Objects/setobject.c

/* set object implementation
   Written and maintained by Raymond D. Hettinger <python@rcn.com>
   Derived from Lib/sets.py and Objects/dictobject.c.

   Copyright (c) 2003-2008 Python Software Foundation.
   All rights reserved.
*/

#include "Python.h"
#include "structmember.h"
#include "stringlib/eq.h"

/* Set a key error with the specified argument, wrapping it in a
 * tuple automatically so that tuple keys are not unpacked as the
 * exception arguments. */
static void
set_key_error(PyObject *arg)
{
    PyObject *tup;
    tup = PyTuple_Pack(1, arg);
    if (!tup)
        return; /* caller will expect error to be set anyway */
    PyErr_SetObject(PyExc_KeyError, tup);
    Py_DECREF(tup);
}

/* This must be >= 1. */
#define PERTURB_SHIFT 5

/* Object used as dummy key to fill deleted entries */
static PyObject *dummy = NULL; /* Initialized by first call to make_new_set() */

#ifdef Py_REF_DEBUG
PyObject *
_PySet_Dummy(void)
{
    return dummy;
}
#endif

#define INIT_NONZERO_SET_SLOTS(so) do {                         \
    (so)->table = (so)->smalltable;                             \
    (so)->mask = PySet_MINSIZE - 1;                             \
    (so)->hash = -1;                                            \
    } while(0)

#define EMPTY_TO_MINSIZE(so) do {                               \
    memset((so)->smalltable, 0, sizeof((so)->smalltable));      \
    (so)->used = (so)->fill = 0;                                \
    INIT_NONZERO_SET_SLOTS(so);                                 \
    } while(0)

/* Reuse scheme to save calls to malloc, free, and memset */
#ifndef PySet_MAXFREELIST
#define PySet_MAXFREELIST 80
#endif
static PySetObject *free_list[PySet_MAXFREELIST];
static int numfree = 0;


/*
The basic lookup function used by all operations.
This is based on Algorithm D from Knuth Vol. 3, Sec. 6.4.
Open addressing is preferred over chaining since the link overhead for
chaining would be substantial (100% with typical malloc overhead).

The initial probe index is computed as hash mod the table size. Subsequent
probe indices are computed as explained in Objects/dictobject.c.

To improve cache locality, each probe is done in pairs.
After the probe is examined, an adjacent entry is then examined as well.
The likelihood is that an adjacent entry is in the same cache line and
can be examined more cheaply than another probe elsewhere in memory.

All arithmetic on hash should ignore overflow.

Unlike the dictionary implementation, the lookkey functions can return
NULL if the rich comparison returns an error.
*/

static setentry *
set_lookkey(PySetObject *so, PyObject *key, Py_hash_t hash)
{
    size_t i, j;  /* Unsigned for defined overflow behavior. */
    size_t perturb;
    setentry *freeslot;
    size_t mask = so->mask;
    setentry *table = so->table;
    setentry *entry;
    int cmp;
    PyObject *startkey;

    i = (size_t)hash & mask;
    entry = &table[i];
    if (entry->key == NULL || entry->key == key)
        return entry;
    if (entry->hash == hash && entry->key != dummy) {
        startkey = entry->key;
        Py_INCREF(startkey);
        cmp = PyObject_RichCompareBool(startkey, key, Py_EQ);
        Py_DECREF(startkey);
        if (cmp < 0)
            return NULL;
        if (table == so->table && entry->key == startkey) {
            if (cmp > 0)
                return entry;
        }
        else {
            /* Start over if the compare altered the set */
            return set_lookkey(so, key, hash);
        }
    }
    freeslot = (entry->key == dummy) ? entry : NULL;

    /* In the loop, key == dummy is by far (factor of 100s)
       the least likely outcome, so test for that last. */
    j = i;
    perturb = hash;
    while (1) {
        j ^= 1;
        entry = &table[j];
        if (entry->key == NULL) {
            if (freeslot != NULL)
                entry = freeslot;
            break;
        }
        if (entry->key == key)
            break;
        if (entry->hash == hash && entry->key != dummy) {
            startkey = entry->key;
            Py_INCREF(startkey);
            cmp = PyObject_RichCompareBool(startkey, key, Py_EQ);
            Py_DECREF(startkey);
            if (cmp < 0)
                return NULL;
            if (table == so->table && entry->key == startkey) {
                if (cmp > 0)
                    break;
            }
            else {
                return set_lookkey(so, key, hash);
            }
        }
        if (entry->key == dummy && freeslot == NULL)
            freeslot = entry;

        i = i * 5 + perturb + 1;
        j = i & mask;
        perturb >>= PERTURB_SHIFT;

        entry = &table[j];
        if (entry->key == NULL) {
            if (freeslot != NULL)
                entry = freeslot;
            break;
        }
        if (entry->key == key)
            break;
        if (entry->hash == hash && entry->key != dummy) {
            startkey = entry->key;
            Py_INCREF(startkey);
            cmp = PyObject_RichCompareBool(startkey, key, Py_EQ);
            Py_DECREF(startkey);
            if (cmp < 0)
                return NULL;
            if (table == so->table && entry->key == startkey) {
                if (cmp > 0)
                    break;
            }
            else {
                return set_lookkey(so, key, hash);
            }
        }
        if (entry->key == dummy && freeslot == NULL)
            freeslot = entry;

    }
    return entry;
}

/*
 * Hacked up version of set_lookkey which can assume keys are always unicode;
 * This means we can always use unicode_eq directly and not have to check to
 * see if the comparison altered the table.
 */
static setentry *
set_lookkey_unicode(PySetObject *so, PyObject *key, Py_hash_t hash)
{
    size_t i, j;  /* Unsigned for defined overflow behavior. */
    size_t perturb;
    setentry *freeslot;
    size_t mask = so->mask;
    setentry *table = so->table;
    setentry *entry;

    /* Make sure this function doesn't have to handle non-unicode keys,
       including subclasses of str; e.g., one reason to subclass
       strings is to override __eq__, and for speed we don't cater to
       that here. */
    if (!PyUnicode_CheckExact(key)) {
        so->lookup = set_lookkey;
        return set_lookkey(so, key, hash);
    }

    i = (size_t)hash & mask;
    entry = &table[i];
    if (entry->key == NULL || entry->key == key)
        return entry;
    if (entry->key == dummy)
        freeslot = entry;
    else {
        if (entry->hash == hash && unicode_eq(entry->key, key))
            return entry;
        freeslot = NULL;
    }

    entry = &table[i ^ 1];
    if (entry->key == NULL)
        return freeslot == NULL ? entry : freeslot;
    if (entry->key == key
        || (entry->hash == hash
            && entry->key != dummy
            && unicode_eq(entry->key, key)))
        return entry;
    if (entry->key == dummy && freeslot == NULL)
        freeslot = entry;

    j = i;
    perturb = hash;
    while (1) {
        j ^= 1;
        entry = &table[j];
        if (entry->key == NULL)
            return freeslot == NULL ? entry : freeslot;
        if (entry->key == key
            || (entry->hash == hash
            && entry->key != dummy
            && unicode_eq(entry->key, key)))
            return entry;
        if (entry->key == dummy && freeslot == NULL)
            freeslot = entry;

        i = i * 5 + perturb + 1;
        j = i & mask;
        perturb >>= PERTURB_SHIFT;

        entry = &table[j];
        if (entry->key == NULL)
            return freeslot == NULL ? entry : freeslot;
        if (entry->key == key
            || (entry->hash == hash
            && entry->key != dummy
            && unicode_eq(entry->key, key)))
            return entry;
        if (entry->key == dummy && freeslot == NULL)
            freeslot = entry;
    }
    assert(0);          /* NOT REACHED */
    return 0;
}

/*
Internal routine to insert a new key into the table.
Used by the public insert routine.
Eats a reference to key.
*/
static int
set_insert_key(PySetObject *so, PyObject *key, Py_hash_t hash)
{
    setentry *entry;

    assert(so->lookup != NULL);
    entry = so->lookup(so, key, hash);
    if (entry == NULL)
        return -1;
    if (entry->key == NULL) {
        /* UNUSED */
        so->fill++;
        entry->key = key;
        entry->hash = hash;
        so->used++;
    } else if (entry->key == dummy) {
        /* DUMMY */
        entry->key = key;
        entry->hash = hash;
        so->used++;
        Py_DECREF(dummy);
    } else {
        /* ACTIVE */
        Py_DECREF(key);
    }
    return 0;
}

/*
Internal routine used by set_table_resize() to insert an item which is
known to be absent from the set.  This routine also assumes that
the set contains no deleted entries.  Besides the performance benefit,
using set_insert_clean() in set_table_resize() is dangerous (SF bug #1456209).
Note that no refcounts are changed by this routine; if needed, the caller
is responsible for incref'ing `key`.
*/
static void
set_insert_clean(PySetObject *so, PyObject *key, Py_hash_t hash)
{
    setentry *table = so->table;
    setentry *entry;
    size_t perturb = hash;
    size_t mask = (size_t)so->mask;
    size_t i, j;

    i = j = (size_t)hash & mask;
    while (1) {
        entry = &table[j];
        if (entry->key == NULL)
            break;
        entry = &table[j ^ 1];
        if (entry->key == NULL)
            break;
        i = i * 5 + perturb + 1;
        j = i & mask;
        perturb >>= PERTURB_SHIFT;
    }
    so->fill++;
    entry->key = key;
    entry->hash = hash;
    so->used++;
}

/*
Restructure the table by allocating a new table and reinserting all
keys again.  When entries have been deleted, the new table may
actually be smaller than the old one.
*/
static int
set_table_resize(PySetObject *so, Py_ssize_t minused)
{
    Py_ssize_t newsize;
    setentry *oldtable, *newtable, *entry;
    Py_ssize_t i;
    int is_oldtable_malloced;
    setentry small_copy[PySet_MINSIZE];
    PyObject *dummy_entry;

    assert(minused >= 0);

