diff --git a/libcudacxx/include/cuda/std/__type_traits/is_arithmetic_integral.h b/libcudacxx/include/cuda/std/__type_traits/is_arithmetic_integral.h
index 0d4da7aa3ff..c5f73e6fb8d 100644
--- a/libcudacxx/include/cuda/std/__type_traits/is_arithmetic_integral.h
+++ b/libcudacxx/include/cuda/std/__type_traits/is_arithmetic_integral.h
@@ -24,6 +24,8 @@
 
 _LIBCUDACXX_BEGIN_NAMESPACE_STD
 
+#if defined(_CCCL_NO_VARIABLE_TEMPLATES)
+
 template <class _Tp>
 struct __is_arithmetic_integral_impl : public false_type
 {};
@@ -57,24 +59,67 @@ struct __is_arithmetic_integral_impl<long long> : public true_type
 template <>
 struct __is_arithmetic_integral_impl<unsigned long long> : public true_type
 {};
-#ifndef _LIBCUDACXX_HAS_NO_INT128
+#  if !defined(_LIBCUDACXX_HAS_NO_INT128)
 template <>
 struct __is_arithmetic_integral_impl<__int128_t> : public true_type
 {};
 template <>
 struct __is_arithmetic_integral_impl<__uint128_t> : public true_type
 {};
-#endif
+#  endif // !_LIBCUDACXX_HAS_NO_INT128
 
 template <class _Tp>
 struct _CCCL_TYPE_VISIBILITY_DEFAULT __is_arithmetic_integral
     : public integral_constant<bool, __is_arithmetic_integral_impl<remove_cv_t<_Tp>>::value>
 {};
 
-#if !defined(_CCCL_NO_VARIABLE_TEMPLATES)
+#else // ^^^ _CCCL_NO_VARIABLE_TEMPLATES ^^^ / vvv !_CCCL_NO_VARIABLE_TEMPLATES vvv
+
 template <class _Tp>
-_CCCL_INLINE_VAR constexpr bool __is_arithmetic_integral_v = __is_arithmetic_integral<_Tp>::value;
-#endif // !_CCCL_NO_VARIABLE_TEMPLATES
+_CCCL_INLINE_VAR constexpr bool __is_arithmetic_integral_v_impl = false;
+
+template <>
+_CCCL_INLINE_VAR constexpr bool __is_arithmetic_integral_v_impl<signed char> = true;
+
+template <>
+_CCCL_INLINE_VAR constexpr bool __is_arithmetic_integral_v_impl<unsigned char> = true;
+
+template <>
+_CCCL_INLINE_VAR constexpr bool __is_arithmetic_integral_v_impl<short> = true;
+
+template <>
+_CCCL_INLINE_VAR constexpr bool __is_arithmetic_integral_v_impl<unsigned short> = true;
+
+template <>
+_CCCL_INLINE_VAR constexpr bool __is_arithmetic_integral_v_impl<int> = true;
+
+template <>
+_CCCL_INLINE_VAR constexpr bool __is_arithmetic_integral_v_impl<unsigned int> = true;
+
+template <>
+_CCCL_INLINE_VAR constexpr bool __is_arithmetic_integral_v_impl<long> = true;
+
+template <>
+_CCCL_INLINE_VAR constexpr bool __is_arithmetic_integral_v_impl<unsigned long> = true;
+
+template <>
+_CCCL_INLINE_VAR constexpr bool __is_arithmetic_integral_v_impl<long long> = true;
+
+template <>
+_CCCL_INLINE_VAR constexpr bool __is_arithmetic_integral_v_impl<unsigned long long> = true;
+
+#  if !defined(_LIBCUDACXX_HAS_NO_INT128)
+template <>
+_CCCL_INLINE_VAR constexpr bool __is_arithmetic_integral_v_impl<__int128_t> = true;
+
+template <>
+_CCCL_INLINE_VAR constexpr bool __is_arithmetic_integral_v_impl<__uint128_t> = true;
+#  endif // !_LIBCUDACXX_HAS_NO_INT128
+
+template <class _Tp>
+_CCCL_INLINE_VAR constexpr bool __is_arithmetic_integral_v = __is_arithmetic_integral_v_impl<remove_cv_t<_Tp>>;
+
+#endif // ^^^ !_CCCL_NO_VARIABLE_TEMPLATES ^^^
 
 _LIBCUDACXX_END_NAMESPACE_STD