remove duplicate pset1 for half and add some comments about why we need expose pmul/add/div/min/max on host

2 files changed, 849 insertions, 79 deletions

diff --git a/Eigen/src/Core/arch/GPU/PacketMath.h b/Eigen/src/Core/arch/GPU/PacketMath.h
index 9e18c5145..1f6a562c5 100644
--- a/Eigen/src/Core/arch/GPU/PacketMath.h
+++ b/Eigen/src/Core/arch/GPU/PacketMath.h
@@ -476,24 +476,29 @@ ptranspose(PacketBlock<double2,2>& kernel) {
   kernel.packet[1].x = tmp;
 }
 
-#endif
+#endif // defined(EIGEN_GPUCC) && defined(EIGEN_USE_GPU)
 
-// Packet math for Eigen::half
-// Most of the following operations require arch >= 3.0
-#if (defined(EIGEN_HAS_CUDA_FP16) && defined(EIGEN_CUDACC) && defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 300) || \
+// Packet4h2 must be defined in the macro without EIGEN_CUDA_ARCH, meaning
+// its corresponding packet_traits<Eigen::half> must be visible on host.
+#if (defined(EIGEN_HAS_CUDA_FP16) && defined(EIGEN_CUDACC)) || \
   (defined(EIGEN_HAS_HIP_FP16) && defined(EIGEN_HIPCC) && defined(EIGEN_HIP_DEVICE_COMPILE)) || \
   (defined(EIGEN_HAS_CUDA_FP16) && defined(__clang__) && defined(__CUDA__))
 
+typedef ulonglong2 Packet4h2;
+template<> struct unpacket_traits<Packet4h2> { typedef Eigen::half type; enum {size=8, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false}; typedef Packet4h2 half; };
+template<> struct is_arithmetic<Packet4h2> { enum { value = true }; };
+
+template<> struct unpacket_traits<half2> { typedef Eigen::half type; enum {size=2, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false}; typedef half2 half; };
 template<> struct is_arithmetic<half2> { enum { value = true }; };
 
 template<> struct packet_traits<Eigen::half> : default_packet_traits
 {
-  typedef half2 type;
-  typedef half2 half;
+  typedef Packet4h2 type;
+  typedef Packet4h2 half;
   enum {
     Vectorizable = 1,
     AlignedOnScalar = 1,
-    size=2,
+    size=8,
     HasHalfPacket = 0,
     HasAdd    = 1,
     HasSub    = 1,
@@ -508,9 +513,8 @@ template<> struct packet_traits<Eigen::half> : default_packet_traits
   };
 };
 
-template<> struct unpacket_traits<half2> { typedef Eigen::half type; enum {size=2, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false}; typedef half2 half; };
-
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pset1<half2>(const Eigen::half& from) {
+template<>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pset1<half2>(const Eigen::half& from) {
 #if !defined(EIGEN_CUDA_ARCH) && !defined(EIGEN_HIP_DEVICE_COMPILE)
   half2 r;
   r.x = from;
@@ -521,23 +525,40 @@ template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pset1<half2>(const Eigen:
 #endif
 }
 
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pload<half2>(const Eigen::half* from) {
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2
+pset1<Packet4h2>(const Eigen::half& from) {
+  Packet4h2 r;
+  half2* p_alias = reinterpret_cast<half2*>(&r);
+  p_alias[0] = pset1<half2>(from);
+  p_alias[1] = pset1<half2>(from);
+  p_alias[2] = pset1<half2>(from);
+  p_alias[3] = pset1<half2>(from);
+  return r;
+}
+
+#if defined(EIGEN_CUDA_ARCH) || defined(EIGEN_HIP_DEVICE_COMPILE) || (defined(EIGEN_CUDACC) && EIGEN_COMP_CLANG && !EIGEN_COMP_NVCC)
+namespace {
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pload(const Eigen::half* from) {
   return *reinterpret_cast<const half2*>(from);
 }
 
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 ploadu<half2>(const Eigen::half* from) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 ploadu(const Eigen::half* from) {
   return __halves2half2(from[0], from[1]);
 }
 
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 ploaddup<half2>(const Eigen::half*  from) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 ploaddup(const Eigen::half*  from) {
   return __halves2half2(from[0], from[0]);
 }
 
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pstore<Eigen::half>(Eigen::half* to, const half2& from) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pstore(Eigen::half* to,
+                                                  const half2& from) {
   *reinterpret_cast<half2*>(to) = from;
 }
 
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pstoreu<Eigen::half>(Eigen::half* to, const half2& from) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pstoreu(Eigen::half* to,
+                                                   const half2& from) {
 #if !defined(EIGEN_CUDA_ARCH) && !defined(EIGEN_HIP_DEVICE_COMPILE)
   to[0] = from.x;
   to[1] = from.y;
@@ -547,8 +568,9 @@ template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pstoreu<Eigen::half>(Eigen
 #endif
 }
 
-template<>
- EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE half2 ploadt_ro<half2, Aligned>(const Eigen::half* from) {
+
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE half2 ploadt_ro_aligned(
+    const Eigen::half* from) {
 
 #if defined(EIGEN_HIP_DEVICE_COMPILE)
 
@@ -565,8 +587,8 @@ template<>
 #endif
 }
 
-template<>
-EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE half2 ploadt_ro<half2, Unaligned>(const Eigen::half* from) {
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE half2 ploadt_ro_unaligned(
+    const Eigen::half* from) {
 
 #if defined(EIGEN_HIP_DEVICE_COMPILE)
 
@@ -583,20 +605,22 @@ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE half2 ploadt_ro<half2, Unaligned>(const Ei
 #endif
 }
 
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pgather<Eigen::half, half2>(const Eigen::half* from, Index stride) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pgather(const Eigen::half* from,
+                                                    Index stride) {
   return __halves2half2(from[0*stride], from[1*stride]);
 }
 
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<Eigen::half, half2>(Eigen::half* to, const half2& from, Index stride) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter(
+    Eigen::half* to, const half2& from, Index stride) {
   to[stride*0] = __low2half(from);
   to[stride*1] = __high2half(from);
 }
 
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half pfirst<half2>(const half2& a) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half pfirst(const half2& a) {
   return __low2half(a);
 }
 
