* find the proper way of nesting the expression in Flagged:

  finally that's more subtle than just using ei_nested, because when
  flagging with NestByValueBit we want to store the expression by value
  already, regardless of whether it already had the NestByValueBit set.
* rename temporary() ----> nestByValue()
* move the old Product.h to disabled/, replace by what was ProductWIP.h
* tweak -O and -g flags for tests and examples
* reorder the tests -- basic things go first
* simplifications, e.g. in many methoeds return derived() and count on
  implicit casting to the actual return type.
* strip some not-really-useful stuff from the heaviest tests

1 files changed, 489 insertions, 0 deletions

diff --git a/disabled/Product.h b/disabled/Product.h
new file mode 100644
index 000000000..5d3e99281
--- /dev/null
+++ b/disabled/Product.h
@@ -0,0 +1,489 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob@math.jussieu.fr>
+// 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_PRODUCT_H
+#define EIGEN_PRODUCT_H
+
+template<int Index, int Size, typename Lhs, typename Rhs>
+struct ei_product_unroller
+{
+  inline static void run(int row, int col, const Lhs& lhs, const Rhs& rhs,
+                               typename Lhs::Scalar &res)
+  {
+    ei_product_unroller<Index-1, Size, Lhs, Rhs>::run(row, col, lhs, rhs, res);
+    res += lhs.coeff(row, Index) * rhs.coeff(Index, col);
+  }
+};
+
+template<int Size, typename Lhs, typename Rhs>
+struct ei_product_unroller<0, Size, Lhs, Rhs>
+{
+  inline static void run(int row, int col, const Lhs& lhs, const Rhs& rhs,
+                               typename Lhs::Scalar &res)
+  {
+    res = lhs.coeff(row, 0) * rhs.coeff(0, col);
+  }
+};
+
+template<int Index, typename Lhs, typename Rhs>
+struct ei_product_unroller<Index, Dynamic, Lhs, Rhs>
+{
+  inline static void run(int, int, const Lhs&, const Rhs&, typename Lhs::Scalar&) {}
+};
+
+// prevent buggy user code from causing an infinite recursion
+template<int Index, typename Lhs, typename Rhs>
+struct ei_product_unroller<Index, 0, Lhs, Rhs>
+{
+  inline 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;
+
+template<int Index, int Size, typename Lhs, typename Rhs, typename PacketScalar>
+struct ei_packet_product_unroller<true, Index, Size, Lhs, Rhs, PacketScalar>
+{
+  inline static void run(int row, int col, const Lhs& lhs, const Rhs& rhs, PacketScalar &res)
+  {
+    ei_packet_product_unroller<true, Index-1, Size, Lhs, Rhs, PacketScalar>::run(row, col, lhs, rhs, res);
+    res =  ei_pmadd(ei_pset1(lhs.coeff(row, Index)), rhs.template packetCoeff<Aligned>(Index, col), res);
+  }
+};
+
+template<int Index, int Size, typename Lhs, typename Rhs, typename PacketScalar>
+struct ei_packet_product_unroller<false, Index, Size, Lhs, Rhs, PacketScalar>
+{
+  inline static void run(int row, int col, const Lhs& lhs, const Rhs& rhs, PacketScalar &res)
+  {
+    ei_packet_product_unroller<false, Index-1, Size, Lhs, Rhs, PacketScalar>::run(row, col, lhs, rhs, res);
+    res =  ei_pmadd(lhs.template packetCoeff<Aligned>(row, Index), ei_pset1(rhs.coeff(Index, col)), res);
+  }
+};
+
+template<int Size, typename Lhs, typename Rhs, typename PacketScalar>
+struct ei_packet_product_unroller<true, 0, Size, Lhs, Rhs, PacketScalar>
+{
+  inline static void run(int row, int col, const Lhs& lhs, const Rhs& rhs, PacketScalar &res)
+  {
+    res = ei_pmul(ei_pset1(lhs.coeff(row, 0)),rhs.template packetCoeff<Aligned>(0, col));
+  }
+};
+
+template<int Size, typename Lhs, typename Rhs, typename PacketScalar>
+struct ei_packet_product_unroller<false, 0, Size, Lhs, Rhs, PacketScalar>
+{
+  inline static void run(int row, int col, const Lhs& lhs, const Rhs& rhs, PacketScalar &res)
+  {
+    res = ei_pmul(lhs.template packetCoeff<Aligned>(row, 0), ei_pset1(rhs.coeff(0, col)));
+  }
+};
+
+template<bool RowMajor, int Index, typename Lhs, typename Rhs, typename PacketScalar>
+struct ei_packet_product_unroller<RowMajor, Index, Dynamic, Lhs, Rhs, PacketScalar>
+{
+  inline static void run(int, int, const Lhs&, const Rhs&, PacketScalar&) {}
+};
+
+template<int Index, typename Lhs, typename Rhs, typename PacketScalar>
+struct ei_packet_product_unroller<false, Index, Dynamic, Lhs, Rhs, PacketScalar>
+{
+  inline 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); }
+};
+
+template<typename Product> struct ProductPacketCoeffImpl<Product, false> {
+  inline static typename Product::PacketScalar execute(const Product& product, int row, int col)
+  { return product._packetCoeffColumnMajor(row,col); }
+};
+
+/** \class Product
+  *
+  * \brief Expression of the product of two matrices
+  *
+  * \param Lhs the type of the left-hand side
+  * \param Rhs the type of the right-hand side
+  * \param EvalMode internal use only
+  *
+  * This class represents an expression of the product of two matrices.
