Add support for Bfloat16 to use vector instructions on Altivec
architecture
diff --git a/Eigen/src/Core/arch/AltiVec/PacketMath.h b/Eigen/src/Core/arch/AltiVec/PacketMath.h
index e0da7c3..09ad0a7 100755
--- a/Eigen/src/Core/arch/AltiVec/PacketMath.h
+++ b/Eigen/src/Core/arch/AltiVec/PacketMath.h
@@ -39,10 +39,10 @@
 typedef __vector unsigned short int      Packet8us;
 typedef __vector int8_t                  Packet16c;
 typedef __vector uint8_t                 Packet16uc;
+typedef eigen_packet_wrapper<__vector unsigned short int,0> Packet8bf;
 
 // We don't want to write the same code all the time, but we need to reuse the constants
 // and it doesn't really work to declare them global, so we define macros instead
-
 #define _EIGEN_DECLARE_CONST_FAST_Packet4f(NAME,X) \
   Packet4f p4f_##NAME = {X, X, X, X}
 
@@ -96,6 +96,7 @@
 static Packet4i  p4i_COUNTDOWN  = { 0, 1, 2, 3 };
 static Packet8s  p8s_COUNTDOWN  = { 0, 1, 2, 3, 4, 5, 6, 7 };
 static Packet8us p8us_COUNTDOWN = { 0, 1, 2, 3, 4, 5, 6, 7 };
+
 static Packet16c  p16c_COUNTDOWN = { 0, 1, 2, 3, 4, 5, 6, 7,
                                     8, 9, 10, 11, 12, 13, 14, 15};
 static Packet16uc p16uc_COUNTDOWN = { 0, 1, 2, 3, 4, 5, 6, 7, 
@@ -108,6 +109,8 @@
 static Packet16uc p16uc_DUPLICATE32_HI = { 0,1,2,3, 0,1,2,3, 4,5,6,7, 4,5,6,7 };
 static Packet16uc p16uc_DUPLICATE16_HI = { 0,1,0,1, 2,3,2,3, 4,5,4,5, 6,7,6,7 };
 static Packet16uc p16uc_DUPLICATE8_HI = { 0,0, 1,1, 2,2, 3,3, 4,4, 5,5, 6,6, 7,7 };
+static const Packet16uc p16uc_DUPLICATE16_EVEN= { 0,1 ,0,1, 4,5, 4,5, 8,9, 8,9, 12,13, 12,13 };
+static const Packet16uc p16uc_DUPLICATE16_ODD = { 2,3 ,2,3, 6,7, 6,7, 10,11, 10,11, 14,15, 14,15 };
 
 static Packet16uc p16uc_QUADRUPLICATE16_HI = { 0,1,0,1,0,1,0,1, 2,3,2,3,2,3,2,3 };
 
@@ -190,6 +193,48 @@
   };
 };
 template <>
+struct packet_traits<bfloat16> : default_packet_traits {
+  typedef Packet8bf type;
+  typedef Packet8bf half;
+  enum {
+    Vectorizable = 1,
+    AlignedOnScalar = 1,
+    size = 8,
+    HasHalfPacket = 0,
+
+    HasAdd = 1,
+    HasSub = 1,
+    HasMul = 1,
+    HasDiv = 1,
+    HasMin = 1,
+    HasMax = 1,
+    HasAbs = 1,
+    HasSin = EIGEN_FAST_MATH,
+    HasCos = EIGEN_FAST_MATH,
+    HasLog = 1,
+    HasExp = 1,
+#ifdef __VSX__
+    HasSqrt = 1,
+#if !EIGEN_COMP_CLANG
+    HasRsqrt = 1,
+#else
+    HasRsqrt = 0,
+#endif
+#else
+    HasSqrt = 0,
+    HasRsqrt = 0,
+    HasTanh = EIGEN_FAST_MATH,
+    HasErf = EIGEN_FAST_MATH,
+#endif
+    HasRound = 1,
+    HasFloor = 1,
+    HasCeil = 1,
+    HasNegate = 1,
+    HasBlend = 1
+  };
+};
+
+template <>
 struct packet_traits<int> : default_packet_traits {
   typedef Packet4i type;
   typedef Packet4i half;
@@ -319,6 +364,12 @@
   enum {size=16, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false};
 };
 
+template<> struct unpacket_traits<Packet8bf>
+{
+  typedef bfloat16 type;
+  typedef Packet8bf          half;
+  enum {size=8, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false};
+};
 inline std::ostream & operator <<(std::ostream & s, const Packet16c & v)
 {
   union {
@@ -421,6 +472,11 @@
   return pload_common<Packet16uc>(from);
 }
 