    /* Find the smallest table size > minused. */
    for (newsize = PySet_MINSIZE;
         newsize <= minused && newsize > 0;
         newsize <<= 1)
        ;
    if (newsize <= 0) {
        PyErr_NoMemory();
        return -1;
    }

    /* Get space for a new table. */
    oldtable = so->table;
    assert(oldtable != NULL);
    is_oldtable_malloced = oldtable != so->smalltable;

    if (newsize == PySet_MINSIZE) {
        /* A large table is shrinking, or we can't get any smaller. */
        newtable = so->smalltable;
        if (newtable == oldtable) {
            if (so->fill == so->used) {
                /* No dummies, so no point doing anything. */
                return 0;
            }
            /* We're not going to resize it, but rebuild the
               table anyway to purge old dummy entries.
               Subtle:  This is *necessary* if fill==size,
               as set_lookkey needs at least one virgin slot to
               terminate failing searches.  If fill < size, it's
               merely desirable, as dummies slow searches. */
            assert(so->fill > so->used);
            memcpy(small_copy, oldtable, sizeof(small_copy));
            oldtable = small_copy;
        }
    }
    else {
        newtable = PyMem_NEW(setentry, newsize);
        if (newtable == NULL) {
            PyErr_NoMemory();
            return -1;
        }
    }

    /* Make the set empty, using the new table. */
    assert(newtable != oldtable);
    so->table = newtable;
    so->mask = newsize - 1;
    memset(newtable, 0, sizeof(setentry) * newsize);
    so->used = 0;
    i = so->fill;
    so->fill = 0;

    /* Copy the data over; this is refcount-neutral for active entries;
       dummy entries aren't copied over, of course */
    dummy_entry = dummy;
    for (entry = oldtable; i > 0; entry++) {
        if (entry->key == NULL) {
            /* UNUSED */
            ;
        } else if (entry->key == dummy_entry) {
            /* DUMMY */
            --i;
            assert(entry->key == dummy);
            Py_DECREF(entry->key);
        } else {
            /* ACTIVE */
            --i;
            set_insert_clean(so, entry->key, entry->hash);
        }
    }

    if (is_oldtable_malloced)
        PyMem_DEL(oldtable);
    return 0;
}

/* CAUTION: set_add_key/entry() must guarantee it won't resize the table */

static int
set_add_entry(PySetObject *so, setentry *entry)
{
    Py_ssize_t n_used;
    PyObject *key = entry->key;
    Py_hash_t hash = entry->hash;

    assert(so->fill <= so->mask);  /* at least one empty slot */
    n_used = so->used;
    Py_INCREF(key);
    if (set_insert_key(so, key, hash) == -1) {
        Py_DECREF(key);
        return -1;
    }
    if (!(so->used > n_used && so->fill*3 >= (so->mask+1)*2))
        return 0;
    return set_table_resize(so, so->used>50000 ? so->used*2 : so->used*4);
}

static int
set_add_key(PySetObject *so, PyObject *key)
{
    Py_hash_t hash;
    Py_ssize_t n_used;

    if (!PyUnicode_CheckExact(key) ||
        (hash = ((PyASCIIObject *) key)->hash) == -1) {
        hash = PyObject_Hash(key);
        if (hash == -1)
            return -1;
    }
    assert(so->fill <= so->mask);  /* at least one empty slot */
    n_used = so->used;
    Py_INCREF(key);
    if (set_insert_key(so, key, hash) == -1) {
        Py_DECREF(key);
        return -1;
    }
    if (!(so->used > n_used && so->fill*3 >= (so->mask+1)*2))
        return 0;
    return set_table_resize(so, so->used>50000 ? so->used*2 : so->used*4);
}

#define DISCARD_NOTFOUND 0
#define DISCARD_FOUND 1

static int
set_discard_entry(PySetObject *so, setentry *oldentry)
{       setentry *entry;
    PyObject *old_key;

    entry = (so->lookup)(so, oldentry->key, oldentry->hash);
    if (entry == NULL)
        return -1;
    if (entry->key == NULL  ||  entry->key == dummy)
        return DISCARD_NOTFOUND;
    old_key = entry->key;
    Py_INCREF(dummy);
    entry->key = dummy;
    so->used--;
    Py_DECREF(old_key);
    return DISCARD_FOUND;
}

static int
set_discard_key(PySetObject *so, PyObject *key)
{
    Py_hash_t hash;
    setentry *entry;
    PyObject *old_key;

    assert (PyAnySet_Check(so));

    if (!PyUnicode_CheckExact(key) ||
        (hash = ((PyASCIIObject *) key)->hash) == -1) {
        hash = PyObject_Hash(key);
        if (hash == -1)
            return -1;
    }
    entry = (so->lookup)(so, key, hash);
    if (entry == NULL)
        return -1;
    if (entry->key == NULL  ||  entry->key == dummy)
        return DISCARD_NOTFOUND;
    old_key = entry->key;
    Py_INCREF(dummy);
    entry->key = dummy;
    so->used--;
    Py_DECREF(old_key);
    return DISCARD_FOUND;
}

static int
set_clear_internal(PySetObject *so)
{
    setentry *entry, *table;
    int table_is_malloced;
    Py_ssize_t fill;
    setentry small_copy[PySet_MINSIZE];
#ifdef Py_DEBUG
    Py_ssize_t i, n;
    assert (PyAnySet_Check(so));

    n = so->mask + 1;
    i = 0;
#endif

    table = so->table;
    assert(table != NULL);
    table_is_malloced = table != so->smalltable;

    /* This is delicate.  During the process of clearing the set,
     * decrefs can cause the set to mutate.  To avoid fatal confusion
     * (voice of experience), we have to make the set empty before
     * clearing the slots, and never refer to anything via so->ref while
     * clearing.
     */
    fill = so->fill;
    if (table_is_malloced)
        EMPTY_TO_MINSIZE(so);

    else if (fill > 0) {
        /* It's a small table with something that needs to be cleared.
         * Afraid the only safe way is to copy the set entries into
         * another small table first.
         */
        memcpy(small_copy, table, sizeof(small_copy));
        table = small_copy;
        EMPTY_TO_MINSIZE(so);
    }
    /* else it's a small table that's already empty */

    /* Now we can finally clear things.  If C had refcounts, we could
     * assert that the refcount on table is 1 now, i.e. that this function
     * has unique access to it, so decref side-effects can't alter it.
     */
    for (entry = table; fill > 0; ++entry) {
#ifdef Py_DEBUG
        assert(i < n);
        ++i;
#endif
        if (entry->key) {
            --fill;
            Py_DECREF(entry->key);
        }
#ifdef Py_DEBUG
        else
            assert(entry->key == NULL);
#endif
    }

    if (table_is_malloced)
        PyMem_DEL(table);
    return 0;
}

/*
 * Iterate over a set table.  Use like so:
 *
 *     Py_ssize_t pos;
 *     setentry *entry;
 *     pos = 0;   # important!  pos should not otherwise be changed by you
 *     while (set_next(yourset, &pos, &entry)) {
 *              Refer to borrowed reference in entry->key.
 *     }
 *
 * CAUTION:  In general, it isn't safe to use set_next in a loop that
 * mutates the table.
 */
static int
set_next(PySetObject *so, Py_ssize_t *pos_ptr, setentry **entry_ptr)
{
    Py_ssize_t i;
    Py_ssize_t mask;
    setentry *table;

    assert (PyAnySet_Check(so));
    i = *pos_ptr;
    assert(i >= 0);
    table = so->table;
    mask = so->mask;
    while (i <= mask && (table[i].key == NULL || table[i].key == dummy))
        i++;
    *pos_ptr = i+1;
    if (i > mask)
        return 0;
    assert(table[i].key != NULL);
    *entry_ptr = &table[i];
    return 1;
}

static void
set_dealloc(PySetObject *so)
{
    setentry *entry;
    Py_ssize_t fill = so->fill;
    PyObject_GC_UnTrack(so);
    Py_TRASHCAN_SAFE_BEGIN(so)
    if (so->weakreflist != NULL)
        PyObject_ClearWeakRefs((PyObject *) so);

    for (entry = so->table; fill > 0; entry++) {
        if (entry->key) {
            --fill;
            Py_DECREF(entry->key);
        }
    }
    if (so->table != so->smalltable)
        PyMem_DEL(so->table);
    if (numfree < PySet_MAXFREELIST && PyAnySet_CheckExact(so))
        free_list[numfree++] = so;
    else
        Py_TYPE(so)->tp_free(so);
    Py_TRASHCAN_SAFE_END(so)
}

static PyObject *
set_repr(PySetObject *so)
{
    PyObject *result=NULL, *keys, *listrepr, *tmp;
    int status = Py_ReprEnter((PyObject*)so);

    if (status != 0) {
        if (status < 0)
            return NULL;
        return PyUnicode_FromFormat("%s(...)", Py_TYPE(so)->tp_name);
    }

    /* shortcut for the empty set */
    if (!so->used) {
        Py_ReprLeave((PyObject*)so);
        return PyUnicode_FromFormat("%s()", Py_TYPE(so)->tp_name);
    }

    keys = PySequence_List((PyObject *)so);
    if (keys == NULL)
        goto done;

