Lib/test/test_set.py

import unittest
from test import support
import gc
import weakref
import operator
import copy
import pickle
import os
from random import randrange, shuffle
import sys
import warnings
import collections

class PassThru(Exception):
    pass

def check_pass_thru():
    raise PassThru
    yield 1

class BadCmp:
    def __hash__(self):
        return 1
    def __eq__(self, other):
        raise RuntimeError

class ReprWrapper:
    'Used to test self-referential repr() calls'
    def __repr__(self):
        return repr(self.value)

class HashCountingInt(int):
    'int-like object that counts the number of times __hash__ is called'
    def __init__(self, *args):
        self.hash_count = 0
    def __hash__(self):
        self.hash_count += 1
        return int.__hash__(self)

class TestJointOps(unittest.TestCase):
    # Tests common to both set and frozenset

    def setUp(self):
        self.word = word = 'simsalabim'
        self.otherword = 'madagascar'
        self.letters = 'abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ'
        self.s = self.thetype(word)
        self.d = dict.fromkeys(word)

    def test_new_or_init(self):
        self.assertRaises(TypeError, self.thetype, [], 2)

    def test_uniquification(self):
        actual = sorted(self.s)
        expected = sorted(self.d)
        self.assertEqual(actual, expected)
        self.assertRaises(PassThru, self.thetype, check_pass_thru())
        self.assertRaises(TypeError, self.thetype, [[]])

    def test_len(self):
        self.assertEqual(len(self.s), len(self.d))

    def test_contains(self):
        for c in self.letters:
            self.assertEqual(c in self.s, c in self.d)
        self.assertRaises(TypeError, self.s.__contains__, [[]])
        s = self.thetype([frozenset(self.letters)])
        self.assertTrue(self.thetype(self.letters) in s)

    def test_union(self):
        u = self.s.union(self.otherword)
        for c in self.letters:
            self.assertEqual(c in u, c in self.d or c in self.otherword)
        self.assertEqual(self.s, self.thetype(self.word))
        self.assertEqual(type(u), self.basetype)
        self.assertRaises(PassThru, self.s.union, check_pass_thru())
        self.assertRaises(TypeError, self.s.union, [[]])
        for C in set, frozenset, dict.fromkeys, str, list, tuple:
            self.assertEqual(self.thetype('abcba').union(C('cdc')), set('abcd'))
            self.assertEqual(self.thetype('abcba').union(C('efgfe')), set('abcefg'))
            self.assertEqual(self.thetype('abcba').union(C('ccb')), set('abc'))
            self.assertEqual(self.thetype('abcba').union(C('ef')), set('abcef'))
            self.assertEqual(self.thetype('abcba').union(C('ef'), C('fg')), set('abcefg'))

    def test_or(self):
        i = self.s.union(self.otherword)
        self.assertEqual(self.s | set(self.otherword), i)
        self.assertEqual(self.s | frozenset(self.otherword), i)
        try:
            self.s | self.otherword
        except TypeError:
            pass
        else:
            self.fail("s|t did not screen-out general iterables")

    def test_intersection(self):
        i = self.s.intersection(self.otherword)
        for c in self.letters:
            self.assertEqual(c in i, c in self.d and c in self.otherword)
        self.assertEqual(self.s, self.thetype(self.word))
        self.assertEqual(type(i), self.basetype)
        self.assertRaises(PassThru, self.s.intersection, check_pass_thru())
        for C in set, frozenset, dict.fromkeys, str, list, tuple:
            self.assertEqual(self.thetype('abcba').intersection(C('cdc')), set('cc'))
            self.assertEqual(self.thetype('abcba').intersection(C('efgfe')), set(''))
            self.assertEqual(self.thetype('abcba').intersection(C('ccb')), set('bc'))
            self.assertEqual(self.thetype('abcba').intersection(C('ef')), set(''))
            self.assertEqual(self.thetype('abcba').intersection(C('cbcf'), C('bag')), set('b'))
        s = self.thetype('abcba')
        z = s.intersection()
        if self.thetype == frozenset():
            self.assertEqual(id(s), id(z))
        else:
            self.assertNotEqual(id(s), id(z))

    def test_isdisjoint(self):
        def f(s1, s2):
            'Pure python equivalent of isdisjoint()'
            return not set(s1).intersection(s2)
        for larg in '', 'a', 'ab', 'abc', 'ababac', 'cdc', 'cc', 'efgfe', 'ccb', 'ef':
            s1 = self.thetype(larg)
            for rarg in '', 'a', 'ab', 'abc', 'ababac', 'cdc', 'cc', 'efgfe', 'ccb', 'ef':
                for C in set, frozenset, dict.fromkeys, str, list, tuple:
                    s2 = C(rarg)
                    actual = s1.isdisjoint(s2)
                    expected = f(s1, s2)
                    self.assertEqual(actual, expected)
                    self.assertTrue(actual is True or actual is False)

    def test_and(self):
        i = self.s.intersection(self.otherword)
        self.assertEqual(self.s & set(self.otherword), i)
        self.assertEqual(self.s & frozenset(self.otherword), i)
        try:
            self.s & self.otherword
        except TypeError:
            pass
        else:
            self.fail("s&t did not screen-out general iterables")

    def test_difference(self):
        i = self.s.difference(self.otherword)
        for c in self.letters:
            self.assertEqual(c in i, c in self.d and c not in self.otherword)
        self.assertEqual(self.s, self.thetype(self.word))
        self.assertEqual(type(i), self.basetype)
        self.assertRaises(PassThru, self.s.difference, check_pass_thru())
        self.assertRaises(TypeError, self.s.difference, [[]])
        for C in set, frozenset, dict.fromkeys, str, list, tuple:
            self.assertEqual(self.thetype('abcba').difference(C('cdc')), set('ab'))
            self.assertEqual(self.thetype('abcba').difference(C('efgfe')), set('abc'))
            self.assertEqual(self.thetype('abcba').difference(C('ccb')), set('a'))
            self.assertEqual(self.thetype('abcba').difference(C('ef')), set('abc'))
            self.assertEqual(self.thetype('abcba').difference(), set('abc'))
            self.assertEqual(self.thetype('abcba').difference(C('a'), C('b')), set('c'))

    def test_sub(self):
        i = self.s.difference(self.otherword)
        self.assertEqual(self.s - set(self.otherword), i)
        self.assertEqual(self.s - frozenset(self.otherword), i)
        try:
            self.s - self.otherword
        except TypeError:
            pass
        else:
            self.fail("s-t did not screen-out general iterables")

    def test_symmetric_difference(self):
        i = self.s.symmetric_difference(self.otherword)
        for c in self.letters:
            self.assertEqual(c in i, (c in self.d) ^ (c in self.otherword))
        self.assertEqual(self.s, self.thetype(self.word))
        self.assertEqual(type(i), self.basetype)
        self.assertRaises(PassThru, self.s.symmetric_difference, check_pass_thru())
        self.assertRaises(TypeError, self.s.symmetric_difference, [[]])
        for C in set, frozenset, dict.fromkeys, str, list, tuple:
            self.assertEqual(self.thetype('abcba').symmetric_difference(C('cdc')), set('abd'))
            self.assertEqual(self.thetype('abcba').symmetric_difference(C('efgfe')), set('abcefg'))
            self.assertEqual(self.thetype('abcba').symmetric_difference(C('ccb')), set('a'))
            self.assertEqual(self.thetype('abcba').symmetric_difference(C('ef')), set('abcef'))

