Use PEP 604 display for ``typing.Optional`` and ``typing.Union`` (#11072)

12 files changed, 305 insertions, 251 deletions

diff --git a/doc/extdev/deprecated.rst b/doc/extdev/deprecated.rst
index 231541392..ecfaeb648 100644
--- a/doc/extdev/deprecated.rst
+++ b/doc/extdev/deprecated.rst
@@ -22,6 +22,11 @@ The following is a list of deprecated interfaces.
      - Removed
      - Alternatives
 
+   * - ``sphinx.util.typing.stringify``
+     - 6.1
+     - 8.0
+     - ``sphinx.util.typing.stringify_annotation``
+
    * - HTML 4 support
      - 5.2
      - 7.0
diff --git a/sphinx/domains/python.py b/sphinx/domains/python.py
index e43f72b5a..d9c0d981e 100644
--- a/sphinx/domains/python.py
+++ b/sphinx/domains/python.py
@@ -176,6 +176,8 @@ def _parse_annotation(annotation: str, env: BuildEnvironment) -> list[Node]:
         elif isinstance(node, ast.Name):
             return [nodes.Text(node.id)]
         elif isinstance(node, ast.Subscript):
+            if getattr(node.value, 'id', '') in {'Optional', 'Union'}:
+                return _unparse_pep_604_annotation(node)
             result = unparse(node.value)
             result.append(addnodes.desc_sig_punctuation('', '['))
             result.extend(unparse(node.slice))
@@ -206,6 +208,28 @@ def _parse_annotation(annotation: str, env: BuildEnvironment) -> list[Node]:
         else:
             raise SyntaxError  # unsupported syntax
 
+    def _unparse_pep_604_annotation(node: ast.Subscript) -> list[Node]:
+        subscript = node.slice
+        if isinstance(subscript, ast.Index):
+            # py38 only
+            subscript = subscript.value  # type: ignore[assignment]
+
+        flattened: list[Node] = []
+        if isinstance(subscript, ast.Tuple):
+            flattened.extend(unparse(subscript.elts[0]))
+            for elt in subscript.elts[1:]:
+                flattened.extend(unparse(ast.BitOr()))
+                flattened.extend(unparse(elt))
+        else:
+            # e.g. a Union[] inside an Optional[]
+            flattened.extend(unparse(subscript))
+
+        if getattr(node.value, 'id', '') == 'Optional':
+            flattened.extend(unparse(ast.BitOr()))
+            flattened.append(nodes.Text('None'))
+
+        return flattened
+
     try:
         tree = ast.parse(annotation, type_comments=True)
         result: list[Node] = []
diff --git a/sphinx/ext/autodoc/__init__.py b/sphinx/ext/autodoc/__init__.py
index d9c0cd09a..f45fb55e0 100644
--- a/sphinx/ext/autodoc/__init__.py
+++ b/sphinx/ext/autodoc/__init__.py
@@ -27,8 +27,7 @@ from sphinx.util import inspect, logging
 from sphinx.util.docstrings import prepare_docstring, separate_metadata
 from sphinx.util.inspect import (evaluate_signature, getdoc, object_description, safe_getattr,
                                  stringify_signature)
-from sphinx.util.typing import OptionSpec, get_type_hints, restify
-from sphinx.util.typing import stringify as stringify_typehint
+from sphinx.util.typing import OptionSpec, get_type_hints, restify, stringify_annotation
 
 if TYPE_CHECKING:
     from sphinx.ext.autodoc.directive import DocumenterBridge
@@ -1902,9 +1901,10 @@ class TypeVarMixin(DataDocumenterMixinBase):
             attrs = [repr(self.object.__name__)]
             for constraint in self.object.__constraints__:
                 if self.config.autodoc_typehints_format == "short":
-                    attrs.append(stringify_typehint(constraint, "smart"))
+                    attrs.append(stringify_annotation(constraint, "smart"))
                 else:
-                    attrs.append(stringify_typehint(constraint))
+                    attrs.append(stringify_annotation(constraint,
+                                                      "fully-qualified-except-typing"))
             if self.object.__bound__:
                 if self.config.autodoc_typehints_format == "short":
                     bound = restify(self.object.__bound__, "smart")
@@ -2027,10 +2027,11 @@ class DataDocumenter(GenericAliasMixin, NewTypeMixin, TypeVarMixin,
                                              self.config.autodoc_type_aliases)
                 if self.objpath[-1] in annotations:
                     if self.config.autodoc_typehints_format == "short":
-                        objrepr = stringify_typehint(annotations.get(self.objpath[-1]),
-                                                     "smart")
+                        objrepr = stringify_annotation(annotations.get(self.objpath[-1]),
+                                                       "smart")
                     else:
-                        objrepr = stringify_typehint(annotations.get(self.objpath[-1]))
+                        objrepr = stringify_annotation(annotations.get(self.objpath[-1]),
+                                                       "fully-qualified-except-typing")
                     self.add_line('   :type: ' + objrepr, sourcename)
 
             try:
@@ -2616,10 +2617,11 @@ class AttributeDocumenter(GenericAliasMixin, NewTypeMixin, SlotsMixin,  # type:
                                              self.config.autodoc_type_aliases)
                 if self.objpath[-1] in annotations:
                     if self.config.autodoc_typehints_format == "short":
-                        objrepr = stringify_typehint(annotations.get(self.objpath[-1]),
-                                                     "smart")
+                        objrepr = stringify_annotation(annotations.get(self.objpath[-1]),
+                                                       "smart")
                     else:
-                        objrepr = stringify_typehint(annotations.get(self.objpath[-1]))
+                        objrepr = stringify_annotation(annotations.get(self.objpath[-1]),
+                                                       "fully-qualified-except-typing")
                     self.add_line('   :type: ' + objrepr, sourcename)
 
             try:
@@ -2744,9 +2746,10 @@ class PropertyDocumenter(DocstringStripSignatureMixin, ClassLevelDocumenter):  #
                                               type_aliases=self.config.autodoc_type_aliases)
                 if signature.return_annotation is not Parameter.empty:
                     if self.config.autodoc_typehints_format == "short":
-                        objrepr = stringify_typehint(signature.return_annotation, "smart")
+                        objrepr = stringify_annotation(signature.return_annotation, "smart")
                     else:
-                        objrepr = stringify_typehint(signature.return_annotation)
+                        objrepr = stringify_annotation(signature.return_annotation,
+                                                       "fully-qualified-except-typing")
                     self.add_line('   :type: ' + objrepr, sourcename)
             except TypeError as exc:
                 logger.warning(__("Failed to get a function signature for %s: %s"),
diff --git a/sphinx/ext/autodoc/typehints.py b/sphinx/ext/autodoc/typehints.py
index 905bfc2af..903883dce 100644
--- a/sphinx/ext/autodoc/typehints.py
+++ b/sphinx/ext/autodoc/typehints.py
@@ -12,7 +12,8 @@ from docutils.nodes import Element
 import sphinx
 from sphinx import addnodes
 from sphinx.application import Sphinx
-from sphinx.util import inspect, typing
+from sphinx.util import inspect
+from sphinx.util.typing import stringify_annotation
 
