tidbitmap.c

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/*-------------------------------------------------------------------------
 *
 * tidbitmap.c
 *    PostgreSQL tuple-id (TID) bitmap package
 *
 * This module provides bitmap data structures that are spiritually
 * similar to Bitmapsets, but are specially adapted to store sets of
 * tuple identifiers (TIDs), or ItemPointers.  In particular, the division
 * of an ItemPointer into BlockNumber and OffsetNumber is catered for.
 * Also, since we wish to be able to store very large tuple sets in
 * memory with this data structure, we support "lossy" storage, in which
 * we no longer remember individual tuple offsets on a page but only the
 * fact that a particular page needs to be visited.
 *
 * The "lossy" storage uses one bit per disk page, so at the standard 8K
 * BLCKSZ, we can represent all pages in 64Gb of disk space in about 1Mb
 * of memory.  People pushing around tables of that size should have a
 * couple of Mb to spare, so we don't worry about providing a second level
 * of lossiness.  In theory we could fall back to page ranges at some
 * point, but for now that seems useless complexity.
 *
 * We also support the notion of candidate matches, or rechecking.  This
 * means we know that a search need visit only some tuples on a page,
 * but we are not certain that all of those tuples are real matches.
 * So the eventual heap scan must recheck the quals for these tuples only,
 * rather than rechecking the quals for all tuples on the page as in the
 * lossy-bitmap case.  Rechecking can be specified when TIDs are inserted
 * into a bitmap, and it can also happen internally when we AND a lossy
 * and a non-lossy page.
 *
 *
 * Copyright (c) 2003-2017, PostgreSQL Global Development Group
 *
 * IDENTIFICATION
 *    src/backend/nodes/tidbitmap.c
 *
 *-------------------------------------------------------------------------
 */
#include "postgres.h"

#include <limits.h>

#include "access/htup_details.h"
#include "nodes/bitmapset.h"
#include "nodes/tidbitmap.h"
#include "storage/lwlock.h"
#include "utils/dsa.h"

/*
 * The maximum number of tuples per page is not large (typically 256 with
 * 8K pages, or 1024 with 32K pages).  So there's not much point in making
 * the per-page bitmaps variable size.  We just legislate that the size
 * is this:
 */
#define MAX_TUPLES_PER_PAGE  MaxHeapTuplesPerPage

/*
 * When we have to switch over to lossy storage, we use a data structure
 * with one bit per page, where all pages having the same number DIV
 * PAGES_PER_CHUNK are aggregated into one chunk.  When a chunk is present
 * and has the bit set for a given page, there must not be a per-page entry
 * for that page in the page table.
 *
 * We actually store both exact pages and lossy chunks in the same hash
 * table, using identical data structures.  (This is because the memory
 * management for hashtables doesn't easily/efficiently allow space to be
 * transferred easily from one hashtable to another.)  Therefore it's best
 * if PAGES_PER_CHUNK is the same as MAX_TUPLES_PER_PAGE, or at least not
 * too different.  But we also want PAGES_PER_CHUNK to be a power of 2 to
 * avoid expensive integer remainder operations.  So, define it like this:
 */
#define PAGES_PER_CHUNK  (BLCKSZ / 32)

/* We use BITS_PER_BITMAPWORD and typedef bitmapword from nodes/bitmapset.h */

#define WORDNUM(x)  ((x) / BITS_PER_BITMAPWORD)
#define BITNUM(x)   ((x) % BITS_PER_BITMAPWORD)

/* number of active words for an exact page: */
#define WORDS_PER_PAGE  ((MAX_TUPLES_PER_PAGE - 1) / BITS_PER_BITMAPWORD + 1)
/* number of active words for a lossy chunk: */
#define WORDS_PER_CHUNK  ((PAGES_PER_CHUNK - 1) / BITS_PER_BITMAPWORD + 1)

/*
 * The hashtable entries are represented by this data structure.  For
 * an exact page, blockno is the page number and bit k of the bitmap
 * represents tuple offset k+1.  For a lossy chunk, blockno is the first
 * page in the chunk (this must be a multiple of PAGES_PER_CHUNK) and
 * bit k represents page blockno+k.  Note that it is not possible to
 * have exact storage for the first page of a chunk if we are using
 * lossy storage for any page in the chunk's range, since the same
 * hashtable entry has to serve both purposes.
 *
 * recheck is used only on exact pages --- it indicates that although
 * only the stated tuples need be checked, the full index qual condition
 * must be checked for each (ie, these are candidate matches).
 */
typedef struct PagetableEntry
{
    BlockNumber blockno;        /* page number (hashtable key) */
    char        status;         /* hash entry status */
    bool        ischunk;        /* T = lossy storage, F = exact */
    bool        recheck;        /* should the tuples be rechecked? */
    bitmapword  words[Max(WORDS_PER_PAGE, WORDS_PER_CHUNK)];
} PagetableEntry;

/*
 * Holds array of pagetable entries.
 */
typedef struct PTEntryArray
{
    pg_atomic_uint32 refcount;  /* no. of iterator attached */
    PagetableEntry ptentry[FLEXIBLE_ARRAY_MEMBER];
} PTEntryArray;

/*
 * We want to avoid the overhead of creating the hashtable, which is
 * comparatively large, when not necessary. Particularly when we are using a
 * bitmap scan on the inside of a nestloop join: a bitmap may well live only
 * long enough to accumulate one entry in such cases.  We therefore avoid
 * creating an actual hashtable until we need two pagetable entries.  When
 * just one pagetable entry is needed, we store it in a fixed field of
 * TIDBitMap.  (NOTE: we don't get rid of the hashtable if the bitmap later
 * shrinks down to zero or one page again.  So, status can be TBM_HASH even
 * when nentries is zero or one.)
 */
typedef enum
{
    TBM_EMPTY,                  /* no hashtable, nentries == 0 */
    TBM_ONE_PAGE,               /* entry1 contains the single entry */
    TBM_HASH                    /* pagetable is valid, entry1 is not */
} TBMStatus;

/*
 * Current iterating state of the TBM.
 */
typedef enum
{
    TBM_NOT_ITERATING,          /* not yet converted to page and chunk array */
    TBM_ITERATING_PRIVATE,      /* converted to local page and chunk array */
    TBM_ITERATING_SHARED        /* converted to shared page and chunk array */
} TBMIteratingState;

