diff --git a/Eigen/src/Core/AssignEvaluator.h b/Eigen/src/Core/AssignEvaluator.h
index 9dbf2c063..2b00d355b 100644
--- a/Eigen/src/Core/AssignEvaluator.h
+++ b/Eigen/src/Core/AssignEvaluator.h
@@ -29,8 +29,8 @@ struct copy_using_evaluator_traits
 {
   typedef typename DstEvaluator::XprType Dst;
   typedef typename Dst::Scalar DstScalar;
-  // TODO recursively find best packet size
-  typedef typename packet_traits<DstScalar>::type PacketType;
+  // TODO distinguish between linear traversal and inner-traversals
+  typedef typename find_best_packet<DstScalar,Dst::SizeAtCompileTime>::type PacketType; 
   
   enum {
     DstFlags = DstEvaluator::Flags,
@@ -55,7 +55,7 @@ private:
               : int(DstFlags)&RowMajorBit ? int(Dst::MaxColsAtCompileTime)
               : int(Dst::MaxRowsAtCompileTime),
     MaxSizeAtCompileTime = Dst::SizeAtCompileTime,
-    PacketSize = packet_traits<DstScalar>::size
+    PacketSize = unpacket_traits<PacketType>::size
   };
 
   enum {
diff --git a/Eigen/src/Core/DenseBase.h b/Eigen/src/Core/DenseBase.h
index 6051f01ac..005f68aa5 100644
--- a/Eigen/src/Core/DenseBase.h
+++ b/Eigen/src/Core/DenseBase.h
@@ -76,7 +76,6 @@ template<typename Derived> class DenseBase
       * It is an alias for the Scalar type */
     typedef Scalar value_type;
     
-    typedef typename internal::packet_traits<Scalar>::type PacketScalar;
     typedef typename NumTraits<Scalar>::Real RealScalar;
 
     typedef internal::special_scalar_op_base<Derived,typename internal::traits<Derived>::Scalar,
@@ -178,6 +177,8 @@ template<typename Derived> class DenseBase
       InnerStrideAtCompileTime = internal::inner_stride_at_compile_time<Derived>::ret,
       OuterStrideAtCompileTime = internal::outer_stride_at_compile_time<Derived>::ret
     };
+    
+    typedef typename internal::find_best_packet<Scalar,SizeAtCompileTime>::type PacketScalar;
 
     enum { IsPlainObjectBase = 0 };
     
diff --git a/Eigen/src/Core/Matrix.h b/Eigen/src/Core/Matrix.h
index b7c90ae16..7221d89a6 100644
--- a/Eigen/src/Core/Matrix.h
+++ b/Eigen/src/Core/Matrix.h
@@ -141,7 +141,8 @@ struct traits<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >
 {
 private:
   // TODO find ideal packet size
-  typedef typename packet_traits<_Scalar>::type PacketScalar;
+  enum { size = internal::size_at_compile_time<_Rows,_Cols>::ret };
+  typedef typename find_best_packet<_Scalar,size>::type PacketScalar;
   enum {
       row_major_bit = _Options&RowMajor ? RowMajorBit : 0,
       is_dynamic_size_storage = _MaxRows==Dynamic || _MaxCols==Dynamic,
diff --git a/Eigen/src/Core/util/XprHelper.h b/Eigen/src/Core/util/XprHelper.h
index 2808dfd6c..f1520e4e2 100644
--- a/Eigen/src/Core/util/XprHelper.h
+++ b/Eigen/src/Core/util/XprHelper.h
@@ -126,6 +126,28 @@ template<typename T> struct unpacket_traits
   };
 };
 
+template<int Size, typename PacketType,
+         bool Stop = (Size%unpacket_traits<PacketType>::size)==0 || is_same<PacketType,typename unpacket_traits<PacketType>::half>::value>
+struct find_best_packet_helper;
+
+template< int Size, typename PacketType>
+struct find_best_packet_helper<Size,PacketType,true>
+{
+  typedef PacketType type;
+};
+
+template<int Size, typename PacketType>
+struct find_best_packet_helper<Size,PacketType,false>
+{
+  typedef typename find_best_packet_helper<Size,typename unpacket_traits<PacketType>::half>::type type;
+};
+
+template<typename T, int Size>
+struct find_best_packet
+{
+  typedef typename find_best_packet_helper<Size,typename packet_traits<T>::type>::type type;
+};
+
 #if EIGEN_MAX_STATIC_ALIGN_BYTES>0
 template<int ArrayBytes, int AlignmentBytes,
          bool Match     =  bool((ArrayBytes%AlignmentBytes)==0),
diff --git a/test/vectorization_logic.cpp b/test/vectorization_logic.cpp
index 18dad6b5d..6ff38ed11 100644
--- a/test/vectorization_logic.cpp
+++ b/test/vectorization_logic.cpp
@@ -101,11 +101,16 @@ bool test_redux(const Xpr&, int traversal, int unrolling)
   return res;
 }
 