 
 def record_typehints(app: Sphinx, objtype: str, name: str, obj: Any,
@@ -30,9 +31,9 @@ def record_typehints(app: Sphinx, objtype: str, name: str, obj: Any,
             sig = inspect.signature(obj, type_aliases=app.config.autodoc_type_aliases)
             for param in sig.parameters.values():
                 if param.annotation is not param.empty:
-                    annotation[param.name] = typing.stringify(param.annotation, mode)
+                    annotation[param.name] = stringify_annotation(param.annotation, mode)
             if sig.return_annotation is not sig.empty:
-                annotation['return'] = typing.stringify(sig.return_annotation, mode)
+                annotation['return'] = stringify_annotation(sig.return_annotation, mode)
     except (TypeError, ValueError):
         pass
 
diff --git a/sphinx/ext/napoleon/docstring.py b/sphinx/ext/napoleon/docstring.py
index 0335ec4f8..5eb6546a4 100644
--- a/sphinx/ext/napoleon/docstring.py
+++ b/sphinx/ext/napoleon/docstring.py
@@ -12,8 +12,7 @@ from sphinx.application import Sphinx
 from sphinx.config import Config as SphinxConfig
 from sphinx.locale import _, __
 from sphinx.util import logging
-from sphinx.util.inspect import stringify_annotation
-from sphinx.util.typing import get_type_hints
+from sphinx.util.typing import get_type_hints, stringify_annotation
 
 logger = logging.getLogger(__name__)
 
@@ -876,7 +875,8 @@ class GoogleDocstring:
                                    ) or {})
                     self._annotations = get_type_hints(self._obj, None, localns)
                 if _name in self._annotations:
-                    return stringify_annotation(self._annotations[_name])
+                    return stringify_annotation(self._annotations[_name],
+                                                'fully-qualified-except-typing')
         # No annotation found
         return ""
 
diff --git a/sphinx/util/inspect.py b/sphinx/util/inspect.py
index 7c0a9f066..26922519a 100644
--- a/sphinx/util/inspect.py
+++ b/sphinx/util/inspect.py
@@ -22,8 +22,7 @@ from typing import Any, Callable, Dict, Mapping, Sequence, cast
 
 from sphinx.pycode.ast import unparse as ast_unparse
 from sphinx.util import logging
-from sphinx.util.typing import ForwardRef
-from sphinx.util.typing import stringify as stringify_annotation
+from sphinx.util.typing import ForwardRef, stringify_annotation
 
 logger = logging.getLogger(__name__)
 
diff --git a/sphinx/util/typing.py b/sphinx/util/typing.py
index 53f32ed46..282230e0c 100644
--- a/sphinx/util/typing.py
+++ b/sphinx/util/typing.py
@@ -11,6 +11,8 @@ from typing import Any, Callable, Dict, ForwardRef, List, Tuple, TypeVar, Union
 from docutils import nodes
 from docutils.parsers.rst.states import Inliner
 
+from sphinx.deprecation import RemovedInSphinx80Warning, deprecated_alias
+
 try:
     from types import UnionType  # type: ignore  # python 3.10 or above
 except ImportError:
@@ -205,9 +207,14 @@ def restify(cls: type | None, mode: str = 'fully-qualified-except-typing') -> st
         return inspect.object_description(cls)
 
 
-def stringify(annotation: Any, mode: str = 'fully-qualified-except-typing') -> str:
+def stringify_annotation(
+    annotation: Any,
+    /,
+    mode: str = 'fully-qualified-except-typing',
+) -> str:
     """Stringify type annotation object.
 
+    :param annotation: The annotation to stringified.
     :param mode: Specify a method how annotations will be stringified.
 
                  'fully-qualified-except-typing'
@@ -219,12 +226,20 @@ def stringify(annotation: Any, mode: str = 'fully-qualified-except-typing') -> s
                      Show the module name and qualified name of the annotation.
     """
     from sphinx.ext.autodoc.mock import ismock, ismockmodule  # lazy loading
-    from sphinx.util import inspect  # lazy loading
+    from sphinx.util.inspect import isNewType  # lazy loading
+
+    if mode not in {'fully-qualified-except-typing', 'fully-qualified', 'smart'}:
+        raise ValueError("'mode' must be one of 'fully-qualified-except-typing', "
+                         f"'fully-qualified', or 'smart'; got {mode!r}.")
 
     if mode == 'smart':
-        modprefix = '~'
+        module_prefix = '~'
     else:
-        modprefix = ''
+        module_prefix = ''
+
+    annotation_qualname = getattr(annotation, '__qualname__', '')
+    annotation_module = getattr(annotation, '__module__', '')
+    annotation_name = getattr(annotation, '__name__', '')
 
     if isinstance(annotation, str):
         if annotation.startswith("'") and annotation.endswith("'"):
@@ -233,104 +248,105 @@ def stringify(annotation: Any, mode: str = 'fully-qualified-except-typing') -> s
         else:
             return annotation
     elif isinstance(annotation, TypeVar):
-        if (annotation.__module__ == 'typing' and
-                mode in ('fully-qualified-except-typing', 'smart')):
-            return annotation.__name__
+        if (annotation_module == 'typing'
+                and mode in {'fully-qualified-except-typing', 'smart'}):
+            return annotation_name
         else:
-            return modprefix + '.'.join([annotation.__module__, annotation.__name__])
-    elif inspect.isNewType(annotation):
+            return module_prefix + f'{annotation_module}.{annotation_name}'
+    elif isNewType(annotation):
         if sys.version_info[:2] >= (3, 10):
             # newtypes have correct module info since Python 3.10+
-            return modprefix + f'{annotation.__module__}.{annotation.__name__}'
+            return module_prefix + f'{annotation_module}.{annotation_name}'
         else:
-            return annotation.__name__
+            return annotation_name
     elif not annotation:
         return repr(annotation)
     elif annotation is NoneType:
         return 'None'
     elif ismockmodule(annotation):
-        return modprefix + annotation.__name__
+        return module_prefix + annotation_name
     elif ismock(annotation):
-        return modprefix + f'{annotation.__module__}.{annotation.__name__}'
+        return module_prefix + f'{annotation_module}.{annotation_name}'
     elif is_invalid_builtin_class(annotation):
-        return modprefix + INVALID_BUILTIN_CLASSES[annotation]
+        return module_prefix + INVALID_BUILTIN_CLASSES[annotation]
     elif str(annotation).startswith('typing.Annotated'):  # for py310+
         pass
-    elif (getattr(annotation, '__module__', None) == 'builtins' and
-          getattr(annotation, '__qualname__', None)):
+    elif annotation_module == 'builtins' and annotation_qualname:
         if hasattr(annotation, '__args__'):  # PEP 585 generic
             return repr(annotation)
         else:
-            return annotation.__qualname__
+            return annotation_qualname
     elif annotation is Ellipsis:
         return '...'
 