/*
 * Here is the representation for a whole TIDBitMap:
 */
struct TIDBitmap
{
    NodeTag     type;           /* to make it a valid Node */
    MemoryContext mcxt;         /* memory context containing me */
    TBMStatus   status;         /* see codes above */
    struct pagetable_hash *pagetable;   /* hash table of PagetableEntry's */
    int         nentries;       /* number of entries in pagetable */
    int         maxentries;     /* limit on same to meet maxbytes */
    int         npages;         /* number of exact entries in pagetable */
    int         nchunks;        /* number of lossy entries in pagetable */
    TBMIteratingState iterating;    /* tbm_begin_iterate called? */
    uint32      lossify_start;  /* offset to start lossifying hashtable at */
    PagetableEntry entry1;      /* used when status == TBM_ONE_PAGE */
    /* these are valid when iterating is true: */
    PagetableEntry **spages;    /* sorted exact-page list, or NULL */
    PagetableEntry **schunks;   /* sorted lossy-chunk list, or NULL */
    dsa_pointer dsapagetable;   /* dsa_pointer to the element array */
    dsa_pointer dsapagetableold;    /* dsa_pointer to the old element array */
    dsa_pointer ptpages;        /* dsa_pointer to the page array */
    dsa_pointer ptchunks;       /* dsa_pointer to the chunk array */
    dsa_area   *dsa;            /* reference to per-query dsa area */
};

/*
 * When iterating over a bitmap in sorted order, a TBMIterator is used to
 * track our progress.  There can be several iterators scanning the same
 * bitmap concurrently.  Note that the bitmap becomes read-only as soon as
 * any iterator is created.
 */
struct TBMIterator
{
    TIDBitmap  *tbm;            /* TIDBitmap we're iterating over */
    int         spageptr;       /* next spages index */
    int         schunkptr;      /* next schunks index */
    int         schunkbit;      /* next bit to check in current schunk */
    TBMIterateResult output;    /* MUST BE LAST (because variable-size) */
};

/*
 * Holds the shared members of the iterator so that multiple processes
 * can jointly iterate.
 */
typedef struct TBMSharedIteratorState
{
    int         nentries;       /* number of entries in pagetable */
    int         maxentries;     /* limit on same to meet maxbytes */
    int         npages;         /* number of exact entries in pagetable */
    int         nchunks;        /* number of lossy entries in pagetable */
    dsa_pointer pagetable;      /* dsa pointers to head of pagetable data */
    dsa_pointer spages;         /* dsa pointer to page array */
    dsa_pointer schunks;        /* dsa pointer to chunk array */
    LWLock      lock;           /* lock to protect below members */
    int         spageptr;       /* next spages index */
    int         schunkptr;      /* next schunks index */
    int         schunkbit;      /* next bit to check in current schunk */
} TBMSharedIteratorState;

/*
 * pagetable iteration array.
 */
typedef struct PTIterationArray
{
    pg_atomic_uint32 refcount;  /* no. of iterator attached */
    int         index[FLEXIBLE_ARRAY_MEMBER];   /* index array */
} PTIterationArray;

/*
 * same as TBMIterator, but it is used for joint iteration, therefore this
 * also holds a reference to the shared state.
 */
struct TBMSharedIterator
{
    TBMSharedIteratorState *state;  /* shared state */
    PTEntryArray *ptbase;       /* pagetable element array */
    PTIterationArray *ptpages;  /* sorted exact page index list */
    PTIterationArray *ptchunks; /* sorted lossy page index list */
    TBMIterateResult output;    /* MUST BE LAST (because variable-size) */
};

/* Local function prototypes */
static void tbm_union_page(TIDBitmap *a, const PagetableEntry *bpage);
static bool tbm_intersect_page(TIDBitmap *a, PagetableEntry *apage,
                   const TIDBitmap *b);
static const PagetableEntry *tbm_find_pageentry(const TIDBitmap *tbm,
                   BlockNumber pageno);
static PagetableEntry *tbm_get_pageentry(TIDBitmap *tbm, BlockNumber pageno);
static bool tbm_page_is_lossy(const TIDBitmap *tbm, BlockNumber pageno);
static void tbm_mark_page_lossy(TIDBitmap *tbm, BlockNumber pageno);
static void tbm_lossify(TIDBitmap *tbm);
static int  tbm_comparator(const void *left, const void *right);
static int tbm_shared_comparator(const void *left, const void *right,
                      void *arg);

/*
 * Simple inline murmur hash implementation for the exact width required, for
 * performance.
 */
static inline uint32
hash_blockno(BlockNumber b)
{
    uint32      h = b;

    h ^= h >> 16;
    h *= 0x85ebca6b;
    h ^= h >> 13;
    h *= 0xc2b2ae35;
    h ^= h >> 16;
    return h;
}

/* define hashtable mapping block numbers to PagetableEntry's */
#define SH_USE_NONDEFAULT_ALLOCATOR
#define SH_PREFIX pagetable
#define SH_ELEMENT_TYPE PagetableEntry
#define SH_KEY_TYPE BlockNumber
#define SH_KEY blockno
#define SH_HASH_KEY(tb, key) hash_blockno(key)
#define SH_EQUAL(tb, a, b) a == b
#define SH_SCOPE static inline
#define SH_DEFINE
#define SH_DECLARE
#include "lib/simplehash.h"


/*
 * tbm_create - create an initially-empty bitmap
 *
 * The bitmap will live in the memory context that is CurrentMemoryContext
 * at the time of this call.  It will be limited to (approximately) maxbytes
 * total memory consumption.  If the DSA passed to this function is not NULL
 * then the memory for storing elements of the underlying page table will
 * be allocated from the DSA.
 */
TIDBitmap *
tbm_create(long maxbytes, dsa_area *dsa)
{
    TIDBitmap  *tbm;
    long        nbuckets;

    /* Create the TIDBitmap struct and zero all its fields */
    tbm = makeNode(TIDBitmap);

    tbm->mcxt = CurrentMemoryContext;
    tbm->status = TBM_EMPTY;

    /*
     * Estimate number of hashtable entries we can have within maxbytes. This
     * estimates the hash cost as sizeof(PagetableEntry), which is good enough
     * for our purpose.  Also count an extra Pointer per entry for the arrays
     * created during iteration readout.
     */
    nbuckets = maxbytes /
        (sizeof(PagetableEntry) + sizeof(Pointer) + sizeof(Pointer));
    nbuckets = Min(nbuckets, INT_MAX - 1);  /* safety limit */
    nbuckets = Max(nbuckets, 16);   /* sanity limit */
    tbm->maxentries = (int) nbuckets;
    tbm->lossify_start = 0;
    tbm->dsa = dsa;
    tbm->dsapagetable = InvalidDsaPointer;
    tbm->dsapagetableold = InvalidDsaPointer;
    tbm->ptpages = InvalidDsaPointer;
    tbm->ptchunks = InvalidDsaPointer;

    return tbm;
}

/*
 * Actually create the hashtable.  Since this is a moderately expensive
 * proposition, we don't do it until we have to.
 */
static void
tbm_create_pagetable(TIDBitmap *tbm)
{
    Assert(tbm->status != TBM_HASH);
    Assert(tbm->pagetable == NULL);

    tbm->pagetable = pagetable_create(tbm->mcxt, 128, tbm);

