def total_ordering(cls):
'Class decorator that fills-in missing ordering methods'
convert = {
'__lt__': [('__gt__', lambda self, other: other < self),
('__le__', lambda self, other: not other < self),
('__ge__', lambda self, other: not self < other)],
'__le__': [('__ge__', lambda self, other: other <= self),
('__lt__', lambda self, other: not other <= self),
('__gt__', lambda self, other: not self <= other)],
'__gt__': [('__lt__', lambda self, other: other > self),
('__ge__', lambda self, other: not other > self),
('__le__', lambda self, other: not self > other)],
'__ge__': [('__le__', lambda self, other: other >= self),
('__gt__', lambda self, other: not other >= self),
('__lt__', lambda self, other: not self >= other)]
}
if hasattr(object, '__lt__'):
roots = [op for op in convert if getattr(cls, op) is not getattr(object, op)]
else:
roots = set(dir(cls)) & set(convert)
assert roots, 'must define at least one ordering operation: < > <= >='
root = max(roots) # prefer __lt __ to __le__ to __gt__ to __ge__
for opname, opfunc in convert[root]:
if opname not in roots:
opfunc.__name__ = opname
opfunc.__doc__ = getattr(int, opname).__doc__
setattr(cls, opname, opfunc)
return cls