diff --git a/Eigen/Core b/Eigen/Core
index d45e45636..c0d209818 100644
--- a/Eigen/Core
+++ b/Eigen/Core
@@ -350,7 +350,7 @@ using std::ptrdiff_t;
 #include "src/Core/CoreIterators.h"
 #include "src/Core/ConditionEstimator.h"
 
-#if defined(EIGEN_VECTORIZE_ALTIVEC) || defined(EIGEN_VECTORIZE_VSX)
+#if defined(EIGEN_VECTORIZE_VSX)
   #include "src/Core/arch/AltiVec/MatrixProduct.h"
 #elif defined EIGEN_VECTORIZE_NEON
   #include "src/Core/arch/NEON/GeneralBlockPanelKernel.h"
diff --git a/Eigen/src/Core/arch/AltiVec/Complex.h b/Eigen/src/Core/arch/AltiVec/Complex.h
index b0f5e97b9..46812f97b 100644
--- a/Eigen/src/Core/arch/AltiVec/Complex.h
+++ b/Eigen/src/Core/arch/AltiVec/Complex.h
@@ -102,6 +102,7 @@ template<> struct packet_traits<std::complex<float> >  : default_packet_traits
     HasAbs2   = 0,
     HasMin    = 0,
     HasMax    = 0,
+    HasSqrt   = 1,
 #ifdef __VSX__
     HasBlend  = 1,
 #endif
@@ -370,6 +371,7 @@ template<> struct packet_traits<std::complex<double> >  : default_packet_traits
     HasAbs2   = 0,
     HasMin    = 0,
     HasMax    = 0,
+    HasSqrt   = 1,
     HasSetLinear = 0
   };
 };
diff --git a/Eigen/src/Core/arch/AltiVec/MathFunctions.h b/Eigen/src/Core/arch/AltiVec/MathFunctions.h
index 977bfc2e7..c85ca13aa 100644
--- a/Eigen/src/Core/arch/AltiVec/MathFunctions.h
+++ b/Eigen/src/Core/arch/AltiVec/MathFunctions.h
@@ -42,16 +42,14 @@ Packet4f pcos<Packet4f>(const Packet4f& _x)
   return pcos_float(_x);
 }
 
+#ifdef __VSX__
 #ifndef EIGEN_COMP_CLANG
 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
 Packet4f prsqrt<Packet4f>(const Packet4f& x)
 {
   return  vec_rsqrt(x);
 }
-#endif
 
-#ifdef __VSX__
-#ifndef EIGEN_COMP_CLANG
 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
 Packet2d prsqrt<Packet2d>(const Packet2d& x)
 {
@@ -76,6 +74,26 @@ Packet2d pexp<Packet2d>(const Packet2d& _x)
 {
   return pexp_double(_x);
 }
+
+template<> EIGEN_STRONG_INLINE Packet8bf psqrt<Packet8bf> (const Packet8bf& a){
+  BF16_TO_F32_UNARY_OP_WRAPPER(psqrt<Packet4f>, a);
+}
+
+#ifndef EIGEN_COMP_CLANG
+template<> EIGEN_STRONG_INLINE Packet8bf prsqrt<Packet8bf> (const Packet8bf& a){
+  BF16_TO_F32_UNARY_OP_WRAPPER(prsqrt<Packet4f>, a);
+}
+#endif
+#else
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet4f psqrt<Packet4f>(const Packet4f& x)
+{
+  Packet4f a;
+  for (Index i = 0; i < packet_traits<float>::size; i++) {
+    a[i] = numext::sqrt(x[i]);
+  }
+  return a;
+}
 #endif
 