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pabs<half2>(const half2& a) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pabs(const half2& a) {
   half a1 = __low2half(a);
   half a2 = __high2half(a);
   half result1 = half_impl::raw_uint16_to_half(a1.x & 0x7FFF);
@@ -604,12 +628,12 @@ template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pabs<half2>(const half2&
   return __halves2half2(result1, result2);
 }
 
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 ptrue<half2>(const half2& a) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 ptrue(const half2& a) {
   half true_half = half_impl::raw_uint16_to_half(0xffffu);
   return pset1<half2>(true_half);
 }
 
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pzero<half2>(const half2& a) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pzero(const half2& a) {
   half false_half = half_impl::raw_uint16_to_half(0x0000u);
   return pset1<half2>(false_half);
 }
@@ -624,7 +648,7 @@ ptranspose(PacketBlock<half2,2>& kernel) {
   kernel.packet[1] = __halves2half2(a2, b2);
 }
 
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 plset<half2>(const Eigen::half& a) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 plset(const Eigen::half& a) {
 #if defined(EIGEN_HIP_DEVICE_COMPILE)
 
   return __halves2half2(a, __hadd(a, __float2half(1.0f)));
@@ -641,10 +665,9 @@ template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 plset<half2>(const Eigen:
 #endif
 }
 
-template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pselect<half2>(const half2& mask,
-                                                           const half2& a,
-                                                           const half2& b) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pselect(const half2& mask,
+                                                    const half2& a,
+                                                    const half2& b) {
   half mask_low = __low2half(mask);
   half mask_high = __high2half(mask);
   half result_low = mask_low == half(0) ? __low2half(b) : __low2half(a);
@@ -652,9 +675,8 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pselect<half2>(const half2& mask,
   return __halves2half2(result_low, result_high);
 }
 
-template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pcmp_eq<half2>(const half2& a,
-                                                           const half2& b) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pcmp_eq(const half2& a,
+                                                    const half2& b) {
   half true_half = half_impl::raw_uint16_to_half(0xffffu);
   half false_half = half_impl::raw_uint16_to_half(0x0000u);
   half a1 = __low2half(a);
@@ -666,9 +688,8 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pcmp_eq<half2>(const half2& a,
   return __halves2half2(eq1, eq2);
 }
 
-template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pcmp_lt<half2>(const half2& a,
-                                                           const half2& b) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pcmp_lt(const half2& a,
+                                                    const half2& b) {
   half true_half = half_impl::raw_uint16_to_half(0xffffu);
   half false_half = half_impl::raw_uint16_to_half(0x0000u);
   half a1 = __low2half(a);
@@ -680,9 +701,8 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pcmp_lt<half2>(const half2& a,
   return __halves2half2(eq1, eq2);
 }
 
-template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pand<half2>(const half2& a,
-                                                        const half2& b) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pand(const half2& a,
+                                                 const half2& b) {
   half a1 = __low2half(a);
   half a2 = __high2half(a);
   half b1 = __low2half(b);
@@ -692,9 +712,8 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pand<half2>(const half2& a,
   return __halves2half2(result1, result2);
 }
 
-template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 por<half2>(const half2& a,
-                                                       const half2& b) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 por(const half2& a,
+                                                const half2& b) {
   half a1 = __low2half(a);
   half a2 = __high2half(a);
   half b1 = __low2half(b);
@@ -704,9 +723,8 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 por<half2>(const half2& a,
   return __halves2half2(result1, result2);
 }
 
-template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pxor<half2>(const half2& a,
-                                                        const half2& b) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pxor(const half2& a,
+                                                 const half2& b) {
   half a1 = __low2half(a);
   half a2 = __high2half(a);
   half b1 = __low2half(b);
@@ -716,9 +734,8 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pxor<half2>(const half2& a,
   return __halves2half2(result1, result2);
 }
 
-template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pandnot<half2>(const half2& a,
-                                                           const half2& b) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pandnot(const half2& a,
+                                                    const half2& b) {
   half a1 = __low2half(a);
   half a2 = __high2half(a);
   half b1 = __low2half(b);
@@ -728,7 +745,8 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pandnot<half2>(const half2& a,
   return __halves2half2(result1, result2);
 }
 
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 padd<half2>(const half2& a, const half2& b) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 padd(const half2& a,
+                                                 const half2& b) {
 #if defined(EIGEN_HIP_DEVICE_COMPILE)
 
   return __hadd2(a, b);
@@ -750,7 +768,8 @@ template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 padd<half2>(const half2&
 #endif
 }
 
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 psub<half2>(const half2& a, const half2& b) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 psub(const half2& a,
+                                                 const half2& b) {
 #if defined(EIGEN_HIP_DEVICE_COMPILE)
 
   return __hsub2(a, b);
@@ -772,7 +791,7 @@ template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 psub<half2>(const half2&
 #endif
 }
 
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pnegate(const half2& a) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pnegate(const half2& a) {
 #if defined(EIGEN_HIP_DEVICE_COMPILE)
 
   return __hneg2(a);
@@ -790,9 +809,10 @@ template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pnegate(const half2& a) {
 #endif
 }
 
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pconj(const half2& a) { return a; }
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pconj(const half2& a) { return a; }
 
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pmul<half2>(const half2& a, const half2& b) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pmul(const half2& a,
+                                                 const half2& b) {
 #if defined(EIGEN_HIP_DEVICE_COMPILE)
 
   return __hmul2(a, b);
@@ -814,7 +834,9 @@ template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pmul<half2>(const half2&
 #endif
 }
 
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pmadd<half2>(const half2& a, const half2& b, const half2& c) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pmadd(const half2& a,
+                                                  const half2& b,
+                                                  const half2& c) {
 #if defined(EIGEN_HIP_DEVICE_COMPILE)
 
    return __hfma2(a, b, c);
@@ -838,7 +860,8 @@ template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pmadd<half2>(const half2&
 #endif
 }
 
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pdiv<half2>(const half2& a, const half2& b) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pdiv(const half2& a,
+                                                 const half2& b) {
 #if defined(EIGEN_HIP_DEVICE_COMPILE)
 
   return __h2div(a, b);
@@ -856,7 +879,8 @@ template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pdiv<half2>(const half2&
 #endif
 }
 