    /* repr(keys)[1:-1] */
    listrepr = PyObject_Repr(keys);
    Py_DECREF(keys);
    if (listrepr == NULL)
        goto done;
    tmp = PyUnicode_Substring(listrepr, 1, PyUnicode_GET_LENGTH(listrepr)-1);
    Py_DECREF(listrepr);
    if (tmp == NULL)
        goto done;
    listrepr = tmp;

    if (Py_TYPE(so) != &PySet_Type)
        result = PyUnicode_FromFormat("%s({%U})",
                                      Py_TYPE(so)->tp_name,
                                      listrepr);
    else
        result = PyUnicode_FromFormat("{%U}", listrepr);
    Py_DECREF(listrepr);
done:
    Py_ReprLeave((PyObject*)so);
    return result;
}

static Py_ssize_t
set_len(PyObject *so)
{
    return ((PySetObject *)so)->used;
}

static int
set_merge(PySetObject *so, PyObject *otherset)
{
    PySetObject *other;
    PyObject *key;
    Py_hash_t hash;
    Py_ssize_t i;
    setentry *entry;

    assert (PyAnySet_Check(so));
    assert (PyAnySet_Check(otherset));

    other = (PySetObject*)otherset;
    if (other == so || other->used == 0)
        /* a.update(a) or a.update({}); nothing to do */
        return 0;
    /* Do one big resize at the start, rather than
     * incrementally resizing as we insert new keys.  Expect
     * that there will be no (or few) overlapping keys.
     */
    if ((so->fill + other->used)*3 >= (so->mask+1)*2) {
       if (set_table_resize(so, (so->used + other->used)*2) != 0)
           return -1;
    }
    for (i = 0; i <= other->mask; i++) {
        entry = &other->table[i];
        key = entry->key;
        hash = entry->hash;
        if (key != NULL &&
            key != dummy) {
            Py_INCREF(key);
            if (set_insert_key(so, key, hash) == -1) {
                Py_DECREF(key);
                return -1;
            }
        }
    }
    return 0;
}

static int
set_contains_key(PySetObject *so, PyObject *key)
{
    Py_hash_t hash;
    setentry *entry;

    if (!PyUnicode_CheckExact(key) ||
        (hash = ((PyASCIIObject *) key)->hash) == -1) {
        hash = PyObject_Hash(key);
        if (hash == -1)
            return -1;
    }
    entry = (so->lookup)(so, key, hash);
    if (entry == NULL)
        return -1;
    key = entry->key;
    return key != NULL && key != dummy;
}

static int
set_contains_entry(PySetObject *so, setentry *entry)
{
    PyObject *key;
    setentry *lu_entry;

    lu_entry = (so->lookup)(so, entry->key, entry->hash);
    if (lu_entry == NULL)
        return -1;
    key = lu_entry->key;
    return key != NULL && key != dummy;
}

static PyObject *
set_pop(PySetObject *so)
{
    Py_ssize_t i = 0;
    setentry *entry;
    PyObject *key;

    assert (PyAnySet_Check(so));
    if (so->used == 0) {
        PyErr_SetString(PyExc_KeyError, "pop from an empty set");
        return NULL;
    }

    /* Set entry to "the first" unused or dummy set entry.  We abuse
     * the hash field of slot 0 to hold a search finger:
     * If slot 0 has a value, use slot 0.
     * Else slot 0 is being used to hold a search finger,
     * and we use its hash value as the first index to look.
     */
    entry = &so->table[0];
    if (entry->key == NULL || entry->key == dummy) {
        i = entry->hash;
        /* The hash field may be a real hash value, or it may be a
         * legit search finger, or it may be a once-legit search
         * finger that's out of bounds now because it wrapped around
         * or the table shrunk -- simply make sure it's in bounds now.
         */
        if (i > so->mask || i < 1)
            i = 1;              /* skip slot 0 */
        while ((entry = &so->table[i])->key == NULL || entry->key==dummy) {
            i++;
            if (i > so->mask)
                i = 1;
        }
    }
    key = entry->key;
    Py_INCREF(dummy);
    entry->key = dummy;
    so->used--;
    so->table[0].hash = i + 1;  /* next place to start */
    return key;
}

PyDoc_STRVAR(pop_doc, "Remove and return an arbitrary set element.\n\
Raises KeyError if the set is empty.");

static int
set_traverse(PySetObject *so, visitproc visit, void *arg)
{
    Py_ssize_t pos = 0;
    setentry *entry;

    while (set_next(so, &pos, &entry))
        Py_VISIT(entry->key);
    return 0;
}

static Py_hash_t
frozenset_hash(PyObject *self)
{
    PySetObject *so = (PySetObject *)self;
    Py_uhash_t h, hash = 1927868237UL;
    setentry *entry;
    Py_ssize_t pos = 0;

    if (so->hash != -1)
        return so->hash;

    hash *= (Py_uhash_t)PySet_GET_SIZE(self) + 1;
    while (set_next(so, &pos, &entry)) {
        /* Work to increase the bit dispersion for closely spaced hash
           values.  The is important because some use cases have many
           combinations of a small number of elements with nearby
           hashes so that many distinct combinations collapse to only
           a handful of distinct hash values. */
        h = entry->hash;
        hash ^= (h ^ (h << 16) ^ 89869747UL)  * 3644798167UL;
    }
    hash = hash * 69069U + 907133923UL;
    if (hash == -1)
        hash = 590923713UL;
    so->hash = hash;
    return hash;
}

/***** Set iterator type ***********************************************/

typedef struct {
    PyObject_HEAD
    PySetObject *si_set; /* Set to NULL when iterator is exhausted */
    Py_ssize_t si_used;
    Py_ssize_t si_pos;
    Py_ssize_t len;
} setiterobject;

static void
setiter_dealloc(setiterobject *si)
{
    Py_XDECREF(si->si_set);
    PyObject_GC_Del(si);
}

static int
setiter_traverse(setiterobject *si, visitproc visit, void *arg)
{
    Py_VISIT(si->si_set);
    return 0;
}

static PyObject *
setiter_len(setiterobject *si)
{
    Py_ssize_t len = 0;
    if (si->si_set != NULL && si->si_used == si->si_set->used)
        len = si->len;
    return PyLong_FromSsize_t(len);
}

PyDoc_STRVAR(length_hint_doc, "Private method returning an estimate of len(list(it)).");

static PyObject *setiter_iternext(setiterobject *si);

static PyObject *
setiter_reduce(setiterobject *si)
{
    PyObject *list;
    setiterobject tmp;

    list = PyList_New(0);
    if (!list)
        return NULL;

    /* copy the iterator state */
    tmp = *si;
    Py_XINCREF(tmp.si_set);

    /* iterate the temporary into a list */
    for(;;) {
        PyObject *element = setiter_iternext(&tmp);
        if (element) {
            if (PyList_Append(list, element)) {
                Py_DECREF(element);
                Py_DECREF(list);
                Py_XDECREF(tmp.si_set);
                return NULL;
            }
            Py_DECREF(element);
        } else
            break;
    }
    Py_XDECREF(tmp.si_set);
    /* check for error */
    if (tmp.si_set != NULL) {
        /* we have an error */
        Py_DECREF(list);
        return NULL;
    }
    return Py_BuildValue("N(N)", _PyObject_GetBuiltin("iter"), list);
}

PyDoc_STRVAR(reduce_doc, "Return state information for pickling.");

static PyMethodDef setiter_methods[] = {
    {"__length_hint__", (PyCFunction)setiter_len, METH_NOARGS, length_hint_doc},
    {"__reduce__", (PyCFunction)setiter_reduce, METH_NOARGS, reduce_doc},
    {NULL,              NULL}           /* sentinel */
};

static PyObject *setiter_iternext(setiterobject *si)
{
    PyObject *key;
    Py_ssize_t i, mask;
    setentry *entry;
    PySetObject *so = si->si_set;

    if (so == NULL)
        return NULL;
    assert (PyAnySet_Check(so));

    if (si->si_used != so->used) {
        PyErr_SetString(PyExc_RuntimeError,
                        "Set changed size during iteration");
        si->si_used = -1; /* Make this state sticky */
        return NULL;
    }

    i = si->si_pos;
    assert(i>=0);
    entry = so->table;
    mask = so->mask;
    while (i <= mask && (entry[i].key == NULL || entry[i].key == dummy))
        i++;
    si->si_pos = i+1;
    if (i > mask)
        goto fail;
    si->len--;
    key = entry[i].key;
    Py_INCREF(key);
    return key;

fail:
    Py_DECREF(so);
    si->si_set = NULL;
    return NULL;
}

PyTypeObject PySetIter_Type = {
    PyVarObject_HEAD_INIT(&PyType_Type, 0)
    "set_iterator",                             /* tp_name */
    sizeof(setiterobject),                      /* tp_basicsize */
    0,                                          /* tp_itemsize */
    /* methods */
    (destructor)setiter_dealloc,                /* tp_dealloc */
    0,                                          /* tp_print */
    0,                                          /* tp_getattr */
    0,                                          /* tp_setattr */
    0,                                          /* tp_reserved */
    0,                                          /* tp_repr */
    0,                                          /* tp_as_number */
    0,                                          /* tp_as_sequence */
    0,                                          /* tp_as_mapping */
    0,                                          /* tp_hash */
    0,                                          /* tp_call */
    0,                                          /* tp_str */
    PyObject_GenericGetAttr,                    /* tp_getattro */
    0,                                          /* tp_setattro */
    0,                                          /* tp_as_buffer */
    Py_TPFLAGS_DEFAULT | Py_TPFLAGS_HAVE_GC,/* tp_flags */
    0,                                          /* tp_doc */
    (traverseproc)setiter_traverse,             /* tp_traverse */
    0,                                          /* tp_clear */
    0,                                          /* tp_richcompare */
    0,                                          /* tp_weaklistoffset */
    PyObject_SelfIter,                          /* tp_iter */
    (iternextfunc)setiter_iternext,             /* tp_iternext */
    setiter_methods,                            /* tp_methods */
    0,
};

static PyObject *
set_iter(PySetObject *so)
{
    setiterobject *si = PyObject_GC_New(setiterobject, &PySetIter_Type);
    if (si == NULL)
        return NULL;
    Py_INCREF(so);
    si->si_set = so;
    si->si_used = so->used;
    si->si_pos = 0;
    si->len = so->used;
    _PyObject_GC_TRACK(si);
    return (PyObject *)si;
}

static int
set_update_internal(PySetObject *so, PyObject *other)
{
    PyObject *key, *it;

    if (PyAnySet_Check(other))
        return set_merge(so, other);

    if (PyDict_CheckExact(other)) {
        PyObject *value;
        Py_ssize_t pos = 0;
        Py_hash_t hash;
        Py_ssize_t dictsize = PyDict_Size(other);

