diff --git a/Eigen/src/Core/arch/AVX/Complex.h b/Eigen/src/Core/arch/AVX/Complex.h
index 16faf1082..5b8ff59bd 100644
--- a/Eigen/src/Core/arch/AVX/Complex.h
+++ b/Eigen/src/Core/arch/AVX/Complex.h
@@ -47,7 +47,7 @@ template<> struct packet_traits<std::complex<float> >  : default_packet_traits
 };
 #endif
 
-template<> struct unpacket_traits<Packet4cf> { typedef std::complex<float> type; enum {size=4, alignment=Aligned32}; typedef Packet2cf half; };
+template<> struct unpacket_traits<Packet4cf> { typedef std::complex<float> type; enum {size=4, alignment=Aligned32, vectorizable=true}; typedef Packet2cf half; };
 
 template<> EIGEN_STRONG_INLINE Packet4cf padd<Packet4cf>(const Packet4cf& a, const Packet4cf& b) { return Packet4cf(_mm256_add_ps(a.v,b.v)); }
 template<> EIGEN_STRONG_INLINE Packet4cf psub<Packet4cf>(const Packet4cf& a, const Packet4cf& b) { return Packet4cf(_mm256_sub_ps(a.v,b.v)); }
@@ -263,7 +263,7 @@ template<> struct packet_traits<std::complex<double> >  : default_packet_traits
 };
 #endif
 
-template<> struct unpacket_traits<Packet2cd> { typedef std::complex<double> type; enum {size=2, alignment=Aligned32}; typedef Packet1cd half; };
+template<> struct unpacket_traits<Packet2cd> { typedef std::complex<double> type; enum {size=2, alignment=Aligned32, vectorizable=true}; typedef Packet1cd half; };
 
 template<> EIGEN_STRONG_INLINE Packet2cd padd<Packet2cd>(const Packet2cd& a, const Packet2cd& b) { return Packet2cd(_mm256_add_pd(a.v,b.v)); }
 template<> EIGEN_STRONG_INLINE Packet2cd psub<Packet2cd>(const Packet2cd& a, const Packet2cd& b) { return Packet2cd(_mm256_sub_pd(a.v,b.v)); }
diff --git a/Eigen/src/Core/arch/AVX/PacketMath.h b/Eigen/src/Core/arch/AVX/PacketMath.h
index c18c18cc3..ee00f1f7d 100644
--- a/Eigen/src/Core/arch/AVX/PacketMath.h
+++ b/Eigen/src/Core/arch/AVX/PacketMath.h
@@ -117,14 +117,14 @@ template<> struct unpacket_traits<Packet8f> {
   typedef float     type;
   typedef Packet4f  half;
   typedef Packet8i  integer_packet;
-  enum {size=8, alignment=Aligned32};
+  enum {size=8, alignment=Aligned32, vectorizable=true};
 };
 template<> struct unpacket_traits<Packet4d> {
   typedef double type;
   typedef Packet2d half;
-  enum {size=4, alignment=Aligned32};
+  enum {size=4, alignment=Aligned32, vectorizable=true};
 };
-template<> struct unpacket_traits<Packet8i> { typedef int    type; typedef Packet4i half; enum {size=8, alignment=Aligned32}; };
+template<> struct unpacket_traits<Packet8i> { typedef int    type; typedef Packet4i half; enum {size=8, alignment=Aligned32, vectorizable=false}; };
 
 template<> EIGEN_STRONG_INLINE Packet8f pset1<Packet8f>(const float&  from) { return _mm256_set1_ps(from); }
 template<> EIGEN_STRONG_INLINE Packet4d pset1<Packet4d>(const double& from) { return _mm256_set1_pd(from); }
diff --git a/Eigen/src/Core/arch/AVX512/Complex.h b/Eigen/src/Core/arch/AVX512/Complex.h
index 7ea72c509..9a89dd01f 100644
--- a/Eigen/src/Core/arch/AVX512/Complex.h
+++ b/Eigen/src/Core/arch/AVX512/Complex.h
@@ -50,7 +50,8 @@ template<> struct unpacket_traits<Packet8cf> {
   typedef std::complex<float> type;
   enum {
     size = 8,
-    alignment=unpacket_traits<Packet16f>::alignment
+    alignment=unpacket_traits<Packet16f>::alignment,
+    vectorizable=true
   };
   typedef Packet4cf half;
 };
@@ -245,7 +246,8 @@ template<> struct unpacket_traits<Packet4cd> {
   typedef std::complex<double> type;
   enum {
     size = 4,
-    alignment = unpacket_traits<Packet8d>::alignment
+    alignment = unpacket_traits<Packet8d>::alignment,
+    vectorizable=true
   };
   typedef Packet2cd half;
 };
diff --git a/Eigen/src/Core/arch/AVX512/PacketMath.h b/Eigen/src/Core/arch/AVX512/PacketMath.h
index a2c9599b6..2199970ad 100644
--- a/Eigen/src/Core/arch/AVX512/PacketMath.h
+++ b/Eigen/src/Core/arch/AVX512/PacketMath.h
@@ -102,19 +102,19 @@ struct unpacket_traits<Packet16f> {
   typedef float type;
   typedef Packet8f half;
   typedef Packet16i integer_packet;
-  enum { size = 16, alignment=Aligned64 };
+  enum { size = 16, alignment=Aligned64, vectorizable=true };
 };
 template <>
 struct unpacket_traits<Packet8d> {
   typedef double type;
   typedef Packet4d half;
-  enum { size = 8, alignment=Aligned64 };
+  enum { size = 8, alignment=Aligned64, vectorizable=true };
 };
 template <>
 struct unpacket_traits<Packet16i> {
   typedef int type;
   typedef Packet8i half;
-  enum { size = 16, alignment=Aligned64 };
+  enum { size = 16, alignment=Aligned64, vectorizable=false };
 };
 
 template <>
diff --git a/Eigen/src/Core/arch/AltiVec/Complex.h b/Eigen/src/Core/arch/AltiVec/Complex.h
index 23dd016f9..440d058d8 100644
--- a/Eigen/src/Core/arch/AltiVec/Complex.h
+++ b/Eigen/src/Core/arch/AltiVec/Complex.h
@@ -60,7 +60,7 @@ template<> struct packet_traits<std::complex<float> >  : default_packet_traits
   };
 };
 
-template<> struct unpacket_traits<Packet2cf> { typedef std::complex<float> type; enum {size=2, alignment=Aligned16}; typedef Packet2cf half; };
+template<> struct unpacket_traits<Packet2cf> { typedef std::complex<float> type; enum {size=2, alignment=Aligned16, vectorizable=true}; typedef Packet2cf half; };
 
 template<> EIGEN_STRONG_INLINE Packet2cf pset1<Packet2cf>(const std::complex<float>&  from)
 {
@@ -286,7 +286,7 @@ template<> struct packet_traits<std::complex<double> >  : default_packet_traits
   };
 };
 
-template<> struct unpacket_traits<Packet1cd> { typedef std::complex<double> type; enum {size=1, alignment=Aligned16}; typedef Packet1cd half; };
+template<> struct unpacket_traits<Packet1cd> { typedef std::complex<double> type; enum {size=1, alignment=Aligned16, vectorizable=true}; typedef Packet1cd half; };
 
 template<> EIGEN_STRONG_INLINE Packet1cd pload <Packet1cd>(const std::complex<double>* from) { return Packet1cd(pload<Packet2d>((const double*)from)); }
 template<> EIGEN_STRONG_INLINE Packet1cd ploadu<Packet1cd>(const std::complex<double>* from) { return Packet1cd(ploadu<Packet2d>((const double*)from)); }
diff --git a/Eigen/src/Core/arch/AltiVec/PacketMath.h b/Eigen/src/Core/arch/AltiVec/PacketMath.h
index 6b347cedb..9535724eb 100755
--- a/Eigen/src/Core/arch/AltiVec/PacketMath.h
+++ b/Eigen/src/Core/arch/AltiVec/PacketMath.h
@@ -192,13 +192,13 @@ template<> struct unpacket_traits<Packet4f>
   typedef float     type;
   typedef Packet4f  half;
   typedef Packet4i  integer_packet;
-  enum {size=4, alignment=Aligned16};
+  enum {size=4, alignment=Aligned16, vectorizable=true};
 };
 template<> struct unpacket_traits<Packet4i>
 {
   typedef int       type;
   typedef Packet4i  half;
-  enum {size=4, alignment=Aligned16};
+  enum {size=4, alignment=Aligned16, vectorizable=false};
 };
 
 inline std::ostream & operator <<(std::ostream & s, const Packet16uc & v)
@@ -921,7 +921,7 @@ template<> struct packet_traits<double> : default_packet_traits
   };
 };
 
-template<> struct unpacket_traits<Packet2d> { typedef double type; enum {size=2, alignment=Aligned16}; typedef Packet2d half; };
+template<> struct unpacket_traits<Packet2d> { typedef double type; enum {size=2, alignment=Aligned16, vectorizable=true}; typedef Packet2d half; };
 
 inline std::ostream & operator <<(std::ostream & s, const Packet2l & v)
 {
diff --git a/Eigen/src/Core/arch/GPU/PacketMath.h b/Eigen/src/Core/arch/GPU/PacketMath.h
index e3b2d56ec..c1b097fb9 100644
--- a/Eigen/src/Core/arch/GPU/PacketMath.h
+++ b/Eigen/src/Core/arch/GPU/PacketMath.h
@@ -90,8 +90,8 @@ template<> struct packet_traits<double> : default_packet_traits
 };
 
 
-template<> struct unpacket_traits<float4>  { typedef float  type; enum {size=4, alignment=Aligned16}; typedef float4 half; };
-template<> struct unpacket_traits<double2> { typedef double type; enum {size=2, alignment=Aligned16}; typedef double2 half; };
+template<> struct unpacket_traits<float4>  { typedef float  type; enum {size=4, alignment=Aligned16, vectorizable=true}; typedef float4 half; };
+template<> struct unpacket_traits<double2> { typedef double type; enum {size=2, alignment=Aligned16, vectorizable=true}; typedef double2 half; };
 
 template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pset1<float4>(const float&  from) {
   return make_float4(from, from, from, from);
diff --git a/Eigen/src/Core/arch/GPU/PacketMathHalf.h b/Eigen/src/Core/arch/GPU/PacketMathHalf.h
index 020baa353..316ac0283 100644
--- a/Eigen/src/Core/arch/GPU/PacketMathHalf.h
+++ b/Eigen/src/Core/arch/GPU/PacketMathHalf.h
@@ -41,7 +41,7 @@ template<> struct packet_traits<Eigen::half> : default_packet_traits
   };
 };
 