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pmin<half2>(const half2& a, const half2& b) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pmin(const half2& a,
+                                                 const half2& b) {
   float a1 = __low2float(a);
   float a2 = __high2float(a);
   float b1 = __low2float(b);
@@ -866,7 +890,8 @@ template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pmin<half2>(const half2&
   return __halves2half2(r1, r2);
 }
 
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pmax<half2>(const half2& a, const half2& b) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pmax(const half2& a,
+                                                 const half2& b) {
   float a1 = __low2float(a);
   float a2 = __high2float(a);
   float b1 = __low2float(b);
@@ -876,7 +901,7 @@ template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pmax<half2>(const half2&
   return __halves2half2(r1, r2);
 }
 
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half predux<half2>(const half2& a) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half predux(const half2& a) {
 #if defined(EIGEN_HIP_DEVICE_COMPILE)
 
   return __hadd(__low2half(a), __high2half(a));
@@ -894,7 +919,7 @@ template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half predux<half2>(const
 #endif
 }
 
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half predux_max<half2>(const half2& a) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half predux_max(const half2& a) {
 #if defined(EIGEN_HIP_DEVICE_COMPILE)
 
   __half first = __low2half(a);
@@ -916,7 +941,7 @@ template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half predux_max<half2>(c
 #endif
 }
 
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half predux_min<half2>(const half2& a) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half predux_min(const half2& a) {
 #if defined(EIGEN_HIP_DEVICE_COMPILE)
 
   __half first = __low2half(a);
@@ -938,7 +963,7 @@ template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half predux_min<half2>(c
 #endif
 }
 
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half predux_mul<half2>(const half2& a) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half predux_mul(const half2& a) {
 #if defined(EIGEN_HIP_DEVICE_COMPILE)
 
   return __hmul(__low2half(a), __high2half(a));
@@ -956,7 +981,7 @@ template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half predux_mul<half2>(c
 #endif
 }
 
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 plog1p<half2>(const half2& a) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 plog1p(const half2& a) {
   float a1 = __low2float(a);
   float a2 = __high2float(a);
   float r1 = log1pf(a1);
@@ -964,7 +989,7 @@ template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 plog1p<half2>(const half2
   return __floats2half2_rn(r1, r2);
 }
 
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pexpm1<half2>(const half2& a) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pexpm1(const half2& a) {
   float a1 = __low2float(a);
   float a2 = __high2float(a);
   float r1 = expm1f(a1);
@@ -975,29 +1000,29 @@ template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pexpm1<half2>(const half2
 #if (EIGEN_CUDA_SDK_VER >= 80000 && defined EIGEN_CUDA_ARCH && EIGEN_CUDA_ARCH >= 530) || \
   defined(EIGEN_HIP_DEVICE_COMPILE)
 
-template<>  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-half2 plog<half2>(const half2& a) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+half2 plog(const half2& a) {
   return h2log(a);
 }
 
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-half2 pexp<half2>(const half2& a) {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+half2 pexp(const half2& a) {
   return h2exp(a);
 }
 
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-half2 psqrt<half2>(const half2& a) {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+half2 psqrt(const half2& a) {
   return h2sqrt(a);
 }
 
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-half2 prsqrt<half2>(const half2& a) {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+half2 prsqrt(const half2& a) {
   return h2rsqrt(a);
 }
 
 #else
 
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 plog<half2>(const half2& a) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 plog(const half2& a) {
   float a1 = __low2float(a);
   float a2 = __high2float(a);
   float r1 = logf(a1);
@@ -1005,7 +1030,7 @@ template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 plog<half2>(const half2&
   return __floats2half2_rn(r1, r2);
 }
 
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pexp<half2>(const half2& a) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pexp(const half2& a) {
   float a1 = __low2float(a);
   float a2 = __high2float(a);
   float r1 = expf(a1);
@@ -1013,7 +1038,7 @@ template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pexp<half2>(const half2&
   return __floats2half2_rn(r1, r2);
 }
 
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 psqrt<half2>(const half2& a) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 psqrt(const half2& a) {
   float a1 = __low2float(a);
   float a2 = __high2float(a);
   float r1 = sqrtf(a1);
@@ -1021,7 +1046,7 @@ template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 psqrt<half2>(const half2&
   return __floats2half2_rn(r1, r2);
 }
 
