diff --git a/Eigen/src/Core/arch/GPU/PacketMath.h b/Eigen/src/Core/arch/GPU/PacketMath.h
index e147fd1b1..e2bcf483a 100644
--- a/Eigen/src/Core/arch/GPU/PacketMath.h
+++ b/Eigen/src/Core/arch/GPU/PacketMath.h
@@ -176,11 +176,22 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float lt_mask(const float& a,
                                                     const float& b) {
   return __int_as_float(a < b ? 0xffffffffu : 0u);
 }
+
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double lt_mask(const double& a,
                                                      const double& b) {
   return __longlong_as_double(a < b ? 0xffffffffffffffffull : 0ull);
 }
 
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float le_mask(const float& a,
+                                                    const float& b) {
+  return __int_as_float(a <= b ? 0xffffffffu : 0u);
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double le_mask(const double& a,
+                                                     const double& b) {
+  return __longlong_as_double(a <= b ? 0xffffffffffffffffull : 0ull);
+}
+
 template <>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pand<float4>(const float4& a,
                                                           const float4& b) {
@@ -242,6 +253,12 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pcmp_lt<float4>(const float4& a,
                      lt_mask(a.w, b.w));
 }
 template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pcmp_le<float4>(const float4& a,
+                                                             const float4& b) {
+  return make_float4(le_mask(a.x, b.x), le_mask(a.y, b.y), le_mask(a.z, b.z),
+                     le_mask(a.w, b.w));
+}
+template <>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
 pcmp_eq<double2>(const double2& a, const double2& b) {
   return make_double2(eq_mask(a.x, b.x), eq_mask(a.y, b.y));
@@ -251,6 +268,11 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
 pcmp_lt<double2>(const double2& a, const double2& b) {
   return make_double2(lt_mask(a.x, b.x), lt_mask(a.y, b.y));
 }
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
+pcmp_le<double2>(const double2& a, const double2& b) {
+  return make_double2(le_mask(a.x, b.x), le_mask(a.y, b.y));
+}
 #endif // defined(EIGEN_CUDA_ARCH) || defined(EIGEN_HIPCC) || (defined(EIGEN_CUDACC) && EIGEN_COMP_CLANG && !EIGEN_COMP_NVCC)
 
 template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 plset<float4>(const float& a) {
@@ -676,6 +698,19 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pcmp_lt(const half2& a,
   return __halves2half2(eq1, eq2);
 }
 
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pcmp_le(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 = __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 __halves2half2(eq1, eq2);
+}
+
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pand(const half2& a,
                                                  const half2& b) {
   half a1 = __low2half(a);
@@ -1257,6 +1292,34 @@ pcmp_eq<Packet4h2>(const Packet4h2& a, const Packet4h2& b) {
   return r;
 }
 
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2
+pcmp_lt<Packet4h2>(const Packet4h2& a, const Packet4h2& b) {
+  Packet4h2 r;
+  half2* r_alias = reinterpret_cast<half2*>(&r);
+  const half2* a_alias = reinterpret_cast<const half2*>(&a);
+  const half2* b_alias = reinterpret_cast<const half2*>(&b);
+  r_alias[0] = pcmp_lt(a_alias[0], b_alias[0]);
+  r_alias[1] = pcmp_lt(a_alias[1], b_alias[1]);
+  r_alias[2] = pcmp_lt(a_alias[2], b_alias[2]);
+  r_alias[3] = pcmp_lt(a_alias[3], b_alias[3]);
+  return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2
+pcmp_le<Packet4h2>(const Packet4h2& a, const Packet4h2& b) {
+  Packet4h2 r;
+  half2* r_alias = reinterpret_cast<half2*>(&r);
+  const half2* a_alias = reinterpret_cast<const half2*>(&a);
+  const half2* b_alias = reinterpret_cast<const half2*>(&b);
+  r_alias[0] = pcmp_le(a_alias[0], b_alias[0]);
+  r_alias[1] = pcmp_le(a_alias[1], b_alias[1]);
+  r_alias[2] = pcmp_le(a_alias[2], b_alias[2]);
+  r_alias[3] = pcmp_le(a_alias[3], b_alias[3]);
+  return r;
+}
+
 template <>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 pand<Packet4h2>(
     const Packet4h2& a, const Packet4h2& b) {