ei_pmadd(tmp, b1, dst[7]);
-              }
-            }
-
-//             if (resIsAligned)
-            {
-              res.template writePacketCoeff<Aligned>(l1i, l1j, ei_padd(res.template packetCoeff<Aligned>(l1i, l1j), ei_preduxp(dst)));
-              if (PacketSize==2)
-                res.template writePacketCoeff<Aligned>(l1i+2,l1j, ei_padd(res.template packetCoeff<Aligned>(l1i+2,l1j), ei_preduxp(&(dst[2]))));
-              if (MaxBlockRows==8)
-              {
-                res.template writePacketCoeff<Aligned>(l1i+4,l1j, ei_padd(res.template packetCoeff<Aligned>(l1i+4,l1j), ei_preduxp(&(dst[4]))));
-                if (PacketSize==2)
-                  res.template writePacketCoeff<Aligned>(l1i+6,l1j, ei_padd(res.template packetCoeff<Aligned>(l1i+6,l1j), ei_preduxp(&(dst[6]))));
-              }
-            }
-//             else
-//             {
-//               // TODO uncommenting this code kill the perf, even though it is never called !!
-//               // this is because dst cannot be a set of registers only
-//               // TODO optimize this loop
-//               // TODO is it better to do one redux at once or packet reduxes + unaligned store ?
-//               for (int w = 0; w<bw; ++w)
-//                 res.coeffRef(l1i+w, l1j) += ei_predux(dst[w]);
-//               std::cout << "!\n";
-//             }
-
-            asm("#eigen endcore");
-          }
-#endif
-        }
-        if (l2blockRemainingRows>0)
-        {
-          // this is an attempt to build an array of kernels, but I did not manage to get it compiles
-//           typedef void (*Kernel)(DestDerived& , int, int, int, int, int, int, int, const Scalar*);
-//           Kernel kernels[8];
-//           kernels[0] = (Kernel)(&Product<Lhs,Rhs,EvalMode>::template _cacheFriendlyEvalKernel<DestDerived, RhsAlignment, ResAlignment, 1>);
-//           kernels[l2blockRemainingRows](res, l2i, l2j, l2k, l2blockRowEndBW, l2blockRowEnd, l2blockColEnd, l2blockSizeEnd, block);
-
-          switch(l2blockRemainingRows)
-          {
-          case 1:_cacheFriendlyEvalKernel<DestDerived, RhsAlignment, ResAlignment, 1>(
-              res, l2i, l2j, l2k, l2blockRowEndBW, l2blockRowEnd, l2blockColEnd, l2blockSizeEnd, block); break;
-          case 2:_cacheFriendlyEvalKernel<DestDerived, RhsAlignment, ResAlignment, 2>(
-              res, l2i, l2j, l2k, l2blockRowEndBW, l2blockRowEnd, l2blockColEnd, l2blockSizeEnd, block); break;
-          case 3:_cacheFriendlyEvalKernel<DestDerived, RhsAlignment, ResAlignment, 3>(
-              res, l2i, l2j, l2k, l2blockRowEndBW, l2blockRowEnd, l2blockColEnd, l2blockSizeEnd, block); break;
-          case 4:_cacheFriendlyEvalKernel<DestDerived, RhsAlignment, ResAlignment, 4>(
-              res, l2i, l2j, l2k, l2blockRowEndBW, l2blockRowEnd, l2blockColEnd, l2blockSizeEnd, block); break;
-          case 5:_cacheFriendlyEvalKernel<DestDerived, RhsAlignment, ResAlignment, 5>(
-              res, l2i, l2j, l2k, l2blockRowEndBW, l2blockRowEnd, l2blockColEnd, l2blockSizeEnd, block); break;
-          case 6:_cacheFriendlyEvalKernel<DestDerived, RhsAlignment, ResAlignment, 6>(
-              res, l2i, l2j, l2k, l2blockRowEndBW, l2blockRowEnd, l2blockColEnd, l2blockSizeEnd, block); break;
-          case 7:_cacheFriendlyEvalKernel<DestDerived, RhsAlignment, ResAlignment, 7>(
-              res, l2i, l2j, l2k, l2blockRowEndBW, l2blockRowEnd, l2blockColEnd, l2blockSizeEnd, block); break;
-          default:
-            ei_internal_assert(false && "internal error"); break;
-          }
-        }
-      }
-    }
-  }
-
-  // handle the part which cannot be processed by the vectorized path
-  if (remainingSize)
-  {
-    res += Product<
-      Block<typename ei_unconst<_LhsNested>::type,Dynamic,Dynamic>,
-      Block<typename ei_unconst<_RhsNested>::type,Dynamic,Dynamic>,
-      NormalProduct>(
-        m_lhs.block(0,size, _rows(), remainingSize),
-        m_rhs.block(size,0, remainingSize, _cols())).lazy();
-//     res += m_lhs.block(0,size, _rows(), remainingSize)._lazyProduct(m_rhs.block(size,0, remainingSize, _cols()));
-  }
-
-//   delete[] block;
+  ei_cache_friendly_product<Scalar>(
+    _rows(), _cols(), m_lhs.cols(),
+    _LhsNested::Flags&RowMajorBit, &(m_lhs.const_cast_derived().coeffRef(0,0)), m_lhs.stride(),
+    _RhsNested::Flags&RowMajorBit, &(m_rhs.const_cast_derived().coeffRef(0,0)), m_rhs.stride(),
+    Flags&RowMajorBit, &(res.coeffRef(0,0)), res.stride()
+  );
 }
 