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 prsqrt<half2>(const half2& a) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 prsqrt(const half2& a) {
   float a1 = __low2float(a);
   float a2 = __high2float(a);
   float r1 = rsqrtf(a1);
@@ -1029,8 +1054,728 @@ template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 prsqrt<half2>(const half2
   return __floats2half2_rn(r1, r2);
 }
 #endif
+} // namespace
+
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2
+pload<Packet4h2>(const Eigen::half* from) {
+  return *reinterpret_cast<const Packet4h2*>(from);
+}
+
+// unaligned load;
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2
+ploadu<Packet4h2>(const Eigen::half* from) {
+  Packet4h2 r;
+  half2* p_alias = reinterpret_cast<half2*>(&r);
+  p_alias[0] = ploadu(from + 0);
+  p_alias[1] = ploadu(from + 2);
+  p_alias[2] = ploadu(from + 4);
+  p_alias[3] = ploadu(from + 6);
+  return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2
+ploaddup<Packet4h2>(const Eigen::half* from) {
+  Packet4h2 r;
+  half2* p_alias = reinterpret_cast<half2*>(&r);
+  p_alias[0] = ploaddup(from + 0);
+  p_alias[1] = ploaddup(from + 1);
+  p_alias[2] = ploaddup(from + 2);
+  p_alias[3] = ploaddup(from + 3);
+  return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pstore<Eigen::half>(
+    Eigen::half* to, const Packet4h2& from) {
+  *reinterpret_cast<Packet4h2*>(to) = from;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pstoreu<Eigen::half>(
+    Eigen::half* to, const Packet4h2& from) {
+  const half2* from_alias = reinterpret_cast<const half2*>(&from);
+  pstoreu(to + 0,from_alias[0]);
+  pstoreu(to + 2,from_alias[1]);
+  pstoreu(to + 4,from_alias[2]);
+  pstoreu(to + 6,from_alias[3]);
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet4h2
+ploadt_ro<Packet4h2, Aligned>(const Eigen::half* from) {
+#if defined(EIGEN_HIP_DEVICE_COMPILE)
+
+  Packet4h2 r;
+  r = __ldg((const Packet4h2*)from);
+  return r;
+#else  // EIGEN_CUDA_ARCH
+
+#if EIGEN_CUDA_ARCH >= 350
+  Packet4h2 r;
+  r = __ldg((const Packet4h2*)from);
+  return r;
+#else
+  Packet4h2 r;
+  half2* r_alias = reinterpret_cast<half2*>(&r);
+  r_alias[0] = ploadt_ro_aligned(from + 0);
+  r_alias[1] = ploadt_ro_aligned(from + 2);
+  r_alias[2] = ploadt_ro_aligned(from + 4);
+  r_alias[3] = ploadt_ro_aligned(from + 6);
+  return r;
+#endif
+
+#endif
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet4h2
+ploadt_ro<Packet4h2, Unaligned>(const Eigen::half* from) {
+  Packet4h2 r;
+  half2* r_alias = reinterpret_cast<half2*>(&r);
+  r_alias[0] = ploadt_ro_unaligned(from + 0);
+  r_alias[1] = ploadt_ro_unaligned(from + 2);
+  r_alias[2] = ploadt_ro_unaligned(from + 4);
+  r_alias[3] = ploadt_ro_unaligned(from + 6);
+  return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2
+pgather<Eigen::half, Packet4h2>(const Eigen::half* from, Index stride) {
+  Packet4h2 r;
+  half2* p_alias = reinterpret_cast<half2*>(&r);
+  p_alias[0] = __halves2half2(from[0 * stride], from[1 * stride]);
+  p_alias[1] = __halves2half2(from[2 * stride], from[3 * stride]);
+  p_alias[2] = __halves2half2(from[4 * stride], from[5 * stride]);
+  p_alias[3] = __halves2half2(from[6 * stride], from[7 * stride]);
+  return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<Eigen::half, Packet4h2>(
+    Eigen::half* to, const Packet4h2& from, Index stride) {
+  const half2* from_alias = reinterpret_cast<const half2*>(&from);
+  pscatter(to + stride * 0, from_alias[0], stride);
+  pscatter(to + stride * 2, from_alias[1], stride);
+  pscatter(to + stride * 4, from_alias[2], stride);
+  pscatter(to + stride * 6, from_alias[3], stride);
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half pfirst<Packet4h2>(
+    const Packet4h2& a) {
+  return pfirst(*(reinterpret_cast<const half2*>(&a)));
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 pabs<Packet4h2>(
+    const Packet4h2& a) {
+  Packet4h2 r;
+  half2* p_alias = reinterpret_cast<half2*>(&r);
+  const half2* a_alias = reinterpret_cast<const half2*>(&a);
+  p_alias[0] = pabs(a_alias[0]);
+  p_alias[1] = pabs(a_alias[1]);
+  p_alias[2] = pabs(a_alias[2]);
+  p_alias[3] = pabs(a_alias[3]);
+  return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 ptrue<Packet4h2>(
+    const Packet4h2& a) {
+  half true_half = half_impl::raw_uint16_to_half(0xffffu);
+  return pset1<Packet4h2>(true_half);
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 pzero<Packet4h2>(const Packet4h2& a) {
+  half false_half = half_impl::raw_uint16_to_half(0x0000u);
+  return pset1<Packet4h2>(false_half);
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose_double(
+    double* d_row0, double* d_row1, double* d_row2, double* d_row3,
+    double* d_row4, double* d_row5, double* d_row6, double* d_row7) {
+  double d_tmp;
+  d_tmp = d_row0[1];
+  d_row0[1] = d_row4[0];
+  d_row4[0] = d_tmp;
+
