New BF16 pcast functions and move type casting to TypeCasting.h
diff --git a/Eigen/Core b/Eigen/Core
index 4d23920..bf0b9c7 100644
--- a/Eigen/Core
+++ b/Eigen/Core
@@ -220,6 +220,7 @@
   #include "src/Core/arch/SSE/Complex.h"
 #elif defined(EIGEN_VECTORIZE_ALTIVEC) || defined(EIGEN_VECTORIZE_VSX)
   #include "src/Core/arch/AltiVec/PacketMath.h"
+  #include "src/Core/arch/AltiVec/TypeCasting.h"
   #include "src/Core/arch/AltiVec/MathFunctions.h"
   #include "src/Core/arch/AltiVec/Complex.h"
 #elif defined EIGEN_VECTORIZE_NEON
diff --git a/Eigen/src/Core/arch/AltiVec/PacketMath.h b/Eigen/src/Core/arch/AltiVec/PacketMath.h
index e016851..5f4ccda 100644
--- a/Eigen/src/Core/arch/AltiVec/PacketMath.h
+++ b/Eigen/src/Core/arch/AltiVec/PacketMath.h
@@ -2697,102 +2697,6 @@
   return vec_sel(elsePacket, thenPacket, mask);
 }
 
-template <>
-struct type_casting_traits<float, int> {
-  enum {
-    VectorizedCast = 1,
-    SrcCoeffRatio = 1,
-    TgtCoeffRatio = 1
-  };
-};
-
-template <>
-struct type_casting_traits<int, float> {
-  enum {
-    VectorizedCast = 1,
-    SrcCoeffRatio = 1,
-    TgtCoeffRatio = 1
-  };
-};
-
-template <>
-struct type_casting_traits<bfloat16, unsigned short int> {
-  enum {
-    VectorizedCast = 1,
-    SrcCoeffRatio = 1,
-    TgtCoeffRatio = 1
-  };
-};
-
-template <>
-struct type_casting_traits<unsigned short int, bfloat16> {
-  enum {
-    VectorizedCast = 1,
-    SrcCoeffRatio = 1,
-    TgtCoeffRatio = 1
-  };
-};
-
-template<> EIGEN_STRONG_INLINE Packet4i pcast<Packet4f, Packet4i>(const Packet4f& a) {
-  return vec_cts(a,0);
-}
-
-template<> EIGEN_STRONG_INLINE Packet4ui pcast<Packet4f, Packet4ui>(const Packet4f& a) {
-  return vec_ctu(a,0);
-}
-
-template<> EIGEN_STRONG_INLINE Packet4f pcast<Packet4i, Packet4f>(const Packet4i& a) {
-  return vec_ctf(a,0);
-}
-
-template<> EIGEN_STRONG_INLINE Packet4f pcast<Packet4ui, Packet4f>(const Packet4ui& a) {
-  return vec_ctf(a,0);
-}
-
-template<> EIGEN_STRONG_INLINE Packet8us pcast<Packet8bf, Packet8us>(const Packet8bf& a) {
-  Packet4f float_even = Bf16ToF32Even(a);
-  Packet4f float_odd = Bf16ToF32Odd(a);
-  Packet4ui int_even = pcast<Packet4f, Packet4ui>(float_even);
-  Packet4ui int_odd = pcast<Packet4f, Packet4ui>(float_odd);
-  const EIGEN_DECLARE_CONST_FAST_Packet4ui(low_mask, 0x0000FFFF);
-  Packet4ui low_even = pand<Packet4ui>(int_even, p4ui_low_mask);
-  Packet4ui low_odd = pand<Packet4ui>(int_odd, p4ui_low_mask);
-
-  //Check values that are bigger than USHRT_MAX (0xFFFF)
-  Packet4bi overflow_selector;
-  if(vec_any_gt(int_even, p4ui_low_mask)){
-    overflow_selector = vec_cmpgt(int_even, p4ui_low_mask);
-    low_even = vec_sel(low_even, p4ui_low_mask, overflow_selector);
-  }
-  if(vec_any_gt(int_odd, p4ui_low_mask)){
-    overflow_selector = vec_cmpgt(int_odd, p4ui_low_mask);
-    low_odd = vec_sel(low_even, p4ui_low_mask, overflow_selector);
-  }
-
-  return pmerge(low_even, low_odd);
-}
-
-template<> EIGEN_STRONG_INLINE Packet8bf pcast<Packet8us, Packet8bf>(const Packet8us& a) {
-  //short -> int -> float -> bfloat16
-  const EIGEN_DECLARE_CONST_FAST_Packet4ui(low_mask, 0x0000FFFF);
-  Packet4ui int_cast = reinterpret_cast<Packet4ui>(a);
-  Packet4ui int_even = pand<Packet4ui>(int_cast, p4ui_low_mask);
-  Packet4ui int_odd = plogical_shift_right<16>(int_cast);
-  Packet4f float_even = pcast<Packet4ui, Packet4f>(int_even);
-  Packet4f float_odd = pcast<Packet4ui, Packet4f>(int_odd);
-  return F32ToBf16(float_even, float_odd);
-}
-
-
-template<> EIGEN_STRONG_INLINE Packet4i preinterpret<Packet4i,Packet4f>(const Packet4f& a) {
-  return reinterpret_cast<Packet4i>(a);
-}
-
-template<> EIGEN_STRONG_INLINE Packet4f preinterpret<Packet4f,Packet4i>(const Packet4i& a) {
-  return reinterpret_cast<Packet4f>(a);
-}
-
-
 
