diff --git a/Eigen/src/Core/MathFunctions.h b/Eigen/src/Core/MathFunctions.h
index def5428c2..ecc6f3883 100644
--- a/Eigen/src/Core/MathFunctions.h
+++ b/Eigen/src/Core/MathFunctions.h
@@ -1015,11 +1015,15 @@ template<typename T> EIGEN_DEVICE_FUNC bool isinf_msvc_helper(T x)
 }
 
 //MSVC defines a _isnan builtin function, but for double only
+#ifndef EIGEN_GPU_COMPILE_PHASE
 EIGEN_DEVICE_FUNC inline bool isnan_impl(const long double& x) { return _isnan(x)!=0; }
+#endif
 EIGEN_DEVICE_FUNC inline bool isnan_impl(const double& x)      { return _isnan(x)!=0; }
 EIGEN_DEVICE_FUNC inline bool isnan_impl(const float& x)       { return _isnan(x)!=0; }
 
+#ifndef EIGEN_GPU_COMPILE_PHASE
 EIGEN_DEVICE_FUNC inline bool isinf_impl(const long double& x) { return isinf_msvc_helper(x); }
+#endif
 EIGEN_DEVICE_FUNC inline bool isinf_impl(const double& x)      { return isinf_msvc_helper(x); }
 EIGEN_DEVICE_FUNC inline bool isinf_impl(const float& x)       { return isinf_msvc_helper(x); }
 
@@ -1033,12 +1037,16 @@ EIGEN_DEVICE_FUNC inline bool isinf_impl(const float& x)       { return isinf_ms
   #define EIGEN_TMP_NOOPT_ATTRIB EIGEN_DEVICE_FUNC inline __attribute__((noinline,optimize("no-finite-math-only")))
 #endif
 
+#ifndef EIGEN_GPU_COMPILE_PHASE
 template<> EIGEN_TMP_NOOPT_ATTRIB bool isnan_impl(const long double& x) { return __builtin_isnan(x); }
+#endif
 template<> EIGEN_TMP_NOOPT_ATTRIB bool isnan_impl(const double& x)      { return __builtin_isnan(x); }
 template<> EIGEN_TMP_NOOPT_ATTRIB bool isnan_impl(const float& x)       { return __builtin_isnan(x); }
 template<> EIGEN_TMP_NOOPT_ATTRIB bool isinf_impl(const double& x)      { return __builtin_isinf(x); }
 template<> EIGEN_TMP_NOOPT_ATTRIB bool isinf_impl(const float& x)       { return __builtin_isinf(x); }
+#ifndef EIGEN_GPU_COMPILE_PHASE
 template<> EIGEN_TMP_NOOPT_ATTRIB bool isinf_impl(const long double& x) { return __builtin_isinf(x); }
+#endif
 
 #undef EIGEN_TMP_NOOPT_ATTRIB
 
@@ -1095,6 +1103,8 @@ EIGEN_ALWAYS_INLINE double mini(const double& x, const double& y)
 {
   return fmin(x, y);
 }
+
+#ifndef EIGEN_GPU_COMPILE_PHASE
 template<>
 EIGEN_DEVICE_FUNC
 EIGEN_ALWAYS_INLINE long double mini(const long double& x, const long double& y)
@@ -1106,6 +1116,7 @@ EIGEN_ALWAYS_INLINE long double mini(const long double& x, const long double& y)
   return fminl(x, y);
 #endif
 }
+#endif
 
 template<typename T>
 EIGEN_DEVICE_FUNC
@@ -1125,6 +1136,7 @@ EIGEN_ALWAYS_INLINE double maxi(const double& x, const double& y)
 {
   return fmax(x, y);
 }
+#ifndef EIGEN_GPU_COMPILE_PHASE
 template<>
 EIGEN_DEVICE_FUNC
 EIGEN_ALWAYS_INLINE long double maxi(const long double& x, const long double& y)
@@ -1137,6 +1149,7 @@ EIGEN_ALWAYS_INLINE long double maxi(const long double& x, const long double& y)
 #endif
 }
 #endif
+#endif
 
 #if defined(SYCL_DEVICE_ONLY)
 
@@ -1300,8 +1313,8 @@ EIGEN_ALWAYS_INLINE double absdiff(const double& x, const double& y)
   return fabs(x - y);
 }
 
-#if !defined(EIGEN_GPUCC)
 // HIP and CUDA do not support long double.
+#ifndef EIGEN_GPU_COMPILE_PHASE
 template<>
 EIGEN_DEVICE_FUNC
 EIGEN_ALWAYS_INLINE long double absdiff(const long double& x, const long double& y) {
diff --git a/Eigen/src/Core/NumTraits.h b/Eigen/src/Core/NumTraits.h
index 0a32d69c0..ff33aa6fb 100644
--- a/Eigen/src/Core/NumTraits.h
+++ b/Eigen/src/Core/NumTraits.h
@@ -243,6 +243,8 @@ template<> struct NumTraits<double> : GenericNumTraits<double>
   static inline double dummy_precision() { return 1e-12; }
 };
 
+// GPU devices treat `long double` as `double`.
+#ifndef EIGEN_GPU_COMPILE_PHASE
 template<> struct NumTraits<long double>
   : GenericNumTraits<long double>
 {
@@ -259,6 +261,7 @@ template<> struct NumTraits<long double>
   }
 #endif
 };
+#endif
 
 template<typename Real_> struct NumTraits<std::complex<Real_> >
   : GenericNumTraits<std::complex<Real_> >
diff --git a/Eigen/src/Core/util/Meta.h b/Eigen/src/Core/util/Meta.h
index 1a5d515ed..740b10f94 100644
--- a/Eigen/src/Core/util/Meta.h
+++ b/Eigen/src/Core/util/Meta.h
@@ -135,7 +135,10 @@ using remove_all_t = typename remove_all<T>::type;
 template<typename T> struct is_arithmetic      { enum { value = false }; };
 template<> struct is_arithmetic<float>         { enum { value = true }; };
 template<> struct is_arithmetic<double>        { enum { value = true }; };
+// GPU devices treat `long double` as `double`.
+#ifndef EIGEN_GPU_COMPILE_PHASE
 template<> struct is_arithmetic<long double>   { enum { value = true }; };
+#endif
 template<> struct is_arithmetic<bool>          { enum { value = true }; };
 template<> struct is_arithmetic<char>          { enum { value = true }; };
 template<> struct is_arithmetic<signed char>   { enum { value = true }; };