+  d_tmp = d_row1[1];
+  d_row1[1] = d_row5[0];
+  d_row5[0] = d_tmp;
+
+  d_tmp = d_row2[1];
+  d_row2[1] = d_row6[0];
+  d_row6[0] = d_tmp;
+
+  d_tmp = d_row3[1];
+  d_row3[1] = d_row7[0];
+  d_row7[0] = d_tmp;
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose_half2(
+    half2* f_row0, half2* f_row1, half2* f_row2, half2* f_row3) {
+  half2 f_tmp;
+  f_tmp = f_row0[1];
+  f_row0[1] = f_row2[0];
+  f_row2[0] = f_tmp;
+
+  f_tmp = f_row1[1];
+  f_row1[1] = f_row3[0];
+  f_row3[0] = f_tmp;
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void
+ptranspose_half(half2& f0, half2& f1) {
+  __half a1 = __low2half(f0);
+  __half a2 = __high2half(f0);
+  __half b1 = __low2half(f1);
+  __half b2 = __high2half(f1);
+  f0 = __halves2half2(a1, b1);
+  f1 = __halves2half2(a2, b2);
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void
+ptranspose(PacketBlock<Packet4h2,8>& kernel) {
+  double* d_row0 = reinterpret_cast<double*>(&kernel.packet[0]);
+  double* d_row1 = reinterpret_cast<double*>(&kernel.packet[1]);
+  double* d_row2 = reinterpret_cast<double*>(&kernel.packet[2]);
+  double* d_row3 = reinterpret_cast<double*>(&kernel.packet[3]);
+  double* d_row4 = reinterpret_cast<double*>(&kernel.packet[4]);
+  double* d_row5 = reinterpret_cast<double*>(&kernel.packet[5]);
+  double* d_row6 = reinterpret_cast<double*>(&kernel.packet[6]);
+  double* d_row7 = reinterpret_cast<double*>(&kernel.packet[7]);
+  ptranspose_double(d_row0, d_row1, d_row2, d_row3,
+                    d_row4, d_row5, d_row6, d_row7);
+
+
+  half2* f_row0 = reinterpret_cast<half2*>(d_row0);
+  half2* f_row1 = reinterpret_cast<half2*>(d_row1);
+  half2* f_row2 = reinterpret_cast<half2*>(d_row2);
+  half2* f_row3 = reinterpret_cast<half2*>(d_row3);
+  ptranspose_half2(f_row0, f_row1, f_row2, f_row3);
+  ptranspose_half(f_row0[0], f_row1[0]);
+  ptranspose_half(f_row0[1], f_row1[1]);
+  ptranspose_half(f_row2[0], f_row3[0]);
+  ptranspose_half(f_row2[1], f_row3[1]);
+
+  f_row0 = reinterpret_cast<half2*>(d_row0 + 1);
+  f_row1 = reinterpret_cast<half2*>(d_row1 + 1);
+  f_row2 = reinterpret_cast<half2*>(d_row2 + 1);
+  f_row3 = reinterpret_cast<half2*>(d_row3 + 1);
+  ptranspose_half2(f_row0, f_row1, f_row2, f_row3);
+  ptranspose_half(f_row0[0], f_row1[0]);
+  ptranspose_half(f_row0[1], f_row1[1]);
+  ptranspose_half(f_row2[0], f_row3[0]);
+  ptranspose_half(f_row2[1], f_row3[1]);
+
+  f_row0 = reinterpret_cast<half2*>(d_row4);
+  f_row1 = reinterpret_cast<half2*>(d_row5);
+  f_row2 = reinterpret_cast<half2*>(d_row6);
+  f_row3 = reinterpret_cast<half2*>(d_row7);
+  ptranspose_half2(f_row0, f_row1, f_row2, f_row3);
+  ptranspose_half(f_row0[0], f_row1[0]);
+  ptranspose_half(f_row0[1], f_row1[1]);
+  ptranspose_half(f_row2[0], f_row3[0]);
+  ptranspose_half(f_row2[1], f_row3[1]);
+
+  f_row0 = reinterpret_cast<half2*>(d_row4 + 1);
+  f_row1 = reinterpret_cast<half2*>(d_row5 + 1);
+  f_row2 = reinterpret_cast<half2*>(d_row6 + 1);
+  f_row3 = reinterpret_cast<half2*>(d_row7 + 1);
+  ptranspose_half2(f_row0, f_row1, f_row2, f_row3);
+  ptranspose_half(f_row0[0], f_row1[0]);
+  ptranspose_half(f_row0[1], f_row1[1]);
+  ptranspose_half(f_row2[0], f_row3[0]);
+  ptranspose_half(f_row2[1], f_row3[1]);
+  
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2
+plset<Packet4h2>(const Eigen::half& a) {
+#if defined(EIGEN_HIP_DEVICE_COMPILE)
+
+  Packet4h2 r;
+  half2* p_alias = reinterpret_cast<half2*>(&r);
+  p_alias[0] = __halves2half2(a, __hadd(a, __float2half(1.0f)));
+  p_alias[1] = __halves2half2(__hadd(a, __float2half(2.0f)),
+                              __hadd(a, __float2half(3.0f)));
+  p_alias[2] = __halves2half2(__hadd(a, __float2half(4.0f)),
+                              __hadd(a, __float2half(5.0f)));
+  p_alias[3] = __halves2half2(__hadd(a, __float2half(6.0f)),
+                              __hadd(a, __float2half(7.0f)));
+  return r;
+#else  // EIGEN_CUDA_ARCH
+
+#if EIGEN_CUDA_ARCH >= 530
+  Packet4h2 r;
+  half2* r_alias = reinterpret_cast<half2*>(&r);
+
+  half2 b = pset1<half2>(a);
+  half2 c;
+  half2 half_offset0 = __halves2half2(__float2half(0.0f),__float2half(2.0f));
+  half2 half_offset1 = __halves2half2(__float2half(4.0f),__float2half(6.0f));
+
+  c = __hadd2(b, half_offset0);
+  r_alias[0] = plset(__low2half(c));
+  r_alias[1] = plset(__high2half(c));
+
+  c = __hadd2(b, half_offset1);
+  r_alias[2] = plset(__low2half(c));
+  r_alias[3] = plset(__high2half(c));
+
+  return r;
+
+#else
+  float f = __half2float(a);
+  Packet4h2 r;
+  half2* p_alias = reinterpret_cast<half2*>(&r);
+  p_alias[0] = __halves2half2(a, __float2half(f + 1.0f));
+  p_alias[1] = __halves2half2(__float2half(f + 2.0f), __float2half(f + 3.0f));
+  p_alias[2] = __halves2half2(__float2half(f + 4.0f), __float2half(f + 5.0f));
+  p_alias[3] = __halves2half2(__float2half(f + 6.0f), __float2half(f + 7.0f));
+  return r;
+#endif
 