    def test_xor(self):
        i = self.s.symmetric_difference(self.otherword)
        self.assertEqual(self.s ^ set(self.otherword), i)
        self.assertEqual(self.s ^ frozenset(self.otherword), i)
        try:
            self.s ^ self.otherword
        except TypeError:
            pass
        else:
            self.fail("s^t did not screen-out general iterables")

    def test_equality(self):
        self.assertEqual(self.s, set(self.word))
        self.assertEqual(self.s, frozenset(self.word))
        self.assertEqual(self.s == self.word, False)
        self.assertNotEqual(self.s, set(self.otherword))
        self.assertNotEqual(self.s, frozenset(self.otherword))
        self.assertEqual(self.s != self.word, True)

    def test_setOfFrozensets(self):
        t = map(frozenset, ['abcdef', 'bcd', 'bdcb', 'fed', 'fedccba'])
        s = self.thetype(t)
        self.assertEqual(len(s), 3)

    def test_sub_and_super(self):
        p, q, r = map(self.thetype, ['ab', 'abcde', 'def'])
        self.assertTrue(p < q)
        self.assertTrue(p <= q)
        self.assertTrue(q <= q)
        self.assertTrue(q > p)
        self.assertTrue(q >= p)
        self.assertFalse(q < r)
        self.assertFalse(q <= r)
        self.assertFalse(q > r)
        self.assertFalse(q >= r)
        self.assertTrue(set('a').issubset('abc'))
        self.assertTrue(set('abc').issuperset('a'))
        self.assertFalse(set('a').issubset('cbs'))
        self.assertFalse(set('cbs').issuperset('a'))

    def test_pickling(self):
        for i in range(pickle.HIGHEST_PROTOCOL + 1):
            p = pickle.dumps(self.s, i)
            dup = pickle.loads(p)
            self.assertEqual(self.s, dup, "%s != %s" % (self.s, dup))
            if type(self.s) not in (set, frozenset):
                self.s.x = 10
                p = pickle.dumps(self.s)
                dup = pickle.loads(p)
                self.assertEqual(self.s.x, dup.x)

    def test_deepcopy(self):
        class Tracer:
            def __init__(self, value):
                self.value = value
            def __hash__(self):
                return self.value
            def __deepcopy__(self, memo=None):
                return Tracer(self.value + 1)
        t = Tracer(10)
        s = self.thetype([t])
        dup = copy.deepcopy(s)
        self.assertNotEqual(id(s), id(dup))
        for elem in dup:
            newt = elem
        self.assertNotEqual(id(t), id(newt))
        self.assertEqual(t.value + 1, newt.value)

    def test_gc(self):
        # Create a nest of cycles to exercise overall ref count check
        class A:
            pass
        s = set(A() for i in range(1000))
        for elem in s:
            elem.cycle = s
            elem.sub = elem
            elem.set = set([elem])

    def test_subclass_with_custom_hash(self):
        # Bug #1257731
        class H(self.thetype):
            def __hash__(self):
                return int(id(self) & 0x7fffffff)
        s=H()
        f=set()
        f.add(s)
        self.assertTrue(s in f)
        f.remove(s)
        f.add(s)
        f.discard(s)

    def test_badcmp(self):
        s = self.thetype([BadCmp()])
        # Detect comparison errors during insertion and lookup
        self.assertRaises(RuntimeError, self.thetype, [BadCmp(), BadCmp()])
        self.assertRaises(RuntimeError, s.__contains__, BadCmp())
        # Detect errors during mutating operations
        if hasattr(s, 'add'):
            self.assertRaises(RuntimeError, s.add, BadCmp())
            self.assertRaises(RuntimeError, s.discard, BadCmp())
            self.assertRaises(RuntimeError, s.remove, BadCmp())

    def test_cyclical_repr(self):
        w = ReprWrapper()
        s = self.thetype([w])
        w.value = s
        if self.thetype == set:
            self.assertEqual(repr(s), '{set(...)}')
        else:
            name = repr(s).partition('(')[0]    # strip class name
            self.assertEqual(repr(s), '%s({%s(...)})' % (name, name))

    def test_cyclical_print(self):
        w = ReprWrapper()
        s = self.thetype([w])
        w.value = s
        fo = open(support.TESTFN, "w")
        try:
            fo.write(str(s))
            fo.close()
            fo = open(support.TESTFN, "r")
            self.assertEqual(fo.read(), repr(s))
        finally:
            fo.close()
            support.unlink(support.TESTFN)

    def test_do_not_rehash_dict_keys(self):
        n = 10
        d = dict.fromkeys(map(HashCountingInt, range(n)))
        self.assertEqual(sum(elem.hash_count for elem in d), n)
        s = self.thetype(d)
        self.assertEqual(sum(elem.hash_count for elem in d), n)
        s.difference(d)
        self.assertEqual(sum(elem.hash_count for elem in d), n)
        if hasattr(s, 'symmetric_difference_update'):
            s.symmetric_difference_update(d)
        self.assertEqual(sum(elem.hash_count for elem in d), n)
        d2 = dict.fromkeys(set(d))
        self.assertEqual(sum(elem.hash_count for elem in d), n)
        d3 = dict.fromkeys(frozenset(d))
        self.assertEqual(sum(elem.hash_count for elem in d), n)
        d3 = dict.fromkeys(frozenset(d), 123)
        self.assertEqual(sum(elem.hash_count for elem in d), n)
        self.assertEqual(d3, dict.fromkeys(d, 123))

    def test_container_iterator(self):
        # Bug #3680: tp_traverse was not implemented for set iterator object
        class C(object):
            pass
        obj = C()
        ref = weakref.ref(obj)
        container = set([obj, 1])
        obj.x = iter(container)
        del obj, container
        gc.collect()
        self.assertTrue(ref() is None, "Cycle was not collected")

class TestSet(TestJointOps):
    thetype = set
    basetype = set

    def test_init(self):
        s = self.thetype()
        s.__init__(self.word)
        self.assertEqual(s, set(self.word))
        s.__init__(self.otherword)
        self.assertEqual(s, set(self.otherword))
        self.assertRaises(TypeError, s.__init__, s, 2);
        self.assertRaises(TypeError, s.__init__, 1);

    def test_constructor_identity(self):
        s = self.thetype(range(3))
        t = self.thetype(s)
        self.assertNotEqual(id(s), id(t))

    def test_set_literal(self):
        s = set([1,2,3])
        t = {1,2,3}
        self.assertEqual(s, t)

    def test_hash(self):
        self.assertRaises(TypeError, hash, self.s)

    def test_clear(self):
        self.s.clear()
        self.assertEqual(self.s, set())
        self.assertEqual(len(self.s), 0)

    def test_copy(self):
        dup = self.s.copy()
        self.assertEqual(self.s, dup)
        self.assertNotEqual(id(self.s), id(dup))
        self.assertEqual(type(dup), self.basetype)

    def test_add(self):
        self.s.add('Q')
        self.assertTrue('Q' in self.s)
        dup = self.s.copy()
        self.s.add('Q')
        self.assertEqual(self.s, dup)
        self.assertRaises(TypeError, self.s.add, [])

    def test_remove(self):
        self.s.remove('a')
        self.assertTrue('a' not in self.s)
        self.assertRaises(KeyError, self.s.remove, 'Q')
        self.assertRaises(TypeError, self.s.remove, [])
        s = self.thetype([frozenset(self.word)])
        self.assertTrue(self.thetype(self.word) in s)
        s.remove(self.thetype(self.word))
        self.assertTrue(self.thetype(self.word) not in s)
        self.assertRaises(KeyError, self.s.remove, self.thetype(self.word))