-template<> struct unpacket_traits<half2> { typedef Eigen::half type; enum {size=2, alignment=Aligned16}; typedef half2 half; };
+template<> struct unpacket_traits<half2> { typedef Eigen::half type; enum {size=2, alignment=Aligned16, vectorizable=true}; typedef half2 half; };
 
 template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pset1<half2>(const Eigen::half& from) {
 
@@ -521,7 +521,7 @@ struct packet_traits<half> : default_packet_traits {
 };
 
 
-template<> struct unpacket_traits<Packet16h> { typedef Eigen::half type; enum {size=16, alignment=Aligned32}; typedef Packet16h half; };
+template<> struct unpacket_traits<Packet16h> { typedef Eigen::half type; enum {size=16, alignment=Aligned32, vectorizable=true}; typedef Packet16h half; };
 
 template<> EIGEN_STRONG_INLINE Packet16h pset1<Packet16h>(const Eigen::half& from) {
   Packet16h result;
@@ -1003,7 +1003,7 @@ struct packet_traits<Eigen::half> : default_packet_traits {
 };
 
 
-template<> struct unpacket_traits<Packet8h> { typedef Eigen::half type; enum {size=8, alignment=Aligned16}; typedef Packet8h half; };
+template<> struct unpacket_traits<Packet8h> { typedef Eigen::half type; enum {size=8, alignment=Aligned16, vectorizable=true}; typedef Packet8h half; };
 
 template<> EIGEN_STRONG_INLINE Packet8h pset1<Packet8h>(const Eigen::half& from) {
   Packet8h result;
@@ -1359,7 +1359,7 @@ struct packet_traits<Eigen::half> : default_packet_traits {
 };
 
 
-template<> struct unpacket_traits<Packet4h> { typedef Eigen::half type; enum {size=4, alignment=Aligned16}; typedef Packet4h half; };
+template<> struct unpacket_traits<Packet4h> { typedef Eigen::half type; enum {size=4, alignment=Aligned16, vectorizable=true}; typedef Packet4h half; };
 
 template<> EIGEN_STRONG_INLINE Packet4h pset1<Packet4h>(const Eigen::half& from) {
   Packet4h result;
diff --git a/Eigen/src/Core/arch/MSA/Complex.h b/Eigen/src/Core/arch/MSA/Complex.h
index 9a45cf51e..fa64d3564 100644
--- a/Eigen/src/Core/arch/MSA/Complex.h
+++ b/Eigen/src/Core/arch/MSA/Complex.h
@@ -127,7 +127,7 @@ struct packet_traits<std::complex<float> > : default_packet_traits {
 template <>
 struct unpacket_traits<Packet2cf> {
   typedef std::complex<float> type;
-  enum { size = 2, alignment = Aligned16 };
+  enum { size = 2, alignment = Aligned16, vectorizable=true };
   typedef Packet2cf half;
 };
 
@@ -500,7 +500,7 @@ struct packet_traits<std::complex<double> > : default_packet_traits {
 template <>
 struct unpacket_traits<Packet1cd> {
   typedef std::complex<double> type;
-  enum { size = 1, alignment = Aligned16 };
+  enum { size = 1, alignment = Aligned16, vectorizable=true };
   typedef Packet1cd half;
 };
 
diff --git a/Eigen/src/Core/arch/MSA/PacketMath.h b/Eigen/src/Core/arch/MSA/PacketMath.h
index 094c874ee..a97156a84 100644
--- a/Eigen/src/Core/arch/MSA/PacketMath.h
+++ b/Eigen/src/Core/arch/MSA/PacketMath.h
@@ -117,14 +117,14 @@ struct packet_traits<int32_t> : default_packet_traits {
 template <>
 struct unpacket_traits<Packet4f> {
   typedef float type;
-  enum { size = 4, alignment = Aligned16 };
+  enum { size = 4, alignment = Aligned16, vectorizable=true };
   typedef Packet4f half;
 };
 
 template <>
 struct unpacket_traits<Packet4i> {
   typedef int32_t type;
-  enum { size = 4, alignment = Aligned16 };
+  enum { size = 4, alignment = Aligned16, vectorizable=true };
   typedef Packet4i half;
 };
 
@@ -925,7 +925,7 @@ struct packet_traits<double> : default_packet_traits {
 template <>
 struct unpacket_traits<Packet2d> {
   typedef double type;
-  enum { size = 2, alignment = Aligned16 };
+  enum { size = 2, alignment = Aligned16, vectorizable=true };
   typedef Packet2d half;
 };
 
diff --git a/Eigen/src/Core/arch/NEON/Complex.h b/Eigen/src/Core/arch/NEON/Complex.h
index 62d107645..d149275b5 100644
--- a/Eigen/src/Core/arch/NEON/Complex.h
+++ b/Eigen/src/Core/arch/NEON/Complex.h
@@ -62,7 +62,7 @@ template<> struct packet_traits<std::complex<float> >  : default_packet_traits
   };
 };
 
-template<> struct unpacket_traits<Packet2cf> { typedef std::complex<float> type; enum {size=2, alignment=Aligned16}; typedef Packet2cf half; };
+template<> struct unpacket_traits<Packet2cf> { typedef std::complex<float> type; enum {size=2, alignment=Aligned16, vectorizable=true}; typedef Packet2cf half; };
 
 template<> EIGEN_STRONG_INLINE Packet2cf pset1<Packet2cf>(const std::complex<float>&  from)
 {
@@ -328,7 +328,7 @@ template<> struct packet_traits<std::complex<double> >  : default_packet_traits
   };
 };
 
-template<> struct unpacket_traits<Packet1cd> { typedef std::complex<double> type; enum {size=1, alignment=Aligned16}; typedef Packet1cd half; };
+template<> struct unpacket_traits<Packet1cd> { typedef std::complex<double> type; enum {size=1, alignment=Aligned16, vectorizable=true}; typedef Packet1cd half; };
 
 template<> EIGEN_STRONG_INLINE Packet1cd pload<Packet1cd>(const std::complex<double>* from) { EIGEN_DEBUG_ALIGNED_LOAD return Packet1cd(pload<Packet2d>((const double*)from)); }
 template<> EIGEN_STRONG_INLINE Packet1cd ploadu<Packet1cd>(const std::complex<double>* from) { EIGEN_DEBUG_UNALIGNED_LOAD return Packet1cd(ploadu<Packet2d>((const double*)from)); }
diff --git a/Eigen/src/Core/arch/NEON/PacketMath.h b/Eigen/src/Core/arch/NEON/PacketMath.h
index 76e6b3966..e8b351849 100644
--- a/Eigen/src/Core/arch/NEON/PacketMath.h
+++ b/Eigen/src/Core/arch/NEON/PacketMath.h
@@ -145,13 +145,13 @@ template<> struct unpacket_traits<Packet4f>
   typedef float     type;
   typedef Packet4f  half;
   typedef Packet4i  integer_packet;
-  enum {size=4, alignment=Aligned16};
+  enum {size=4, alignment=Aligned16, vectorizable=true};
 };
 template<> struct unpacket_traits<Packet4i>
 {
   typedef int32_t   type;
   typedef Packet4i  half;
-  enum {size=4, alignment=Aligned16};
+  enum {size=4, alignment=Aligned16, vectorizable=true};
 };
 
 template<> EIGEN_STRONG_INLINE Packet4f pset1<Packet4f>(const float&  from) { return vdupq_n_f32(from); }
@@ -657,7 +657,7 @@ template<> struct packet_traits<double>  : default_packet_traits
   };
 };
 
-template<> struct unpacket_traits<Packet2d> { typedef double  type; enum {size=2, alignment=Aligned16}; typedef Packet2d half; };
+template<> struct unpacket_traits<Packet2d> { typedef double  type; enum {size=2, alignment=Aligned16, vectorizable=true}; typedef Packet2d half; };
 
 template<> EIGEN_STRONG_INLINE Packet2d pset1<Packet2d>(const double&  from) { return vdupq_n_f64(from); }
 
diff --git a/Eigen/src/Core/arch/SSE/Complex.h b/Eigen/src/Core/arch/SSE/Complex.h
index e51966f0d..f39988eac 100644
--- a/Eigen/src/Core/arch/SSE/Complex.h
+++ b/Eigen/src/Core/arch/SSE/Complex.h
@@ -50,7 +50,7 @@ template<> struct packet_traits<std::complex<float> >  : default_packet_traits
 };
 #endif
 
-template<> struct unpacket_traits<Packet2cf> { typedef std::complex<float> type; enum {size=2, alignment=Aligned16}; typedef Packet2cf half; };
+template<> struct unpacket_traits<Packet2cf> { typedef std::complex<float> type; enum {size=2, alignment=Aligned16, vectorizable=true}; typedef Packet2cf half; };
 
 template<> EIGEN_STRONG_INLINE Packet2cf padd<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(_mm_add_ps(a.v,b.v)); }
 template<> EIGEN_STRONG_INLINE Packet2cf psub<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(_mm_sub_ps(a.v,b.v)); }
@@ -283,7 +283,7 @@ template<> struct packet_traits<std::complex<double> >  : default_packet_traits
 };
 #endif
 
-template<> struct unpacket_traits<Packet1cd> { typedef std::complex<double> type; enum {size=1, alignment=Aligned16}; typedef Packet1cd half; };
+template<> struct unpacket_traits<Packet1cd> { typedef std::complex<double> type; enum {size=1, alignment=Aligned16, vectorizable=true}; typedef Packet1cd half; };
 
 template<> EIGEN_STRONG_INLINE Packet1cd padd<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(_mm_add_pd(a.v,b.v)); }
 template<> EIGEN_STRONG_INLINE Packet1cd psub<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(_mm_sub_pd(a.v,b.v)); }
diff --git a/Eigen/src/Core/arch/SSE/PacketMath.h b/Eigen/src/Core/arch/SSE/PacketMath.h
index ebc540e24..9c3750af0 100755
--- a/Eigen/src/Core/arch/SSE/PacketMath.h
+++ b/Eigen/src/Core/arch/SSE/PacketMath.h
@@ -166,17 +166,17 @@ template<> struct unpacket_traits<Packet4f> {
   typedef float     type;
   typedef Packet4f  half;
   typedef Packet4i  integer_packet;
-  enum {size=4, alignment=Aligned16};
+  enum {size=4, alignment=Aligned16, vectorizable=true};
 };
 template<> struct unpacket_traits<Packet2d> {
   typedef double    type;
   typedef Packet2d  half;
-  enum {size=2, alignment=Aligned16};
+  enum {size=2, alignment=Aligned16, vectorizable=true};
 };
 template<> struct unpacket_traits<Packet4i> {
   typedef int       type;
   typedef Packet4i  half;
-  enum {size=4, alignment=Aligned16};
+  enum {size=4, alignment=Aligned16, vectorizable=false};
 };
 