    /* If entry1 is valid, push it into the hashtable */
    if (tbm->status == TBM_ONE_PAGE)
    {
        PagetableEntry *page;
        bool        found;
        char        oldstatus;

        page = pagetable_insert(tbm->pagetable,
                                tbm->entry1.blockno,
                                &found);
        Assert(!found);
        oldstatus = page->status;
        memcpy(page, &tbm->entry1, sizeof(PagetableEntry));
        page->status = oldstatus;
    }

    tbm->status = TBM_HASH;
}

/*
 * tbm_free - free a TIDBitmap
 */
void
tbm_free(TIDBitmap *tbm)
{
    if (tbm->pagetable)
        pagetable_destroy(tbm->pagetable);
    if (tbm->spages)
        pfree(tbm->spages);
    if (tbm->schunks)
        pfree(tbm->schunks);
    pfree(tbm);
}

/*
 * tbm_free_shared_area - free shared state
 *
 * Free shared iterator state, Also free shared pagetable and iterator arrays
 * memory if they are not referred by any of the shared iterator i.e recount
 * is becomes 0.
 */
void
tbm_free_shared_area(dsa_area *dsa, dsa_pointer dp)
{
    TBMSharedIteratorState *istate = dsa_get_address(dsa, dp);
    PTEntryArray *ptbase;
    PTIterationArray *ptpages;
    PTIterationArray *ptchunks;

    if (DsaPointerIsValid(istate->pagetable))
    {
        ptbase = dsa_get_address(dsa, istate->pagetable);
        if (pg_atomic_sub_fetch_u32(&ptbase->refcount, 1) == 0)
            dsa_free(dsa, istate->pagetable);
    }
    if (DsaPointerIsValid(istate->spages))
    {
        ptpages = dsa_get_address(dsa, istate->spages);
        if (pg_atomic_sub_fetch_u32(&ptpages->refcount, 1) == 0)
            dsa_free(dsa, istate->spages);
    }
    if (DsaPointerIsValid(istate->schunks))
    {
        ptchunks = dsa_get_address(dsa, istate->schunks);
        if (pg_atomic_sub_fetch_u32(&ptchunks->refcount, 1) == 0)
            dsa_free(dsa, istate->schunks);
    }

    dsa_free(dsa, dp);
}

/*
 * tbm_add_tuples - add some tuple IDs to a TIDBitmap
 *
 * If recheck is true, then the recheck flag will be set in the
 * TBMIterateResult when any of these tuples are reported out.
 */
void
tbm_add_tuples(TIDBitmap *tbm, const ItemPointer tids, int ntids,
               bool recheck)
{
    BlockNumber currblk = InvalidBlockNumber;
    PagetableEntry *page = NULL;    /* only valid when currblk is valid */
    int         i;

    Assert(tbm->iterating == TBM_NOT_ITERATING);
    for (i = 0; i < ntids; i++)
    {
        BlockNumber blk = ItemPointerGetBlockNumber(tids + i);
        OffsetNumber off = ItemPointerGetOffsetNumber(tids + i);
        int         wordnum,
                    bitnum;

        /* safety check to ensure we don't overrun bit array bounds */
        if (off < 1 || off > MAX_TUPLES_PER_PAGE)
            elog(ERROR, "tuple offset out of range: %u", off);

        /*
         * Look up target page unless we already did.  This saves cycles when
         * the input includes consecutive tuples on the same page, which is
         * common enough to justify an extra test here.
         */
        if (blk != currblk)
        {
            if (tbm_page_is_lossy(tbm, blk))
                page = NULL;    /* remember page is lossy */
            else
                page = tbm_get_pageentry(tbm, blk);
            currblk = blk;
        }

        if (page == NULL)
            continue;           /* whole page is already marked */

        if (page->ischunk)
        {
            /* The page is a lossy chunk header, set bit for itself */
            wordnum = bitnum = 0;
        }
        else
        {
            /* Page is exact, so set bit for individual tuple */
            wordnum = WORDNUM(off - 1);
            bitnum = BITNUM(off - 1);
        }
        page->words[wordnum] |= ((bitmapword) 1 << bitnum);
        page->recheck |= recheck;

        if (tbm->nentries > tbm->maxentries)
        {
            tbm_lossify(tbm);
            /* Page could have been converted to lossy, so force new lookup */
            currblk = InvalidBlockNumber;
        }
    }
}

/*
 * tbm_add_page - add a whole page to a TIDBitmap
 *
 * This causes the whole page to be reported (with the recheck flag)
 * when the TIDBitmap is scanned.
 */
void
tbm_add_page(TIDBitmap *tbm, BlockNumber pageno)
{
    /* Enter the page in the bitmap, or mark it lossy if already present */
    tbm_mark_page_lossy(tbm, pageno);
    /* If we went over the memory limit, lossify some more pages */
    if (tbm->nentries > tbm->maxentries)
        tbm_lossify(tbm);
}

/*
 * tbm_union - set union
 *
 * a is modified in-place, b is not changed
 */
void
tbm_union(TIDBitmap *a, const TIDBitmap *b)
{
    Assert(!a->iterating);
    /* Nothing to do if b is empty */
    if (b->nentries == 0)
        return;
    /* Scan through chunks and pages in b, merge into a */
    if (b->status == TBM_ONE_PAGE)
        tbm_union_page(a, &b->entry1);
    else
    {
        pagetable_iterator i;
        PagetableEntry *bpage;

        Assert(b->status == TBM_HASH);
        pagetable_start_iterate(b->pagetable, &i);
        while ((bpage = pagetable_iterate(b->pagetable, &i)) != NULL)
            tbm_union_page(a, bpage);
    }
}

