diff --git a/Eigen/src/Core/arch/AVX512/MathFunctions.h b/Eigen/src/Core/arch/AVX512/MathFunctions.h
index 0e57d7c33..399be0ee4 100644
--- a/Eigen/src/Core/arch/AVX512/MathFunctions.h
+++ b/Eigen/src/Core/arch/AVX512/MathFunctions.h
@@ -14,6 +14,9 @@ namespace Eigen {
 
 namespace internal {
 
+// Disable the code for older versions of gcc that don't support many of the required avx512 instrinsics.
+#if EIGEN_GNUC_AT_LEAST(5, 3)
+
 #define _EIGEN_DECLARE_CONST_Packet16f(NAME, X) \
   const Packet16f p16f_##NAME = pset1<Packet16f>(X)
 
@@ -30,6 +33,7 @@ namespace internal {
 // Computes log(x) as log(2^e * m) = C*e + log(m), where the constant C =log(2)
 // and m is in the range [sqrt(1/2),sqrt(2)). In this range, the logarithm can
 // be easily approximated by a polynomial centered on m=1 for stability.
+#if defined(EIGEN_VECTORIZE_AVX512DQ)
 template <>
 EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet16f
 plog<Packet16f>(const Packet16f& _x) {
@@ -118,6 +122,7 @@ plog<Packet16f>(const Packet16f& _x) {
   return _mm512_mask_blend_ps(iszero_mask, p16f_minus_inf,
                               _mm512_mask_blend_ps(invalid_mask, p16f_nan, x));
 }
+#endif
 
 // Exponential function. Works by writing "x = m*log(2) + r" where
 // "m = floor(x/log(2)+1/2)" and "r" is the remainder. The result is then
@@ -382,6 +387,7 @@ EIGEN_STRONG_INLINE Packet16f prsqrt<Packet16f>(const Packet16f& x) {
   return _mm512_rsqrt28_ps(x);
 }
 #endif
+#endif
 
 }  // end namespace internal
 
diff --git a/Eigen/src/Core/arch/AVX512/PacketMath.h b/Eigen/src/Core/arch/AVX512/PacketMath.h
index 671b6f30a..fd5a90141 100644
--- a/Eigen/src/Core/arch/AVX512/PacketMath.h
+++ b/Eigen/src/Core/arch/AVX512/PacketMath.h
@@ -54,14 +54,17 @@ template<> struct packet_traits<float>  : default_packet_traits
     AlignedOnScalar = 1,
     size = 16,
     HasHalfPacket = 1,
-    HasLog = 1,
-    HasExp = 1,
     HasDiv = 1,
-    HasBlend = 1,
+    HasBlend = 0,
+#if EIGEN_GNUC_AT_LEAST(5, 3)
+#ifdef EIGEN_VECTORIZE_AVX512DQ
+    HasLog = 1,
+#endif
+    HasExp = 1,
     HasSqrt = 1,
     HasRsqrt = 1,
-    HasSelect = 1,
-    HasEq = 1
+#endif
+    HasSelect = 1
   };
  };
 template<> struct packet_traits<double> : default_packet_traits
@@ -73,13 +76,11 @@ template<> struct packet_traits<double> : default_packet_traits
     AlignedOnScalar = 1,
     size = 8,
     HasHalfPacket = 1,
-    HasExp = 0,
-    HasDiv = 1,
-    HasBlend = 1,
+#if EIGEN_GNUC_AT_LEAST(5, 3)
     HasSqrt = 1,
     HasRsqrt = EIGEN_FAST_MATH,
-    HasSelect = 1,
-    HasEq = 1
+#endif
+
   };
 };