 #ifndef EIGEN_VECTORIZE_AVX
diff --git a/Eigen/src/Core/arch/SYCL/InteropHeaders.h b/Eigen/src/Core/arch/SYCL/InteropHeaders.h
index c1da40d14..294cb101a 100644
--- a/Eigen/src/Core/arch/SYCL/InteropHeaders.h
+++ b/Eigen/src/Core/arch/SYCL/InteropHeaders.h
@@ -88,7 +88,7 @@ SYCL_ARITHMETIC(cl::sycl::cl_double2)
 #define SYCL_UNPACKET_TRAITS(packet_type, unpacket_type, lengths)\
 template<> struct unpacket_traits<packet_type>  {\
   typedef unpacket_type  type;\
-  enum {size=lengths, alignment=Aligned16};\
+  enum {size=lengths, alignment=Aligned16, vectorizable=true};\
   typedef packet_type half;\
 };
 SYCL_UNPACKET_TRAITS(cl::sycl::cl_float4, float, 4)
diff --git a/Eigen/src/Core/arch/ZVector/Complex.h b/Eigen/src/Core/arch/ZVector/Complex.h
index 95aba428f..167c3ee4c 100644
--- a/Eigen/src/Core/arch/ZVector/Complex.h
+++ b/Eigen/src/Core/arch/ZVector/Complex.h
@@ -91,8 +91,8 @@ template<> struct packet_traits<std::complex<double> >  : default_packet_traits
   };
 };
 
-template<> struct unpacket_traits<Packet2cf> { typedef std::complex<float>  type; enum {size=2, alignment=Aligned16}; typedef Packet2cf half; };
-template<> struct unpacket_traits<Packet1cd> { typedef std::complex<double> type; enum {size=1, alignment=Aligned16}; typedef Packet1cd half; };
+template<> struct unpacket_traits<Packet2cf> { typedef std::complex<float>  type; enum {size=2, alignment=Aligned16, vectorizable=true}; typedef Packet2cf half; };
+template<> struct unpacket_traits<Packet1cd> { typedef std::complex<double> type; enum {size=1, alignment=Aligned16, vectorizable=true}; typedef Packet1cd half; };
 
 /* Forward declaration */
 EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet2cf,2>& kernel);
diff --git a/Eigen/src/Core/arch/ZVector/PacketMath.h b/Eigen/src/Core/arch/ZVector/PacketMath.h
index 0b37f4992..c8e90f1a8 100755
--- a/Eigen/src/Core/arch/ZVector/PacketMath.h
+++ b/Eigen/src/Core/arch/ZVector/PacketMath.h
@@ -239,9 +239,9 @@ template<> struct packet_traits<double> : default_packet_traits
   };
 };
 
-template<> struct unpacket_traits<Packet4i> { typedef int    type; enum {size=4, alignment=Aligned16}; typedef Packet4i half; };
-template<> struct unpacket_traits<Packet4f> { typedef float  type; enum {size=4, alignment=Aligned16}; typedef Packet4f half; };
-template<> struct unpacket_traits<Packet2d> { typedef double type; enum {size=2, alignment=Aligned16}; typedef Packet2d half; };
+template<> struct unpacket_traits<Packet4i> { typedef int    type; enum {size=4, alignment=Aligned16, vectorizable=true}; typedef Packet4i half; };
+template<> struct unpacket_traits<Packet4f> { typedef float  type; enum {size=4, alignment=Aligned16, vectorizable=true}; typedef Packet4f half; };
+template<> struct unpacket_traits<Packet2d> { typedef double type; enum {size=2, alignment=Aligned16, vectorizable=true}; typedef Packet2d half; };
 
 /* Forward declaration */
 EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet4f,4>& kernel);
diff --git a/Eigen/src/Core/products/GeneralBlockPanelKernel.h b/Eigen/src/Core/products/GeneralBlockPanelKernel.h
index 86767d0e9..030c7740a 100644
--- a/Eigen/src/Core/products/GeneralBlockPanelKernel.h
+++ b/Eigen/src/Core/products/GeneralBlockPanelKernel.h
@@ -15,7 +15,13 @@ namespace Eigen {
 
 namespace internal {
 
-template<typename _LhsScalar, typename _RhsScalar, bool _ConjLhs=false, bool _ConjRhs=false, int Arch=Architecture::Target>
+enum PacketSizeType {
+  PacketFull = 0,
+  PacketHalf,
+  PacketQuarter
+};
+
+template<typename _LhsScalar, typename _RhsScalar, bool _ConjLhs=false, bool _ConjRhs=false, int Arch=Architecture::Target, int _PacketSize=PacketFull>
 class gebp_traits;
 
 
@@ -365,6 +371,43 @@ struct QuadPacket
   const Packet& get(const FixedInt<3>&) const { return B3; }
 };
 
+template <int N, typename T1, typename T2, typename T3>
+struct packet_conditional { typedef T3 type; };
+
+template <typename T1, typename T2, typename T3>
+struct packet_conditional<PacketFull, T1, T2, T3> { typedef T1 type; };
+
+template <typename T1, typename T2, typename T3>
+struct packet_conditional<PacketHalf, T1, T2, T3> { typedef T2 type; };
+
+#define PACKET_DECL_COND_PREFIX(prefix, name, packet_size)         \
+  typedef typename packet_conditional<packet_size,                 \
+                                      typename packet_traits<name ## Scalar>::type, \
+                                      typename packet_traits<name ## Scalar>::half, \
+                                      typename unpacket_traits<typename packet_traits<name ## Scalar>::half>::half>::type \
+  prefix ## name ## Packet
+
+#define PACKET_DECL_COND(name, packet_size)                        \
+  typedef typename packet_conditional<packet_size,                 \
+                                      typename packet_traits<name ## Scalar>::type, \
+                                      typename packet_traits<name ## Scalar>::half, \
+                                      typename unpacket_traits<typename packet_traits<name ## Scalar>::half>::half>::type \
+  name ## Packet
+
+#define PACKET_DECL_COND_SCALAR_PREFIX(prefix, packet_size)        \
+  typedef typename packet_conditional<packet_size,                 \
+                                      typename packet_traits<Scalar>::type, \
+                                      typename packet_traits<Scalar>::half, \
+                                      typename unpacket_traits<typename packet_traits<Scalar>::half>::half>::type \
+  prefix ## ScalarPacket
+
+#define PACKET_DECL_COND_SCALAR(packet_size)                       \
+  typedef typename packet_conditional<packet_size,                 \
+                                      typename packet_traits<Scalar>::type, \
+                                      typename packet_traits<Scalar>::half, \
+                                      typename unpacket_traits<typename packet_traits<Scalar>::half>::half>::type \
+  ScalarPacket
+
 /* Vectorization logic
  *  real*real: unpack rhs to constant packets, ...
  * 
@@ -375,7 +418,7 @@ struct QuadPacket
  *  cplx*real : unpack rhs to constant packets, ...
  *  real*cplx : load lhs as (a0,a0,a1,a1), and mul as usual
  */
-template<typename _LhsScalar, typename _RhsScalar, bool _ConjLhs, bool _ConjRhs, int Arch>
+template<typename _LhsScalar, typename _RhsScalar, bool _ConjLhs, bool _ConjRhs, int Arch, int _PacketSize>
 class gebp_traits
 {
 public:
@@ -383,13 +426,17 @@ public:
   typedef _RhsScalar RhsScalar;
   typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;
 
+  PACKET_DECL_COND_PREFIX(_, Lhs, _PacketSize);
+  PACKET_DECL_COND_PREFIX(_, Rhs, _PacketSize);
+  PACKET_DECL_COND_PREFIX(_, Res, _PacketSize);
+
   enum {
     ConjLhs = _ConjLhs,
     ConjRhs = _ConjRhs,
-    Vectorizable = packet_traits<LhsScalar>::Vectorizable && packet_traits<RhsScalar>::Vectorizable,
-    LhsPacketSize = Vectorizable ? packet_traits<LhsScalar>::size : 1,
-    RhsPacketSize = Vectorizable ? packet_traits<RhsScalar>::size : 1,
-    ResPacketSize = Vectorizable ? packet_traits<ResScalar>::size : 1,
+    Vectorizable = unpacket_traits<_LhsPacket>::vectorizable && unpacket_traits<_RhsPacket>::vectorizable,
+    LhsPacketSize = Vectorizable ? unpacket_traits<_LhsPacket>::size : 1,
+    RhsPacketSize = Vectorizable ? unpacket_traits<_RhsPacket>::size : 1,
+    ResPacketSize = Vectorizable ? unpacket_traits<_ResPacket>::size : 1,
     
     NumberOfRegisters = EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS,
 
@@ -413,9 +460,6 @@ public:
     RhsProgress = 1
   };
 
-  typedef typename packet_traits<LhsScalar>::type  _LhsPacket;
-  typedef typename packet_traits<RhsScalar>::type  _RhsPacket;
-  typedef typename packet_traits<ResScalar>::type  _ResPacket;
 
   typedef typename conditional<Vectorizable,_LhsPacket,LhsScalar>::type LhsPacket;
   typedef typename conditional<Vectorizable,_RhsPacket,RhsScalar>::type RhsPacket;
@@ -503,21 +547,25 @@ public:
 
 };
 
-template<typename RealScalar, bool _ConjLhs, int Arch>
-class gebp_traits<std::complex<RealScalar>, RealScalar, _ConjLhs, false, Arch>
+template<typename RealScalar, bool _ConjLhs, int Arch, int _PacketSize>
+class gebp_traits<std::complex<RealScalar>, RealScalar, _ConjLhs, false, Arch, _PacketSize>
 {
 public:
   typedef std::complex<RealScalar> LhsScalar;
   typedef RealScalar RhsScalar;
   typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;
 
+  PACKET_DECL_COND_PREFIX(_, Lhs, _PacketSize);
+  PACKET_DECL_COND_PREFIX(_, Rhs, _PacketSize);
+  PACKET_DECL_COND_PREFIX(_, Res, _PacketSize);
+
   enum {
     ConjLhs = _ConjLhs,
     ConjRhs = false,
-    Vectorizable = packet_traits<LhsScalar>::Vectorizable && packet_traits<RhsScalar>::Vectorizable,
-    LhsPacketSize = Vectorizable ? packet_traits<LhsScalar>::size : 1,
-    RhsPacketSize = Vectorizable ? packet_traits<RhsScalar>::size : 1,
-    ResPacketSize = Vectorizable ? packet_traits<ResScalar>::size : 1,
+    Vectorizable = unpacket_traits<_LhsPacket>::vectorizable && unpacket_traits<_RhsPacket>::vectorizable,
+    LhsPacketSize = Vectorizable ? unpacket_traits<_LhsPacket>::size : 1,
+    RhsPacketSize = Vectorizable ? unpacket_traits<_RhsPacket>::size : 1,
+    ResPacketSize = Vectorizable ? unpacket_traits<_ResPacket>::size : 1,
     
