bitmapset.c

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/*-------------------------------------------------------------------------
 *
 * bitmapset.c
 *    PostgreSQL generic bitmap set package
 *
 * A bitmap set can represent any set of nonnegative integers, although
 * it is mainly intended for sets where the maximum value is not large,
 * say at most a few hundred.  By convention, we always represent a set with
 * the minimum possible number of words, i.e, there are never any trailing
 * zero words.  Enforcing this requires that an empty set is represented as
 * NULL.  Because an empty Bitmapset is represented as NULL, a non-NULL
 * Bitmapset always has at least 1 Bitmapword.  We can exploit this fact to
 * speed up various loops over the Bitmapset's words array by using "do while"
 * loops instead of "for" loops.  This means the code does not waste time
 * checking the loop condition before the first iteration.  For Bitmapsets
 * containing only a single word (likely the majority of them) this halves the
 * number of loop condition checks.
 *
 * Callers must ensure that the set returned by functions in this file which
 * adjust the members of an existing set is assigned to all pointers pointing
 * to that existing set.  No guarantees are made that we'll ever modify the
 * existing set in-place and return it.
 *
 * To help find bugs caused by callers failing to record the return value of
 * the function which manipulates an existing set, we support building with
 * REALLOCATE_BITMAPSETS.  This results in the set being reallocated each time
 * the set is altered and the existing being pfreed.  This is useful as if any
 * references still exist to the old set, we're more likely to notice as
 * any users of the old set will be accessing pfree'd memory.  This option is
 * only intended to be used for debugging.
 *
 * Copyright (c) 2003-2026, PostgreSQL Global Development Group
 *
 * IDENTIFICATION
 *    src/backend/nodes/bitmapset.c
 *
 *-------------------------------------------------------------------------
 */
#include "postgres.h"
 
#include "common/hashfn.h"
#include "common/int.h"
#include "nodes/bitmapset.h"
#include "nodes/pg_list.h"
#include "port/pg_bitutils.h"
 
 
#define WORDNUM(x)  ((x) / BITS_PER_BITMAPWORD)
#define BITNUM(x)   ((x) % BITS_PER_BITMAPWORD)
 
#define BITMAPSET_SIZE(nwords)  \
    (offsetof(Bitmapset, words) + (nwords) * sizeof(bitmapword))
 
/*----------
 * This is a well-known cute trick for isolating the rightmost one-bit
 * in a word.  It assumes two's complement arithmetic.  Consider any
 * nonzero value, and focus attention on the rightmost one.  The value is
 * then something like
 *              xxxxxx10000
 * where x's are unspecified bits.  The two's complement negative is formed
 * by inverting all the bits and adding one.  Inversion gives
 *              yyyyyy01111
 * where each y is the inverse of the corresponding x.  Incrementing gives
 *              yyyyyy10000
 * and then ANDing with the original value gives
 *              00000010000
 * This works for all cases except original value = zero, where of course
 * we get zero.
 *----------
 */
#define RIGHTMOST_ONE(x) ((signedbitmapword) (x) & -((signedbitmapword) (x)))
 
#define HAS_MULTIPLE_ONES(x)    ((bitmapword) RIGHTMOST_ONE(x) != (x))
 
#ifdef USE_ASSERT_CHECKING
/*
 * bms_is_valid_set - for cassert builds to check for valid sets
 */
static bool
bms_is_valid_set(const Bitmapset *a)
{
    /* NULL is the correct representation of an empty set */
    if (a == NULL)
        return true;
 
    /* check the node tag is set correctly.  pfree'd pointer, maybe? */
    if (!IsA(a, Bitmapset))
        return false;
 
    /* trailing zero words are not allowed */
    if (a->words[a->nwords - 1] == 0)
        return false;
 
    return true;
}
#endif
 
#ifdef REALLOCATE_BITMAPSETS
/*
 * bms_copy_and_free
 *      Only required in REALLOCATE_BITMAPSETS builds.  Provide a simple way
 *      to return a freshly allocated set and pfree the original.
 *
 * Note: callers which accept multiple sets must be careful when calling this
 * function to clone one parameter as other parameters may point to the same
 * set.  A good option is to call this just before returning the resulting
 * set.
 */
static Bitmapset *
bms_copy_and_free(Bitmapset *a)
{
    Bitmapset  *c = bms_copy(a);
 
    bms_free(a);
    return c;
}
#endif
 
/*
 * bms_copy - make a palloc'd copy of a bitmapset
 */
Bitmapset *
bms_copy(const Bitmapset *a)
{
    Bitmapset  *result;
    size_t      size;
 
    Assert(bms_is_valid_set(a));
 
    if (a == NULL)
        return NULL;
 
    size = BITMAPSET_SIZE(a->nwords);
    result = (Bitmapset *) palloc(size);
    memcpy(result, a, size);
    return result;
}
 
/*
 * bms_equal - are two bitmapsets equal? or both NULL?
 */
bool
bms_equal(const Bitmapset *a, const Bitmapset *b)
{
    int         i;
 
    Assert(bms_is_valid_set(a));
    Assert(bms_is_valid_set(b));
 
    /* Handle cases where either input is NULL */
    if (a == NULL)
    {
        if (b == NULL)
            return true;
        return false;
    }
    else if (b == NULL)
        return false;
 