/* Process one page of b during a union op */
static void
tbm_union_page(TIDBitmap *a, const PagetableEntry *bpage)
{
    PagetableEntry *apage;
    int         wordnum;

    if (bpage->ischunk)
    {
        /* Scan b's chunk, mark each indicated page lossy in a */
        for (wordnum = 0; wordnum < WORDS_PER_CHUNK; wordnum++)
        {
            bitmapword  w = bpage->words[wordnum];

            if (w != 0)
            {
                BlockNumber pg;

                pg = bpage->blockno + (wordnum * BITS_PER_BITMAPWORD);
                while (w != 0)
                {
                    if (w & 1)
                        tbm_mark_page_lossy(a, pg);
                    pg++;
                    w >>= 1;
                }
            }
        }
    }
    else if (tbm_page_is_lossy(a, bpage->blockno))
    {
        /* page is already lossy in a, nothing to do */
        return;
    }
    else
    {
        apage = tbm_get_pageentry(a, bpage->blockno);
        if (apage->ischunk)
        {
            /* The page is a lossy chunk header, set bit for itself */
            apage->words[0] |= ((bitmapword) 1 << 0);
        }
        else
        {
            /* Both pages are exact, merge at the bit level */
            for (wordnum = 0; wordnum < WORDS_PER_PAGE; wordnum++)
                apage->words[wordnum] |= bpage->words[wordnum];
            apage->recheck |= bpage->recheck;
        }
    }

    if (a->nentries > a->maxentries)
        tbm_lossify(a);
}

/*
 * tbm_intersect - set intersection
 *
 * a is modified in-place, b is not changed
 */
void
tbm_intersect(TIDBitmap *a, const TIDBitmap *b)
{
    Assert(!a->iterating);
    /* Nothing to do if a is empty */
    if (a->nentries == 0)
        return;
    /* Scan through chunks and pages in a, try to match to b */
    if (a->status == TBM_ONE_PAGE)
    {
        if (tbm_intersect_page(a, &a->entry1, b))
        {
            /* Page is now empty, remove it from a */
            Assert(!a->entry1.ischunk);
            a->npages--;
            a->nentries--;
            Assert(a->nentries == 0);
            a->status = TBM_EMPTY;
        }
    }
    else
    {
        pagetable_iterator i;
        PagetableEntry *apage;

        Assert(a->status == TBM_HASH);
        pagetable_start_iterate(a->pagetable, &i);
        while ((apage = pagetable_iterate(a->pagetable, &i)) != NULL)
        {
            if (tbm_intersect_page(a, apage, b))
            {
                /* Page or chunk is now empty, remove it from a */
                if (apage->ischunk)
                    a->nchunks--;
                else
                    a->npages--;
                a->nentries--;
                if (!pagetable_delete(a->pagetable, apage->blockno))
                    elog(ERROR, "hash table corrupted");
            }
        }
    }
}

/*
 * Process one page of a during an intersection op
 *
 * Returns TRUE if apage is now empty and should be deleted from a
 */
static bool
tbm_intersect_page(TIDBitmap *a, PagetableEntry *apage, const TIDBitmap *b)
{
    const PagetableEntry *bpage;
    int         wordnum;

    if (apage->ischunk)
    {
        /* Scan each bit in chunk, try to clear */
        bool        candelete = true;

        for (wordnum = 0; wordnum < WORDS_PER_CHUNK; wordnum++)
        {
            bitmapword  w = apage->words[wordnum];

            if (w != 0)
            {
                bitmapword  neww = w;
                BlockNumber pg;
                int         bitnum;

                pg = apage->blockno + (wordnum * BITS_PER_BITMAPWORD);
                bitnum = 0;
                while (w != 0)
                {
                    if (w & 1)
                    {
                        if (!tbm_page_is_lossy(b, pg) &&
                            tbm_find_pageentry(b, pg) == NULL)
                        {
                            /* Page is not in b at all, lose lossy bit */
                            neww &= ~((bitmapword) 1 << bitnum);
                        }
                    }
                    pg++;
                    bitnum++;
                    w >>= 1;
                }
                apage->words[wordnum] = neww;
                if (neww != 0)
                    candelete = false;
            }
        }
        return candelete;
    }
    else if (tbm_page_is_lossy(b, apage->blockno))
    {
        /*
         * Some of the tuples in 'a' might not satisfy the quals for 'b', but
         * because the page 'b' is lossy, we don't know which ones. Therefore
         * we mark 'a' as requiring rechecks, to indicate that at most those
         * tuples set in 'a' are matches.
         */
        apage->recheck = true;
        return false;
    }
    else
    {
        bool        candelete = true;

        bpage = tbm_find_pageentry(b, apage->blockno);
        if (bpage != NULL)
        {
            /* Both pages are exact, merge at the bit level */
            Assert(!bpage->ischunk);
            for (wordnum = 0; wordnum < WORDS_PER_PAGE; wordnum++)
            {
                apage->words[wordnum] &= bpage->words[wordnum];
                if (apage->words[wordnum] != 0)
                    candelete = false;
            }
            apage->recheck |= bpage->recheck;
        }
        /* If there is no matching b page, we can just delete the a page */
        return candelete;
    }
}

/*
 * tbm_is_empty - is a TIDBitmap completely empty?
 */
bool
tbm_is_empty(const TIDBitmap *tbm)
{
    return (tbm->nentries == 0);
}

/*
 * tbm_begin_iterate - prepare to iterate through a TIDBitmap
 *
 * The TBMIterator struct is created in the caller's memory context.
 * For a clean shutdown of the iteration, call tbm_end_iterate; but it's
 * okay to just allow the memory context to be released, too.  It is caller's
 * responsibility not to touch the TBMIterator anymore once the TIDBitmap
 * is freed.
 *
 * NB: after this is called, it is no longer allowed to modify the contents
 * of the bitmap.  However, you can call this multiple times to scan the
 * contents repeatedly, including parallel scans.
 */
TBMIterator *
tbm_begin_iterate(TIDBitmap *tbm)
{
    TBMIterator *iterator;

    Assert(tbm->iterating != TBM_ITERATING_SHARED);

    /*
     * Create the TBMIterator struct, with enough trailing space to serve the
     * needs of the TBMIterateResult sub-struct.
     */
    iterator = (TBMIterator *) palloc(sizeof(TBMIterator) +
                                      MAX_TUPLES_PER_PAGE * sizeof(OffsetNumber));
    iterator->tbm = tbm;

    /*
     * Initialize iteration pointers.
     */
    iterator->spageptr = 0;
    iterator->schunkptr = 0;
    iterator->schunkbit = 0;