     NumberOfRegisters = EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS,
     nr = 4,
@@ -532,10 +580,6 @@ public:
     RhsProgress = 1
   };
 
-  typedef typename packet_traits<LhsScalar>::type  _LhsPacket;
-  typedef typename packet_traits<RhsScalar>::type  _RhsPacket;
-  typedef typename packet_traits<ResScalar>::type  _ResPacket;
-
   typedef typename conditional<Vectorizable,_LhsPacket,LhsScalar>::type LhsPacket;
   typedef typename conditional<Vectorizable,_RhsPacket,RhsScalar>::type RhsPacket;
   typedef typename conditional<Vectorizable,_ResPacket,ResScalar>::type ResPacket;
@@ -714,8 +758,8 @@ template<typename Packet> struct unpacket_traits<DoublePacket<Packet> > {
 //   return res;
 // }
 
-template<typename RealScalar, bool _ConjLhs, bool _ConjRhs, int Arch>
-class gebp_traits<std::complex<RealScalar>, std::complex<RealScalar>, _ConjLhs, _ConjRhs,Arch>
+template<typename RealScalar, bool _ConjLhs, bool _ConjRhs, int Arch, int _PacketSize>
+class gebp_traits<std::complex<RealScalar>, std::complex<RealScalar>, _ConjLhs, _ConjRhs, Arch, _PacketSize >
 {
 public:
   typedef std::complex<RealScalar>  Scalar;
@@ -723,15 +767,21 @@ public:
   typedef std::complex<RealScalar>  RhsScalar;
   typedef std::complex<RealScalar>  ResScalar;
   
+  PACKET_DECL_COND_PREFIX(_, Lhs, _PacketSize);
+  PACKET_DECL_COND_PREFIX(_, Rhs, _PacketSize);
+  PACKET_DECL_COND_PREFIX(_, Res, _PacketSize);
+  PACKET_DECL_COND(Real, _PacketSize);
+  PACKET_DECL_COND_SCALAR(_PacketSize);
+
   enum {
     ConjLhs = _ConjLhs,
     ConjRhs = _ConjRhs,
-    Vectorizable = packet_traits<RealScalar>::Vectorizable
-                && packet_traits<Scalar>::Vectorizable,
-    ResPacketSize  = Vectorizable ? packet_traits<ResScalar>::size  : 1,
-    LhsPacketSize  = Vectorizable ? packet_traits<LhsScalar>::size  : 1,
-    RhsPacketSize  = Vectorizable ? packet_traits<RhsScalar>::size  : 1,
-    RealPacketSize = Vectorizable ? packet_traits<RealScalar>::size : 1,
+    Vectorizable = unpacket_traits<RealPacket>::vectorizable
+                && unpacket_traits<ScalarPacket>::vectorizable,
+    ResPacketSize   = Vectorizable ? unpacket_traits<_ResPacket>::size : 1,
+    LhsPacketSize = Vectorizable ? unpacket_traits<_LhsPacket>::size : 1,
+    RhsPacketSize = Vectorizable ? unpacket_traits<RhsScalar>::size : 1,
+    RealPacketSize  = Vectorizable ? unpacket_traits<RealPacket>::size : 1,
 
     // FIXME: should depend on NumberOfRegisters
     nr = 4,
@@ -741,8 +791,6 @@ public:
     RhsProgress = 1
   };
   
-  typedef typename packet_traits<RealScalar>::type RealPacket;
-  typedef typename packet_traits<Scalar>::type     ScalarPacket;
   typedef DoublePacket<RealPacket>                 DoublePacketType;
 
   typedef typename conditional<Vectorizable,ScalarPacket,Scalar>::type LhsPacket4Packing;
@@ -876,8 +924,8 @@ protected:
   conj_helper<LhsScalar,RhsScalar,ConjLhs,ConjRhs> cj;
 };
 
-template<typename RealScalar, bool _ConjRhs, int Arch>
-class gebp_traits<RealScalar, std::complex<RealScalar>, false, _ConjRhs, Arch>
+template<typename RealScalar, bool _ConjRhs, int Arch, int _PacketSize>
+class gebp_traits<RealScalar, std::complex<RealScalar>, false, _ConjRhs, Arch, _PacketSize >
 {
 public:
   typedef std::complex<RealScalar>  Scalar;
@@ -885,14 +933,25 @@ public:
   typedef Scalar      RhsScalar;
   typedef Scalar      ResScalar;
 
+  PACKET_DECL_COND_PREFIX(_, Lhs, _PacketSize);
+  PACKET_DECL_COND_PREFIX(_, Rhs, _PacketSize);
+  PACKET_DECL_COND_PREFIX(_, Res, _PacketSize);
+  PACKET_DECL_COND_PREFIX(_, Real, _PacketSize);
+  PACKET_DECL_COND_SCALAR_PREFIX(_, _PacketSize);
+
+#undef PACKET_DECL_COND_SCALAR_PREFIX
+#undef PACKET_DECL_COND_PREFIX
+#undef PACKET_DECL_COND_SCALAR
+#undef PACKET_DECL_COND
+
   enum {
     ConjLhs = false,
     ConjRhs = _ConjRhs,
-    Vectorizable = packet_traits<RealScalar>::Vectorizable
-                && packet_traits<Scalar>::Vectorizable,
-    LhsPacketSize = Vectorizable ? packet_traits<LhsScalar>::size : 1,
-    RhsPacketSize = Vectorizable ? packet_traits<RhsScalar>::size : 1,
-    ResPacketSize = Vectorizable ? packet_traits<ResScalar>::size : 1,
+    Vectorizable = unpacket_traits<_RealPacket>::vectorizable
+                && unpacket_traits<_ScalarPacket>::vectorizable,
+    LhsPacketSize = Vectorizable ? unpacket_traits<_LhsPacket>::size : 1,
+    RhsPacketSize = Vectorizable ? unpacket_traits<_RhsPacket>::size : 1,
+    ResPacketSize = Vectorizable ? unpacket_traits<_ResPacket>::size : 1,
     
     NumberOfRegisters = EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS,
     // FIXME: should depend on NumberOfRegisters
@@ -903,10 +962,6 @@ public:
     RhsProgress = 1
   };
 
-  typedef typename packet_traits<LhsScalar>::type  _LhsPacket;
-  typedef typename packet_traits<RhsScalar>::type  _RhsPacket;
-  typedef typename packet_traits<ResScalar>::type  _ResPacket;
-
   typedef typename conditional<Vectorizable,_LhsPacket,LhsScalar>::type LhsPacket;
   typedef typename conditional<Vectorizable,_RhsPacket,RhsScalar>::type RhsPacket;
   typedef typename conditional<Vectorizable,_ResPacket,ResScalar>::type ResPacket;
@@ -998,9 +1053,9 @@ protected:
 
 #if EIGEN_ARCH_ARM64 && defined EIGEN_VECTORIZE_NEON
 
-template<>
-struct gebp_traits <float, float, false, false,Architecture::NEON>
- : gebp_traits<float,float,false,false,Architecture::Generic>
+template<int _PacketSize>
+struct gebp_traits <float, float, false, false,Architecture::NEON,_PacketSize>
+ : gebp_traits<float,float,false,false,Architecture::Generic,_PacketSize>
 {
   typedef float RhsPacket;
 
@@ -1121,7 +1176,10 @@ struct gebp_traits <double, double, false, false,Architecture::NEON>
 template<typename LhsScalar, typename RhsScalar, typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
 struct gebp_kernel
 {
-  typedef gebp_traits<LhsScalar,RhsScalar,ConjugateLhs,ConjugateRhs> Traits;
+  typedef gebp_traits<LhsScalar,RhsScalar,ConjugateLhs,ConjugateRhs,Architecture::Target> Traits;
+  typedef gebp_traits<LhsScalar,RhsScalar,ConjugateLhs,ConjugateRhs,Architecture::Target,PacketHalf> HalfTraits;
+  typedef gebp_traits<LhsScalar,RhsScalar,ConjugateLhs,ConjugateRhs,Architecture::Target,PacketQuarter> QuarterTraits;
+  
   typedef typename Traits::ResScalar ResScalar;
   typedef typename Traits::LhsPacket LhsPacket;
   typedef typename Traits::RhsPacket RhsPacket;
@@ -1131,19 +1189,34 @@ struct gebp_kernel
 
   typedef typename RhsPanelHelper<RhsPacket, RhsPacketx4, 15>::type RhsPanel15;
 
-  typedef gebp_traits<RhsScalar,LhsScalar,ConjugateRhs,ConjugateLhs> SwappedTraits;
+  typedef gebp_traits<RhsScalar,LhsScalar,ConjugateRhs,ConjugateLhs,Architecture::Target> SwappedTraits;
+
   typedef typename SwappedTraits::ResScalar SResScalar;
   typedef typename SwappedTraits::LhsPacket SLhsPacket;
   typedef typename SwappedTraits::RhsPacket SRhsPacket;
   typedef typename SwappedTraits::ResPacket SResPacket;
   typedef typename SwappedTraits::AccPacket SAccPacket;
 
+  typedef typename HalfTraits::LhsPacket LhsPacketHalf;
+  typedef typename HalfTraits::RhsPacket RhsPacketHalf;
+  typedef typename HalfTraits::ResPacket ResPacketHalf;
+  typedef typename HalfTraits::AccPacket AccPacketHalf;
+
+  typedef typename QuarterTraits::LhsPacket LhsPacketQuarter;
+  typedef typename QuarterTraits::RhsPacket RhsPacketQuarter;
+  typedef typename QuarterTraits::ResPacket ResPacketQuarter;
+  typedef typename QuarterTraits::AccPacket AccPacketQuarter;
+
   typedef typename DataMapper::LinearMapper LinearMapper;
 
   enum {
     Vectorizable  = Traits::Vectorizable,
     LhsProgress   = Traits::LhsProgress,
+    LhsProgressHalf      = HalfTraits::LhsProgress,
+    LhsProgressQuarter   = QuarterTraits::LhsProgress,
     RhsProgress   = Traits::RhsProgress,
+    RhsProgressHalf      = HalfTraits::RhsProgress,
+    RhsProgressQuarter   = QuarterTraits::RhsProgress,
     ResPacketSize = Traits::ResPacketSize
   };
 
