diff --git a/Eigen/src/Core/arch/CUDA/Half.h b/Eigen/src/Core/arch/CUDA/Half.h
index 7f484b636..927be0493 100644
--- a/Eigen/src/Core/arch/CUDA/Half.h
+++ b/Eigen/src/Core/arch/CUDA/Half.h
@@ -175,11 +175,17 @@ __device__ bool operator != (const half& a, const half& b) {
   return __hne(a, b);
 }
 __device__ bool operator < (const half& a, const half& b) {
+  return __hlt(a, b);
+}
+__device__ bool operator <= (const half& a, const half& b) {
   return __hle(a, b);
 }
 __device__ bool operator > (const half& a, const half& b) {
   return __hgt(a, b);
 }
+__device__ bool operator >= (const half& a, const half& b) {
+  return __hge(a, b);
+}
 
 #else  // Emulate support for half floats
 
@@ -228,9 +234,15 @@ static inline EIGEN_DEVICE_FUNC bool operator != (const half& a, const half& b)
 static inline EIGEN_DEVICE_FUNC bool operator < (const half& a, const half& b) {
   return float(a) < float(b);
 }
+static inline EIGEN_DEVICE_FUNC bool operator <= (const half& a, const half& b) {
+  return float(a) <= float(b);
+}
 static inline EIGEN_DEVICE_FUNC bool operator > (const half& a, const half& b) {
   return float(a) > float(b);
 }
+static inline EIGEN_DEVICE_FUNC bool operator >= (const half& a, const half& b) {
+  return float(a) >= float(b);
+}
 
 #endif  // Emulate support for half floats