 //---------- double ----------
 #ifdef EIGEN_VECTORIZE_VSX
@@ -2805,7 +2709,6 @@
 typedef __vector __bool long         Packet2bl;
 #endif
 
-static Packet2l  p2l_ONE  = { 1, 1 };
 static Packet2l  p2l_ZERO = reinterpret_cast<Packet2l>(p4i_ZERO);
 static Packet2ul p2ul_SIGN = { 0x8000000000000000ull, 0x8000000000000000ull };
 static Packet2ul p2ul_PREV0DOT5 = { 0x3FDFFFFFFFFFFFFFull, 0x3FDFFFFFFFFFFFFFull };
@@ -3082,34 +2985,10 @@
   return reinterpret_cast<Packet2d>(vec_perm(tmp, tmp, p16uc_DUPSIGN));
 }
 #endif
-// VSX support varies between different compilers and even different
-// versions of the same compiler.  For gcc version >= 4.9.3, we can use
-// vec_cts to efficiently convert Packet2d to Packet2l.  Otherwise, use
-// a slow version that works with older compilers. 
-// Update: apparently vec_cts/vec_ctf intrinsics for 64-bit doubles
-// are buggy, https://gcc.gnu.org/bugzilla/show_bug.cgi?id=70963
-template<>
-inline Packet2l pcast<Packet2d, Packet2l>(const Packet2d& x) {
-#if EIGEN_GNUC_STRICT_AT_LEAST(7,1,0)
-  return vec_cts(x, 0);    // TODO: check clang version.
-#else
-  double tmp[2];
-  memcpy(tmp, &x, sizeof(tmp));
-  Packet2l l = { static_cast<long long>(tmp[0]),
-                 static_cast<long long>(tmp[1]) };
-  return l;
-#endif
-}
 
-template<>
-inline Packet2d pcast<Packet2l, Packet2d>(const Packet2l& x) {
-  unsigned long long tmp[2];
-  memcpy(tmp, &x, sizeof(tmp));
-  Packet2d d = { static_cast<double>(tmp[0]),
-                 static_cast<double>(tmp[1]) };
-  return d;
-}
+template<> inline Packet2l pcast<Packet2d, Packet2l>(const Packet2d& x);
 
