diff --git a/Eigen/src/Core/arch/AVX512/PacketMath.h b/Eigen/src/Core/arch/AVX512/PacketMath.h
index 0580b80f8..14ef93c55 100644
--- a/Eigen/src/Core/arch/AVX512/PacketMath.h
+++ b/Eigen/src/Core/arch/AVX512/PacketMath.h
@@ -59,8 +59,8 @@ template<> struct packet_traits<float>  : default_packet_traits
     HasLog = 1,
 #endif
     HasExp = 1,
-    HasSqrt = 1,
-    HasRsqrt = 1,
+    HasSqrt = EIGEN_FAST_MATH,
+    HasRsqrt = EIGEN_FAST_MATH,
 #endif
     HasDiv = 1
   };
@@ -75,7 +75,7 @@ template<> struct packet_traits<double> : default_packet_traits
     size = 8,
     HasHalfPacket = 1,
 #if EIGEN_GNUC_AT_LEAST(5, 3)
-    HasSqrt = 1,
+    HasSqrt = EIGEN_FAST_MATH,
     HasRsqrt = EIGEN_FAST_MATH,
 #endif
     HasDiv = 1
@@ -719,7 +719,7 @@ vecs)
   blend1 = _mm256_blend_ps(sum1, sum2, 0xcc);
   blend2 = _mm256_blend_ps(sum3, sum4, 0xcc);
 
-  final = padd(final, _mm256_blend_ps(blend1, blend2, 0xf0));
+  final = _mm256_add_ps(final, _mm256_blend_ps(blend1, blend2, 0xf0));
 
   hsum1 = _mm256_hadd_ps(vecs8_0, vecs9_0);
   hsum2 = _mm256_hadd_ps(vecs10_0, vecs11_0);
@@ -769,7 +769,7 @@ vecs)
   blend1 = _mm256_blend_ps(sum1, sum2, 0xcc);
   blend2 = _mm256_blend_ps(sum3, sum4, 0xcc);
 
-  final_1 = padd(final_1, _mm256_blend_ps(blend1, blend2, 0xf0));
+  final_1 = _mm256_add_ps(final_1, _mm256_blend_ps(blend1, blend2, 0xf0));
 
   __m512 final_output;
 
@@ -819,7 +819,7 @@ template<> EIGEN_STRONG_INLINE Packet8d preduxp<Packet8d>(const Packet8d* vecs)
   tmp1 = _mm256_hadd_pd(vecs2_1, vecs3_1);
   tmp1 = _mm256_add_pd(tmp1, _mm256_permute2f128_pd(tmp1, tmp1, 1));
 
-  final_0 = padd(final_0, _mm256_blend_pd(tmp0, tmp1, 0xC));
+  final_0 = _mm256_add_pd(final_0, _mm256_blend_pd(tmp0, tmp1, 0xC));
 
   tmp0 = _mm256_hadd_pd(vecs4_0, vecs5_0);
   tmp0 = _mm256_add_pd(tmp0, _mm256_permute2f128_pd(tmp0, tmp0, 1));
@@ -835,7 +835,7 @@ template<> EIGEN_STRONG_INLINE Packet8d preduxp<Packet8d>(const Packet8d* vecs)
   tmp1 = _mm256_hadd_pd(vecs6_1, vecs7_1);
   tmp1 = _mm256_add_pd(tmp1, _mm256_permute2f128_pd(tmp1, tmp1, 1));
 
-  final_1 = padd(final_1, _mm256_blend_pd(tmp0, tmp1, 0xC));
+  final_1 = _mm256_add_pd(final_1, _mm256_blend_pd(tmp0, tmp1, 0xC));
 
   __m512d final_output = _mm512_insertf64x4(final_output, final_0, 0);
 
@@ -844,55 +844,54 @@ template<> EIGEN_STRONG_INLINE Packet8d preduxp<Packet8d>(const Packet8d* vecs)
 