    def test_remove_keyerror_unpacking(self):
        # bug:  www.python.org/sf/1576657
        for v1 in ['Q', (1,)]:
            try:
                self.s.remove(v1)
            except KeyError as e:
                v2 = e.args[0]
                self.assertEqual(v1, v2)
            else:
                self.fail()

    def test_remove_keyerror_set(self):
        key = self.thetype([3, 4])
        try:
            self.s.remove(key)
        except KeyError as e:
            self.assertTrue(e.args[0] is key,
                         "KeyError should be {0}, not {1}".format(key,
                                                                  e.args[0]))
        else:
            self.fail()

    def test_discard(self):
        self.s.discard('a')
        self.assertTrue('a' not in self.s)
        self.s.discard('Q')
        self.assertRaises(TypeError, self.s.discard, [])
        s = self.thetype([frozenset(self.word)])
        self.assertTrue(self.thetype(self.word) in s)
        s.discard(self.thetype(self.word))
        self.assertTrue(self.thetype(self.word) not in s)
        s.discard(self.thetype(self.word))

    def test_pop(self):
        for i in range(len(self.s)):
            elem = self.s.pop()
            self.assertTrue(elem not in self.s)
        self.assertRaises(KeyError, self.s.pop)

    def test_update(self):
        retval = self.s.update(self.otherword)
        self.assertEqual(retval, None)
        for c in (self.word + self.otherword):
            self.assertTrue(c in self.s)
        self.assertRaises(PassThru, self.s.update, check_pass_thru())
        self.assertRaises(TypeError, self.s.update, [[]])
        for p, q in (('cdc', 'abcd'), ('efgfe', 'abcefg'), ('ccb', 'abc'), ('ef', 'abcef')):
            for C in set, frozenset, dict.fromkeys, str, list, tuple:
                s = self.thetype('abcba')
                self.assertEqual(s.update(C(p)), None)
                self.assertEqual(s, set(q))
        for p in ('cdc', 'efgfe', 'ccb', 'ef', 'abcda'):
            q = 'ahi'
            for C in set, frozenset, dict.fromkeys, str, list, tuple:
                s = self.thetype('abcba')
                self.assertEqual(s.update(C(p), C(q)), None)
                self.assertEqual(s, set(s) | set(p) | set(q))

    def test_ior(self):
        self.s |= set(self.otherword)
        for c in (self.word + self.otherword):
            self.assertTrue(c in self.s)

    def test_intersection_update(self):
        retval = self.s.intersection_update(self.otherword)
        self.assertEqual(retval, None)
        for c in (self.word + self.otherword):
            if c in self.otherword and c in self.word:
                self.assertTrue(c in self.s)
            else:
                self.assertTrue(c not in self.s)
        self.assertRaises(PassThru, self.s.intersection_update, check_pass_thru())
        self.assertRaises(TypeError, self.s.intersection_update, [[]])
        for p, q in (('cdc', 'c'), ('efgfe', ''), ('ccb', 'bc'), ('ef', '')):
            for C in set, frozenset, dict.fromkeys, str, list, tuple:
                s = self.thetype('abcba')
                self.assertEqual(s.intersection_update(C(p)), None)
                self.assertEqual(s, set(q))
                ss = 'abcba'
                s = self.thetype(ss)
                t = 'cbc'
                self.assertEqual(s.intersection_update(C(p), C(t)), None)
                self.assertEqual(s, set('abcba')&set(p)&set(t))

    def test_iand(self):
        self.s &= set(self.otherword)
        for c in (self.word + self.otherword):
            if c in self.otherword and c in self.word:
                self.assertTrue(c in self.s)
            else:
                self.assertTrue(c not in self.s)

    def test_difference_update(self):
        retval = self.s.difference_update(self.otherword)
        self.assertEqual(retval, None)
        for c in (self.word + self.otherword):
            if c in self.word and c not in self.otherword:
                self.assertTrue(c in self.s)
            else:
                self.assertTrue(c not in self.s)
        self.assertRaises(PassThru, self.s.difference_update, check_pass_thru())
        self.assertRaises(TypeError, self.s.difference_update, [[]])
        self.assertRaises(TypeError, self.s.symmetric_difference_update, [[]])
        for p, q in (('cdc', 'ab'), ('efgfe', 'abc'), ('ccb', 'a'), ('ef', 'abc')):
            for C in set, frozenset, dict.fromkeys, str, list, tuple:
                s = self.thetype('abcba')
                self.assertEqual(s.difference_update(C(p)), None)
                self.assertEqual(s, set(q))

                s = self.thetype('abcdefghih')
                s.difference_update()
                self.assertEqual(s, self.thetype('abcdefghih'))

                s = self.thetype('abcdefghih')
                s.difference_update(C('aba'))
                self.assertEqual(s, self.thetype('cdefghih'))

                s = self.thetype('abcdefghih')
                s.difference_update(C('cdc'), C('aba'))
                self.assertEqual(s, self.thetype('efghih'))

    def test_isub(self):
        self.s -= set(self.otherword)
        for c in (self.word + self.otherword):
            if c in self.word and c not in self.otherword:
                self.assertTrue(c in self.s)
            else:
                self.assertTrue(c not in self.s)

    def test_symmetric_difference_update(self):
        retval = self.s.symmetric_difference_update(self.otherword)
        self.assertEqual(retval, None)
        for c in (self.word + self.otherword):
            if (c in self.word) ^ (c in self.otherword):
                self.assertTrue(c in self.s)
            else:
                self.assertTrue(c not in self.s)
        self.assertRaises(PassThru, self.s.symmetric_difference_update, check_pass_thru())
        self.assertRaises(TypeError, self.s.symmetric_difference_update, [[]])
        for p, q in (('cdc', 'abd'), ('efgfe', 'abcefg'), ('ccb', 'a'), ('ef', 'abcef')):
            for C in set, frozenset, dict.fromkeys, str, list, tuple:
                s = self.thetype('abcba')
                self.assertEqual(s.symmetric_difference_update(C(p)), None)
                self.assertEqual(s, set(q))

    def test_ixor(self):
        self.s ^= set(self.otherword)
        for c in (self.word + self.otherword):
            if (c in self.word) ^ (c in self.otherword):
                self.assertTrue(c in self.s)
            else:
                self.assertTrue(c not in self.s)

    def test_inplace_on_self(self):
        t = self.s.copy()
        t |= t
        self.assertEqual(t, self.s)
        t &= t
        self.assertEqual(t, self.s)
        t -= t
        self.assertEqual(t, self.thetype())
        t = self.s.copy()
        t ^= t
        self.assertEqual(t, self.thetype())

    def test_weakref(self):
        s = self.thetype('gallahad')
        p = weakref.proxy(s)
        self.assertEqual(str(p), str(s))
        s = None
        self.assertRaises(ReferenceError, str, p)

    def test_rich_compare(self):
        class TestRichSetCompare:
            def __gt__(self, some_set):
                self.gt_called = True
                return False
            def __lt__(self, some_set):
                self.lt_called = True
                return False
            def __ge__(self, some_set):
                self.ge_called = True
                return False
            def __le__(self, some_set):
                self.le_called = True
                return False

        # This first tries the bulitin rich set comparison, which doesn't know
        # how to handle the custom object. Upon returning NotImplemented, the
        # corresponding comparison on the right object is invoked.
        myset = {1, 2, 3}

        myobj = TestRichSetCompare()
        myset < myobj
        self.assertTrue(myobj.gt_called)

        myobj = TestRichSetCompare()
        myset > myobj
        self.assertTrue(myobj.lt_called)

        myobj = TestRichSetCompare()
        myset <= myobj
        self.assertTrue(myobj.ge_called)

        myobj = TestRichSetCompare()
        myset >= myobj
        self.assertTrue(myobj.le_called)

