Add a Symbolic::FixedExpr helper expression to make sure the compiler fully optimize the usage of last and end.

Eigen/src/Core/ArithmeticSequence.h

@@ -378,6 +378,7 @@ public:
 
   Index size() const { return (m_last-m_first+m_incr)/m_incr; }
   Index operator[](Index i) const { return m_first + i * m_incr; }
+  Index first() const { return m_first; }
 
   const FirstType& firstObject() const { return m_first; }
   const LastType&  lastObject()  const { return m_last; }

Eigen/src/Core/util/IndexedViewHelper.h

@@ -58,7 +58,9 @@ static const Symbolic::SymbolExpr<internal::symbolic_last_tag> last;
 #ifdef EIGEN_PARSED_BY_DOXYGEN
 static const auto end = last+1;
 #else
-static const Symbolic::AddExpr<Symbolic::SymbolExpr<internal::symbolic_last_tag>,Symbolic::ValueExpr> end(last+1);
+// Using a FixedExpr<1> expression is important here to make sure the compiler
+// can fully optimize the computation starting indices with zero overhead.
+static const Symbolic::AddExpr<Symbolic::SymbolExpr<internal::symbolic_last_tag>,Symbolic::FixedExpr<1> > end(last+Symbolic::FixedExpr<1>());
 #endif
 
 } // end namespace placeholders

Eigen/src/Core/util/SymbolicIndex.h

@@ -124,6 +124,17 @@ struct is_symbolic {
   enum { value = internal::is_convertible<T,BaseExpr<T> >::value };
 };
 
+// Simple wrapper around a compile-time value,
+// It is similar to ValueExpr(N) but this version helps the compiler to generate better code.
+template<int N>
+class FixedExpr : public BaseExpr<FixedExpr<N> > {
+public:
+  FixedExpr() {}
+  template<typename T>
+  Index eval_impl(const T&) const { return N; }
+};
+
+
 /** Represents the actual value of a symbol identified by its tag
   *
   * It is the return type of SymbolValue::operator=, and most of the time this is only way it is used.