Disable cuda Eigen::half vectorization on host.

All cuda `__half` functions are device-only in CUDA 9, including
conversions. Host-side conversions were added in CUDA 10.
The existing code doesn't build prior to 10.0.

All arithmetic functions are always device-only, so there's
therefore no reason to use vectorization on the host at all.

Modified the code to disable vectorization for `__half` on host,
which required also updating the `TensorReductionGpu` implementation
which previously made assumptions about available packets.
diff --git a/Eigen/src/Core/arch/GPU/PacketMath.h b/Eigen/src/Core/arch/GPU/PacketMath.h
index 689110d..25c45fd 100644
--- a/Eigen/src/Core/arch/GPU/PacketMath.h
+++ b/Eigen/src/Core/arch/GPU/PacketMath.h
@@ -493,9 +493,10 @@
 
 #endif // defined(EIGEN_GPUCC) && defined(EIGEN_USE_GPU)
 
-// 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_HAS_HIP_FP16)
+// Half-packet functions are not available on the host for CUDA 9.0-9.2, only
+// on device. There is no benefit to using them on the host anyways, since they are
+// emulated.
+#if (defined(EIGEN_HAS_CUDA_FP16) || defined(EIGEN_HAS_HIP_FP16)) && defined(EIGEN_GPU_COMPILE_PHASE)
 
 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; };
@@ -526,42 +527,9 @@
   };
 };
 
-namespace {
-// This is equivalent to make_half2, which is undocumented and doesn't seem to always exist.
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 combine_half(const __half& a, const __half& b) {
-#if defined(EIGEN_GPU_COMPILE_PHASE)
-  return __halves2half2(a, b);
-#else
-  // Round-about way since __halves2half2 is a __device__ function.
-  return __floats2half2_rn(__half2float(a), __half2float(b));
-#endif
-}
-
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE __half get_half2_low(const half2& a) {
-#if defined(EIGEN_GPU_COMPILE_PHASE)
-  return __low2half(a);
-#else
-  return __float2half(__low2float(a));
-#endif
-}
-
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE __half get_half2_high(const half2& a) {
-#if defined(EIGEN_GPU_COMPILE_PHASE)
-  return __high2half(a);
-#else
-  return __float2half(__high2float(a));
-#endif
-}
-} // namespace
-
 template<>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pset1<half2>(const Eigen::half& from) {
-#if defined(EIGEN_GPU_COMPILE_PHASE)
   return __half2half2(from);
-#else
-  const float f = __half2float(from);
-  return __floats2half2_rn(f, f);
-#endif
 }
 
 template <>
@@ -576,8 +544,6 @@
   return r;
 }
 
-// We now need this visible on both host and device.
-// #if defined(EIGEN_CUDA_ARCH) || defined(EIGEN_HIPCC) || (defined(EIGEN_CUDACC) && EIGEN_COMP_CLANG && !EIGEN_COMP_NVCC)
 namespace {
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pload(const Eigen::half* from) {
@@ -585,11 +551,11 @@
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 ploadu(const Eigen::half* from) {
-  return combine_half(from[0], from[1]);
+  return __halves2half2(from[0], from[1]);
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 ploaddup(const Eigen::half*  from) {
-  return combine_half(from[0], from[0]);
+  return __halves2half2(from[0], from[0]);
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pstore(Eigen::half* to,
@@ -599,8 +565,8 @@
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pstoreu(Eigen::half* to,
                                                    const half2& from) {
-  to[0] = get_half2_low(from);
-  to[1] = get_half2_high(from);
+  to[0] = __low2half(from);
+  to[1] = __high2half(from);
 }
 
 
@@ -610,7 +576,7 @@
   // Input is guaranteed to be properly aligned.
   return __ldg(reinterpret_cast<const half2*>(from));
 #else
-  return combine_half(*(from+0), *(from+1));
+  return __halves2half2(*(from+0), *(from+1));
 #endif
 }
 