+template<> EIGEN_STRONG_INLINE Packet8bf pload<Packet8bf>(const bfloat16*     from)
+{
+  return pload_common<Packet8us>(reinterpret_cast<const unsigned short int*>(from));
+}
+
 template <typename Packet>
 EIGEN_STRONG_INLINE void pstore_common(__UNPACK_TYPE__(Packet)* to, const Packet& from){
   // some versions of GCC throw "unused-but-set-parameter" (float *to).
@@ -431,7 +487,7 @@
   vec_xst(from, 0, to);
 #else
   vec_st(from, 0, to);
-#endif 
+#endif
 }
 
 template<> EIGEN_STRONG_INLINE void pstore<float>(float*   to, const Packet4f& from)
@@ -454,6 +510,11 @@
   pstore_common<Packet8us>(to, from);
 }
 
+template<> EIGEN_STRONG_INLINE void pstore<bfloat16>(bfloat16*       to, const Packet8bf& from)
+{
+  pstore_common<Packet8us>(reinterpret_cast<unsigned short int*>(to), from);
+}
+
 template<> EIGEN_STRONG_INLINE void pstore<int8_t>(int8_t*       to, const Packet16c& from)
 {
   pstore_common<Packet16c>(to, from);
@@ -513,6 +574,10 @@
   return reinterpret_cast<Packet4f>(pset1<Packet4i>(from));
 }
 
+template<> EIGEN_STRONG_INLINE Packet8bf pset1<Packet8bf>(const bfloat16&    from)   {
+  return pset1_size8<Packet8us>(reinterpret_cast<const unsigned short int&>(from));
+}
+
 template<typename Packet> EIGEN_STRONG_INLINE void
 pbroadcast4_common(const __UNPACK_TYPE__(Packet) *a,
                       Packet& a0, Packet& a1, Packet& a2, Packet& a3)
@@ -700,6 +765,7 @@
 
 template<> EIGEN_STRONG_INLINE Packet4f   padd<Packet4f>  (const Packet4f&   a, const Packet4f&   b) { return a + b; }
 template<> EIGEN_STRONG_INLINE Packet4i   padd<Packet4i>  (const Packet4i&   a, const Packet4i&   b) { return a + b; }
+template<> EIGEN_STRONG_INLINE Packet4ui   padd<Packet4ui>  (const Packet4ui&   a, const Packet4ui&   b) { return a + b; }
 template<> EIGEN_STRONG_INLINE Packet8s   padd<Packet8s>  (const Packet8s&   a, const Packet8s&   b) { return a + b; }
 template<> EIGEN_STRONG_INLINE Packet8us  padd<Packet8us> (const Packet8us&  a, const Packet8us&  b) { return a + b; }
 template<> EIGEN_STRONG_INLINE Packet16c  padd<Packet16c> (const Packet16c&  a, const Packet16c&  b) { return a + b; }
@@ -721,6 +787,7 @@
 template<> EIGEN_STRONG_INLINE Packet16c  pmul<Packet16c> (const Packet16c&  a, const Packet16c&  b) { return vec_mul(a,b); }
 template<> EIGEN_STRONG_INLINE Packet16uc pmul<Packet16uc>(const Packet16uc& a, const Packet16uc& b) { return vec_mul(a,b); }
 
+
 template<> EIGEN_STRONG_INLINE Packet4f pdiv<Packet4f>(const Packet4f& a, const Packet4f& b)
 {
 #ifndef __VSX__  // VSX actually provides a div instruction
@@ -765,6 +832,7 @@
 template<> EIGEN_STRONG_INLINE Packet16c pmin<Packet16c>(const Packet16c& a, const Packet16c& b) { return vec_min(a, b); }
 template<> EIGEN_STRONG_INLINE Packet16uc pmin<Packet16uc>(const Packet16uc& a, const Packet16uc& b) { return vec_min(a, b); }
 
+
 template<> EIGEN_STRONG_INLINE Packet4f pmax<Packet4f>(const Packet4f& a, const Packet4f& b)
 {
   #ifdef __VSX__
@@ -785,6 +853,7 @@
 template<> EIGEN_STRONG_INLINE Packet4f pcmp_le(const Packet4f& a, const Packet4f& b) { return reinterpret_cast<Packet4f>(vec_cmple(a,b)); }
 template<> EIGEN_STRONG_INLINE Packet4f pcmp_lt(const Packet4f& a, const Packet4f& b) { return reinterpret_cast<Packet4f>(vec_cmplt(a,b)); }
 template<> EIGEN_STRONG_INLINE Packet4f pcmp_eq(const Packet4f& a, const Packet4f& b) { return reinterpret_cast<Packet4f>(vec_cmpeq(a,b)); }
+
 template<> EIGEN_STRONG_INLINE Packet4f pcmp_lt_or_nan(const Packet4f& a, const Packet4f& b) {
   Packet4f c = reinterpret_cast<Packet4f>(vec_cmpge(a,b));
   return vec_nor(c,c);
@@ -793,12 +862,26 @@
 