 #endif // EIGEN_PRODUCT_H

Eigen/src/Core/Transpose.h

@@ -69,6 +69,8 @@ template<typename MatrixType> class Transpose
     int _rows() const { return m_matrix.cols(); }
     int _cols() const { return m_matrix.rows(); }
 
+    int _stride(void) const { return m_matrix.stride(); }
+
     Scalar& _coeffRef(int row, int col)
     {
       return m_matrix.const_cast_derived().coeffRef(col, row);

Eigen/src/Core/Triangular.h

@@ -67,7 +67,7 @@ struct ei_traits<Triangular<Mode, MatrixType> >
     ColsAtCompileTime = MatrixType::ColsAtCompileTime,
     MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
     MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
-    Flags = (_MatrixTypeNested::Flags & ~(VectorizableBit | Like1DArrayBit)) | Mode,
+    Flags = (_MatrixTypeNested::Flags & ~(VectorizableBit | Like1DArrayBit | DirectAccessBit)) | Mode,
     CoeffReadCost = _MatrixTypeNested::CoeffReadCost
   };
 };

Eigen/src/Core/util/Constants.h

@@ -43,18 +43,18 @@ const unsigned int NullDiagBit = 0x40;      ///< means all diagonal coefficients
 const unsigned int UnitDiagBit = 0x80;      ///< means all diagonal coefficients are equal to 1
 const unsigned int NullLowerBit = 0x200;    ///< means the strictly triangular lower part is 0
 const unsigned int NullUpperBit = 0x400;    ///< means the strictly triangular upper part is 0
-const unsigned int ReferencableBit = 0x800; ///< means the expression is writable through MatrixBase::coeffRef(int,int)
+const unsigned int DirectAccessBit = 0x800; ///< means the underlying matrix data can be direclty accessed
 
 enum { Upper=NullLowerBit, Lower=NullUpperBit };
 enum { Aligned=0, UnAligned=1 };
 
 // list of flags that are lost by default
-const unsigned int DefaultLostFlagMask = ~(VectorizableBit | Like1DArrayBit | ReferencableBit
+const unsigned int DefaultLostFlagMask = ~(VectorizableBit | Like1DArrayBit | DirectAccessBit
   | NullDiagBit | UnitDiagBit | NullLowerBit | NullUpperBit);
 
 enum { ConditionalJumpCost = 5 };
 enum CornerType { TopLeft, TopRight, BottomLeft, BottomRight };
 enum DirectionType { Vertical, Horizontal };
-enum ProductEvaluationMode { NormalProduct, CacheOptimalProduct, LazyProduct};
+enum ProductEvaluationMode { NormalProduct, CacheFriendlyProduct, LazyProduct};
 
 #endif // EIGEN_CONSTANTS_H