 // Hyperbolic Tangent function.
diff --git a/Eigen/src/Core/arch/AltiVec/PacketMath.h b/Eigen/src/Core/arch/AltiVec/PacketMath.h
index fceff293f..5ec06c458 100644
--- a/Eigen/src/Core/arch/AltiVec/PacketMath.h
+++ b/Eigen/src/Core/arch/AltiVec/PacketMath.h
@@ -177,16 +177,19 @@ struct packet_traits<float> : default_packet_traits {
 #else
     HasRsqrt = 0,
 #endif
+    HasTanh = EIGEN_FAST_MATH,
+    HasErf = EIGEN_FAST_MATH,
+    HasRint = 1,
 #else
     HasSqrt = 0,
     HasRsqrt = 0,
+    HasTanh = 0,
+    HasErf = 0,
+    HasRint = 0,
 #endif
-    HasTanh = EIGEN_FAST_MATH,
-    HasErf = EIGEN_FAST_MATH,
     HasRound = 1,
     HasFloor = 1,
     HasCeil = 1,
-    HasRint = 1,
     HasNegate = 1,
     HasBlend = 1
   };
@@ -219,16 +222,17 @@ struct packet_traits<bfloat16> : default_packet_traits {
 #else
     HasRsqrt = 0,
 #endif
+    HasRint = 1,
 #else
     HasSqrt = 0,
     HasRsqrt = 0,
-    HasTanh = EIGEN_FAST_MATH,
-    HasErf = EIGEN_FAST_MATH,
+    HasRint = 0,
 #endif
+    HasTanh = 0,
+    HasErf = 0,
     HasRound = 1,
     HasFloor = 1,
     HasCeil = 1,
-    HasRint = 1,
     HasNegate = 1,
     HasBlend = 1
   };
@@ -1042,9 +1046,11 @@ template<> EIGEN_STRONG_INLINE Packet4i pmadd(const Packet4i& a, const Packet4i&
 template<> EIGEN_STRONG_INLINE Packet8s pmadd(const Packet8s& a, const Packet8s& b, const Packet8s& c) { return vec_madd(a,b,c); }
 template<> EIGEN_STRONG_INLINE Packet8us pmadd(const Packet8us& a, const Packet8us& b, const Packet8us& c) { return vec_madd(a,b,c); }
 
+#ifdef __VSX__
 template<> EIGEN_STRONG_INLINE Packet4f pmsub(const Packet4f& a, const Packet4f& b, const Packet4f& c) { return vec_msub(a,b,c); }
 template<> EIGEN_STRONG_INLINE Packet4f pnmadd(const Packet4f& a, const Packet4f& b, const Packet4f& c) { return vec_nmsub(a,b,c); }
 template<> EIGEN_STRONG_INLINE Packet4f pnmsub(const Packet4f& a, const Packet4f& b, const Packet4f& c) { return vec_nmadd(a,b,c); }
+#endif
 
 template<> EIGEN_STRONG_INLINE Packet4f pmin<Packet4f>(const Packet4f& a, const Packet4f& b)
 {
@@ -1089,19 +1095,29 @@ template<> EIGEN_STRONG_INLINE Packet4f pcmp_lt_or_nan(const Packet4f& a, const
   return vec_nor(c,c);
 }
 
+#ifdef __VSX__
 template<> EIGEN_STRONG_INLINE Packet4i pcmp_le(const Packet4i& a, const Packet4i& b) { return reinterpret_cast<Packet4i>(vec_cmple(a,b)); }
+#endif
 template<> EIGEN_STRONG_INLINE Packet4i pcmp_lt(const Packet4i& a, const Packet4i& b) { return reinterpret_cast<Packet4i>(vec_cmplt(a,b)); }
 template<> EIGEN_STRONG_INLINE Packet4i pcmp_eq(const Packet4i& a, const Packet4i& b) { return reinterpret_cast<Packet4i>(vec_cmpeq(a,b)); }
+#ifdef __VSX__
 template<> EIGEN_STRONG_INLINE Packet8s pcmp_le(const Packet8s& a, const Packet8s& b) { return reinterpret_cast<Packet8s>(vec_cmple(a,b)); }
+#endif
 template<> EIGEN_STRONG_INLINE Packet8s pcmp_lt(const Packet8s& a, const Packet8s& b) { return reinterpret_cast<Packet8s>(vec_cmplt(a,b)); }
 template<> EIGEN_STRONG_INLINE Packet8s pcmp_eq(const Packet8s& a, const Packet8s& b) { return reinterpret_cast<Packet8s>(vec_cmpeq(a,b)); }
+#ifdef __VSX__
 template<> EIGEN_STRONG_INLINE Packet8us pcmp_le(const Packet8us& a, const Packet8us& b) { return reinterpret_cast<Packet8us>(vec_cmple(a,b)); }
+#endif
 template<> EIGEN_STRONG_INLINE Packet8us pcmp_lt(const Packet8us& a, const Packet8us& b) { return reinterpret_cast<Packet8us>(vec_cmplt(a,b)); }
 template<> EIGEN_STRONG_INLINE Packet8us pcmp_eq(const Packet8us& a, const Packet8us& b) { return reinterpret_cast<Packet8us>(vec_cmpeq(a,b)); }
+#ifdef __VSX__
 template<> EIGEN_STRONG_INLINE Packet16c pcmp_le(const Packet16c& a, const Packet16c& b) { return reinterpret_cast<Packet16c>(vec_cmple(a,b)); }
+#endif
 template<> EIGEN_STRONG_INLINE Packet16c pcmp_lt(const Packet16c& a, const Packet16c& b) { return reinterpret_cast<Packet16c>(vec_cmplt(a,b)); }
 template<> EIGEN_STRONG_INLINE Packet16c pcmp_eq(const Packet16c& a, const Packet16c& b) { return reinterpret_cast<Packet16c>(vec_cmpeq(a,b)); }
+#ifdef __VSX__
 template<> EIGEN_STRONG_INLINE Packet16uc pcmp_le(const Packet16uc& a, const Packet16uc& b) { return reinterpret_cast<Packet16uc>(vec_cmple(a,b)); }
+#endif
 template<> EIGEN_STRONG_INLINE Packet16uc pcmp_lt(const Packet16uc& a, const Packet16uc& b) { return reinterpret_cast<Packet16uc>(vec_cmplt(a,b)); }
 template<> EIGEN_STRONG_INLINE Packet16uc pcmp_eq(const Packet16uc& a, const Packet16uc& b) { return reinterpret_cast<Packet16uc>(vec_cmpeq(a,b)); }
 