-template<typename Scalar, bool Enable = internal::packet_traits<Scalar>::Vectorizable> struct vectorization_logic
+template<typename Scalar, bool Enable = internal::packet_traits<Scalar>::Vectorizable>
+struct vectorization_logic
 {
   typedef internal::packet_traits<Scalar> PacketTraits;
+  
+  typedef typename internal::packet_traits<Scalar>::type PacketType;
+  typedef typename internal::unpacket_traits<PacketType>::half HalfPacketType;
   enum {
-    PacketSize = PacketTraits::size
+    PacketSize = internal::unpacket_traits<PacketType>::size,
+    HalfPacketSize = internal::unpacket_traits<HalfPacketType>::size
   };
   static void run()
   {
@@ -179,9 +184,9 @@ template<typename Scalar, bool Enable = internal::packet_traits<Scalar>::Vectori
               
       VERIFY(test_assign(Matrix3(),Matrix3().cwiseQuotient(Matrix3()),
         PacketTraits::HasDiv ? LinearVectorizedTraversal : LinearTraversal,CompleteUnrolling));
-        
+      
       VERIFY(test_assign(Matrix<Scalar,17,17>(),Matrix<Scalar,17,17>()+Matrix<Scalar,17,17>(),
-        LinearTraversal,NoUnrolling));
+        HalfPacketSize==1 ? InnerVectorizedTraversal : LinearTraversal,NoUnrolling));
         
       VERIFY(test_assign(Matrix11(),Matrix<Scalar,17,17>().template block<PacketSize,PacketSize>(2,3)+Matrix<Scalar,17,17>().template block<PacketSize,PacketSize>(8,4),
         DefaultTraversal,PacketSize>4?InnerUnrolling:CompleteUnrolling));
@@ -221,8 +226,6 @@ template<typename Scalar, bool Enable = internal::packet_traits<Scalar>::Vectori
 
     VERIFY(test_redux(VectorX(10),
       LinearVectorizedTraversal,NoUnrolling));
-
-    
   }
 };
 
@@ -231,6 +234,113 @@ template<typename Scalar> struct vectorization_logic<Scalar,false>
   static void run() {}
 };
 