    /* can't be equal if the word counts don't match */
    if (a->nwords != b->nwords)
        return false;
 
    /* check each word matches */
    i = 0;
    do
    {
        if (a->words[i] != b->words[i])
            return false;
    } while (++i < a->nwords);
 
    return true;
}
 
/*
 * bms_compare - qsort-style comparator for bitmapsets
 *
 * This guarantees to report values as equal iff bms_equal would say they are
 * equal.  Otherwise, the highest-numbered bit that is set in one value but
 * not the other determines the result.  (This rule means that, for example,
 * {6} is greater than {5}, which seems plausible.)
 */
int
bms_compare(const Bitmapset *a, const Bitmapset *b)
{
    int         i;
 
    Assert(bms_is_valid_set(a));
    Assert(bms_is_valid_set(b));
 
    /* Handle cases where either input is NULL */
    if (a == NULL)
        return (b == NULL) ? 0 : -1;
    else if (b == NULL)
        return +1;
 
    /* the set with the most words must be greater */
    if (a->nwords != b->nwords)
        return (a->nwords > b->nwords) ? +1 : -1;
 
    i = a->nwords - 1;
    do
    {
        bitmapword  aw = a->words[i];
        bitmapword  bw = b->words[i];
 
        if (aw != bw)
            return (aw > bw) ? +1 : -1;
    } while (--i >= 0);
    return 0;
}
 
/*
 * bms_make_singleton - build a bitmapset containing a single member
 */
Bitmapset *
bms_make_singleton(int x)
{
    Bitmapset  *result;
    int         wordnum,
                bitnum;
 
    if (x < 0)
        elog(ERROR, "negative bitmapset member not allowed");
    wordnum = WORDNUM(x);
    bitnum = BITNUM(x);
    result = (Bitmapset *) palloc0(BITMAPSET_SIZE(wordnum + 1));
    result->type = T_Bitmapset;
    result->nwords = wordnum + 1;
    result->words[wordnum] = ((bitmapword) 1 << bitnum);
    return result;
}
 
/*
 * bms_free - free a bitmapset
 *
 * Same as pfree except for allowing NULL input
 */
void
bms_free(Bitmapset *a)
{
    if (a)
        pfree(a);
}
 
 
/*
 * bms_union - create and return a new set containing all members from both
 * input sets.  Both inputs are left unmodified.
 */
Bitmapset *
bms_union(const Bitmapset *a, const Bitmapset *b)
{
    Bitmapset  *result;
    const Bitmapset *other;
    int         otherlen;
    int         i;
 
    Assert(bms_is_valid_set(a));
    Assert(bms_is_valid_set(b));
 
    /* Handle cases where either input is NULL */
    if (a == NULL)
        return bms_copy(b);
    if (b == NULL)
        return bms_copy(a);
    /* Identify shorter and longer input; copy the longer one */
    if (a->nwords <= b->nwords)
    {
        result = bms_copy(b);
        other = a;
    }
    else
    {
        result = bms_copy(a);
        other = b;
    }
    /* And union the shorter input into the result */
    otherlen = other->nwords;
    i = 0;
    do
    {
        result->words[i] |= other->words[i];
    } while (++i < otherlen);
    return result;
}
 
/*
 * bms_intersect - create and return a new set containing members which both
 * input sets have in common.  Both inputs are left unmodified.
 */
Bitmapset *
bms_intersect(const Bitmapset *a, const Bitmapset *b)
{
    Bitmapset  *result;
    const Bitmapset *other;
    int         lastnonzero;
    int         resultlen;
    int         i;
 
    Assert(bms_is_valid_set(a));
    Assert(bms_is_valid_set(b));
 
    /* Handle cases where either input is NULL */
    if (a == NULL || b == NULL)
        return NULL;
 
    /* Identify shorter and longer input; copy the shorter one */
    if (a->nwords <= b->nwords)
    {
        result = bms_copy(a);
        other = b;
    }
    else
    {
        result = bms_copy(b);
        other = a;
    }
    /* And intersect the longer input with the result */
    resultlen = result->nwords;
    lastnonzero = -1;
    i = 0;
    do
    {
        result->words[i] &= other->words[i];
 
        if (result->words[i] != 0)
            lastnonzero = i;
    } while (++i < resultlen);
    /* If we computed an empty result, we must return NULL */
    if (lastnonzero == -1)
    {
        pfree(result);
        return NULL;
    }
 
    /* get rid of trailing zero words */
    result->nwords = lastnonzero + 1;
    return result;
}
 
/*
 * bms_difference - create and return a new set containing all the members of
 * 'a' without the members of 'b'.
 */
Bitmapset *
bms_difference(const Bitmapset *a, const Bitmapset *b)
{
    Bitmapset  *result;
    int         i;
 
    Assert(bms_is_valid_set(a));
    Assert(bms_is_valid_set(b));
 
    /* Handle cases where either input is NULL */
    if (a == NULL)
        return NULL;
    if (b == NULL)
        return bms_copy(a);
 
    /*
     * In Postgres' usage, an empty result is a very common case, so it's
     * worth optimizing for that by testing bms_nonempty_difference().  This
     * saves us a palloc/pfree cycle compared to checking after-the-fact.
     */
    if (!bms_nonempty_difference(a, b))
        return NULL;
 
    /* Copy the left input */
    result = bms_copy(a);
 
