gh-128772: Fix pydoc for methods with __module__ is None

Lib/pydoc.py

@@ -245,7 +245,7 @@ def parentname(object, modname):
     if necessary) or module."""
     if '.' in object.__qualname__:
         name = object.__qualname__.rpartition('.')[0]
-        if object.__module__ != modname:
+        if object.__module__ != modname and object.__module__ is not None:
             return object.__module__ + '.' + name
         else:
             return name

Lib/test/test_pydoc/module_none.py

@@ -0,0 +1,8 @@
+def func():
+    pass
+func.__module__ = None
+
+class A:
+    def method(self):
+        pass
+    method.__module__ = None

Lib/test/test_pydoc/test_pydoc.py

@@ -1903,6 +1903,11 @@ def a_fn_with_https_link():
             html
         )
 
+    def test_module_none(self):
+        # Issue #128772
+        from test.test_pydoc import module_none
+        pydoc.render_doc(module_none)
+
 
 class PydocFodderTest(unittest.TestCase):
     def tearDown(self):

Misc/NEWS.d/next/Library/2025-01-22-13-29-06.gh-issue-128772.6YrxYM.rst

@@ -0,0 +1,2 @@
+Fix :mod:`pydoc` for methods with the ``__module__`` attribute equal to
+``None``.