@@ -1154,11 +1227,11 @@ struct gebp_kernel
 };
 
 template<typename LhsScalar, typename RhsScalar, typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs,
-  int SwappedLhsProgress = gebp_traits<RhsScalar,LhsScalar,ConjugateRhs,ConjugateLhs>::LhsProgress>
+int SwappedLhsProgress = gebp_traits<RhsScalar,LhsScalar,ConjugateRhs,ConjugateLhs,Architecture::Target>::LhsProgress>
 struct last_row_process_16_packets
 {
-  typedef gebp_traits<LhsScalar,RhsScalar,ConjugateLhs,ConjugateRhs> Traits;
-  typedef gebp_traits<RhsScalar,LhsScalar,ConjugateRhs,ConjugateLhs> SwappedTraits;
+  typedef gebp_traits<LhsScalar,RhsScalar,ConjugateLhs,ConjugateRhs,Architecture::Target> Traits;
+  typedef gebp_traits<RhsScalar,LhsScalar,ConjugateRhs,ConjugateLhs,Architecture::Target> SwappedTraits;
 
   typedef typename Traits::ResScalar ResScalar;
   typedef typename SwappedTraits::LhsPacket SLhsPacket;
@@ -1186,8 +1259,8 @@ struct last_row_process_16_packets
 
 template<typename LhsScalar, typename RhsScalar, typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
 struct last_row_process_16_packets<LhsScalar, RhsScalar, Index, DataMapper,  mr,  nr, ConjugateLhs,  ConjugateRhs, 16> {
-  typedef gebp_traits<LhsScalar,RhsScalar,ConjugateLhs,ConjugateRhs> Traits;
-  typedef gebp_traits<RhsScalar,LhsScalar,ConjugateRhs,ConjugateLhs> SwappedTraits;
+  typedef gebp_traits<LhsScalar,RhsScalar,ConjugateLhs,ConjugateRhs,Architecture::Target> Traits;
+  typedef gebp_traits<RhsScalar,LhsScalar,ConjugateRhs,ConjugateLhs,Architecture::Target> SwappedTraits;
 
   typedef typename Traits::ResScalar ResScalar;
   typedef typename SwappedTraits::LhsPacket SLhsPacket;
@@ -1233,6 +1306,202 @@ struct last_row_process_16_packets<LhsScalar, RhsScalar, Index, DataMapper,  mr,
   }
 };
 
+template<int nr, Index LhsProgress, Index RhsProgress, typename LhsScalar, typename RhsScalar, typename ResScalar, typename AccPacket, typename LhsPacket, typename RhsPacket, typename ResPacket, typename GEBPTraits, typename LinearMapper, typename DataMapper>
+struct lhs_process_one_packet
+{
+  typedef typename GEBPTraits::RhsPacketx4 RhsPacketx4;
+
+  EIGEN_STRONG_INLINE void peeled_kc_onestep(Index K, const LhsScalar* blA, const RhsScalar* blB, GEBPTraits traits, LhsPacket *A0, RhsPacketx4 *rhs_panel, RhsPacket *T0, AccPacket *C0, AccPacket *C1, AccPacket *C2, AccPacket *C3)
+  {
+        EIGEN_ASM_COMMENT("begin step of gebp micro kernel 1X4");
+        EIGEN_ASM_COMMENT("Note: these asm comments work around bug 935!");
+        traits.loadLhs(&blA[(0+1*K)*LhsProgress], *A0);
+        traits.loadRhs(&blB[(0+4*K)*RhsProgress], *rhs_panel);
+        traits.madd(*A0, *rhs_panel, *C0, *T0, fix<0>);
+        traits.madd(*A0, *rhs_panel, *C1, *T0, fix<1>);
+        traits.madd(*A0, *rhs_panel, *C2, *T0, fix<2>);
+        traits.madd(*A0, *rhs_panel, *C3, *T0, fix<3>);
+        EIGEN_ASM_COMMENT("end step of gebp micro kernel 1X4");
+  }
+
+  EIGEN_STRONG_INLINE void operator()(
+    const DataMapper& res, const LhsScalar* blockA, const RhsScalar* blockB, ResScalar alpha,
+    Index peelStart, Index peelEnd, Index strideA, Index strideB, Index offsetA, Index offsetB,
+    int prefetch_res_offset, Index peeled_kc, Index pk, Index cols, Index depth, Index packet_cols4)
+  {
+    GEBPTraits traits;
+
+    // loops on each largest micro horizontal panel of lhs
+    // (LhsProgress x depth)
+    for(Index i=peelStart; i<peelEnd; i+=LhsProgress)
+    {
+      // loops on each largest micro vertical panel of rhs (depth * nr)
+      for(Index j2=0; j2<packet_cols4; j2+=nr)
+      {
+        // We select a LhsProgress x nr micro block of res
+        // which is entirely stored into 1 x nr registers.
+
+        const LhsScalar* blA = &blockA[i*strideA+offsetA*(LhsProgress)];
+        prefetch(&blA[0]);
+
+        // gets res block as register
+        AccPacket C0, C1, C2, C3;
+        traits.initAcc(C0);
+        traits.initAcc(C1);
+        traits.initAcc(C2);
+        traits.initAcc(C3);
+
+        LinearMapper r0 = res.getLinearMapper(i, j2 + 0);
+        LinearMapper r1 = res.getLinearMapper(i, j2 + 1);
+        LinearMapper r2 = res.getLinearMapper(i, j2 + 2);
+        LinearMapper r3 = res.getLinearMapper(i, j2 + 3);
+
+        r0.prefetch(prefetch_res_offset);
+        r1.prefetch(prefetch_res_offset);
+        r2.prefetch(prefetch_res_offset);
+        r3.prefetch(prefetch_res_offset);
+
+        // performs "inner" products
+        const RhsScalar* blB = &blockB[j2*strideB+offsetB*nr];
+        prefetch(&blB[0]);
+        LhsPacket A0;
+
+        for(Index k=0; k<peeled_kc; k+=pk)
+        {
+          EIGEN_ASM_COMMENT("begin gebp micro kernel 1/half/quarterX4");
+          RhsPacketx4 rhs_panel;
+          RhsPacket T0;
+
+          internal::prefetch(blB+(48+0));
+          peeled_kc_onestep(0, blA, blB, traits, &A0, &rhs_panel, &T0, &C0, &C1, &C2, &C3);
+          peeled_kc_onestep(1, blA, blB, traits, &A0, &rhs_panel, &T0, &C0, &C1, &C2, &C3);
+          peeled_kc_onestep(2, blA, blB, traits, &A0, &rhs_panel, &T0, &C0, &C1, &C2, &C3);
+          peeled_kc_onestep(3, blA, blB, traits, &A0, &rhs_panel, &T0, &C0, &C1, &C2, &C3);
+          internal::prefetch(blB+(48+16));
+          peeled_kc_onestep(4, blA, blB, traits, &A0, &rhs_panel, &T0, &C0, &C1, &C2, &C3);
+          peeled_kc_onestep(5, blA, blB, traits, &A0, &rhs_panel, &T0, &C0, &C1, &C2, &C3);
+          peeled_kc_onestep(6, blA, blB, traits, &A0, &rhs_panel, &T0, &C0, &C1, &C2, &C3);
+          peeled_kc_onestep(7, blA, blB, traits, &A0, &rhs_panel, &T0, &C0, &C1, &C2, &C3);
+
+          blB += pk*4*RhsProgress;
+          blA += pk*LhsProgress;
+
+          EIGEN_ASM_COMMENT("end gebp micro kernel 1/half/quarterX4");
+        }
+
+        // process remaining peeled loop
+        for(Index k=peeled_kc; k<depth; k++)
+        {
+          RhsPacketx4 rhs_panel;
+          RhsPacket T0;
+          peeled_kc_onestep(0, blA, blB, traits, &A0, &rhs_panel, &T0, &C0, &C1, &C2, &C3);
+          blB += 4*RhsProgress;
+          blA += LhsProgress;
+        }
+
+        ResPacket R0, R1;
+        ResPacket alphav = pset1<ResPacket>(alpha);
+
+        R0 = r0.template loadPacket<ResPacket>(0);
+        R1 = r1.template loadPacket<ResPacket>(0);
+        traits.acc(C0, alphav, R0);
+        traits.acc(C1,  alphav, R1);
+        r0.storePacket(0, R0);
+        r1.storePacket(0, R1);
+
+        R0 = r2.template loadPacket<ResPacket>(0);
+        R1 = r3.template loadPacket<ResPacket>(0);
+        traits.acc(C2,  alphav, R0);
+        traits.acc(C3,  alphav, R1);
+        r2.storePacket(0, R0);
+        r3.storePacket(0, R1);
+      }
+
+      // Deal with remaining columns of the rhs
+      for(Index j2=packet_cols4; j2<cols; j2++)
+      {
+        // One column at a time
+        const LhsScalar* blA = &blockA[i*strideA+offsetA*(LhsProgress)];
+        prefetch(&blA[0]);
+
+        // gets res block as register
+        AccPacket C0;
+        traits.initAcc(C0);
+
+        LinearMapper r0 = res.getLinearMapper(i, j2);
+
+        // performs "inner" products
+        const RhsScalar* blB = &blockB[j2*strideB+offsetB];
+        LhsPacket A0;
+
+        for(Index k= 0; k<peeled_kc; k+=pk)
+        {
+          EIGEN_ASM_COMMENT("begin gebp micro kernel 1/half/quarterX1");
+          RhsPacket B_0;
+
+#define EIGEN_GEBGP_ONESTEP(K)                                          \
+	      do {                                                      \
+		EIGEN_ASM_COMMENT("begin step of gebp micro kernel 1/half/quarterX1"); \
+		EIGEN_ASM_COMMENT("Note: these asm comments work around bug 935!"); \
+    /* FIXME: why unaligned???? */ \
+		traits.loadLhsUnaligned(&blA[(0+1*K)*LhsProgress], A0); \
+		traits.loadRhs(&blB[(0+K)*RhsProgress], B_0);		\
+		traits.madd(A0, B_0, C0, B_0, fix<0>);				\
+		EIGEN_ASM_COMMENT("end step of gebp micro kernel 1/half/quarterX1"); \
+	      } while(false);
+
+          EIGEN_GEBGP_ONESTEP(0);
+          EIGEN_GEBGP_ONESTEP(1);
+          EIGEN_GEBGP_ONESTEP(2);
+          EIGEN_GEBGP_ONESTEP(3);
+          EIGEN_GEBGP_ONESTEP(4);
+          EIGEN_GEBGP_ONESTEP(5);
+          EIGEN_GEBGP_ONESTEP(6);
+          EIGEN_GEBGP_ONESTEP(7);
+
+          blB += pk*RhsProgress;
+          blA += pk*LhsProgress;
+
+          EIGEN_ASM_COMMENT("end gebp micro kernel 1/half/quarterX1");
+        }
+
+        // process remaining peeled loop
+        for(Index k=peeled_kc; k<depth; k++)
+        {
+          RhsPacket B_0;
+          EIGEN_GEBGP_ONESTEP(0);
+          blB += RhsProgress;
+          blA += LhsProgress;
+        }
+#undef EIGEN_GEBGP_ONESTEP
+        ResPacket R0;
+        ResPacket alphav = pset1<ResPacket>(alpha);
+        R0 = r0.template loadPacket<ResPacket>(0);
+        traits.acc(C0, alphav, R0);
+        r0.storePacket(0, R0);
+      }
+    }
+  }
+};
+
+template<int nr, Index LhsProgress, Index RhsProgress, typename LhsScalar, typename RhsScalar, typename ResScalar, typename AccPacket, typename LhsPacket, typename RhsPacket, typename ResPacket, typename GEBPTraits, typename LinearMapper, typename DataMapper>
+struct lhs_process_fraction_of_packet : lhs_process_one_packet<nr, LhsProgress, RhsProgress, LhsScalar, RhsScalar, ResScalar, AccPacket, LhsPacket, RhsPacket, ResPacket, GEBPTraits, LinearMapper, DataMapper>
+{
+
+EIGEN_STRONG_INLINE void peeled_kc_onestep(Index K, const LhsScalar* blA, const RhsScalar* blB, GEBPTraits traits, LhsPacket *A0, RhsPacket *B_0, RhsPacket *B1, RhsPacket *B2, RhsPacket *B3, AccPacket *C0, AccPacket *C1, AccPacket *C2, AccPacket *C3)
+  {
+        EIGEN_ASM_COMMENT("begin step of gebp micro kernel 1X4");
+        EIGEN_ASM_COMMENT("Note: these asm comments work around bug 935!");
+        traits.loadLhsUnaligned(&blA[(0+1*K)*(LhsProgress)], *A0);
+        traits.broadcastRhs(&blB[(0+4*K)*RhsProgress], *B_0, *B1, *B2, *B3);
+        traits.madd(*A0, *B_0, *C0, *B_0);
+        traits.madd(*A0, *B1,  *C1, *B1);
+        traits.madd(*A0, *B2,  *C2, *B2);
+        traits.madd(*A0, *B3,  *C3, *B3);
+        EIGEN_ASM_COMMENT("end step of gebp micro kernel 1X4");
+  }
+};
+
 template<typename LhsScalar, typename RhsScalar, typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
 EIGEN_DONT_INLINE
 void gebp_kernel<LhsScalar,RhsScalar,Index,DataMapper,mr,nr,ConjugateLhs,ConjugateRhs>
@@ -1249,10 +1518,12 @@ void gebp_kernel<LhsScalar,RhsScalar,Index,DataMapper,mr,nr,ConjugateLhs,Conjuga
     Index packet_cols4 = nr>=4 ? (cols/4) * 4 : 0;
     const Index peeled_mc3 = mr>=3*Traits::LhsProgress ? (rows/(3*LhsProgress))*(3*LhsProgress) : 0;
     const Index peeled_mc2 = mr>=2*Traits::LhsProgress ? peeled_mc3+((rows-peeled_mc3)/(2*LhsProgress))*(2*LhsProgress) : 0;
-    const Index peeled_mc1 = mr>=1*Traits::LhsProgress ? (rows/(1*LhsProgress))*(1*LhsProgress) : 0;
+    const Index peeled_mc1 = mr>=1*Traits::LhsProgress ? peeled_mc2+((rows-peeled_mc2)/(1*LhsProgress))*(1*LhsProgress) : 0;
+    const Index peeled_mc_half = mr>=LhsProgressHalf ? peeled_mc1+((rows-peeled_mc1)/(LhsProgressHalf))*(LhsProgressHalf) : 0;
+    const Index peeled_mc_quarter = mr>=LhsProgressQuarter ? peeled_mc_half+((rows-peeled_mc_half)/(LhsProgressQuarter))*(LhsProgressQuarter) : 0;
     enum { pk = 8 }; // NOTE Such a large peeling factor is important for large matrices (~ +5% when >1000 on Haswell)
     const Index peeled_kc  = depth & ~(pk-1);
-    const Index prefetch_res_offset = 32/sizeof(ResScalar);    
+    const int prefetch_res_offset = 32/sizeof(ResScalar);    
 //     const Index depth2     = depth & ~1;
 