-    module = getattr(annotation, '__module__', None)
-    modprefix = ''
-    if module == 'typing' and getattr(annotation, '__forward_arg__', None):
-        qualname = annotation.__forward_arg__
-    elif module == 'typing':
-        if getattr(annotation, '_name', None):
-            qualname = annotation._name
-        elif getattr(annotation, '__qualname__', None):
-            qualname = annotation.__qualname__
-        else:
-            qualname = stringify(annotation.__origin__).replace('typing.', '')  # ex. Union
-
+    module_prefix = ''
+    annotation_forward_arg = getattr(annotation, '__forward_arg__', None)
+    if (annotation_qualname
+            or (annotation_module == 'typing' and not annotation_forward_arg)):
         if mode == 'smart':
-            modprefix = '~%s.' % module
+            module_prefix = f'~{annotation_module}.'
         elif mode == 'fully-qualified':
-            modprefix = '%s.' % module
-    elif hasattr(annotation, '__qualname__'):
-        if mode == 'smart':
-            modprefix = '~%s.' % module
+            module_prefix = f'{annotation_module}.'
+        elif annotation_module != 'typing' and mode == 'fully-qualified-except-typing':
+            module_prefix = f'{annotation_module}.'
+
+    if annotation_module == 'typing':
+        if annotation_forward_arg:
+            # handle ForwardRefs
+            qualname = annotation_forward_arg
         else:
-            modprefix = '%s.' % module
-        qualname = annotation.__qualname__
+            _name = getattr(annotation, '_name', '')
+            if _name:
+                qualname = _name
+            elif annotation_qualname:
+                qualname = annotation_qualname
+            else:
+                qualname = stringify_annotation(
+                    annotation.__origin__, 'fully-qualified-except-typing'
+                ).replace('typing.', '')  # ex. Union
+    elif annotation_qualname:
+        qualname = annotation_qualname
     elif hasattr(annotation, '__origin__'):
         # instantiated generic provided by a user
-        qualname = stringify(annotation.__origin__, mode)
-    elif UnionType and isinstance(annotation, UnionType):  # types.Union (for py3.10+)
-        qualname = 'types.Union'
+        qualname = stringify_annotation(annotation.__origin__, mode)
+    elif UnionType and isinstance(annotation, UnionType):  # types.UnionType (for py3.10+)
+        qualname = 'types.UnionType'
     else:
         # we weren't able to extract the base type, appending arguments would
         # only make them appear twice
         return repr(annotation)
 
-    if getattr(annotation, '__args__', None):
-        if not isinstance(annotation.__args__, (list, tuple)):
+    annotation_args = getattr(annotation, '__args__', None)
+    if annotation_args:
+        if not isinstance(annotation_args, (list, tuple)):
             # broken __args__ found
             pass
-        elif qualname in ('Optional', 'Union'):
-            if len(annotation.__args__) > 1 and annotation.__args__[-1] is NoneType:
-                if len(annotation.__args__) > 2:
-                    args = ', '.join(stringify(a, mode) for a in annotation.__args__[:-1])
-                    return f'{modprefix}Optional[{modprefix}Union[{args}]]'
-                else:
-                    return f'{modprefix}Optional[{stringify(annotation.__args__[0], mode)}]'
-            else:
-                args = ', '.join(stringify(a, mode) for a in annotation.__args__)
-                return f'{modprefix}Union[{args}]'
-        elif qualname == 'types.Union':
-            if len(annotation.__args__) > 1 and None in annotation.__args__:
-                args = ' | '.join(stringify(a) for a in annotation.__args__ if a)
-                return f'{modprefix}Optional[{args}]'
-            else:
-                return ' | '.join(stringify(a) for a in annotation.__args__)
+        elif qualname in {'Optional', 'Union', 'types.UnionType'}:
+            return ' | '.join(stringify_annotation(a, mode) for a in annotation_args)
         elif qualname == 'Callable':
-            args = ', '.join(stringify(a, mode) for a in annotation.__args__[:-1])
-            returns = stringify(annotation.__args__[-1], mode)
-            return f'{modprefix}{qualname}[[{args}], {returns}]'
+            args = ', '.join(stringify_annotation(a, mode) for a in annotation_args[:-1])
+            returns = stringify_annotation(annotation_args[-1], mode)
+            return f'{module_prefix}Callable[[{args}], {returns}]'
         elif qualname == 'Literal':
-            args = ', '.join(repr(a) for a in annotation.__args__)
-            return f'{modprefix}{qualname}[{args}]'
+            args = ', '.join(repr(a) for a in annotation_args)
+            return f'{module_prefix}Literal[{args}]'
         elif str(annotation).startswith('typing.Annotated'):  # for py39+
-            return stringify(annotation.__args__[0], mode)
-        elif all(is_system_TypeVar(a) for a in annotation.__args__):
+            return stringify_annotation(annotation_args[0], mode)
+        elif all(is_system_TypeVar(a) for a in annotation_args):
             # Suppress arguments if all system defined TypeVars (ex. Dict[KT, VT])
-            return modprefix + qualname
+            return module_prefix + qualname
         else:
-            args = ', '.join(stringify(a, mode) for a in annotation.__args__)
-            return f'{modprefix}{qualname}[{args}]'
+            args = ', '.join(stringify_annotation(a, mode) for a in annotation_args)
+            return f'{module_prefix}{qualname}[{args}]'
+
+    return module_prefix + qualname
+
 
-    return modprefix + qualname
+deprecated_alias(__name__,
+                 {
+                     'stringify': stringify_annotation,
+                 },
+                 RemovedInSphinx80Warning,
+                 {
+                     'stringify': 'sphinx.util.typing.stringify_annotation',
+                 })
diff --git a/tests/test_domain_py.py b/tests/test_domain_py.py
index c4b87c737..19fcfd36f 100644
--- a/tests/test_domain_py.py
+++ b/tests/test_domain_py.py
@@ -866,10 +866,11 @@ def test_pyattribute(app):
     assert_node(doctree[1][1][1], ([desc_signature, ([desc_name, "attr"],
                                                      [desc_annotation, ([desc_sig_punctuation, ':'],
                                                                         desc_sig_space,
-                                                                        [pending_xref, "Optional"],
-                                                                        [desc_sig_punctuation, "["],
                                                                         [pending_xref, "str"],
-                                                                        [desc_sig_punctuation, "]"])],
+                                                                        desc_sig_space,
+                                                                        [desc_sig_punctuation, "|"],
+                                                                        desc_sig_space,
+                                                                        [pending_xref, "None"])],
                                                      [desc_annotation, (desc_sig_space,
                                                                         [desc_sig_punctuation, '='],
                                                                         desc_sig_space,
@@ -877,7 +878,7 @@ def test_pyattribute(app):
                                                      )],
                                    [desc_content, ()]))
     assert_node(doctree[1][1][1][0][1][2], pending_xref, **{"py:class": "Class"})
-    assert_node(doctree[1][1][1][0][1][4], pending_xref, **{"py:class": "Class"})
+    assert_node(doctree[1][1][1][0][1][6], pending_xref, **{"py:class": "Class"})
     assert 'Class.attr' in domain.objects
     assert domain.objects['Class.attr'] == ('index', 'Class.attr', 'attribute', False)
 
diff --git a/tests/test_ext_autodoc.py b/tests/test_ext_autodoc.py
index ec4388bf0..8f723deb4 100644
--- a/tests/test_ext_autodoc.py
+++ b/tests/test_ext_autodoc.py
@@ -808,7 +808,7 @@ def test_autodoc_imported_members(app):
                "imported-members": None,
                "ignore-module-all": None}
     actual = do_autodoc(app, 'module', 'target', options)
-    assert '.. py:function:: function_to_be_imported(app: ~typing.Optional[Sphinx]) -> str' in actual
+    assert '.. py:function:: function_to_be_imported(app: Sphinx | None) -> str' in actual
 
 
 @pytest.mark.sphinx('html', testroot='ext-autodoc')
diff --git a/tests/test_ext_autodoc_configs.py b/tests/test_ext_autodoc_configs.py
index 7ce8ed3d6..aa6a357a3 100644
--- a/tests/test_ext_autodoc_configs.py
+++ b/tests/test_ext_autodoc_configs.py
@@ -662,7 +662,7 @@ def test_mocked_module_imports(app, warning):
                     confoverrides={'autodoc_typehints': "signature"})
 def test_autodoc_typehints_signature(app):
     if sys.version_info[:2] <= (3, 10):
-        type_o = "~typing.Optional[~typing.Any]"
+        type_o = "~typing.Any | None"
     else:
         type_o = "~typing.Any"
 
@@ -1304,7 +1304,7 @@ def test_autodoc_type_aliases(app):
         '',
         '.. py:data:: variable3',
         '   :module: target.autodoc_type_aliases',
-        '   :type: ~typing.Optional[int]',
+        '   :type: int | None',
         '',
         '   docstring',
         '',
@@ -1375,7 +1375,7 @@ def test_autodoc_type_aliases(app):
         '',
         '.. py:data:: variable3',
         '   :module: target.autodoc_type_aliases',
-        '   :type: ~typing.Optional[myint]',
+        '   :type: myint | None',
         '',
         '   docstring',
         '',
@@ -1409,7 +1409,7 @@ def test_autodoc_typehints_description_and_type_aliases(app):
                     confoverrides={'autodoc_typehints_format': "fully-qualified"})
 def test_autodoc_typehints_format_fully_qualified(app):
     if sys.version_info[:2] <= (3, 10):
-        type_o = "typing.Optional[typing.Any]"
+        type_o = "typing.Any | None"
     else:
         type_o = "typing.Any"
 
diff --git a/tests/test_util_inspect.py b/tests/test_util_inspect.py
index c7f9914cc..089804630 100644
--- a/tests/test_util_inspect.py
+++ b/tests/test_util_inspect.py
@@ -15,15 +15,15 @@ import pytest
 
 from sphinx.util import inspect
 from sphinx.util.inspect import TypeAliasForwardRef, TypeAliasNamespace, stringify_signature
-from sphinx.util.typing import stringify
+from sphinx.util.typing import stringify_annotation
 
 
 def test_TypeAliasForwardRef():
     alias = TypeAliasForwardRef('example')
-    assert stringify(alias) == 'example'
+    assert stringify_annotation(alias, 'fully-qualified-except-typing') == 'example'
 
     alias = Optional[alias]
-    assert stringify(alias) == 'Optional[example]'
+    assert stringify_annotation(alias, 'fully-qualified-except-typing') == 'example | None'
 
 
 def test_TypeAliasNamespace():
@@ -173,7 +173,7 @@ def test_signature_annotations():
 
     # Union types
     sig = inspect.signature(f3)
-    assert stringify_signature(sig) == '(x: typing.Union[str, numbers.Integral]) -> None'
+    assert stringify_signature(sig) == '(x: str | numbers.Integral) -> None'
 
     # Quoted annotations
     sig = inspect.signature(f4)
@@ -190,7 +190,7 @@ def test_signature_annotations():
     # Space around '=' for defaults
     sig = inspect.signature(f7)
     if sys.version_info[:2] <= (3, 10):
-        assert stringify_signature(sig) == '(x: typing.Optional[int] = None, y: dict = {}) -> None'
+        assert stringify_signature(sig) == '(x: int | None = None, y: dict = {}) -> None'
     else:
         assert stringify_signature(sig) == '(x: int = None, y: dict = {}) -> None'
 
@@ -215,12 +215,12 @@ def test_signature_annotations():
 
     # optional
     sig = inspect.signature(f13)
-    assert stringify_signature(sig) == '() -> typing.Optional[str]'
+    assert stringify_signature(sig) == '() -> str | None'
 
     # optional union
     sig = inspect.signature(f20)
-    assert stringify_signature(sig) in ('() -> typing.Optional[typing.Union[int, str]]',
-                                        '() -> typing.Optional[typing.Union[str, int]]')
+    assert stringify_signature(sig) in ('() -> int | str | None',
+                                        '() -> str | int | None')
 
     # Any
     sig = inspect.signature(f14)
@@ -239,7 +239,7 @@ def test_signature_annotations():
     assert stringify_signature(sig) == '(*, arg3, arg4)'
 
     sig = inspect.signature(f18)
-    assert stringify_signature(sig) == ('(self, arg1: typing.Union[int, typing.Tuple] = 10) -> '
+    assert stringify_signature(sig) == ('(self, arg1: int | typing.Tuple = 10) -> '
                                         'typing.List[typing.Dict]')
 
     # annotations for variadic and keyword parameters
@@ -255,7 +255,7 @@ def test_signature_annotations():
     assert stringify_signature(sig) == '(self) -> typing.List[tests.typing_test_data.Node]'
 
     sig = inspect.signature(Node.__init__)
-    assert stringify_signature(sig) == '(self, parent: typing.Optional[tests.typing_test_data.Node]) -> None'
+    assert stringify_signature(sig) == '(self, parent: tests.typing_test_data.Node | None) -> None'
 
     # show_annotation is False
     sig = inspect.signature(f7)
@@ -264,14 +264,14 @@ def test_signature_annotations():
     # show_return_annotation is False
     sig = inspect.signature(f7)
     if sys.version_info[:2] <= (3, 10):
-        assert stringify_signature(sig, show_return_annotation=False) == '(x: typing.Optional[int] = None, y: dict = {})'
+        assert stringify_signature(sig, show_return_annotation=False) == '(x: int | None = None, y: dict = {})'
     else:
         assert stringify_signature(sig, show_return_annotation=False) == '(x: int = None, y: dict = {})'
 