        /* Do one big resize at the start, rather than
        * incrementally resizing as we insert new keys.  Expect
        * that there will be no (or few) overlapping keys.
        */
        if (dictsize == -1)
            return -1;
        if ((so->fill + dictsize)*3 >= (so->mask+1)*2) {
            if (set_table_resize(so, (so->used + dictsize)*2) != 0)
                return -1;
        }
        while (_PyDict_Next(other, &pos, &key, &value, &hash)) {
            setentry an_entry;

            an_entry.hash = hash;
            an_entry.key = key;
            if (set_add_entry(so, &an_entry) == -1)
                return -1;
        }
        return 0;
    }

    it = PyObject_GetIter(other);
    if (it == NULL)
        return -1;

    while ((key = PyIter_Next(it)) != NULL) {
        if (set_add_key(so, key) == -1) {
            Py_DECREF(it);
            Py_DECREF(key);
            return -1;
        }
        Py_DECREF(key);
    }
    Py_DECREF(it);
    if (PyErr_Occurred())
        return -1;
    return 0;
}

static PyObject *
set_update(PySetObject *so, PyObject *args)
{
    Py_ssize_t i;

    for (i=0 ; i<PyTuple_GET_SIZE(args) ; i++) {
        PyObject *other = PyTuple_GET_ITEM(args, i);
        if (set_update_internal(so, other) == -1)
            return NULL;
    }
    Py_RETURN_NONE;
}

PyDoc_STRVAR(update_doc,
"Update a set with the union of itself and others.");

static PyObject *
make_new_set(PyTypeObject *type, PyObject *iterable)
{
    PySetObject *so = NULL;

    if (dummy == NULL) { /* Auto-initialize dummy */
        dummy = PyUnicode_FromString("<dummy key>");
        if (dummy == NULL)
            return NULL;
    }

    /* create PySetObject structure */
    if (numfree &&
        (type == &PySet_Type  ||  type == &PyFrozenSet_Type)) {
        so = free_list[--numfree];
        assert (so != NULL && PyAnySet_CheckExact(so));
        Py_TYPE(so) = type;
        _Py_NewReference((PyObject *)so);
        EMPTY_TO_MINSIZE(so);
        PyObject_GC_Track(so);
    } else {
        so = (PySetObject *)type->tp_alloc(type, 0);
        if (so == NULL)
            return NULL;
        /* tp_alloc has already zeroed the structure */
        assert(so->table == NULL && so->fill == 0 && so->used == 0);
        INIT_NONZERO_SET_SLOTS(so);
    }

    so->lookup = set_lookkey_unicode;
    so->weakreflist = NULL;

    if (iterable != NULL) {
        if (set_update_internal(so, iterable) == -1) {
            Py_DECREF(so);
            return NULL;
        }
    }

    return (PyObject *)so;
}

static PyObject *
make_new_set_basetype(PyTypeObject *type, PyObject *iterable)
{
    if (type != &PySet_Type && type != &PyFrozenSet_Type) {
        if (PyType_IsSubtype(type, &PySet_Type))
            type = &PySet_Type;
        else
            type = &PyFrozenSet_Type;
    }
    return make_new_set(type, iterable);
}

/* The empty frozenset is a singleton */
static PyObject *emptyfrozenset = NULL;

static PyObject *
frozenset_new(PyTypeObject *type, PyObject *args, PyObject *kwds)
{
    PyObject *iterable = NULL, *result;

    if (type == &PyFrozenSet_Type && !_PyArg_NoKeywords("frozenset()", kwds))
        return NULL;

    if (!PyArg_UnpackTuple(args, type->tp_name, 0, 1, &iterable))
        return NULL;

    if (type != &PyFrozenSet_Type)
        return make_new_set(type, iterable);

    if (iterable != NULL) {
        /* frozenset(f) is idempotent */
        if (PyFrozenSet_CheckExact(iterable)) {
            Py_INCREF(iterable);
            return iterable;
        }
        result = make_new_set(type, iterable);
        if (result == NULL || PySet_GET_SIZE(result))
            return result;
        Py_DECREF(result);
    }
    /* The empty frozenset is a singleton */
    if (emptyfrozenset == NULL)
        emptyfrozenset = make_new_set(type, NULL);
    Py_XINCREF(emptyfrozenset);
    return emptyfrozenset;
}

int
PySet_ClearFreeList(void)
{
    int freelist_size = numfree;
    PySetObject *so;

    while (numfree) {
        numfree--;
        so = free_list[numfree];
        PyObject_GC_Del(so);
    }
    return freelist_size;
}

void
PySet_Fini(void)
{
    PySet_ClearFreeList();
    Py_CLEAR(dummy);
    Py_CLEAR(emptyfrozenset);
}

/* Print summary info about the state of the optimized allocator */
void
_PySet_DebugMallocStats(FILE *out)
{
    _PyDebugAllocatorStats(out,
                           "free PySetObject",
                           numfree, sizeof(PySetObject));
}


static PyObject *
set_new(PyTypeObject *type, PyObject *args, PyObject *kwds)
{
    if (type == &PySet_Type && !_PyArg_NoKeywords("set()", kwds))
        return NULL;

    return make_new_set(type, NULL);
}

/* set_swap_bodies() switches the contents of any two sets by moving their
   internal data pointers and, if needed, copying the internal smalltables.
   Semantically equivalent to:

     t=set(a); a.clear(); a.update(b); b.clear(); b.update(t); del t

   The function always succeeds and it leaves both objects in a stable state.
   Useful for creating temporary frozensets from sets for membership testing
   in __contains__(), discard(), and remove().  Also useful for operations
   that update in-place (by allowing an intermediate result to be swapped
   into one of the original inputs).
*/

static void
set_swap_bodies(PySetObject *a, PySetObject *b)
{
    Py_ssize_t t;
    setentry *u;
    setentry *(*f)(PySetObject *so, PyObject *key, Py_ssize_t hash);
    setentry tab[PySet_MINSIZE];
    Py_hash_t h;

    t = a->fill;     a->fill   = b->fill;        b->fill  = t;
    t = a->used;     a->used   = b->used;        b->used  = t;
    t = a->mask;     a->mask   = b->mask;        b->mask  = t;

    u = a->table;
    if (a->table == a->smalltable)
        u = b->smalltable;
    a->table  = b->table;
    if (b->table == b->smalltable)
        a->table = a->smalltable;
    b->table = u;

    f = a->lookup;   a->lookup = b->lookup;      b->lookup = f;

    if (a->table == a->smalltable || b->table == b->smalltable) {
        memcpy(tab, a->smalltable, sizeof(tab));
        memcpy(a->smalltable, b->smalltable, sizeof(tab));
        memcpy(b->smalltable, tab, sizeof(tab));
    }

    if (PyType_IsSubtype(Py_TYPE(a), &PyFrozenSet_Type)  &&
        PyType_IsSubtype(Py_TYPE(b), &PyFrozenSet_Type)) {
        h = a->hash;     a->hash = b->hash;  b->hash = h;
    } else {
        a->hash = -1;
        b->hash = -1;
    }
}

static PyObject *
set_copy(PySetObject *so)
{
    return make_new_set_basetype(Py_TYPE(so), (PyObject *)so);
}

static PyObject *
frozenset_copy(PySetObject *so)
{
    if (PyFrozenSet_CheckExact(so)) {
        Py_INCREF(so);
        return (PyObject *)so;
    }
    return set_copy(so);
}

PyDoc_STRVAR(copy_doc, "Return a shallow copy of a set.");

static PyObject *
set_clear(PySetObject *so)
{
    set_clear_internal(so);
    Py_RETURN_NONE;
}

PyDoc_STRVAR(clear_doc, "Remove all elements from this set.");

static PyObject *
set_union(PySetObject *so, PyObject *args)
{
    PySetObject *result;
    PyObject *other;
    Py_ssize_t i;

    result = (PySetObject *)set_copy(so);
    if (result == NULL)
        return NULL;

    for (i=0 ; i<PyTuple_GET_SIZE(args) ; i++) {
        other = PyTuple_GET_ITEM(args, i);
        if ((PyObject *)so == other)
            continue;
        if (set_update_internal(result, other) == -1) {
            Py_DECREF(result);
            return NULL;
        }
    }
    return (PyObject *)result;
}