    # C API test only available in a debug build
    if hasattr(set, "test_c_api"):
        def test_c_api(self):
            self.assertEqual(set('abc').test_c_api(), True)

class SetSubclass(set):
    pass

class TestSetSubclass(TestSet):
    thetype = SetSubclass
    basetype = set

class SetSubclassWithKeywordArgs(set):
    def __init__(self, iterable=[], newarg=None):
        set.__init__(self, iterable)

class TestSetSubclassWithKeywordArgs(TestSet):

    def test_keywords_in_subclass(self):
        'SF bug #1486663 -- this used to erroneously raise a TypeError'
        SetSubclassWithKeywordArgs(newarg=1)

class TestFrozenSet(TestJointOps):
    thetype = frozenset
    basetype = frozenset

    def test_init(self):
        s = self.thetype(self.word)
        s.__init__(self.otherword)
        self.assertEqual(s, set(self.word))

    def test_singleton_empty_frozenset(self):
        f = frozenset()
        efs = [frozenset(), frozenset([]), frozenset(()), frozenset(''),
               frozenset(), frozenset([]), frozenset(()), frozenset(''),
               frozenset(range(0)), frozenset(frozenset()),
               frozenset(f), f]
        # All of the empty frozensets should have just one id()
        self.assertEqual(len(set(map(id, efs))), 1)

    def test_constructor_identity(self):
        s = self.thetype(range(3))
        t = self.thetype(s)
        self.assertEqual(id(s), id(t))

    def test_hash(self):
        self.assertEqual(hash(self.thetype('abcdeb')),
                         hash(self.thetype('ebecda')))

        # make sure that all permutations give the same hash value
        n = 100
        seq = [randrange(n) for i in range(n)]
        results = set()
        for i in range(200):
            shuffle(seq)
            results.add(hash(self.thetype(seq)))
        self.assertEqual(len(results), 1)

    def test_copy(self):
        dup = self.s.copy()
        self.assertEqual(id(self.s), id(dup))

    def test_frozen_as_dictkey(self):
        seq = list(range(10)) + list('abcdefg') + ['apple']
        key1 = self.thetype(seq)
        key2 = self.thetype(reversed(seq))
        self.assertEqual(key1, key2)
        self.assertNotEqual(id(key1), id(key2))
        d = {}
        d[key1] = 42
        self.assertEqual(d[key2], 42)

    def test_hash_caching(self):
        f = self.thetype('abcdcda')
        self.assertEqual(hash(f), hash(f))

    def test_hash_effectiveness(self):
        n = 13
        hashvalues = set()
        addhashvalue = hashvalues.add
        elemmasks = [(i+1, 1<<i) for i in range(n)]
        for i in range(2**n):
            addhashvalue(hash(frozenset([e for e, m in elemmasks if m&i])))
        self.assertEqual(len(hashvalues), 2**n)

class FrozenSetSubclass(frozenset):
    pass

class TestFrozenSetSubclass(TestFrozenSet):
    thetype = FrozenSetSubclass
    basetype = frozenset

    def test_constructor_identity(self):
        s = self.thetype(range(3))
        t = self.thetype(s)
        self.assertNotEqual(id(s), id(t))

    def test_copy(self):
        dup = self.s.copy()
        self.assertNotEqual(id(self.s), id(dup))

    def test_nested_empty_constructor(self):
        s = self.thetype()
        t = self.thetype(s)
        self.assertEqual(s, t)

    def test_singleton_empty_frozenset(self):
        Frozenset = self.thetype
        f = frozenset()
        F = Frozenset()
        efs = [Frozenset(), Frozenset([]), Frozenset(()), Frozenset(''),
               Frozenset(), Frozenset([]), Frozenset(()), Frozenset(''),
               Frozenset(range(0)), Frozenset(Frozenset()),
               Frozenset(frozenset()), f, F, Frozenset(f), Frozenset(F)]
        # All empty frozenset subclass instances should have different ids
        self.assertEqual(len(set(map(id, efs))), len(efs))

# Tests taken from test_sets.py =============================================

empty_set = set()

#==============================================================================

class TestBasicOps(unittest.TestCase):

    def test_repr(self):
        if self.repr is not None:
            self.assertEqual(repr(self.set), self.repr)

    def test_print(self):
        try:
            fo = open(support.TESTFN, "w")
            fo.write(str(self.set))
            fo.close()
            fo = open(support.TESTFN, "r")
            self.assertEqual(fo.read(), repr(self.set))
        finally:
            fo.close()
            support.unlink(support.TESTFN)

    def test_length(self):
        self.assertEqual(len(self.set), self.length)

    def test_self_equality(self):
        self.assertEqual(self.set, self.set)

    def test_equivalent_equality(self):
        self.assertEqual(self.set, self.dup)

    def test_copy(self):
        self.assertEqual(self.set.copy(), self.dup)

    def test_self_union(self):
        result = self.set | self.set
        self.assertEqual(result, self.dup)

    def test_empty_union(self):
        result = self.set | empty_set
        self.assertEqual(result, self.dup)

    def test_union_empty(self):
        result = empty_set | self.set
        self.assertEqual(result, self.dup)

    def test_self_intersection(self):
        result = self.set & self.set
        self.assertEqual(result, self.dup)

    def test_empty_intersection(self):
        result = self.set & empty_set
        self.assertEqual(result, empty_set)

    def test_intersection_empty(self):
        result = empty_set & self.set
        self.assertEqual(result, empty_set)

    def test_self_isdisjoint(self):
        result = self.set.isdisjoint(self.set)
        self.assertEqual(result, not self.set)

    def test_empty_isdisjoint(self):
        result = self.set.isdisjoint(empty_set)
        self.assertEqual(result, True)

    def test_isdisjoint_empty(self):
        result = empty_set.isdisjoint(self.set)
        self.assertEqual(result, True)

    def test_self_symmetric_difference(self):
        result = self.set ^ self.set
        self.assertEqual(result, empty_set)

    def checkempty_symmetric_difference(self):
        result = self.set ^ empty_set
        self.assertEqual(result, self.set)

    def test_self_difference(self):
        result = self.set - self.set
        self.assertEqual(result, empty_set)

    def test_empty_difference(self):
        result = self.set - empty_set
        self.assertEqual(result, self.dup)

    def test_empty_difference_rev(self):
        result = empty_set - self.set
        self.assertEqual(result, empty_set)

    def test_iteration(self):
        for v in self.set:
            self.assertTrue(v in self.values)
        setiter = iter(self.set)
        # note: __length_hint__ is an internal undocumented API,
        # don't rely on it in your own programs
        self.assertEqual(setiter.__length_hint__(), len(self.set))

    def test_pickling(self):
        p = pickle.dumps(self.set)
        copy = pickle.loads(p)
        self.assertEqual(self.set, copy,
                         "%s != %s" % (self.set, copy))

#------------------------------------------------------------------------------

class TestBasicOpsEmpty(TestBasicOps):
    def setUp(self):
        self.case   = "empty set"
        self.values = []
        self.set    = set(self.values)
        self.dup    = set(self.values)
        self.length = 0
        self.repr   = "set()"