    /*
     * If we have a hashtable, create and fill the sorted page lists, unless
     * we already did that for a previous iterator.  Note that the lists are
     * attached to the bitmap not the iterator, so they can be used by more
     * than one iterator.
     */
    if (tbm->status == TBM_HASH && tbm->iterating == TBM_NOT_ITERATING)
    {
        pagetable_iterator i;
        PagetableEntry *page;
        int         npages;
        int         nchunks;

        if (!tbm->spages && tbm->npages > 0)
            tbm->spages = (PagetableEntry **)
                MemoryContextAlloc(tbm->mcxt,
                                   tbm->npages * sizeof(PagetableEntry *));
        if (!tbm->schunks && tbm->nchunks > 0)
            tbm->schunks = (PagetableEntry **)
                MemoryContextAlloc(tbm->mcxt,
                                   tbm->nchunks * sizeof(PagetableEntry *));

        npages = nchunks = 0;
        pagetable_start_iterate(tbm->pagetable, &i);
        while ((page = pagetable_iterate(tbm->pagetable, &i)) != NULL)
        {
            if (page->ischunk)
                tbm->schunks[nchunks++] = page;
            else
                tbm->spages[npages++] = page;
        }
        Assert(npages == tbm->npages);
        Assert(nchunks == tbm->nchunks);
        if (npages > 1)
            qsort(tbm->spages, npages, sizeof(PagetableEntry *),
                  tbm_comparator);
        if (nchunks > 1)
            qsort(tbm->schunks, nchunks, sizeof(PagetableEntry *),
                  tbm_comparator);
    }

    tbm->iterating = TBM_ITERATING_PRIVATE;

    return iterator;
}

/*
 * tbm_prepare_shared_iterate - prepare shared iteration state for a TIDBitmap.
 *
 * The necessary shared state will be allocated from the DSA passed to
 * tbm_create, so that multiple processes can attach to it and iterate jointly.
 *
 * This will convert the pagetable hash into page and chunk array of the index
 * into pagetable array.
 */
dsa_pointer
tbm_prepare_shared_iterate(TIDBitmap *tbm)
{
    dsa_pointer dp;
    TBMSharedIteratorState *istate;
    PTEntryArray *ptbase = NULL;
    PTIterationArray *ptpages = NULL;
    PTIterationArray *ptchunks = NULL;

    Assert(tbm->dsa != NULL);
    Assert(tbm->iterating != TBM_ITERATING_PRIVATE);

    /*
     * Allocate TBMSharedIteratorState from DSA to hold the shared members and
     * lock, this will also be used by multiple worker for shared iterate.
     */
    dp = dsa_allocate0(tbm->dsa, sizeof(TBMSharedIteratorState));
    istate = dsa_get_address(tbm->dsa, dp);

    /*
     * If we're not already iterating, create and fill the sorted page lists.
     * (If we are, the sorted page lists are already stored in the TIDBitmap,
     * and we can just reuse them.)
     */
    if (tbm->iterating == TBM_NOT_ITERATING)
    {
        pagetable_iterator i;
        PagetableEntry *page;
        int         idx;
        int         npages;
        int         nchunks;

        /*
         * Allocate the page and chunk array memory from the DSA to share
         * across multiple processes.
         */
        if (tbm->npages)
        {
            tbm->ptpages = dsa_allocate(tbm->dsa, sizeof(PTIterationArray) +
                                        tbm->npages * sizeof(int));
            ptpages = dsa_get_address(tbm->dsa, tbm->ptpages);
            pg_atomic_init_u32(&ptpages->refcount, 0);
        }
        if (tbm->nchunks)
        {
            tbm->ptchunks = dsa_allocate(tbm->dsa, sizeof(PTIterationArray) +
                                         tbm->nchunks * sizeof(int));
            ptchunks = dsa_get_address(tbm->dsa, tbm->ptchunks);
            pg_atomic_init_u32(&ptchunks->refcount, 0);
        }

        /*
         * If TBM status is TBM_HASH then iterate over the pagetable and
         * convert it to page and chunk arrays.  But if it's in the
         * TBM_ONE_PAGE mode then directly allocate the space for one entry
         * from the DSA.
         */
        npages = nchunks = 0;
        if (tbm->status == TBM_HASH)
        {
            ptbase = dsa_get_address(tbm->dsa, tbm->dsapagetable);

            pagetable_start_iterate(tbm->pagetable, &i);
            while ((page = pagetable_iterate(tbm->pagetable, &i)) != NULL)
            {
                idx = page - ptbase->ptentry;
                if (page->ischunk)
                    ptchunks->index[nchunks++] = idx;
                else
                    ptpages->index[npages++] = idx;
            }

            Assert(npages == tbm->npages);
            Assert(nchunks == tbm->nchunks);
        }
        else if (tbm->status == TBM_ONE_PAGE)
        {
            /*
             * In one page mode allocate the space for one pagetable entry,
             * initialize it, and directly store its index (i.e. 0) in the
             * page array.
             */
            tbm->dsapagetable = dsa_allocate(tbm->dsa, sizeof(PTEntryArray) +
                                             sizeof(PagetableEntry));
            ptbase = dsa_get_address(tbm->dsa, tbm->dsapagetable);
            memcpy(ptbase->ptentry, &tbm->entry1, sizeof(PagetableEntry));
            ptpages->index[0] = 0;
        }

        if (ptbase != NULL)
            pg_atomic_init_u32(&ptbase->refcount, 0);
        if (npages > 1)
            qsort_arg((void *) (ptpages->index), npages, sizeof(int),
                      tbm_shared_comparator, (void *) ptbase->ptentry);
        if (nchunks > 1)
            qsort_arg((void *) (ptchunks->index), nchunks, sizeof(int),
                      tbm_shared_comparator, (void *) ptbase->ptentry);
    }

    /*
     * Store the TBM members in the shared state so that we can share them
     * across multiple processes.
     */
    istate->nentries = tbm->nentries;
    istate->maxentries = tbm->maxentries;
    istate->npages = tbm->npages;
    istate->nchunks = tbm->nchunks;
    istate->pagetable = tbm->dsapagetable;
    istate->spages = tbm->ptpages;
    istate->schunks = tbm->ptchunks;

    ptbase = dsa_get_address(tbm->dsa, tbm->dsapagetable);
    ptpages = dsa_get_address(tbm->dsa, tbm->ptpages);
    ptchunks = dsa_get_address(tbm->dsa, tbm->ptchunks);

    /*
     * For every shared iterator, referring to pagetable and iterator array,
     * increase the refcount by 1 so that while freeing the shared iterator we
     * don't free pagetable and iterator array until its refcount becomes 0.
     */
    if (ptbase != NULL)
        pg_atomic_add_fetch_u32(&ptbase->refcount, 1);
    if (ptpages != NULL)
        pg_atomic_add_fetch_u32(&ptpages->refcount, 1);
    if (ptchunks != NULL)
        pg_atomic_add_fetch_u32(&ptchunks->refcount, 1);

