postgres/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) 2003-2018, 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"
#include "utils/hashutils.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);

/* 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) murmurhash32(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;

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

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

	tbm->maxentries = (int) tbm_calculate_entries(maxbytes);
	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;
	}
}

/*
 * tbm_calculate_entries
 *
 * Estimate number of hashtable entries we can have within maxbytes.
 */
long
tbm_calculate_entries(double maxbytes)
{
	long		nbuckets;

	/*
	 * 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 */

	return nbuckets;
}