 template<> EIGEN_STRONG_INLINE Packet4f pand<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_and(a, b); }
 template<> EIGEN_STRONG_INLINE Packet4i pand<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_and(a, b); }
+template<> EIGEN_STRONG_INLINE Packet4ui pand<Packet4ui>(const Packet4ui& a, const Packet4ui& b) { return vec_and(a, b); }
+template<> EIGEN_STRONG_INLINE Packet8us pand<Packet8us>(const Packet8us& a, const Packet8us& b) { return vec_and(a, b); }
+template<> EIGEN_STRONG_INLINE Packet8bf pand<Packet8bf>(const Packet8bf& a, const Packet8bf& b) {
+  return pand<Packet8us>(a, b);
+}
+
 
 template<> EIGEN_STRONG_INLINE Packet4f por<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_or(a, b); }
 template<> EIGEN_STRONG_INLINE Packet4i por<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_or(a, b); }
+template<> EIGEN_STRONG_INLINE Packet8s por<Packet8s>(const Packet8s& a, const Packet8s& b) { return vec_or(a, b); }
+template<> EIGEN_STRONG_INLINE Packet8us por<Packet8us>(const Packet8us& a, const Packet8us& b) { return vec_or(a, b); }
+template<> EIGEN_STRONG_INLINE Packet8bf por<Packet8bf>(const Packet8bf& a, const Packet8bf& b) {
+  return por<Packet8us>(a, b);
+}
 
 template<> EIGEN_STRONG_INLINE Packet4f pxor<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_xor(a, b); }
 template<> EIGEN_STRONG_INLINE Packet4i pxor<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_xor(a, b); }
+template<> EIGEN_STRONG_INLINE Packet8bf pxor<Packet8bf>(const Packet8bf& a, const Packet8bf& b) { 
+  return pxor<Packet8us>(a, b);
+}
 
 template<> EIGEN_STRONG_INLINE Packet4f pandnot<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_and(a, vec_nor(b, b)); }
 template<> EIGEN_STRONG_INLINE Packet4i pandnot<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_and(a, vec_nor(b, b)); }
@@ -806,6 +889,7 @@
 template<> EIGEN_STRONG_INLINE Packet4f pselect(const Packet4f& mask, const Packet4f& a, const Packet4f& b) {
   return vec_sel(b, a, reinterpret_cast<Packet4ui>(mask));
 }
+
 template<> EIGEN_STRONG_INLINE Packet4f pround<Packet4f>(const Packet4f& a) {
     Packet4f t = vec_add(reinterpret_cast<Packet4f>(vec_or(vec_and(reinterpret_cast<Packet4ui>(a), p4ui_SIGN), p4ui_PREV0DOT5)), a);
     Packet4f res;
@@ -852,6 +936,10 @@
 {
   return ploadu_common<Packet8us>(from);
 }
+template<> EIGEN_STRONG_INLINE Packet8bf ploadu<Packet8bf>(const bfloat16* from)
+{
+  return ploadu_common<Packet8us>(reinterpret_cast<const unsigned short int*>(from));
+}
 template<> EIGEN_STRONG_INLINE Packet16c ploadu<Packet16c>(const int8_t* from)
 {
   return ploadu_common<Packet16c>(from);
@@ -909,6 +997,11 @@
   return vec_perm(p, p, p16uc_QUADRUPLICATE16_HI);
 }
 
+template<> EIGEN_STRONG_INLINE Packet8bf ploadquad<Packet8bf>(const bfloat16*     from)
+{
+  return ploadquad<Packet8us>(reinterpret_cast<const unsigned short int*>(from));
+}
+
 template<> EIGEN_STRONG_INLINE Packet16c ploaddup<Packet16c>(const int8_t*     from)
 {
   Packet16c p;
@@ -962,6 +1055,10 @@
 {
   pstoreu_common<Packet8us>(to, from);
 }
+template<> EIGEN_STRONG_INLINE void pstoreu<bfloat16>(bfloat16*      to, const Packet8bf& from)
+{
+  pstoreu_common<Packet8us>(reinterpret_cast<unsigned short int*>(to), from);
+}
 template<> EIGEN_STRONG_INLINE void pstoreu<int8_t>(int8_t*      to, const Packet16c& from)
 {
   pstoreu_common<Packet16c>(to, from);
@@ -977,17 +1074,17 @@
 template<> EIGEN_STRONG_INLINE float  pfirst<Packet4f>(const Packet4f& a) { EIGEN_ALIGN16 float x; vec_ste(a, 0, &x); return x; }
 template<> EIGEN_STRONG_INLINE int    pfirst<Packet4i>(const Packet4i& a) { EIGEN_ALIGN16 int   x; vec_ste(a, 0, &x); return x; }
 