@@ -619,31 +585,31 @@
 #if defined(EIGEN_GPU_HAS_LDG)
   return __halves2half2(__ldg(from+0), __ldg(from+1));
 #else
-  return combine_half(*(from+0), *(from+1));
+  return __halves2half2(*(from+0), *(from+1));
 #endif
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pgather(const Eigen::half* from,
                                                     Index stride) {
-  return combine_half(from[0*stride], from[1*stride]);
+  return __halves2half2(from[0*stride], from[1*stride]);
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter(
     Eigen::half* to, const half2& from, Index stride) {
-  to[stride*0] = get_half2_low(from);
-  to[stride*1] = get_half2_high(from);
+  to[stride*0] = __low2half(from);
+  to[stride*1] = __high2half(from);
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half pfirst(const half2& a) {
-  return get_half2_low(a);
+  return __low2half(a);
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pabs(const half2& a) {
-  half a1 = get_half2_low(a);
-  half a2 = get_half2_high(a);
+  half a1 = __low2half(a);
+  half a2 = __high2half(a);
   half result1 = half_impl::raw_uint16_to_half(a1.x & 0x7FFF);
   half result2 = half_impl::raw_uint16_to_half(a2.x & 0x7FFF);
-  return combine_half(result1, result2);
+  return __halves2half2(result1, result2);
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 ptrue(const half2& /*a*/) {
@@ -658,12 +624,12 @@
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void
 ptranspose(PacketBlock<half2,2>& kernel) {
-  __half a1 = get_half2_low(kernel.packet[0]);
-  __half a2 = get_half2_high(kernel.packet[0]);
-  __half b1 = get_half2_low(kernel.packet[1]);
-  __half b2 = get_half2_high(kernel.packet[1]);
-  kernel.packet[0] = combine_half(a1, b1);
-  kernel.packet[1] = combine_half(a2, b2);
+  __half a1 = __low2half(kernel.packet[0]);
+  __half a2 = __high2half(kernel.packet[0]);
+  __half b1 = __low2half(kernel.packet[1]);
+  __half b2 = __high2half(kernel.packet[1]);
+  kernel.packet[0] = __halves2half2(a1, b1);
+  kernel.packet[1] = __halves2half2(a2, b2);
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 plset(const Eigen::half& a) {
@@ -671,88 +637,88 @@
   return __halves2half2(a, __hadd(a, __float2half(1.0f)));
 #else
   float f = __half2float(a) + 1.0f;
-  return combine_half(a, __float2half(f));
+  return __halves2half2(a, __float2half(f));
 #endif
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pselect(const half2& mask,
                                                     const half2& a,
                                                     const half2& b) {
-  half mask_low = get_half2_low(mask);
-  half mask_high = get_half2_high(mask);
-  half result_low = mask_low == half(0) ? get_half2_low(b) : get_half2_low(a);
-  half result_high = mask_high == half(0) ? get_half2_high(b) : get_half2_high(a);
-  return combine_half(result_low, result_high);
+  half mask_low = __low2half(mask);
+  half mask_high = __high2half(mask);
+  half result_low = mask_low == half(0) ? __low2half(b) : __low2half(a);
+  half result_high = mask_high == half(0) ? __high2half(b) : __high2half(a);
+  return __halves2half2(result_low, result_high);
 }
 
 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 = get_half2_low(a);
-  half a2 = get_half2_high(a);
-  half b1 = get_half2_low(b);
-  half b2 = get_half2_high(b);
+  half a1 = __low2half(a);
+  half a2 = __high2half(a);
+  half b1 = __low2half(b);
+  half b2 = __high2half(b);
   half eq1 = __half2float(a1) == __half2float(b1) ? true_half : false_half;
   half eq2 = __half2float(a2) == __half2float(b2) ? true_half : false_half;
-  return combine_half(eq1, eq2);
+  return __halves2half2(eq1, eq2);
 }
 
 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 = get_half2_low(a);
-  half a2 = get_half2_high(a);
-  half b1 = get_half2_low(b);
-  half b2 = get_half2_high(b);
+  half a1 = __low2half(a);
+  half a2 = __high2half(a);
+  half b1 = __low2half(b);
+  half b2 = __high2half(b);
   half eq1 = __half2float(a1) < __half2float(b1) ? true_half : false_half;
   half eq2 = __half2float(a2) < __half2float(b2) ? true_half : false_half;
-  return combine_half(eq1, eq2);
+  return __halves2half2(eq1, eq2);
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pand(const half2& a,
                                                  const half2& b) {
-  half a1 = get_half2_low(a);
-  half a2 = get_half2_high(a);
-  half b1 = get_half2_low(b);
-  half b2 = get_half2_high(b);
+  half a1 = __low2half(a);
+  half a2 = __high2half(a);
+  half b1 = __low2half(b);
+  half b2 = __high2half(b);
   half result1 = half_impl::raw_uint16_to_half(a1.x & b1.x);
   half result2 = half_impl::raw_uint16_to_half(a2.x & b2.x);
-  return combine_half(result1, result2);
+  return __halves2half2(result1, result2);
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 por(const half2& a,
                                                 const half2& b) {
-  half a1 = get_half2_low(a);
-  half a2 = get_half2_high(a);
-  half b1 = get_half2_low(b);
-  half b2 = get_half2_high(b);
+  half a1 = __low2half(a);
+  half a2 = __high2half(a);
+  half b1 = __low2half(b);
+  half b2 = __high2half(b);
   half result1 = half_impl::raw_uint16_to_half(a1.x | b1.x);
   half result2 = half_impl::raw_uint16_to_half(a2.x | b2.x);
-  return combine_half(result1, result2);
+  return __halves2half2(result1, result2);
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pxor(const half2& a,
                                                  const half2& b) {
-  half a1 = get_half2_low(a);
-  half a2 = get_half2_high(a);
-  half b1 = get_half2_low(b);
-  half b2 = get_half2_high(b);
+  half a1 = __low2half(a);
+  half a2 = __high2half(a);
+  half b1 = __low2half(b);
+  half b2 = __high2half(b);
   half result1 = half_impl::raw_uint16_to_half(a1.x ^ b1.x);
   half result2 = half_impl::raw_uint16_to_half(a2.x ^ b2.x);
-  return combine_half(result1, result2);
+  return __halves2half2(result1, result2);
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pandnot(const half2& a,
                                                     const half2& b) {
-  half a1 = get_half2_low(a);
-  half a2 = get_half2_high(a);
-  half b1 = get_half2_low(b);
-  half b2 = get_half2_high(b);
+  half a1 = __low2half(a);
+  half a2 = __high2half(a);
+  half b1 = __low2half(b);
+  half b2 = __high2half(b);
   half result1 = half_impl::raw_uint16_to_half(a1.x & ~b1.x);
   half result2 = half_impl::raw_uint16_to_half(a2.x & ~b2.x);
-  return combine_half(result1, result2);
+  return __halves2half2(result1, result2);
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 padd(const half2& a,
@@ -851,9 +817,9 @@
   float a2 = __high2float(a);
   float b1 = __low2float(b);
   float b2 = __high2float(b);
-  __half r1 = a1 < b1 ? get_half2_low(a) : get_half2_low(b);
-  __half r2 = a2 < b2 ? get_half2_high(a) : get_half2_high(b);
-  return combine_half(r1, r2);
+  __half r1 = a1 < b1 ? __low2half(a) : __low2half(b);
+  __half r2 = a2 < b2 ? __high2half(a) : __high2half(b);
+  return __halves2half2(r1, r2);
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pmax(const half2& a,
@@ -862,9 +828,9 @@
   float a2 = __high2float(a);
   float b1 = __low2float(b);
   float b2 = __high2float(b);
-  __half r1 = a1 > b1 ? get_half2_low(a) : get_half2_low(b);
-  __half r2 = a2 > b2 ? get_half2_high(a) : get_half2_high(b);
-  return combine_half(r1, r2);
+  __half r1 = a1 > b1 ? __low2half(a) : __low2half(b);
+  __half r2 = a2 > b2 ? __high2half(a) : __high2half(b);
+  return __halves2half2(r1, r2);
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half predux(const half2& a) {
@@ -885,7 +851,7 @@
 #else
   float a1 = __low2float(a);
   float a2 = __high2float(a);
-  return a1 > a2 ? get_half2_low(a) : get_half2_high(a);
+  return a1 > a2 ? __low2half(a) : __high2half(a);
 #endif
 }
 
@@ -897,7 +863,7 @@
 #else
   float a1 = __low2float(a);
   float a2 = __high2float(a);
-  return a1 < a2 ? get_half2_low(a) : get_half2_high(a);
+  return a1 < a2 ? __low2half(a) : __high2half(a);
 #endif
 }
 