PyDoc_STRVAR(union_doc,
 "Return the union of sets as a new set.\n\
\n\
(i.e. all elements that are in either set.)");

static PyObject *
set_or(PySetObject *so, PyObject *other)
{
    PySetObject *result;

    if (!PyAnySet_Check(so) || !PyAnySet_Check(other))
        Py_RETURN_NOTIMPLEMENTED;

    result = (PySetObject *)set_copy(so);
    if (result == NULL)
        return NULL;
    if ((PyObject *)so == other)
        return (PyObject *)result;
    if (set_update_internal(result, other) == -1) {
        Py_DECREF(result);
        return NULL;
    }
    return (PyObject *)result;
}

static PyObject *
set_ior(PySetObject *so, PyObject *other)
{
    if (!PyAnySet_Check(other))
        Py_RETURN_NOTIMPLEMENTED;

    if (set_update_internal(so, other) == -1)
        return NULL;
    Py_INCREF(so);
    return (PyObject *)so;
}

static PyObject *
set_intersection(PySetObject *so, PyObject *other)
{
    PySetObject *result;
    PyObject *key, *it, *tmp;

    if ((PyObject *)so == other)
        return set_copy(so);

    result = (PySetObject *)make_new_set_basetype(Py_TYPE(so), NULL);
    if (result == NULL)
        return NULL;

    if (PyAnySet_Check(other)) {
        Py_ssize_t pos = 0;
        setentry *entry;

        if (PySet_GET_SIZE(other) > PySet_GET_SIZE(so)) {
            tmp = (PyObject *)so;
            so = (PySetObject *)other;
            other = tmp;
        }

        while (set_next((PySetObject *)other, &pos, &entry)) {
            int rv = set_contains_entry(so, entry);
            if (rv == -1) {
                Py_DECREF(result);
                return NULL;
            }
            if (rv) {
                if (set_add_entry(result, entry) == -1) {
                    Py_DECREF(result);
                    return NULL;
                }
            }
        }
        return (PyObject *)result;
    }

    it = PyObject_GetIter(other);
    if (it == NULL) {
        Py_DECREF(result);
        return NULL;
    }

    while ((key = PyIter_Next(it)) != NULL) {
        int rv;
        setentry entry;
        Py_hash_t hash = PyObject_Hash(key);

        if (hash == -1) {
            Py_DECREF(it);
            Py_DECREF(result);
            Py_DECREF(key);
            return NULL;
        }
        entry.hash = hash;
        entry.key = key;
        rv = set_contains_entry(so, &entry);
        if (rv == -1) {
            Py_DECREF(it);
            Py_DECREF(result);
            Py_DECREF(key);
            return NULL;
        }
        if (rv) {
            if (set_add_entry(result, &entry) == -1) {
                Py_DECREF(it);
                Py_DECREF(result);
                Py_DECREF(key);
                return NULL;
            }
        }
        Py_DECREF(key);
    }
    Py_DECREF(it);
    if (PyErr_Occurred()) {
        Py_DECREF(result);
        return NULL;
    }
    return (PyObject *)result;
}

static PyObject *
set_intersection_multi(PySetObject *so, PyObject *args)
{
    Py_ssize_t i;
    PyObject *result = (PyObject *)so;

    if (PyTuple_GET_SIZE(args) == 0)
        return set_copy(so);

    Py_INCREF(so);
    for (i=0 ; i<PyTuple_GET_SIZE(args) ; i++) {
        PyObject *other = PyTuple_GET_ITEM(args, i);
        PyObject *newresult = set_intersection((PySetObject *)result, other);
        if (newresult == NULL) {
            Py_DECREF(result);
            return NULL;
        }
        Py_DECREF(result);
        result = newresult;
    }
    return result;
}

PyDoc_STRVAR(intersection_doc,
"Return the intersection of two sets as a new set.\n\
\n\
(i.e. all elements that are in both sets.)");

static PyObject *
set_intersection_update(PySetObject *so, PyObject *other)
{
    PyObject *tmp;

    tmp = set_intersection(so, other);
    if (tmp == NULL)
        return NULL;
    set_swap_bodies(so, (PySetObject *)tmp);
    Py_DECREF(tmp);
    Py_RETURN_NONE;
}

static PyObject *
set_intersection_update_multi(PySetObject *so, PyObject *args)
{
    PyObject *tmp;

    tmp = set_intersection_multi(so, args);
    if (tmp == NULL)
        return NULL;
    set_swap_bodies(so, (PySetObject *)tmp);
    Py_DECREF(tmp);
    Py_RETURN_NONE;
}

PyDoc_STRVAR(intersection_update_doc,
"Update a set with the intersection of itself and another.");

static PyObject *
set_and(PySetObject *so, PyObject *other)
{
    if (!PyAnySet_Check(so) || !PyAnySet_Check(other))
        Py_RETURN_NOTIMPLEMENTED;
    return set_intersection(so, other);
}

static PyObject *
set_iand(PySetObject *so, PyObject *other)
{
    PyObject *result;

    if (!PyAnySet_Check(other))
        Py_RETURN_NOTIMPLEMENTED;
    result = set_intersection_update(so, other);
    if (result == NULL)
        return NULL;
    Py_DECREF(result);
    Py_INCREF(so);
    return (PyObject *)so;
}

static PyObject *
set_isdisjoint(PySetObject *so, PyObject *other)
{
    PyObject *key, *it, *tmp;

    if ((PyObject *)so == other) {
        if (PySet_GET_SIZE(so) == 0)
            Py_RETURN_TRUE;
        else
            Py_RETURN_FALSE;
    }

    if (PyAnySet_CheckExact(other)) {
        Py_ssize_t pos = 0;
        setentry *entry;

        if (PySet_GET_SIZE(other) > PySet_GET_SIZE(so)) {
            tmp = (PyObject *)so;
            so = (PySetObject *)other;
            other = tmp;
        }
        while (set_next((PySetObject *)other, &pos, &entry)) {
            int rv = set_contains_entry(so, entry);
            if (rv == -1)
                return NULL;
            if (rv)
                Py_RETURN_FALSE;
        }
        Py_RETURN_TRUE;
    }

    it = PyObject_GetIter(other);
    if (it == NULL)
        return NULL;

    while ((key = PyIter_Next(it)) != NULL) {
        int rv;
        setentry entry;
        Py_hash_t hash = PyObject_Hash(key);

        if (hash == -1) {
            Py_DECREF(key);
            Py_DECREF(it);
            return NULL;
        }
        entry.hash = hash;
        entry.key = key;
        rv = set_contains_entry(so, &entry);
        Py_DECREF(key);
        if (rv == -1) {
            Py_DECREF(it);
            return NULL;
        }
        if (rv) {
            Py_DECREF(it);
            Py_RETURN_FALSE;
        }
    }
    Py_DECREF(it);
    if (PyErr_Occurred())
        return NULL;
    Py_RETURN_TRUE;
}

PyDoc_STRVAR(isdisjoint_doc,
"Return True if two sets have a null intersection.");

static int
set_difference_update_internal(PySetObject *so, PyObject *other)
{
    if ((PyObject *)so == other)
        return set_clear_internal(so);

    if (PyAnySet_Check(other)) {
        setentry *entry;
        Py_ssize_t pos = 0;

        while (set_next((PySetObject *)other, &pos, &entry))
            if (set_discard_entry(so, entry) == -1)
                return -1;
    } else {
        PyObject *key, *it;
        it = PyObject_GetIter(other);
        if (it == NULL)
            return -1;

        while ((key = PyIter_Next(it)) != NULL) {
            if (set_discard_key(so, key) == -1) {
                Py_DECREF(it);
                Py_DECREF(key);
                return -1;
            }
            Py_DECREF(key);
        }
        Py_DECREF(it);
        if (PyErr_Occurred())
            return -1;
    }
    /* If more than 1/5 are dummies, then resize them away. */
    if ((so->fill - so->used) * 5 < so->mask)
        return 0;
    return set_table_resize(so, so->used>50000 ? so->used*2 : so->used*4);
}

static PyObject *
set_difference_update(PySetObject *so, PyObject *args)
{
    Py_ssize_t i;

    for (i=0 ; i<PyTuple_GET_SIZE(args) ; i++) {
        PyObject *other = PyTuple_GET_ITEM(args, i);
        if (set_difference_update_internal(so, other) == -1)
            return NULL;
    }
    Py_RETURN_NONE;
}

PyDoc_STRVAR(difference_update_doc,
"Remove all elements of another set from this set.");

static PyObject *
set_copy_and_difference(PySetObject *so, PyObject *other)
{
    PyObject *result;

    result = set_copy(so);
    if (result == NULL)
        return NULL;
    if (set_difference_update_internal((PySetObject *) result, other) != -1)
        return result;
    Py_DECREF(result);
    return NULL;
}

static PyObject *
set_difference(PySetObject *so, PyObject *other)
{
    PyObject *result;
    setentry *entry;
    Py_ssize_t pos = 0;

    if (!PyAnySet_Check(other)  && !PyDict_CheckExact(other)) {
        return set_copy_and_difference(so, other);
    }

    /* If len(so) much more than len(other), it's more efficient to simply copy
     * so and then iterate other looking for common elements. */
    if ((PySet_GET_SIZE(so) >> 2) > PyObject_Size(other)) {
        return set_copy_and_difference(so, other);
    }

    result = make_new_set_basetype(Py_TYPE(so), NULL);
    if (result == NULL)
        return NULL;

    if (PyDict_CheckExact(other)) {
        while (set_next(so, &pos, &entry)) {
            setentry entrycopy;
            entrycopy.hash = entry->hash;
            entrycopy.key = entry->key;
            if (!_PyDict_Contains(other, entry->key, entry->hash)) {
                if (set_add_entry((PySetObject *)result, &entrycopy) == -1) {
                    Py_DECREF(result);
                    return NULL;
                }
            }
        }
        return result;
    }

    /* Iterate over so, checking for common elements in other. */
    while (set_next(so, &pos, &entry)) {
        int rv = set_contains_entry((PySetObject *)other, entry);
        if (rv == -1) {
            Py_DECREF(result);
            return NULL;
        }
        if (!rv) {
            if (set_add_entry((PySetObject *)result, entry) == -1) {
                Py_DECREF(result);
                return NULL;
            }
        }
    }
    return result;
}

static PyObject *
set_difference_multi(PySetObject *so, PyObject *args)
{
    Py_ssize_t i;
    PyObject *result, *other;

    if (PyTuple_GET_SIZE(args) == 0)
        return set_copy(so);

    other = PyTuple_GET_ITEM(args, 0);
    result = set_difference(so, other);
    if (result == NULL)
        return NULL;

    for (i=1 ; i<PyTuple_GET_SIZE(args) ; i++) {
        other = PyTuple_GET_ITEM(args, i);
        if (set_difference_update_internal((PySetObject *)result, other) == -1) {
            Py_DECREF(result);
            return NULL;
        }
    }
    return result;
}

