diff --git a/Eigen/Core b/Eigen/Core
index 834ff9415..7107f83d0 100644
--- a/Eigen/Core
+++ b/Eigen/Core
@@ -333,6 +333,7 @@ using std::ptrdiff_t;
 
 #if defined EIGEN_VECTORIZE_CUDA
   #include "src/Core/arch/CUDA/PacketMath.h"
+  #include "src/Core/arch/CUDA/PacketMathHalf.h"
   #include "src/Core/arch/CUDA/MathFunctions.h"
   #include "src/Core/arch/CUDA/TypeCasting.h"
 #endif
diff --git a/Eigen/src/Core/arch/CUDA/PacketMathHalf.h b/Eigen/src/Core/arch/CUDA/PacketMathHalf.h
new file mode 100644
index 000000000..7f99376fb
--- /dev/null
+++ b/Eigen/src/Core/arch/CUDA/PacketMathHalf.h
@@ -0,0 +1,220 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_PACKET_MATH_HALF_CUDA_H
+#define EIGEN_PACKET_MATH_HALF_CUDA_H
+
+namespace Eigen {
+
+namespace internal {
+
+#if defined(EIGEN_HAS_CUDA_FP16)
+
+// Make sure this is only available when targeting a GPU: we don't want to
+// introduce conflicts between these packet_traits definitions and the ones
+// we'll use on the host side (SSE, AVX, ...)
+#if defined(__CUDACC__) && defined(EIGEN_USE_GPU)
+
+#if defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 530
+
+__device__ half operator + (const half& a, const half& b) {
+  return __hadd(a, b);
+}
+__device__ half operator * (const half& a, const half& b) {
+  return __hmul(a, b);
+}
+__device__ half operator - (const half& a, const half& b) {
+  return __hsub(a, b);
+}
+__device__ half operator / (const half& a, const half& b) {
+  assert(false && "tbd");
+  return half();
+}
+__device__ half operator - (const half& a) {
+  return __hneg(a);
+}
+
+
+template<> struct is_arithmetic<half2> { enum { value = true }; };
+
+template<> struct packet_traits<half> : default_packet_traits
+{
+  typedef half2 type;
+  typedef half2 half;
+  enum {
+    Vectorizable = 1,
+    AlignedOnScalar = 1,
+    size=2,
+    HasHalfPacket = 0,
+
+    HasDiv  = 1,
+    HasLog  = 1,
+    HasExp  = 1,
+    HasSqrt = 1,
+    HasRsqrt = 1,
+    HasLGamma = 1,
+    HasDiGamma = 1,
+    HasErf = 1,
+    HasErfc = 1,
+
+    HasBlend = 0,
+  };
+};
+
+
+template<> struct unpacket_traits<half2> { typedef half type; enum {size=2, alignment=Aligned16}; typedef half2 half; };
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pset1<half2>(const half& from) {
+  return __half2half2(from);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 plset<half2>(const half& a) {
+  return __halves2half2(a, __hadd(a, __float2half(1)));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 padd<half2>(const half2& a, const half2& b) {
+  return __hadd2(a, b);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 psub<half2>(const half2& a, const half2& b) {
+  return __hsub2(a, b);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pnegate(const half2& a) {
+  return __hneg2(a);
+}
+
+template<> 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) {
+  return __hmul2(a, b);
+}
+
+ template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pmadd<half2>(const half2& a, const half2& b, const half2& c) {
+   return __hfma2(a, b, c);
+ }
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pdiv<half2>(const half2& a, const half2& b) {
+  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);
+}
+
+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);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pload<half2>(const half* from) {
+  return *reinterpret_cast<const half2*>(from);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 ploadu<half2>(const half* from) {
+  return __halves2half2(from[0], from[1]);
+}
+
+template<> EIGEN_STRONG_INLINE half2 ploaddup<half2>(const half*  from) {
+  return __halves2half2(from[0], from[0]);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pstore<half>(half* to, const half2& from) {
+  *reinterpret_cast<half2*>(to) = from;
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pstoreu<half>(half* to, const half2& from) {
+  to[0] = __low2half(from);
+  to[1] = __high2half(from);
+}
+
+template<>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE half2 ploadt_ro<half2, Aligned>(const half* from) {
+  return __ldg((const half2*)from);
+}
+
+template<>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE half2 ploadt_ro<half2, Unaligned>(const half* from) {
+  return __halves2half2(__ldg(from+0), __ldg(from+1));
+}
+
+template<> EIGEN_DEVICE_FUNC inline half2 pgather<half, half2>(const half* from, Index stride) {
+  return __halves2half2(from[0*stride], from[1*stride]);
+}
+
+template<> EIGEN_DEVICE_FUNC inline void pscatter<half, half2>(half* to, const half2& from, Index stride) {
+  to[stride*0] = __low2half(from);
+  to[stride*1] = __high2half(from);
+}
+
+template<> EIGEN_DEVICE_FUNC inline half pfirst<half2>(const half2& a) {
+  return __low2half(a);
+}
+
+template<> EIGEN_DEVICE_FUNC inline half predux<half2>(const half2& a) {
+  return __hadd(__low2half(a), __high2half(a));
+}
+
+template<> EIGEN_DEVICE_FUNC inline half predux_max<half2>(const half2& a) {
+  half first = __low2half(a);
+  half second = __high2half(a);
+  return __hgt(first, second) ? first : second;
+}
+
+template<> EIGEN_DEVICE_FUNC inline half predux_min<half2>(const half2& a) {
+  half first = __low2half(a);
+  half second = __high2half(a);
+  return __hlt(first, second) ? first : second;
+}
+
+template<> EIGEN_DEVICE_FUNC inline half predux_mul<half2>(const half2& a) {
+  return __hmul(__low2half(a), __high2half(a));
+}
+
+template<> EIGEN_DEVICE_FUNC inline half2 pabs<half2>(const half2& a) {
+  assert(false && "tbd");
+  return half2();
+}
+
+
+EIGEN_DEVICE_FUNC inline void
+ptranspose(PacketBlock<half2,2>& kernel) {
+  assert(false && "tbd");
+  //  half tmp = kernel.packet[0].y;
+  //  kernel.packet[0].y = kernel.packet[1].x;
+  //  kernel.packet[1].x = tmp;
+}
+
+#endif
+#endif
+#endif
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+
+#endif // EIGEN_PACKET_MATH_HALF_CUDA_H
diff --git a/unsupported/test/cxx11_tensor_of_float16_cuda.cu b/unsupported/test/cxx11_tensor_of_float16_cuda.cu
index aee222a14..26c18a718 100644
--- a/unsupported/test/cxx11_tensor_of_float16_cuda.cu
+++ b/unsupported/test/cxx11_tensor_of_float16_cuda.cu
@@ -20,6 +20,7 @@
 using Eigen::Tensor;
 
