bpo-37479: on Enum subclasses with mixins, __format__ uses overridden __str__ (GH-14545)

* bpo-37479: on Enum subclasses with mixins, __format__ uses overridden __str__
diff --git a/Lib/enum.py b/Lib/enum.py
index 403f747..69a7f49 100644
--- a/Lib/enum.py
+++ b/Lib/enum.py
@@ -622,8 +622,9 @@
         # we can get strange results with the Enum name showing up instead of
         # the value
 
-        # pure Enum branch
-        if self._member_type_ is object:
+        # pure Enum branch, or branch with __str__ explicitly overridden
+        str_overridden = type(self).__str__ != Enum.__str__
+        if self._member_type_ is object or str_overridden:
             cls = str
             val = str(self)
         # mix-in branch
diff --git a/Lib/test/test_enum.py b/Lib/test/test_enum.py
index 47081cf..fcfa7d9 100644
--- a/Lib/test/test_enum.py
+++ b/Lib/test/test_enum.py
@@ -445,12 +445,63 @@
         self.assertEqual('{:<20}'.format(Season.SPRING),
                          '{:<20}'.format(str(Season.SPRING)))
 
-    def test_format_enum_custom(self):
+    def test_str_override_enum(self):
+        class EnumWithStrOverrides(Enum):
+            one = auto()
+            two = auto()
+
+            def __str__(self):
+                return 'Str!'
+        self.assertEqual(str(EnumWithStrOverrides.one), 'Str!')
+        self.assertEqual('{}'.format(EnumWithStrOverrides.one), 'Str!')
+
+    def test_format_override_enum(self):
+        class EnumWithFormatOverride(Enum):
+            one = 1.0
+            two = 2.0
+            def __format__(self, spec):
+                return 'Format!!'
+        self.assertEqual(str(EnumWithFormatOverride.one), 'EnumWithFormatOverride.one')
+        self.assertEqual('{}'.format(EnumWithFormatOverride.one), 'Format!!')
+
+    def test_str_and_format_override_enum(self):
+        class EnumWithStrFormatOverrides(Enum):
+            one = auto()
+            two = auto()
+            def __str__(self):
+                return 'Str!'
+            def __format__(self, spec):
+                return 'Format!'
+        self.assertEqual(str(EnumWithStrFormatOverrides.one), 'Str!')
+        self.assertEqual('{}'.format(EnumWithStrFormatOverrides.one), 'Format!')
+
+    def test_str_override_mixin(self):
+        class MixinEnumWithStrOverride(float, Enum):
+            one = 1.0
+            two = 2.0
+            def __str__(self):
+                return 'Overridden!'
+        self.assertEqual(str(MixinEnumWithStrOverride.one), 'Overridden!')
+        self.assertEqual('{}'.format(MixinEnumWithStrOverride.one), 'Overridden!')
+
+    def test_str_and_format_override_mixin(self):
+        class MixinWithStrFormatOverrides(float, Enum):
+            one = 1.0
+            two = 2.0
+            def __str__(self):
+                return 'Str!'
+            def __format__(self, spec):
+                return 'Format!'
+        self.assertEqual(str(MixinWithStrFormatOverrides.one), 'Str!')
+        self.assertEqual('{}'.format(MixinWithStrFormatOverrides.one), 'Format!')
+
+    def test_format_override_mixin(self):
         class TestFloat(float, Enum):
             one = 1.0
             two = 2.0
             def __format__(self, spec):
                 return 'TestFloat success!'
+        self.assertEqual(str(TestFloat.one), 'TestFloat.one')
         self.assertEqual('{}'.format(TestFloat.one), 'TestFloat success!')
 
     def assertFormatIsValue(self, spec, member):