@@ -1068,10 +1034,10 @@
 pgather<Eigen::half, Packet4h2>(const Eigen::half* from, Index stride) {
   Packet4h2 r;
   half2* p_alias = reinterpret_cast<half2*>(&r);
-  p_alias[0] = combine_half(from[0 * stride], from[1 * stride]);
-  p_alias[1] = combine_half(from[2 * stride], from[3 * stride]);
-  p_alias[2] = combine_half(from[4 * stride], from[5 * stride]);
-  p_alias[3] = combine_half(from[6 * stride], from[7 * stride]);
+  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;
 }
 
@@ -1152,12 +1118,12 @@
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void
 ptranspose_half(half2& f0, half2& f1) {
-  __half a1 = get_half2_low(f0);
-  __half a2 = get_half2_high(f0);
-  __half b1 = get_half2_low(f1);
-  __half b2 = get_half2_high(f1);
-  f0 = combine_half(a1, b1);
-  f1 = combine_half(a2, b2);
+  __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
@@ -1254,10 +1220,10 @@
   float f = __half2float(a);
   Packet4h2 r;
   half2* p_alias = reinterpret_cast<half2*>(&r);
-  p_alias[0] = combine_half(a, __float2half(f + 1.0f));
-  p_alias[1] = combine_half(__float2half(f + 2.0f), __float2half(f + 3.0f));
-  p_alias[2] = combine_half(__float2half(f + 4.0f), __float2half(f + 5.0f));
-  p_alias[3] = combine_half(__float2half(f + 6.0f), __float2half(f + 7.0f));
+  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
 }
@@ -1477,9 +1443,9 @@
 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 = combine_half(predux_max(a_alias[0]),
+  half2 m0 = __halves2half2(predux_max(a_alias[0]),
                             predux_max(a_alias[1]));
-  half2 m1 = combine_half(predux_max(a_alias[2]),
+  half2 m1 = __halves2half2(predux_max(a_alias[2]),
                             predux_max(a_alias[3]));
   __half first  = predux_max(m0);
   __half second = predux_max(m1);
@@ -1496,9 +1462,9 @@
 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 = combine_half(predux_min(a_alias[0]),
+  half2 m0 = __halves2half2(predux_min(a_alias[0]),
                             predux_min(a_alias[1]));
-  half2 m1 = combine_half(predux_min(a_alias[2]),
+  half2 m1 = __halves2half2(predux_min(a_alias[2]),
                             predux_min(a_alias[3]));
   __half first  = predux_min(m0);
   __half second = predux_min(m1);
@@ -1652,9 +1618,9 @@
   float a2 = __high2float(a);
   float b1 = __low2float(b);
   float b2 = __high2float(b);
-  __half r1 = a1 < b1 ? get_half2_low(a) : get_half2_low(b);
-  __half r2 = a2 < b2 ? get_half2_high(a) : get_half2_high(b);
-  return combine_half(r1, r2);
+  __half r1 = a1 < b1 ? __low2half(a) : __low2half(b);
+  __half r2 = a2 < b2 ? __high2half(a) : __high2half(b);
+  return __halves2half2(r1, r2);
 }
 
 template<>
@@ -1664,14 +1630,12 @@
   float a2 = __high2float(a);
   float b1 = __low2float(b);
   float b2 = __high2float(b);
-  __half r1 = a1 > b1 ? get_half2_low(a) : get_half2_low(b);
-  __half r2 = a2 > b2 ? get_half2_high(a) : get_half2_high(b);
-  return combine_half(r1, r2);
+  __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) || defined(EIGEN_HIPCC) || (defined(EIGEN_CUDACC) && EIGEN_COMP_CLANG && !EIGEN_COMP_NVCC)
-
-#endif // defined(EIGEN_HAS_CUDA_FP16) || defined(EIGEN_HAS_HIP_FP16)
+#endif // (defined(EIGEN_HAS_CUDA_FP16) || defined(EIGEN_HAS_HIP_FP16)) && defined(EIGEN_GPU_COMPILE_PHASE)
 