@@ -1154,6 +1170,7 @@ template<> EIGEN_STRONG_INLINE Packet4f pround<Packet4f>(const Packet4f& a)
 }
 template<> EIGEN_STRONG_INLINE Packet4f pceil<Packet4f>(const  Packet4f& a) { return vec_ceil(a); }
 template<> EIGEN_STRONG_INLINE Packet4f pfloor<Packet4f>(const Packet4f& a) { return vec_floor(a); }
+#ifdef __VSX__
 template<> EIGEN_STRONG_INLINE Packet4f print<Packet4f>(const Packet4f& a)
 {
     Packet4f res;
@@ -1164,6 +1181,7 @@ template<> EIGEN_STRONG_INLINE Packet4f print<Packet4f>(const Packet4f& a)
 
     return res;
 }
+#endif
 
 template<typename Packet> EIGEN_STRONG_INLINE Packet ploadu_common(const __UNPACK_TYPE__(Packet)* from)
 {
@@ -1706,12 +1724,6 @@ template<> EIGEN_STRONG_INLINE Packet8bf psub<Packet8bf>(const Packet8bf& a, con
   BF16_TO_F32_BINARY_OP_WRAPPER(psub<Packet4f>, a, b);
 }
 
-template<> EIGEN_STRONG_INLINE Packet8bf psqrt<Packet8bf> (const Packet8bf& a){
-  BF16_TO_F32_UNARY_OP_WRAPPER(vec_sqrt, a);
-}
-template<> EIGEN_STRONG_INLINE Packet8bf prsqrt<Packet8bf> (const Packet8bf& a){
-  BF16_TO_F32_UNARY_OP_WRAPPER(prsqrt<Packet4f>, a);
-}
 template<> EIGEN_STRONG_INLINE Packet8bf pexp<Packet8bf> (const Packet8bf& a){
   BF16_TO_F32_UNARY_OP_WRAPPER(pexp_float, a);
 }
@@ -1755,9 +1767,11 @@ template<> EIGEN_STRONG_INLINE Packet8bf pceil<Packet8bf> (const Packet8bf& a){
 template<> EIGEN_STRONG_INLINE Packet8bf pround<Packet8bf> (const Packet8bf& a){
   BF16_TO_F32_UNARY_OP_WRAPPER(pround<Packet4f>, a);
 }
+#ifdef __VSX__
 template<> EIGEN_STRONG_INLINE Packet8bf print<Packet8bf> (const Packet8bf& a){
   BF16_TO_F32_UNARY_OP_WRAPPER(print<Packet4f>, a);
 }
+#endif
 template<> EIGEN_STRONG_INLINE Packet8bf pmadd(const Packet8bf& a, const Packet8bf& b, const Packet8bf& c) {
   Packet4f a_even = Bf16ToF32Even(a);
   Packet4f a_odd = Bf16ToF32Odd(a);