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, a NULL pointer is always
 * accepted by all operations to represent the empty set.  (But beware
 * that this is not the only representation of the empty set.  Use
 * bms_is_empty() in preference to testing for NULL.)
 *
 *
 * Copyright (c) 2003-2013, PostgreSQL Global Development Group
 *
 * IDENTIFICATION
 *    src/backend/nodes/bitmapset.c
 *
 *-------------------------------------------------------------------------
 */
#include "postgres.h"

#include "access/hash.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))


/*
 * Lookup tables to avoid need for bit-by-bit groveling
 *
 * rightmost_one_pos[x] gives the bit number (0-7) of the rightmost one bit
 * in a nonzero byte value x.  The entry for x=0 is never used.
 *
 * number_of_ones[x] gives the number of one-bits (0-8) in a byte value x.
 *
 * We could make these tables larger and reduce the number of iterations
 * in the functions that use them, but bytewise shifts and masks are
 * especially fast on many machines, so working a byte at a time seems best.
 */

static const uint8 rightmost_one_pos[256] = {
    0, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
    4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
    5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
    4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
    6, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
    4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
    5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
    4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
    7, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
    4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
    5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
    4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
    6, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
    4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
    5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
    4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0
};

static const uint8 number_of_ones[256] = {
    0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4,
    1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5,
    1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5,
    2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6,
    1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5,
    2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6,
    2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6,
    3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7,
    1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5,
    2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6,
    2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6,
    3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7,
    2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6,
    3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7,
    3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7,
    4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8
};


/*
 * bms_copy - make a palloc'd copy of a bitmapset
 */
Bitmapset *
bms_copy(const Bitmapset *a)
{
    Bitmapset  *result;
    size_t      size;

    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?
 *
 * This is logical not physical equality; in particular, a NULL pointer will
 * be reported as equal to a palloc'd value containing no members.
 */
bool
bms_equal(const Bitmapset *a, const Bitmapset *b)
{
    const Bitmapset *shorter;
    const Bitmapset *longer;
    int         shortlen;
    int         longlen;
    int         i;

    /* Handle cases where either input is NULL */
    if (a == NULL)
    {
        if (b == NULL)
            return true;
        return bms_is_empty(b);
    }
    else if (b == NULL)
        return bms_is_empty(a);
    /* Identify shorter and longer input */
    if (a->nwords <= b->nwords)
    {
        shorter = a;
        longer = b;
    }
    else
    {
        shorter = b;
        longer = a;
    }
    /* And process */
    shortlen = shorter->nwords;
    for (i = 0; i < shortlen; i++)
    {
        if (shorter->words[i] != longer->words[i])
            return false;
    }
    longlen = longer->nwords;
    for (; i < longlen; i++)
    {
        if (longer->words[i] != 0)
            return false;
    }
    return true;
}

/*
 * 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->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);
}


/*
 * These operations all make a freshly palloc'd result,
 * leaving their inputs untouched
 */


/*
 * bms_union - set union
 */
Bitmapset *
bms_union(const Bitmapset *a, const Bitmapset *b)
{
    Bitmapset  *result;
    const Bitmapset *other;
    int         otherlen;
    int         i;

    /* 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;
    for (i = 0; i < otherlen; i++)
        result->words[i] |= other->words[i];
    return result;
}

/*
 * bms_intersect - set intersection
 */
Bitmapset *
bms_intersect(const Bitmapset *a, const Bitmapset *b)
{
    Bitmapset  *result;
    const Bitmapset *other;
    int         resultlen;
    int         i;

    /* 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;
    for (i = 0; i < resultlen; i++)
        result->words[i] &= other->words[i];
    return result;
}

/*
 * bms_difference - set difference (ie, A without members of B)
 */
Bitmapset *
bms_difference(const Bitmapset *a, const Bitmapset *b)
{
    Bitmapset  *result;
    int         shortlen;
    int         i;

    /* Handle cases where either input is NULL */
    if (a == NULL)
        return NULL;
    if (b == NULL)
        return bms_copy(a);
    /* Copy the left input */
    result = bms_copy(a);
    /* And remove b's bits from result */
    shortlen = Min(a->nwords, b->nwords);
    for (i = 0; i < shortlen; i++)
        result->words[i] &= ~b->words[i];
    return result;
}

/*
 * bms_is_subset - is A a subset of B?
 */
bool
bms_is_subset(const Bitmapset *a, const Bitmapset *b)
{
    int         shortlen;
    int         longlen;
    int         i;

    /* Handle cases where either input is NULL */
    if (a == NULL)
        return true;            /* empty set is a subset of anything */
    if (b == NULL)
        return bms_is_empty(a);
    /* Check common words */
    shortlen = Min(a->nwords, b->nwords);
    for (i = 0; i < shortlen; i++)
    {
        if ((a->words[i] & ~b->words[i]) != 0)
            return false;
    }
    /* Check extra words */
    if (a->nwords > b->nwords)
    {
        longlen = a->nwords;
        for (; i < longlen; i++)
        {
            if (a->words[i] != 0)
                return false;
        }
    }
    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         longlen;
    int         i;

