[3.11] Provided better example for logging cookbook (GH-101164) (GH-101184)

Co-authored-by: Vladimir Malinovskii <galqiwi@galqiwi.ru>
Co-authored-by: Vinay Sajip <vinay_sajip@yahoo.co.uk>

Doc/howto/logging-cookbook.rst

@@ -1982,26 +1982,47 @@ Using a rotator and namer to customize log rotation processing
 --------------------------------------------------------------
 
 An example of how you can define a namer and rotator is given in the following
-snippet, which shows zlib-based compression of the log file::
+runnable script, which shows gzip compression of the log file::
+
+    import gzip
+    import logging
+    import logging.handlers
+    import os
+    import shutil
 
     def namer(name):
         return name + ".gz"
 
     def rotator(source, dest):
-        with open(source, "rb") as sf:
-            data = sf.read()
-            compressed = zlib.compress(data, 9)
-            with open(dest, "wb") as df:
-                df.write(compressed)
+        with open(source, 'rb') as f_in:
+            with gzip.open(dest, 'wb') as f_out:
+                shutil.copyfileobj(f_in, f_out)
         os.remove(source)
 
-    rh = logging.handlers.RotatingFileHandler(...)
+
+    rh = logging.handlers.RotatingFileHandler('rotated.log', maxBytes=128, backupCount=5)
     rh.rotator = rotator
     rh.namer = namer
 
-These are not "true" .gz files, as they are bare compressed data, with no
-"container" such as you’d find in an actual gzip file. This snippet is just
-for illustration purposes.
+    root = logging.getLogger()
+    root.setLevel(logging.INFO)
+    root.addHandler(rh)
+    f = logging.Formatter('%(asctime)s %(message)s')
+    rh.setFormatter(f)
+    for i in range(1000):
+        root.info(f'Message no. {i + 1}')
+
+After running this, you will see six new files, five of which are compressed:
+
+.. code-block:: shell-session
+
+    $ ls rotated.log*
+    rotated.log       rotated.log.2.gz  rotated.log.4.gz
+    rotated.log.1.gz  rotated.log.3.gz  rotated.log.5.gz
+    $ zcat rotated.log.1.gz
+    2023-01-20 02:28:17,767 Message no. 996
+    2023-01-20 02:28:17,767 Message no. 997
+    2023-01-20 02:28:17,767 Message no. 998
 
 A more elaborate multiprocessing example
 ----------------------------------------