 #undef EIGEN_GPU_HAS_LDG
 #undef EIGEN_CUDA_HAS_FP16_ARITHMETIC
diff --git a/Eigen/src/Core/arch/GPU/TypeCasting.h b/Eigen/src/Core/arch/GPU/TypeCasting.h
index 7545462..c8195bb 100644
--- a/Eigen/src/Core/arch/GPU/TypeCasting.h
+++ b/Eigen/src/Core/arch/GPU/TypeCasting.h
@@ -15,8 +15,7 @@
 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))
-
+    (defined(EIGEN_HAS_HIP_FP16) && defined(EIGEN_HIP_DEVICE_COMPILE))
 
 template <>
 struct type_casting_traits<Eigen::half, float> {
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorMeta.h b/unsupported/Eigen/CXX11/src/Tensor/TensorMeta.h
index a6181d3..b90a1dc 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorMeta.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorMeta.h
@@ -52,7 +52,7 @@
 };
 
 // For CUDA packet types when using a GpuDevice
-#if defined(EIGEN_USE_GPU) && defined(EIGEN_HAS_GPU_FP16)
+#if defined(EIGEN_USE_GPU) && defined(EIGEN_HAS_GPU_FP16) && defined(EIGEN_GPU_COMPILE_PHASE)
 
 typedef ulonglong2 Packet4h2;
 template<>
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorReductionGpu.h b/unsupported/Eigen/CXX11/src/Tensor/TensorReductionGpu.h
index db4e8d8..315ccc1 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorReductionGpu.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorReductionGpu.h
@@ -98,6 +98,7 @@
     }
   }
 }
+#ifdef EIGEN_GPU_COMPILE_PHASE
 // reduction should be associative since reduction is not atomic in wide vector but atomic in half2 operations
 template <typename R>
 __device__ inline void atomicReduce(Packet4h2* output, Packet4h2 accum, R& reducer) {
@@ -107,6 +108,7 @@
     atomicReduce(houtput+i,*(haccum+i),reducer);
   }
 }
+#endif  // EIGEN_GPU_COMPILE_PHASE
 #endif  // EIGEN_HAS_GPU_FP16
 
 template <>
@@ -213,8 +215,8 @@
 #ifdef EIGEN_HAS_GPU_FP16
 template <typename Self,
           typename Reducer, typename Index>
-__global__ EIGEN_HIP_LAUNCH_BOUNDS_1024 void ReductionInitFullReduxKernelHalfFloat(Reducer reducer, const Self input, Index num_coeffs,
-                                                      packet_traits<Eigen::half>::type* scratch) {
+__global__ EIGEN_HIP_LAUNCH_BOUNDS_1024 void ReductionInitFullReduxKernelHalfFloat(
+    Reducer reducer, const Self input, Index num_coeffs, half* scratch) {
   eigen_assert(blockDim.x == 1);
   eigen_assert(gridDim.x == 1);
   typedef packet_traits<Eigen::half>::type packet_type;
@@ -224,15 +226,16 @@
     half2* h2scratch = reinterpret_cast<half2*>(scratch);
     for (Index i = num_coeffs - packet_remainder; i + 2 <= num_coeffs; i += 2) {
       *h2scratch =
-          __halves2half2(input.m_impl.coeff(i), input.m_impl.coeff(i + 1));
+          __halves2half2(input.coeff(i), input.coeff(i + 1));
       h2scratch++;
     }
     if ((num_coeffs & 1) != 0) {
-      half lastCoeff = input.m_impl.coeff(num_coeffs - 1);
+      half lastCoeff = input.coeff(num_coeffs - 1);
       *h2scratch = __halves2half2(lastCoeff, reducer.initialize());
     }
   } else {
-    *scratch = reducer.template initializePacket<packet_type>();
+    packet_type reduce = reducer.template initializePacket<packet_type>();
+    internal::pstoreu(scratch, reduce);
   }
 }
 