     # unqualified_typehints is True
     sig = inspect.signature(f7)
     if sys.version_info[:2] <= (3, 10):
-        assert stringify_signature(sig, unqualified_typehints=True) == '(x: ~typing.Optional[int] = None, y: dict = {}) -> None'
+        assert stringify_signature(sig, unqualified_typehints=True) == '(x: int | None = None, y: dict = {}) -> None'
     else:
         assert stringify_signature(sig, unqualified_typehints=True) == '(x: int = None, y: dict = {}) -> None'
 
diff --git a/tests/test_util_typing.py b/tests/test_util_typing.py
index 0cca1913e..89afb0021 100644
--- a/tests/test_util_typing.py
+++ b/tests/test_util_typing.py
@@ -10,7 +10,7 @@ from typing import (Any, Callable, Dict, Generator, List, NewType, Optional, Tup
 import pytest
 
 from sphinx.ext.autodoc import mock
-from sphinx.util.typing import restify, stringify
+from sphinx.util.typing import restify, stringify_annotation
 
 
 class MyClass1:
@@ -198,169 +198,174 @@ def test_restify_mock():
         assert restify(unknown.secret.Class, "smart") == ':py:class:`~unknown.secret.Class`'
 
 
-def test_stringify():
-    assert stringify(int) == "int"
-    assert stringify(int, "smart") == "int"
+def test_stringify_annotation():
+    assert stringify_annotation(int, 'fully-qualified-except-typing') == "int"
+    assert stringify_annotation(int, "smart") == "int"
 
-    assert stringify(str) == "str"
-    assert stringify(str, "smart") == "str"
+    assert stringify_annotation(str, 'fully-qualified-except-typing') == "str"
+    assert stringify_annotation(str, "smart") == "str"
 
-    assert stringify(None) == "None"
-    assert stringify(None, "smart") == "None"
+    assert stringify_annotation(None, 'fully-qualified-except-typing') == "None"
+    assert stringify_annotation(None, "smart") == "None"
 
-    assert stringify(Integral) == "numbers.Integral"
-    assert stringify(Integral, "smart") == "~numbers.Integral"
+    assert stringify_annotation(Integral, 'fully-qualified-except-typing') == "numbers.Integral"
+    assert stringify_annotation(Integral, "smart") == "~numbers.Integral"
 
-    assert stringify(Struct) == "struct.Struct"
-    assert stringify(Struct, "smart") == "~struct.Struct"
+    assert stringify_annotation(Struct, 'fully-qualified-except-typing') == "struct.Struct"
+    assert stringify_annotation(Struct, "smart") == "~struct.Struct"
 
-    assert stringify(TracebackType) == "types.TracebackType"
-    assert stringify(TracebackType, "smart") == "~types.TracebackType"
+    assert stringify_annotation(TracebackType, 'fully-qualified-except-typing') == "types.TracebackType"
+    assert stringify_annotation(TracebackType, "smart") == "~types.TracebackType"
 
-    assert stringify(Any) == "Any"
-    assert stringify(Any, "fully-qualified") == "typing.Any"
-    assert stringify(Any, "smart") == "~typing.Any"
+    assert stringify_annotation(Any, 'fully-qualified-except-typing') == "Any"
+    assert stringify_annotation(Any, "fully-qualified") == "typing.Any"
+    assert stringify_annotation(Any, "smart") == "~typing.Any"
 
 
 def test_stringify_type_hints_containers():
-    assert stringify(List) == "List"
-    assert stringify(List, "fully-qualified") == "typing.List"
-    assert stringify(List, "smart") == "~typing.List"
+    assert stringify_annotation(List, 'fully-qualified-except-typing') == "List"
+    assert stringify_annotation(List, "fully-qualified") == "typing.List"
+    assert stringify_annotation(List, "smart") == "~typing.List"
 
-    assert stringify(Dict) == "Dict"
-    assert stringify(Dict, "fully-qualified") == "typing.Dict"
-    assert stringify(Dict, "smart") == "~typing.Dict"
+    assert stringify_annotation(Dict, 'fully-qualified-except-typing') == "Dict"
+    assert stringify_annotation(Dict, "fully-qualified") == "typing.Dict"
+    assert stringify_annotation(Dict, "smart") == "~typing.Dict"
 
-    assert stringify(List[int]) == "List[int]"
-    assert stringify(List[int], "fully-qualified") == "typing.List[int]"
-    assert stringify(List[int], "smart") == "~typing.List[int]"
+    assert stringify_annotation(List[int], 'fully-qualified-except-typing') == "List[int]"
+    assert stringify_annotation(List[int], "fully-qualified") == "typing.List[int]"
+    assert stringify_annotation(List[int], "smart") == "~typing.List[int]"
 
-    assert stringify(List[str]) == "List[str]"
-    assert stringify(List[str], "fully-qualified") == "typing.List[str]"
-    assert stringify(List[str], "smart") == "~typing.List[str]"
+    assert stringify_annotation(List[str], 'fully-qualified-except-typing') == "List[str]"
+    assert stringify_annotation(List[str], "fully-qualified") == "typing.List[str]"
+    assert stringify_annotation(List[str], "smart") == "~typing.List[str]"
 
-    assert stringify(Dict[str, float]) == "Dict[str, float]"
-    assert stringify(Dict[str, float], "fully-qualified") == "typing.Dict[str, float]"
-    assert stringify(Dict[str, float], "smart") == "~typing.Dict[str, float]"
+    assert stringify_annotation(Dict[str, float], 'fully-qualified-except-typing') == "Dict[str, float]"
+    assert stringify_annotation(Dict[str, float], "fully-qualified") == "typing.Dict[str, float]"
+    assert stringify_annotation(Dict[str, float], "smart") == "~typing.Dict[str, float]"
 
-    assert stringify(Tuple[str, str, str]) == "Tuple[str, str, str]"
-    assert stringify(Tuple[str, str, str], "fully-qualified") == "typing.Tuple[str, str, str]"
-    assert stringify(Tuple[str, str, str], "smart") == "~typing.Tuple[str, str, str]"
+    assert stringify_annotation(Tuple[str, str, str], 'fully-qualified-except-typing') == "Tuple[str, str, str]"
+    assert stringify_annotation(Tuple[str, str, str], "fully-qualified") == "typing.Tuple[str, str, str]"
+    assert stringify_annotation(Tuple[str, str, str], "smart") == "~typing.Tuple[str, str, str]"
 
-    assert stringify(Tuple[str, ...]) == "Tuple[str, ...]"
-    assert stringify(Tuple[str, ...], "fully-qualified") == "typing.Tuple[str, ...]"
-    assert stringify(Tuple[str, ...], "smart") == "~typing.Tuple[str, ...]"
+    assert stringify_annotation(Tuple[str, ...], 'fully-qualified-except-typing') == "Tuple[str, ...]"
+    assert stringify_annotation(Tuple[str, ...], "fully-qualified") == "typing.Tuple[str, ...]"
+    assert stringify_annotation(Tuple[str, ...], "smart") == "~typing.Tuple[str, ...]"
 
