merge

Lib/functools.py

@@ -89,110 +89,115 @@ def wraps(wrapped,
 ### total_ordering class decorator
 ################################################################################
 
-# The correct way to indicate that a comparison operation doesn't
-# recognise the other type is to return NotImplemented and let the
-# interpreter handle raising TypeError if both operands return
-# NotImplemented from their respective comparison methods
-#
-# This makes the implementation of total_ordering more complicated, since
-# we need to be careful not to trigger infinite recursion when two
-# different types that both use this decorator encounter each other.
-#
-# For example, if a type implements __lt__, it's natural to define
-# __gt__ as something like:
-#
-#    lambda self, other: not self < other and not self == other
-#
-# However, using the operator syntax like that ends up invoking the full
-# type checking machinery again and means we can end up bouncing back and
-# forth between the two operands until we run out of stack space.
-#
-# The solution is to define helper functions that invoke the appropriate
-# magic methods directly, ensuring we only try each operand once, and
-# return NotImplemented immediately if it is returned from the
-# underlying user provided method. Using this scheme, the __gt__ derived
-# from a user provided __lt__ becomes:
-#
-#    'def __gt__(self, other):' + _not_op_and_not_eq % '__lt__'
+# The total ordering functions all invoke the root magic method directly
+# rather than using the corresponding operator.  This avoids possible
+# infinite recursion that could occur when the operator dispatch logic
+# detects a NotImplemented result and then calls a reflected method.
 
-# "not a < b" handles "a >= b"
-# "not a <= b" handles "a > b"
-# "not a >= b" handles "a < b"
-# "not a > b" handles "a <= b"
-_not_op = '''
-    op_result = self.%s(other)
-    if op_result is NotImplemented:
-        return NotImplemented
-    return not op_result
-'''
-
-# "a > b or a == b" handles "a >= b"
-# "a < b or a == b" handles "a <= b"
-_op_or_eq = '''
-    op_result = self.%s(other)
-    if op_result is NotImplemented:
-        return NotImplemented
-    return op_result or self == other
-'''
-
-# "not (a < b or a == b)" handles "a > b"
-# "not a < b and a != b" is equivalent
-# "not (a > b or a == b)" handles "a < b"
-# "not a > b and a != b" is equivalent
-_not_op_and_not_eq = '''
-    op_result = self.%s(other)
+def _gt_from_lt(self, other):
+    '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 NotImplemented
     return not op_result and self != other
-'''
 
-# "not a <= b or a == b" handles "a >= b"
-# "not a >= b or a == b" handles "a <= b"
-_not_op_or_eq = '''
-    op_result = self.%s(other)
+def _le_from_lt(self, other):
+    '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):
+    'Return a >= b.  Computed by @total_ordering from (not a < b).'
+    op_result = self.__lt__(other)
+    if op_result is NotImplemented:
+        return NotImplemented
+    return not op_result
+
+def _ge_from_le(self, other):
+    '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 NotImplemented
     return not op_result or self == other
-'''
 
-# "a <= b and not a == b" handles "a < b"
-# "a >= b and not a == b" handles "a > b"
-_op_and_not_eq = '''
-    op_result = self.%s(other)
+def _lt_from_le(self, other):
+    'Return a < b.  Computed by @total_ordering from (a <= b) and (a != b).'
+    op_result = self.__le__(other)
     if op_result is NotImplemented:
         return NotImplemented
     return op_result and self != other
-'''
+
+def _gt_from_le(self, other):
+    'Return a > b.  Computed by @total_ordering from (not a <= b).'
+    op_result = self.__le__(other)
+    if op_result is NotImplemented:
+        return NotImplemented
+    return not op_result
+
+def _lt_from_gt(self, other):
+    '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 NotImplemented
+    return not op_result and self != other
+
+def _ge_from_gt(self, other):
+    '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):
+    'Return a <= b.  Computed by @total_ordering from (not a > b).'
+    op_result = self.__gt__(other)
+    if op_result is NotImplemented:
+        return NotImplemented
+    return not op_result
+
+def _le_from_ge(self, other):
+    '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 NotImplemented
+    return not op_result or self == other
+
+def _gt_from_ge(self, other):
+    'Return a > b.  Computed by @total_ordering from (a >= b) and (a != b).'
+    op_result = self.__ge__(other)
+    if op_result is NotImplemented:
+        return NotImplemented
+    return op_result and self != other
+
+def _lt_from_ge(self, other):
+    'Return a < b.  Computed by @total_ordering from (not a >= b).'
+    op_result = self.__ge__(other)
+    if op_result is NotImplemented:
+        return NotImplemented
+    return not op_result
 
 def total_ordering(cls):
     """Class decorator that fills in missing ordering methods"""
     convert = {
-        '__lt__': {'__gt__': _not_op_and_not_eq,
-                   '__le__': _op_or_eq,
-                   '__ge__': _not_op},
-        '__le__': {'__ge__': _not_op_or_eq,
-                   '__lt__': _op_and_not_eq,
-                   '__gt__': _not_op},
-        '__gt__': {'__lt__': _not_op_and_not_eq,
-                   '__ge__': _op_or_eq,
-                   '__le__': _not_op},
-        '__ge__': {'__le__': _not_op_or_eq,
-                   '__gt__': _op_and_not_eq,
-                   '__lt__': _not_op}
+        '__lt__': [('__gt__', _gt_from_lt),
+                   ('__le__', _le_from_lt),
+                   ('__ge__', _ge_from_lt)],
+        '__le__': [('__ge__', _ge_from_le),
+                   ('__lt__', _lt_from_le),
+                   ('__gt__', _gt_from_le)],
+        '__gt__': [('__lt__', _lt_from_gt),
+                   ('__ge__', _ge_from_gt),
+                   ('__le__', _le_from_gt)],
+        '__ge__': [('__le__', _le_from_ge),
+                   ('__gt__', _gt_from_ge),
+                   ('__lt__', _lt_from_ge)]
     }
     # Find user-defined comparisons (not those inherited from object).
     roots = [op for op in convert if getattr(cls, op, None) is not getattr(object, op, None)]
     if not roots:
         raise ValueError('must define at least one ordering operation: < > <= >=')
     root = max(roots)       # prefer __lt__ to __le__ to __gt__ to __ge__
-    for opname, opfunc in convert[root].items():
+    for opname, opfunc in convert[root]:
         if opname not in roots:
-            namespace = {}
-            exec('def %s(self, other):%s' % (opname, opfunc % root), namespace)
-            opfunc = namespace[opname]
-            opfunc.__qualname__ = '%s.%s' % (cls.__qualname__, opname)
-            opfunc.__module__ = cls.__module__
-            opfunc.__doc__ = getattr(int, opname).__doc__
+            opfunc.__name__ = opname
             setattr(cls, opname, opfunc)
     return cls