+  * It is the return type of the operator* between matrices, and most of the time
+  * this is the only way it is used.
+  *
+  * \sa class Sum, class Difference
+  */
+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)))
+              ? CacheFriendlyProduct : NormalProduct };
+};
+
+template<typename Lhs, typename Rhs, int EvalMode>
+struct ei_traits<Product<Lhs, Rhs, EvalMode> >
+{
+  typedef typename Lhs::Scalar Scalar;
+  typedef typename ei_nested<Lhs,Rhs::ColsAtCompileTime>::type LhsNested;
+  typedef typename ei_nested<Rhs,Lhs::RowsAtCompileTime>::type RhsNested;
+  typedef typename ei_unref<LhsNested>::type _LhsNested;
+  typedef typename ei_unref<RhsNested>::type _RhsNested;
+  enum {
+    LhsCoeffReadCost = _LhsNested::CoeffReadCost,
+    RhsCoeffReadCost = _RhsNested::CoeffReadCost,
+    LhsFlags = _LhsNested::Flags,
+    RhsFlags = _RhsNested::Flags,
+    RowsAtCompileTime = Lhs::RowsAtCompileTime,
+    ColsAtCompileTime = Rhs::ColsAtCompileTime,
+    MaxRowsAtCompileTime = Lhs::MaxRowsAtCompileTime,
+    MaxColsAtCompileTime = Rhs::MaxColsAtCompileTime,
+    _RhsVectorizable = (RhsFlags & RowMajorBit) && (RhsFlags & VectorizableBit) && (ColsAtCompileTime % ei_packet_traits<Scalar>::size == 0),
+    _LhsVectorizable = (!(LhsFlags & RowMajorBit)) && (LhsFlags & VectorizableBit) && (RowsAtCompileTime % ei_packet_traits<Scalar>::size == 0),
+    _Vectorizable = (_LhsVectorizable || _RhsVectorizable) ? 1 : 0,
+    _RowMajor = (RhsFlags & RowMajorBit)
+              && (EvalMode==(int)CacheFriendlyProduct ? (int)LhsFlags & RowMajorBit : (!_LhsVectorizable)),
+    _LostBits = HereditaryBits & ~(
+                (_RowMajor ? 0 : RowMajorBit)
+              | ((RowsAtCompileTime == Dynamic || ColsAtCompileTime == Dynamic) ? 0 : LargeBit)),
+    Flags = ((unsigned int)(LhsFlags | RhsFlags) & _LostBits)
+          | EvalBeforeAssigningBit
+          | EvalBeforeNestingBit
+          | (_Vectorizable ? VectorizableBit : 0),
+    CoeffReadCost
+      = Lhs::ColsAtCompileTime == Dynamic
+      ? Dynamic
+      : Lhs::ColsAtCompileTime
+        * (NumTraits<Scalar>::MulCost + LhsCoeffReadCost + RhsCoeffReadCost)
+        + (Lhs::ColsAtCompileTime - 1) * NumTraits<Scalar>::AddCost
+  };
+};
+
+template<typename Lhs, typename Rhs, int EvalMode> class Product : ei_no_assignment_operator,
+  public MatrixBase<Product<Lhs, Rhs, EvalMode> >
+{
+  public:
+
+    EIGEN_GENERIC_PUBLIC_INTERFACE(Product)
+    friend class ProductPacketCoeffImpl<Product,Flags&RowMajorBit>;
+    typedef typename ei_traits<Product>::LhsNested LhsNested;
+    typedef typename ei_traits<Product>::RhsNested RhsNested;
+    typedef typename ei_traits<Product>::_LhsNested _LhsNested;
+    typedef typename ei_traits<Product>::_RhsNested _RhsNested;
+
+    inline Product(const Lhs& lhs, const Rhs& rhs)
+      : m_lhs(lhs), m_rhs(rhs)
+    {
+      ei_assert(lhs.cols() == rhs.rows());
+    }
+
+    /** \internal */
+    template<typename DestDerived, int AlignedMode>
+    void _cacheOptimalEval(DestDerived& res, ei_meta_false) const;