     if sys.version_info[:2] <= (3, 10):
-        assert stringify(Tuple[()]) == "Tuple[()]"
-        assert stringify(Tuple[()], "fully-qualified") == "typing.Tuple[()]"
-        assert stringify(Tuple[()], "smart") == "~typing.Tuple[()]"
+        assert stringify_annotation(Tuple[()], 'fully-qualified-except-typing') == "Tuple[()]"
+        assert stringify_annotation(Tuple[()], "fully-qualified") == "typing.Tuple[()]"
+        assert stringify_annotation(Tuple[()], "smart") == "~typing.Tuple[()]"
     else:
-        assert stringify(Tuple[()]) == "Tuple"
-        assert stringify(Tuple[()], "fully-qualified") == "typing.Tuple"
-        assert stringify(Tuple[()], "smart") == "~typing.Tuple"
+        assert stringify_annotation(Tuple[()], 'fully-qualified-except-typing') == "Tuple"
+        assert stringify_annotation(Tuple[()], "fully-qualified") == "typing.Tuple"
+        assert stringify_annotation(Tuple[()], "smart") == "~typing.Tuple"
 
-    assert stringify(List[Dict[str, Tuple]]) == "List[Dict[str, Tuple]]"
-    assert stringify(List[Dict[str, Tuple]], "fully-qualified") == "typing.List[typing.Dict[str, typing.Tuple]]"
-    assert stringify(List[Dict[str, Tuple]], "smart") == "~typing.List[~typing.Dict[str, ~typing.Tuple]]"
+    assert stringify_annotation(List[Dict[str, Tuple]], 'fully-qualified-except-typing') == "List[Dict[str, Tuple]]"
+    assert stringify_annotation(List[Dict[str, Tuple]], "fully-qualified") == "typing.List[typing.Dict[str, typing.Tuple]]"
+    assert stringify_annotation(List[Dict[str, Tuple]], "smart") == "~typing.List[~typing.Dict[str, ~typing.Tuple]]"
 
-    assert stringify(MyList[Tuple[int, int]]) == "tests.test_util_typing.MyList[Tuple[int, int]]"
-    assert stringify(MyList[Tuple[int, int]], "fully-qualified") == "tests.test_util_typing.MyList[typing.Tuple[int, int]]"
-    assert stringify(MyList[Tuple[int, int]], "smart") == "~tests.test_util_typing.MyList[~typing.Tuple[int, int]]"
+    assert stringify_annotation(MyList[Tuple[int, int]], 'fully-qualified-except-typing') == "tests.test_util_typing.MyList[Tuple[int, int]]"
+    assert stringify_annotation(MyList[Tuple[int, int]], "fully-qualified") == "tests.test_util_typing.MyList[typing.Tuple[int, int]]"
+    assert stringify_annotation(MyList[Tuple[int, int]], "smart") == "~tests.test_util_typing.MyList[~typing.Tuple[int, int]]"
 
-    assert stringify(Generator[None, None, None]) == "Generator[None, None, None]"
-    assert stringify(Generator[None, None, None], "fully-qualified") == "typing.Generator[None, None, None]"
-    assert stringify(Generator[None, None, None], "smart") == "~typing.Generator[None, None, None]"
+    assert stringify_annotation(Generator[None, None, None], 'fully-qualified-except-typing') == "Generator[None, None, None]"
+    assert stringify_annotation(Generator[None, None, None], "fully-qualified") == "typing.Generator[None, None, None]"
+    assert stringify_annotation(Generator[None, None, None], "smart") == "~typing.Generator[None, None, None]"
 
 
 @pytest.mark.skipif(sys.version_info[:2] <= (3, 8), reason='python 3.9+ is required.')
 def test_stringify_type_hints_pep_585():
-    assert stringify(list[int]) == "list[int]"
-    assert stringify(list[int], "smart") == "list[int]"
+    assert stringify_annotation(list[int], 'fully-qualified-except-typing') == "list[int]"
+    assert stringify_annotation(list[int], "smart") == "list[int]"
 
-    assert stringify(list[str]) == "list[str]"
-    assert stringify(list[str], "smart") == "list[str]"
+    assert stringify_annotation(list[str], 'fully-qualified-except-typing') == "list[str]"
+    assert stringify_annotation(list[str], "smart") == "list[str]"
 
-    assert stringify(dict[str, float]) == "dict[str, float]"
-    assert stringify(dict[str, float], "smart") == "dict[str, float]"
+    assert stringify_annotation(dict[str, float], 'fully-qualified-except-typing') == "dict[str, float]"
+    assert stringify_annotation(dict[str, float], "smart") == "dict[str, float]"
 
-    assert stringify(tuple[str, str, str]) == "tuple[str, str, str]"
-    assert stringify(tuple[str, str, str], "smart") == "tuple[str, str, str]"
+    assert stringify_annotation(tuple[str, str, str], 'fully-qualified-except-typing') == "tuple[str, str, str]"
+    assert stringify_annotation(tuple[str, str, str], "smart") == "tuple[str, str, str]"
 
-    assert stringify(tuple[str, ...]) == "tuple[str, ...]"
-    assert stringify(tuple[str, ...], "smart") == "tuple[str, ...]"
+    assert stringify_annotation(tuple[str, ...], 'fully-qualified-except-typing') == "tuple[str, ...]"
+    assert stringify_annotation(tuple[str, ...], "smart") == "tuple[str, ...]"
 
-    assert stringify(tuple[()]) == "tuple[()]"
-    assert stringify(tuple[()], "smart") == "tuple[()]"
+    assert stringify_annotation(tuple[()], 'fully-qualified-except-typing') == "tuple[()]"
+    assert stringify_annotation(tuple[()], "smart") == "tuple[()]"
 
-    assert stringify(list[dict[str, tuple]]) == "list[dict[str, tuple]]"
-    assert stringify(list[dict[str, tuple]], "smart") == "list[dict[str, tuple]]"
+    assert stringify_annotation(list[dict[str, tuple]], 'fully-qualified-except-typing') == "list[dict[str, tuple]]"
+    assert stringify_annotation(list[dict[str, tuple]], "smart") == "list[dict[str, tuple]]"
 
-    assert stringify(type[int]) == "type[int]"
-    assert stringify(type[int], "smart") == "type[int]"
+    assert stringify_annotation(type[int], 'fully-qualified-except-typing') == "type[int]"
+    assert stringify_annotation(type[int], "smart") == "type[int]"
 
 
 @pytest.mark.skipif(sys.version_info[:2] <= (3, 8), reason='python 3.9+ is required.')
 def test_stringify_Annotated():
     from typing import Annotated  # type: ignore
-    assert stringify(Annotated[str, "foo", "bar"]) == "str"
-    assert stringify(Annotated[str, "foo", "bar"], "smart") == "str"
+    assert stringify_annotation(Annotated[str, "foo", "bar"], 'fully-qualified-except-typing') == "str"
+    assert stringify_annotation(Annotated[str, "foo", "bar"], "smart") == "str"
 
 
 def test_stringify_type_hints_string():
-    assert stringify("int") == "int"
-    assert stringify("int", "smart") == "int"
+    assert stringify_annotation("int", 'fully-qualified-except-typing') == "int"
+    assert stringify_annotation("int", 'fully-qualified') == "int"
+    assert stringify_annotation("int", "smart") == "int"
 