    /* Initialize the iterator lock */
    LWLockInitialize(&istate->lock, LWTRANCHE_TBM);

    /* Initialize the shared iterator state */
    istate->schunkbit = 0;
    istate->schunkptr = 0;
    istate->spageptr = 0;

    tbm->iterating = TBM_ITERATING_SHARED;

    return dp;
}

/*
 * tbm_extract_page_tuple - extract the tuple offsets from a page
 *
 * The extracted offsets are stored into TBMIterateResult.
 */
static inline int
tbm_extract_page_tuple(PagetableEntry *page, TBMIterateResult *output)
{
    int         wordnum;
    int         ntuples = 0;

    for (wordnum = 0; wordnum < WORDS_PER_PAGE; wordnum++)
    {
        bitmapword  w = page->words[wordnum];

        if (w != 0)
        {
            int         off = wordnum * BITS_PER_BITMAPWORD + 1;

            while (w != 0)
            {
                if (w & 1)
                    output->offsets[ntuples++] = (OffsetNumber) off;
                off++;
                w >>= 1;
            }
        }
    }

    return ntuples;
}

/*
 *  tbm_advance_schunkbit - Advance the chunkbit
 */
static inline void
tbm_advance_schunkbit(PagetableEntry *chunk, int *schunkbitp)
{
    int         schunkbit = *schunkbitp;

    while (schunkbit < PAGES_PER_CHUNK)
    {
        int         wordnum = WORDNUM(schunkbit);
        int         bitnum = BITNUM(schunkbit);

        if ((chunk->words[wordnum] & ((bitmapword) 1 << bitnum)) != 0)
            break;
        schunkbit++;
    }

    *schunkbitp = schunkbit;
}

/*
 * tbm_iterate - scan through next page of a TIDBitmap
 *
 * Returns a TBMIterateResult representing one page, or NULL if there are
 * no more pages to scan.  Pages are guaranteed to be delivered in numerical
 * order.  If result->ntuples < 0, then the bitmap is "lossy" and failed to
 * remember the exact tuples to look at on this page --- the caller must
 * examine all tuples on the page and check if they meet the intended
 * condition.  If result->recheck is true, only the indicated tuples need
 * be examined, but the condition must be rechecked anyway.  (For ease of
 * testing, recheck is always set true when ntuples < 0.)
 */
TBMIterateResult *
tbm_iterate(TBMIterator *iterator)
{
    TIDBitmap  *tbm = iterator->tbm;
    TBMIterateResult *output = &(iterator->output);

    Assert(tbm->iterating == TBM_ITERATING_PRIVATE);

    /*
     * If lossy chunk pages remain, make sure we've advanced schunkptr/
     * schunkbit to the next set bit.
     */
    while (iterator->schunkptr < tbm->nchunks)
    {
        PagetableEntry *chunk = tbm->schunks[iterator->schunkptr];
        int         schunkbit = iterator->schunkbit;

        tbm_advance_schunkbit(chunk, &schunkbit);
        if (schunkbit < PAGES_PER_CHUNK)
        {
            iterator->schunkbit = schunkbit;
            break;
        }
        /* advance to next chunk */
        iterator->schunkptr++;
        iterator->schunkbit = 0;
    }

    /*
     * If both chunk and per-page data remain, must output the numerically
     * earlier page.
     */
    if (iterator->schunkptr < tbm->nchunks)
    {
        PagetableEntry *chunk = tbm->schunks[iterator->schunkptr];
        BlockNumber chunk_blockno;

        chunk_blockno = chunk->blockno + iterator->schunkbit;
        if (iterator->spageptr >= tbm->npages ||
            chunk_blockno < tbm->spages[iterator->spageptr]->blockno)
        {
            /* Return a lossy page indicator from the chunk */
            output->blockno = chunk_blockno;
            output->ntuples = -1;
            output->recheck = true;
            iterator->schunkbit++;
            return output;
        }
    }

    if (iterator->spageptr < tbm->npages)
    {
        PagetableEntry *page;
        int         ntuples;

        /* In ONE_PAGE state, we don't allocate an spages[] array */
        if (tbm->status == TBM_ONE_PAGE)
            page = &tbm->entry1;
        else
            page = tbm->spages[iterator->spageptr];

        /* scan bitmap to extract individual offset numbers */
        ntuples = tbm_extract_page_tuple(page, output);
        output->blockno = page->blockno;
        output->ntuples = ntuples;
        output->recheck = page->recheck;
        iterator->spageptr++;
        return output;
    }

    /* Nothing more in the bitmap */
    return NULL;
}

/*
 *  tbm_shared_iterate - scan through next page of a TIDBitmap
 *
 *  As above, but this will iterate using an iterator which is shared
 *  across multiple processes.  We need to acquire the iterator LWLock,
 *  before accessing the shared members.
 */
TBMIterateResult *
tbm_shared_iterate(TBMSharedIterator *iterator)
{
    TBMIterateResult *output = &iterator->output;
    TBMSharedIteratorState *istate = iterator->state;
    PagetableEntry *ptbase = NULL;
    int        *idxpages = NULL;
    int        *idxchunks = NULL;

    if (iterator->ptbase != NULL)
        ptbase = iterator->ptbase->ptentry;
    if (iterator->ptpages != NULL)
        idxpages = iterator->ptpages->index;
    if (iterator->ptchunks != NULL)
        idxchunks = iterator->ptchunks->index;

    /* Acquire the LWLock before accessing the shared members */
    LWLockAcquire(&istate->lock, LW_EXCLUSIVE);

    /*
     * If lossy chunk pages remain, make sure we've advanced schunkptr/
     * schunkbit to the next set bit.
     */
    while (istate->schunkptr < istate->nchunks)
    {
        PagetableEntry *chunk = &ptbase[idxchunks[istate->schunkptr]];
        int         schunkbit = istate->schunkbit;

        tbm_advance_schunkbit(chunk, &schunkbit);
        if (schunkbit < PAGES_PER_CHUNK)
        {
            istate->schunkbit = schunkbit;
            break;
        }
        /* advance to next chunk */
        istate->schunkptr++;
        istate->schunkbit = 0;
    }

    /*
     * If both chunk and per-page data remain, must output the numerically
     * earlier page.
     */
    if (istate->schunkptr < istate->nchunks)
    {
        PagetableEntry *chunk = &ptbase[idxchunks[istate->schunkptr]];
        BlockNumber chunk_blockno;

        chunk_blockno = chunk->blockno + istate->schunkbit;

        if (istate->spageptr >= istate->npages ||
            chunk_blockno < ptbase[idxpages[istate->spageptr]].blockno)
        {
            /* Return a lossy page indicator from the chunk */
            output->blockno = chunk_blockno;
            output->ntuples = -1;
            output->recheck = true;
            istate->schunkbit++;