 #endif
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2
+pselect<Packet4h2>(const Packet4h2& mask, const Packet4h2& a,
+                   const Packet4h2& b) {
+  Packet4h2 r;
+  half2* r_alias = reinterpret_cast<half2*>(&r);
+  const half2* mask_alias = reinterpret_cast<const half2*>(&mask);
+  const half2* a_alias = reinterpret_cast<const half2*>(&a);
+  const half2* b_alias = reinterpret_cast<const half2*>(&b);
+  r_alias[0] = pselect(mask_alias[0], a_alias[0], b_alias[0]);
+  r_alias[1] = pselect(mask_alias[1], a_alias[1], b_alias[1]);
+  r_alias[2] = pselect(mask_alias[2], a_alias[2], b_alias[2]);
+  r_alias[3] = pselect(mask_alias[3], a_alias[3], b_alias[3]);
+  return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2
+pcmp_eq<Packet4h2>(const Packet4h2& a, const Packet4h2& b) {
+  Packet4h2 r;
+  half2* r_alias = reinterpret_cast<half2*>(&r);
+  const half2* a_alias = reinterpret_cast<const half2*>(&a);
+  const half2* b_alias = reinterpret_cast<const half2*>(&b);
+  r_alias[0] = pcmp_eq(a_alias[0], b_alias[0]);
+  r_alias[1] = pcmp_eq(a_alias[1], b_alias[1]);
+  r_alias[2] = pcmp_eq(a_alias[2], b_alias[2]);
+  r_alias[3] = pcmp_eq(a_alias[3], b_alias[3]);
+  return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 pand<Packet4h2>(
+    const Packet4h2& a, const Packet4h2& b) {
+  Packet4h2 r;
+  half2* r_alias = reinterpret_cast<half2*>(&r);
+  const half2* a_alias = reinterpret_cast<const half2*>(&a);
+  const half2* b_alias = reinterpret_cast<const half2*>(&b);
+  r_alias[0] = pand(a_alias[0], b_alias[0]);
+  r_alias[1] = pand(a_alias[1], b_alias[1]);
+  r_alias[2] = pand(a_alias[2], b_alias[2]);
+  r_alias[3] = pand(a_alias[3], b_alias[3]);
+  return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 por<Packet4h2>(
+    const Packet4h2& a, const Packet4h2& b) {
+  Packet4h2 r;
+  half2* r_alias = reinterpret_cast<half2*>(&r);
+  const half2* a_alias = reinterpret_cast<const half2*>(&a);
+  const half2* b_alias = reinterpret_cast<const half2*>(&b);
+  r_alias[0] = por(a_alias[0], b_alias[0]);
+  r_alias[1] = por(a_alias[1], b_alias[1]);
+  r_alias[2] = por(a_alias[2], b_alias[2]);
+  r_alias[3] = por(a_alias[3], b_alias[3]);
+  return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 pxor<Packet4h2>(
+    const Packet4h2& a, const Packet4h2& b) {
+  Packet4h2 r;
+  half2* r_alias = reinterpret_cast<half2*>(&r);
+  const half2* a_alias = reinterpret_cast<const half2*>(&a);
+  const half2* b_alias = reinterpret_cast<const half2*>(&b);
+  r_alias[0] = pxor(a_alias[0], b_alias[0]);
+  r_alias[1] = pxor(a_alias[1], b_alias[1]);
+  r_alias[2] = pxor(a_alias[2], b_alias[2]);
+  r_alias[3] = pxor(a_alias[3], b_alias[3]);
+  return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2
+pandnot<Packet4h2>(const Packet4h2& a, const Packet4h2& b) {
+  Packet4h2 r;
+  half2* r_alias = reinterpret_cast<half2*>(&r);
+  const half2* a_alias = reinterpret_cast<const half2*>(&a);
+  const half2* b_alias = reinterpret_cast<const half2*>(&b);
+  r_alias[0] = pandnot(a_alias[0], b_alias[0]);
+  r_alias[1] = pandnot(a_alias[1], b_alias[1]);
+  r_alias[2] = pandnot(a_alias[2], b_alias[2]);
+  r_alias[3] = pandnot(a_alias[3], b_alias[3]);
+  return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 padd<Packet4h2>(
+    const Packet4h2& a, const Packet4h2& b) {
+  Packet4h2 r;
+  half2* r_alias = reinterpret_cast<half2*>(&r);
+  const half2* a_alias = reinterpret_cast<const half2*>(&a);
+  const half2* b_alias = reinterpret_cast<const half2*>(&b);
+  r_alias[0] = padd(a_alias[0], b_alias[0]);
+  r_alias[1] = padd(a_alias[1], b_alias[1]);
+  r_alias[2] = padd(a_alias[2], b_alias[2]);
+  r_alias[3] = padd(a_alias[3], b_alias[3]);
+  return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 psub<Packet4h2>(
+    const Packet4h2& a, const Packet4h2& b) {
+  Packet4h2 r;
+  half2* r_alias = reinterpret_cast<half2*>(&r);
+  const half2* a_alias = reinterpret_cast<const half2*>(&a);
+  const half2* b_alias = reinterpret_cast<const half2*>(&b);
+  r_alias[0] = psub(a_alias[0], b_alias[0]);
+  r_alias[1] = psub(a_alias[1], b_alias[1]);
+  r_alias[2] = psub(a_alias[2], b_alias[2]);
+  r_alias[3] = psub(a_alias[3], b_alias[3]);
+  return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 pnegate(const Packet4h2& a) {
+  Packet4h2 r;
+  half2* r_alias = reinterpret_cast<half2*>(&r);
+  const half2* a_alias = reinterpret_cast<const half2*>(&a);
+  r_alias[0] = pnegate(a_alias[0]);
+  r_alias[1] = pnegate(a_alias[1]);
+  r_alias[2] = pnegate(a_alias[2]);
+  r_alias[3] = pnegate(a_alias[3]);
+  return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 pconj(const Packet4h2& a) {
+  return a;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 pmul<Packet4h2>(
+    const Packet4h2& a, const Packet4h2& b) {
+  Packet4h2 r;
+  half2* r_alias = reinterpret_cast<half2*>(&r);
+  const half2* a_alias = reinterpret_cast<const half2*>(&a);
+  const half2* b_alias = reinterpret_cast<const half2*>(&b);
+  r_alias[0] = pmul(a_alias[0], b_alias[0]);
+  r_alias[1] = pmul(a_alias[1], b_alias[1]);
+  r_alias[2] = pmul(a_alias[2], b_alias[2]);
+  r_alias[3] = pmul(a_alias[3], b_alias[3]);
+  return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 pmadd<Packet4h2>(
+    const Packet4h2& a, const Packet4h2& b, const Packet4h2& c) {
+  Packet4h2 r;
+  half2* r_alias = reinterpret_cast<half2*>(&r);
+  const half2* a_alias = reinterpret_cast<const half2*>(&a);
+  const half2* b_alias = reinterpret_cast<const half2*>(&b);
+  const half2* c_alias = reinterpret_cast<const half2*>(&c);
+  r_alias[0] = pmadd(a_alias[0], b_alias[0], c_alias[0]);
+  r_alias[1] = pmadd(a_alias[1], b_alias[1], c_alias[1]);
+  r_alias[2] = pmadd(a_alias[2], b_alias[2], c_alias[2]);
+  r_alias[3] = pmadd(a_alias[3], b_alias[3], c_alias[3]);
+  return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 pdiv<Packet4h2>(
+    const Packet4h2& a, const Packet4h2& b) {
+  Packet4h2 r;
+  half2* r_alias = reinterpret_cast<half2*>(&r);
+  const half2* a_alias = reinterpret_cast<const half2*>(&a);
+  const half2* b_alias = reinterpret_cast<const half2*>(&b);
+  r_alias[0] = pdiv(a_alias[0], b_alias[0]);
+  r_alias[1] = pdiv(a_alias[1], b_alias[1]);
+  r_alias[2] = pdiv(a_alias[2], b_alias[2]);
+  r_alias[3] = pdiv(a_alias[3], b_alias[3]);
+  return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 pmin<Packet4h2>(
+    const Packet4h2& a, const Packet4h2& b) {
+  Packet4h2 r;
+  half2* r_alias = reinterpret_cast<half2*>(&r);
+  const half2* a_alias = reinterpret_cast<const half2*>(&a);
+  const half2* b_alias = reinterpret_cast<const half2*>(&b);
+  r_alias[0] = pmin(a_alias[0], b_alias[0]);
+  r_alias[1] = pmin(a_alias[1], b_alias[1]);
+  r_alias[2] = pmin(a_alias[2], b_alias[2]);
+  r_alias[3] = pmin(a_alias[3], b_alias[3]);
+  return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 pmax<Packet4h2>(
+    const Packet4h2& a, const Packet4h2& b) {
+  Packet4h2 r;
+  half2* r_alias = reinterpret_cast<half2*>(&r);
+  const half2* a_alias = reinterpret_cast<const half2*>(&a);
+  const half2* b_alias = reinterpret_cast<const half2*>(&b);