     //---------- Process 3 * LhsProgress rows at once ----------
@@ -1718,176 +1989,29 @@ void gebp_kernel<LhsScalar,RhsScalar,Index,DataMapper,mr,nr,ConjugateLhs,Conjuga
     //---------- Process 1 * LhsProgress rows at once ----------
     if(mr>=1*Traits::LhsProgress)
     {
-      // loops on each largest micro horizontal panel of lhs (1*LhsProgress x depth)
-      for(Index i=peeled_mc2; i<peeled_mc1; i+=1*LhsProgress)
-      {
-        // loops on each largest micro vertical panel of rhs (depth * nr)
-        for(Index j2=0; j2<packet_cols4; j2+=nr)
-        {
-          // We select a 1*Traits::LhsProgress x nr micro block of res which is entirely
-          // stored into 1 x nr registers.
-          
-          const LhsScalar* blA = &blockA[i*strideA+offsetA*(1*Traits::LhsProgress)];
-          prefetch(&blA[0]);
-
-          // gets res block as register
-          AccPacket C0, C1, C2, C3;
-          traits.initAcc(C0);
-          traits.initAcc(C1);
-          traits.initAcc(C2);
-          traits.initAcc(C3);
-
-          LinearMapper r0 = res.getLinearMapper(i, j2 + 0);
-          LinearMapper r1 = res.getLinearMapper(i, j2 + 1);
-          LinearMapper r2 = res.getLinearMapper(i, j2 + 2);
-          LinearMapper r3 = res.getLinearMapper(i, j2 + 3);
-
-          r0.prefetch(prefetch_res_offset);
-          r1.prefetch(prefetch_res_offset);
-          r2.prefetch(prefetch_res_offset);
-          r3.prefetch(prefetch_res_offset);
-
-          // performs "inner" products
-          const RhsScalar* blB = &blockB[j2*strideB+offsetB*nr];
-          prefetch(&blB[0]);
-          LhsPacket A0;
-
-          for(Index k=0; k<peeled_kc; k+=pk)
-          {
-            EIGEN_ASM_COMMENT("begin gebp micro kernel 1pX4");
-            RhsPacketx4 rhs_panel;
-            RhsPacket T0;
-
-#define EIGEN_GEBGP_ONESTEP(K) \
-            do {                                                                  \
-              EIGEN_ASM_COMMENT("begin step of gebp micro kernel 1pX4");          \
-              EIGEN_ASM_COMMENT("Note: these asm comments work around bug 935!"); \
-              traits.loadLhs(&blA[(0+1*K)*LhsProgress], A0);                      \
-              traits.loadRhs(&blB[(0+4*K)*RhsProgress], rhs_panel);               \
-              traits.madd(A0, rhs_panel, C0, T0, fix<0>);                         \
-              traits.madd(A0, rhs_panel, C1, T0, fix<1>);                         \
-              traits.madd(A0, rhs_panel, C2, T0, fix<2>);                         \
-              traits.madd(A0, rhs_panel, C3, T0, fix<3>);                         \
-              EIGEN_ASM_COMMENT("end step of gebp micro kernel 1pX4");            \
-            } while(false)
-            
-            internal::prefetch(blB+(48+0));
-            EIGEN_GEBGP_ONESTEP(0);
-            EIGEN_GEBGP_ONESTEP(1);
-            EIGEN_GEBGP_ONESTEP(2);
-            EIGEN_GEBGP_ONESTEP(3);
-            internal::prefetch(blB+(48+16));
-            EIGEN_GEBGP_ONESTEP(4);
-            EIGEN_GEBGP_ONESTEP(5);
-            EIGEN_GEBGP_ONESTEP(6);
-            EIGEN_GEBGP_ONESTEP(7);
-
-            blB += pk*4*RhsProgress;
-            blA += pk*1*LhsProgress;
-
-            EIGEN_ASM_COMMENT("end gebp micro kernel 1pX4");
-          }
-          // process remaining peeled loop
-          for(Index k=peeled_kc; k<depth; k++)
-          {
-            RhsPacketx4 rhs_panel;
-            RhsPacket T0;
-            EIGEN_GEBGP_ONESTEP(0);
-            blB += 4*RhsProgress;
-            blA += 1*LhsProgress;
-          }
-#undef EIGEN_GEBGP_ONESTEP
-
-          ResPacket R0, R1;
-          ResPacket alphav = pset1<ResPacket>(alpha);
-
-          R0 = r0.template loadPacket<ResPacket>(0 * Traits::ResPacketSize);
-          R1 = r1.template loadPacket<ResPacket>(0 * Traits::ResPacketSize);
-          traits.acc(C0, alphav, R0);
-          traits.acc(C1,  alphav, R1);
-          r0.storePacket(0 * Traits::ResPacketSize, R0);
-          r1.storePacket(0 * Traits::ResPacketSize, R1);
-
-          R0 = r2.template loadPacket<ResPacket>(0 * Traits::ResPacketSize);
-          R1 = r3.template loadPacket<ResPacket>(0 * Traits::ResPacketSize);
-          traits.acc(C2,  alphav, R0);
-          traits.acc(C3,  alphav, R1);
-          r2.storePacket(0 * Traits::ResPacketSize, R0);
-          r3.storePacket(0 * Traits::ResPacketSize, R1);
-        }
-
-        // Deal with remaining columns of the rhs
-        for(Index j2=packet_cols4; j2<cols; j2++)
-        {
-          // One column at a time
-          const LhsScalar* blA = &blockA[i*strideA+offsetA*(1*Traits::LhsProgress)];
-          prefetch(&blA[0]);
-
-          // gets res block as register
-          AccPacket C0;
-          traits.initAcc(C0);
-
-          LinearMapper r0 = res.getLinearMapper(i, j2);
-
-          // performs "inner" products
-          const RhsScalar* blB = &blockB[j2*strideB+offsetB];
-          LhsPacket A0;
-
-          for(Index k=0; k<peeled_kc; k+=pk)
-          {
-            EIGEN_ASM_COMMENT("begin gebp micro kernel 1pX1");
-            RhsPacket B_0;
-        
-#define EIGEN_GEBGP_ONESTEP(K) \
-            do {                                                                  \
-              EIGEN_ASM_COMMENT("begin step of gebp micro kernel 1pX1");          \
-              EIGEN_ASM_COMMENT("Note: these asm comments work around bug 935!"); \
-              traits.loadLhs(&blA[(0+1*K)*LhsProgress], A0);                      \
-              traits.loadRhs(&blB[(0+K)*RhsProgress], B_0);                       \
-              traits.madd(A0, B_0, C0, B_0, fix<0>);                              \
-              EIGEN_ASM_COMMENT("end step of gebp micro kernel 1pX1");            \
-            } while(false);
-
-            EIGEN_GEBGP_ONESTEP(0);
-            EIGEN_GEBGP_ONESTEP(1);
-            EIGEN_GEBGP_ONESTEP(2);
-            EIGEN_GEBGP_ONESTEP(3);
-            EIGEN_GEBGP_ONESTEP(4);
-            EIGEN_GEBGP_ONESTEP(5);
-            EIGEN_GEBGP_ONESTEP(6);
-            EIGEN_GEBGP_ONESTEP(7);
-
-            blB += pk*RhsProgress;
-            blA += pk*1*Traits::LhsProgress;
-
-            EIGEN_ASM_COMMENT("end gebp micro kernel 1pX1");
-          }
-
-          // process remaining peeled loop
-          for(Index k=peeled_kc; k<depth; k++)
-          {
-            RhsPacket B_0;
-            EIGEN_GEBGP_ONESTEP(0);
-            blB += RhsProgress;
-            blA += 1*Traits::LhsProgress;
-          }
-#undef EIGEN_GEBGP_ONESTEP
-          ResPacket R0;
-          ResPacket alphav = pset1<ResPacket>(alpha);
-          R0 = r0.template loadPacket<ResPacket>(0 * Traits::ResPacketSize);
-          traits.acc(C0, alphav, R0);
-          r0.storePacket(0 * Traits::ResPacketSize, R0);
-        }
-      }
+      lhs_process_one_packet<nr, LhsProgress, RhsProgress, LhsScalar, RhsScalar, ResScalar, AccPacket, LhsPacket, RhsPacket, ResPacket, Traits, LinearMapper, DataMapper> p;
+      p(res, blockA, blockB, alpha, peeled_mc2, peeled_mc1, strideA, strideB, offsetA, offsetB, prefetch_res_offset, peeled_kc, pk, cols, depth, packet_cols4);
+    }
+    //---------- Process LhsProgressHalf rows at once ----------
+    if((LhsProgressHalf < LhsProgress) && mr>=LhsProgressHalf)
+    {
+      lhs_process_fraction_of_packet<nr, LhsProgressHalf, RhsProgressHalf, LhsScalar, RhsScalar, ResScalar, AccPacketHalf, LhsPacketHalf, RhsPacketHalf, ResPacketHalf, HalfTraits, LinearMapper, DataMapper> p;
+      p(res, blockA, blockB, alpha, peeled_mc1, peeled_mc_half, strideA, strideB, offsetA, offsetB, prefetch_res_offset, peeled_kc, pk, cols, depth, packet_cols4);
+    }
+    //---------- Process LhsProgressQuarter rows at once ----------
+    if((LhsProgressQuarter < LhsProgressHalf) && mr>=LhsProgressQuarter)
+    {
+      lhs_process_fraction_of_packet<nr, LhsProgressQuarter, RhsProgressQuarter, LhsScalar, RhsScalar, ResScalar, AccPacketQuarter, LhsPacketQuarter, RhsPacketQuarter, ResPacketQuarter, QuarterTraits, LinearMapper, DataMapper> p;
+      p(res, blockA, blockB, alpha, peeled_mc_half, peeled_mc_quarter, strideA, strideB, offsetA, offsetB, prefetch_res_offset, peeled_kc, pk, cols, depth, packet_cols4);
     }
     //---------- Process remaining rows, 1 at once ----------
-    if(peeled_mc1<rows)
+    if(peeled_mc_quarter<rows)
     {
       // loop on each panel of the rhs
       for(Index j2=0; j2<packet_cols4; j2+=nr)
       {
         // loop on each row of the lhs (1*LhsProgress x depth)
-        for(Index i=peeled_mc1; i<rows; i+=1)
+        for(Index i=peeled_mc_quarter; i<rows; i+=1)
         {
           const LhsScalar* blA = &blockA[i*strideA+offsetA];
           prefetch(&blA[0]);
@@ -2030,7 +2154,7 @@ void gebp_kernel<LhsScalar,RhsScalar,Index,DataMapper,mr,nr,ConjugateLhs,Conjuga
       for(Index j2=packet_cols4; j2<cols; j2++)
       {
         // loop on each row of the lhs (1*LhsProgress x depth)
-        for(Index i=peeled_mc1; i<rows; i+=1)
+        for(Index i=peeled_mc_quarter; i<rows; i+=1)
         {
           const LhsScalar* blA = &blockA[i*strideA+offsetA];
           prefetch(&blA[0]);
@@ -2077,7 +2201,13 @@ template<typename Scalar, typename Index, typename DataMapper, int Pack1, int Pa
 EIGEN_DONT_INLINE void gemm_pack_lhs<Scalar, Index, DataMapper, Pack1, Pack2, Packet, ColMajor, Conjugate, PanelMode>
   ::operator()(Scalar* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride, Index offset)
 {
-  enum { PacketSize = unpacket_traits<Packet>::size };
+  typedef typename unpacket_traits<Packet>::half HalfPacket;
+  typedef typename unpacket_traits<typename unpacket_traits<Packet>::half>::half QuarterPacket;
+  enum { PacketSize = unpacket_traits<Packet>::size,
+         HalfPacketSize = unpacket_traits<HalfPacket>::size,
+         QuarterPacketSize = unpacket_traits<QuarterPacket>::size,
+         HasHalf = (int)HalfPacketSize < (int)PacketSize,
+         HasQuarter = (int)QuarterPacketSize < (int)HalfPacketSize};
 