 template <>
 EIGEN_STRONG_INLINE float predux<Packet16f>(const Packet16f& a) {
-  //#ifdef EIGEN_VECTORIZE_AVX512DQ
-#if 0
-  Packet8f lane0 = _mm512_extractf32x8_ps(a, 0);
-  Packet8f lane1 = _mm512_extractf32x8_ps(a, 1);
-  Packet8f sum = padd(lane0, lane1);
-  Packet8f tmp0 = _mm256_hadd_ps(sum, _mm256_permute2f128_ps(a, a, 1));
+#ifdef EIGEN_VECTORIZE_AVX512DQ
+  __m256 lane0 = _mm512_extractf32x8_ps(a, 0);
+  __m256 lane1 = _mm512_extractf32x8_ps(a, 1);
+  __m256 sum = _mm256_add_ps(lane0, lane1);
+  __m256 tmp0 = _mm256_hadd_ps(sum, _mm256_permute2f128_ps(a, a, 1));
   tmp0 = _mm256_hadd_ps(tmp0, tmp0);
-  return pfirst(_mm256_hadd_ps(tmp0, tmp0));
+  return _mm_cvtss_f32(_mm256_castps256_ps128(_mm256_hadd_ps(tmp0, tmp0)));
 #else
-  Packet4f lane0 = _mm512_extractf32x4_ps(a, 0);
-  Packet4f lane1 = _mm512_extractf32x4_ps(a, 1);
-  Packet4f lane2 = _mm512_extractf32x4_ps(a, 2);
-  Packet4f lane3 = _mm512_extractf32x4_ps(a, 3);
-  Packet4f sum = padd(padd(lane0, lane1), padd(lane2, lane3));
+  __m128 lane0 = _mm512_extractf32x4_ps(a, 0);
+  __m128 lane1 = _mm512_extractf32x4_ps(a, 1);
+  __m128 lane2 = _mm512_extractf32x4_ps(a, 2);
+  __m128 lane3 = _mm512_extractf32x4_ps(a, 3);
+  __m128 sum = _mm_add_ps(_mm_add_ps(lane0, lane1), _mm_add_ps(lane2, lane3));
   sum = _mm_hadd_ps(sum, sum);
   sum = _mm_hadd_ps(sum, _mm_permute_ps(sum, 1));
-  return pfirst(sum);
+  return _mm_cvtss_f32(sum);
 #endif
 }
 template <>
 EIGEN_STRONG_INLINE double predux<Packet8d>(const Packet8d& a) {
-  Packet4d lane0 = _mm512_extractf64x4_pd(a, 0);
-  Packet4d lane1 = _mm512_extractf64x4_pd(a, 1);
-  Packet4d sum = padd(lane0, lane1);
-  Packet4d tmp0 = _mm256_hadd_pd(sum, _mm256_permute2f128_pd(sum, sum, 1));
-  return pfirst(_mm256_hadd_pd(tmp0, tmp0));
+  __m256d lane0 = _mm512_extractf64x4_pd(a, 0);
+  __m256d lane1 = _mm512_extractf64x4_pd(a, 1);
+  __m256d sum = _mm256_add_pd(lane0, lane1);
+  __m256d tmp0 = _mm256_hadd_pd(sum, _mm256_permute2f128_pd(sum, sum, 1));
+  return _mm_cvtsd_f64(_mm256_castpd256_pd128(_mm256_hadd_pd(tmp0, tmp0)));
 }
 
 template <>
 EIGEN_STRONG_INLINE Packet8f predux_downto4<Packet16f>(const Packet16f& a) {
 #ifdef EIGEN_VECTORIZE_AVX512DQ
-  Packet8f lane0 = _mm512_extractf32x8_ps(a, 0);
-  Packet8f lane1 = _mm512_extractf32x8_ps(a, 1);
-  return padd(lane0, lane1);
+  __m256 lane0 = _mm512_extractf32x8_ps(a, 0);
+  __m256 lane1 = _mm512_extractf32x8_ps(a, 1);
+  return _mm256_add_ps(lane0, lane1);
 #else
-  Packet4f lane0 = _mm512_extractf32x4_ps(a, 0);
-  Packet4f lane1 = _mm512_extractf32x4_ps(a, 1);
-  Packet4f lane2 = _mm512_extractf32x4_ps(a, 2);
-  Packet4f lane3 = _mm512_extractf32x4_ps(a, 3);
-  Packet4f sum0 = padd(lane0, lane2);
-  Packet4f sum1 = padd(lane1, lane3);
+  __m128 lane0 = _mm512_extractf32x4_ps(a, 0);
+  __m128 lane1 = _mm512_extractf32x4_ps(a, 1);
+  __m128 lane2 = _mm512_extractf32x4_ps(a, 2);
+  __m128 lane3 = _mm512_extractf32x4_ps(a, 3);
+  __m128 sum0 = _mm_add_ps(lane0, lane2);
+  __m128 sum1 = _mm_add_ps(lane1, lane3);
   return _mm256_insertf128_ps(_mm256_castps128_ps256(sum0), sum1, 1);
 #endif
 }
 template <>
 EIGEN_STRONG_INLINE Packet4d predux_downto4<Packet8d>(const Packet8d& a) {
-  Packet4d lane0 = _mm512_extractf64x4_pd(a, 0);
-  Packet4d lane1 = _mm512_extractf64x4_pd(a, 1);
-  Packet4d res = padd(lane0, lane1);
+  __m256d lane0 = _mm512_extractf64x4_pd(a, 0);
+  __m256d lane1 = _mm512_extractf64x4_pd(a, 1);
+  __m256d res = _mm256_add_pd(lane0, lane1);
   return res;
 }
 