            LWLockRelease(&istate->lock);
            return output;
        }
    }

    if (istate->spageptr < istate->npages)
    {
        PagetableEntry *page = &ptbase[idxpages[istate->spageptr]];
        int         ntuples;

        /* scan bitmap to extract individual offset numbers */
        ntuples = tbm_extract_page_tuple(page, output);
        output->blockno = page->blockno;
        output->ntuples = ntuples;
        output->recheck = page->recheck;
        istate->spageptr++;

        LWLockRelease(&istate->lock);

        return output;
    }

    LWLockRelease(&istate->lock);

    /* Nothing more in the bitmap */
    return NULL;
}

/*
 * tbm_end_iterate - finish an iteration over a TIDBitmap
 *
 * Currently this is just a pfree, but it might do more someday.  (For
 * instance, it could be useful to count open iterators and allow the
 * bitmap to return to read/write status when there are no more iterators.)
 */
void
tbm_end_iterate(TBMIterator *iterator)
{
    pfree(iterator);
}

/*
 * tbm_end_shared_iterate - finish a shared iteration over a TIDBitmap
 *
 * This doesn't free any of the shared state associated with the iterator,
 * just our backend-private state.
 */
void
tbm_end_shared_iterate(TBMSharedIterator *iterator)
{
    pfree(iterator);
}

/*
 * tbm_find_pageentry - find a PagetableEntry for the pageno
 *
 * Returns NULL if there is no non-lossy entry for the pageno.
 */
static const PagetableEntry *
tbm_find_pageentry(const TIDBitmap *tbm, BlockNumber pageno)
{
    const PagetableEntry *page;

    if (tbm->nentries == 0)     /* in case pagetable doesn't exist */
        return NULL;

    if (tbm->status == TBM_ONE_PAGE)
    {
        page = &tbm->entry1;
        if (page->blockno != pageno)
            return NULL;
        Assert(!page->ischunk);
        return page;
    }

    page = pagetable_lookup(tbm->pagetable, pageno);
    if (page == NULL)
        return NULL;
    if (page->ischunk)
        return NULL;            /* don't want a lossy chunk header */
    return page;
}

/*
 * tbm_get_pageentry - find or create a PagetableEntry for the pageno
 *
 * If new, the entry is marked as an exact (non-chunk) entry.
 *
 * This may cause the table to exceed the desired memory size.  It is
 * up to the caller to call tbm_lossify() at the next safe point if so.
 */
static PagetableEntry *
tbm_get_pageentry(TIDBitmap *tbm, BlockNumber pageno)
{
    PagetableEntry *page;
    bool        found;

    if (tbm->status == TBM_EMPTY)
    {
        /* Use the fixed slot */
        page = &tbm->entry1;
        found = false;
        tbm->status = TBM_ONE_PAGE;
    }
    else
    {
        if (tbm->status == TBM_ONE_PAGE)
        {
            page = &tbm->entry1;
            if (page->blockno == pageno)
                return page;
            /* Time to switch from one page to a hashtable */
            tbm_create_pagetable(tbm);
        }

        /* Look up or create an entry */
        page = pagetable_insert(tbm->pagetable, pageno, &found);
    }

    /* Initialize it if not present before */
    if (!found)
    {
        char        oldstatus = page->status;

        MemSet(page, 0, sizeof(PagetableEntry));
        page->status = oldstatus;
        page->blockno = pageno;
        /* must count it too */
        tbm->nentries++;
        tbm->npages++;
    }

    return page;
}

/*
 * tbm_page_is_lossy - is the page marked as lossily stored?
 */
static bool
tbm_page_is_lossy(const TIDBitmap *tbm, BlockNumber pageno)
{
    PagetableEntry *page;
    BlockNumber chunk_pageno;
    int         bitno;

    /* we can skip the lookup if there are no lossy chunks */
    if (tbm->nchunks == 0)
        return false;
    Assert(tbm->status == TBM_HASH);

    bitno = pageno % PAGES_PER_CHUNK;
    chunk_pageno = pageno - bitno;

    page = pagetable_lookup(tbm->pagetable, chunk_pageno);

    if (page != NULL && page->ischunk)
    {
        int         wordnum = WORDNUM(bitno);
        int         bitnum = BITNUM(bitno);

        if ((page->words[wordnum] & ((bitmapword) 1 << bitnum)) != 0)
            return true;
    }
    return false;
}

/*
 * tbm_mark_page_lossy - mark the page number as lossily stored
 *
 * This may cause the table to exceed the desired memory size.  It is
 * up to the caller to call tbm_lossify() at the next safe point if so.
 */
static void
tbm_mark_page_lossy(TIDBitmap *tbm, BlockNumber pageno)
{
    PagetableEntry *page;
    bool        found;
    BlockNumber chunk_pageno;
    int         bitno;
    int         wordnum;
    int         bitnum;

    /* We force the bitmap into hashtable mode whenever it's lossy */
    if (tbm->status != TBM_HASH)
        tbm_create_pagetable(tbm);

    bitno = pageno % PAGES_PER_CHUNK;
    chunk_pageno = pageno - bitno;

    /*
     * Remove any extant non-lossy entry for the page.  If the page is its own
     * chunk header, however, we skip this and handle the case below.
     */
    if (bitno != 0)
    {
        if (pagetable_delete(tbm->pagetable, pageno))
        {
            /* It was present, so adjust counts */
            tbm->nentries--;
            tbm->npages--;      /* assume it must have been non-lossy */
        }
    }

    /* Look up or create entry for chunk-header page */
    page = pagetable_insert(tbm->pagetable, chunk_pageno, &found);

    /* Initialize it if not present before */
    if (!found)
    {
        char        oldstatus = page->status;

        MemSet(page, 0, sizeof(PagetableEntry));
        page->status = oldstatus;
        page->blockno = chunk_pageno;
        page->ischunk = true;
        /* must count it too */
        tbm->nentries++;
        tbm->nchunks++;
    }
    else if (!page->ischunk)
    {
        char        oldstatus = page->status;

        /* chunk header page was formerly non-lossy, make it lossy */
        MemSet(page, 0, sizeof(PagetableEntry));
        page->status = oldstatus;
        page->blockno = chunk_pageno;
        page->ischunk = true;
        /* we assume it had some tuple bit(s) set, so mark it lossy */
        page->words[0] = ((bitmapword) 1 << 0);
        /* adjust counts */
        tbm->nchunks++;
        tbm->npages--;
    }