+template<typename Scalar, bool Enable = !internal::is_same<typename internal::unpacket_traits<typename internal::packet_traits<Scalar>::type>::half,
+                                                           typename internal::packet_traits<Scalar>::type>::value >
+struct vectorization_logic_half
+{
+  typedef internal::packet_traits<Scalar> PacketTraits;
+  typedef typename internal::unpacket_traits<typename internal::packet_traits<Scalar>::type>::half PacketType;
+  enum {
+    PacketSize = internal::unpacket_traits<PacketType>::size
+  };
+  static void run()
+  {
+    
+    typedef Matrix<Scalar,PacketSize,1> Vector1;
+    typedef Matrix<Scalar,PacketSize,PacketSize> Matrix11;
+    typedef Matrix<Scalar,5*PacketSize,7,ColMajor> Matrix57;
+    typedef Matrix<Scalar,5*PacketSize,7,DontAlign|ColMajor> Matrix57u;
+//     typedef Matrix<Scalar,(Matrix11::Flags&RowMajorBit)?16:4*PacketSize,(Matrix11::Flags&RowMajorBit)?4*PacketSize:16> Matrix44;
+//     typedef Matrix<Scalar,(Matrix11::Flags&RowMajorBit)?16:4*PacketSize,(Matrix11::Flags&RowMajorBit)?4*PacketSize:16,DontAlign|EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION> Matrix44u;
+//     typedef Matrix<Scalar,4*PacketSize,4*PacketSize,ColMajor> Matrix44c;
+//     typedef Matrix<Scalar,4*PacketSize,4*PacketSize,RowMajor> Matrix44r;
+
+    typedef Matrix<Scalar,
+        (PacketSize==8 ? 4 : PacketSize==4 ? 2 : PacketSize==2 ? 1 : /*PacketSize==1 ?*/ 1),
+        (PacketSize==8 ? 2 : PacketSize==4 ? 2 : PacketSize==2 ? 2 : /*PacketSize==1 ?*/ 1)
+      > Matrix1;
+
+    typedef Matrix<Scalar,
+        (PacketSize==8 ? 4 : PacketSize==4 ? 2 : PacketSize==2 ? 1 : /*PacketSize==1 ?*/ 1),
+        (PacketSize==8 ? 2 : PacketSize==4 ? 2 : PacketSize==2 ? 2 : /*PacketSize==1 ?*/ 1),
+      DontAlign|((Matrix1::Flags&RowMajorBit)?RowMajor:ColMajor)> Matrix1u;
+
+    // this type is made such that it can only be vectorized when viewed as a linear 1D vector
+    typedef Matrix<Scalar,
+        (PacketSize==8 ? 4 : PacketSize==4 ? 6 : PacketSize==2 ? ((Matrix11::Flags&RowMajorBit)?2:3) : /*PacketSize==1 ?*/ 1),
+        (PacketSize==8 ? 6 : PacketSize==4 ? 2 : PacketSize==2 ? ((Matrix11::Flags&RowMajorBit)?3:2) : /*PacketSize==1 ?*/ 3)
+      > Matrix3;
+    
+    #if !EIGEN_GCC_AND_ARCH_DOESNT_WANT_STACK_ALIGNMENT
+    VERIFY(test_assign(Vector1(),Vector1(),
+      InnerVectorizedTraversal,CompleteUnrolling));
+    VERIFY(test_assign(Vector1(),Vector1()+Vector1(),
+      InnerVectorizedTraversal,CompleteUnrolling));
+    VERIFY(test_assign(Vector1(),Vector1().cwiseProduct(Vector1()),
+      InnerVectorizedTraversal,CompleteUnrolling));
+    VERIFY(test_assign(Vector1(),Vector1().template cast<Scalar>(),
+      InnerVectorizedTraversal,CompleteUnrolling));
+
+
+    VERIFY(test_assign(Vector1(),Vector1(),
+      InnerVectorizedTraversal,CompleteUnrolling));
+    VERIFY(test_assign(Vector1(),Vector1()+Vector1(),
+      InnerVectorizedTraversal,CompleteUnrolling));
+    VERIFY(test_assign(Vector1(),Vector1().cwiseProduct(Vector1()),
+      InnerVectorizedTraversal,CompleteUnrolling));
+
+    VERIFY(test_assign(Matrix57(),Matrix57()+Matrix57(),
+      InnerVectorizedTraversal,InnerUnrolling));
+
+    VERIFY(test_assign(Matrix57u(),Matrix57()+Matrix57(),
+      LinearTraversal,NoUnrolling));
+
+    VERIFY(test_assign(Matrix1u(),Matrix1()+Matrix1(),
+      LinearTraversal,CompleteUnrolling));
+        
+    if(PacketSize>1)
+    {
+      typedef Matrix<Scalar,3,3,ColMajor> Matrix33c;
+      VERIFY(test_assign(Matrix33c().row(2),Matrix33c().row(1)+Matrix33c().row(1),
+        LinearTraversal,CompleteUnrolling));
+      VERIFY(test_assign(Matrix33c().col(0),Matrix33c().col(1)+Matrix33c().col(1),
+        LinearTraversal,CompleteUnrolling));
+              
+      VERIFY(test_assign(Matrix3(),Matrix3().cwiseQuotient(Matrix3()),
+        PacketTraits::HasDiv ? LinearVectorizedTraversal : LinearTraversal,CompleteUnrolling));
+        
+      VERIFY(test_assign(Matrix<Scalar,17,17>(),Matrix<Scalar,17,17>()+Matrix<Scalar,17,17>(),
+        LinearTraversal,NoUnrolling));
+        
+      VERIFY(test_assign(Matrix11(),Matrix<Scalar,17,17>().template block<PacketSize,PacketSize>(2,3)+Matrix<Scalar,17,17>().template block<PacketSize,PacketSize>(8,4),
+        DefaultTraversal,PacketSize>4?InnerUnrolling:CompleteUnrolling));
+    }
+    
+    VERIFY(test_redux(Matrix3(),
+      LinearVectorizedTraversal,CompleteUnrolling));
+
+    VERIFY(test_redux(Matrix57(),
+      LinearVectorizedTraversal,CompleteUnrolling));
+
+    VERIFY(test_redux(Matrix57().template block<PacketSize,3>(1,0),
+      DefaultTraversal,CompleteUnrolling));
+
+    VERIFY((test_assign<
+            Map<Matrix<Scalar,EIGEN_PLAIN_ENUM_MAX(2,PacketSize),EIGEN_PLAIN_ENUM_MAX(2,PacketSize)>, AlignedMax, InnerStride<3*PacketSize> >,
+            Matrix<Scalar,EIGEN_PLAIN_ENUM_MAX(2,PacketSize),EIGEN_PLAIN_ENUM_MAX(2,PacketSize)>
+            >(DefaultTraversal,CompleteUnrolling)));
+
+    VERIFY((test_assign(Matrix57(), Matrix<Scalar,5*PacketSize,3>()*Matrix<Scalar,3,7>(),
+                        InnerVectorizedTraversal, CompleteUnrolling)));
+    #endif
+  }
+};
+
+template<typename Scalar> struct vectorization_logic_half<Scalar,false>
+{
+  static void run() {}
+};
+
 void test_vectorization_logic()
 {
 
@@ -242,6 +352,12 @@ void test_vectorization_logic()
   CALL_SUBTEST( vectorization_logic<std::complex<float> >::run() );
   CALL_SUBTEST( vectorization_logic<std::complex<double> >::run() );
   
+  CALL_SUBTEST( vectorization_logic_half<int>::run() );
+  CALL_SUBTEST( vectorization_logic_half<float>::run() );
+  CALL_SUBTEST( vectorization_logic_half<double>::run() );
+  CALL_SUBTEST( vectorization_logic_half<std::complex<float> >::run() );
+  CALL_SUBTEST( vectorization_logic_half<std::complex<double> >::run() );
+  
   if(internal::packet_traits<float>::Vectorizable)
   {
     VERIFY(test_assign(Matrix<float,3,3>(),Matrix<float,3,3>()+Matrix<float,3,3>(),