bpo-42500: Fix recursion in or after except (GH-23568)

* Use counter, rather boolean state when handling soft overflows.
diff --git a/Lib/test/test_exceptions.py b/Lib/test/test_exceptions.py
index 4dbf5fe..1bdd3f2 100644
--- a/Lib/test/test_exceptions.py
+++ b/Lib/test/test_exceptions.py
@@ -1046,7 +1046,7 @@ def gen():
                 # tstate->recursion_depth is equal to (recursion_limit - 1)
                 # and is equal to recursion_limit when _gen_throw() calls
                 # PyErr_NormalizeException().
-                recurse(setrecursionlimit(depth + 2) - depth - 1)
+                recurse(setrecursionlimit(depth + 2) - depth)
             finally:
                 sys.setrecursionlimit(recursionlimit)
                 print('Done.')
@@ -1076,6 +1076,54 @@ def test_recursion_normalizing_infinite_exception(self):
                       b'while normalizing an exception', err)
         self.assertIn(b'Done.', out)
 
+
+    def test_recursion_in_except_handler(self):
+
+        def set_relative_recursion_limit(n):
+            depth = 1
+            while True:
+                try:
+                    sys.setrecursionlimit(depth)
+                except RecursionError:
+                    depth += 1
+                else:
+                    break
+            sys.setrecursionlimit(depth+n)
+
+        def recurse_in_except():
+            try:
+                1/0
+            except:
+                recurse_in_except()
+
+        def recurse_after_except():
+            try:
+                1/0
+            except:
+                pass
+            recurse_after_except()
+
+        def recurse_in_body_and_except():
+            try:
+                recurse_in_body_and_except()
+            except:
+                recurse_in_body_and_except()
+
+        recursionlimit = sys.getrecursionlimit()
+        try:
+            set_relative_recursion_limit(10)
+            for func in (recurse_in_except, recurse_after_except, recurse_in_body_and_except):
+                with self.subTest(func=func):
+                    try:
+                        func()
+                    except RecursionError:
+                        pass
+                    else:
+                        self.fail("Should have raised a RecursionError")
+        finally:
+            sys.setrecursionlimit(recursionlimit)
+
+
     @cpython_only
     def test_recursion_normalizing_with_no_memory(self):
         # Issue #30697. Test that in the abort that occurs when there is no
@@ -1112,7 +1160,7 @@ def raiseMemError():
             except MemoryError as e:
                 tb = e.__traceback__
             else:
-                self.fail("Should have raises a MemoryError")
+                self.fail("Should have raised a MemoryError")
             return traceback.format_tb(tb)
 
         tb1 = raiseMemError()
diff --git a/Lib/test/test_sys.py b/Lib/test/test_sys.py
index 173ef9e..3860656 100644
--- a/Lib/test/test_sys.py
+++ b/Lib/test/test_sys.py
@@ -221,7 +221,7 @@ def test_recursionlimit_recovery(self):
         def f():
             f()
         try:
-            for depth in (10, 25, 50, 75, 100, 250, 1000):
+            for depth in (50, 75, 100, 250, 1000):
                 try:
                     sys.setrecursionlimit(depth)
                 except RecursionError:
@@ -231,17 +231,17 @@ def f():
 
                 # Issue #5392: test stack overflow after hitting recursion
                 # limit twice
-                self.assertRaises(RecursionError, f)
-                self.assertRaises(RecursionError, f)
+                with self.assertRaises(RecursionError):
+                    f()
+                with self.assertRaises(RecursionError):
+                    f()
         finally:
             sys.setrecursionlimit(oldlimit)
 
     @test.support.cpython_only
     def test_setrecursionlimit_recursion_depth(self):
         # Issue #25274: Setting a low recursion limit must be blocked if the
-        # current recursion depth is already higher than the "lower-water
-        # mark". Otherwise, it may not be possible anymore to
-        # reset the overflowed flag to 0.
+        # current recursion depth is already higher than limit.
 
         from _testinternalcapi import get_recursion_depth
 
@@ -262,42 +262,10 @@ def set_recursion_limit_at_depth(depth, limit):
             sys.setrecursionlimit(1000)
 
             for limit in (10, 25, 50, 75, 100, 150, 200):
-                # formula extracted from _Py_RecursionLimitLowerWaterMark()
-                if limit > 200:
-                    depth = limit - 50
-                else:
-                    depth = limit * 3 // 4
-                set_recursion_limit_at_depth(depth, limit)
+                set_recursion_limit_at_depth(limit, limit)
         finally:
             sys.setrecursionlimit(oldlimit)
 
-    # The error message is specific to CPython
-    @test.support.cpython_only
-    def test_recursionlimit_fatalerror(self):
-        # A fatal error occurs if a second recursion limit is hit when recovering
-        # from a first one.
-        code = textwrap.dedent("""
-            import sys
-
-            def f():
-                try:
-                    f()
-                except RecursionError:
-                    f()
-
-            sys.setrecursionlimit(%d)
-            f()""")
-        with test.support.SuppressCrashReport():
-            for i in (50, 1000):
-                sub = subprocess.Popen([sys.executable, '-c', code % i],
-                    stderr=subprocess.PIPE)
-                err = sub.communicate()[1]
-                self.assertTrue(sub.returncode, sub.returncode)
-                self.assertIn(
-                    b"Fatal Python error: _Py_CheckRecursiveCall: "
-                    b"Cannot recover from stack overflow",
-                    err)
-
     def test_getwindowsversion(self):
         # Raise SkipTest if sys doesn't have getwindowsversion attribute
         test.support.get_attribute(sys, "getwindowsversion")