 #ifdef EIGEN_HAS_CUDA_FP16
+
 void test_cuda_conversion() {
   Eigen::CudaStreamDevice stream;
   Eigen::GpuDevice gpu_device(&stream);
@@ -53,11 +54,53 @@ void test_cuda_conversion() {
   gpu_device.deallocate(d_half);
   gpu_device.deallocate(d_conv);
 }
+
+void test_cuda_elementwise() {
+  Eigen::CudaStreamDevice stream;
+  Eigen::GpuDevice gpu_device(&stream);
+  int num_elem = 101;
+
+  float* d_float1 = (float*)gpu_device.allocate(num_elem * sizeof(float));
+  float* d_float2 = (float*)gpu_device.allocate(num_elem * sizeof(float));
+  float* d_res_half = (float*)gpu_device.allocate(num_elem * sizeof(float));
+  float* d_res_float = (float*)gpu_device.allocate(num_elem * sizeof(float));
+
+  Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_float1(
+      d_float1, num_elem);
+  Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_float2(
+      d_float2, num_elem);
+  Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_res_half(
+      d_res_half, num_elem);
+  Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_res_float(
+      d_res_float, num_elem);
+
+  gpu_float1.device(gpu_device) = gpu_float1.random();
+  gpu_float2.device(gpu_device) = gpu_float2.random();
+  gpu_res_float.device(gpu_device) = (gpu_float1 + gpu_float2) * gpu_float1;
+  gpu_res_half.device(gpu_device) = ((gpu_float1.cast<half>() + gpu_float2.cast<half>()) * gpu_float1.cast<half>()).cast<float>();
+
+  Tensor<float, 1> half_prec(num_elem);
+  Tensor<float, 1> full_prec(num_elem);
+  gpu_device.memcpyDeviceToHost(half_prec.data(), d_res_half, num_elem*sizeof(float));
+  gpu_device.memcpyDeviceToHost(full_prec.data(), d_res_float, num_elem*sizeof(float));
+
+  for (int i = 0; i < num_elem; ++i) {
+    VERIFY_IS_APPROX(full_prec(i), half_prec(i));
+  }
+
+  gpu_device.deallocate(d_float1);
+  gpu_device.deallocate(d_float2);
+  gpu_device.deallocate(d_res_half);
+  gpu_device.deallocate(d_res_float);
+}
+
 #endif
 
+
 void test_cxx11_tensor_of_float16_cuda()
 {
 #ifdef EIGEN_HAS_CUDA_FP16
   CALL_SUBTEST_1(test_cuda_conversion());
+  CALL_SUBTEST_1(test_cuda_element_wise());
 #endif
 }