+    #ifdef EIGEN_VECTORIZE
+    template<typename DestDerived, int AlignedMode>
+    void _cacheOptimalEval(DestDerived& res, ei_meta_true) const;
+    #endif
+
+  private:
+
+    inline int _rows() const { return m_lhs.rows(); }
+    inline int _cols() const { return m_rhs.cols(); }
+
+    const Scalar _coeff(int row, int col) const
+    {
+      Scalar res;
+      const bool unroll = CoeffReadCost <= EIGEN_UNROLLING_LIMIT;
+      if(unroll)
+      {
+        ei_product_unroller<Lhs::ColsAtCompileTime-1,
+                            unroll ? Lhs::ColsAtCompileTime : Dynamic,
+                            _LhsNested, _RhsNested>
+          ::run(row, col, m_lhs, m_rhs, res);
+      }
+      else
+      {
+        res = m_lhs.coeff(row, 0) * m_rhs.coeff(0, col);
+        for(int i = 1; i < m_lhs.cols(); i++)
+          res += m_lhs.coeff(row, i) * m_rhs.coeff(i, col);
+      }
+      return res;
+    }
+
+    template<int LoadMode>
+    const PacketScalar _packetCoeff(int row, int col) const
+    {
+      if(Lhs::ColsAtCompileTime <= EIGEN_UNROLLING_LIMIT)
+      {
+        PacketScalar res;
+        ei_packet_product_unroller<Flags&RowMajorBit, Lhs::ColsAtCompileTime-1,
+                            Lhs::ColsAtCompileTime <= EIGEN_UNROLLING_LIMIT
+                              ? Lhs::ColsAtCompileTime : Dynamic,
+                            _LhsNested, _RhsNested, PacketScalar>
+          ::run(row, col, m_lhs, m_rhs, res);
+        return res;
+      }
+      else
+        return ProductPacketCoeffImpl<Product,Flags&RowMajorBit>::execute(*this, row, col);
+    }
+
+    const PacketScalar _packetCoeffRowMajor(int row, int col) const
+    {
+      PacketScalar res;
+      res = ei_pmul(ei_pset1(m_lhs.coeff(row, 0)),m_rhs.template packetCoeff<Aligned>(0, col));
+      for(int i = 1; i < m_lhs.cols(); i++)
+        res =  ei_pmadd(ei_pset1(m_lhs.coeff(row, i)), m_rhs.template packetCoeff<Aligned>(i, col), res);
+      return res;
+    }
+
+    const PacketScalar _packetCoeffColumnMajor(int row, int col) const
+    {
+      PacketScalar res;
+      res = ei_pmul(m_lhs.template packetCoeff<Aligned>(row, 0), ei_pset1(m_rhs.coeff(0, col)));
+      for(int i = 1; i < m_lhs.cols(); i++)
+        res =  ei_pmadd(m_lhs.template packetCoeff<Aligned>(row, i), ei_pset1(m_rhs.coeff(i, col)), res);
+      return res;
+//       const PacketScalar tmp[4];
+//       ei_punpack(m_rhs.packetCoeff(0,col), tmp);
+//
+//       return
+//         ei_pmadd(m_lhs.packetCoeff(row, 0), tmp[0],
+//           ei_pmadd(m_lhs.packetCoeff(row, 1), tmp[1],
+//             ei_pmadd(m_lhs.packetCoeff(row, 2), tmp[2]
+//               ei_pmul(m_lhs.packetCoeff(row, 3), tmp[3]))));
+    }
+
+
+  protected:
+    const LhsNested m_lhs;
+    const RhsNested m_rhs;
+};
+
+/** \returns the matrix product of \c *this and \a other.
+  *
+  * \note This function causes an immediate evaluation. If you want to perform a matrix product
+  * without immediate evaluation, call .lazy() on one of the matrices before taking the product.
