[postgresql] / src / backend / nodes / tidbitmap.c

/*-------------------------------------------------------------------------
 *
 * 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 and
                         * directly store its index i.e. 0 in page array
                         */
                        tbm->dsapagetable = dsa_allocate(tbm->dsa, sizeof(PTEntryArray) +
                                                                                         sizeof(PagetableEntry));
                        ptbase = dsa_get_address(tbm->dsa, tbm->dsapagetable);
                        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_allocate0(tbm->dsa, sizeof(PTEntryArray) + size);

        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;
        }
}