-template<typename Packet> EIGEN_STRONG_INLINE __UNPACK_TYPE__(Packet) pfirst_common(const Packet& a) { 
+template<typename Packet> EIGEN_STRONG_INLINE __UNPACK_TYPE__(Packet) pfirst_common(const Packet& a) {
   EIGEN_ALIGN16 __UNPACK_TYPE__(Packet) x;
   vec_ste(a, 0, &x);
   return x;
 }
 
-template<> EIGEN_STRONG_INLINE short int pfirst<Packet8s>(const Packet8s& a) { 
+template<> EIGEN_STRONG_INLINE short int pfirst<Packet8s>(const Packet8s& a) {
   return pfirst_common<Packet8s>(a);
 }
 
-template<> EIGEN_STRONG_INLINE unsigned short int pfirst<Packet8us>(const Packet8us& a) { 
+template<> EIGEN_STRONG_INLINE unsigned short int pfirst<Packet8us>(const Packet8us& a) {
   return pfirst_common<Packet8us>(a);
 }
 
@@ -1025,6 +1122,10 @@
 {
   return vec_perm(a, a, p16uc_REVERSE8);
 }
+template<> EIGEN_STRONG_INLINE Packet8bf preverse(const Packet8bf& a)
+{
+  return preverse<Packet8us>(a);
+}
 
 template<> EIGEN_STRONG_INLINE Packet4f pabs(const Packet4f& a) { return vec_abs(a); }
 template<> EIGEN_STRONG_INLINE Packet4i pabs(const Packet4i& a) { return vec_abs(a); }
@@ -1032,6 +1133,10 @@
 template<> EIGEN_STRONG_INLINE Packet8us pabs(const Packet8us& a) { return a; }
 template<> EIGEN_STRONG_INLINE Packet16c pabs(const Packet16c& a) { return vec_abs(a); }
 template<> EIGEN_STRONG_INLINE Packet16uc pabs(const Packet16uc& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet8bf  pabs(const Packet8bf& a) {
+  _EIGEN_DECLARE_CONST_FAST_Packet8us(abs_mask,0x7FFF);
+  return pand<Packet8us>(p8us_abs_mask, a);
+}
 