+  r_alias[0] = pmax(a_alias[0], b_alias[0]);
+  r_alias[1] = pmax(a_alias[1], b_alias[1]);
+  r_alias[2] = pmax(a_alias[2], b_alias[2]);
+  r_alias[3] = pmax(a_alias[3], b_alias[3]);
+  return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half predux<Packet4h2>(
+    const Packet4h2& a) {
+  const half2* a_alias = reinterpret_cast<const half2*>(&a);
+
+  return predux(a_alias[0]) + predux(a_alias[1]) +
+         predux(a_alias[2]) + predux(a_alias[3]);
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half predux_max<Packet4h2>(
+    const Packet4h2& a) {
+  const half2* a_alias = reinterpret_cast<const half2*>(&a);
+  half2 m0 = __halves2half2(predux_max(a_alias[0]),
+                            predux_max(a_alias[1]));
+  half2 m1 = __halves2half2(predux_max(a_alias[2]),
+                            predux_max(a_alias[3]));
+  __half first  = predux_max(m0);
+  __half second = predux_max(m1);
+#if EIGEN_CUDA_ARCH >= 530
+  return (__hgt(first, second) ? first : second);
+#else
+  float ffirst  = __half2float(first);
+  float fsecond = __half2float(second);
+  return (ffirst > fsecond)? first: second;
+#endif
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half predux_min<Packet4h2>(
+    const Packet4h2& a) {
+  const half2* a_alias = reinterpret_cast<const half2*>(&a);
+  half2 m0 = __halves2half2(predux_min(a_alias[0]),
+                            predux_min(a_alias[1]));
+  half2 m1 = __halves2half2(predux_min(a_alias[2]),
+                            predux_min(a_alias[3]));
+  __half first  = predux_min(m0);
+  __half second = predux_min(m1);
+#if EIGEN_CUDA_ARCH >= 530
+  return (__hlt(first, second) ? first : second);
+#else
+  float ffirst  = __half2float(first);
+  float fsecond = __half2float(second);
+  return (ffirst < fsecond)? first: second;
+#endif
+}
+
+// likely overflow/underflow
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half predux_mul<Packet4h2>(
+    const Packet4h2& a) {
+  const half2* a_alias = reinterpret_cast<const half2*>(&a);
+  return predux_mul(pmul(pmul(a_alias[0], a_alias[1]),
+                                       pmul(a_alias[2], a_alias[3])));
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2
+plog1p<Packet4h2>(const Packet4h2& a) {
+  Packet4h2 r;
+  half2* r_alias = reinterpret_cast<half2*>(&r);
+  const half2* a_alias = reinterpret_cast<const half2*>(&a);
+  r_alias[0] = plog1p(a_alias[0]);
+  r_alias[1] = plog1p(a_alias[1]);
+  r_alias[2] = plog1p(a_alias[2]);
+  r_alias[3] = plog1p(a_alias[3]);
+  return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2
+pexpm1<Packet4h2>(const Packet4h2& a) {
+  Packet4h2 r;
+  half2* r_alias = reinterpret_cast<half2*>(&r);
+  const half2* a_alias = reinterpret_cast<const half2*>(&a);
+  r_alias[0] = pexpm1(a_alias[0]);
+  r_alias[1] = pexpm1(a_alias[1]);
+  r_alias[2] = pexpm1(a_alias[2]);
+  r_alias[3] = pexpm1(a_alias[3]);
+  return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 plog<Packet4h2>(const Packet4h2& a) {
+  Packet4h2 r;
+  half2* r_alias = reinterpret_cast<half2*>(&r);
+  const half2* a_alias = reinterpret_cast<const half2*>(&a);
+  r_alias[0] = plog(a_alias[0]);
+  r_alias[1] = plog(a_alias[1]);
+  r_alias[2] = plog(a_alias[2]);
+  r_alias[3] = plog(a_alias[3]);
+  return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 pexp<Packet4h2>(const Packet4h2& a) {
+  Packet4h2 r;
+  half2* r_alias = reinterpret_cast<half2*>(&r);
+  const half2* a_alias = reinterpret_cast<const half2*>(&a);
+  r_alias[0] = pexp(a_alias[0]);
+  r_alias[1] = pexp(a_alias[1]);
+  r_alias[2] = pexp(a_alias[2]);
+  r_alias[3] = pexp(a_alias[3]);
+  return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 psqrt<Packet4h2>(const Packet4h2& a) {
+  Packet4h2 r;
+  half2* r_alias = reinterpret_cast<half2*>(&r);
+  const half2* a_alias = reinterpret_cast<const half2*>(&a);
+  r_alias[0] = psqrt(a_alias[0]);
+  r_alias[1] = psqrt(a_alias[1]);
+  r_alias[2] = psqrt(a_alias[2]);
+  r_alias[3] = psqrt(a_alias[3]);
+  return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2
+prsqrt<Packet4h2>(const Packet4h2& a) {
+  Packet4h2 r;
+  half2* r_alias = reinterpret_cast<half2*>(&r);
+  const half2* a_alias = reinterpret_cast<const half2*>(&a);
+  r_alias[0] = prsqrt(a_alias[0]);
+  r_alias[1] = prsqrt(a_alias[1]);
+  r_alias[2] = prsqrt(a_alias[2]);
+  r_alias[3] = prsqrt(a_alias[3]);
+  return r;
+}
+
+// The following specialized padd, pmul, pdiv, pmin, pmax, pset1 are needed for
+// the implementation of GPU half reduction.
+template<>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 padd<half2>(const half2& a,
+                                                        const half2& b) {
+#if defined(EIGEN_HIP_DEVICE_COMPILE)
+
+  return __hadd2(a, b);
+
+#else  // EIGEN_CUDA_ARCH
+
+#if EIGEN_CUDA_ARCH >= 530
+  return __hadd2(a, b);
+#else
+  float a1 = __low2float(a);
+  float a2 = __high2float(a);
+  float b1 = __low2float(b);
+  float b2 = __high2float(b);
+  float r1 = a1 + b1;
+  float r2 = a2 + b2;
+  return __floats2half2_rn(r1, r2);
+#endif
+
+#endif
+}
+
+template<>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pmul<half2>(const half2& a,
+                                                        const half2& b) {
+#if defined(EIGEN_HIP_DEVICE_COMPILE)
+
+  return __hmul2(a, b);
+
+#else  // EIGEN_CUDA_ARCH
+
+#if EIGEN_CUDA_ARCH >= 530
+  return __hmul2(a, b);
+#else
+  float a1 = __low2float(a);
+  float a2 = __high2float(a);
+  float b1 = __low2float(b);
+  float b2 = __high2float(b);
+  float r1 = a1 * b1;
+  float r2 = a2 * b2;
+  return __floats2half2_rn(r1, r2);
+#endif
+
+#endif
+}
+
+template<>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pdiv<half2>(const half2& a,
+                                                        const half2& b) {
+#if defined(EIGEN_HIP_DEVICE_COMPILE)
+
+  return __h2div(a, b);
+
+#else // EIGEN_CUDA_ARCH
+
+  float a1 = __low2float(a);
+  float a2 = __high2float(a);
+  float b1 = __low2float(b);
+  float b2 = __high2float(b);
+  float r1 = a1 / b1;
+  float r2 = a2 / b2;
+  return __floats2half2_rn(r1, r2);
+
+#endif
+}
+
+template<>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pmin<half2>(const half2& a,
+                                                        const half2& b) {
+  float a1 = __low2float(a);
+  float a2 = __high2float(a);
+  float b1 = __low2float(b);
+  float b2 = __high2float(b);
+  __half r1 = a1 < b1 ? __low2half(a) : __low2half(b);
+  __half r2 = a2 < b2 ? __high2half(a) : __high2half(b);
+  return __halves2half2(r1, r2);
+}
+
+template<>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pmax<half2>(const half2& a,
+                                                        const half2& b) {
+  float a1 = __low2float(a);
+  float a2 = __high2float(a);
+  float b1 = __low2float(b);
+  float b2 = __high2float(b);
+  __half r1 = a1 > b1 ? __low2half(a) : __low2half(b);
+  __half r2 = a2 > b2 ? __high2half(a) : __high2half(b);
+  return __halves2half2(r1, r2);
+}
+
+#endif // defined(EIGEN_CUDA_ARCH)
+
+#endif // defined(EIGEN_HAS_CUDA_FP16) && defined(EIGEN_CUDACC)
 
