diff --git a/Eigen/src/Core/arch/AVX/PacketMath.h b/Eigen/src/Core/arch/AVX/PacketMath.h
index dc1a1d6b0..247ee4efd 100644
--- a/Eigen/src/Core/arch/AVX/PacketMath.h
+++ b/Eigen/src/Core/arch/AVX/PacketMath.h
@@ -262,10 +262,6 @@ template<> EIGEN_STRONG_INLINE Packet4d peven_mask(const Packet4d& /*a*/) { retu
 template<> EIGEN_STRONG_INLINE Packet8f pload1<Packet8f>(const float*  from) { return _mm256_broadcast_ss(from); }
 template<> EIGEN_STRONG_INLINE Packet4d pload1<Packet4d>(const double* from) { return _mm256_broadcast_sd(from); }
 
-template<> EIGEN_STRONG_INLINE Packet8f plset<Packet8f>(const float& a) { return _mm256_add_ps(_mm256_set1_ps(a), _mm256_set_ps(7.0,6.0,5.0,4.0,3.0,2.0,1.0,0.0)); }
-template<> EIGEN_STRONG_INLINE Packet4d plset<Packet4d>(const double& a) { return _mm256_add_pd(_mm256_set1_pd(a), _mm256_set_pd(3.0,2.0,1.0,0.0)); }
-template<> EIGEN_STRONG_INLINE Packet8i plset<Packet8i>(const int& a) { return _mm256_add_epi32(_mm256_set1_epi32(a), _mm256_set_epi32(7,6,5,4,3,2,1,0)); }
-
 template<> EIGEN_STRONG_INLINE Packet8f padd<Packet8f>(const Packet8f& a, const Packet8f& b) { return _mm256_add_ps(a,b); }
 template<> EIGEN_STRONG_INLINE Packet4d padd<Packet4d>(const Packet4d& a, const Packet4d& b) { return _mm256_add_pd(a,b); }
 template<> EIGEN_STRONG_INLINE Packet8i padd<Packet8i>(const Packet8i& a, const Packet8i& b) {
@@ -278,6 +274,10 @@ template<> EIGEN_STRONG_INLINE Packet8i padd<Packet8i>(const Packet8i& a, const
 #endif
 }
 
+template<> EIGEN_STRONG_INLINE Packet8f plset<Packet8f>(const float& a) { return padd(pset1(a), _mm256_set_ps(7.0,6.0,5.0,4.0,3.0,2.0,1.0,0.0)); }
+template<> EIGEN_STRONG_INLINE Packet4d plset<Packet4d>(const double& a) { return padd(pset1(a), _mm256_set_pd(3.0,2.0,1.0,0.0)); }
+template<> EIGEN_STRONG_INLINE Packet8i plset<Packet8i>(const int& a) { return padd(pset1(a), _mm256_set_epi32(7,6,5,4,3,2,1,0)); }
+
 template<> EIGEN_STRONG_INLINE Packet8f psub<Packet8f>(const Packet8f& a, const Packet8f& b) { return _mm256_sub_ps(a,b); }
 template<> EIGEN_STRONG_INLINE Packet4d psub<Packet4d>(const Packet4d& a, const Packet4d& b) { return _mm256_sub_pd(a,b); }
 template<> EIGEN_STRONG_INLINE Packet8i psub<Packet8i>(const Packet8i& a, const Packet8i& b) {
@@ -300,7 +300,7 @@ template<> EIGEN_STRONG_INLINE Packet4d pnegate(const Packet4d& a)
 }
 template<> EIGEN_STRONG_INLINE Packet8i pnegate(const Packet8i& a)
 {
-  return _mm256_sub_epi32(_mm256_set1_epi32(0), a);
+  return psub(pzero(a), a);
 }
 
 template<> EIGEN_STRONG_INLINE Packet8f pconj(const Packet8f& a) { return a; }
@@ -419,7 +419,13 @@ template<> EIGEN_STRONG_INLINE Packet4d pmin<Packet4d>(const Packet4d& a, const
 #endif
 }
 template<> EIGEN_STRONG_INLINE Packet8i pmin<Packet8i>(const Packet8i& a, const Packet8i& b) {
+#ifdef EIGEN_VECTORIZE_AVX2
   return _mm256_min_epi32(a, b);
+#else
+  __m128i lo = _mm_min_epi32(_mm256_extractf128_si256(a, 0), _mm256_extractf128_si256(b, 0));
+  __m128i hi = _mm_min_epi32(_mm256_extractf128_si256(a, 1), _mm256_extractf128_si256(b, 1));
+  return _mm256_insertf128_si256(_mm256_castsi128_si256(lo), (hi), 1);
+#endif
 }
 
