diff --git a/Lib/functools.py b/Lib/functools.py
index 91e9685b984..fb2e4bdfbb2 100644
--- a/Lib/functools.py
+++ b/Lib/functools.py
@@ -94,80 +94,80 @@ def wraps(wrapped,
 # infinite recursion that could occur when the operator dispatch logic
 # detects a NotImplemented result and then calls a reflected method.
 
-def _gt_from_lt(self, other):
+def _gt_from_lt(self, other, NotImplemented=NotImplemented):
     'Return a > b.  Computed by @total_ordering from (not a < b) and (a != b).'
     op_result = self.__lt__(other)
     if op_result is NotImplemented:
         return op_result
     return not op_result and self != other
 
-def _le_from_lt(self, other):
+def _le_from_lt(self, other, NotImplemented=NotImplemented):
     'Return a <= b.  Computed by @total_ordering from (a < b) or (a == b).'
     op_result = self.__lt__(other)
     return op_result or self == other
 
-def _ge_from_lt(self, other):
+def _ge_from_lt(self, other, NotImplemented=NotImplemented):
     'Return a >= b.  Computed by @total_ordering from (not a < b).'
     op_result = self.__lt__(other)
     if op_result is NotImplemented:
         return op_result
     return not op_result
 
-def _ge_from_le(self, other):
+def _ge_from_le(self, other, NotImplemented=NotImplemented):
     'Return a >= b.  Computed by @total_ordering from (not a <= b) or (a == b).'
     op_result = self.__le__(other)
     if op_result is NotImplemented:
         return op_result
     return not op_result or self == other
 
-def _lt_from_le(self, other):
+def _lt_from_le(self, other, NotImplemented=NotImplemented):
     'Return a < b.  Computed by @total_ordering from (a <= b) and (a != b).'
     op_result = self.__le__(other)
     if op_result is NotImplemented:
         return op_result
     return op_result and self != other
 
-def _gt_from_le(self, other):
+def _gt_from_le(self, other, NotImplemented=NotImplemented):
     'Return a > b.  Computed by @total_ordering from (not a <= b).'
     op_result = self.__le__(other)
     if op_result is NotImplemented:
         return op_result
     return not op_result
 
-def _lt_from_gt(self, other):
+def _lt_from_gt(self, other, NotImplemented=NotImplemented):
     'Return a < b.  Computed by @total_ordering from (not a > b) and (a != b).'
     op_result = self.__gt__(other)
     if op_result is NotImplemented:
         return op_result
     return not op_result and self != other
 
-def _ge_from_gt(self, other):
+def _ge_from_gt(self, other, NotImplemented=NotImplemented):
     'Return a >= b.  Computed by @total_ordering from (a > b) or (a == b).'
     op_result = self.__gt__(other)
     return op_result or self == other
 
-def _le_from_gt(self, other):
+def _le_from_gt(self, other, NotImplemented=NotImplemented):
     'Return a <= b.  Computed by @total_ordering from (not a > b).'
     op_result = self.__gt__(other)
     if op_result is NotImplemented:
         return op_result
     return not op_result
 
-def _le_from_ge(self, other):
+def _le_from_ge(self, other, NotImplemented=NotImplemented):
     'Return a <= b.  Computed by @total_ordering from (not a >= b) or (a == b).'
     op_result = self.__ge__(other)
     if op_result is NotImplemented:
         return op_result
     return not op_result or self == other
 
-def _gt_from_ge(self, other):
+def _gt_from_ge(self, other, NotImplemented=NotImplemented):
     'Return a > b.  Computed by @total_ordering from (a >= b) and (a != b).'
     op_result = self.__ge__(other)
     if op_result is NotImplemented:
         return op_result
     return op_result and self != other
 
-def _lt_from_ge(self, other):
+def _lt_from_ge(self, other, NotImplemented=NotImplemented):
     'Return a < b.  Computed by @total_ordering from (not a >= b).'
     op_result = self.__ge__(other)
     if op_result is NotImplemented: