diff --git a/Eigen/src/Core/arch/CUDA/PacketMathHalf.h b/Eigen/src/Core/arch/CUDA/PacketMathHalf.h
index 4f052dc..5138650 100644
--- a/Eigen/src/Core/arch/CUDA/PacketMathHalf.h
+++ b/Eigen/src/Core/arch/CUDA/PacketMathHalf.h
@@ -264,6 +264,30 @@
 #endif
 }
 
+#if defined __CUDACC_VER__ && __CUDACC_VER__ >= 80000 && defined __CUDA_ARCH__ && __CUDA_ARCH__ >= 530
+
+template<>  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+half2 plog<half2>(const half2& a) {
+  return h2log(a);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+half2 pexp<half2>(const half2& a) {
+  return h2exp(a);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+half2 psqrt<half2>(const half2& a) {
+  return h2sqrt(a);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+half2 prsqrt<half2>(const half2& a) {
+  return h2rsqrt(a);
+}
+
+#else
+
 template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 plog<half2>(const half2& a) {
   float a1 = __low2float(a);
   float a2 = __high2float(a);
@@ -296,6 +320,8 @@
   return __floats2half2_rn(r1, r2);
 }
 
+#endif
+
 #elif defined EIGEN_VECTORIZE_AVX
 
 typedef struct {
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorReductionCuda.h b/unsupported/Eigen/CXX11/src/Tensor/TensorReductionCuda.h
index 4f2dfcb..7368768 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorReductionCuda.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorReductionCuda.h
@@ -291,7 +291,7 @@
   #ifdef EIGEN_HAS_CUDA_FP16
   static const bool HasOptimizedImplementation = !Op::IsStateful &&
       (internal::is_same<typename Self::CoeffReturnType, float>::value ||
-       internal::is_same<typename Self::CoeffReturnType, Eigen::half>::value);
+       (internal::is_same<typename Self::CoeffReturnType, Eigen::half>::value && Op::PacketAccess));
 #else
   static const bool HasOptimizedImplementation = !Op::IsStateful &&
                                                  internal::is_same<typename Self::CoeffReturnType, float>::value;
@@ -475,12 +475,6 @@
 
 template <typename Self, typename Op>
 struct InnerReductionLauncher {
-  // Unfortunately nvidia doesn't support well exotic types such as complex,
-  // so reduce the scope of the optimized version of the code to the simple case
-  // of floats.
-  static const bool HasOptimizedImplementation = !Op::IsStateful &&
-                                                 internal::is_same<typename Self::CoeffReturnType, float>::value;
-
   template <typename OutputType>
   static EIGEN_DEVICE_FUNC bool run(const Self&, Op&, const GpuDevice&, OutputType*, typename Self::Index, typename Self::Index) {
     assert(false && "Should only be called to reduce floats and half floats on a gpu device");
@@ -561,7 +555,7 @@
 #ifdef EIGEN_HAS_CUDA_FP16
   static const bool HasOptimizedImplementation = !Op::IsStateful &&
       (internal::is_same<typename Self::CoeffReturnType, float>::value ||
-       internal::is_same<typename Self::CoeffReturnType, Eigen::half>::value);
+       (internal::is_same<typename Self::CoeffReturnType, Eigen::half>::value && Op::PacketAccess));
 #else
   static const bool HasOptimizedImplementation = !Op::IsStateful &&
                                                  internal::is_same<typename Self::CoeffReturnType, float>::value;