PyDoc_STRVAR(difference_doc,
"Return the difference of two or more sets as a new set.\n\
\n\
(i.e. all elements that are in this set but not the others.)");
static PyObject *
set_sub(PySetObject *so, PyObject *other)
{
    if (!PyAnySet_Check(so) || !PyAnySet_Check(other))
        Py_RETURN_NOTIMPLEMENTED;
    return set_difference(so, other);
}

static PyObject *
set_isub(PySetObject *so, PyObject *other)
{
    if (!PyAnySet_Check(other))
        Py_RETURN_NOTIMPLEMENTED;
    if (set_difference_update_internal(so, other) == -1)
        return NULL;
    Py_INCREF(so);
    return (PyObject *)so;
}

static PyObject *
set_symmetric_difference_update(PySetObject *so, PyObject *other)
{
    PySetObject *otherset;
    PyObject *key;
    Py_ssize_t pos = 0;
    setentry *entry;

    if ((PyObject *)so == other)
        return set_clear(so);

    if (PyDict_CheckExact(other)) {
        PyObject *value;
        int rv;
        Py_hash_t hash;
        while (_PyDict_Next(other, &pos, &key, &value, &hash)) {
            setentry an_entry;

            Py_INCREF(key);
            an_entry.hash = hash;
            an_entry.key = key;

            rv = set_discard_entry(so, &an_entry);
            if (rv == -1) {
                Py_DECREF(key);
                return NULL;
            }
            if (rv == DISCARD_NOTFOUND) {
                if (set_add_entry(so, &an_entry) == -1) {
                    Py_DECREF(key);
                    return NULL;
                }
            }
            Py_DECREF(key);
        }
        Py_RETURN_NONE;
    }

    if (PyAnySet_Check(other)) {
        Py_INCREF(other);
        otherset = (PySetObject *)other;
    } else {
        otherset = (PySetObject *)make_new_set_basetype(Py_TYPE(so), other);
        if (otherset == NULL)
            return NULL;
    }

    while (set_next(otherset, &pos, &entry)) {
        int rv = set_discard_entry(so, entry);
        if (rv == -1) {
            Py_DECREF(otherset);
            return NULL;
        }
        if (rv == DISCARD_NOTFOUND) {
            if (set_add_entry(so, entry) == -1) {
                Py_DECREF(otherset);
                return NULL;
            }
        }
    }
    Py_DECREF(otherset);
    Py_RETURN_NONE;
}

PyDoc_STRVAR(symmetric_difference_update_doc,
"Update a set with the symmetric difference of itself and another.");

static PyObject *
set_symmetric_difference(PySetObject *so, PyObject *other)
{
    PyObject *rv;
    PySetObject *otherset;

    otherset = (PySetObject *)make_new_set_basetype(Py_TYPE(so), other);
    if (otherset == NULL)
        return NULL;
    rv = set_symmetric_difference_update(otherset, (PyObject *)so);
    if (rv == NULL)
        return NULL;
    Py_DECREF(rv);
    return (PyObject *)otherset;
}

PyDoc_STRVAR(symmetric_difference_doc,
"Return the symmetric difference of two sets as a new set.\n\
\n\
(i.e. all elements that are in exactly one of the sets.)");

static PyObject *
set_xor(PySetObject *so, PyObject *other)
{
    if (!PyAnySet_Check(so) || !PyAnySet_Check(other))
        Py_RETURN_NOTIMPLEMENTED;
    return set_symmetric_difference(so, other);
}

static PyObject *
set_ixor(PySetObject *so, PyObject *other)
{
    PyObject *result;

    if (!PyAnySet_Check(other))
        Py_RETURN_NOTIMPLEMENTED;
    result = set_symmetric_difference_update(so, other);
    if (result == NULL)
        return NULL;
    Py_DECREF(result);
    Py_INCREF(so);
    return (PyObject *)so;
}

static PyObject *
set_issubset(PySetObject *so, PyObject *other)
{
    setentry *entry;
    Py_ssize_t pos = 0;

    if (!PyAnySet_Check(other)) {
        PyObject *tmp, *result;
        tmp = make_new_set(&PySet_Type, other);
        if (tmp == NULL)
            return NULL;
        result = set_issubset(so, tmp);
        Py_DECREF(tmp);
        return result;
    }
    if (PySet_GET_SIZE(so) > PySet_GET_SIZE(other))
        Py_RETURN_FALSE;

    while (set_next(so, &pos, &entry)) {
        int rv = set_contains_entry((PySetObject *)other, entry);
        if (rv == -1)
            return NULL;
        if (!rv)
            Py_RETURN_FALSE;
    }
    Py_RETURN_TRUE;
}

PyDoc_STRVAR(issubset_doc, "Report whether another set contains this set.");

static PyObject *
set_issuperset(PySetObject *so, PyObject *other)
{
    PyObject *tmp, *result;

    if (!PyAnySet_Check(other)) {
        tmp = make_new_set(&PySet_Type, other);
        if (tmp == NULL)
            return NULL;
        result = set_issuperset(so, tmp);
        Py_DECREF(tmp);
        return result;
    }
    return set_issubset((PySetObject *)other, (PyObject *)so);
}

PyDoc_STRVAR(issuperset_doc, "Report whether this set contains another set.");

static PyObject *
set_richcompare(PySetObject *v, PyObject *w, int op)
{
    PyObject *r1, *r2;

    if(!PyAnySet_Check(w))
        Py_RETURN_NOTIMPLEMENTED;

    switch (op) {
    case Py_EQ:
        if (PySet_GET_SIZE(v) != PySet_GET_SIZE(w))
            Py_RETURN_FALSE;
        if (v->hash != -1  &&
            ((PySetObject *)w)->hash != -1 &&
            v->hash != ((PySetObject *)w)->hash)
            Py_RETURN_FALSE;
        return set_issubset(v, w);
    case Py_NE:
        r1 = set_richcompare(v, w, Py_EQ);
        if (r1 == NULL)
            return NULL;
        r2 = PyBool_FromLong(PyObject_Not(r1));
        Py_DECREF(r1);
        return r2;
    case Py_LE:
        return set_issubset(v, w);
    case Py_GE:
        return set_issuperset(v, w);
    case Py_LT:
        if (PySet_GET_SIZE(v) >= PySet_GET_SIZE(w))
            Py_RETURN_FALSE;
        return set_issubset(v, w);
    case Py_GT:
        if (PySet_GET_SIZE(v) <= PySet_GET_SIZE(w))
            Py_RETURN_FALSE;
        return set_issuperset(v, w);
    }
    Py_RETURN_NOTIMPLEMENTED;
}

static PyObject *
set_add(PySetObject *so, PyObject *key)
{
    if (set_add_key(so, key) == -1)
        return NULL;
    Py_RETURN_NONE;
}

PyDoc_STRVAR(add_doc,
"Add an element to a set.\n\
\n\
This has no effect if the element is already present.");

static int
set_contains(PySetObject *so, PyObject *key)
{
    PyObject *tmpkey;
    int rv;

    rv = set_contains_key(so, key);
    if (rv == -1) {
        if (!PySet_Check(key) || !PyErr_ExceptionMatches(PyExc_TypeError))
            return -1;
        PyErr_Clear();
        tmpkey = make_new_set(&PyFrozenSet_Type, key);
        if (tmpkey == NULL)
            return -1;
        rv = set_contains_key(so, tmpkey);
        Py_DECREF(tmpkey);
    }
    return rv;
}

static PyObject *
set_direct_contains(PySetObject *so, PyObject *key)
{
    long result;

    result = set_contains(so, key);
    if (result == -1)
        return NULL;
    return PyBool_FromLong(result);
}

PyDoc_STRVAR(contains_doc, "x.__contains__(y) <==> y in x.");

static PyObject *
set_remove(PySetObject *so, PyObject *key)
{
    PyObject *tmpkey;
    int rv;

    rv = set_discard_key(so, key);
    if (rv == -1) {
        if (!PySet_Check(key) || !PyErr_ExceptionMatches(PyExc_TypeError))
            return NULL;
        PyErr_Clear();
        tmpkey = make_new_set(&PyFrozenSet_Type, key);
        if (tmpkey == NULL)
            return NULL;
        rv = set_discard_key(so, tmpkey);
        Py_DECREF(tmpkey);
        if (rv == -1)
            return NULL;
    }

    if (rv == DISCARD_NOTFOUND) {
        set_key_error(key);
        return NULL;
    }
    Py_RETURN_NONE;
}

PyDoc_STRVAR(remove_doc,
"Remove an element from a set; it must be a member.\n\
\n\
If the element is not a member, raise a KeyError.");

static PyObject *
set_discard(PySetObject *so, PyObject *key)
{
    PyObject *tmpkey;
    int rv;

    rv = set_discard_key(so, key);
    if (rv == -1) {
        if (!PySet_Check(key) || !PyErr_ExceptionMatches(PyExc_TypeError))
            return NULL;
        PyErr_Clear();
        tmpkey = make_new_set(&PyFrozenSet_Type, key);
        if (tmpkey == NULL)
            return NULL;
        rv = set_discard_key(so, tmpkey);
        Py_DECREF(tmpkey);
        if (rv == -1)
            return NULL;
    }
    Py_RETURN_NONE;
}

PyDoc_STRVAR(discard_doc,
"Remove an element from a set if it is a member.\n\
\n\
If the element is not a member, do nothing.");

static PyObject *
set_reduce(PySetObject *so)
{
    PyObject *keys=NULL, *args=NULL, *result=NULL, *dict=NULL;
    _Py_IDENTIFIER(__dict__);

    keys = PySequence_List((PyObject *)so);
    if (keys == NULL)
        goto done;
    args = PyTuple_Pack(1, keys);
    if (args == NULL)
        goto done;
    dict = _PyObject_GetAttrId((PyObject *)so, &PyId___dict__);
    if (dict == NULL) {
        PyErr_Clear();
        dict = Py_None;
        Py_INCREF(dict);
    }
    result = PyTuple_Pack(3, Py_TYPE(so), args, dict);
done:
    Py_XDECREF(args);
    Py_XDECREF(keys);
    Py_XDECREF(dict);
    return result;
}

static PyObject *
set_sizeof(PySetObject *so)
{
    Py_ssize_t res;

    res = sizeof(PySetObject);
    if (so->table != so->smalltable)
        res = res + (so->mask + 1) * sizeof(setentry);
    return PyLong_FromSsize_t(res);
}