#------------------------------------------------------------------------------

class TestBasicOpsSingleton(TestBasicOps):
    def setUp(self):
        self.case   = "unit set (number)"
        self.values = [3]
        self.set    = set(self.values)
        self.dup    = set(self.values)
        self.length = 1
        self.repr   = "{3}"

    def test_in(self):
        self.assertTrue(3 in self.set)

    def test_not_in(self):
        self.assertTrue(2 not in self.set)

#------------------------------------------------------------------------------

class TestBasicOpsTuple(TestBasicOps):
    def setUp(self):
        self.case   = "unit set (tuple)"
        self.values = [(0, "zero")]
        self.set    = set(self.values)
        self.dup    = set(self.values)
        self.length = 1
        self.repr   = "{(0, 'zero')}"

    def test_in(self):
        self.assertTrue((0, "zero") in self.set)

    def test_not_in(self):
        self.assertTrue(9 not in self.set)

#------------------------------------------------------------------------------

class TestBasicOpsTriple(TestBasicOps):
    def setUp(self):
        self.case   = "triple set"
        self.values = [0, "zero", operator.add]
        self.set    = set(self.values)
        self.dup    = set(self.values)
        self.length = 3
        self.repr   = None

#------------------------------------------------------------------------------

class TestBasicOpsString(TestBasicOps):
    def setUp(self):
        self.case   = "string set"
        self.values = ["a", "b", "c"]
        self.set    = set(self.values)
        self.dup    = set(self.values)
        self.length = 3
        self.repr   = "{'a', 'c', 'b'}"

#------------------------------------------------------------------------------

class TestBasicOpsBytes(TestBasicOps):
    def setUp(self):
        self.case   = "string set"
        self.values = [b"a", b"b", b"c"]
        self.set    = set(self.values)
        self.dup    = set(self.values)
        self.length = 3
        self.repr   = "{b'a', b'c', b'b'}"

#------------------------------------------------------------------------------

class TestBasicOpsMixedStringBytes(TestBasicOps):
    def setUp(self):
        self.warning_filters = warnings.filters[:]
        warnings.simplefilter('ignore', BytesWarning)
        self.case   = "string and bytes set"
        self.values = ["a", "b", b"a", b"b"]
        self.set    = set(self.values)
        self.dup    = set(self.values)
        self.length = 4
        self.repr   = "{'a', b'a', 'b', b'b'}"

    def tearDown(self):
        warnings.filters = self.warning_filters

#==============================================================================

def baditer():
    raise TypeError
    yield True

def gooditer():
    yield True

class TestExceptionPropagation(unittest.TestCase):
    """SF 628246:  Set constructor should not trap iterator TypeErrors"""

    def test_instanceWithException(self):
        self.assertRaises(TypeError, set, baditer())

    def test_instancesWithoutException(self):
        # All of these iterables should load without exception.
        set([1,2,3])
        set((1,2,3))
        set({'one':1, 'two':2, 'three':3})
        set(range(3))
        set('abc')
        set(gooditer())

    def test_changingSizeWhileIterating(self):
        s = set([1,2,3])
        try:
            for i in s:
                s.update([4])
        except RuntimeError:
            pass
        else:
            self.fail("no exception when changing size during iteration")

#==============================================================================

class TestSetOfSets(unittest.TestCase):
    def test_constructor(self):
        inner = frozenset([1])
        outer = set([inner])
        element = outer.pop()
        self.assertEqual(type(element), frozenset)
        outer.add(inner)        # Rebuild set of sets with .add method
        outer.remove(inner)
        self.assertEqual(outer, set())   # Verify that remove worked
        outer.discard(inner)    # Absence of KeyError indicates working fine

#==============================================================================

class TestBinaryOps(unittest.TestCase):
    def setUp(self):
        self.set = set((2, 4, 6))

    def test_eq(self):              # SF bug 643115
        self.assertEqual(self.set, set({2:1,4:3,6:5}))

    def test_union_subset(self):
        result = self.set | set([2])
        self.assertEqual(result, set((2, 4, 6)))

    def test_union_superset(self):
        result = self.set | set([2, 4, 6, 8])
        self.assertEqual(result, set([2, 4, 6, 8]))

    def test_union_overlap(self):
        result = self.set | set([3, 4, 5])
        self.assertEqual(result, set([2, 3, 4, 5, 6]))

    def test_union_non_overlap(self):
        result = self.set | set([8])
        self.assertEqual(result, set([2, 4, 6, 8]))

    def test_intersection_subset(self):
        result = self.set & set((2, 4))
        self.assertEqual(result, set((2, 4)))

    def test_intersection_superset(self):
        result = self.set & set([2, 4, 6, 8])
        self.assertEqual(result, set([2, 4, 6]))

    def test_intersection_overlap(self):
        result = self.set & set([3, 4, 5])
        self.assertEqual(result, set([4]))

    def test_intersection_non_overlap(self):
        result = self.set & set([8])
        self.assertEqual(result, empty_set)

    def test_isdisjoint_subset(self):
        result = self.set.isdisjoint(set((2, 4)))
        self.assertEqual(result, False)

    def test_isdisjoint_superset(self):
        result = self.set.isdisjoint(set([2, 4, 6, 8]))
        self.assertEqual(result, False)

    def test_isdisjoint_overlap(self):
        result = self.set.isdisjoint(set([3, 4, 5]))
        self.assertEqual(result, False)

    def test_isdisjoint_non_overlap(self):
        result = self.set.isdisjoint(set([8]))
        self.assertEqual(result, True)

    def test_sym_difference_subset(self):
        result = self.set ^ set((2, 4))
        self.assertEqual(result, set([6]))

    def test_sym_difference_superset(self):
        result = self.set ^ set((2, 4, 6, 8))
        self.assertEqual(result, set([8]))

    def test_sym_difference_overlap(self):
        result = self.set ^ set((3, 4, 5))
        self.assertEqual(result, set([2, 3, 5, 6]))

    def test_sym_difference_non_overlap(self):
        result = self.set ^ set([8])
        self.assertEqual(result, set([2, 4, 6, 8]))

#==============================================================================

class TestUpdateOps(unittest.TestCase):
    def setUp(self):
        self.set = set((2, 4, 6))

    def test_union_subset(self):
        self.set |= set([2])
        self.assertEqual(self.set, set((2, 4, 6)))

    def test_union_superset(self):
        self.set |= set([2, 4, 6, 8])
        self.assertEqual(self.set, set([2, 4, 6, 8]))

    def test_union_overlap(self):
        self.set |= set([3, 4, 5])
        self.assertEqual(self.set, set([2, 3, 4, 5, 6]))

    def test_union_non_overlap(self):
        self.set |= set([8])
        self.assertEqual(self.set, set([2, 4, 6, 8]))

    def test_union_method_call(self):
        self.set.update(set([3, 4, 5]))
        self.assertEqual(self.set, set([2, 3, 4, 5, 6]))

    def test_intersection_subset(self):
        self.set &= set((2, 4))
        self.assertEqual(self.set, set((2, 4)))

    def test_intersection_superset(self):
        self.set &= set([2, 4, 6, 8])
        self.assertEqual(self.set, set([2, 4, 6]))

    def test_intersection_overlap(self):
        self.set &= set([3, 4, 5])
        self.assertEqual(self.set, set([4]))

    def test_intersection_non_overlap(self):
        self.set &= set([8])
        self.assertEqual(self.set, empty_set)

    def test_intersection_method_call(self):
        self.set.intersection_update(set([3, 4, 5]))
        self.assertEqual(self.set, set([4]))

    def test_sym_difference_subset(self):
        self.set ^= set((2, 4))
        self.assertEqual(self.set, set([6]))