   EIGEN_ASM_COMMENT("EIGEN PRODUCT PACK LHS");
   EIGEN_UNUSED_VARIABLE(stride);
@@ -2089,9 +2219,12 @@ EIGEN_DONT_INLINE void gemm_pack_lhs<Scalar, Index, DataMapper, Pack1, Pack2, Pa
 
   const Index peeled_mc3 = Pack1>=3*PacketSize ? (rows/(3*PacketSize))*(3*PacketSize) : 0;
   const Index peeled_mc2 = Pack1>=2*PacketSize ? peeled_mc3+((rows-peeled_mc3)/(2*PacketSize))*(2*PacketSize) : 0;
-  const Index peeled_mc1 = Pack1>=1*PacketSize ? (rows/(1*PacketSize))*(1*PacketSize) : 0;
-  const Index peeled_mc0 = Pack2>=1*PacketSize ? peeled_mc1
-                         : Pack2>1             ? (rows/Pack2)*Pack2 : 0;
+  const Index peeled_mc1 = Pack1>=1*PacketSize ? peeled_mc2+((rows-peeled_mc2)/(1*PacketSize))*(1*PacketSize) : 0;
+  const Index peeled_mc_half = Pack1>=HalfPacketSize ? peeled_mc1+((rows-peeled_mc1)/(HalfPacketSize))*(HalfPacketSize) : 0;
+  const Index peeled_mc_quarter = Pack1>=QuarterPacketSize ? (rows/(QuarterPacketSize))*(QuarterPacketSize) : 0;
+  const Index last_lhs_progress = rows > peeled_mc_quarter ? (rows - peeled_mc_quarter) & ~1 : 0;
+  const Index peeled_mc0 = Pack2>=PacketSize ? peeled_mc_quarter
+                         : Pack2>1 && last_lhs_progress ? (rows/last_lhs_progress)*last_lhs_progress : 0;
 
   Index i=0;
 
@@ -2150,20 +2283,60 @@ EIGEN_DONT_INLINE void gemm_pack_lhs<Scalar, Index, DataMapper, Pack1, Pack2, Pa
       if(PanelMode) count += (1*PacketSize) * (stride-offset-depth);
     }
   }
-  // Pack scalars
-  if(Pack2<PacketSize && Pack2>1)
+  // Pack half packets
+  if(HasHalf && Pack1>=HalfPacketSize)
   {
-    for(; i<peeled_mc0; i+=Pack2)
+    for(; i<peeled_mc_half; i+=HalfPacketSize)
     {
-      if(PanelMode) count += Pack2 * offset;
+      if(PanelMode) count += (HalfPacketSize) * offset;
 
       for(Index k=0; k<depth; k++)
-        for(Index w=0; w<Pack2; w++)
-          blockA[count++] = cj(lhs(i+w, k));
-
-      if(PanelMode) count += Pack2 * (stride-offset-depth);
+      {
+        HalfPacket A;
+        A = lhs.template loadPacket<HalfPacket>(i+0*(HalfPacketSize), k);
+        pstoreu(blockA+count, cj.pconj(A));
+        count+=HalfPacketSize;
+      }
+      if(PanelMode) count += (HalfPacketSize) * (stride-offset-depth);
     }
   }
+  // Pack quarter packets
+  if(HasQuarter && Pack1>=QuarterPacketSize)
+  {
+    for(; i<peeled_mc_quarter; i+=QuarterPacketSize)
+    {
+      if(PanelMode) count += (QuarterPacketSize) * offset;
+
+      for(Index k=0; k<depth; k++)
+      {
+        QuarterPacket A;
+        A = lhs.template loadPacket<QuarterPacket>(i+0*(QuarterPacketSize), k);
+        pstoreu(blockA+count, cj.pconj(A));
+        count+=QuarterPacketSize;
+      }
+      if(PanelMode) count += (QuarterPacketSize) * (stride-offset-depth);
+    }
+  }
+  // Pack2 may be *smaller* than PacketSize—that happens for
+  // products like real * complex, where we have to go half the
+  // progress on the lhs in order to duplicate those operands to
+  // address both real & imaginary parts on the rhs. This portion will
+  // pack those half ones until they match the number expected on the
+  // last peeling loop at this point (for the rhs).
+  if(Pack2<PacketSize && Pack2>1)
+  {
+    for(; i<peeled_mc0; i+=last_lhs_progress)
+    {
+      if(PanelMode) count += last_lhs_progress * offset;
+
+      for(Index k=0; k<depth; k++)
+        for(Index w=0; w<last_lhs_progress; w++)
+          blockA[count++] = cj(lhs(i+w, k));
+
+      if(PanelMode) count += last_lhs_progress * (stride-offset-depth);
+    }
+  }
+  // Pack scalars
   for(; i<rows; i++)
   {
     if(PanelMode) count += offset;
@@ -2184,7 +2357,13 @@ template<typename Scalar, typename Index, typename DataMapper, int Pack1, int Pa
 EIGEN_DONT_INLINE void gemm_pack_lhs<Scalar, Index, DataMapper, Pack1, Pack2, Packet, RowMajor, Conjugate, PanelMode>
   ::operator()(Scalar* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride, Index offset)
 {
-  enum { PacketSize = unpacket_traits<Packet>::size };
+  typedef typename unpacket_traits<Packet>::half HalfPacket;
+  typedef typename unpacket_traits<typename unpacket_traits<Packet>::half>::half QuarterPacket;
+  enum { PacketSize = unpacket_traits<Packet>::size,
+         HalfPacketSize = unpacket_traits<HalfPacket>::size,
+         QuarterPacketSize = unpacket_traits<QuarterPacket>::size,
+         HasHalf = (int)HalfPacketSize < (int)PacketSize,
+         HasQuarter = (int)QuarterPacketSize < (int)HalfPacketSize};
 