 template<int N> EIGEN_STRONG_INLINE Packet4i parithmetic_shift_right(Packet4i a)
 { return vec_sra(a,reinterpret_cast<Packet4ui>(pset1<Packet4i>(N))); }
@@ -1039,6 +1144,175 @@
 { return vec_sr(a,reinterpret_cast<Packet4ui>(pset1<Packet4i>(N))); }
 template<int N> EIGEN_STRONG_INLINE Packet4i plogical_shift_left(Packet4i a)
 { return vec_sl(a,reinterpret_cast<Packet4ui>(pset1<Packet4i>(N))); }
+template<int N> EIGEN_STRONG_INLINE Packet4f plogical_shift_left(Packet4f a)
+{
+  const _EIGEN_DECLARE_CONST_FAST_Packet4ui(mask, N);
+  Packet4ui r = vec_sl(reinterpret_cast<Packet4ui>(a), p4ui_mask);
+  return reinterpret_cast<Packet4f>(r);
+}
+
+template<int N> EIGEN_STRONG_INLINE Packet4f plogical_shift_right(Packet4f a)
+{
+  const _EIGEN_DECLARE_CONST_FAST_Packet4ui(mask, N);
+  Packet4ui r = vec_sr(reinterpret_cast<Packet4ui>(a), p4ui_mask);
+  return reinterpret_cast<Packet4f>(r);
+}
+
+template<int N> EIGEN_STRONG_INLINE Packet4ui plogical_shift_right(Packet4ui a)
+{
+  const _EIGEN_DECLARE_CONST_FAST_Packet4ui(mask, N);
+  return vec_sr(a, p4ui_mask);
+}
+
+template<int N> EIGEN_STRONG_INLINE Packet4ui plogical_shift_left(Packet4ui a)
+{
+  const _EIGEN_DECLARE_CONST_FAST_Packet4ui(mask, N);
+  return vec_sl(a, p4ui_mask);
+}
+
+template<int N> EIGEN_STRONG_INLINE Packet8us plogical_shift_left(Packet8us a)
+{
+  const _EIGEN_DECLARE_CONST_FAST_Packet8us(mask, N);
+  return vec_sl(a, p8us_mask);
+}
+
+EIGEN_STRONG_INLINE Packet4f Bf16ToF32Even(const Packet8bf& bf){
+  return plogical_shift_left<16>(reinterpret_cast<Packet4f>(bf.m_val));
+}
+
+EIGEN_STRONG_INLINE Packet4f Bf16ToF32Odd(const Packet8bf& bf){
+  const _EIGEN_DECLARE_CONST_FAST_Packet4ui(high_mask, 0xFFFF0000);
+  return pand<Packet4f>(
+    reinterpret_cast<Packet4f>(bf.m_val),
+    reinterpret_cast<Packet4f>(p4ui_high_mask)
+  );
+}
+
+EIGEN_STRONG_INLINE Packet8bf F32ToBf16(Packet4f p4f){
+  Packet4ui input = reinterpret_cast<Packet4ui>(p4f);
+  Packet4ui lsb = plogical_shift_right<16>(input);
+  lsb = pand<Packet4ui>(lsb, reinterpret_cast<Packet4ui>(p4i_ONE));
+
+  _EIGEN_DECLARE_CONST_FAST_Packet4ui(BIAS,0x7FFFu);
+  Packet4ui rounding_bias = padd<Packet4ui>(lsb, p4ui_BIAS);
+  input = padd<Packet4ui>(input, rounding_bias);
+
+  //Test NaN and Subnormal - Begin
+  const _EIGEN_DECLARE_CONST_FAST_Packet4ui(exp_mask, 0x7F800000);
+  Packet4ui exp = pand<Packet4ui>(p4ui_exp_mask, reinterpret_cast<Packet4ui>(p4f));
+
+  const _EIGEN_DECLARE_CONST_FAST_Packet4ui(mantissa_mask, 0x7FFFFF);
+  Packet4ui mantissa = pand<Packet4ui>(p4ui_mantissa_mask, reinterpret_cast<Packet4ui>(p4f));
+
+  const _EIGEN_DECLARE_CONST_FAST_Packet4ui(max_exp, 0x7F800000);
+  Packet4bi is_max_exp = vec_cmpeq(exp, p4ui_max_exp);
+  Packet4bi is_zero_exp = vec_cmpeq(exp, reinterpret_cast<Packet4ui>(p4i_ZERO));
+
+  Packet4bi is_mant_not_zero = vec_cmpne(mantissa, reinterpret_cast<Packet4ui>(p4i_ZERO));
+  Packet4ui nan_selector = pand<Packet4ui>(
+      reinterpret_cast<Packet4ui>(is_max_exp),
+      reinterpret_cast<Packet4ui>(is_mant_not_zero)
+  );
+
+  Packet4ui subnormal_selector = pand<Packet4ui>(
+      reinterpret_cast<Packet4ui>(is_zero_exp),
+      reinterpret_cast<Packet4ui>(is_mant_not_zero)
+  );
+
+  const _EIGEN_DECLARE_CONST_FAST_Packet4ui(nan, 0x7FC00000);
+  input = vec_sel(input, p4ui_nan, nan_selector);
+  input = vec_sel(input, reinterpret_cast<Packet4ui>(p4f), subnormal_selector);
+  //Test NaN and Subnormal - End
+
+  input = plogical_shift_right<16>(input);
+  return reinterpret_cast<Packet8us>(input);
+}
+
+EIGEN_STRONG_INLINE Packet8bf F32ToBf16(Packet4f even, Packet4f odd){
+  Packet4f bf_odd, bf_even;
+  bf_odd = reinterpret_cast<Packet4f>(F32ToBf16(odd).m_val);
+  bf_odd = plogical_shift_left<16>(bf_odd);
+  bf_even = reinterpret_cast<Packet4f>(F32ToBf16(even).m_val);
+  return reinterpret_cast<Packet8us>(por<Packet4f>(bf_even, bf_odd));
+}
+#define BF16_TO_F32_UNARY_OP_WRAPPER(OP, A) \
+  Packet4f a_even = Bf16ToF32Even(A);\
+  Packet4f a_odd = Bf16ToF32Odd(A);\
+  Packet4f op_even = OP(a_even);\
+  Packet4f op_odd = OP(a_odd);\
+  return F32ToBf16(op_even, op_odd);\
+
+#define BF16_TO_F32_BINARY_OP_WRAPPER(OP, A, B) \
+  Packet4f a_even = Bf16ToF32Even(A);\
+  Packet4f a_odd = Bf16ToF32Odd(A);\
+  Packet4f b_even = Bf16ToF32Even(B);\
+  Packet4f b_odd = Bf16ToF32Odd(B);\
+  Packet4f op_even = OP(a_even, b_even);\
+  Packet4f op_odd = OP(a_odd, b_odd);\
+  return F32ToBf16(op_even, op_odd);\
+
+template<> EIGEN_STRONG_INLINE Packet8bf padd<Packet8bf>(const Packet8bf& a, const Packet8bf& b) {
+  BF16_TO_F32_BINARY_OP_WRAPPER(padd<Packet4f>, a, b);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf pmul<Packet8bf>(const Packet8bf& a, const Packet8bf& b) {
+  BF16_TO_F32_BINARY_OP_WRAPPER(pmul<Packet4f>, a, b);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf pdiv<Packet8bf>(const Packet8bf& a, const Packet8bf& b) {
+  BF16_TO_F32_BINARY_OP_WRAPPER(pdiv<Packet4f>, a, b);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf pnegate<Packet8bf>(const Packet8bf& a) {
+  BF16_TO_F32_UNARY_OP_WRAPPER(pnegate<Packet4f>, a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf psub<Packet8bf>(const Packet8bf& a, const Packet8bf& b) {
+  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 pmadd(const Packet8bf& a, const Packet8bf& b, const Packet8bf& c) {
+  Packet4f a_even = Bf16ToF32Even(a);
+  Packet4f a_odd = Bf16ToF32Odd(a);
+  Packet4f b_even = Bf16ToF32Even(b);
+  Packet4f b_odd = Bf16ToF32Odd(b);
+  Packet4f c_even = Bf16ToF32Even(c);
+  Packet4f c_odd = Bf16ToF32Odd(c);
+  Packet4f pmadd_even = pmadd<Packet4f>(a_even, b_even, c_even);
+  Packet4f pmadd_odd = pmadd<Packet4f>(a_odd, b_odd, c_odd);
+  return F32ToBf16(pmadd_even, pmadd_odd);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf pmin<Packet8bf>(const Packet8bf& a, const Packet8bf& b) {
+  BF16_TO_F32_BINARY_OP_WRAPPER(pmin<Packet4f>, a, b);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf pmax<Packet8bf>(const Packet8bf& a, const Packet8bf& b) {
+  BF16_TO_F32_BINARY_OP_WRAPPER(pmax<Packet4f>, a, b);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf pcmp_lt(const Packet8bf& a, const Packet8bf& b) {
+  BF16_TO_F32_BINARY_OP_WRAPPER(pcmp_lt<Packet4f>, a, b);
+}
+template<> EIGEN_STRONG_INLINE Packet8bf pcmp_le(const Packet8bf& a, const Packet8bf& b) {
+  BF16_TO_F32_BINARY_OP_WRAPPER(pcmp_le<Packet4f>, a, b);
+}
+template<> EIGEN_STRONG_INLINE Packet8bf pcmp_eq(const Packet8bf& a, const Packet8bf& b) {
+  BF16_TO_F32_BINARY_OP_WRAPPER(pcmp_eq<Packet4f>, a, b);
+}
+
+template<> EIGEN_STRONG_INLINE bfloat16 pfirst(const Packet8bf& a) {
+  return Eigen::bfloat16_impl::raw_uint16_to_bfloat16((pfirst<Packet8us>(a)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf ploaddup<Packet8bf>(const  bfloat16*     from)
+{
+  return ploaddup<Packet8us>(reinterpret_cast<const unsigned short int*>(from));
+}
 
