diff --git a/Doc/extending/extending.rst b/Doc/extending/extending.rst
index 918c751b009761..fd63495674651b 100644
--- a/Doc/extending/extending.rst
+++ b/Doc/extending/extending.rst
@@ -204,17 +204,32 @@ value must be in a particular range or must satisfy other conditions,
 :c:data:`PyExc_ValueError` is appropriate.
 
 You can also define a new exception that is unique to your module.
-For this, you can declare a static global object variable at the beginning
-of the file::
+The simplest way to do this is to declare a static global object variable at
+the beginning of the file::
 
-   static PyObject *SpamError;
+   static PyObject *SpamError = NULL;
 
-and initialize it with an exception object in the module's
+and initialize it by calling :c:func:`PyErr_NewException` in the module's
 :c:data:`Py_mod_exec` function (:c:func:`!spam_module_exec`)::
 
+   SpamError = PyErr_NewException("spam.error", NULL, NULL);
+
+Since :c:data:`!SpamError` is a global variable, it will be overwitten every time
+the module is reinitialized, when the :c:data:`Py_mod_exec` function is called.
+
+For now, let's avoid the issue: we will block repeated initialization by raising an
+:py:exc:`ImportError`::
+
+   static PyObject *SpamError = NULL;
+
    static int
    spam_module_exec(PyObject *m)
    {
+       if (SpamError != NULL) {
+           PyErr_SetString(PyExc_ImportError,
+                           "cannot initialize spam module more than once");
+           return -1;
+       }
        SpamError = PyErr_NewException("spam.error", NULL, NULL);
        if (PyModule_AddObjectRef(m, "SpamError", SpamError) < 0) {
            return -1;
@@ -253,6 +268,11 @@ needed to ensure that it will not be discarded, causing :c:data:`!SpamError` to
 become a dangling pointer. Should it become a dangling pointer, C code which
 raises the exception could cause a core dump or other unintended side effects.
 
+For now, the :c:func:`Py_DECREF` call to remove this reference is missing.
+Even when the Python interpreter shuts down, the global :c:data:`!SpamError`
+variable will not be garbage-collected. It will "leak".
+We did, however, ensure that this will happen at most once per process.
+
 We discuss the use of :c:macro:`PyMODINIT_FUNC` as a function return type later in this
 sample.
 
diff --git a/Doc/library/logging.handlers.rst b/Doc/library/logging.handlers.rst
index 63ef533e82c658..8f3aa1dfdd0cde 100644
--- a/Doc/library/logging.handlers.rst
+++ b/Doc/library/logging.handlers.rst
@@ -352,6 +352,10 @@ module, supports rotation of disk log files.
       Outputs the record to the file, catering for rollover as described
       previously.
 
+   .. method:: shouldRollover(record)
+
+      See if the supplied record would cause the file to exceed the configured size limit.
+
 .. _timed-rotating-file-handler:
 
 TimedRotatingFileHandler
@@ -459,7 +463,11 @@ timed intervals.
    .. method:: getFilesToDelete()
 
       Returns a list of filenames which should be deleted as part of rollover. These
-      are the absolute paths of the oldest backup log files written by the handler.
+
+   .. method:: shouldRollover(record)
+
+      See if enough time has passed for a rollover to occur and if it has, compute
+      the next rollover time.
 
 .. _socket-handler:
 
diff --git a/Doc/library/math.rst b/Doc/library/math.rst
index 394a462b9468e5..11d3b756e21322 100644
--- a/Doc/library/math.rst
+++ b/Doc/library/math.rst
@@ -10,8 +10,8 @@
 
 --------------
 
-This module provides access to the mathematical functions defined by the C
-standard.
+This module provides access to common mathematical functions and constants,
+including those defined by the C standard.
 
 These functions cannot be used with complex numbers; use the functions of the
 same name from the :mod:`cmath` module if you require support for complex
diff --git a/Doc/library/typing.rst b/Doc/library/typing.rst
index dd8ea3c364f49a..69df09c779592a 100644
--- a/Doc/library/typing.rst
+++ b/Doc/library/typing.rst
@@ -3530,28 +3530,32 @@ Constant
 .. data:: TYPE_CHECKING
 
    A special constant that is assumed to be ``True`` by 3rd party static
-   type checkers. It is ``False`` at runtime.
+   type checkers. It's ``False`` at runtime.
+
+   A module which is expensive to import, and which only contain types
+   used for typing annotations, can be safely imported inside an
+   ``if TYPE_CHECKING:`` block.  This prevents the module from actually
+   being imported at runtime; annotations aren't eagerly evaluated
+   (see :pep:`649`) so using undefined symbols in annotations is
+   harmless--as long as you don't later examine them.
+   Your static type analysis tool will set ``TYPE_CHECKING`` to
+   ``True`` during static type analysis, which means the module will
+   be imported and the types will be checked properly during such analysis.
 
    Usage::
 
       if TYPE_CHECKING:
           import expensive_mod
 
-      def fun(arg: 'expensive_mod.SomeType') -> None:
+      def fun(arg: expensive_mod.SomeType) -> None:
           local_var: expensive_mod.AnotherType = other_fun()
 
-   The first type annotation must be enclosed in quotes, making it a
-   "forward reference", to hide the ``expensive_mod`` reference from the
-   interpreter runtime.  Type annotations for local variables are not
-   evaluated, so the second annotation does not need to be enclosed in quotes.
-
-   .. note::
-
-      If ``from __future__ import annotations`` is used,
-      annotations are not evaluated at function definition time.
-      Instead, they are stored as strings in ``__annotations__``.
-      This makes it unnecessary to use quotes around the annotation
-      (see :pep:`563`).
+   If you occasionally need to examine type annotations at runtime
+   which may contain undefined symbols, use
+   :meth:`annotationlib.get_annotations` with a ``format`` parameter
+   of :attr:`annotationlib.Format.STRING` or
+   :attr:`annotationlib.Format.FORWARDREF` to safely retrieve the
+   annotations without raising :exc:`NameError`.
 
    .. versionadded:: 3.5.2