@@ -907,58 +906,59 @@ EIGEN_STRONG_INLINE float predux_mul<Packet16f>(const Packet16f& a) {
   res = pmul(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 3, 2)));
   return pfirst(pmul(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 0, 1))));
 #else
-  Packet4f lane0 = _mm512_extractf32x4_ps(a, 0);
-  Packet4f lane1 = _mm512_extractf32x4_ps(a, 1);
-  Packet4f lane2 = _mm512_extractf32x4_ps(a, 2);
-  Packet4f lane3 = _mm512_extractf32x4_ps(a, 3);
-  Packet4f res = pmul(pmul(lane0, lane1), pmul(lane2, lane3));
+  __m128 lane0 = _mm512_extractf32x4_ps(a, 0);
+  __m128 lane1 = _mm512_extractf32x4_ps(a, 1);
+  __m128 lane2 = _mm512_extractf32x4_ps(a, 2);
+  __m128 lane3 = _mm512_extractf32x4_ps(a, 3);
+  __m128 res = pmul(pmul(lane0, lane1), pmul(lane2, lane3));
   res = pmul(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 3, 2)));
   return pfirst(pmul(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 0, 1))));
 #endif
 }
 template <>
 EIGEN_STRONG_INLINE double predux_mul<Packet8d>(const Packet8d& a) {
-  Packet4d lane0 = _mm512_extractf64x4_pd(a, 0);
-  Packet4d lane1 = _mm512_extractf64x4_pd(a, 1);
-  Packet4d res = pmul(lane0, lane1);
+  __m256d lane0 = _mm512_extractf64x4_pd(a, 0);
+  __m256d lane1 = _mm512_extractf64x4_pd(a, 1);
+  __m256d res = pmul(lane0, lane1);
   res = pmul(res, _mm256_permute2f128_pd(res, res, 1));
   return pfirst(pmul(res, _mm256_shuffle_pd(res, res, 1)));
 }
 
 template <>
 EIGEN_STRONG_INLINE float predux_min<Packet16f>(const Packet16f& a) {
-  Packet4f lane0 = _mm512_extractf32x4_ps(a, 0);
-  Packet4f lane1 = _mm512_extractf32x4_ps(a, 1);
-  Packet4f lane2 = _mm512_extractf32x4_ps(a, 2);
-  Packet4f lane3 = _mm512_extractf32x4_ps(a, 3);
-  Packet4f res = _mm_min_ps(_mm_min_ps(lane0, lane1), _mm_min_ps(lane2, lane3));
+  __m128 lane0 = _mm512_extractf32x4_ps(a, 0);
+  __m128 lane1 = _mm512_extractf32x4_ps(a, 1);
+  __m128 lane2 = _mm512_extractf32x4_ps(a, 2);
+  __m128 lane3 = _mm512_extractf32x4_ps(a, 3);
+  __m128 res = _mm_min_ps(_mm_min_ps(lane0, lane1), _mm_min_ps(lane2, lane3));
   res = _mm_min_ps(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 3, 2)));
   return pfirst(_mm_min_ps(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 0, 1))));
 }
 template <>
 EIGEN_STRONG_INLINE double predux_min<Packet8d>(const Packet8d& a) {
-  Packet4d lane0 = _mm512_extractf64x4_pd(a, 0);
-  Packet4d lane1 = _mm512_extractf64x4_pd(a, 1);
-  Packet4d res = _mm256_min_pd(lane0, lane1);
+  __m256d lane0 = _mm512_extractf64x4_pd(a, 0);
+  __m256d lane1 = _mm512_extractf64x4_pd(a, 1);
+  __m256d res = _mm256_min_pd(lane0, lane1);
   res = _mm256_min_pd(res, _mm256_permute2f128_pd(res, res, 1));
   return pfirst(_mm256_min_pd(res, _mm256_shuffle_pd(res, res, 1)));
 }
 
 template <>
 EIGEN_STRONG_INLINE float predux_max<Packet16f>(const Packet16f& a) {
-  Packet4f lane0 = _mm512_extractf32x4_ps(a, 0);
-  Packet4f lane1 = _mm512_extractf32x4_ps(a, 1);
-  Packet4f lane2 = _mm512_extractf32x4_ps(a, 2);
-  Packet4f lane3 = _mm512_extractf32x4_ps(a, 3);
-  Packet4f res = _mm_max_ps(_mm_max_ps(lane0, lane1), _mm_max_ps(lane2, lane3));
+  __m128 lane0 = _mm512_extractf32x4_ps(a, 0);
+  __m128 lane1 = _mm512_extractf32x4_ps(a, 1);
+  __m128 lane2 = _mm512_extractf32x4_ps(a, 2);
+  __m128 lane3 = _mm512_extractf32x4_ps(a, 3);
+  __m128 res = _mm_max_ps(_mm_max_ps(lane0, lane1), _mm_max_ps(lane2, lane3));
   res = _mm_max_ps(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 3, 2)));
   return pfirst(_mm_max_ps(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 0, 1))));
 }
+
 template <>
 EIGEN_STRONG_INLINE double predux_max<Packet8d>(const Packet8d& a) {
-  Packet4d lane0 = _mm512_extractf64x4_pd(a, 0);
-  Packet4d lane1 = _mm512_extractf64x4_pd(a, 1);
-  Packet4d res = _mm256_max_pd(lane0, lane1);
+  __m256d lane0 = _mm512_extractf64x4_pd(a, 0);
+  __m256d lane1 = _mm512_extractf64x4_pd(a, 1);
+  __m256d res = _mm256_max_pd(lane0, lane1);
   res = _mm256_max_pd(res, _mm256_permute2f128_pd(res, res, 1));
   return pfirst(_mm256_max_pd(res, _mm256_shuffle_pd(res, res, 1)));
 }