    /* And remove b's bits from result */
    if (result->nwords > b->nwords)
    {
        /*
         * We'll never need to remove trailing zero words when 'a' has more
         * words than 'b' as the additional words must be non-zero.
         */
        i = 0;
        do
        {
            result->words[i] &= ~b->words[i];
        } while (++i < b->nwords);
    }
    else
    {
        int         lastnonzero = -1;
 
        /* we may need to remove trailing zero words from the result. */
        i = 0;
        do
        {
            result->words[i] &= ~b->words[i];
 
            /* remember the last non-zero word */
            if (result->words[i] != 0)
                lastnonzero = i;
        } while (++i < result->nwords);
 
        /* trim off trailing zero words */
        result->nwords = lastnonzero + 1;
    }
    Assert(result->nwords != 0);
 
    /* Need not check for empty result, since we handled that case above */
    return result;
}
 
/*
 * bms_offset_members
 *      Creates a new Bitmapset with all members of 'a' adjusted to add the
 *      value of 'offset' to each member.
 *
 * Members that would become negative as a result of a negative offset will
 * be removed from the set, whereas too large an offset, which would result in
 * a member going > INT_MAX, will result in an ERROR.
 */
Bitmapset *
bms_offset_members(const Bitmapset *a, int offset)
{
    Bitmapset  *result;
    int         offset_words;
    int         offset_bits;
    int         new_nwords;
    int         old_nwords;
    int32       high_bit;
    int         old_highest;
    int         new_highest;
 
    Assert(bms_is_valid_set(a));
 
    /* nothing to do for empty sets */
    if (a == NULL)
        return NULL;
 
    old_nwords = a->nwords;
    offset_words = WORDNUM(offset);
    offset_bits = BITNUM(offset);
    high_bit = bmw_leftmost_one_pos(a->words[a->nwords - 1]);
    old_highest = (old_nwords - 1) * BITS_PER_BITMAPWORD + high_bit;
 
    /* don't create a set with a member that doesn't fit into an int32 */
    if (pg_add_s32_overflow(old_highest, offset, &new_highest))
        elog(ERROR, "bitmapset overflow");
    /* return NULL if the new set would be empty */
    else if (new_highest < 0)
        return NULL;
 
    new_nwords = WORDNUM(new_highest) + 1;
    result = (Bitmapset *) palloc0(BITMAPSET_SIZE(new_nwords));
    result->type = T_Bitmapset;
    result->nwords = new_nwords;
 
    /* handle zero and positive offsets (bitshift left) */
    if (offset >= 0)
    {
        /*
         * We special-case offsetting only by whole words, so we don't have to
         * special-case bitshifting by BITS_PER_BITMAPWORD places, which has
         * an undefined behavior.
         */
        if (offset_bits == 0)
        {
            int         i = 0;
 
            /*
             * The old set is guaranteed to have at least 1 word, so use
             * do/while to save the redundant initial loop bounds check.
             */
            do
            {
                Assert(i + offset_words < new_nwords);
                result->words[i + offset_words] = a->words[i];
            } while (++i < old_nwords);
        }
        else
        {
            int         carry_bits = BITS_PER_BITMAPWORD - offset_bits;
            bitmapword  prev_carry = 0;
            int         i = 0;
 
            do
            {
                bitmapword  carry = (a->words[i] >> carry_bits);
 
                Assert(i + offset_words < new_nwords);
                /* shift bits up and carry bits from the previous word */
                result->words[i + offset_words] = (a->words[i] << offset_bits) | prev_carry;
                prev_carry = carry;
            } while (++i < old_nwords);
            result->words[new_nwords - 1] |= prev_carry;
        }
    }
 
    /* handle negative offset (bitshift right) */
    else
    {
        /* make the negative offset_words and offset_bits positive */
        offset_words = 0 - offset_words;
        offset_bits = 0 - offset_bits;
 
        /* as above, special case shifting only by whole words */
        if (offset_bits == 0)
        {
            int         i = 0;
 
            do
            {
                Assert(i + offset_words < old_nwords);
                result->words[i] = a->words[i + offset_words];
            } while (++i < new_nwords);
        }
        else
        {
            int         carry_bits = BITS_PER_BITMAPWORD - offset_bits;
            bitmapword  prev_carry = 0;
            int         i = new_nwords - 1;
 
            /* carry bits from any word just above where the loop starts */
            if (old_nwords > new_nwords + offset_words)
                prev_carry = (a->words[new_nwords + offset_words] << carry_bits);
 
            /*
             * We loop backward over the array so we correctly carry bits from
             * higher words.
             */
            do
            {
                bitmapword  carry = (a->words[i + offset_words] << carry_bits);
 
                Assert(i + offset_words < old_nwords);
 
                /* shift bits down and carry bits from the previous word */
                result->words[i] = (a->words[i + offset_words] >> offset_bits) | prev_carry;
                prev_carry = carry;
            } while (--i >= 0);
        }
    }
 
    return result;
}
 
/*
 * bms_is_subset - is A a subset of B?
 */
bool
bms_is_subset(const Bitmapset *a, const Bitmapset *b)
{
    int         i;
 
    Assert(bms_is_valid_set(a));
    Assert(bms_is_valid_set(b));
 