 template<> EIGEN_STRONG_INLINE Packet4f pfrexp<Packet4f>(const Packet4f& a, Packet4f& exponent) {
   return pfrexp_float(a,exponent);
@@ -1070,6 +1344,13 @@
   return pfirst(sum);
 }
 
+template<> EIGEN_STRONG_INLINE bfloat16 predux<Packet8bf>(const Packet8bf& a)
+{
+  float redux_even = predux<Packet4f>(Bf16ToF32Even(a));
+  float redux_odd  = predux<Packet4f>(Bf16ToF32Odd(a));
+  float f32_result = redux_even + redux_odd;
+  return bfloat16(f32_result);
+}
 template<typename Packet> EIGEN_STRONG_INLINE __UNPACK_TYPE__(Packet) predux_size8(const Packet& a)
 {
   union{
@@ -1166,6 +1447,15 @@
   return pfirst(octo);
 }
 
+template<> EIGEN_STRONG_INLINE bfloat16 predux_mul<Packet8bf>(const Packet8bf& a)
+{
+  float redux_even = predux_mul<Packet4f>(Bf16ToF32Even(a));
+  float redux_odd  = predux_mul<Packet4f>(Bf16ToF32Odd(a));
+  float f32_result = redux_even * redux_odd;
+  return bfloat16(f32_result);
+}
+
+
 template<> EIGEN_STRONG_INLINE int8_t predux_mul<Packet16c>(const Packet16c& a)
 {
   Packet16c pair, quad, octo, result;
@@ -1211,6 +1501,14 @@
   return predux_min4<Packet4i>(a);
 }
 