 template<> EIGEN_STRONG_INLINE Packet8f pmax<Packet8f>(const Packet8f& a, const Packet8f& b) {
@@ -445,7 +451,13 @@ template<> EIGEN_STRONG_INLINE Packet4d pmax<Packet4d>(const Packet4d& a, const
 #endif
 }
 template<> EIGEN_STRONG_INLINE Packet8i pmax<Packet8i>(const Packet8i& a, const Packet8i& b) {
+#ifdef EIGEN_VECTORIZE_AVX2
   return _mm256_max_epi32(a, b);
+#else
+  __m128i lo = _mm_max_epi32(_mm256_extractf128_si256(a, 0), _mm256_extractf128_si256(b, 0));
+  __m128i hi = _mm_max_epi32(_mm256_extractf128_si256(a, 1), _mm256_extractf128_si256(b, 1));
+  return _mm256_insertf128_si256(_mm256_castsi128_si256(lo), (hi), 1);
+#endif
 }
 
 // Add specializations for min/max with prescribed NaN progation.
@@ -641,17 +653,25 @@ template<> EIGEN_STRONG_INLINE Packet8f ploaddup<Packet8f>(const float* from)
   // then we can perform a consistent permutation on the global register to get everything in shape:
   return  _mm256_permute_ps(tmp, _MM_SHUFFLE(3,3,2,2));
 }
-// Loads 2 doubles from memory a returns the packet {a0, a0  a1, a1}
+// Loads 2 doubles from memory a returns the packet {a0, a0, a1, a1}
 template<> EIGEN_STRONG_INLINE Packet4d ploaddup<Packet4d>(const double* from)
 {
   Packet4d tmp = _mm256_broadcast_pd((const __m128d*)(const void*)from);
   return  _mm256_permute_pd(tmp, 3<<2);
 }
-// Loads 4 integers from memory a returns the packet {a0, a0  a1, a1, a2, a2, a3, a3}
+// Loads 4 integers from memory a returns the packet {a0, a0, a1, a1, a2, a2, a3, a3}
 template<> EIGEN_STRONG_INLINE Packet8i ploaddup<Packet8i>(const int* from)
 {
-  Packet8i a = _mm256_castsi128_si256(pload<Packet4i>(from));
+#ifdef EIGEN_VECTORIZE_AVX2
+  const Packet8i a = _mm256_castsi128_si256(pload<Packet4i>(from));
   return _mm256_permutevar8x32_epi32(a, _mm256_setr_epi32(0, 0, 1, 1, 2, 2, 3, 3));
+#else
+  __m256 tmp = _mm256_broadcast_ps((const __m128*)(const void*)from);
+  // mimic an "inplace" permutation of the lower 128bits using a blend
+  tmp = _mm256_blend_ps(tmp,_mm256_castps128_ps256(_mm_permute_ps( _mm256_castps256_ps128(tmp), _MM_SHUFFLE(1,0,1,0))), 15);
+  // then we can perform a consistent permutation on the global register to get everything in shape:
+  return  _mm256_castps_si256(_mm256_permute_ps(tmp, _MM_SHUFFLE(3,3,2,2)));
+#endif
 }
 
 // Loads 2 floats from memory a returns the packet {a0, a0  a0, a0, a1, a1, a1, a1}
@@ -662,7 +682,7 @@ template<> EIGEN_STRONG_INLINE Packet8f ploadquad<Packet8f>(const float* from)
 }
 template<> EIGEN_STRONG_INLINE Packet8i ploadquad<Packet8i>(const int* from)
 {
-  return _mm256_inserti128_si256(_mm256_set1_epi32(*from), _mm_set1_epi32(*(from+1)), 1);
+  return _mm256_insertf128_si256(_mm256_set1_epi32(*from), _mm_set1_epi32(*(from+1)), 1);
 }
 
 template<> EIGEN_STRONG_INLINE void pstore<float>(float*   to, const Packet8f& from) { EIGEN_DEBUG_ALIGNED_STORE _mm256_store_ps(to, from); }
@@ -723,13 +743,13 @@ template<> EIGEN_DEVICE_FUNC inline void pscatter<double, Packet4d>(double* to,
 }
 template<> EIGEN_DEVICE_FUNC inline void pscatter<int, Packet8i>(int* to, const Packet8i& from, Index stride)
 {
-  __m128i low = _mm256_extracti128_si256(from, 0);
+  __m128i low = _mm256_extractf128_si256(from, 0);
   to[stride*0] = _mm_extract_epi32(low, 0);
   to[stride*1] = _mm_extract_epi32(low, 1);
   to[stride*2] = _mm_extract_epi32(low, 2);
   to[stride*3] = _mm_extract_epi32(low, 3);
 