    /* Handle cases where either input is NULL */
    if (a == NULL)
        return true;            /* empty set is a subset of anything */
    if (b == NULL)
        return false;
 
    /* 'a' can't be a subset of 'b' if it contains more words */
    if (a->nwords > b->nwords)
        return false;
 
    /* Check all 'a' members are set in 'b' */
    i = 0;
    do
    {
        if ((a->words[i] & ~b->words[i]) != 0)
            return false;
    } while (++i < a->nwords);
    return true;
}
 
/*
 * bms_subset_compare - compare A and B for equality/subset relationships
 *
 * This is more efficient than testing bms_is_subset in both directions.
 */
BMS_Comparison
bms_subset_compare(const Bitmapset *a, const Bitmapset *b)
{
    BMS_Comparison result;
    int         shortlen;
    int         i;
 
    Assert(bms_is_valid_set(a));
    Assert(bms_is_valid_set(b));
 
    /* Handle cases where either input is NULL */
    if (a == NULL)
    {
        if (b == NULL)
            return BMS_EQUAL;
        return BMS_SUBSET1;
    }
    if (b == NULL)
        return BMS_SUBSET2;
 
    /* Check common words */
    result = BMS_EQUAL;         /* status so far */
    shortlen = Min(a->nwords, b->nwords);
    i = 0;
    do
    {
        bitmapword  aword = a->words[i];
        bitmapword  bword = b->words[i];
 
        if ((aword & ~bword) != 0)
        {
            /* a is not a subset of b */
            if (result == BMS_SUBSET1)
                return BMS_DIFFERENT;
            result = BMS_SUBSET2;
        }
        if ((bword & ~aword) != 0)
        {
            /* b is not a subset of a */
            if (result == BMS_SUBSET2)
                return BMS_DIFFERENT;
            result = BMS_SUBSET1;
        }
    } while (++i < shortlen);
    /* Check extra words */
    if (a->nwords > b->nwords)
    {
        /* if a has more words then a is not a subset of b */
        if (result == BMS_SUBSET1)
            return BMS_DIFFERENT;
        return BMS_SUBSET2;
    }
    else if (a->nwords < b->nwords)
    {
        /* if b has more words then b is not a subset of a */
        if (result == BMS_SUBSET2)
            return BMS_DIFFERENT;
        return BMS_SUBSET1;
    }
    return result;
}
 
/*
 * bms_is_member - is X a member of A?
 */
bool
bms_is_member(int x, const Bitmapset *a)
{
    int         wordnum,
                bitnum;
 
    Assert(bms_is_valid_set(a));
 
    /* XXX better to just return false for x<0 ? */
    if (x < 0)
        elog(ERROR, "negative bitmapset member not allowed");
    if (a == NULL)
        return false;
 
    wordnum = WORDNUM(x);
    bitnum = BITNUM(x);
    if (wordnum >= a->nwords)
        return false;
    if ((a->words[wordnum] & ((bitmapword) 1 << bitnum)) != 0)
        return true;
    return false;
}
 
/*
 * bms_member_index
 *      determine 0-based index of member x in the bitmap
 *
 * Returns (-1) when x is not a member.
 */
int
bms_member_index(Bitmapset *a, int x)
{
    int         bitnum;
    int         wordnum;
    int         result = 0;
    bitmapword  mask;
 
    Assert(bms_is_valid_set(a));
 
    /* return -1 if not a member of the bitmap */
    if (!bms_is_member(x, a))
        return -1;
 
    wordnum = WORDNUM(x);
    bitnum = BITNUM(x);
 
    /* count bits in preceding words */
    result += pg_popcount((const char *) a->words,
                          wordnum * sizeof(bitmapword));
 
    /*
     * Now add bits of the last word, but only those before the item. We can
     * do that by applying a mask and then using popcount again. To get
     * 0-based index, we want to count only preceding bits, not the item
     * itself, so we subtract 1.
     */
    mask = ((bitmapword) 1 << bitnum) - 1;
    result += bmw_popcount(a->words[wordnum] & mask);
 
    return result;
}
 
/*
 * bms_overlap - do sets overlap (ie, have a nonempty intersection)?
 */
bool
bms_overlap(const Bitmapset *a, const Bitmapset *b)
{
    int         shortlen;
    int         i;
 
    Assert(bms_is_valid_set(a));
    Assert(bms_is_valid_set(b));
 
    /* Handle cases where either input is NULL */
    if (a == NULL || b == NULL)
        return false;
    /* Check words in common */
    shortlen = Min(a->nwords, b->nwords);
    i = 0;
    do
    {
        if ((a->words[i] & b->words[i]) != 0)
            return true;
    } while (++i < shortlen);
    return false;
}
 
/*
 * bms_overlap_list - does a set overlap an integer list?
 */
bool
bms_overlap_list(const Bitmapset *a, const List *b)
{
    ListCell   *lc;
    int         wordnum,
                bitnum;
 
    Assert(bms_is_valid_set(a));
 
    if (a == NULL || b == NIL)
        return false;
 
    foreach(lc, b)
    {
        int         x = lfirst_int(lc);
 
        if (x < 0)
            elog(ERROR, "negative bitmapset member not allowed");
        wordnum = WORDNUM(x);
        bitnum = BITNUM(x);
        if (wordnum < a->nwords)
            if ((a->words[wordnum] & ((bitmapword) 1 << bitnum)) != 0)
                return true;
    }
 
    return false;
}
 
/*
 * bms_nonempty_difference - do sets have a nonempty difference?
 *
 * i.e., are any members set in 'a' that are not also set in 'b'.
 */
bool
bms_nonempty_difference(const Bitmapset *a, const Bitmapset *b)
{
    int         i;
 