 } // end namespace internal
 
diff --git a/Eigen/src/Core/arch/GPU/TypeCasting.h b/Eigen/src/Core/arch/GPU/TypeCasting.h
index c278f3fe8..754546225 100644
--- a/Eigen/src/Core/arch/GPU/TypeCasting.h
+++ b/Eigen/src/Core/arch/GPU/TypeCasting.h
@@ -17,12 +17,13 @@ namespace internal {
 #if (defined(EIGEN_HAS_CUDA_FP16) && defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 300) || \
   (defined(EIGEN_HAS_HIP_FP16) && defined(EIGEN_HIP_DEVICE_COMPILE))
 
+
 template <>
 struct type_casting_traits<Eigen::half, float> {
   enum {
     VectorizedCast = 1,
-    SrcCoeffRatio = 2,
-    TgtCoeffRatio = 1
+    SrcCoeffRatio = 1,
+    TgtCoeffRatio = 2
   };
 };
 
@@ -32,15 +33,39 @@ template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pcast<half2, float4>(con
   return make_float4(r1.x, r1.y, r2.x, r2.y);
 }
 
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 pcast<float4, Packet4h2>(const float4& a, const float4& b) {
+  Packet4h2 r;
+  half2* r_alias=reinterpret_cast<half2*>(&r);
+  r_alias[0]=__floats2half2_rn(a.x,a.y);
+  r_alias[1]=__floats2half2_rn(a.z,a.w);
+  r_alias[2]=__floats2half2_rn(b.x,b.y);
+  r_alias[3]=__floats2half2_rn(b.z,b.w);
+  return r;
+}
+
 template <>
 struct type_casting_traits<float, Eigen::half> {
   enum {
     VectorizedCast = 1,
-    SrcCoeffRatio = 1,
-    TgtCoeffRatio = 2
+    SrcCoeffRatio = 2,
+    TgtCoeffRatio = 1
   };
 };
 
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pcast<Packet4h2, float4>(const Packet4h2& a) {
+  // Simply discard the second half of the input
+  float4 r;
+  const half2* a_alias=reinterpret_cast<const half2*>(&a);
+  float2 r1 = __half22float2(a_alias[0]);
+  float2 r2 = __half22float2(a_alias[1]);
+  r.x=static_cast<float>(r1.x);
+  r.y=static_cast<float>(r1.y);
+  r.z=static_cast<float>(r2.x);
+  r.w=static_cast<float>(r2.y);
+  return r;
+}
+
 template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pcast<float4, half2>(const float4& a) {
   // Simply discard the second half of the input
   return __floats2half2_rn(a.x, a.y);