    /* Handle cases where either input is NULL */
    if (a == NULL)
    {
        if (b == NULL)
            return BMS_EQUAL;
        return bms_is_empty(b) ? BMS_EQUAL : BMS_SUBSET1;
    }
    if (b == NULL)
        return bms_is_empty(a) ? BMS_EQUAL : BMS_SUBSET2;
    /* Check common words */
    result = BMS_EQUAL;         /* status so far */
    shortlen = Min(a->nwords, b->nwords);
    for (i = 0; i < shortlen; i++)
    {
        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;
        }
    }
    /* Check extra words */
    if (a->nwords > b->nwords)
    {
        longlen = a->nwords;
        for (; i < longlen; i++)
        {
            if (a->words[i] != 0)
            {
                /* a is not a subset of b */
                if (result == BMS_SUBSET1)
                    return BMS_DIFFERENT;
                result = BMS_SUBSET2;
            }
        }
    }
    else if (a->nwords < b->nwords)
    {
        longlen = b->nwords;
        for (; i < longlen; i++)
        {
            if (b->words[i] != 0)
            {
                /* b is not a subset of a */
                if (result == BMS_SUBSET2)
                    return BMS_DIFFERENT;
                result = 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;

    /* 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_overlap - do sets overlap (ie, have a nonempty intersection)?
 */
bool
bms_overlap(const Bitmapset *a, const Bitmapset *b)
{
    int         shortlen;
    int         i;

    /* Handle cases where either input is NULL */
    if (a == NULL || b == NULL)
        return false;
    /* Check words in common */
    shortlen = Min(a->nwords, b->nwords);
    for (i = 0; i < shortlen; i++)
    {
        if ((a->words[i] & b->words[i]) != 0)
            return true;
    }
    return false;
}

/*
 * bms_nonempty_difference - do sets have a nonempty difference?
 */
bool
bms_nonempty_difference(const Bitmapset *a, const Bitmapset *b)
{
    int         shortlen;
    int         i;

    /* Handle cases where either input is NULL */
    if (a == NULL)
        return false;
    if (b == NULL)
        return !bms_is_empty(a);
    /* Check words in common */
    shortlen = Min(a->nwords, b->nwords);
    for (i = 0; i < shortlen; i++)
    {
        if ((a->words[i] & ~b->words[i]) != 0)
            return true;
    }
    /* Check extra words in a */
    for (; i < a->nwords; i++)
    {
        if (a->words[i] != 0)
            return true;
    }
    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;

    if (a == NULL)
        elog(ERROR, "bitmapset is empty");
    nwords = a->nwords;
    for (wordnum = 0; wordnum < nwords; wordnum++)
    {
        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;
            while ((w & 255) == 0)
            {
                w >>= 8;
                result += 8;
            }
            result += rightmost_one_pos[w & 255];
        }
    }
    if (result < 0)
        elog(ERROR, "bitmapset is empty");
    return result;
}

/*
 * bms_num_members - count members of set
 */
int
bms_num_members(const Bitmapset *a)
{
    int         result = 0;
    int         nwords;
    int         wordnum;

    if (a == NULL)
        return 0;
    nwords = a->nwords;
    for (wordnum = 0; wordnum < nwords; wordnum++)
    {
        bitmapword  w = a->words[wordnum];

        /* we assume here that bitmapword is an unsigned type */
        while (w != 0)
        {
            result += number_of_ones[w & 255];
            w >>= 8;
        }
    }
    return result;
}

/*
 * 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;

    if (a == NULL)
        return BMS_EMPTY_SET;
    nwords = a->nwords;
    for (wordnum = 0; wordnum < nwords; wordnum++)
    {
        bitmapword  w = a->words[wordnum];

        if (w != 0)
        {
            if (result != BMS_EMPTY_SET || HAS_MULTIPLE_ONES(w))
                return BMS_MULTIPLE;
            result = BMS_SINGLETON;
        }
    }
    return result;
}

/*
 * bms_is_empty - is a set empty?
 *
 * This is even faster than bms_membership().
 */
bool
bms_is_empty(const Bitmapset *a)
{
    int         nwords;
    int         wordnum;

    if (a == NULL)
        return true;
    nwords = a->nwords;
    for (wordnum = 0; wordnum < nwords; wordnum++)
    {
        bitmapword  w = a->words[wordnum];

        if (w != 0)
            return false;
    }
    return true;
}


/*
 * These operations all "recycle" their non-const inputs, ie, either
 * return the modified input or pfree it if it can't hold the result.
 *
 * These should generally be used in the style
 *
 *      foo = bms_add_member(foo, x);
 */