    def test_sym_difference_superset(self):
        self.set ^= set((2, 4, 6, 8))
        self.assertEqual(self.set, set([8]))

    def test_sym_difference_overlap(self):
        self.set ^= set((3, 4, 5))
        self.assertEqual(self.set, set([2, 3, 5, 6]))

    def test_sym_difference_non_overlap(self):
        self.set ^= set([8])
        self.assertEqual(self.set, set([2, 4, 6, 8]))

    def test_sym_difference_method_call(self):
        self.set.symmetric_difference_update(set([3, 4, 5]))
        self.assertEqual(self.set, set([2, 3, 5, 6]))

    def test_difference_subset(self):
        self.set -= set((2, 4))
        self.assertEqual(self.set, set([6]))

    def test_difference_superset(self):
        self.set -= set((2, 4, 6, 8))
        self.assertEqual(self.set, set([]))

    def test_difference_overlap(self):
        self.set -= set((3, 4, 5))
        self.assertEqual(self.set, set([2, 6]))

    def test_difference_non_overlap(self):
        self.set -= set([8])
        self.assertEqual(self.set, set([2, 4, 6]))

    def test_difference_method_call(self):
        self.set.difference_update(set([3, 4, 5]))
        self.assertEqual(self.set, set([2, 6]))

#==============================================================================

class TestMutate(unittest.TestCase):
    def setUp(self):
        self.values = ["a", "b", "c"]
        self.set = set(self.values)

    def test_add_present(self):
        self.set.add("c")
        self.assertEqual(self.set, set("abc"))

    def test_add_absent(self):
        self.set.add("d")
        self.assertEqual(self.set, set("abcd"))

    def test_add_until_full(self):
        tmp = set()
        expected_len = 0
        for v in self.values:
            tmp.add(v)
            expected_len += 1
            self.assertEqual(len(tmp), expected_len)
        self.assertEqual(tmp, self.set)

    def test_remove_present(self):
        self.set.remove("b")
        self.assertEqual(self.set, set("ac"))

    def test_remove_absent(self):
        try:
            self.set.remove("d")
            self.fail("Removing missing element should have raised LookupError")
        except LookupError:
            pass

    def test_remove_until_empty(self):
        expected_len = len(self.set)
        for v in self.values:
            self.set.remove(v)
            expected_len -= 1
            self.assertEqual(len(self.set), expected_len)

    def test_discard_present(self):
        self.set.discard("c")
        self.assertEqual(self.set, set("ab"))

    def test_discard_absent(self):
        self.set.discard("d")
        self.assertEqual(self.set, set("abc"))

    def test_clear(self):
        self.set.clear()
        self.assertEqual(len(self.set), 0)

    def test_pop(self):
        popped = {}
        while self.set:
            popped[self.set.pop()] = None
        self.assertEqual(len(popped), len(self.values))
        for v in self.values:
            self.assertTrue(v in popped)

    def test_update_empty_tuple(self):
        self.set.update(())
        self.assertEqual(self.set, set(self.values))

    def test_update_unit_tuple_overlap(self):
        self.set.update(("a",))
        self.assertEqual(self.set, set(self.values))

    def test_update_unit_tuple_non_overlap(self):
        self.set.update(("a", "z"))
        self.assertEqual(self.set, set(self.values + ["z"]))

#==============================================================================

class TestSubsets(unittest.TestCase):

    case2method = {"<=": "issubset",
                   ">=": "issuperset",
                  }

    reverse = {"==": "==",
               "!=": "!=",
               "<":  ">",
               ">":  "<",
               "<=": ">=",
               ">=": "<=",
              }

    def test_issubset(self):
        x = self.left
        y = self.right
        for case in "!=", "==", "<", "<=", ">", ">=":
            expected = case in self.cases
            # Test the binary infix spelling.
            result = eval("x" + case + "y", locals())
            self.assertEqual(result, expected)
            # Test the "friendly" method-name spelling, if one exists.
            if case in TestSubsets.case2method:
                method = getattr(x, TestSubsets.case2method[case])
                result = method(y)
                self.assertEqual(result, expected)

            # Now do the same for the operands reversed.
            rcase = TestSubsets.reverse[case]
            result = eval("y" + rcase + "x", locals())
            self.assertEqual(result, expected)
            if rcase in TestSubsets.case2method:
                method = getattr(y, TestSubsets.case2method[rcase])
                result = method(x)
                self.assertEqual(result, expected)
#------------------------------------------------------------------------------

class TestSubsetEqualEmpty(TestSubsets):
    left  = set()
    right = set()
    name  = "both empty"
    cases = "==", "<=", ">="

#------------------------------------------------------------------------------

class TestSubsetEqualNonEmpty(TestSubsets):
    left  = set([1, 2])
    right = set([1, 2])
    name  = "equal pair"
    cases = "==", "<=", ">="

#------------------------------------------------------------------------------

class TestSubsetEmptyNonEmpty(TestSubsets):
    left  = set()
    right = set([1, 2])
    name  = "one empty, one non-empty"
    cases = "!=", "<", "<="

#------------------------------------------------------------------------------

class TestSubsetPartial(TestSubsets):
    left  = set([1])
    right = set([1, 2])
    name  = "one a non-empty proper subset of other"
    cases = "!=", "<", "<="

#------------------------------------------------------------------------------

class TestSubsetNonOverlap(TestSubsets):
    left  = set([1])
    right = set([2])
    name  = "neither empty, neither contains"
    cases = "!="

#==============================================================================

class TestOnlySetsInBinaryOps(unittest.TestCase):

    def test_eq_ne(self):
        # Unlike the others, this is testing that == and != *are* allowed.
        self.assertEqual(self.other == self.set, False)
        self.assertEqual(self.set == self.other, False)
        self.assertEqual(self.other != self.set, True)
        self.assertEqual(self.set != self.other, True)

    def test_ge_gt_le_lt(self):
        self.assertRaises(TypeError, lambda: self.set < self.other)
        self.assertRaises(TypeError, lambda: self.set <= self.other)
        self.assertRaises(TypeError, lambda: self.set > self.other)
        self.assertRaises(TypeError, lambda: self.set >= self.other)

        self.assertRaises(TypeError, lambda: self.other < self.set)
        self.assertRaises(TypeError, lambda: self.other <= self.set)
        self.assertRaises(TypeError, lambda: self.other > self.set)
        self.assertRaises(TypeError, lambda: self.other >= self.set)

    def test_update_operator(self):
        try:
            self.set |= self.other
        except TypeError:
            pass
        else:
            self.fail("expected TypeError")

    def test_update(self):
        if self.otherIsIterable:
            self.set.update(self.other)
        else:
            self.assertRaises(TypeError, self.set.update, self.other)

    def test_union(self):
        self.assertRaises(TypeError, lambda: self.set | self.other)
        self.assertRaises(TypeError, lambda: self.other | self.set)
        if self.otherIsIterable:
            self.set.union(self.other)
        else:
            self.assertRaises(TypeError, self.set.union, self.other)

    def test_intersection_update_operator(self):
        try:
            self.set &= self.other
        except TypeError:
            pass
        else:
            self.fail("expected TypeError")

    def test_intersection_update(self):
        if self.otherIsIterable:
            self.set.intersection_update(self.other)
        else:
            self.assertRaises(TypeError,
                              self.set.intersection_update,
                              self.other)