+template<> EIGEN_STRONG_INLINE bfloat16 predux_min<Packet8bf>(const Packet8bf& a)
+{
+  float redux_even = predux_min<Packet4f>(Bf16ToF32Even(a));
+  float redux_odd  = predux_min<Packet4f>(Bf16ToF32Odd(a));
+  float f32_result = (std::min)(redux_even, redux_odd);
+  return bfloat16(f32_result);
+}
+
 template<> EIGEN_STRONG_INLINE short int predux_min<Packet8s>(const Packet8s& a)
 {
   Packet8s pair, quad, octo;
@@ -1283,6 +1581,14 @@
   return predux_max4<Packet4i>(a);
 }
 
+template<> EIGEN_STRONG_INLINE bfloat16 predux_max<Packet8bf>(const Packet8bf& a)
+{
+  float redux_even = predux_max<Packet4f>(Bf16ToF32Even(a));
+  float redux_odd  = predux_max<Packet4f>(Bf16ToF32Odd(a));
+  float f32_result = (std::max)(redux_even, redux_odd);
+  return bfloat16(f32_result);
+}
+
 template<> EIGEN_STRONG_INLINE short int predux_max<Packet8s>(const Packet8s& a)
 {
   Packet8s pair, quad, octo;
@@ -1391,6 +1697,21 @@
   kernel.packet[3] = vec_mergel(t1, t3);
 }
 
+
+EIGEN_DEVICE_FUNC inline void
+ptranspose(PacketBlock<Packet8bf,4>& kernel) {
+  Packet8us t0, t1, t2, t3;
+
+  t0 = vec_mergeh(kernel.packet[0].m_val, kernel.packet[2].m_val);
+  t1 = vec_mergel(kernel.packet[0].m_val, kernel.packet[2].m_val);
+  t2 = vec_mergeh(kernel.packet[1].m_val, kernel.packet[3].m_val);
+  t3 = vec_mergel(kernel.packet[1].m_val, kernel.packet[3].m_val);
+  kernel.packet[0] = vec_mergeh(t0, t2);
+  kernel.packet[1] = vec_mergel(t0, t2);
+  kernel.packet[2] = vec_mergeh(t1, t3);
+  kernel.packet[3] = vec_mergel(t1, t3);
+}
+
 EIGEN_DEVICE_FUNC inline void
 ptranspose(PacketBlock<Packet16c,4>& kernel) {
   Packet16c t0, t1, t2, t3;
@@ -1481,6 +1802,37 @@
 }
 
 EIGEN_DEVICE_FUNC inline void
+ptranspose(PacketBlock<Packet8bf,8>& kernel) {
+  Packet8bf v[8], sum[8];
+
+  v[0] = vec_mergeh(kernel.packet[0].m_val, kernel.packet[4].m_val);
+  v[1] = vec_mergel(kernel.packet[0].m_val, kernel.packet[4].m_val);
+  v[2] = vec_mergeh(kernel.packet[1].m_val, kernel.packet[5].m_val);
+  v[3] = vec_mergel(kernel.packet[1].m_val, kernel.packet[5].m_val);
+  v[4] = vec_mergeh(kernel.packet[2].m_val, kernel.packet[6].m_val);
+  v[5] = vec_mergel(kernel.packet[2].m_val, kernel.packet[6].m_val);
+  v[6] = vec_mergeh(kernel.packet[3].m_val, kernel.packet[7].m_val);
+  v[7] = vec_mergel(kernel.packet[3].m_val, kernel.packet[7].m_val);
+  sum[0] = vec_mergeh(v[0].m_val, v[4].m_val);
+  sum[1] = vec_mergel(v[0].m_val, v[4].m_val);
+  sum[2] = vec_mergeh(v[1].m_val, v[5].m_val);
+  sum[3] = vec_mergel(v[1].m_val, v[5].m_val);
+  sum[4] = vec_mergeh(v[2].m_val, v[6].m_val);
+  sum[5] = vec_mergel(v[2].m_val, v[6].m_val);
+  sum[6] = vec_mergeh(v[3].m_val, v[7].m_val);
+  sum[7] = vec_mergel(v[3].m_val, v[7].m_val);
+
+  kernel.packet[0] = vec_mergeh(sum[0].m_val, sum[4].m_val);
+  kernel.packet[1] = vec_mergel(sum[0].m_val, sum[4].m_val);
+  kernel.packet[2] = vec_mergeh(sum[1].m_val, sum[5].m_val);
+  kernel.packet[3] = vec_mergel(sum[1].m_val, sum[5].m_val);
+  kernel.packet[4] = vec_mergeh(sum[2].m_val, sum[6].m_val);
+  kernel.packet[5] = vec_mergel(sum[2].m_val, sum[6].m_val);
+  kernel.packet[6] = vec_mergeh(sum[3].m_val, sum[7].m_val);
+  kernel.packet[7] = vec_mergel(sum[3].m_val, sum[7].m_val);
+}
+
+EIGEN_DEVICE_FUNC inline void
 ptranspose(PacketBlock<Packet16c,16>& kernel) {
   Packet16c step1[16], step2[16], step3[16];
 