    Assert(bms_is_valid_set(a));
    Assert(bms_is_valid_set(b));
 
    /* Handle cases where either input is NULL */
    if (a == NULL)
        return false;
    if (b == NULL)
        return true;
    /* if 'a' has more words then it must contain additional members */
    if (a->nwords > b->nwords)
        return true;
    /* Check all 'a' members are set in 'b' */
    i = 0;
    do
    {
        if ((a->words[i] & ~b->words[i]) != 0)
            return true;
    } while (++i < a->nwords);
    return false;
}
 
/*
 * bms_singleton_member - return the sole integer member of set
 *
 * Raises error if |a| is not 1.
 */
int
bms_singleton_member(const Bitmapset *a)
{
    int         result = -1;
    int         nwords;
    int         wordnum;
 
    Assert(bms_is_valid_set(a));
 
    if (a == NULL)
        elog(ERROR, "bitmapset is empty");
 
    nwords = a->nwords;
    wordnum = 0;
    do
    {
        bitmapword  w = a->words[wordnum];
 
        if (w != 0)
        {
            if (result >= 0 || HAS_MULTIPLE_ONES(w))
                elog(ERROR, "bitmapset has multiple members");
            result = wordnum * BITS_PER_BITMAPWORD;
            result += bmw_rightmost_one_pos(w);
        }
    } while (++wordnum < nwords);
 
    /* we don't expect non-NULL sets to be empty */
    Assert(result >= 0);
    return result;
}
 
/*
 * bms_get_singleton_member
 *
 * Test whether the given set is a singleton.
 * If so, set *member to the value of its sole member, and return true.
 * If not, return false, without changing *member.
 *
 * This is more convenient and faster than calling bms_membership() and then
 * bms_singleton_member(), if we don't care about distinguishing empty sets
 * from multiple-member sets.
 */
bool
bms_get_singleton_member(const Bitmapset *a, int *member)
{
    int         result = -1;
    int         nwords;
    int         wordnum;
 
    Assert(bms_is_valid_set(a));
 
    if (a == NULL)
        return false;
 
    nwords = a->nwords;
    wordnum = 0;
    do
    {
        bitmapword  w = a->words[wordnum];
 
        if (w != 0)
        {
            if (result >= 0 || HAS_MULTIPLE_ONES(w))
                return false;
            result = wordnum * BITS_PER_BITMAPWORD;
            result += bmw_rightmost_one_pos(w);
        }
    } while (++wordnum < nwords);
 
    /* we don't expect non-NULL sets to be empty */
    Assert(result >= 0);
    *member = result;
    return true;
}
 
/*
 * bms_num_members - count members of set
 */
int
bms_num_members(const Bitmapset *a)
{
    Assert(bms_is_valid_set(a));
 
    if (a == NULL)
        return 0;
 
    /* fast-path for common case */
    if (a->nwords == 1)
        return bmw_popcount(a->words[0]);
 
    return pg_popcount((const char *) a->words,
                       a->nwords * sizeof(bitmapword));
}
 
/*
 * bms_membership - does a set have zero, one, or multiple members?
 *
 * This is faster than making an exact count with bms_num_members().
 */
BMS_Membership
bms_membership(const Bitmapset *a)
{
    BMS_Membership result = BMS_EMPTY_SET;
    int         nwords;
    int         wordnum;
 
    Assert(bms_is_valid_set(a));
 
    if (a == NULL)
        return BMS_EMPTY_SET;
 
    nwords = a->nwords;
    wordnum = 0;
    do
    {
        bitmapword  w = a->words[wordnum];
 
        if (w != 0)
        {
            if (result != BMS_EMPTY_SET || HAS_MULTIPLE_ONES(w))
                return BMS_MULTIPLE;
            result = BMS_SINGLETON;
        }
    } while (++wordnum < nwords);
    return result;
}
 
 
/*
 * bms_add_member - add a specified member to set
 *
 * 'a' is recycled when possible.
 */
Bitmapset *
bms_add_member(Bitmapset *a, int x)
{
    int         wordnum,
                bitnum;
 
    Assert(bms_is_valid_set(a));
 
    if (x < 0)
        elog(ERROR, "negative bitmapset member not allowed");
    if (a == NULL)
        return bms_make_singleton(x);
 
    wordnum = WORDNUM(x);
    bitnum = BITNUM(x);
 
    /* enlarge the set if necessary */
    if (wordnum >= a->nwords)
    {
        int         oldnwords = a->nwords;
        int         i;
 
        a = (Bitmapset *) repalloc(a, BITMAPSET_SIZE(wordnum + 1));
        a->nwords = wordnum + 1;
        /* zero out the enlarged portion */
        i = oldnwords;
        do
        {
            a->words[i] = 0;
        } while (++i < a->nwords);
    }
 
    a->words[wordnum] |= ((bitmapword) 1 << bitnum);
 