/*
 * bms_add_member - add a specified member to set
 *
 * Input set is modified or recycled!
 */
Bitmapset *
bms_add_member(Bitmapset *a, int x)
{
    int         wordnum,
                bitnum;

    if (x < 0)
        elog(ERROR, "negative bitmapset member not allowed");
    if (a == NULL)
        return bms_make_singleton(x);
    wordnum = WORDNUM(x);
    bitnum = BITNUM(x);
    if (wordnum >= a->nwords)
    {
        /* Slow path: make a larger set and union the input set into it */
        Bitmapset  *result;
        int         nwords;
        int         i;

        result = bms_make_singleton(x);
        nwords = a->nwords;
        for (i = 0; i < nwords; i++)
            result->words[i] |= a->words[i];
        pfree(a);
        return result;
    }
    /* Fast path: x fits in existing set */
    a->words[wordnum] |= ((bitmapword) 1 << bitnum);
    return a;
}

/*
 * bms_del_member - remove a specified member from set
 *
 * No error if x is not currently a member of set
 *
 * Input set is modified in-place!
 */
Bitmapset *
bms_del_member(Bitmapset *a, int x)
{
    int         wordnum,
                bitnum;

    if (x < 0)
        elog(ERROR, "negative bitmapset member not allowed");
    if (a == NULL)
        return NULL;
    wordnum = WORDNUM(x);
    bitnum = BITNUM(x);
    if (wordnum < a->nwords)
        a->words[wordnum] &= ~((bitmapword) 1 << bitnum);
    return a;
}

/*
 * bms_add_members - like bms_union, but left input is recycled
 */
Bitmapset *
bms_add_members(Bitmapset *a, const Bitmapset *b)
{
    Bitmapset  *result;
    const Bitmapset *other;
    int         otherlen;
    int         i;

    /* Handle cases where either input is NULL */
    if (a == NULL)
        return bms_copy(b);
    if (b == NULL)
        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;
    for (i = 0; i < otherlen; i++)
        result->words[i] |= other->words[i];
    if (result != a)
        pfree(a);
    return result;
}

/*
 * bms_int_members - like bms_intersect, but left input is recycled
 */
Bitmapset *
bms_int_members(Bitmapset *a, const Bitmapset *b)
{
    int         shortlen;
    int         i;

    /* 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);
    for (i = 0; i < shortlen; i++)
        a->words[i] &= b->words[i];
    for (; i < a->nwords; i++)
        a->words[i] = 0;
    return a;
}

/*
 * bms_del_members - like bms_difference, but left input is recycled
 */
Bitmapset *
bms_del_members(Bitmapset *a, const Bitmapset *b)
{
    int         shortlen;
    int         i;

    /* Handle cases where either input is NULL */
    if (a == NULL)
        return NULL;
    if (b == NULL)
        return a;
    /* Remove b's bits from a; we need never copy */
    shortlen = Min(a->nwords, b->nwords);
    for (i = 0; i < shortlen; i++)
        a->words[i] &= ~b->words[i];
    return a;
}

/*
 * bms_join - like bms_union, but *both* inputs are recycled
 */
Bitmapset *
bms_join(Bitmapset *a, Bitmapset *b)
{
    Bitmapset  *result;
    Bitmapset  *other;
    int         otherlen;
    int         i;

    /* Handle cases where either input is NULL */
    if (a == NULL)
        return b;
    if (b == NULL)
        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;
    for (i = 0; i < otherlen; i++)
        result->words[i] |= other->words[i];
    if (other != result)        /* pure paranoia */
        pfree(other);
    return result;
}

/*----------
 * bms_first_member - find and remove first member of a set
 *
 * Returns -1 if set is empty.  NB: set is destructively modified!
 *
 * This is intended as support for iterating through the members of a set.
 * The typical pattern is
 *
 *          tmpset = bms_copy(inputset);
 *          while ((x = bms_first_member(tmpset)) >= 0)
 *              process member x;
 *          bms_free(tmpset);
 *----------
 */
int
bms_first_member(Bitmapset *a)
{
    int         nwords;
    int         wordnum;

    if (a == NULL)
        return -1;
    nwords = a->nwords;
    for (wordnum = 0; wordnum < nwords; wordnum++)
    {
        bitmapword  w = a->words[wordnum];

        if (w != 0)
        {
            int         result;

            w = RIGHTMOST_ONE(w);
            a->words[wordnum] &= ~w;

            result = wordnum * BITS_PER_BITMAPWORD;
            while ((w & 255) == 0)
            {
                w >>= 8;
                result += 8;
            }
            result += rightmost_one_pos[w & 255];
            return result;
        }
    }
    return -1;
}

/*
 * bms_hash_value - compute a hash key for a Bitmapset
 *
 * Note: we must ensure that any two bitmapsets that are bms_equal() will
 * hash to the same value; in practice this means that trailing all-zero
 * words must not affect the result.  Hence we strip those before applying
 * hash_any().
 */
uint32
bms_hash_value(const Bitmapset *a)
{
    int         lastword;

    if (a == NULL)
        return 0;               /* All empty sets hash to 0 */
    for (lastword = a->nwords; --lastword >= 0;)
    {
        if (a->words[lastword] != 0)
            break;
    }
    if (lastword < 0)
        return 0;               /* All empty sets hash to 0 */
    return DatumGetUInt32(hash_any((const unsigned char *) a->words,
                                   (lastword + 1) * sizeof(bitmapword)));
}