bpo-35780: Fix errors in lru_cache() C code (GH-11623)

diff --git a/Lib/functools.py b/Lib/functools.py
index ab7d71e..6233c30 100644
--- a/Lib/functools.py
+++ b/Lib/functools.py
@@ -454,7 +454,7 @@
 
 def _make_key(args, kwds, typed,
              kwd_mark = (object(),),
-             fasttypes = {int, str, frozenset, type(None)},
+             fasttypes = {int, str},
              tuple=tuple, type=type, len=len):
     """Make a cache key from optionally typed positional and keyword arguments
 
@@ -510,8 +510,11 @@
 
     # 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.
-    if maxsize is not None and not isinstance(maxsize, int):
+    # integer or None.  Negative maxsize is treated as 0.
+    if isinstance(maxsize, int):
+        if maxsize < 0:
+            maxsize = 0
+    elif maxsize is not None:
         raise TypeError('Expected maxsize to be an integer or None')
 
     def decorating_function(user_function):
@@ -578,6 +581,7 @@
                     link[NEXT] = root
                     hits += 1
                     return result
+                misses += 1
             result = user_function(*args, **kwds)
             with lock:
                 if key in cache:
@@ -615,7 +619,6 @@
                     # Use the cache_len bound method instead of the len() function
                     # which could potentially be wrapped in an lru_cache itself.
                     full = (cache_len() >= maxsize)
-                misses += 1
             return result
 
     def cache_info():
diff --git a/Lib/test/test_functools.py b/Lib/test/test_functools.py
index ffbd0fc..63a9ade 100644
--- a/Lib/test/test_functools.py
+++ b/Lib/test/test_functools.py
@@ -1233,6 +1233,33 @@
         self.assertEqual(misses, 4)
         self.assertEqual(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
+        # (this arises in recursive calls and in multi-threading).
+        # This cause the cache to have orphan links not referenced
+        # by the cache dictionary.
+
+        once = True                 # Modified by f(x) below
+
+        @self.module.lru_cache(maxsize=10)
+        def f(x):
+            nonlocal once
+            rv = f'.{x}.'
+            if x == 20 and once:
+                once = False
+                rv = f(x)
+            return rv
+
+        # Fill the cache
+        for x in range(15):
+            self.assertEqual(f(x), f'.{x}.')
+        self.assertEqual(f.cache_info().currsize, 10)
+
+        # Make a recursive call and make sure the cache remains full
+        self.assertEqual(f(20), '.20.')
+        self.assertEqual(f.cache_info().currsize, 10)
+
     def test_lru_hash_only_once(self):
         # To protect against weird reentrancy bugs and to improve
         # efficiency when faced with slow __hash__ methods, the
@@ -1329,7 +1356,7 @@
         for i in (0, 1):
             self.assertEqual([eq(n) for n in range(150)], list(range(150)))
         self.assertEqual(eq.cache_info(),
-            self.module._CacheInfo(hits=0, misses=300, maxsize=-10, currsize=1))
+            self.module._CacheInfo(hits=0, misses=300, maxsize=0, currsize=0))
 
     def test_lru_with_exceptions(self):
         # Verify that user_function exceptions get passed through without