+template<> inline Packet2d pcast<Packet2l, Packet2d>(const Packet2l& x);
 
 // Packet2l shifts.
 // For POWER8 we simply use vec_sr/l. 
@@ -3290,7 +3169,7 @@
 
 template<> EIGEN_STRONG_INLINE Packet2d pblend(const Selector<2>& ifPacket, const Packet2d& thenPacket, const Packet2d& elsePacket) {
   Packet2l select = { ifPacket.select[0], ifPacket.select[1] };
-  Packet2bl mask = reinterpret_cast<Packet2bl>( vec_cmpeq(reinterpret_cast<Packet2d>(select), reinterpret_cast<Packet2d>(p2l_ONE)) );
+  Packet2ul mask = reinterpret_cast<Packet2ul>(pnegate(reinterpret_cast<Packet2l>(select)));
   return vec_sel(elsePacket, thenPacket, mask);
 }
 
diff --git a/Eigen/src/Core/arch/AltiVec/TypeCasting.h b/Eigen/src/Core/arch/AltiVec/TypeCasting.h
new file mode 100644
index 0000000..bda63d8
--- /dev/null
+++ b/Eigen/src/Core/arch/AltiVec/TypeCasting.h
@@ -0,0 +1,178 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2019 Rasmus Munk Larsen <rmlarsen@google.com>
+// Copyright (C) 2023 Chip Kerchner (chip.kerchner@ibm.com)
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_TYPE_CASTING_ALTIVEC_H
+#define EIGEN_TYPE_CASTING_ALTIVEC_H
+
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+template <>
+struct type_casting_traits<float, int> {
+  enum {
+    VectorizedCast = 1,
+    SrcCoeffRatio = 1,
+    TgtCoeffRatio = 1
+  };
+};
+
+template <>
+struct type_casting_traits<int, float> {
+  enum {
+    VectorizedCast = 1,
+    SrcCoeffRatio = 1,
+    TgtCoeffRatio = 1
+  };
+};
+
+template <>
+struct type_casting_traits<bfloat16, unsigned short int> {
+  enum {
+    VectorizedCast = 1,
+    SrcCoeffRatio = 1,
+    TgtCoeffRatio = 1
+  };
+};
+
+template <>
+struct type_casting_traits<unsigned short int, bfloat16> {
+  enum {
+    VectorizedCast = 1,
+    SrcCoeffRatio = 1,
+    TgtCoeffRatio = 1
+  };
+};
+
+template<> EIGEN_STRONG_INLINE Packet4i pcast<Packet4f, Packet4i>(const Packet4f& a) {
+  return vec_cts(a,0);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4ui pcast<Packet4f, Packet4ui>(const Packet4f& a) {
+  return vec_ctu(a,0);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pcast<Packet4i, Packet4f>(const Packet4i& a) {
+  return vec_ctf(a,0);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pcast<Packet4ui, Packet4f>(const Packet4ui& a) {
+  return vec_ctf(a,0);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8us pcast<Packet8bf, Packet8us>(const Packet8bf& a) {
+  Packet4f float_even = Bf16ToF32Even(a);
+  Packet4f float_odd = Bf16ToF32Odd(a);
+  Packet4ui int_even = pcast<Packet4f, Packet4ui>(float_even);
+  Packet4ui int_odd = pcast<Packet4f, Packet4ui>(float_odd);
+  const EIGEN_DECLARE_CONST_FAST_Packet4ui(low_mask, 0x0000FFFF);
+  Packet4ui low_even = pand<Packet4ui>(int_even, p4ui_low_mask);
+  Packet4ui low_odd = pand<Packet4ui>(int_odd, p4ui_low_mask);
+
+  //Check values that are bigger than USHRT_MAX (0xFFFF)
+  Packet4bi overflow_selector;
+  if(vec_any_gt(int_even, p4ui_low_mask)){
+    overflow_selector = vec_cmpgt(int_even, p4ui_low_mask);