-    assert stringify("str") == "str"
-    assert stringify("str", "smart") == "str"
+    assert stringify_annotation("str", 'fully-qualified-except-typing') == "str"
+    assert stringify_annotation("str", 'fully-qualified') == "str"
+    assert stringify_annotation("str", "smart") == "str"
 
-    assert stringify(List["int"]) == "List[int]"
-    assert stringify(List["int"], "smart") == "~typing.List[int]"
+    assert stringify_annotation(List["int"], 'fully-qualified-except-typing') == "List[int]"
+    assert stringify_annotation(List["int"], 'fully-qualified') == "typing.List[int]"
+    assert stringify_annotation(List["int"], "smart") == "~typing.List[int]"
 
-    assert stringify("Tuple[str]") == "Tuple[str]"
-    assert stringify("Tuple[str]", "smart") == "Tuple[str]"
+    assert stringify_annotation("Tuple[str]", 'fully-qualified-except-typing') == "Tuple[str]"
+    assert stringify_annotation("Tuple[str]", 'fully-qualified') == "Tuple[str]"
+    assert stringify_annotation("Tuple[str]", "smart") == "Tuple[str]"
 
-    assert stringify("unknown") == "unknown"
-    assert stringify("unknown", "smart") == "unknown"
+    assert stringify_annotation("unknown", 'fully-qualified-except-typing') == "unknown"
+    assert stringify_annotation("unknown", 'fully-qualified') == "unknown"
+    assert stringify_annotation("unknown", "smart") == "unknown"
 
 
 def test_stringify_type_hints_Callable():
-    assert stringify(Callable) == "Callable"
-    assert stringify(Callable, "fully-qualified") == "typing.Callable"
-    assert stringify(Callable, "smart") == "~typing.Callable"
+    assert stringify_annotation(Callable, 'fully-qualified-except-typing') == "Callable"
+    assert stringify_annotation(Callable, "fully-qualified") == "typing.Callable"
+    assert stringify_annotation(Callable, "smart") == "~typing.Callable"
 
-    assert stringify(Callable[[str], int]) == "Callable[[str], int]"
-    assert stringify(Callable[[str], int], "fully-qualified") == "typing.Callable[[str], int]"
-    assert stringify(Callable[[str], int], "smart") == "~typing.Callable[[str], int]"
+    assert stringify_annotation(Callable[[str], int], 'fully-qualified-except-typing') == "Callable[[str], int]"
+    assert stringify_annotation(Callable[[str], int], "fully-qualified") == "typing.Callable[[str], int]"
+    assert stringify_annotation(Callable[[str], int], "smart") == "~typing.Callable[[str], int]"
 
-    assert stringify(Callable[..., int]) == "Callable[[...], int]"
-    assert stringify(Callable[..., int], "fully-qualified") == "typing.Callable[[...], int]"
-    assert stringify(Callable[..., int], "smart") == "~typing.Callable[[...], int]"
+    assert stringify_annotation(Callable[..., int], 'fully-qualified-except-typing') == "Callable[[...], int]"
+    assert stringify_annotation(Callable[..., int], "fully-qualified") == "typing.Callable[[...], int]"
+    assert stringify_annotation(Callable[..., int], "smart") == "~typing.Callable[[...], int]"
 
 
 def test_stringify_type_hints_Union():
-    assert stringify(Optional[int]) == "Optional[int]"
-    assert stringify(Optional[int], "fully-qualified") == "typing.Optional[int]"
-    assert stringify(Optional[int], "smart") == "~typing.Optional[int]"
+    assert stringify_annotation(Optional[int], 'fully-qualified-except-typing') == "int | None"
+    assert stringify_annotation(Optional[int], "fully-qualified") == "int | None"
+    assert stringify_annotation(Optional[int], "smart") == "int | None"
 
-    assert stringify(Union[str, None]) == "Optional[str]"
-    assert stringify(Union[str, None], "fully-qualified") == "typing.Optional[str]"
-    assert stringify(Union[str, None], "smart") == "~typing.Optional[str]"
+    assert stringify_annotation(Union[str, None], 'fully-qualified-except-typing') == "str | None"
+    assert stringify_annotation(Union[str, None], "fully-qualified") == "str | None"
+    assert stringify_annotation(Union[str, None], "smart") == "str | None"
 
-    assert stringify(Union[int, str]) == "Union[int, str]"
-    assert stringify(Union[int, str], "fully-qualified") == "typing.Union[int, str]"
-    assert stringify(Union[int, str], "smart") == "~typing.Union[int, str]"
+    assert stringify_annotation(Union[int, str], 'fully-qualified-except-typing') == "int | str"
+    assert stringify_annotation(Union[int, str], "fully-qualified") == "int | str"
+    assert stringify_annotation(Union[int, str], "smart") == "int | str"
 
-    assert stringify(Union[int, Integral]) == "Union[int, numbers.Integral]"
-    assert stringify(Union[int, Integral], "fully-qualified") == "typing.Union[int, numbers.Integral]"
-    assert stringify(Union[int, Integral], "smart") == "~typing.Union[int, ~numbers.Integral]"
+    assert stringify_annotation(Union[int, Integral], 'fully-qualified-except-typing') == "int | numbers.Integral"
+    assert stringify_annotation(Union[int, Integral], "fully-qualified") == "int | numbers.Integral"
+    assert stringify_annotation(Union[int, Integral], "smart") == "int | ~numbers.Integral"
 
-    assert (stringify(Union[MyClass1, MyClass2]) ==
-            "Union[tests.test_util_typing.MyClass1, tests.test_util_typing.<MyClass2>]")
-    assert (stringify(Union[MyClass1, MyClass2], "fully-qualified") ==
-            "typing.Union[tests.test_util_typing.MyClass1, tests.test_util_typing.<MyClass2>]")
-    assert (stringify(Union[MyClass1, MyClass2], "smart") ==
-            "~typing.Union[~tests.test_util_typing.MyClass1, ~tests.test_util_typing.<MyClass2>]")
+    assert (stringify_annotation(Union[MyClass1, MyClass2], 'fully-qualified-except-typing') ==
+            "tests.test_util_typing.MyClass1 | tests.test_util_typing.<MyClass2>")
+    assert (stringify_annotation(Union[MyClass1, MyClass2], "fully-qualified") ==
+            "tests.test_util_typing.MyClass1 | tests.test_util_typing.<MyClass2>")
+    assert (stringify_annotation(Union[MyClass1, MyClass2], "smart") ==
+            "~tests.test_util_typing.MyClass1 | ~tests.test_util_typing.<MyClass2>")
 
 
 def test_stringify_type_hints_typevars():
@@ -368,72 +373,72 @@ def test_stringify_type_hints_typevars():
     T_co = TypeVar('T_co', covariant=True)
     T_contra = TypeVar('T_contra', contravariant=True)
 
