bpo-36772 Allow lru_cache to be used as decorator without making a function call (GH-13048)

diff --git a/Lib/functools.py b/Lib/functools.py
index c863341..30964a6 100644
--- a/Lib/functools.py
+++ b/Lib/functools.py
@@ -518,14 +518,18 @@
     # The internals of the lru_cache are encapsulated for thread safety and
     # to allow the implementation to change (including a possible C version).
 
-    # Early detection of an erroneous call to @lru_cache without any arguments
-    # resulting in the inner function being passed to maxsize instead of an
-    # integer or None.  Negative maxsize is treated as 0.
     if isinstance(maxsize, int):
+        # Negative maxsize is treated as 0
         if maxsize < 0:
             maxsize = 0
+    elif callable(maxsize) and isinstance(typed, bool):
+        # The user_function was passed in directly via the maxsize argument
+        user_function, maxsize = maxsize, 128
+        wrapper = _lru_cache_wrapper(user_function, maxsize, typed, _CacheInfo)
+        return update_wrapper(wrapper, user_function)
     elif maxsize is not None:
-        raise TypeError('Expected maxsize to be an integer or None')
+        raise TypeError(
+            'Expected first argument to be an integer, a callable, or None')
 
     def decorating_function(user_function):
         wrapper = _lru_cache_wrapper(user_function, maxsize, typed, _CacheInfo)
diff --git a/Lib/test/test_functools.py b/Lib/test/test_functools.py
index b89d779..8fee1c6 100644
--- a/Lib/test/test_functools.py
+++ b/Lib/test/test_functools.py
@@ -1251,6 +1251,18 @@
         self.assertEqual(misses, 4)
         self.assertEqual(currsize, 2)
 
+    def test_lru_no_args(self):
+        @self.module.lru_cache
+        def square(x):
+            return x ** 2
+
+        self.assertEqual(list(map(square, [10, 20, 10])),
+                         [100, 400, 100])
+        self.assertEqual(square.cache_info().hits, 1)
+        self.assertEqual(square.cache_info().misses, 2)
+        self.assertEqual(square.cache_info().maxsize, 128)
+        self.assertEqual(square.cache_info().currsize, 2)
+
     def test_lru_bug_35780(self):
         # C version of the lru_cache was not checking to see if
         # the user function call has already modified the cache
@@ -1582,13 +1594,6 @@
         self.assertEqual(test_func(DoubleEq(2)),    # Trigger a re-entrant __eq__ call
                          DoubleEq(2))               # Verify the correct return value
 
-    def test_early_detection_of_bad_call(self):
-        # Issue #22184
-        with self.assertRaises(TypeError):
-            @functools.lru_cache
-            def f():
-                pass
-
     def test_lru_method(self):
         class X(int):
             f_cnt = 0