#ifdef REALLOCATE_BITMAPSETS
 
    /*
     * There's no guarantee that the repalloc returned a new pointer, so copy
     * and free unconditionally here.
     */
    a = bms_copy_and_free(a);
#endif
 
    return a;
}
 
/*
 * bms_del_member - remove a specified member from set
 *
 * No error if x is not currently a member of set
 *
 * 'a' is recycled when possible.
 */
Bitmapset *
bms_del_member(Bitmapset *a, int x)
{
    int         wordnum,
                bitnum;
 
    Assert(bms_is_valid_set(a));
 
    if (x < 0)
        elog(ERROR, "negative bitmapset member not allowed");
    if (a == NULL)
        return NULL;
 
    wordnum = WORDNUM(x);
    bitnum = BITNUM(x);
 
#ifdef REALLOCATE_BITMAPSETS
    a = bms_copy_and_free(a);
#endif
 
    /* member can't exist.  Return 'a' unmodified */
    if (unlikely(wordnum >= a->nwords))
        return a;
 
    a->words[wordnum] &= ~((bitmapword) 1 << bitnum);
 
    /* when last word becomes empty, trim off all trailing empty words */
    if (a->words[wordnum] == 0 && wordnum == a->nwords - 1)
    {
        /* find the last non-empty word and make that the new final word */
        for (int i = wordnum - 1; i >= 0; i--)
        {
            if (a->words[i] != 0)
            {
                a->nwords = i + 1;
                return a;
            }
        }
 
        /* the set is now empty */
        pfree(a);
        return NULL;
    }
    return a;
}
 
/*
 * bms_add_members - like bms_union, but left input is recycled when possible
 */
Bitmapset *
bms_add_members(Bitmapset *a, const Bitmapset *b)
{
    Bitmapset  *result;
    const Bitmapset *other;
    int         otherlen;
    int         i;
 
    Assert(bms_is_valid_set(a));
    Assert(bms_is_valid_set(b));
 
    /* Handle cases where either input is NULL */
    if (a == NULL)
        return bms_copy(b);
    if (b == NULL)
    {
#ifdef REALLOCATE_BITMAPSETS
        a = bms_copy_and_free(a);
#endif
 
        return a;
    }
    /* Identify shorter and longer input; copy the longer one if needed */
    if (a->nwords < b->nwords)
    {
        result = bms_copy(b);
        other = a;
    }
    else
    {
        result = a;
        other = b;
    }
    /* And union the shorter input into the result */
    otherlen = other->nwords;
    i = 0;
    do
    {
        result->words[i] |= other->words[i];
    } while (++i < otherlen);
    if (result != a)
        pfree(a);
#ifdef REALLOCATE_BITMAPSETS
    else
        result = bms_copy_and_free(result);
#endif
 
    return result;
}
 
/*
 * bms_replace_members
 *      Remove all existing members from 'a' and repopulate the set with members
 *      from 'b', recycling 'a', when possible.
 */
Bitmapset *
bms_replace_members(Bitmapset *a, const Bitmapset *b)
{
    int         i;
 
    Assert(bms_is_valid_set(a));
    Assert(bms_is_valid_set(b));
 
    if (a == NULL)
        return bms_copy(b);
    if (b == NULL)
    {
        pfree(a);
        return NULL;
    }
 
    if (a->nwords < b->nwords)
        a = (Bitmapset *) repalloc(a, BITMAPSET_SIZE(b->nwords));
 
    i = 0;
    do
    {
        a->words[i] = b->words[i];
    } while (++i < b->nwords);
 
    a->nwords = b->nwords;
 
#ifdef REALLOCATE_BITMAPSETS
 
    /*
     * There's no guarantee that the repalloc returned a new pointer, so copy
     * and free unconditionally here.
     */
    a = bms_copy_and_free(a);
#endif
 
    return a;
}
 
/*
 * bms_add_range
 *      Add members in the range of 'lower' to 'upper' to the set.
 *
 * Note this could also be done by calling bms_add_member in a loop, however,
 * using this function will be faster when the range is large as we work at
 * the bitmapword level rather than at bit level.
 */
Bitmapset *
bms_add_range(Bitmapset *a, int lower, int upper)
{
    int         lwordnum,
                lbitnum,
                uwordnum,
                ushiftbits,
                wordnum;
 
    Assert(bms_is_valid_set(a));
 
    /* do nothing if nothing is called for, without further checking */
    if (upper < lower)
    {
#ifdef REALLOCATE_BITMAPSETS
        a = bms_copy_and_free(a);
#endif
 
        return a;
    }
 
    if (lower < 0)
        elog(ERROR, "negative bitmapset member not allowed");
    uwordnum = WORDNUM(upper);
 
    if (a == NULL)
    {
        a = (Bitmapset *) palloc0(BITMAPSET_SIZE(uwordnum + 1));
        a->type = T_Bitmapset;
        a->nwords = uwordnum + 1;
    }
    else if (uwordnum >= a->nwords)
    {
        int         oldnwords = a->nwords;
        int         i;
 
        /* ensure we have enough words to store the upper bit */
        a = (Bitmapset *) repalloc(a, BITMAPSET_SIZE(uwordnum + 1));
        a->nwords = uwordnum + 1;
        /* zero out the enlarged portion */
        i = oldnwords;
        do
        {
            a->words[i] = 0;
        } while (++i < a->nwords);
    }
 
    wordnum = lwordnum = WORDNUM(lower);
 
    lbitnum = BITNUM(lower);
    ushiftbits = BITS_PER_BITMAPWORD - (BITNUM(upper) + 1);
 