@@ -258,8 +261,9 @@
 
 template <int BlockSize, int NumPerThread, typename Self,
           typename Reducer, typename Index>
-__global__ EIGEN_HIP_LAUNCH_BOUNDS_1024 void FullReductionKernelHalfFloat(Reducer reducer, const Self input, Index num_coeffs,
-                                    half* output, packet_traits<Eigen::half>::type* scratch) {
+__global__ EIGEN_HIP_LAUNCH_BOUNDS_1024 void FullReductionKernelHalfFloat(
+    Reducer reducer, const Self input, Index num_coeffs,
+    half* output, half* scratch) {
   typedef typename packet_traits<Eigen::half>::type PacketType;
   const int packet_width = unpacket_traits<PacketType>::size;
   eigen_assert(NumPerThread % packet_width == 0);
@@ -273,19 +277,20 @@
       int rem = num_coeffs % packet_width;
       if (rem != 0) {
         half2* p_scratch = reinterpret_cast<half2*>(scratch);
-        *scratch = reducer.template initializePacket<PacketType>();
+        pstoreu(scratch, reducer.template initializePacket<PacketType>());
         for (int i = 0; i < rem / 2; i++) {
           *p_scratch = __halves2half2(
-              input.m_impl.coeff(num_coeffs - packet_width + 2 * i),
-              input.m_impl.coeff(num_coeffs - packet_width + 2 * i + 1));
+              input.coeff(num_coeffs - packet_width + 2 * i),
+              input.coeff(num_coeffs - packet_width + 2 * i + 1));
           p_scratch++;
         }
         if ((num_coeffs & 1) != 0) {
-          half last = input.m_impl.coeff(num_coeffs - 1);
+          half last = input.coeff(num_coeffs - 1);
           *p_scratch = __halves2half2(last, reducer.initialize());
         }
       } else {
-        *scratch = reducer.template initializePacket<PacketType>();
+        PacketType reduce = reducer.template initializePacket<PacketType>();
+        pstoreu(scratch, reduce);
       }
     }
     __syncthreads();
@@ -298,7 +303,7 @@
   for (Index i = 0; i < max_iter; i += BlockSize) {
     const Index index = first_index + packet_width * i;
     eigen_assert(index + packet_width < num_coeffs);
-    PacketType val = input.m_impl.template packet<Unaligned>(index);
+    PacketType val = input.template packet<Unaligned>(index);
     reducer.reducePacket(val, &accum);
   }
 
@@ -337,7 +342,7 @@
   }
 
   if ((threadIdx.x & (warpSize - 1)) == 0) {
-    atomicReduce(scratch, accum, reducer);
+    atomicReduce(reinterpret_cast<PacketType*>(scratch), accum, reducer);
   }
 
   __syncthreads();
@@ -357,17 +362,21 @@
 }
 
 template <typename Op>
-__global__ EIGEN_HIP_LAUNCH_BOUNDS_1024 void ReductionCleanupKernelHalfFloat(Op reducer, half* output, packet_traits<Eigen::half>::type* scratch) {
+__global__ EIGEN_HIP_LAUNCH_BOUNDS_1024 void ReductionCleanupKernelHalfFloat(Op reducer, half* output, half* scratch) {
   eigen_assert(threadIdx.x == 1);
-  half2* pscratch = reinterpret_cast<half2*>(scratch);
-  half tmp = __float2half(0.f);
   typedef packet_traits<Eigen::half>::type packet_type;
-  for (int i = 0; i < unpacket_traits<packet_type>::size; i += 2) {
-    reducer.reduce(__low2half(*pscratch), &tmp);
-    reducer.reduce(__high2half(*pscratch), &tmp);
-    pscratch++;
+  if (unpacket_traits<packet_type>::size == 1) {
+    *output = *scratch;
+  } else {
+    half2* pscratch = reinterpret_cast<half2*>(scratch);
+    half tmp = __float2half(0.f);
+    for (int i = 0; i < unpacket_traits<packet_type>::size; i += 2) {
+      reducer.reduce(__low2half(*pscratch), &tmp);
+      reducer.reduce(__high2half(*pscratch), &tmp);
+      pscratch++;
+    }
+    *output = tmp;
   }
-  *output = tmp;
 }
 
 #endif // EIGEN_HAS_GPU_FP16
@@ -416,13 +425,11 @@
 struct FullReductionLauncher<Self, Op, Eigen::half, true> {
   static void run(const Self& self, Op& reducer, const GpuDevice& device, half* output, typename Self::Index num_coeffs) {
     typedef typename Self::Index Index;
-    typedef typename packet_traits<Eigen::half>::type PacketType;
 
     const int block_size = 256;
     const int num_per_thread = 128;
     const int num_blocks = divup<int>(num_coeffs, block_size * num_per_thread);
-    PacketType* scratch = static_cast<PacketType*>(device.scratchpad());
-    // half2* scratch = static_cast<half2*>(device.scratchpad());
+    half* scratch = static_cast<half*>(device.scratchpad());
 
     if (num_blocks > 1) {
       // We initialize the output and the scrathpad outside the reduction kernel when we can't be sure that there