More clever evaluation of arguments: now it occurs in earlier, in operator*,

before the Product<> type is constructed. This resets template depth on each
intermediate evaluation, and gives simpler code. Introducing
ei_eval_if_expensive<Derived, n> which evaluates Derived if it's worth it
given that each of its coeffs will be accessed n times. Operator*
uses this with adequate values of n to evaluate args exactly when needed.

Eigen/src/Core/ForwardDeclarations.h

@@ -27,6 +27,7 @@
 
 template<typename T> struct ei_traits;
 template<typename Lhs, typename Rhs> struct ei_product_eval_mode;
+template<typename T> struct NumTraits;
 
 template<typename _Scalar, int _Rows, int _Cols, unsigned int _Flags, int _MaxRows, int _MaxCols> class Matrix;
 template<typename ExpressionType> class Lazy;
@@ -89,6 +90,13 @@ template<typename T> struct ei_eval
                  ei_traits<T>::MaxColsAtCompileTime> type;
 };
 
+template<typename T, int n> struct ei_eval_if_expensive
+{
+  enum { eval = n * NumTraits<typename T::Scalar>::ReadCost < (n-1) * T::CoeffReadCost };
+  typedef typename ei_meta_if<eval, typename T::Eval, T>::ret type;
+  typedef typename ei_meta_if<eval, typename T::Eval, T&>::ret reftype;
+};
+
 template<typename T> struct ei_eval_unless_lazy
 {
   typedef typename ei_meta_if<ei_traits<T>::Flags & LazyBit,

Eigen/src/Core/Product.h

@@ -78,6 +78,7 @@ template<typename Lhs, typename Rhs, int EvalMode>
 struct ei_traits<Product<Lhs, Rhs, EvalMode> >
 {
   typedef typename Lhs::Scalar Scalar;
+#if 0
   typedef typename ei_meta_if<
                      (int)NumTraits<Scalar>::ReadCost < (int)Lhs::CoeffReadCost,
                      typename Lhs::Eval,
@@ -95,6 +96,7 @@ struct ei_traits<Product<Lhs, Rhs, EvalMode> >
                      (int)NumTraits<Scalar>::ReadCost < (int)Rhs::CoeffReadCost,
                      typename Rhs::Eval,
                      typename Rhs::XprCopy>::ret ActualRhsXprCopy;
+#endif
   enum {
     RowsAtCompileTime = Lhs::RowsAtCompileTime,
     ColsAtCompileTime = Rhs::ColsAtCompileTime,
@@ -107,7 +109,7 @@ struct ei_traits<Product<Lhs, Rhs, EvalMode> >
       = Lhs::ColsAtCompileTime == Dynamic
       ? Dynamic
       : Lhs::ColsAtCompileTime
-        * (NumTraits<Scalar>::MulCost + ActualLhs::CoeffReadCost + ActualRhs::CoeffReadCost)
+        * (NumTraits<Scalar>::MulCost + Lhs::CoeffReadCost + Rhs::CoeffReadCost)
         + (Lhs::ColsAtCompileTime - 1) * NumTraits<Scalar>::AddCost
   };
 };
@@ -115,7 +117,7 @@ struct ei_traits<Product<Lhs, Rhs, EvalMode> >
 template<typename Lhs, typename Rhs> struct ei_product_eval_mode
 {
   enum{ value = Lhs::MaxRowsAtCompileTime == Dynamic || Rhs::MaxColsAtCompileTime == Dynamic
-                  ? CacheOptimal : UnrolledDotProduct };
+              ? CacheOptimal : UnrolledDotProduct };
 };
 
 template<typename Lhs, typename Rhs, int EvalMode> class Product : ei_no_assignment_operator,
@@ -124,11 +126,12 @@ template<typename Lhs, typename Rhs, int EvalMode> class Product : ei_no_assignm
   public:
 
     EIGEN_GENERIC_PUBLIC_INTERFACE(Product)
+#if 0
     typedef typename ei_traits<Product>::ActualLhs ActualLhs;
     typedef typename ei_traits<Product>::ActualRhs ActualRhs;
     typedef typename ei_traits<Product>::ActualLhsXprCopy ActualLhsXprCopy;
     typedef typename ei_traits<Product>::ActualRhsXprCopy ActualRhsXprCopy;
-
+#endif
     Product(const Lhs& lhs, const Rhs& rhs)
       : m_lhs(lhs), m_rhs(rhs)
     {
@@ -153,7 +156,7 @@ template<typename Lhs, typename Rhs, int EvalMode> class Product : ei_no_assignm
         ei_product_unroller<Lhs::ColsAtCompileTime-1,
                             Lhs::ColsAtCompileTime <= EIGEN_UNROLLING_LIMIT
                               ? Lhs::ColsAtCompileTime : Dynamic,
-                            ActualLhs, ActualRhs>
+                            Lhs, Rhs>
           ::run(row, col, m_lhs, m_rhs, res);
       else
       {
@@ -165,8 +168,8 @@ template<typename Lhs, typename Rhs, int EvalMode> class Product : ei_no_assignm
     }
 
   protected:
-    const ActualLhsXprCopy m_lhs;
+    const typename Lhs::XprCopy m_lhs;
-    const ActualRhsXprCopy m_rhs;
+    const typename Rhs::XprCopy m_rhs;
 };
 
 /** \returns the matrix product of \c *this and \a other.
@@ -181,7 +184,10 @@ template<typename OtherDerived>
 const typename ei_eval_unless_lazy<Product<Derived, OtherDerived> >::type
 MatrixBase<Derived>::operator*(const MatrixBase<OtherDerived> &other) const
 {
-  return Product<Derived, OtherDerived>(derived(), other.derived()).eval();
+  typedef ei_eval_if_expensive<Derived, OtherDerived::ColsAtCompileTime> Lhs;
+  typedef ei_eval_if_expensive<OtherDerived, Derived::RowsAtCompileTime> Rhs;
+  return Product<typename Lhs::type, typename Rhs::type>
+           (typename Lhs::reftype(derived()), typename Rhs::reftype(other.derived())).eval();
 }
 
 /** replaces \c *this by \c *this * \a other.