+  *
+  * \sa lazy(), operator*=(const MatrixBase&)
+  */
+template<typename Derived>
+template<typename OtherDerived>
+inline const Product<Derived,OtherDerived>
+MatrixBase<Derived>::operator*(const MatrixBase<OtherDerived> &other) const
+{
+  return Product<Derived,OtherDerived>(derived(), other.derived());
+}
+
+/** replaces \c *this by \c *this * \a other.
+  *
+  * \returns a reference to \c *this
+  */
+template<typename Derived>
+template<typename OtherDerived>
+inline Derived &
+MatrixBase<Derived>::operator*=(const MatrixBase<OtherDerived> &other)
+{
+  return *this = *this * other;
+}
+
+template<typename Derived>
+template<typename Lhs, typename Rhs>
+inline Derived& MatrixBase<Derived>::lazyAssign(const Product<Lhs,Rhs,CacheFriendlyProduct>& product)
+{
+  product.template _cacheOptimalEval<Derived, Aligned>(derived(),
+    #ifdef EIGEN_VECTORIZE
+    typename ei_meta_if<Flags & VectorizableBit, ei_meta_true, ei_meta_false>::ret()
+    #else
+    ei_meta_false()
+    #endif
+    );
+  return derived();
+}
+
+template<typename Lhs, typename Rhs, int EvalMode>
+template<typename DestDerived, int AlignedMode>
+void Product<Lhs,Rhs,EvalMode>::_cacheOptimalEval(DestDerived& res, ei_meta_false) const
+{
+  res.setZero();
+  const int cols4 = m_lhs.cols() & 0xfffffffC;
+  if (Lhs::Flags&RowMajorBit)
+  {
+//     std::cout << "opt rhs\n";
+    int j=0;
+    for(; j<cols4; j+=4)
+    {
+      for(int k=0; k<this->rows(); ++k)
+      {
+        const Scalar tmp0 = m_lhs.coeff(k,j  );
+        const Scalar tmp1 = m_lhs.coeff(k,j+1);
+        const Scalar tmp2 = m_lhs.coeff(k,j+2);
+        const Scalar tmp3 = m_lhs.coeff(k,j+3);
+        for (int i=0; i<this->cols(); ++i)
+          res.coeffRef(k,i) += tmp0 * m_rhs.coeff(j+0,i) + tmp1 * m_rhs.coeff(j+1,i)
+                             + tmp2 * m_rhs.coeff(j+2,i) + tmp3 * m_rhs.coeff(j+3,i);
+      }
+    }
+    for(; j<m_lhs.cols(); ++j)
+    {
+      for(int k=0; k<this->rows(); ++k)
+      {
+        const Scalar tmp = m_rhs.coeff(k,j);
+        for (int i=0; i<this->cols(); ++i)
+          res.coeffRef(k,i) += tmp * m_lhs.coeff(j,i);
+      }
+    }
+  }
+  else
+  {
+//     std::cout << "opt lhs\n";
+    int j = 0;
+    for(; j<cols4; j+=4)
+    {
+      for(int k=0; k<this->cols(); ++k)
+      {
+        const Scalar tmp0 = m_rhs.coeff(j  ,k);
+        const Scalar tmp1 = m_rhs.coeff(j+1,k);
+        const Scalar tmp2 = m_rhs.coeff(j+2,k);
+        const Scalar tmp3 = m_rhs.coeff(j+3,k);
+        for (int i=0; i<this->rows(); ++i)
+          res.coeffRef(i,k) += tmp0 * m_lhs.coeff(i,j+0) + tmp1 * m_lhs.coeff(i,j+1)
+                             + tmp2 * m_lhs.coeff(i,j+2) + tmp3 * m_lhs.coeff(i,j+3);
+      }
+    }
+    for(; j<m_lhs.cols(); ++j)
+    {
+      for(int k=0; k<this->cols(); ++k)
+      {
+        const Scalar tmp = m_rhs.coeff(j,k);
+        for (int i=0; i<this->rows(); ++i)
+          res.coeffRef(i,k) += tmp * m_lhs.coeff(i,j);
+      }
+    }
+  }
+}
+
+#ifdef EIGEN_VECTORIZE
+template<typename Lhs, typename Rhs, int EvalMode>
+template<typename DestDerived, int AlignedMode>
+void Product<Lhs,Rhs,EvalMode>::_cacheOptimalEval(DestDerived& res, ei_meta_true) const
+{
+
+  if (((Lhs::Flags&RowMajorBit) && (_cols() % ei_packet_traits<Scalar>::size != 0))
+    || (_rows() % ei_packet_traits<Scalar>::size != 0))