    /* Now set the original target page's bit */
    wordnum = WORDNUM(bitno);
    bitnum = BITNUM(bitno);
    page->words[wordnum] |= ((bitmapword) 1 << bitnum);
}

/*
 * tbm_lossify - lose some information to get back under the memory limit
 */
static void
tbm_lossify(TIDBitmap *tbm)
{
    pagetable_iterator i;
    PagetableEntry *page;

    /*
     * XXX Really stupid implementation: this just lossifies pages in
     * essentially random order.  We should be paying some attention to the
     * number of bits set in each page, instead.
     *
     * Since we are called as soon as nentries exceeds maxentries, we should
     * push nentries down to significantly less than maxentries, or else we'll
     * just end up doing this again very soon.  We shoot for maxentries/2.
     */
    Assert(tbm->iterating == TBM_NOT_ITERATING);
    Assert(tbm->status == TBM_HASH);

    pagetable_start_iterate_at(tbm->pagetable, &i, tbm->lossify_start);
    while ((page = pagetable_iterate(tbm->pagetable, &i)) != NULL)
    {
        if (page->ischunk)
            continue;           /* already a chunk header */

        /*
         * If the page would become a chunk header, we won't save anything by
         * converting it to lossy, so skip it.
         */
        if ((page->blockno % PAGES_PER_CHUNK) == 0)
            continue;

        /* This does the dirty work ... */
        tbm_mark_page_lossy(tbm, page->blockno);

        if (tbm->nentries <= tbm->maxentries / 2)
        {
            /*
             * We have made enough room. Remember where to start lossifying
             * next round, so we evenly iterate over the hashtable.
             */
            tbm->lossify_start = i.cur;
            break;
        }

        /*
         * Note: tbm_mark_page_lossy may have inserted a lossy chunk into the
         * hashtable and may have deleted the non-lossy chunk.  We can
         * continue the same hash table scan, since failure to visit one
         * element or visiting the newly inserted element, isn't fatal.
         */
    }

    /*
     * With a big bitmap and small work_mem, it's possible that we cannot get
     * under maxentries.  Again, if that happens, we'd end up uselessly
     * calling tbm_lossify over and over.  To prevent this from becoming a
     * performance sink, force maxentries up to at least double the current
     * number of entries.  (In essence, we're admitting inability to fit
     * within work_mem when we do this.)  Note that this test will not fire if
     * we broke out of the loop early; and if we didn't, the current number of
     * entries is simply not reducible any further.
     */
    if (tbm->nentries > tbm->maxentries / 2)
        tbm->maxentries = Min(tbm->nentries, (INT_MAX - 1) / 2) * 2;
}

/*
 * qsort comparator to handle PagetableEntry pointers.
 */
static int
tbm_comparator(const void *left, const void *right)
{
    BlockNumber l = (*((PagetableEntry *const *) left))->blockno;
    BlockNumber r = (*((PagetableEntry *const *) right))->blockno;

    if (l < r)
        return -1;
    else if (l > r)
        return 1;
    return 0;
}

/*
 * As above, but this will get index into PagetableEntry array.  Therefore,
 * it needs to get actual PagetableEntry using the index before comparing the
 * blockno.
 */
static int
tbm_shared_comparator(const void *left, const void *right, void *arg)
{
    PagetableEntry *base = (PagetableEntry *) arg;
    PagetableEntry *lpage = &base[*(int *) left];
    PagetableEntry *rpage = &base[*(int *) right];

    if (lpage->blockno < rpage->blockno)
        return -1;
    else if (lpage->blockno > rpage->blockno)
        return 1;
    return 0;
}

/*
 *  tbm_attach_shared_iterate
 *
 *  Allocate a backend-private iterator and attach the shared iterator state
 *  to it so that multiple processed can iterate jointly.
 *
 *  We also converts the DSA pointers to local pointers and store them into
 *  our private iterator.
 */
TBMSharedIterator *
tbm_attach_shared_iterate(dsa_area *dsa, dsa_pointer dp)
{
    TBMSharedIterator *iterator;
    TBMSharedIteratorState *istate;

    /*
     * Create the TBMSharedIterator struct, with enough trailing space to
     * serve the needs of the TBMIterateResult sub-struct.
     */
    iterator = (TBMSharedIterator *) palloc0(sizeof(TBMSharedIterator) +
                                             MAX_TUPLES_PER_PAGE * sizeof(OffsetNumber));

    istate = (TBMSharedIteratorState *) dsa_get_address(dsa, dp);

    iterator->state = istate;

    iterator->ptbase = dsa_get_address(dsa, istate->pagetable);

    if (istate->npages)
        iterator->ptpages = dsa_get_address(dsa, istate->spages);
    if (istate->nchunks)
        iterator->ptchunks = dsa_get_address(dsa, istate->schunks);

    return iterator;
}

/*
 * pagetable_allocate
 *
 * Callback function for allocating the memory for hashtable elements.
 * Allocate memory for hashtable elements, using DSA if available.
 */
static inline void *
pagetable_allocate(pagetable_hash *pagetable, Size size)
{
    TIDBitmap  *tbm = (TIDBitmap *) pagetable->private_data;
    PTEntryArray *ptbase;

    if (tbm->dsa == NULL)
        return MemoryContextAllocExtended(pagetable->ctx, size,
                                          MCXT_ALLOC_HUGE | MCXT_ALLOC_ZERO);

    /*
     * Save the dsapagetable reference in dsapagetableold before allocating
     * new memory so that pagetable_free can free the old entry.
     */
    tbm->dsapagetableold = tbm->dsapagetable;
    tbm->dsapagetable = dsa_allocate_extended(tbm->dsa,
                                              sizeof(PTEntryArray) + size,
                                              DSA_ALLOC_HUGE | DSA_ALLOC_ZERO);
    ptbase = dsa_get_address(tbm->dsa, tbm->dsapagetable);

    return ptbase->ptentry;
}

/*
 * pagetable_free
 *
 * Callback function for freeing hash table elements.
 */
static inline void
pagetable_free(pagetable_hash *pagetable, void *pointer)
{
    TIDBitmap  *tbm = (TIDBitmap *) pagetable->private_data;

    /* pfree the input pointer if DSA is not available */
    if (tbm->dsa == NULL)
        pfree(pointer);
    else if (DsaPointerIsValid(tbm->dsapagetableold))
    {
        dsa_free(tbm->dsa, tbm->dsapagetableold);
        tbm->dsapagetableold = InvalidDsaPointer;
    }
}