    def test_intersection(self):
        self.assertRaises(TypeError, lambda: self.set & self.other)
        self.assertRaises(TypeError, lambda: self.other & self.set)
        if self.otherIsIterable:
            self.set.intersection(self.other)
        else:
            self.assertRaises(TypeError, self.set.intersection, self.other)

    def test_sym_difference_update_operator(self):
        try:
            self.set ^= self.other
        except TypeError:
            pass
        else:
            self.fail("expected TypeError")

    def test_sym_difference_update(self):
        if self.otherIsIterable:
            self.set.symmetric_difference_update(self.other)
        else:
            self.assertRaises(TypeError,
                              self.set.symmetric_difference_update,
                              self.other)

    def test_sym_difference(self):
        self.assertRaises(TypeError, lambda: self.set ^ self.other)
        self.assertRaises(TypeError, lambda: self.other ^ self.set)
        if self.otherIsIterable:
            self.set.symmetric_difference(self.other)
        else:
            self.assertRaises(TypeError, self.set.symmetric_difference, self.other)

    def test_difference_update_operator(self):
        try:
            self.set -= self.other
        except TypeError:
            pass
        else:
            self.fail("expected TypeError")

    def test_difference_update(self):
        if self.otherIsIterable:
            self.set.difference_update(self.other)
        else:
            self.assertRaises(TypeError,
                              self.set.difference_update,
                              self.other)

    def test_difference(self):
        self.assertRaises(TypeError, lambda: self.set - self.other)
        self.assertRaises(TypeError, lambda: self.other - self.set)
        if self.otherIsIterable:
            self.set.difference(self.other)
        else:
            self.assertRaises(TypeError, self.set.difference, self.other)

#------------------------------------------------------------------------------

class TestOnlySetsNumeric(TestOnlySetsInBinaryOps):
    def setUp(self):
        self.set   = set((1, 2, 3))
        self.other = 19
        self.otherIsIterable = False

#------------------------------------------------------------------------------

class TestOnlySetsDict(TestOnlySetsInBinaryOps):
    def setUp(self):
        self.set   = set((1, 2, 3))
        self.other = {1:2, 3:4}
        self.otherIsIterable = True

#------------------------------------------------------------------------------

class TestOnlySetsOperator(TestOnlySetsInBinaryOps):
    def setUp(self):
        self.set   = set((1, 2, 3))
        self.other = operator.add
        self.otherIsIterable = False

#------------------------------------------------------------------------------

class TestOnlySetsTuple(TestOnlySetsInBinaryOps):
    def setUp(self):
        self.set   = set((1, 2, 3))
        self.other = (2, 4, 6)
        self.otherIsIterable = True

#------------------------------------------------------------------------------

class TestOnlySetsString(TestOnlySetsInBinaryOps):
    def setUp(self):
        self.set   = set((1, 2, 3))
        self.other = 'abc'
        self.otherIsIterable = True

#------------------------------------------------------------------------------

class TestOnlySetsGenerator(TestOnlySetsInBinaryOps):
    def setUp(self):
        def gen():
            for i in range(0, 10, 2):
                yield i
        self.set   = set((1, 2, 3))
        self.other = gen()
        self.otherIsIterable = True

#==============================================================================

class TestCopying(unittest.TestCase):

    def test_copy(self):
        dup = self.set.copy()
        dup_list = sorted(dup, key=repr)
        set_list = sorted(self.set, key=repr)
        self.assertEqual(len(dup_list), len(set_list))
        for i in range(len(dup_list)):
            self.assertTrue(dup_list[i] is set_list[i])

    def test_deep_copy(self):
        dup = copy.deepcopy(self.set)
        ##print type(dup), repr(dup)
        dup_list = sorted(dup, key=repr)
        set_list = sorted(self.set, key=repr)
        self.assertEqual(len(dup_list), len(set_list))
        for i in range(len(dup_list)):
            self.assertEqual(dup_list[i], set_list[i])

#------------------------------------------------------------------------------

class TestCopyingEmpty(TestCopying):
    def setUp(self):
        self.set = set()

#------------------------------------------------------------------------------

class TestCopyingSingleton(TestCopying):
    def setUp(self):
        self.set = set(["hello"])

#------------------------------------------------------------------------------

class TestCopyingTriple(TestCopying):
    def setUp(self):
        self.set = set(["zero", 0, None])

#------------------------------------------------------------------------------

class TestCopyingTuple(TestCopying):
    def setUp(self):
        self.set = set([(1, 2)])

#------------------------------------------------------------------------------

class TestCopyingNested(TestCopying):
    def setUp(self):
        self.set = set([((1, 2), (3, 4))])

#==============================================================================

class TestIdentities(unittest.TestCase):
    def setUp(self):
        self.a = set('abracadabra')
        self.b = set('alacazam')

    def test_binopsVsSubsets(self):
        a, b = self.a, self.b
        self.assertTrue(a - b < a)
        self.assertTrue(b - a < b)
        self.assertTrue(a & b < a)
        self.assertTrue(a & b < b)
        self.assertTrue(a | b > a)
        self.assertTrue(a | b > b)
        self.assertTrue(a ^ b < a | b)

    def test_commutativity(self):
        a, b = self.a, self.b
        self.assertEqual(a&b, b&a)
        self.assertEqual(a|b, b|a)
        self.assertEqual(a^b, b^a)
        if a != b:
            self.assertNotEqual(a-b, b-a)

    def test_summations(self):
        # check that sums of parts equal the whole
        a, b = self.a, self.b
        self.assertEqual((a-b)|(a&b)|(b-a), a|b)
        self.assertEqual((a&b)|(a^b), a|b)
        self.assertEqual(a|(b-a), a|b)
        self.assertEqual((a-b)|b, a|b)
        self.assertEqual((a-b)|(a&b), a)
        self.assertEqual((b-a)|(a&b), b)
        self.assertEqual((a-b)|(b-a), a^b)

    def test_exclusion(self):
        # check that inverse operations show non-overlap
        a, b, zero = self.a, self.b, set()
        self.assertEqual((a-b)&b, zero)
        self.assertEqual((b-a)&a, zero)
        self.assertEqual((a&b)&(a^b), zero)

# Tests derived from test_itertools.py =======================================

def R(seqn):
    'Regular generator'
    for i in seqn:
        yield i

class G:
    'Sequence using __getitem__'
    def __init__(self, seqn):
        self.seqn = seqn
    def __getitem__(self, i):
        return self.seqn[i]

class I:
    'Sequence using iterator protocol'
    def __init__(self, seqn):
        self.seqn = seqn
        self.i = 0
    def __iter__(self):
        return self
    def __next__(self):
        if self.i >= len(self.seqn): raise StopIteration
        v = self.seqn[self.i]
        self.i += 1
        return v

class Ig:
    'Sequence using iterator protocol defined with a generator'
    def __init__(self, seqn):
        self.seqn = seqn
        self.i = 0
    def __iter__(self):
        for val in self.seqn:
            yield val

class X:
    'Missing __getitem__ and __iter__'
    def __init__(self, seqn):
        self.seqn = seqn
        self.i = 0
    def __next__(self):
        if self.i >= len(self.seqn): raise StopIteration
        v = self.seqn[self.i]
        self.i += 1
        return v

class N:
    'Iterator missing __next__()'
    def __init__(self, seqn):
        self.seqn = seqn
        self.i = 0
    def __iter__(self):
        return self

class E:
    'Test propagation of exceptions'
    def __init__(self, seqn):
        self.seqn = seqn
        self.i = 0
    def __iter__(self):
        return self
    def __next__(self):
        3 // 0