-  __m128i high = _mm256_extracti128_si256(from, 1);
+  __m128i high = _mm256_extractf128_si256(from, 1);
   to[stride*4] = _mm_extract_epi32(high, 0);
   to[stride*5] = _mm_extract_epi32(high, 1);
   to[stride*6] = _mm_extract_epi32(high, 2);
@@ -803,7 +823,13 @@ template<> EIGEN_STRONG_INLINE Packet4d pabs(const Packet4d& a)
 }
 template<> EIGEN_STRONG_INLINE Packet8i pabs(const Packet8i& a)
 {
+#ifdef EIGEN_VECTORIZE_AVX2
   return _mm256_abs_epi32(a);
+#else
+  __m128i lo = _mm_abs_epi32(_mm256_extractf128_si256(a, 0));
+  __m128i hi = _mm_abs_epi32(_mm256_extractf128_si256(a, 1));
+  return _mm256_insertf128_si256(_mm256_castsi128_si256(lo), (hi), 1);
+#endif
 }
 
 template<> EIGEN_STRONG_INLINE Packet8f pfrexp<Packet8f>(const Packet8f& a, Packet8f& exponent) {
@@ -989,16 +1015,27 @@ ptranspose(PacketBlock<Packet8f,4>& kernel) {
 #define MM256_SHUFFLE_EPI32(A, B, M) \
   _mm256_castps_si256(_mm256_shuffle_ps(_mm256_castsi256_ps(A), _mm256_castsi256_ps(B), M))
 
+#ifdef EIGEN_VECTORIZE_AVX2
+#define MM256_UNPACKLO_EPI32(A, B) \
+  _mm256_castps_si256(_mm256_unpacklo_ps(_mm256_castsi256_ps(A), _mm256_castsi256_ps(B)))
+#define MM256_UNPACKHI_EPI32(A, B) \
+  _mm256_castps_si256(_mm256_unpackhi_ps(_mm256_castsi256_ps(A), _mm256_castsi256_ps(B)))
+#else
+#define MM256_UNPACKLO_EPI32(A, B) _mm256_unpacklo_ps(A, B)
+#define MM256_UNPACKHI_EPI32(A, B) _mm256_unpackhi_ps(A, B)
+#endif
+
+
 EIGEN_DEVICE_FUNC inline void
 ptranspose(PacketBlock<Packet8i,8>& kernel) {
-  __m256i T0 = _mm256_unpacklo_epi32(kernel.packet[0], kernel.packet[1]);
-  __m256i T1 = _mm256_unpackhi_epi32(kernel.packet[0], kernel.packet[1]);
-  __m256i T2 = _mm256_unpacklo_epi32(kernel.packet[2], kernel.packet[3]);
-  __m256i T3 = _mm256_unpackhi_epi32(kernel.packet[2], kernel.packet[3]);
-  __m256i T4 = _mm256_unpacklo_epi32(kernel.packet[4], kernel.packet[5]);
-  __m256i T5 = _mm256_unpackhi_epi32(kernel.packet[4], kernel.packet[5]);
-  __m256i T6 = _mm256_unpacklo_epi32(kernel.packet[6], kernel.packet[7]);
-  __m256i T7 = _mm256_unpackhi_epi32(kernel.packet[6], kernel.packet[7]);
+  __m256i T0 = MM256_UNPACKLO_EPI32(kernel.packet[0], kernel.packet[1]);
+  __m256i T1 = MM256_UNPACKHI_EPI32(kernel.packet[0], kernel.packet[1]);
+  __m256i T2 = MM256_UNPACKLO_EPI32(kernel.packet[2], kernel.packet[3]);
+  __m256i T3 = MM256_UNPACKHI_EPI32(kernel.packet[2], kernel.packet[3]);
+  __m256i T4 = MM256_UNPACKLO_EPI32(kernel.packet[4], kernel.packet[5]);
+  __m256i T5 = MM256_UNPACKHI_EPI32(kernel.packet[4], kernel.packet[5]);
+  __m256i T6 = MM256_UNPACKLO_EPI32(kernel.packet[6], kernel.packet[7]);
+  __m256i T7 = MM256_UNPACKHI_EPI32(kernel.packet[6], kernel.packet[7]);
   __m256i S0 = MM256_SHUFFLE_EPI32(T0,T2,_MM_SHUFFLE(1,0,1,0));
   __m256i S1 = MM256_SHUFFLE_EPI32(T0,T2,_MM_SHUFFLE(3,2,3,2));
   __m256i S2 = MM256_SHUFFLE_EPI32(T1,T3,_MM_SHUFFLE(1,0,1,0));
@@ -1019,10 +1056,10 @@ ptranspose(PacketBlock<Packet8i,8>& kernel) {
 
 EIGEN_DEVICE_FUNC inline void
 ptranspose(PacketBlock<Packet8i,4>& kernel) {
-  __m256i T0 = _mm256_unpacklo_epi32(kernel.packet[0], kernel.packet[1]);
-  __m256i T1 = _mm256_unpackhi_epi32(kernel.packet[0], kernel.packet[1]);
-  __m256i T2 = _mm256_unpacklo_epi32(kernel.packet[2], kernel.packet[3]);
-  __m256i T3 = _mm256_unpackhi_epi32(kernel.packet[2], kernel.packet[3]);
+  __m256i T0 = MM256_UNPACKLO_EPI32(kernel.packet[0], kernel.packet[1]);
+  __m256i T1 = MM256_UNPACKHI_EPI32(kernel.packet[0], kernel.packet[1]);
+  __m256i T2 = MM256_UNPACKLO_EPI32(kernel.packet[2], kernel.packet[3]);
+  __m256i T3 = MM256_UNPACKHI_EPI32(kernel.packet[2], kernel.packet[3]);
 
   __m256i S0 = MM256_SHUFFLE_EPI32(T0,T2,_MM_SHUFFLE(1,0,1,0));
   __m256i S1 = MM256_SHUFFLE_EPI32(T0,T2,_MM_SHUFFLE(3,2,3,2));
diff --git a/Eigen/src/Core/arch/AVX512/PacketMath.h b/Eigen/src/Core/arch/AVX512/PacketMath.h
index 6ce15c677..0810f66ee 100644
--- a/Eigen/src/Core/arch/AVX512/PacketMath.h
+++ b/Eigen/src/Core/arch/AVX512/PacketMath.h
@@ -1028,7 +1028,7 @@ template<> EIGEN_STRONG_INLINE Packet8d pldexp<Packet8d>(const Packet8d& a, cons
 
 // AVX512F does not define _mm512_extracti32x8_epi32 to extract _m256i from _m512i
 #define EIGEN_EXTRACT_8i_FROM_16i(INPUT, OUTPUT)                           \
-  __m256i OUTPUT##_0 = _mm512_extracti32x8_epi32(INPUT, 0)                 \
+  __m256i OUTPUT##_0 = _mm512_extracti32x8_epi32(INPUT, 0);                \
   __m256i OUTPUT##_1 = _mm512_extracti32x8_epi32(INPUT, 1) 
 #else
 #define EIGEN_EXTRACT_8f_FROM_16f(INPUT, OUTPUT)                \
@@ -1037,7 +1037,7 @@ template<> EIGEN_STRONG_INLINE Packet8d pldexp<Packet8d>(const Packet8d& a, cons
       _mm512_extractf32x4_ps(INPUT, 1), 1);                     \
   __m256 OUTPUT##_1 = _mm256_insertf128_ps(                     \
       _mm256_castps128_ps256(_mm512_extractf32x4_ps(INPUT, 2)), \
-      _mm512_extractf32x4_ps(INPUT, 3), 1);
+      _mm512_extractf32x4_ps(INPUT, 3), 1)
 
 #define EIGEN_EXTRACT_8i_FROM_16i(INPUT, OUTPUT)                    \
   __m256i OUTPUT##_0 = _mm256_insertf128_si256(                     \
@@ -1045,7 +1045,7 @@ template<> EIGEN_STRONG_INLINE Packet8d pldexp<Packet8d>(const Packet8d& a, cons
       _mm512_extracti32x4_epi32(INPUT, 1), 1);                      \
   __m256i OUTPUT##_1 = _mm256_insertf128_si256(                     \
       _mm256_castsi128_si256(_mm512_extracti32x4_epi32(INPUT, 2)),  \
-      _mm512_extracti32x4_epi32(INPUT, 3), 1);
+      _mm512_extracti32x4_epi32(INPUT, 3), 1)
 #endif
 
 #ifdef EIGEN_VECTORIZE_AVX512DQ