PyDoc_STRVAR(sizeof_doc, "S.__sizeof__() -> size of S in memory, in bytes");
static int
set_init(PySetObject *self, PyObject *args, PyObject *kwds)
{
    PyObject *iterable = NULL;

    if (!PyAnySet_Check(self))
        return -1;
    if (PySet_Check(self) && !_PyArg_NoKeywords("set()", kwds))
        return -1;
    if (!PyArg_UnpackTuple(args, Py_TYPE(self)->tp_name, 0, 1, &iterable))
        return -1;
    set_clear_internal(self);
    self->hash = -1;
    if (iterable == NULL)
        return 0;
    return set_update_internal(self, iterable);
}

static PySequenceMethods set_as_sequence = {
    set_len,                            /* sq_length */
    0,                                  /* sq_concat */
    0,                                  /* sq_repeat */
    0,                                  /* sq_item */
    0,                                  /* sq_slice */
    0,                                  /* sq_ass_item */
    0,                                  /* sq_ass_slice */
    (objobjproc)set_contains,           /* sq_contains */
};

/* set object ********************************************************/

#ifdef Py_DEBUG
static PyObject *test_c_api(PySetObject *so);

PyDoc_STRVAR(test_c_api_doc, "Exercises C API.  Returns True.\n\
All is well if assertions don't fail.");
#endif

static PyMethodDef set_methods[] = {
    {"add",             (PyCFunction)set_add,           METH_O,
     add_doc},
    {"clear",           (PyCFunction)set_clear,         METH_NOARGS,
     clear_doc},
    {"__contains__",(PyCFunction)set_direct_contains,           METH_O | METH_COEXIST,
     contains_doc},
    {"copy",            (PyCFunction)set_copy,          METH_NOARGS,
     copy_doc},
    {"discard",         (PyCFunction)set_discard,       METH_O,
     discard_doc},
    {"difference",      (PyCFunction)set_difference_multi,      METH_VARARGS,
     difference_doc},
    {"difference_update",       (PyCFunction)set_difference_update,     METH_VARARGS,
     difference_update_doc},
    {"intersection",(PyCFunction)set_intersection_multi,        METH_VARARGS,
     intersection_doc},
    {"intersection_update",(PyCFunction)set_intersection_update_multi,          METH_VARARGS,
     intersection_update_doc},
    {"isdisjoint",      (PyCFunction)set_isdisjoint,    METH_O,
     isdisjoint_doc},
    {"issubset",        (PyCFunction)set_issubset,      METH_O,
     issubset_doc},
    {"issuperset",      (PyCFunction)set_issuperset,    METH_O,
     issuperset_doc},
    {"pop",             (PyCFunction)set_pop,           METH_NOARGS,
     pop_doc},
    {"__reduce__",      (PyCFunction)set_reduce,        METH_NOARGS,
     reduce_doc},
    {"remove",          (PyCFunction)set_remove,        METH_O,
     remove_doc},
    {"__sizeof__",      (PyCFunction)set_sizeof,        METH_NOARGS,
     sizeof_doc},
    {"symmetric_difference",(PyCFunction)set_symmetric_difference,      METH_O,
     symmetric_difference_doc},
    {"symmetric_difference_update",(PyCFunction)set_symmetric_difference_update,        METH_O,
     symmetric_difference_update_doc},
#ifdef Py_DEBUG
    {"test_c_api",      (PyCFunction)test_c_api,        METH_NOARGS,
     test_c_api_doc},
#endif
    {"union",           (PyCFunction)set_union,         METH_VARARGS,
     union_doc},
    {"update",          (PyCFunction)set_update,        METH_VARARGS,
     update_doc},
    {NULL,              NULL}   /* sentinel */
};

static PyNumberMethods set_as_number = {
    0,                                  /*nb_add*/
    (binaryfunc)set_sub,                /*nb_subtract*/
    0,                                  /*nb_multiply*/
    0,                                  /*nb_remainder*/
    0,                                  /*nb_divmod*/
    0,                                  /*nb_power*/
    0,                                  /*nb_negative*/
    0,                                  /*nb_positive*/
    0,                                  /*nb_absolute*/
    0,                                  /*nb_bool*/
    0,                                  /*nb_invert*/
    0,                                  /*nb_lshift*/
    0,                                  /*nb_rshift*/
    (binaryfunc)set_and,                /*nb_and*/
    (binaryfunc)set_xor,                /*nb_xor*/
    (binaryfunc)set_or,                 /*nb_or*/
    0,                                  /*nb_int*/
    0,                                  /*nb_reserved*/
    0,                                  /*nb_float*/
    0,                                  /*nb_inplace_add*/
    (binaryfunc)set_isub,               /*nb_inplace_subtract*/
    0,                                  /*nb_inplace_multiply*/
    0,                                  /*nb_inplace_remainder*/
    0,                                  /*nb_inplace_power*/
    0,                                  /*nb_inplace_lshift*/
    0,                                  /*nb_inplace_rshift*/
    (binaryfunc)set_iand,               /*nb_inplace_and*/
    (binaryfunc)set_ixor,               /*nb_inplace_xor*/
    (binaryfunc)set_ior,                /*nb_inplace_or*/
};

PyDoc_STRVAR(set_doc,
"set() -> new empty set object\n\
set(iterable) -> new set object\n\
\n\
Build an unordered collection of unique elements.");

PyTypeObject PySet_Type = {
    PyVarObject_HEAD_INIT(&PyType_Type, 0)
    "set",                              /* tp_name */
    sizeof(PySetObject),                /* tp_basicsize */
    0,                                  /* tp_itemsize */
    /* methods */
    (destructor)set_dealloc,            /* tp_dealloc */
    0,                                  /* tp_print */
    0,                                  /* tp_getattr */
    0,                                  /* tp_setattr */
    0,                                  /* tp_reserved */
    (reprfunc)set_repr,                 /* tp_repr */
    &set_as_number,                     /* tp_as_number */
    &set_as_sequence,                   /* tp_as_sequence */
    0,                                  /* tp_as_mapping */
    PyObject_HashNotImplemented,        /* tp_hash */
    0,                                  /* tp_call */
    0,                                  /* tp_str */
    PyObject_GenericGetAttr,            /* tp_getattro */
    0,                                  /* tp_setattro */
    0,                                  /* tp_as_buffer */
    Py_TPFLAGS_DEFAULT | Py_TPFLAGS_HAVE_GC |
        Py_TPFLAGS_BASETYPE,            /* tp_flags */
    set_doc,                            /* tp_doc */
    (traverseproc)set_traverse,         /* tp_traverse */
    (inquiry)set_clear_internal,        /* tp_clear */
    (richcmpfunc)set_richcompare,       /* tp_richcompare */
    offsetof(PySetObject, weakreflist), /* tp_weaklistoffset */
    (getiterfunc)set_iter,              /* tp_iter */
    0,                                  /* tp_iternext */
    set_methods,                        /* tp_methods */
    0,                                  /* tp_members */
    0,                                  /* tp_getset */
    0,                                  /* tp_base */
    0,                                  /* tp_dict */
    0,                                  /* tp_descr_get */
    0,                                  /* tp_descr_set */
    0,                                  /* tp_dictoffset */
    (initproc)set_init,                 /* tp_init */
    PyType_GenericAlloc,                /* tp_alloc */
    set_new,                            /* tp_new */
    PyObject_GC_Del,                    /* tp_free */
};

/* frozenset object ********************************************************/


static PyMethodDef frozenset_methods[] = {
    {"__contains__",(PyCFunction)set_direct_contains,           METH_O | METH_COEXIST,
     contains_doc},
    {"copy",            (PyCFunction)frozenset_copy,    METH_NOARGS,
     copy_doc},
    {"difference",      (PyCFunction)set_difference_multi,      METH_VARARGS,
     difference_doc},
    {"intersection",(PyCFunction)set_intersection_multi,        METH_VARARGS,
     intersection_doc},
    {"isdisjoint",      (PyCFunction)set_isdisjoint,    METH_O,
     isdisjoint_doc},
    {"issubset",        (PyCFunction)set_issubset,      METH_O,
     issubset_doc},
    {"issuperset",      (PyCFunction)set_issuperset,    METH_O,
     issuperset_doc},
    {"__reduce__",      (PyCFunction)set_reduce,        METH_NOARGS,
     reduce_doc},
    {"__sizeof__",      (PyCFunction)set_sizeof,        METH_NOARGS,
     sizeof_doc},
    {"symmetric_difference",(PyCFunction)set_symmetric_difference,      METH_O,
     symmetric_difference_doc},
    {"union",           (PyCFunction)set_union,         METH_VARARGS,
     union_doc},
    {NULL,              NULL}   /* sentinel */
};

static PyNumberMethods frozenset_as_number = {
    0,                                  /*nb_add*/
    (binaryfunc)set_sub,                /*nb_subtract*/
    0,                                  /*nb_multiply*/
    0,                                  /*nb_remainder*/
    0,                                  /*nb_divmod*/
    0,                                  /*nb_power*/
    0,                                  /*nb_negative*/
    0,                                  /*nb_positive*/
    0,                                  /*nb_absolute*/
    0,                                  /*nb_bool*/
    0,                                  /*nb_invert*/
    0,                                  /*nb_lshift*/
    0,                                  /*nb_rshift*/
    (binaryfunc)set_and,                /*nb_and*/
    (binaryfunc)set_xor,                /*nb_xor*/
    (binaryfunc)set_or,                 /*nb_or*/
};

PyDoc_STRVAR(frozenset_doc,
"frozenset() -> empty frozenset object\n\
frozenset(iterable) -> frozenset object\n\
\n\
Build an immutable unordered collection of unique elements.");