+  {
+    return _cacheOptimalEval<DestDerived, AlignedMode>(res, ei_meta_false());
+  }
+
+  res.setZero();
+  const int cols4 = m_lhs.cols() & 0xfffffffC;
+  if (Lhs::Flags&RowMajorBit)
+  {
+//     std::cout << "packet rhs\n";
+    int j=0;
+    for(; j<cols4; j+=4)
+    {
+      for(int k=0; k<this->rows(); k++)
+      {
+        const typename ei_packet_traits<Scalar>::type tmp0 = ei_pset1(m_lhs.coeff(k,j+0));
+        const typename ei_packet_traits<Scalar>::type tmp1 = ei_pset1(m_lhs.coeff(k,j+1));
+        const typename ei_packet_traits<Scalar>::type tmp2 = ei_pset1(m_lhs.coeff(k,j+2));
+        const typename ei_packet_traits<Scalar>::type tmp3 = ei_pset1(m_lhs.coeff(k,j+3));
+        for (int i=0; i<this->cols(); i+=ei_packet_traits<Scalar>::size)
+        {
+          res.template writePacketCoeff<AlignedMode>(k,i,
+            ei_pmadd(tmp0, m_rhs.template packetCoeff<AlignedMode>(j+0,i),
+              ei_pmadd(tmp1, m_rhs.template packetCoeff<AlignedMode>(j+1,i),
+                ei_pmadd(tmp2, m_rhs.template packetCoeff<AlignedMode>(j+2,i),
+                  ei_pmadd(tmp3, m_rhs.template packetCoeff<AlignedMode>(j+3,i),
+                    res.template packetCoeff<AlignedMode>(k,i)))))
+          );
+        }
+      }
+    }
+    for(; j<m_lhs.cols(); ++j)
+    {
+      for(int k=0; k<this->rows(); k++)
+      {
+        const typename ei_packet_traits<Scalar>::type tmp = ei_pset1(m_lhs.coeff(k,j));
+        for (int i=0; i<this->cols(); i+=ei_packet_traits<Scalar>::size)
+          res.template writePacketCoeff<AlignedMode>(k,i,
+            ei_pmadd(tmp, m_rhs.template packetCoeff<AlignedMode>(j,i), res.template packetCoeff<AlignedMode>(k,i)));
+      }
+    }
+  }
+  else
+  {
+//     std::cout << "packet lhs\n";
+    int k=0;
+    for(; k<cols4; k+=4)
+    {
+      for(int j=0; j<this->cols(); j+=1)
+      {
+        const typename ei_packet_traits<Scalar>::type tmp0 = ei_pset1(m_rhs.coeff(k+0,j));
+        const typename ei_packet_traits<Scalar>::type tmp1 = ei_pset1(m_rhs.coeff(k+1,j));
+        const typename ei_packet_traits<Scalar>::type tmp2 = ei_pset1(m_rhs.coeff(k+2,j));
+        const typename ei_packet_traits<Scalar>::type tmp3 = ei_pset1(m_rhs.coeff(k+3,j));
+
+        for (int i=0; i<this->rows(); i+=ei_packet_traits<Scalar>::size)
+        {
+          res.template writePacketCoeff<AlignedMode>(i,j,
+            ei_pmadd(tmp0, m_lhs.template packetCoeff<AlignedMode>(i,k),
+              ei_pmadd(tmp1, m_lhs.template packetCoeff<AlignedMode>(i,k+1),
+                ei_pmadd(tmp2, m_lhs.template packetCoeff<AlignedMode>(i,k+2),
+                  ei_pmadd(tmp3, m_lhs.template packetCoeff<AlignedMode>(i,k+3),
+                    res.template packetCoeff<AlignedMode>(i,j)))))
+          );
+        }
+      }
+    }
+    for(; k<m_lhs.cols(); ++k)
+    {
+      for(int j=0; j<this->cols(); j++)
+      {
+        const typename ei_packet_traits<Scalar>::type tmp = ei_pset1(m_rhs.coeff(k,j));
+        for (int i=0; i<this->rows(); i+=ei_packet_traits<Scalar>::size)
+          res.template writePacketCoeff<AlignedMode>(k,j,
+            ei_pmadd(tmp, m_lhs.template packetCoeff<AlignedMode>(i,k), res.template packetCoeff<AlignedMode>(i,j)));
+      }
+    }
+  }
+}
+#endif // EIGEN_VECTORIZE
+
+#endif // EIGEN_PRODUCT_H