@@ -1656,6 +2008,10 @@
   return vec_sel(elsePacket, thenPacket, mask);
 }
 
+template<> EIGEN_STRONG_INLINE Packet8bf pblend(const Selector<8>& ifPacket, const Packet8bf& thenPacket, const Packet8bf& elsePacket) {
+  return pblend<Packet8us>(ifPacket, thenPacket, elsePacket);
+}
+
 template<> EIGEN_STRONG_INLINE Packet16c pblend(const Selector<16>& ifPacket, const Packet16c& thenPacket, const Packet16c& elsePacket) {
   Packet16uc select = { ifPacket.select[0], ifPacket.select[1], ifPacket.select[2], ifPacket.select[3],
                        ifPacket.select[4], ifPacket.select[5], ifPacket.select[6], ifPacket.select[7],
@@ -1694,15 +2050,78 @@
   };
 };
 
+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);
+  }
+
+  low_odd = plogical_shift_left<16>(low_odd);
+
+  Packet4ui int_final = por<Packet4ui>(low_even, low_odd);
+  return reinterpret_cast<Packet8us>(int_final);
+}
+
+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);
 }
@@ -2024,6 +2443,8 @@
   Packet2bl mask = reinterpret_cast<Packet2bl>( vec_cmpeq(reinterpret_cast<Packet2d>(select), reinterpret_cast<Packet2d>(p2l_ONE)) );
   return vec_sel(elsePacket, thenPacket, mask);
 }
+
+
 #endif // __VSX__
 } // end namespace internal
 
diff --git a/test/packetmath.cpp b/test/packetmath.cpp
index 0fe2910..c8ea313 100644
--- a/test/packetmath.cpp
+++ b/test/packetmath.cpp
@@ -247,6 +247,20 @@
     data1[i + PacketSize] = internal::random<bool>() ? data1[i] : Scalar(0);
   }
   CHECK_CWISE2_IF(true, internal::pcmp_eq, internal::pcmp_eq);
+
+  //Test (-0) == (0) for signed operations
+  for (int i = 0; i < PacketSize; ++i) {
+    data1[i] = Scalar(-0.0);
+    data1[i + PacketSize] = internal::random<bool>() ? data1[i] : Scalar(0);
+  }
+  CHECK_CWISE2_IF(true, internal::pcmp_eq, internal::pcmp_eq);
+
+  //Test NaN
+  for (int i = 0; i < PacketSize; ++i) {
+    data1[i] = std::numeric_limits<Scalar>::quiet_NaN();
+    data1[i + PacketSize] = internal::random<bool>() ? data1[i] : Scalar(0);
+  }
+  CHECK_CWISE2_IF(true, internal::pcmp_eq, internal::pcmp_eq);
 }
 
 // Packet16b representing bool does not support ptrue, pandnot or pcmp_eq, since the scalar path
@@ -255,6 +269,22 @@
 void packetmath_boolean_mask_ops<bool, internal::packet_traits<bool>::type>() {}
 
 template <typename Scalar, typename Packet>
+void packetmath_minus_zero_add() {
+  const int PacketSize = internal::unpacket_traits<Packet>::size;
+  const int size = 2 * PacketSize;
+  EIGEN_ALIGN_MAX Scalar data1[size];
+  EIGEN_ALIGN_MAX Scalar data2[size];
+  EIGEN_ALIGN_MAX Scalar ref[size];
+
+  for (int i = 0; i < PacketSize; ++i) {
+    data1[i] = Scalar(-0.0);
+    data1[i + PacketSize] = Scalar(-0.0);
+  }
+  CHECK_CWISE2_IF(internal::packet_traits<Scalar>::HasAdd, REF_ADD, internal::padd);
+}
+
+
+template <typename Scalar, typename Packet>
 void packetmath() {
   typedef internal::packet_traits<Scalar> PacketTraits;
   const int PacketSize = internal::unpacket_traits<Packet>::size;
@@ -454,6 +484,7 @@
 
   packetmath_boolean_mask_ops<Scalar, Packet>();
   packetmath_pcast_ops_runner<Scalar, Packet>::run();
+  packetmath_minus_zero_add<Scalar, Packet>();
 }
 
 template <typename Scalar, typename Packet>