    /*
     * Special case when lwordnum is the same as uwordnum we must perform the
     * upper and lower masking on the word.
     */
    if (lwordnum == uwordnum)
    {
        a->words[lwordnum] |= ~(bitmapword) (((bitmapword) 1 << lbitnum) - 1)
            & (~(bitmapword) 0) >> ushiftbits;
    }
    else
    {
        /* turn on lbitnum and all bits left of it */
        a->words[wordnum++] |= ~(bitmapword) (((bitmapword) 1 << lbitnum) - 1);
 
        /* turn on all bits for any intermediate words */
        while (wordnum < uwordnum)
            a->words[wordnum++] = ~(bitmapword) 0;
 
        /* turn on upper's bit and all bits right of it. */
        a->words[uwordnum] |= (~(bitmapword) 0) >> ushiftbits;
    }
 
#ifdef REALLOCATE_BITMAPSETS
 
    /*
     * There's no guarantee that the repalloc returned a new pointer, so copy
     * and free unconditionally here.
     */
    a = bms_copy_and_free(a);
#endif
 
    return a;
}
 
/*
 * bms_int_members - like bms_intersect, but left input is recycled when
 * possible
 */
Bitmapset *
bms_int_members(Bitmapset *a, const Bitmapset *b)
{
    int         lastnonzero;
    int         shortlen;
    int         i;
 
    Assert(bms_is_valid_set(a));
    Assert(bms_is_valid_set(b));
 
    /* Handle cases where either input is NULL */
    if (a == NULL)
        return NULL;
    if (b == NULL)
    {
        pfree(a);
        return NULL;
    }
 
    /* Intersect b into a; we need never copy */
    shortlen = Min(a->nwords, b->nwords);
    lastnonzero = -1;
    i = 0;
    do
    {
        a->words[i] &= b->words[i];
 
        if (a->words[i] != 0)
            lastnonzero = i;
    } while (++i < shortlen);
 
    /* If we computed an empty result, we must return NULL */
    if (lastnonzero == -1)
    {
        pfree(a);
        return NULL;
    }
 
    /* get rid of trailing zero words */
    a->nwords = lastnonzero + 1;
 
#ifdef REALLOCATE_BITMAPSETS
    a = bms_copy_and_free(a);
#endif
 
    return a;
}
 
/*
 * bms_del_members - delete members in 'a' that are set in 'b'.  'a' is
 * recycled when possible.
 */
Bitmapset *
bms_del_members(Bitmapset *a, const Bitmapset *b)
{
    int         i;
 
    Assert(bms_is_valid_set(a));
    Assert(bms_is_valid_set(b));
 
    /* Handle cases where either input is NULL */
    if (a == NULL)
        return NULL;
    if (b == NULL)
    {
#ifdef REALLOCATE_BITMAPSETS
        a = bms_copy_and_free(a);
#endif
 
        return a;
    }
 
    /* Remove b's bits from a; we need never copy */
    if (a->nwords > b->nwords)
    {
        /*
         * We'll never need to remove trailing zero words when 'a' has more
         * words than 'b'.
         */
        i = 0;
        do
        {
            a->words[i] &= ~b->words[i];
        } while (++i < b->nwords);
    }
    else
    {
        int         lastnonzero = -1;
 
        /* we may need to remove trailing zero words from the result. */
        i = 0;
        do
        {
            a->words[i] &= ~b->words[i];
 
            /* remember the last non-zero word */
            if (a->words[i] != 0)
                lastnonzero = i;
        } while (++i < a->nwords);
 
        /* check if 'a' has become empty */
        if (lastnonzero == -1)
        {
            pfree(a);
            return NULL;
        }
 
        /* trim off any trailing zero words */
        a->nwords = lastnonzero + 1;
    }
 
#ifdef REALLOCATE_BITMAPSETS
    a = bms_copy_and_free(a);
#endif
 
    return a;
}
 
/*
 * bms_join - like bms_union, but *either* input *may* be recycled
 */
Bitmapset *
bms_join(Bitmapset *a, Bitmapset *b)
{
    Bitmapset  *result;
    Bitmapset  *other;
    int         otherlen;
    int         i;
 
    Assert(bms_is_valid_set(a));
    Assert(bms_is_valid_set(b));
 
    /* Handle cases where either input is NULL */
    if (a == NULL)
    {
#ifdef REALLOCATE_BITMAPSETS
        b = bms_copy_and_free(b);
#endif
 
        return b;
    }
    if (b == NULL)
    {
#ifdef REALLOCATE_BITMAPSETS
        a = bms_copy_and_free(a);
#endif
 
        return a;
    }
 
    /* Identify shorter and longer input; use longer one as result */
    if (a->nwords < b->nwords)
    {
        result = b;
        other = a;
    }
    else
    {
        result = a;
        other = b;
    }
    /* And union the shorter input into the result */
    otherlen = other->nwords;
    i = 0;
    do
    {
        result->words[i] |= other->words[i];
    } while (++i < otherlen);
    if (other != result)        /* pure paranoia */
        pfree(other);
 