   EIGEN_ASM_COMMENT("EIGEN PRODUCT PACK LHS");
   EIGEN_UNUSED_VARIABLE(stride);
@@ -2192,37 +2371,51 @@ EIGEN_DONT_INLINE void gemm_pack_lhs<Scalar, Index, DataMapper, Pack1, Pack2, Pa
   eigen_assert(((!PanelMode) && stride==0 && offset==0) || (PanelMode && stride>=depth && offset<=stride));
   conj_if<NumTraits<Scalar>::IsComplex && Conjugate> cj;
   Index count = 0;
+  bool gone_half = false, gone_quarter = false, gone_last = false;
 
-//   const Index peeled_mc3 = Pack1>=3*PacketSize ? (rows/(3*PacketSize))*(3*PacketSize) : 0;
-//   const Index peeled_mc2 = Pack1>=2*PacketSize ? peeled_mc3+((rows-peeled_mc3)/(2*PacketSize))*(2*PacketSize) : 0;
-//   const Index peeled_mc1 = Pack1>=1*PacketSize ? (rows/(1*PacketSize))*(1*PacketSize) : 0;
-
-  int pack = Pack1;
   Index i = 0;
+  int pack = Pack1;
+  int psize = PacketSize;
   while(pack>0)
   {
     Index remaining_rows = rows-i;
-    Index peeled_mc = i+(remaining_rows/pack)*pack;
+    Index peeled_mc = gone_last ? Pack2>1 ? (rows/pack)*pack : 0 : i+(remaining_rows/pack)*pack;
+    Index starting_pos = i;
     for(; i<peeled_mc; i+=pack)
     {
       if(PanelMode) count += pack * offset;
 
-      const Index peeled_k = (depth/PacketSize)*PacketSize;
       Index k=0;
-      if(pack>=PacketSize)
+      if(pack>=psize && psize >= QuarterPacketSize)
       {
-        for(; k<peeled_k; k+=PacketSize)
+        const Index peeled_k = (depth/psize)*psize;
+        for(; k<peeled_k; k+=psize)
         {
-          for (Index m = 0; m < pack; m += PacketSize)
+          for (Index m = 0; m < pack; m += psize)
           {
-            PacketBlock<Packet> kernel;
-            for (int p = 0; p < PacketSize; ++p) kernel.packet[p] = lhs.template loadPacket<Packet>(i+p+m, k);
-            ptranspose(kernel);
-            for (int p = 0; p < PacketSize; ++p) pstore(blockA+count+m+(pack)*p, cj.pconj(kernel.packet[p]));
+            if (psize == PacketSize) {
+              PacketBlock<Packet> kernel;
+              for (int p = 0; p < psize; ++p) kernel.packet[p] = lhs.template loadPacket<Packet>(i+p+m, k);
+              ptranspose(kernel);
+              for (int p = 0; p < psize; ++p) pstore(blockA+count+m+(pack)*p, cj.pconj(kernel.packet[p]));
+            } else if (HasHalf && psize == HalfPacketSize) {
+              gone_half = true;
+              PacketBlock<HalfPacket> kernel_half;
+              for (int p = 0; p < psize; ++p) kernel_half.packet[p] = lhs.template loadPacket<HalfPacket>(i+p+m, k);
+              ptranspose(kernel_half);
+              for (int p = 0; p < psize; ++p) pstore(blockA+count+m+(pack)*p, cj.pconj(kernel_half.packet[p]));
+            } else if (HasQuarter && psize == QuarterPacketSize) {
+              gone_quarter = true;
+              PacketBlock<QuarterPacket> kernel_quarter;
+              for (int p = 0; p < psize; ++p) kernel_quarter.packet[p] = lhs.template loadPacket<QuarterPacket>(i+p+m, k);
+              ptranspose(kernel_quarter);
+              for (int p = 0; p < psize; ++p) pstore(blockA+count+m+(pack)*p, cj.pconj(kernel_quarter.packet[p]));
+	    }
           }
-          count += PacketSize*pack;
+          count += psize*pack;
         }
       }
+
       for(; k<depth; k++)
       {
         Index w=0;
@@ -2245,9 +2438,28 @@ EIGEN_DONT_INLINE void gemm_pack_lhs<Scalar, Index, DataMapper, Pack1, Pack2, Pa
       if(PanelMode) count += pack * (stride-offset-depth);
     }
 
-    pack -= PacketSize;
-    if(pack<Pack2 && (pack+PacketSize)!=Pack2)
-      pack = Pack2;
+    pack -= psize;
+    Index left = rows - i;
+    if (pack <= 0) {
+      if (!gone_last &&
+          (starting_pos == i || left >= psize/2 || left >= psize/4) &&
+          ((psize/2 == HalfPacketSize && HasHalf && !gone_half) ||
+           (psize/2 == QuarterPacketSize && HasQuarter && !gone_quarter))) {
+        psize /= 2;
+        pack = psize;
+        continue;
+      }
+      // Pack2 may be *smaller* than PacketSize—that happens for
+      // products like real * complex, where we have to go half the
+      // progress on the lhs in order to duplicate those operands to
+      // address both real & imaginary parts on the rhs. This portion will
+      // pack those half ones until they match the number expected on the
+      // last peeling loop at this point (for the rhs).
+      if (Pack2 < PacketSize && !gone_last) {
+        gone_last = true;
+        psize = pack = left & ~1;
+      }
+    }
   }
 
   for(; i<rows; i++)
diff --git a/Eigen/src/Core/products/SelfadjointMatrixMatrix.h b/Eigen/src/Core/products/SelfadjointMatrixMatrix.h
index c84c71609..673073601 100644
--- a/Eigen/src/Core/products/SelfadjointMatrixMatrix.h
+++ b/Eigen/src/Core/products/SelfadjointMatrixMatrix.h
@@ -45,14 +45,23 @@ struct symm_pack_lhs
   }
   void operator()(Scalar* blockA, const Scalar* _lhs, Index lhsStride, Index cols, Index rows)
   {
-    enum { PacketSize = packet_traits<Scalar>::size };
+    typedef typename unpacket_traits<typename packet_traits<Scalar>::type>::half HalfPacket;
+    typedef typename unpacket_traits<typename unpacket_traits<typename packet_traits<Scalar>::type>::half>::half QuarterPacket;
+    enum { PacketSize = packet_traits<Scalar>::size,
+           HalfPacketSize = unpacket_traits<HalfPacket>::size,
+           QuarterPacketSize = unpacket_traits<QuarterPacket>::size,
+           HasHalf = (int)HalfPacketSize < (int)PacketSize,
+           HasQuarter = (int)QuarterPacketSize < (int)HalfPacketSize};
+
     const_blas_data_mapper<Scalar,Index,StorageOrder> lhs(_lhs,lhsStride);
     Index count = 0;
     //Index peeled_mc3 = (rows/Pack1)*Pack1;
     
     const Index peeled_mc3 = Pack1>=3*PacketSize ? (rows/(3*PacketSize))*(3*PacketSize) : 0;
     const Index peeled_mc2 = Pack1>=2*PacketSize ? peeled_mc3+((rows-peeled_mc3)/(2*PacketSize))*(2*PacketSize) : 0;
-    const Index peeled_mc1 = Pack1>=1*PacketSize ? (rows/(1*PacketSize))*(1*PacketSize) : 0;
+    const Index peeled_mc1 = Pack1>=1*PacketSize ? peeled_mc2+((rows-peeled_mc2)/(1*PacketSize))*(1*PacketSize) : 0;
+    const Index peeled_mc_half = Pack1>=HalfPacketSize ? peeled_mc1+((rows-peeled_mc1)/(HalfPacketSize))*(HalfPacketSize) : 0;
+    const Index peeled_mc_quarter = Pack1>=QuarterPacketSize ? peeled_mc_half+((rows-peeled_mc_half)/(QuarterPacketSize))*(QuarterPacketSize) : 0;
     
     if(Pack1>=3*PacketSize)
       for(Index i=0; i<peeled_mc3; i+=3*PacketSize)
@@ -66,8 +75,16 @@ struct symm_pack_lhs
       for(Index i=peeled_mc2; i<peeled_mc1; i+=1*PacketSize)
         pack<1*PacketSize>(blockA, lhs, cols, i, count);
 
+    if(HasHalf && Pack1>=HalfPacketSize)
+      for(Index i=peeled_mc1; i<peeled_mc_half; i+=HalfPacketSize)
+        pack<HalfPacketSize>(blockA, lhs, cols, i, count);
+
+    if(HasQuarter && Pack1>=QuarterPacketSize)
+      for(Index i=peeled_mc_half; i<peeled_mc_quarter; i+=QuarterPacketSize)
+        pack<QuarterPacketSize>(blockA, lhs, cols, i, count);
+
     // do the same with mr==1
-    for(Index i=peeled_mc1; i<rows; i++)
+    for(Index i=peeled_mc_quarter; i<rows; i++)
     {
       for(Index k=0; k<i; k++)
         blockA[count++] = lhs(i, k);                   // normal
diff --git a/Eigen/src/Core/util/XprHelper.h b/Eigen/src/Core/util/XprHelper.h
index 836ff4711..91c2e42e4 100644
--- a/Eigen/src/Core/util/XprHelper.h
+++ b/Eigen/src/Core/util/XprHelper.h
@@ -184,7 +184,8 @@ template<typename T> struct unpacket_traits
   enum
   {
     size = 1,
-    alignment = 1
+    alignment = 1,
+    vectorizable = false
   };
 };