+    low_even = vec_sel(low_even, p4ui_low_mask, overflow_selector);
+  }
+  if(vec_any_gt(int_odd, p4ui_low_mask)){
+    overflow_selector = vec_cmpgt(int_odd, p4ui_low_mask);
+    low_odd = vec_sel(low_even, p4ui_low_mask, overflow_selector);
+  }
+
+  return pmerge(low_even, low_odd);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf pcast<Packet8us, Packet8bf>(const Packet8us& a) {
+  //short -> int -> float -> bfloat16
+  const EIGEN_DECLARE_CONST_FAST_Packet4ui(low_mask, 0x0000FFFF);
+  Packet4ui int_cast = reinterpret_cast<Packet4ui>(a);
+  Packet4ui int_even = pand<Packet4ui>(int_cast, p4ui_low_mask);
+  Packet4ui int_odd = plogical_shift_right<16>(int_cast);
+  Packet4f float_even = pcast<Packet4ui, Packet4f>(int_even);
+  Packet4f float_odd = pcast<Packet4ui, Packet4f>(int_odd);
+  return F32ToBf16(float_even, float_odd);
+}
+
+template <>
+struct type_casting_traits<bfloat16, float> {
+  enum {
+    VectorizedCast = 1,
+    SrcCoeffRatio = 1,
+    TgtCoeffRatio = 2
+  };
+};
+
+template<> EIGEN_STRONG_INLINE Packet4f pcast<Packet8bf, Packet4f>(const Packet8bf& a) {
+  Packet8us z = pset1<Packet8us>(0);
+#ifdef _BIG_ENDIAN
+  return reinterpret_cast<Packet4f>(vec_mergeh(a.m_val, z));
+#else
+  return reinterpret_cast<Packet4f>(vec_mergeh(z, a.m_val));
+#endif
+}
+
+template <>
+struct type_casting_traits<float, bfloat16> {
+  enum {
+    VectorizedCast = 1,
+    SrcCoeffRatio = 2,
+    TgtCoeffRatio = 1
+  };
+};
+
+template<> EIGEN_STRONG_INLINE Packet8bf pcast<Packet4f, Packet8bf>(const Packet4f& a, const Packet4f &b) {
+  return F32ToBf16Both(a, b);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4i preinterpret<Packet4i,Packet4f>(const Packet4f& a) {
+  return reinterpret_cast<Packet4i>(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f preinterpret<Packet4f,Packet4i>(const Packet4i& a) {
+  return reinterpret_cast<Packet4f>(a);
+}
+
+#ifdef EIGEN_VECTORIZE_VSX
+// VSX support varies between different compilers and even different
+// versions of the same compiler.  For gcc version >= 4.9.3, we can use
+// vec_cts to efficiently convert Packet2d to Packet2l.  Otherwise, use
+// a slow version that works with older compilers.
+// Update: apparently vec_cts/vec_ctf intrinsics for 64-bit doubles
+// are buggy, https://gcc.gnu.org/bugzilla/show_bug.cgi?id=70963
+template<>
+inline Packet2l pcast<Packet2d, Packet2l>(const Packet2d& x) {
+#if EIGEN_GNUC_STRICT_AT_LEAST(7,1,0)
+  return vec_cts(x, 0);    // TODO: check clang version.
+#else
+  double tmp[2];
+  memcpy(tmp, &x, sizeof(tmp));
+  Packet2l l = { static_cast<long long>(tmp[0]),
+                 static_cast<long long>(tmp[1]) };
+  return l;
+#endif
+}
+
+template<>
+inline Packet2d pcast<Packet2l, Packet2d>(const Packet2l& x) {
+  unsigned long long tmp[2];
+  memcpy(tmp, &x, sizeof(tmp));
+  Packet2d d = { static_cast<double>(tmp[0]),
+                 static_cast<double>(tmp[1]) };
+  return d;
+}
+#endif
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_TYPE_CASTING_ALTIVEC_H