#ifdef REALLOCATE_BITMAPSETS
    result = bms_copy_and_free(result);
#endif
 
    return result;
}
 
/*
 * bms_next_member - find next member of a set
 *
 * Returns smallest member greater than "prevbit", or -2 if there is none.
 * "prevbit" must NOT be less than -1, or the behavior is unpredictable.
 *
 * This is intended as support for iterating through the members of a set.
 * The typical pattern is
 *
 *          x = -1;
 *          while ((x = bms_next_member(inputset, x)) >= 0)
 *              process member x;
 *
 * Notice that when there are no more members, we return -2, not -1 as you
 * might expect.  The rationale for that is to allow distinguishing the
 * loop-not-started state (x == -1) from the loop-completed state (x == -2).
 * It makes no difference in simple loop usage, but complex iteration logic
 * might need such an ability.
 */
int
bms_next_member(const Bitmapset *a, int prevbit)
{
    unsigned int currbit = prevbit;
    int         nwords;
    bitmapword  mask;
 
    Assert(bms_is_valid_set(a));
 
    if (a == NULL)
        return -2;
    nwords = a->nwords;
 
    /* use an unsigned int to avoid the risk that int overflows */
    currbit++;
    mask = (~(bitmapword) 0) << BITNUM(currbit);
    for (int wordnum = WORDNUM(currbit); wordnum < nwords; wordnum++)
    {
        bitmapword  w = a->words[wordnum];
 
        /* ignore bits before currbit */
        w &= mask;
 
        if (w != 0)
        {
            int         result;
 
            result = wordnum * BITS_PER_BITMAPWORD;
            result += bmw_rightmost_one_pos(w);
            return result;
        }
 
        /* in subsequent words, consider all bits */
        mask = (~(bitmapword) 0);
    }
    return -2;
}
 
/*
 * bms_prev_member - find prev member of a set
 *
 * Returns largest member less than "prevbit", or -2 if there is none.
 * "prevbit" must NOT be more than one above the highest possible bit that can
 * be set in the Bitmapset at its current size.
 *
 * To ease finding the highest set bit for the initial loop, the special
 * prevbit value of -1 can be passed to have the function find the highest
 * valued member in the set.
 *
 * This is intended as support for iterating through the members of a set in
 * reverse.  The typical pattern is
 *
 *          x = -1;
 *          while ((x = bms_prev_member(inputset, x)) >= 0)
 *              process member x;
 *
 * Notice that when there are no more members, we return -2, not -1 as you
 * might expect.  The rationale for that is to allow distinguishing the
 * loop-not-started state (x == -1) from the loop-completed state (x == -2).
 * It makes no difference in simple loop usage, but complex iteration logic
 * might need such an ability.
 */
int
bms_prev_member(const Bitmapset *a, int prevbit)
{
    unsigned int currbit;
    int         ushiftbits;
    bitmapword  mask;
 
    Assert(bms_is_valid_set(a));
 
    /*
     * If set is NULL or if there are no more bits to the right then we've
     * nothing to do.
     */
    if (a == NULL || prevbit == 0)
        return -2;
 
    /* Validate callers didn't give us something out of range */
    Assert(prevbit < 0 || prevbit <= (unsigned int) (a->nwords * BITS_PER_BITMAPWORD));
 
    /*
     * Transform -1 (or any negative number) to the highest possible bit we
     * could have set.  We do this in unsigned math to avoid the risk of
     * overflowing a signed int.
     */
    if (prevbit < 0)
        currbit = (unsigned int) a->nwords * BITS_PER_BITMAPWORD - 1;
    else
        currbit = prevbit - 1;
 
    ushiftbits = BITS_PER_BITMAPWORD - (BITNUM(currbit) + 1);
    mask = (~(bitmapword) 0) >> ushiftbits;
    for (int wordnum = WORDNUM(currbit); wordnum >= 0; wordnum--)
    {
        bitmapword  w = a->words[wordnum];
 
        /* mask out bits left of currbit */
        w &= mask;
 
        if (w != 0)
        {
            int         result;
 
            result = wordnum * BITS_PER_BITMAPWORD;
            result += bmw_leftmost_one_pos(w);
            return result;
        }
 
        /* in subsequent words, consider all bits */
        mask = (~(bitmapword) 0);
    }
    return -2;
}
 
/*
 * bms_hash_value - compute a hash key for a Bitmapset
 */
uint32
bms_hash_value(const Bitmapset *a)
{
    Assert(bms_is_valid_set(a));
 
    if (a == NULL)
        return 0;               /* All empty sets hash to 0 */
    return DatumGetUInt32(hash_any((const unsigned char *) a->words,
                                   a->nwords * sizeof(bitmapword)));
}
 
/*
 * bitmap_hash - hash function for keys that are (pointers to) Bitmapsets
 *
 * Note: don't forget to specify bitmap_match as the match function!
 */
uint32
bitmap_hash(const void *key, Size keysize)
{
    Assert(keysize == sizeof(Bitmapset *));
    return bms_hash_value(*((const Bitmapset *const *) key));
}
 
/*
 * bitmap_match - match function to use with bitmap_hash
 */
int
bitmap_match(const void *key1, const void *key2, Size keysize)
{
    Assert(keysize == sizeof(Bitmapset *));
    return !bms_equal(*((const Bitmapset *const *) key1),
                      *((const Bitmapset *const *) key2));
}