-    assert stringify(T) == "tests.test_util_typing.T"
-    assert stringify(T, "smart") == "~tests.test_util_typing.T"
+    assert stringify_annotation(T, 'fully-qualified-except-typing') == "tests.test_util_typing.T"
+    assert stringify_annotation(T, "smart") == "~tests.test_util_typing.T"
 
-    assert stringify(T_co) == "tests.test_util_typing.T_co"
-    assert stringify(T_co, "smart") == "~tests.test_util_typing.T_co"
+    assert stringify_annotation(T_co, 'fully-qualified-except-typing') == "tests.test_util_typing.T_co"
+    assert stringify_annotation(T_co, "smart") == "~tests.test_util_typing.T_co"
 
-    assert stringify(T_contra) == "tests.test_util_typing.T_contra"
-    assert stringify(T_contra, "smart") == "~tests.test_util_typing.T_contra"
+    assert stringify_annotation(T_contra, 'fully-qualified-except-typing') == "tests.test_util_typing.T_contra"
+    assert stringify_annotation(T_contra, "smart") == "~tests.test_util_typing.T_contra"
 
-    assert stringify(List[T]) == "List[tests.test_util_typing.T]"
-    assert stringify(List[T], "smart") == "~typing.List[~tests.test_util_typing.T]"
+    assert stringify_annotation(List[T], 'fully-qualified-except-typing') == "List[tests.test_util_typing.T]"
+    assert stringify_annotation(List[T], "smart") == "~typing.List[~tests.test_util_typing.T]"
 
     if sys.version_info[:2] >= (3, 10):
-        assert stringify(MyInt) == "tests.test_util_typing.MyInt"
-        assert stringify(MyInt, "smart") == "~tests.test_util_typing.MyInt"
+        assert stringify_annotation(MyInt, 'fully-qualified-except-typing') == "tests.test_util_typing.MyInt"
+        assert stringify_annotation(MyInt, "smart") == "~tests.test_util_typing.MyInt"
     else:
-        assert stringify(MyInt) == "MyInt"
-        assert stringify(MyInt, "smart") == "MyInt"
+        assert stringify_annotation(MyInt, 'fully-qualified-except-typing') == "MyInt"
+        assert stringify_annotation(MyInt, "smart") == "MyInt"
 
 
 def test_stringify_type_hints_custom_class():
-    assert stringify(MyClass1) == "tests.test_util_typing.MyClass1"
-    assert stringify(MyClass1, "smart") == "~tests.test_util_typing.MyClass1"
+    assert stringify_annotation(MyClass1, 'fully-qualified-except-typing') == "tests.test_util_typing.MyClass1"
+    assert stringify_annotation(MyClass1, "smart") == "~tests.test_util_typing.MyClass1"
 
-    assert stringify(MyClass2) == "tests.test_util_typing.<MyClass2>"
-    assert stringify(MyClass2, "smart") == "~tests.test_util_typing.<MyClass2>"
+    assert stringify_annotation(MyClass2, 'fully-qualified-except-typing') == "tests.test_util_typing.<MyClass2>"
+    assert stringify_annotation(MyClass2, "smart") == "~tests.test_util_typing.<MyClass2>"
 
 
 def test_stringify_type_hints_alias():
     MyStr = str
     MyTuple = Tuple[str, str]
 
-    assert stringify(MyStr) == "str"
-    assert stringify(MyStr, "smart") == "str"
+    assert stringify_annotation(MyStr, 'fully-qualified-except-typing') == "str"
+    assert stringify_annotation(MyStr, "smart") == "str"
 
-    assert stringify(MyTuple) == "Tuple[str, str]"  # type: ignore
-    assert stringify(MyTuple, "smart") == "~typing.Tuple[str, str]"  # type: ignore
+    assert stringify_annotation(MyTuple) == "Tuple[str, str]"  # type: ignore
+    assert stringify_annotation(MyTuple, "smart") == "~typing.Tuple[str, str]"  # type: ignore
 
 
 def test_stringify_type_Literal():
     from typing import Literal  # type: ignore
-    assert stringify(Literal[1, "2", "\r"]) == "Literal[1, '2', '\\r']"
-    assert stringify(Literal[1, "2", "\r"], "fully-qualified") == "typing.Literal[1, '2', '\\r']"
-    assert stringify(Literal[1, "2", "\r"], "smart") == "~typing.Literal[1, '2', '\\r']"
+    assert stringify_annotation(Literal[1, "2", "\r"], 'fully-qualified-except-typing') == "Literal[1, '2', '\\r']"
+    assert stringify_annotation(Literal[1, "2", "\r"], "fully-qualified") == "typing.Literal[1, '2', '\\r']"
+    assert stringify_annotation(Literal[1, "2", "\r"], "smart") == "~typing.Literal[1, '2', '\\r']"
 
 
 @pytest.mark.skipif(sys.version_info[:2] <= (3, 9), reason='python 3.10+ is required.')
 def test_stringify_type_union_operator():
-    assert stringify(int | None) == "int | None"  # type: ignore
-    assert stringify(int | None, "smart") == "int | None"  # type: ignore
+    assert stringify_annotation(int | None) == "int | None"  # type: ignore
+    assert stringify_annotation(int | None, "smart") == "int | None"  # type: ignore
 
-    assert stringify(int | str) == "int | str"  # type: ignore
-    assert stringify(int | str, "smart") == "int | str"  # type: ignore
+    assert stringify_annotation(int | str) == "int | str"  # type: ignore
+    assert stringify_annotation(int | str, "smart") == "int | str"  # type: ignore
 
-    assert stringify(int | str | None) == "int | str | None"  # type: ignore
-    assert stringify(int | str | None, "smart") == "int | str | None"  # type: ignore
+    assert stringify_annotation(int | str | None) == "int | str | None"  # type: ignore
+    assert stringify_annotation(int | str | None, "smart") == "int | str | None"  # type: ignore
 
 
 def test_stringify_broken_type_hints():
-    assert stringify(BrokenType) == 'tests.test_util_typing.BrokenType'
-    assert stringify(BrokenType, "smart") == '~tests.test_util_typing.BrokenType'
+    assert stringify_annotation(BrokenType, 'fully-qualified-except-typing') == 'tests.test_util_typing.BrokenType'
+    assert stringify_annotation(BrokenType, "smart") == '~tests.test_util_typing.BrokenType'
 
 
 def test_stringify_mock():
     with mock(['unknown']):
         import unknown
-        assert stringify(unknown) == 'unknown'
-        assert stringify(unknown.secret.Class) == 'unknown.secret.Class'
-        assert stringify(unknown.secret.Class, "smart") == 'unknown.secret.Class'
+        assert stringify_annotation(unknown, 'fully-qualified-except-typing') == 'unknown'
+        assert stringify_annotation(unknown.secret.Class, 'fully-qualified-except-typing') == 'unknown.secret.Class'
+        assert stringify_annotation(unknown.secret.Class, "smart") == 'unknown.secret.Class'