PyTypeObject PyFrozenSet_Type = {
    PyVarObject_HEAD_INIT(&PyType_Type, 0)
    "frozenset",                        /* tp_name */
    sizeof(PySetObject),                /* tp_basicsize */
    0,                                  /* tp_itemsize */
    /* methods */
    (destructor)set_dealloc,            /* tp_dealloc */
    0,                                  /* tp_print */
    0,                                  /* tp_getattr */
    0,                                  /* tp_setattr */
    0,                                  /* tp_reserved */
    (reprfunc)set_repr,                 /* tp_repr */
    &frozenset_as_number,               /* tp_as_number */
    &set_as_sequence,                   /* tp_as_sequence */
    0,                                  /* tp_as_mapping */
    frozenset_hash,                     /* tp_hash */
    0,                                  /* tp_call */
    0,                                  /* tp_str */
    PyObject_GenericGetAttr,            /* tp_getattro */
    0,                                  /* tp_setattro */
    0,                                  /* tp_as_buffer */
    Py_TPFLAGS_DEFAULT | Py_TPFLAGS_HAVE_GC |
        Py_TPFLAGS_BASETYPE,            /* tp_flags */
    frozenset_doc,                      /* tp_doc */
    (traverseproc)set_traverse,         /* tp_traverse */
    (inquiry)set_clear_internal,        /* tp_clear */
    (richcmpfunc)set_richcompare,       /* tp_richcompare */
    offsetof(PySetObject, weakreflist),         /* tp_weaklistoffset */
    (getiterfunc)set_iter,              /* tp_iter */
    0,                                  /* tp_iternext */
    frozenset_methods,                  /* tp_methods */
    0,                                  /* tp_members */
    0,                                  /* tp_getset */
    0,                                  /* tp_base */
    0,                                  /* tp_dict */
    0,                                  /* tp_descr_get */
    0,                                  /* tp_descr_set */
    0,                                  /* tp_dictoffset */
    0,                                  /* tp_init */
    PyType_GenericAlloc,                /* tp_alloc */
    frozenset_new,                      /* tp_new */
    PyObject_GC_Del,                    /* tp_free */
};


/***** C API functions *************************************************/

PyObject *
PySet_New(PyObject *iterable)
{
    return make_new_set(&PySet_Type, iterable);
}

PyObject *
PyFrozenSet_New(PyObject *iterable)
{
    return make_new_set(&PyFrozenSet_Type, iterable);
}

Py_ssize_t
PySet_Size(PyObject *anyset)
{
    if (!PyAnySet_Check(anyset)) {
        PyErr_BadInternalCall();
        return -1;
    }
    return PySet_GET_SIZE(anyset);
}

int
PySet_Clear(PyObject *set)
{
    if (!PySet_Check(set)) {
        PyErr_BadInternalCall();
        return -1;
    }
    return set_clear_internal((PySetObject *)set);
}

int
PySet_Contains(PyObject *anyset, PyObject *key)
{
    if (!PyAnySet_Check(anyset)) {
        PyErr_BadInternalCall();
        return -1;
    }
    return set_contains_key((PySetObject *)anyset, key);
}

int
PySet_Discard(PyObject *set, PyObject *key)
{
    if (!PySet_Check(set)) {
        PyErr_BadInternalCall();
        return -1;
    }
    return set_discard_key((PySetObject *)set, key);
}

int
PySet_Add(PyObject *anyset, PyObject *key)
{
    if (!PySet_Check(anyset) &&
        (!PyFrozenSet_Check(anyset) || Py_REFCNT(anyset) != 1)) {
        PyErr_BadInternalCall();
        return -1;
    }
    return set_add_key((PySetObject *)anyset, key);
}

int
_PySet_NextEntry(PyObject *set, Py_ssize_t *pos, PyObject **key, Py_hash_t *hash)
{
    setentry *entry;

    if (!PyAnySet_Check(set)) {
        PyErr_BadInternalCall();
        return -1;
    }
    if (set_next((PySetObject *)set, pos, &entry) == 0)
        return 0;
    *key = entry->key;
    *hash = entry->hash;
    return 1;
}

PyObject *
PySet_Pop(PyObject *set)
{
    if (!PySet_Check(set)) {
        PyErr_BadInternalCall();
        return NULL;
    }
    return set_pop((PySetObject *)set);
}

int
_PySet_Update(PyObject *set, PyObject *iterable)
{
    if (!PySet_Check(set)) {
        PyErr_BadInternalCall();
        return -1;
    }
    return set_update_internal((PySetObject *)set, iterable);
}

#ifdef Py_DEBUG

/* Test code to be called with any three element set.
   Returns True and original set is restored. */

#define assertRaises(call_return_value, exception)              \
    do {                                                        \
        assert(call_return_value);                              \
        assert(PyErr_ExceptionMatches(exception));              \
        PyErr_Clear();                                          \
    } while(0)

static PyObject *
test_c_api(PySetObject *so)
{
    Py_ssize_t count;
    char *s;
    Py_ssize_t i;
    PyObject *elem=NULL, *dup=NULL, *t, *f, *dup2, *x;
    PyObject *ob = (PyObject *)so;
    Py_hash_t hash;
    PyObject *str;

    /* Verify preconditions */
    assert(PyAnySet_Check(ob));
    assert(PyAnySet_CheckExact(ob));
    assert(!PyFrozenSet_CheckExact(ob));

    /* so.clear(); so |= set("abc"); */
    str = PyUnicode_FromString("abc");
    if (str == NULL)
        return NULL;
    set_clear_internal(so);
    if (set_update_internal(so, str) == -1) {
        Py_DECREF(str);
        return NULL;
    }
    Py_DECREF(str);

    /* Exercise type/size checks */
    assert(PySet_Size(ob) == 3);
    assert(PySet_GET_SIZE(ob) == 3);

    /* Raise TypeError for non-iterable constructor arguments */
    assertRaises(PySet_New(Py_None) == NULL, PyExc_TypeError);
    assertRaises(PyFrozenSet_New(Py_None) == NULL, PyExc_TypeError);

    /* Raise TypeError for unhashable key */
    dup = PySet_New(ob);
    assertRaises(PySet_Discard(ob, dup) == -1, PyExc_TypeError);
    assertRaises(PySet_Contains(ob, dup) == -1, PyExc_TypeError);
    assertRaises(PySet_Add(ob, dup) == -1, PyExc_TypeError);

    /* Exercise successful pop, contains, add, and discard */
    elem = PySet_Pop(ob);
    assert(PySet_Contains(ob, elem) == 0);
    assert(PySet_GET_SIZE(ob) == 2);
    assert(PySet_Add(ob, elem) == 0);
    assert(PySet_Contains(ob, elem) == 1);
    assert(PySet_GET_SIZE(ob) == 3);
    assert(PySet_Discard(ob, elem) == 1);
    assert(PySet_GET_SIZE(ob) == 2);
    assert(PySet_Discard(ob, elem) == 0);
    assert(PySet_GET_SIZE(ob) == 2);

    /* Exercise clear */
    dup2 = PySet_New(dup);
    assert(PySet_Clear(dup2) == 0);
    assert(PySet_Size(dup2) == 0);
    Py_DECREF(dup2);

    /* Raise SystemError on clear or update of frozen set */
    f = PyFrozenSet_New(dup);
    assertRaises(PySet_Clear(f) == -1, PyExc_SystemError);
    assertRaises(_PySet_Update(f, dup) == -1, PyExc_SystemError);
    assert(PySet_Add(f, elem) == 0);
    Py_INCREF(f);
    assertRaises(PySet_Add(f, elem) == -1, PyExc_SystemError);
    Py_DECREF(f);
    Py_DECREF(f);

    /* Exercise direct iteration */
    i = 0, count = 0;
    while (_PySet_NextEntry((PyObject *)dup, &i, &x, &hash)) {
        s = _PyUnicode_AsString(x);
        assert(s && (s[0] == 'a' || s[0] == 'b' || s[0] == 'c'));
        count++;
    }
    assert(count == 3);

    /* Exercise updates */
    dup2 = PySet_New(NULL);
    assert(_PySet_Update(dup2, dup) == 0);
    assert(PySet_Size(dup2) == 3);
    assert(_PySet_Update(dup2, dup) == 0);
    assert(PySet_Size(dup2) == 3);
    Py_DECREF(dup2);

    /* Raise SystemError when self argument is not a set or frozenset. */
    t = PyTuple_New(0);
    assertRaises(PySet_Size(t) == -1, PyExc_SystemError);
    assertRaises(PySet_Contains(t, elem) == -1, PyExc_SystemError);
    Py_DECREF(t);

    /* Raise SystemError when self argument is not a set. */
    f = PyFrozenSet_New(dup);
    assert(PySet_Size(f) == 3);
    assert(PyFrozenSet_CheckExact(f));
    assertRaises(PySet_Discard(f, elem) == -1, PyExc_SystemError);
    assertRaises(PySet_Pop(f) == NULL, PyExc_SystemError);
    Py_DECREF(f);

    /* Raise KeyError when popping from an empty set */
    assert(PyNumber_InPlaceSubtract(ob, ob) == ob);
    Py_DECREF(ob);
    assert(PySet_GET_SIZE(ob) == 0);
    assertRaises(PySet_Pop(ob) == NULL, PyExc_KeyError);

    /* Restore the set from the copy using the PyNumber API */
    assert(PyNumber_InPlaceOr(ob, dup) == ob);
    Py_DECREF(ob);

    /* Verify constructors accept NULL arguments */
    f = PySet_New(NULL);
    assert(f != NULL);
    assert(PySet_GET_SIZE(f) == 0);
    Py_DECREF(f);
    f = PyFrozenSet_New(NULL);
    assert(f != NULL);
    assert(PyFrozenSet_CheckExact(f));
    assert(PySet_GET_SIZE(f) == 0);
    Py_DECREF(f);

    Py_DECREF(elem);
    Py_DECREF(dup);
    Py_RETURN_TRUE;
}

#undef assertRaises

#endif