class S:
    'Test immediate stop'
    def __init__(self, seqn):
        pass
    def __iter__(self):
        return self
    def __next__(self):
        raise StopIteration

from itertools import chain
def L(seqn):
    'Test multiple tiers of iterators'
    return chain(map(lambda x:x, R(Ig(G(seqn)))))

class TestVariousIteratorArgs(unittest.TestCase):

    def test_constructor(self):
        for cons in (set, frozenset):
            for s in ("123", "", range(1000), ('do', 1.2), range(2000,2200,5)):
                for g in (G, I, Ig, S, L, R):
                    self.assertEqual(sorted(cons(g(s)), key=repr), sorted(g(s), key=repr))
                self.assertRaises(TypeError, cons , X(s))
                self.assertRaises(TypeError, cons , N(s))
                self.assertRaises(ZeroDivisionError, cons , E(s))

    def test_inline_methods(self):
        s = set('november')
        for data in ("123", "", range(1000), ('do', 1.2), range(2000,2200,5), 'december'):
            for meth in (s.union, s.intersection, s.difference, s.symmetric_difference, s.isdisjoint):
                for g in (G, I, Ig, L, R):
                    expected = meth(data)
                    actual = meth(G(data))
                    if isinstance(expected, bool):
                        self.assertEqual(actual, expected)
                    else:
                        self.assertEqual(sorted(actual, key=repr), sorted(expected, key=repr))
                self.assertRaises(TypeError, meth, X(s))
                self.assertRaises(TypeError, meth, N(s))
                self.assertRaises(ZeroDivisionError, meth, E(s))

    def test_inplace_methods(self):
        for data in ("123", "", range(1000), ('do', 1.2), range(2000,2200,5), 'december'):
            for methname in ('update', 'intersection_update',
                             'difference_update', 'symmetric_difference_update'):
                for g in (G, I, Ig, S, L, R):
                    s = set('january')
                    t = s.copy()
                    getattr(s, methname)(list(g(data)))
                    getattr(t, methname)(g(data))
                    self.assertEqual(sorted(s, key=repr), sorted(t, key=repr))

                self.assertRaises(TypeError, getattr(set('january'), methname), X(data))
                self.assertRaises(TypeError, getattr(set('january'), methname), N(data))
                self.assertRaises(ZeroDivisionError, getattr(set('january'), methname), E(data))

# Application tests (based on David Eppstein's graph recipes ====================================

def powerset(U):
    """Generates all subsets of a set or sequence U."""
    U = iter(U)
    try:
        x = frozenset([next(U)])
        for S in powerset(U):
            yield S
            yield S | x
    except StopIteration:
        yield frozenset()

def cube(n):
    """Graph of n-dimensional hypercube."""
    singletons = [frozenset([x]) for x in range(n)]
    return dict([(x, frozenset([x^s for s in singletons]))
                 for x in powerset(range(n))])

def linegraph(G):
    """Graph, the vertices of which are edges of G,
    with two vertices being adjacent iff the corresponding
    edges share a vertex."""
    L = {}
    for x in G:
        for y in G[x]:
            nx = [frozenset([x,z]) for z in G[x] if z != y]
            ny = [frozenset([y,z]) for z in G[y] if z != x]
            L[frozenset([x,y])] = frozenset(nx+ny)
    return L

def faces(G):
    'Return a set of faces in G.  Where a face is a set of vertices on that face'
    # currently limited to triangles,squares, and pentagons
    f = set()
    for v1, edges in G.items():
        for v2 in edges:
            for v3 in G[v2]:
                if v1 == v3:
                    continue
                if v1 in G[v3]:
                    f.add(frozenset([v1, v2, v3]))
                else:
                    for v4 in G[v3]:
                        if v4 == v2:
                            continue
                        if v1 in G[v4]:
                            f.add(frozenset([v1, v2, v3, v4]))
                        else:
                            for v5 in G[v4]:
                                if v5 == v3 or v5 == v2:
                                    continue
                                if v1 in G[v5]:
                                    f.add(frozenset([v1, v2, v3, v4, v5]))
    return f


class TestGraphs(unittest.TestCase):

    def test_cube(self):

        g = cube(3)                             # vert --> {v1, v2, v3}
        vertices1 = set(g)
        self.assertEqual(len(vertices1), 8)     # eight vertices
        for edge in g.values():
            self.assertEqual(len(edge), 3)      # each vertex connects to three edges
        vertices2 = set(v for edges in g.values() for v in edges)
        self.assertEqual(vertices1, vertices2)  # edge vertices in original set

        cubefaces = faces(g)
        self.assertEqual(len(cubefaces), 6)     # six faces
        for face in cubefaces:
            self.assertEqual(len(face), 4)      # each face is a square

    def test_cuboctahedron(self):

        # http://en.wikipedia.org/wiki/Cuboctahedron
        # 8 triangular faces and 6 square faces
        # 12 indentical vertices each connecting a triangle and square

        g = cube(3)
        cuboctahedron = linegraph(g)            # V( --> {V1, V2, V3, V4}
        self.assertEqual(len(cuboctahedron), 12)# twelve vertices

        vertices = set(cuboctahedron)
        for edges in cuboctahedron.values():
            self.assertEqual(len(edges), 4)     # each vertex connects to four other vertices
        othervertices = set(edge for edges in cuboctahedron.values() for edge in edges)
        self.assertEqual(vertices, othervertices)   # edge vertices in original set

        cubofaces = faces(cuboctahedron)
        facesizes = collections.defaultdict(int)
        for face in cubofaces:
            facesizes[len(face)] += 1
        self.assertEqual(facesizes[3], 8)       # eight triangular faces
        self.assertEqual(facesizes[4], 6)       # six square faces

        for vertex in cuboctahedron:
            edge = vertex                       # Cuboctahedron vertices are edges in Cube
            self.assertEqual(len(edge), 2)      # Two cube vertices define an edge
            for cubevert in edge:
                self.assertTrue(cubevert in g)


#==============================================================================

def test_main(verbose=None):
    test_classes = (
        TestSet,
        TestSetSubclass,
        TestSetSubclassWithKeywordArgs,
        TestFrozenSet,
        TestFrozenSetSubclass,
        TestSetOfSets,
        TestExceptionPropagation,
        TestBasicOpsEmpty,
        TestBasicOpsSingleton,
        TestBasicOpsTuple,
        TestBasicOpsTriple,
        TestBasicOpsString,
        TestBasicOpsBytes,
        TestBasicOpsMixedStringBytes,
        TestBinaryOps,
        TestUpdateOps,
        TestMutate,
        TestSubsetEqualEmpty,
        TestSubsetEqualNonEmpty,
        TestSubsetEmptyNonEmpty,
        TestSubsetPartial,
        TestSubsetNonOverlap,
        TestOnlySetsNumeric,
        TestOnlySetsDict,
        TestOnlySetsOperator,
        TestOnlySetsTuple,
        TestOnlySetsString,
        TestOnlySetsGenerator,
        TestCopyingEmpty,
        TestCopyingSingleton,
        TestCopyingTriple,
        TestCopyingTuple,
        TestCopyingNested,
        TestIdentities,
        TestVariousIteratorArgs,
        TestGraphs,
        )

    support.run_unittest(*test_classes)

    # verify reference counting
    if verbose and hasattr(sys, "gettotalrefcount"):
        import gc
        counts = [None] * 5
        for i in range(len(counts)):
            support.run_unittest(*test_classes)
            gc.collect()
            counts[i] = sys.gettotalrefcount()
        print(counts)

if __name__ == "__main__":
    test_main(verbose=True)