diff --git a/Eigen/src/Core/arch/CUDA/Half.h b/Eigen/src/Core/arch/CUDA/Half.h
index c2ff207ba..4d91420d0 100644
--- a/Eigen/src/Core/arch/CUDA/Half.h
+++ b/Eigen/src/Core/arch/CUDA/Half.h
@@ -391,6 +391,9 @@ EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half exp(const half& a) {
 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half log(const half& a) {
   return half(::logf(float(a)));
 }
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half log1p(const half& a) {
+  return half(::log1pf(float(a)));
+}
 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half log10(const half& a) {
   return half(::log10f(float(a)));
 }
diff --git a/Eigen/src/Core/arch/CUDA/MathFunctions.h b/Eigen/src/Core/arch/CUDA/MathFunctions.h
index 5b5bf4c94..0348b41db 100644
--- a/Eigen/src/Core/arch/CUDA/MathFunctions.h
+++ b/Eigen/src/Core/arch/CUDA/MathFunctions.h
@@ -31,6 +31,18 @@ double2 plog<double2>(const double2& a)
   return make_double2(log(a.x), log(a.y));
 }
 
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+float4 plog1p<float4>(const float4& a)
+{
+  return make_float4(log1pf(a.x), log1pf(a.y), log1pf(a.z), log1pf(a.w));
+}
+
+template<>  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+double2 plog1p<double2>(const double2& a)
+{
+  return make_double2(log1p(a.x), log1p(a.y));
+}
+
 template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
 float4 pexp<float4>(const float4& a)
 {
diff --git a/Eigen/src/Core/arch/CUDA/PacketMathHalf.h b/Eigen/src/Core/arch/CUDA/PacketMathHalf.h
index 0bf891d24..a757ea45b 100644
--- a/Eigen/src/Core/arch/CUDA/PacketMathHalf.h
+++ b/Eigen/src/Core/arch/CUDA/PacketMathHalf.h
@@ -34,7 +34,8 @@ template<> struct packet_traits<Eigen::half> : default_packet_traits
     HasSqrt   = 1,
     HasRsqrt  = 1,
     HasExp    = 1,
-    HasLog = 1
+    HasLog    = 1,
+    HasLog1p  = 1
   };
 };
 
@@ -273,6 +274,11 @@ half2 plog<half2>(const half2& a) {
   return h2log(a);
 }
 
+template<>  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+half2 plog1p<half2>(const half2& a) {
+  return h2log1p(a);
+}
+
 template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
 half2 pexp<half2>(const half2& a) {
   return h2exp(a);
@@ -298,6 +304,14 @@ 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 plog1p<half2>(const half2& a) {
+  float a1 = __low2float(a);
+  float a2 = __high2float(a);
+  float r1 = log1pf(a1);
+  float r2 = log1pf(a2);
+  return __floats2half2_rn(r1, r2);
+}
+
 template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pexp<half2>(const half2& a) {
   float a1 = __low2float(a);
   float a2 = __high2float(a);
diff --git a/test/half_float.cpp b/test/half_float.cpp
index 6f299a346..f8d438e2f 100644
--- a/test/half_float.cpp
+++ b/test/half_float.cpp
@@ -189,6 +189,11 @@ void test_basic_functions()
   VERIFY_IS_EQUAL(float(log(half(1.0f))), 0.0f);
   VERIFY_IS_APPROX(float(numext::log(half(10.0f))), 2.30273f);
   VERIFY_IS_APPROX(float(log(half(10.0f))), 2.30273f);
+
+  VERIFY_IS_EQUAL(float(numext::log1p(half(0.0f))), 0.0f);
+  VERIFY_IS_EQUAL(float(log1p(half(0.0f))), 0.0f);
+  VERIFY_IS_APPROX(float(numext::log1p(half(10.0f))), 2.3978953f);
+  VERIFY_IS_APPROX(float(log1p(half(10.0f))), 2.3978953f);
 }
 
 void test_trigonometric_functions()
diff --git a/test/packetmath.cpp b/test/packetmath.cpp
index ea1786be2..77cbf3e5b 100644
--- a/test/packetmath.cpp
+++ b/test/packetmath.cpp
@@ -402,6 +402,7 @@ template<typename Scalar> void packetmath_real()
     data1[internal::random<int>(0, PacketSize)] = 0;
   CHECK_CWISE1_IF(PacketTraits::HasSqrt, std::sqrt, internal::psqrt);
   CHECK_CWISE1_IF(PacketTraits::HasLog, std::log, internal::plog);
+  CHECK_CWISE1_IF(PacketTraits::HasLog1p, std::log1p, internal::plog1p);
 #if EIGEN_HAS_C99_MATH && (__cplusplus > 199711L)
   CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasLGamma, std::lgamma, internal::plgamma);
   CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasErf, std::erf, internal::perf);